WO2024103113A1

WO2024103113A1 - Machine-learning based method and system for design of mixing devices

Info

Publication number: WO2024103113A1
Application number: PCT/AU2023/051157
Authority: WO
Inventors: Gerald PEREIRA; David Howard; Paulus LAHUR; Michael BREEDON; Philip KILBY
Original assignee: Commonwealth Scientific And Industrial Research Organisation
Priority date: 2022-11-18
Filing date: 2023-11-15
Publication date: 2024-05-23
Also published as: AU2023382068A1

Abstract

This disclosure relates to a method of designing a static mixer for mixing a fluid along a fluid flow path. The method comprises determining a form parameter value associated with form parameters; and a dimension parameter value associated with dimension parameters; determining, by a shape generator, a candidate static mixer design based on the form parameter value and the dimension parameter value, the candidate static mixer design being configured as an integral module for insertion into the fluid flow path to deflect the fluid; apply a computational fluid dynamics algorithm, to the candidate static mixer design to determine a fitness value; iteratively optimising the design parameters by repeatedly performing the steps of determining the candidate static mixer design and determining the fitness value; wherein optimising the design parameters improves the fitness value; and in response to the fitness value satisfying a fitness threshold, selecting the candidate static mixer design.

Description

Machine-learning based method and system for design of mixing devices

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority from Australian Provisional Patent Application No 2022903490 filed on 18 November 2022 and Australian Provisional Patent Application No. 2023900653 filed on 10 March 2023, the contents of which are incorporated herein by reference in their entirety.

Technical Field

[0001] The present invention relates to the field of computer-assisted design of complex geometries. In particular, the present invention relates to iterative computer- assisted design of mixing devices.

Background

[0002] Fluid flow through mixing devices, in particular static mixers is important in a variety of industries such as chemical and bio-chemical synthesis, extraction processes, and polymer synthesis. The geometry of the static mixers, through which fluid is forced within the processing component, plays a fundamental role in determining how well the processing component performs for a specific application.

[0003] There are numerous unique geometries for static mixers and the geometries of high performing static mixers can be intricate and complex. It is desirable to be able to identify a geometry for a static mixer that will perform well for intended specific application, whilst ameliorating the high cost associated with the manufacture of several designs and experimental testing of each candidate static mixer design before identifying the most suitable mixer design for a given application.

[0004] Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application. [0005] Throughout this specification the word ‘comprise’, or variations such as ‘comprises’ or ‘comprising’, will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps.

Summary

[0006] The present inventors have undertaken significant research and development into alternative improved mixer devices (e.g. static mixers) and have advantageously identified a computational workflow that can predict the optimal design (i.e., solid geometry) for certain fluid flow applications. It has been found that there are two (independent) components to the design process. Firstly, an underlying (numerical) physical model which can allow a user to obtain useful quantitative measures which can be then used to assess the suitability of a particular computer design. Secondly, an Artificial Intelligence (Al) algorithm that can take into consideration the measures from the numerical model and then based on these predict enhanced mixer geometries which improve the performance a mixer device for a given application.

[0007] There is provided a method of designing a static mixer, the method comprising: determining, one or more design parameters comprising: one or more form parameters defining a form of at least one design component; and one or more dimension parameters defining a dimension associated with the at least one design component. The method further comprises determining, by a design algorithm executing on a first processing device: a form parameter value associated with the one or more form parameters; and a dimension parameter value associated with the one or more dimension parameters. The method further comprises: determining, by a shape generator, a candidate static mixer design based on the form parameter value and the dimension parameter value, the candidate static mixer design being configured as an integral module for insertion into the fluid flow path to deflect the fluid; apply a computational fluid dynamics algorithm, executing on a second processing device, to the candidate static mixer design to determine a fitness value; iteratively optimising the design parameters by repeatedly performing the steps of (i) determining the candidate static mixer design and (ii) determining the fitness value, wherein optimising the design parameters improves the fitness value; and in response to the fitness value satisfying a fitness threshold, selecting the candidate static mixer design.

[0008] In some embodiments, the method further comprises generating a design description of the candidate static mixer design; and controlling an additive printing machine, in accordance with the design description, to manufacture a static mixer.

[0009] In some embodiments, determining the candidate static mixer design comprises replicating a template shape component to generate multiple repetitions of the template shape component to generate a plurality of shape components.

[0010] In some embodiments, generating the multiple repetitions is configured by the design parameters.

[0011] In some embodiments, the multiple repetitions are arranged along a longitudinal axis of the static mixer.

[0012] In some embodiments, determining the candidate static mixer design comprises virtually connecting the plurality of shape components.

[0013] In some embodiments, the one or more form parameters further comprise one or more recursive relationship parameters to define a relationship between the plurality of shape components.

[0014] In some embodiments, the method comprises determining, by the design algorithm a recursion parameter value associated with the one or more recursive relationship parameters and determining, by the shape generator, the candidate static mixer design is further based on the recursive relationship parameter.

[0015] In some embodiments, the one or more recursive relationship parameters define how a template shape is generated multiple times in each of the multiple repetitions.

[0016] In some embodiments, the form parameters comprise at least one angle parameter that defines an angle of one of the multiple repetitions of the template shape in relation to the static mixer.

[0017] In some embodiments, determining the candidate static mixer design comprises adding one or more support structures to support the plurality of shape components. [0018] In some embodiments, the method further comprises virtually connecting the plurality of shape components to the support structures.

[0019] In some embodiments, determining the candidate static mixer design comprises determining intersections of the plurality of shape components.

[0020] In some embodiments, the template shape comprises a branch configured by the one or more dimension parameters and determining the candidate static mixer design comprises replicating the branch to generate a plurality of branches along the longitudinal shape of the static mixer and arranged according to the one or more form parameters.

[0021] In some embodiments, generating each of the plurality of branches comprises for each branch, one or more twigs originating from that branch as configured by the one or more form parameters.

[0022] In some embodiments, the template shape comprises a triangle, the triangle is configured by three points and each point is a form parameter, and determining the candidate static mixer design comprises replicating the triangle to generate a plurality of triangles along the longitudinal shape of the static mixer and arranged according to the one or more form parameters.

[0023] In some embodiments, the template shape comprises two triangles, the two triangles share two points to define a connection line between the two triangles.

[0024] In some embodiments, the design parameters comprise, one or more of manufacturing constraints; or parameters related to the specific intended purpose for the static mixer.

[0025] In some embodiments, the fitness value comprises an indication of one or more of: a surface area of a substrate; a substrate adsorption rate; a cumulative adsorption level; a transport-to-substrate measure; an electric field of the static mixer; a pressure drop caused by the static mixer; an indication of fluid flow; an indication of fluid turbulence; a flow impediment measure; a stagnant flow region; a bulk mixing level; a measure of adsorption uniformity; a measure of shear; heat transfer; temperature gradients; temperature homogeneity; and/or a residence time distribution. [0026] In some embodiments, the method further comprises: in response to the fitness value not satisfying the fitness threshold: determining, by the design algorithm, a second candidate static mixer design based on the candidate static mixer design; applying the computational fluid dynamics algorithm, to the second candidate static mixer design to determine a second fitness value; and in response to the second fitness value satisfying a second fitness threshold, selecting the second candidate static mixer design to be manufactured.

[0027] In some embodiments, the method further comprises determining the second fitness threshold based on the fitness value.

[0028] In some embodiments, the design algorithm comprises an evolutionary design algorithm.

[0029] In some embodiments, determining a second candidate static mixer design comprises, determining a second candidate static mixer design based on the candidate static mixer design and the fitness value.

[0030] In some embodiments, the evolutionary design algorithm comprises a shape generator algorithm and a grid generator algorithm.

[0031] In some embodiments, determining a candidate static mixer design comprises: determining a set of genes defining the candidate static mixer design; determining, using the shape generator algorithm, a candidate static mixer shape based on the set of genes; and determining, using the grid generator algorithm, a candidate static mixer volume based on the candidate static mixer shape.

[0032] In some embodiments, determining a set of genes comprises determining a set of genes based on the design parameters.

[0033] In some embodiments, determining a candidate static mixer design comprises determining a plurality of candidate static mixer designs.

[0034] In some embodiments, applying a computational fluid dynamics algorithm comprises: for each candidate static mixer design of the plurality of candidate static mixer designs, apply a computational fluid dynamics algorithm, executing on the processing device, to the candidate static mixer design to determine a respective fitness value.

[0035] In some embodiments, the method further comprises selecting one of the plurality of static mixer designs, based on the plurality of respective fitness values.

[0036] In some embodiments, the computational fluid dynamics algorithm comprises a numerical module configured to calculate the velocity field of fluid flowing through the candidate static mixer design.

[0037] In some embodiments, the computational fluid dynamics algorithm applies a Lattice Boltzmann method.

[0038] In some embodiments, the design parameters define a least one post configured to extend along the length of the static mixer.

[0039] In some embodiments, the method further comprises: amending the candidate static mixer design to include a post configured to extend along the length of the static mixer.

[0040] In some embodiments, the static mixer design is constrained to be insertable into a mixer tube.

[0041] In some embodiments, the method further comprises generating a design description comprising a stereolithographic file.

[0042] In some embodiments, the first processing device comprises the second processing device.

[0043] There is provided a system comprising one or more processors; and memory comprising computer executable instructions, which when executed by the one or more processors, cause the system to perform the above.

[0044] There is provided a machine -readable storage medium storing instructions which, when executed by one or more processors, cause the one or more processors to perform the above method.

[0045] There is provided a static mixer made from the above method. [0046] There is provided a catalytic static mixer comprising the above static mixer and a catalytic coating.

Brief Description of Drawings

[0047] The invention will now be described with reference to the accompanying drawings, in which:

[0048] Figure 1 illustrates the architecture of a design system performing an iterative workflow, according to an embodiment;

[0049] Figure 2 illustrates a flowchart of a method performed by the grid generator module, according to an embodiment;

[0050] Figure 3 is a flowchart illustrating a method performed by the design system, according to an embodiment;

[0051] Figure 4 is a graph of the progression of a Pareto front for an evolutionary design process in which the design parameters define a solid central shaft, according to an embodiment;

[0052] Figure 5 is a graph of Pareto fronts for five different computer experiments, according to an embodiment.

[0053] Figure 6 is a graph of Pareto fronts for another five different computer experiments, according to an embodiment;

[0054] Figure 7 is a schematic representation of the electrochemical flow reactor, according to an embodiment;

[0055] Figure 8 is a visual representation of a surface grid of a reference mixer, according to an embodiment;

[0056] Figure 9 is a visual representation of a surface grid of an example tree-like structure of a candidate static mixer design, according to an embodiment;

[0057] Figure 10 is a visual representation of a surface grid of a first example ribbon structure of a candidate static mixer design, according to an embodiment;

[0058] Figure 11 is a visual representation of a surface grid of a second example ribbon structure of a candidate static mixer design, according to an embodiment; [0059] Figure 12 is a visual representation of a surface grid of a third example ribbon structure of a candidate static mixer design, according to an embodiment;

[0060] Figure 13 is a visual representation of a volume grid of the surface grid of Fig.

8, according to an embodiment;

[0061] Figure 14 is a visual representation of a volume grid of the surface grid of Fig.

9, according to an embodiment;

[0062] Figure 15 is a visual representation of a volume grid of the surface grid of Fig.

10, according to an embodiment;

[0063] Figure 16 is a visual representation of a volume grid of the surface grid of Fig.

11, according to an embodiment;

[0064] Figure 17 is a visual representation of a volume grid of the surface grid of Fig.

12, according to an embodiment;

[0065] Figure 18 is a graph illustrating the chronoamperometric response of the experimentally evaluated static mixers in a electrochemical flow reactor, according to an embodiment; and

[0066] Figure 19 is a graph illustrating the corresponding copper ion removal rate as determined by ICP-OES, for the static mixers featured in Figure 18, according to an embodiment.

[0067] Figure 20 illustrates four tree structures generated with different parameter values to show the vast design space that can be explored.

[0068] Figure 21 illustrates four ribbon structures generated with different parameter values to show the vast design space that can be explored.

Description of Embodiments

[0069] Static mixers may be composed of metallic substances, ceramics, polymers, inorganic materials, glasses, alloys, composites, natural products, or combinations or derivatives thereof. Traditionally, these static mixer structures have been manufactured through moulds or casts; however, as three-dimensional (3D) printing technology has improved, static mixers may now be 3D printed. Depending on the capabilities of the 3D printer, this manufacturing technique may allow for an improved range of design complexity for the static mixers.

[0070] With this advance in production of the structures, there is the option to explore unique and more complex static mixer designs to determine designs which provide improved performance over existing static mixer designs.

[0071] Traditionally, design improvement of static mixers has been led by a human designer’s intuition, knowledge, experience, which may be supported by some numerical modelling. However, to test whether a new static mixer design performs well for a given application, the new static mixer may need to be manufactured and tested experimentally. Disadvantages associated with this approach include the time and cost associated with manufacturing and experimentally testing each candidate static mixer design to identify a desirable design. This associated time and cost often limits the extent of the design space that can be explored to identify a preferable static mixer design.

[0072] An example application for static mixers is the extraction of a dissolved heavy metal or mineral from a contaminated solution. The contaminated solution (liquid or gas) flows through a narrow, long tubular reactor which comprises an outer tube and an internal static mixer, isolated by a membrane or solid separator element. Physically as the fluid flows through the reactor (along a fluid flow path, such as through a mixing tube), the fluid is mixed and a chemical component is extracted by adsorption and subsequent chemical reaction (including catalytic or electrochemical) - onto the solid substrate of the static mixer, which results in an increase in mixing element thickness as material is coated or plated onto the static mixer.

[0073] Since adsorption occurs at the substrate surface, it is desirable to maximise the surface area of the substrate; however, maximising the surface area of the substrate may have two consequences on the flow of fluid along the fluid flow path through the static mixer. Firstly, if the substrate area is increased, the solid’s volume may also be increased, which results in a greater obstruction to fluid flow within the reactor. This can lead to, at worst, blockage of the tube or to a lesser extent curtail the flow. Secondly, the fluid should ideally mix and to be maximally dispersed to all regions of the static mixer to result in a uniform adsorption onto the entire substrate. Accordingly, for this example application, it is desirable to arrive at a design for a static mixer that optimises the two parameters of maximising surface area of the substrate and maximising mixture and dispersion of the fluid. For other applications, there may be different or additional parameters to consider (such as pressure gradient, shear rate, etc)

[0074] Provided herein is an iterative computational workflow that is configured to determine a design for a static mixer that will perform well for an intended flow application.

[0075] The computational workflow comprises an evolutionary design (ED) algorithm configured to generate candidate static mixer designs, and a computational fluid dynamics (CFD) algorithm, configured to numerically evaluate the performance of the candidate static mixer designs for a specific application. The evolutionary design algorithm and the CFD algorithm operate iteratively to arrive at one or more well performing static mixer designs.

Design workflow

[0076] With similarities to natural evolution, the computational workflow is based on iterations over multiple, successive generations with each generation comprising of multiple children. In one embodiment, one or more initial designs (parent designs) are input to an evolutionary design (ED) module, which is configured to perform an evolutionary design algorithm. Over many generations, the improvement in fitness values converge until a threshold is met and the computational workflow outputs the best performing static mixer design(s).

[0077] In one embodiment, the computational workflow designs a static mixer for a specific application. In one embodiment, the computational workflow designs a static mixer for the decontamination of a heavy metal solution. A heavy metal solution may be decontaminated by passing the solution through an electrochemical cell comprising an inner, solid, metallic electrode and an outer cylindrical metal casing (positive electrode) and a separator or membrane.

[0078] The contaminated solution needs to come in contact with the inner metallic electrode, whereupon heavy metal ions come into contact with the inner electrode at which point the heavy metal ions are extracted out of solution with an associated current from inner to outer electrode. It is desirable to make the electrochemical cell as efficient as possible and thus maximise the heavy metal extraction rate. The main criteria for selecting the shape of the inner electrode are (i) maximal substrate adsorption and (ii) the electrode must not impede the flow or cause stagnant regions of flow and allow mixing of the fluid with all parts of the inner electrode. These two criteria oppose each other since increasing substrate adsorption is related to the substrate surface area and increasing surface area generally also increases volume of solid which will tend to impede the flow.

Figure 1 - Software architecture

[0079] Figure 1 illustrates the architecture of a design system 100 embodying the computation workflow, according to an embodiment. The design system 100 may be embodied by one or more software modules. The software modules may be executed on one or more processors (also referred to as processing devices, computational devices, or computers).

[0080] The design system 100 comprises a plurality of sub-modules that work in conjunction to determine a preferred design for a static mixer. In particular, the design system 100 comprises a control module 102, an evolutionary design module 104, a generator module 106 and a computational fluid dynamics module 108.

[0081] The control module 102 is configured to control the operation of the evolutionary design module 104, the generator module 106 and the computational fluid dynamics module 108 during execution of these modules. In one embodiment, the control module 102 performs method 300 as illustrated in Figure 3.

Evolutionary design module

[0082] The ED module 104 is configured to operate in iterations, generating a new generation of candidate static mixer designs in each iteration. A generation of static mixer designs may comprise one or more static mixer designs.

[0083] In each iteration, the ED module 104 is configured to apply an evolutionary design algorithm to an existing set of genes, which define one or more first candidate static mixer designs, to determine evolved set of genes, which define a new generation (e.g. a second set) of candidate static mixer designs. The ED module applies the determines an evolved set of genes that the ED module predicts are likely to define static mixers that perform better than the previous generation of candidate static mixer designs (or, on the first iteration, better than the initial parent designs).

[0084] For some situations, evolutionary design algorithms are particularly suited for determining an optimised design because the evolutionary design algorithms can efficiently explore vast regions of a complex design space and generate a diverse range of useful solutions. In one embodiment, the ED module 104 is based on Evolutionary Design (ED) (Eiben and Smith, 2003; Cheney et al, 2013), which are population-based, iterative optimisers. In one embodiment, the ED algorithm, performed by the ED module, comprises a machine -learning algorithm. In one embodiment, the ED algorithm, performed by the ED module, comprises artificial intelligence.

[0085] The inputs to the ED module 102 are the design parameters 114 and the fitness values 128 of one or more previous candidate static mixer designs, wherein the fitness values are determined by the CFD module 108.

[0086] In one embodiment, in an initial iteration of the ED module 102, the inputs to the ED module are the design parameters 114, designs of one or more initial parent static mixers, and fitness values associated with the one or more initial parent static mixers. In one embodiment, the fitness values are provided by the CFD module, as detailed below.

[0087] In one embodiment, the ED module 104 determines one or more first candidate static mixer designs based on the one or more design parameters, then the ED module determines one or more second candidate static mixer designs based on the one or more first candidate static mixer designs. The ED module may determine the one or more second candidate static mixer designs based on the one or more first candidate static mixer designs and fitness values associated with the one or more first candidate static mixer designs.

[0088] In one embodiment, the ED module 104, performs cross-overs and gene mutations between the genes of a previous generation of candidate designs to determine gene sets for a new generation of candidate designs. In one embodiment, the ED module 104 applies the Nondominated Sorting Genetic Algorithm II (NSGAII) as described in [Deb]. The ED module may configure the algorithm with default parameter values.

Design parameters

[0089] The control module 102 provides design parameters 114 to the ED module 104. In one embodiment, the design parameters comprise information which can guide the ED module’s development of static mixer designs. In one embodiment, the design parameters comprise information which can be used by the ED module to constrain the static mixer designs produced by the ED module.

[0090] The design parameters may comprise the physical dimensions of the static mixer to be designed, such as a length and a diameter. The physical dimensions may define spatial boundaries beyond which the features of the static mixer design should not protrude. The design parameters may further comprise a 3D print resolution (e.g., grain size), or other physical parameters related to the manufacture of the static mixer.

[0091] In one embodiment, the design parameters comprise a base geometry which defines the basic geometry of the static mixers to be designed by the ED module 104. The based geometry can be defined by one or more form parameters that define the form (i.e. the shape) of at least one design component. In one embodiment, the base geometry (form parameters) comprises an indication of whether the static mixer to be designed comprises a tree-shaped (tree-like) static mixer, a ribbon static mixer, a helical mixer or another base type of static mixer.

[0092] In one embodiment, the base geometry defines the inclusion of one or more support structures, such as shafts or posts extending along the longitudinal dimension of the static mixer. It is noted that the term support structure refers to a permanent support structure, which is a permanent feature of the static mixer in the sense that it remains in the static mixer after production, e.g., after 3D printing, to support the individual shape components. This is in contrast to other temporary mechanical structures used during 3D printing that hold overhanging features, for example, and are removed after the 3D printing. Those holding features are not part of the design of the static mixer but merely production aides. [0093] For example, in response to the base geometry defining a single-post geometry, the ED module 104 designs a candidate static mixer which comprises a solid central post extending along the longitudinal dimension of the static mixer. The post is designed to provide rigidity to the static mixer. The base geometry may define a position or an orientation of the post. For example, the base geometry may define the post to be located on any position of the static mixer. If the base geometry defines a single post, preferably the ED module designs a candidate static mixer in which the single post is located at a central location along the length of the post. If the base geometry defines a plurality of posts, preferably the ED module designs a candidate static mixer in which the posts are equidistant from each other. Preferably, the ED module designs a candidate static mixer in which the posts are located toward the outer periphery of the static mixer.

[0094] In one embodiment, the base geometry defines a four-post geometry in which the four posts extend along the longitudinal dimension of the static mixer. In one embodiment, in response to the base geometry defining the four-post geometry, the ED module 104 designs a candidate static mixer in which the four posts are located, equidistant from each other, on the outer periphery of the mixer and extend along the entire length of the mixer, effectively mechanically reinforcing the structure of the mixing element.

[0095] In one embodiment, the base geometry defines a plurality of branches and leaves extending from one or more posts. In one embodiment, the base geometry causes the ED module 104 to attach a plurality of ribbon shapes extending from, or intersecting one or more posts. In some embodiments, the base geometry causes the ED module 104 to include a plurality of leaves on the ribbon shapes. In some embodiments the leaves are arranged to create a canopy of leaves arranged in a spiral orientation as defined by the form parameter.

[0096] In one embodiment, the design parameters comprise a longitudinal uniformity parameter which indicates whether the ED module 104 should design the candidate static mixers which uniformity of design along the length of the static mixer design. Design guidance

[0097] In one embodiment, the design parameters 114 comprise design guidance parameters. An unguided evolutionary design algorithm may face fundamental challenges in generating a static mixer design, because there is an infinite number of possible designs for a static mixer and also there are constraints imposed by the 3D Printing process which need to be adhered to. Accordingly, it may be desirable to reduce the possible design space to a much smaller, and more easily explorable design space.

[0098] The design space may be reduced by providing the evolutionary design module 104 with some design guidance. Design guidance may be determined through consideration of existing static mixer designs that perform well for intended application. Additionally, design guidance may be determined through consideration of nature, where living beings have adapted to specific environment by developing certain geometric features.

[0099] Design guidance may also be determined through an understanding of fluid dynamics. For example, in some situations, non-uniform sizes of branches, ribbons or leaves is advantageous at mixing fluid. Additionally, in some situations a repetitive pattern or branches, ribbons or leaves are efficient at controlling flow direction. This understanding of fluid dynamics can be expressed as guidance to the ED module 104, in the form of basic static mixer shapes that can be composed, by the ED module 104, into much more complex shapes. In some embodiments, the ED module 104 can determine a plurality of variations to these basic shapes, to be performance tested by the CFD module 108.

Parent designs

[0100] In some embodiments, the design parameters comprise one or more initial parent designs. The ED module 104 can be configured to determine candidate static mixer designs based on the one or more initial parent designs. The one or more initial parent designs may comprise a reference static mixer design, an existing well-performing static mixer design, or a static mixer design as chosen or determined by the human operator. Preferably, a well-performing static mixer design is a design that achieves or exceeds at least one of the fitness objective for a particular application. Fitness objectives

[0101] In one embodiment, the design parameters 114 comprise one or more fitness objectives. The design parameters may further comprise one or more desired fitness values associated with a fitness objective. In one embodiment, each fitness objective is associated with a desired fitness value.

[0102] The fitness objectives represent performance attributes of the static mixer. Fitness objectives may differ depending upon the intended application for the static mixer being designed by the ED module 102. In one embodiment, the fitness objectives comprise a ‘transportto substrate’ fitness objective. ‘Transport to substrate’ is ameasure of the percentage of tracer particles achieving impact with the substrate of the static mixer. For one application, the desired fitness value for the ‘transportto substrate’ fitness objective may be 60% or greater.

[0103] Fitness objectives may be evaluated by the CFD module 108. The ED module 102 may be configured to evolve a static mixer design that provides improved, or optimised, performance with regard to at least one fitness objective during the evolutionary design process. This may be referred to as designing to optimise a fitness objective. The ED module 102 may be configured to design to optimise more than one fitness objective concurrently. The ED module 102 may be configured to find a design that provides an acceptable performance balance between two or more fitness objectives, with regard to desired fitness values.

[0104] The CFD module 108 also receives an indication of the fitness objectives 126 from the control module 102. The CFD module evaluates how each candidate design performs with regard to each fitness objective, and provides one or more fitness values 122, in relation to each fitness objective for each candidate design evaluated by the CFD module, to the control module.

[0105] From the control module 102, the ED module 104 receives the fitness values 128, wherein the fitness values provide an indication of how each candidate design performs with regard to each fitness objective 126. The ED module 104 may compare a fitness value for a fitness objective with a desired fitness value associated with that fitness objective. [0106] Example fitness objective categories include ‘bulk mixing’, which provides an indication of the extent of mixing of the fluids traversing the static mixer; ‘transport-to- substrate’ which provides an indication of adsorption on the surface of the static mixer; and a measure of cavitation events, which provides an indication of the formation micro- bubbles/bubbles. Fitness objectives may include a measure of the surface area of a substrate of the static mixer, a substrate adsorption or absorption rate; a cumulative adsorption rate; an electric field of the static mixer; a pressure drop or gradient caused by the static mixer; an indication of fluid turbulence; a measure of adsorption uniformity; a measure of shear; and/or a residence time distribution. Other fitness objectives may include, heat transfer, temperature gradients, temperature homogeneity.

Genes

[0107] The ED module 104 describes a static mixer design in terms of a set of one or more genes. A set of genes is a set of numerical parameters that describe shape characteristics (form parameters and dimension parameters) of the static mixer design. Each gene has a specific role in defining certain geometric parameters. For example, a gene can refer to the size (dimension), location (form), distance (dimension or form), or orientation (form) of a geometric parameter. A gene can affect either a single or multiple geometric features. A geometric parameter, on the other hand, can be a product of a single gene or multiple genes working together. Having many-to-many mapping between genes and geometric parameters allows for a rich combination that can lead to a large variation in shapes for a static mixer.

[0108] Each gene is associated with a value or a value range. In one embodiment, each gene has a value within the range of [0.0, 1.0], This value is mapped to a specific geometric parameter, which may be a form or a dimension parameter, which falls within a certain predefined range, for example an angle within the range of [-90, 90] degrees for a form parameter.

[0109] By defining the geometric feature associated with the gene, and the predefined range or value associated with the gene, the sensitivity to the value change in the gene can be set. In one embodiment, the gene values can be real number, integer number and Boolean values. The following table shows the mapping from gene to geometric parameter as the function of parameter type.

Generator algorithm

[0110] The generator module 106 comprises a shape generator 110 and a grid generator 112. The shape generator (SG) 110 receives a set of genes 116 from the ED module 104 and expresses the genes 116 into a candidate static mixer design by using the form parameters and the dimension parameters to generate the candidate static mixer design.

[0111] The generator module 106 outputs the static mixer geometry to the CFD module 108 so that the CFD module can determine how well the geometry performs in a certain fluid mixing scenario and summarised as its performance index.

Shape generator module

[0112] The role of the shape generator (SG) module 110 is to take a set of genes from ED module 104 as the shape parameters (e.g. form and dimension parameters) and construct a static mixer surface grid 120 based on the set of genes.

[0113] It is desirable that the design system 100 is computationally robust and able to complete its task without error, despite dealing with very complex and sometimes unpredictable shapes. This involves a strategy that goes beyond the design of SG module 110 alone. The design of the SG module 110 is considered together with other components in the downstream of the design system 100.

[0114] In one embodiment, the SG module 110 defines the surface grid 120 in terms of a Cartesian grid. In one embodiment, the SG module 110 defines the surface grid 120 in terms of a set of triangles as defined by the form parameters. The smallest unit in the surface grid is a voxel, which is a regular cube that can be either defined as a solid cube or a fluid cube.

[0115] In another embodiment, the SG module 110 defines the surface grid 120 in terms of a body-fitted grids such as unstructured tetrahedral grid. In some embodiments, a body-fitted grid may be post-processed to avoid cells that are too small or have large aspect ratio, because this may adversely affect the performance of the entire CFD simulation.

Mapping genes into shapes

[0116] The SG module 110 is configured to map the genes 116 that define a candidate static mixer design determined by the ED module 104, into a surface grid 120 that represents the candidate static mixer design. This may involve the generation of multiple repetitions of a template shape, such as triangle shape or a branch shape, as configured by the design parameters.

[0117] The number of possible candidate static mixer designs is the permutation of all possible values of the genes, so, in some embodiments, it is desirable to keep the number of genes low. Having a small number of genes does not necessarily mean that the SG module 110 cannot make complex shapes. The genes can be used recursively to achieve a high degree of complexity, as defined by a recursive relationship parameter. It is worth noting, that forcing the number of genes to be too low may restrict the variety of candidate static mixer designs produced by the ED module 104 and, therefore may reduce the chance of identifying a high performing mixer. For example, generating a helical pipe using only the pipe diameter, coil diameter and pitch for the gene variations, results in a limited design space compared to using dimension parameters as well as form parameters. The form parameters are particularly useful to vary the form (i.e. shape) of the design more drastically between the different generations compared to using only dimension parameters.

Tree mixer

[0118] In one embodiment, the genes 116 defines a tree-like geometry for a static mixer where the overall form of the tree is governed by the form parameters. The SG module 110 takes the genes 116 as input. The SG module 110 creates a tree-like structure starting with a support structure, such as a trunk, at the centre of the mixer, extending the entire length in longitudinal axis of the mixer to provide structural integrity. A branch can be considered a template shape and so the SG module 110 creates multiple repetitions of the template shape to create multiple branches from the trunk along the longitudinal axis of the mixer according to the gene values associated with the form parameters. The branches, in turn, can spawn children branches (e.g. twigs) in a recursive fashion. The SG module uses the genes to determine: the property of a branch (dimensions like diameter, length, and form like orientation) and the number of child branches attached to a parent branch or trunk, which are also form parameters. Children branches are arranged in a helical fashion along the parent branch and the progressive rotation angle of the repetitions along the longitudinal axis of the mixer to form the helix can also be defined by the form parameters.

[0119] In one embodiment, the shape of the tree is determined by 12 parameters, which comprise 4 groups of 3 floating point numbers within each group. Each value ranges between 0.0 and 1.0 to be compatible with the genetic algorithm.

[0120] These are normalised values, which will be mapped to value range specific to each parameter. An example design parameter list is given below:

No. Name Xmin Xmax Note

0 (Unused) Formerly used for trunk

1 (Unused) Formerly used for trunk

2 Branch count 5 Int(trunk length)

3 Branch length 1.0 3.0

4 Branch diameter 0.3 Trunk diameter

5 Branch angle 0.0 Pi Pi/2:perpendicular to trunk

6 Max level of branching 1 3 1 :branch, 2:twig, 3 : small twig

7 Twig count 1 2 * int(round(branch length))

8 Diameter branching factor 0.6 1.0

9 Eength branching factor 0.5 1.0

10 Count branching factor 0.5 2.0

11 Angle branching factor 0.5 1.0

Example values: Trunk length = 40.0 Trunk diameter = 1.0

[0121] Branching factor is used to calculate the properties of of twigs with respect to the branch they share. This applies recursively to smaller twigs. For example: Branch diameter = 0.4

Diameter branching factor = 0.7

Diameter of Twig = 0.4 x 0.7 = 0.28

Diameter of smaller twig = 0.28 x 0.7 = 0.196

Diameter of even smaller twig = 0.196 x 0.7 = 0.1372

[0122] It is noted that structural parameters, such as branch count, angle, max branching level, twig count, count branching factor and angle branching factor are considered form parameters, while branch length, branch diameter, diameter branching factor, length branching factor, trunk length and trunk diameter are considered dimension parameters.

Ribbon mixer

[0123] In one embodiment, the genes 116 defines a ribbon geometry for a static mixer. The SG module 110 takes the genes 116 as input. The SG module uses the genes to create a set of interconnected vectors in 3D, which can also be referred to as a template shape component. The interconnected vectors may include three vectors to define a triangle or another number of vectors to create other polygons. The SG module 110 uses the vectors to create a ribbon based structure for a static mixer. The ribbon template is replicated along the length of the mixer to generate multiple repetitions of the interconnected vectors along the longitudinal axis of the mixer. The ribbons are arranged in a helical configuration, where the linear and angular interval between adjacent ribbon is set using genes. The SG module may add support structures, such as beams to ensure the structural integrity of the mixer. The SG module produces a surface grid of the complete assembly as output.

[0124] The disclosed method can generate a large variation of complex geometries. The geometry consists of a unit ribbon (serving as the template) that is replicated in a helical fashion along the longitudinal axis of the mixer to generate multiple repetitions of the unit ribbon. The parameters (or the “genes”) for an individual mixer is a set of floating numbers. In this particular embodiment, 30 real numbers between 0 and 1 are used. They represent the following parameters:

• Parameters 1 - 27: They are interpreted as 9 vectors, where each vector has 3 real numbers. These vectors are used to generate a unit ribbon. • Parameter 28: the number of unit ribbons in a standard length.

• Parameter 29: the twist angle between adjacent unit ribbons.

• Parameter 30: reserved for future use.

[0125] A unit ribbon is constructed by stringing the 9 vectors together such that the starting point of a succeeding vector is the mid-point of the preceding vector. This means the last two points of the preceding vector are the first two points of the succeeding vector, resulting in 10 consecutive points used in the nine vectors: P1P2P3, P2P3P4, ... , P8P9P10. These points are then used to form a series of triangles such that each vector defines the three points of one triangle. Since the vectors share two points, the triangles are connected on one of their edges. The three points in each triangle are design parameters and may be considered form parameters, because they define the form of the triangles, as well as dimension parameters because they also define the size of the triangles. The points are varied by the genetic algorithm to explore the design space.

[0126] It is also possible to have more than 9 vectors, leading to more than three triangles. In yet another embodiment, each vector has more than three points to represent a general polygon. In that case, the vectors still share (overlap) by two points to make a line connection between the shape components.

[0127] As the last step in the construction of a unit ribbon, these triangles are converted into thin prisms by adding a predefined thickness, which is a dimension parameter. In embodiments where the template shape is a more general polygon, adding the thickness results in a polytope or polyhedron.

[0128] This unit ribbon is then replicated along the longitudinal axis, at a predefined longitudinal interval, which is a form parameter, and while twisting it around the axis as defined by an angle parameter, which is also a form parameter. The genetic algorithm can now explore a vast design space by modifying the design parameters including the triangle points, the longitudinal interval of repetition and the angle parameter of the twist.

Example surface grids

[0129] Figure 8 illustrates a visual representation of a reference surface grid 800, according to an embodiment. Figures 9 to 12 illustrate a visual representation of surface grids produced by the SG module 110, according to embodiments. Surface grid 800 is a surface grid of the reference mixer (previously studied and calibrated in Bayatsarmadi et al, 2020). The reference mixer has been predefined and has not been produced by the ED module 104. Surface grid 900 is a surface grid of an example tree-like structure of a candidate static mixer design produced by the ED module 104. Surface grid 1000 is a surface grid of a first example ribbon structure of a candidate static mixer design produced by the ED module 104. Surface grid 1100 is a surface grid of a second example ribbon structure of a candidate static mixer design produced by the ED module 104. Surface grid 1200 is a surface grid of a third example ribbon structure of a candidate static mixer design produced by the ED module 104.

Grid generator module

[0130] The generator module 106 further comprises a grid generator (GG) module 112. The GG module is configured to, for each of the candidate static mixer designs 340 determined by the ED algorithm 104, generate a volume grid 122 from the surface grid 120 output by the SG module 110. The CFD module 108 uses the volume grid 122 to perform a performance evaluation of a candidate static mixer design.

[0131] In one embodiment, the SG module 110 communicates the surface grid 120 to GG module 112 via a solid surface described in a format known as stereolithographic (.STL) file. A .STL file is a common format in computer aided design (CAD) and three dimensional (3D) printing. In one embodiment, the surface grid 120 describes a set of triangles forming a solid surface of a static mixer design.

[0132] Advantageously, the GG module 112 can accept a surface grid 120 that is not fully or accurately defined in terms of all aspects of the design. For example, the GG module 112 permits overlapping and intersecting solid bodies within the surface grid 120, or even a solid that is not perfectly water tight.

[0133] This tolerance of the GG module 112 can significantly reduce the computational burden in operating the SG module 110, because the SG module does not have to compute a high quality surface. In one embodiment, the output of the SG module 110 may comprise a description of a complex configuration of freely intersecting simple shapes. Resolution approximation

[0134] The GG module produces a volume grid 122 that approximates the shape of a candidate static mixer design 340 determined by the ED module 104. Although the volume grid 122 may be only an approximation of the shape of a candidate static mixer design 340 determined by the ED module 104, in many situations, the approximation of the design is within the resolution range of a 3D printer technology in any case.

Figure 2 - Grid generator method

[0135] Figure 2 illustrates a flowchart of a method 200 performed by the grid generator module 112, according to an embodiment. In step 202, the GG module 112 reads, as an input, the design parameter fde 114. In step 202, the GG module reads, as an input, the surface grid file 120.

[0136] In step 206, the GG module generates a Cartesian grid, given the computational domain and grid resolution. In step 208, the GG module identifies voxels intersecting solid surface. This is a fast geometric query that determines whether a voxel intersects any triangle or other shape. In some embodiments, the actual computation of intersection is not required. In some embodiments, for efficiency, the GG module is configured to perform filtering out of cases where such intersection is clearly not possible. In one embodiment, the GG module determines intersections of shapes and connects those shapes along the one or more intersecting edges. This can be particularly useful where the SG module first replicates the template shape and then adds a support structure. In that case, the GG module can connect the multiple repetitions of the template shape to the support structure by calculating the intersection between the multiple repetitions and the support structure and then making connections along those intersections.

[0137] In step 210, the GG module identifies fluid voxels. The GG module determines a point in the domain that is known to be within fluid, and given that point, the GG module sets the voxel that contains that point, as well as all connected non-intersected voxels as fluid voxels.

[0138] In step 212, the GG module 112 identifies the rest of the voxels as solid, including the intersected voxels. In step 214, the GG module flags voxels that are outside the mixing tube and may remove those voxels or project the flagged voxels onto an inner diameter of the mixing tube. This means that the GG module 112 constrains the mixer design to be insertable into the mixing tube of the reactor, that is, the diameter of the mixer design does not exceed the inner diameter of the mixing tube anywhere along its longitudinal axis.

[0139] In step 216, the GG module 112 identifies the fluid-solid interface grid and, in step 218, outputs the fluid-solid grid as a volume grid 122. The volume grid 122 may be described as a .STL file. The volume grid 122 may be used by the CFD module 108 to evaluate the performance of the static mixer design defined by the volume grid 122. In some embodiments, the volume grid 122 is used by a 3D printer to define a static mixer design.

[0140] Advantageously, the GG module 112 is able to produce a volume grid even when the inputted surface grid contains gaps, overlapping triangles, has non-consistent orientation, protrudes outside the computational domain or has incomplete parts. The tolerance of the GG module 112 reduces the level of robustness needed for the SG module 110.

Example volume grids

[0141] Figures 13 to 17 illustrate a visual representation of volume grids produced by the GG module 112, according to embodiments. Volume grid 1300 is a volume grid of the surface grid 800 of the reference mixer. The reference mixer has been predefined and has not been produced by the ED module 104. Volume grid 1400 is a volume grid of the surface grid 900 of the example tree-like structure of a candidate static mixer design produced by the ED module 104. Volume grid 1500 is a volume grid of surface grid 1000 of the first example ribbon structure of a candidate static mixer design produced by the ED module 104. Volume grid 1600 is a volume grid of surface grid 1100 of the second example ribbon structure of a candidate static mixer design produced by the ED module 104. Volume grid 1700 is a volume grid of surface grid 1200 of the third example ribbon structure of a candidate static mixer design produced by the ED module 104.

[0142] In all example static mixer designs illustrated in Figs. 8 to 17, valid volume grids are created, even when the input surface grid protrudes out of the spatial boundaries of the static mixer. When determining the volume grid, the GG module 112 truncates features that protrude out of the spatial boundaries.

Computational Fluid Dynamics module

[0143] The CFD module 108 performs computational fluid dynamics calculations in accordance with one or more computational fluid dynamics algorithms, wherein the computational fluid dynamics algorithms use modelling, numerical analysis, data structures to analyse and solve calculations pertaining to the flow of fluid. Computational fluid dynamics algorithms may comprise modelling techniques including finite difference, finite element, finite volume and/or smoothed particle hydrodynamics, or any combination thereof.

[0144] In one embodiment, the CFD module 108 applies the Lattice Boltzmann method to evaluate the performance of a candidate static mixer design. The Lattice Boltzmann method is a numerical fluid dynamical method that solves the Boltzmann Transport equation. The Boltzmann Transport equation describes the statistical behaviour of a thermodynamic system and its approach to equilibrium.

[0145] It can be shown, via a Chapman-Enskog expansion the solution of this equation is equivalent to the solution of the famous Navier-Stokes equations (Faber, 1995) for fluid flow.

[0146] The Lattice Boltzmann method is a rapid, easily parallelized numerical method which calculates the velocity field of fluid in complicated geometries and can be comparable with experimental observations.

[0147] An input into the CFD module 108 is a volume grid 122. In one embodiment, the volume grid 122 is defined by a stereolithographic (STL) file. STL files are discretised on a Cartesian lattice. Each lattice point can either be occupied by solid material or a void (which is then available for fluid flow). In one embodiment, since the Lattice Boltzmann method also operates on a Cartesian lattice, the Lattice Boltzmann method may be readily applied, by the CFD module, to the volume grid (122).

[0148] Advantageously, complicated boundary geometries can be easily simulated with the Lattice Boltzmann method. In other CFD techniques, treating the solid boundaries appropriately can lead to extreme complications and inaccurate results, due to inability of the technique to adequately model the boundary conditions.

[0149] The central quantity in the Boltzmann transport equation, from which the Lattice Boltzmann method is derived, is the particle distribution function, /(r.u.t). which denotes the distribution of particles at position r, travelling with velocity u at time t. In the Lattice Boltzmann method, this distribution function may be discretised on a regular lattice so that particle positions are restricted to the lattice vertices (or nodes) with discrete velocity directions, ei. Generally, Lattice Boltzmann models can be classified as DmQn where m denotes the number of dimensions of space and n the number of velocity directions. Common examples in 1, 2 and 3 dimensions are D1Q3, D2Q9 and D3Q19 and the discretised distribution function is denoted fi (r,t) where i = l,..n. The set of n vectors for each Lattice Boltzmann model are provided in (Kruger et al, 2017).

[0150] The time evolution of these distribution functions satisfies

[0151] The term ff^q is the equilibrium Maxwell distribution (written in terms of equilibrium velocities) is given by

where p is the density and wt are weights which are defined for the given D3Q19 model (Kruger et al, 2017).

[0152] In Equation (2), the black dots between vectors represent a dot product operation. In Equation (1), T represents a relaxation time and it can be shown to be related to kinematic viscosity via v = C_S T- 1/2) where c_s is the sound speed and c ² equals 1/3. The pressure, P, in this model is given by the equation of state P = c_s ²p. The LB equation (1) is single relaxation time (SRT) scheme, because only one relaxation time is involved. [0153] The relationship to macroscopic parameters such as density and velocity are given by

P = f and pu = fe_r ⁽³⁾

[0154] Once the CFD module 108 determines the velocity field, the CFD module can determine important quantities such as the amount of adsorption that occurs in the reactor and the amount of fluid mixing that occurs. The flow regime for these reactors is governed by the dimensions (size of gaps) in which fluid flow and also the maximum pressure a pump may deliver, before breakdown of the pump.

[0155] Based on these two criteria, the CFD module can determine that the flow is certainly not turbulent. The Reynolds number, Re (Re = pLu/v, where L is size of a fluid gap, u is the magnitude of a typical fluid velocity and v is viscosity), for the flow is under 100. (It is noted that turbulence only is important for flows with Reynolds numbers over 2000.)

[0156] In one embodiment, to determine the two measures of substrate transport and fluid mixing, the CFD module 108 allows fictitious, massless (tracer) particles to flow in the LB calculated velocity field. The trajectory of these massless particles is followed using a simple equation for advancement of a particle according to the local velocity field, i.e.

[0157] Equation (4) is discretised both with respect to time and space and solved with a fourth order Runga-Kutta scheme (Press et al, 1996). From Equation (4), the CFD module 108 can determine how many particles end up on the substrate and how the particles mix through the reactor. The two fitness values corresponding to the fitness objectives substrate transport and fluid mixing, are normalized to vary between zero (0) and one hundred (100). A value of zero corresponds to an extremely poor measure while a value of 100 corresponds to the best possible value of the measure. [0158] In one embodiment, the CFD module 108 is configured to perform numerical modelling approaches such as multiphysics methods to resolve additional fitness values, such as electric fields.

Iterative evolutionary improvement

[0159] The ED algorithm, performed by the ED module 104, and the CFD algorithm, performed by the CFD module 108, are coupled via the control module 102, such that the fitness values measured by the CFD module are passed to the ED module to allow the ED module to determine the next generation of candidate static mixer designs.

[0160] In one embodiment, the evolutionary design module 104 evolves an initial population of one or more parent designs over a plurality of generations to determine one or more improved candidate static mixer designs, wherein improvement is determined based on the fitness values for the individual candidate static mixer designs, as determined by the CFD module 108.

[0161] The initial population of parent designs comprise of K individuals, wherein K comprises one or more, who are then all evaluated by the CFB module 108 with regard to the fitness objectives. In one embodiment, the fitness objectives comprise an indication of substrate transport and fluid mixing. The CFP module 108 provides fitness values, for the fitness objectives, for the initial population of parent designs. The fitness values for the K initial parent designs are transferred to the ED module 104 which carries out an analysis on these parent designs and from them predicts a set of new individual (or children) designs. The set of children designs may comprise N candidate static mixer designs. K can be any number equal to or greater than 1. N can be any number equal to or greater than 1. In one embodiment, N is 16. In one embodiment K is equal to N.

[0162] This process is iterated, the performance of the N children static mixer designs are determined by the CFD module 108 which evaluates their fitness with respect to the fitness objectives, and communicates the fitness values back to ED module 104. In this way the design system 100 iteratively evolve a static mixer design that performs well with regard to fitness objectives, with the constraints of the design parameters.

[0163] In some embodiments, the design system 100 is configured to compare the fitness values determined by the CFD module 108 for one generation of candidate static mixer designs with the fitness values determined by the CFD module 108 for a subsequent generation of candidate static mixer designs, to determine an indication of a rate of change of the fitness values. Accordingly, the progress of the fitness function over generations can be tracked and when this function slows, the system has evolved to a preferred solution for this family. On average this takes the 100-200 generations.

[0164] In one embodiment, the control module 102 is configured to generate a design description of the candidate static mixer design. The design description may comprise a .STL file. In one embodiment, the control module 102 is configured to control an additive printing machine, in accordance with the design description, to manufacture a static mixer.

Figure 3 - Method Flowchart

[0165] Figure 3 is a flowchart illustrating a method 300 performed by the design system 100, which is controlled by the control module 102, according to an embodiment.

[0166] In step 302, the control module 102 determines the design parameters. Design parameters may comprise the physical dimensions of the static mixer to be designed, such as a length and a diameter. The design parameters may further comprise a 3D print resolution (e.g. grain size), and other physical parameters of the desired static mixer.

[0167] In step 304, the control algorithm 102 configures the CFD algorithm 108 so that it will be able to calculate appropriate fitness objectives for the specific application. The fitness objectives may be selected by the control algorithm 102 in light of the intended application or applications for the static mixer being designed.

[0168] In one embodiment, method 300 may comprise developing one or more initial parent designs. The initial parent designs may be referred to as one or more first candidate static mixers. From the initial parent designs the evolutionary design algorithm 104 can generate subsequent generations of candidate static mixer designs.

[0169] In one embodiment, the genes for the one or more initial parent designs are determined by the ED module 104 in step 306. In such an embodiment, the method 300 may proceed from step 304 to step 306, bypassing step 308. [0170] In one embodiment, the genes 118 for the one or more initial parent designs are determined by humans, based on an informed understanding of the underlying process, physics, and chemistry of static mixers for one or more intended applications.

[0171] Accordingly, in step 308, the control algorithm 102 receives information indicative of initial static mixer designs. These designs are referred to as parent designs. In one embodiment, the control algorithm 102 receives K parent designs. In one embodiment, K equals 16.

[0172] Each of the K parent designs are each described by a set of genes 118. A set of genes is a set of numerical parameters that refer to shape characteristics of the static mixer design. During the process 300, the control algorithm 102 determines at least one set of genes 118, wherein the set of genes defines a static mixer design that performs in terms of the fitness objectives defined by the control algorithm 102.

[0173] In step 310, the generator module 106 generates the CAD geometry for each of the static mixer designs determined in step 306 or 308.

[0174] The CAD geometry for each candidate static mixer design can be defined in any suitable CAD format. In one embodiment, the CAD geometry is defined in a stereolithography (.STL) file. In one embodiment, the generator module 106 determines a voxelised version of a CAD geometry for the candidate static mixer designs, wherein the voxelised version is a format compatible with the 3D Printing resolution.

[0175] In some embodiments, the generator module 106 also performs a checking process to confirm that the CAD geometry for each candidate static mixer design is a legitimate geometry, e.g., that it does not possess some flaws that would make the design unsuitable for static mixing. For example, the generator module 106 may check to confirm that there is a flow path for the flow of fluid from one end of the static mixer to the other end or that there are no topological discontinuities in the mixing element design.

[0176] In step 312, the CFD algorithm 108 performs computational fluid dynamics performance evaluation on each of the candidate static mixer designs 340.

[0177] To complete the CFD processing in a shorter amount of time, the CFD module 108 may perform the CFD processing over a plurality of processors, which may operate in parallel. For example, in one embodiment, the CFD algorithm 108 each of the N candidate static mixer designs 340 are passed to N separate compute processors (all on the same HPC platform) for evaluation by the CFD algorithm 108.

[0178] The CFD module 108 and/or the ED module 104 may utilise one or more of the following computing techniques, distributed computing, grid computing, cloud computing, localised co-processor or accelerator board, or computing across multiple platforms using a combination of job schedulers not on the same HPC platform.

Determining satisfactory fitness values

[0179] The control algorithm 102 receives fitness values 122, associated with the fitness objectives, from the CFD module 108 for each of the candidate static mixer designs 340. The number and type of fitness objectives may vary depending upon the intended application for the static mixers.

[0180] In embodiments, up to M (preferably 2) fitness objectives are evaluated to determine the performance of the new geometry of the candidate static mixers for the specific application. The fitness values (corresponding to the individual fitness measures) range between 0 (poor static-mixer) and 100 (excellent static-mixer).

[0181] In step 314, the control module 102 considers at least one of the fitness values 122, produced by the CFD module 108, to determine whether the fitness value 122 satisfies a fitness threshold. How the control module 102 determines whether the fitness value satisfies the fitness threshold are satisfactory may differ based on the design parameters, an intended application for the static mixers, available computational resources or other factors.

[0182] In one embodiment, the fitness threshold is indicative of a number of iterations of the workflow, and the control module 102 considers whether the fitness values satisfy the fitness threshold by comparing a number of iterations of the workflow performed by the control module 102 to the fitness threshold.

[0183] In one embodiment, the fitness threshold is indicative of a level of fitness for at least one fitness objective, and the control module 102 considers whether the fitness values satisfy the fitness threshold by comparing at least one fitness value to the fitness threshold.

[0184] In one embodiment, the fitness threshold is indicative of a change in fitness values from one generation to the next generation for at least one fitness objective, and the control module 102 considers whether the fitness values satisfy the fitness threshold by comparing the change in fitness values from one generation to the next generation to the fitness threshold.

[0185] In one embodiment, the control module 102 compares the fitness values from the N candidate designs 340 with the fitness values of the previous Q (usually 5-10) generations of candidate static mixer designs.

[0186] In one embodiment, the control module 102 determines whether the fitness values, measured by the CFD module 110, have converged or are sufficiently converging. In one embodiment, the control module 102 determines a convergence level. In one embodiment, the fitness threshold is indicative of a convergence level threshold. For example, the fitness threshold may be indicative of the fitness values not increasing significantly (i.e. less than 0.001) from one generation of candidate designs 340 to the next generation of candidate designs. In one embodiment, the control module 102 considers whether the fitness values satisfy the fitness threshold by comparing the convergence level to the fitness threshold.

Continuing the loop

[0187] If the control module 102 determines that the convergence criterion has not been satisfied, the control module may control the ED module 104 to design another generation of one or more candidate static mixer designs, in step 306. In one embodiment, the control module controls the ED module 104 to perform another iteration of step 306, to determine one or more second candidate static mixer designs based on the one or more first candidate static mixer designs. The ED module may determine the one or more second candidate static mixer designs based on the one or more first candidate static mixer designs and based on fitness values, determined by the CFD module 108, associated with the one or more first candidate static mixer designs. [0188] The control module 102 may control the CFD module 108 to evaluate the performance of the candidate designs produced by the ED module 104. By repeating the loop, the control module 102 iteratively optimises the design parameters by repeatedly performing the steps of (i) determining the candidate static mixer design and (ii) determining the fitness value. The control module 102 optimises the design parameters to improve the fitness value. For example, the control module 102, together with the ED module 104, select candidate static mixer designs with respective design parameters that have an improved fitness value.

[0189] In one embodiment, the set of fitness values for each of the N candidate static mixer designs 340 is passed to the control module 102, and then to the ED module 104, via 128, to guide the ED module’s generation 306 of the next generation of candidate static mixer designs.

Exiting the loop

[0190] If the control module 102 determines that the convergence criterion has been satisfied, the control module stops the iterative design/test loop and proceeds to step 316. In step 316, the control module 102 selects a static mixer design from the set of candidate static mixer designs evaluated by the CFD module 108.

[0191] In one embodiment, the control module 102 selects a static mixer design based on the Pareto front of a graph of the fitness values for the set of candidate static mixer designs. With reference to the example fitness values in graph 400 of Fig. 4, in one embodiment, preferred designs selected are those that are closest to the intersection of the Pareto front (which extends approximately from symbol 416 to symbol 414) and the central diagonal 412 of the graph 400 of fitness objectives for two independent fitness values.

[0192] In one embodiment, the control module 102 selects more than one of the candidate static mixer designs.

[0193] In response to selecting a candidate static mixer design in step 316, the control module may output a digital representation of the static mixer design selected in step 316. The digital representation may comprise a stereolithographic file (.STL). [0194] In optional step 318, the digital representation be transferred to a manufacturing system to manufacture the static mixer. The manufacturing system may comprise a 3D printer for processing and printing. The manufacturing system may utilise manufacturing techniques comprising printing directly from catalytic metals (e.g. solid platinum), coatings, gradient coatings, decorated coatings (e.g. covering in nanoparticles) and/or selectively patterned coatings, or any combination thereof.

[0195] In some embodiments, the 3D printer is configured to advise if the given static mixer geometry is unsuitable for printing. In some embodiments, the 3D printer outputs a solid metal 3D printed static mixer. The printed static mixer can be transferred to a workshop and fitted with inlets and outlets and undergo experimental validation.

[0196] In some embodiments, the manufacturing system comprises a system to generate a casting a core for use in a foundry, the use of emerging additive/subtractive machining equipment, or standard production techniques such as multi-axis CNC technology which could also fabricate mixers with larger feature sizes than state-of-the- art 3d metal printing. In one embodiment, the manufacturing system is configured to metallise a conductive polymer mixer and dissolve the superstructure to leave a delicate metallic mixing element.

[0197] Steps of method 300 may be performed on one or more processing devices (e.g. processors, servers, computers, application specific integrated devices, field- programmable gate arrays, or other device configured to perform calculations in accordance with machine-readable instructions). For example, the ED module 104 may execute on a first processing device and the CFD module 108 may execute on a second processing device. Alternatively, the ED module and the CFD module may execute on the same processing device.

Application specific designs

[0198] There are many applications for static mixers. In particular, static mixers incorporating catalysts, generally referred to as catalytic static mixers or CSMs. CSMs can be produced using the static mixers designed according to this invention using known electrochemical, chemical dipping, decoration or any other techniques known in the art. In one embodiment, for example, static mixers or CSMs may find applications in hydrogenation / dehydrogenation reactions in a flow chemistry reactors, hydrogen generation, electrowinning, electroplating, electrochemical removal of heavy metal ions, reactions involving the mixing of poorly miscible fluids or fluids/gases, polymer synthesis via emulsions which require large shear rate and narrow residence time distribution, absorption (in addition to adsorption), sorbent applications, and/or direct air capture technology. Applications could also include methods to those trained in the state- of-the-art and would find general applicability in chemical engineering and chemistry applications.

[0199] Differences in the design features of static mixer designs may lend a static mixer to be more suitable for one application than another application.

[0200] Accordingly, a static mixer that performs well for one application may not perform well in another application. Similarly, a static mixer that is unsuitable for one application, may be quite suitable for another application.

[0201] The evolutionary design process, and the CFD evaluation process may take into account the intended application of the static mixer.

Example design system results

[0202] In one embodiment, the design parameters comprise a base-geometry which defines a solid central shaft (or post) extending along the longitudinal dimension of the static mixer. The static mixer design comprised a plurality of branches and leaves extending from the central solid shaft. In other embodiments, the static mixer design comprised a plurality of leaves arranged on a spiral ribbon shaped mixer that extends along the longitudinal axis of the mixer. Preferably, the leaves are arranged to create a canopy of leaves arranged in a spiral orientation. Ribbon shaped mixers can also include one or more posts that extend along the longitudinal axis, the posts either intersect the canopy of leaves or the leaves are designed to arise from the one or more posts.

[0203] In the above examples, the ED algorithm was configured to determine 16 children in each design generation. The children designs were evaluated, by the CFD algorithm, to determine at least two fitness objectives: a ‘transport to the substrate’ measure and a ‘bulk mixing’ measure. To obtain these two fitness objectives, the CFD algorithm solved for the velocity field through the reactor using the LB method. Then using the velocity field, the CFD algorithm constructed tracer maps according to Equation 4.

Figure 4 - Pareto front - Solid central shaft

[0204] In the field of multi -objective optimisation, the Pareto front (also called the Pareto frontier or Pareto curve) represents a set of ‘Pareto efficient’ solutions.

[0205] Figure 4 is a graph 400 of the progression of a Pareto front for an evolutionary design process in which the design parameters define a solid central shaft (e.g. a single post), according to an embodiment.

[0206] Each plot point on the graph 400 represents a measure of fitness values for a static mixer design produced by the ED algorithm. Different shaped symbols (e.g. circle, square, triangle and diamond) on the graph 400 represent the fitness objectives for static mixer designs from different generations. In particular, the circular plot points, which are clustered together at area 404 of the graph 400, indicate fitness values for generation 1 designs. Square shaped plot points, such as plot point 406, indicate fitness values for generation 20 designs, diamond shaped plot points, such as plot point 408, indicate fitness values for generation 100 designs, and triangular shaped plot points, such as plot point 410, indicate fitness values for generation 150 designs.

[0207] The Pareto front (for each generation) is represented by the symbols. Line 412 represents the central diagonal for graph 400.

[0208] Figure 4 displays the progress of the Pareto front (extending from symbol 404 to symbol 416) for execution of our computer experiment (with a single post connected to branches and leaves). Each of the Generation 1 designs, indicated by plot points 404, produced a close-to-zero measurement for the ‘transport to substrate’ fitness value, and produced a small (less than 20) measurement for the ‘bulk mixing’ fitness value. By Generation 20, indicated by the square plot points, the Pareto front has expanded to a wider range of ‘transport to substrate’ values (from around 10 to around 75) and also larger ‘bulk mixing’ values (up to 35).

[0209] By Generation 100, indicated by the diamond plot points, the Pareto front has further expanded out for both the ‘transport to substrate’ fitness value (extending up to very close to 100 with plot point 414) and for the ‘bulk mixing’ fitness value (extending up to 50 with plot point 416, which happens to be collocated with a Generation 150 plot point).

[0210] From generation 100 to 150 there is small increase in the Pareto front. Many of the best fitness values at the Generation 100 are replicated at Generation 150 and any new ones are only marginally better than those at Generation 100. This indicates that there is little to be gained by iterating this workflow past 150 generations (especially given the significant computational expense). At this point, the workflow has converged to an optimal set of solutions.

[0211] In principle, it would be desirable for the Pareto front to evolve towards the top right-hand side of the graph 400, close to one hundred for both fitness objectives. However, this may not be practical. Based on the results illustrated in graph 400, it appears that it is quite difficult to get close to 100 for the ‘bulk mixing’ fitness value, with maximums only around 50. In contrast, the ‘transport to substrate’ value approaches 100 quite easily, because this result can be accomplished by all tracers being blocked from flowing through the static mixer. However, the high ‘transport to substrate’ value comes at the expense of a close to zero ‘bulk mixing’, such geometries may not actually be useful for most applications.

Vast design space explored

[0212] Considering the example illustrated in Figure 4, the preferred static mixer designs were determined in generation 150. If 16 candidate static mixer designs were considered in each of the 150 generations, the performance of 2400 (16x150) static mixer designs were considered by the computational fluid dynamics algorithms of the CFD module 108.

[0213] Using an embodiment of the design system 100, the inventors were able to explore the performance of a vast array of candidate static mixer designs, including many variations of each of tree-like mixers and ribbon mixers. The candidate static mixer designs evolved and evaluated by design system 100 varied in terms of their respective base geometries. The candidate static mixer designs evolved and evaluated by design system 100 also varied in terms of the number, shape, angle, arrangement, and combinations of polytope structures (e.g. projections).

[0214] It would not be feasible to explore such a vast design space through traditional experimental workflow or design experiment methods comprising the design, manufacture and testing of candidate static mixer designs.

Figure 5 - Pareto front - Tree mixers

[0215] In one embodiment, the workflow may be initiated with one or more initial parent design for static mixers. There is no certainty that the workflow will evolve this initial set of designs to a desirable static mixer design. In particular, the initial set of designs are unlikely to span the entire space of possible geometries. For this reason, in one example, the workflow may be applied in a plurality of independent experiments, with different sets of initial parent designs.

[0216] Figure 5 is a graph 500 of Pareto fronts for five independent computer experiments in which candidate static mixers were evolved from five different initial parent designs or initial design parameters, according to an embodiment. For each of the five independent experiments, the design parameters defined a geometry with one central post, with attached branches and leaves. The converged Pareto fronts from the five independent experiments generally fall along the same curve. For one of the experiments (brown crosses) for large values of the ‘transport to substrate’ measure (i.e., greater than seventy) fall below the other four experiments. However, it is desirable to obtain those geometries with largest values for the two measures (that is closest to central diagonal). For that reason, geometries corresponding to the two arrowed fitness values were selected for 3D printing.

Figure 6 - Pareto front - Ribbon mixers

[0217] Figure 6 is agraph 600 ofPareto fronts for five different, independent, computer experiments in which candidate static mixers were evolved from five different initial parent designs or initial design parameters, according to an embodiment. For each of the five independent experiments, the design parameters defined a geometry comprising ribbon structures. [0218] As with the experiments illustrated in Figure 5, the five computer experiments were run to convergence. In comparison to the Pareto front from the one-post geometry (in Fig. 5), the ‘bulk mixing’ measure has generally reached larger values (up to 70). Also, the maximum value of the ‘transport to substrate’ measure reaches out to about 85 (compared to 100 for the one-post geometries). To achieve these changes in the Pareto fronts, the ED module 104 was configured with design parameters which biased it away from very bulk geometries, which tend to restrict flow.

[0219] For comparison purposes, the performance of candidate static mixer designs may be compared to the performance of a reference static mixer. In one embodiment, the reference mixer has fitness values (3, 45).

Experimental procedure

[0220] The inventors performed an experimental procedure to determine the performance of the preferred static mixer designs selected by the control module 102 in step 316. The experimental procedure comprised an electrochemical experiment which extracted copper from a contaminated solution. The results of this experiment were compared with the results of a similar experiment which utilised an existing static mixer which was found to completely decontaminate a solution within 24 hours.

[0221] The inventors tested two different families of designs - a one-post structure and a four-post structure. In total four new and different designs were 3D Printed and then tested experimentally. The inventors also tested an existing design to compare the improvement in performance. All the new (computer predicted) designs performed better than the existing design. The best performing mixers showed a 45% improvement in amount of copper extracted over a four-hour period compared to the existing design.

[0222] After an extensive optimisation of the Pareto front to optimise transport to the surface of the static mixer, a select number of representative static mixer electrodes were printed in stainless steel and evaluated for their ability to electrochemically plate copper from a 200ppm copper ion solution. Experiments were conducted with 2 litres of lOOppm Cu²⁺ 0.0 IM H2SO4 solution prepared with Milli-Q water, which was recirculated through the electrochemical reactor for a maximum of 24hrs. Reglo-D peristaltic pumps were used fortesting solution recirculation and set to a static flow rate of 50 mL/min, feeding both the interstitial space between the separator and the through the inlet of the static mixer. Electrochemical assessment was conducted with a Biologic SP-150 Potentiostat operating in a chronoamperometric testing sequence biasing the working electrode (WE) at -2.5V, in this configuration, the static mixer was the WE and the counter electrode (CE) was the outer shell of the flow reactor, a 20pm separator (GenPore Reading, USA) was used to separate the CE and WE. Aliquots of testing solution were extracted from the reticulated testing solution at regular intervals, and subsequently analysed for the remaining Cu²⁺ concentration using an Agilent 5900 ICP-OES. A schematic representation of the electrochemical flow reactor utilised in this experiment is illustrated in Figure 7. In particular, Figure 7 is a schematic representation of an electrochemical flow reactor 700, according to an embodiment.

[0223] A set of experiments were carried out with the Static-Mixer Electrode (SME) previously described in the literature (Bayatsarmadi et al, 2020) and denoted here as benchmark mixer (shown as 800, Fig. 8). In the evolution of the static mixer design, a design geometry was established featuring a single central post (SKI, shown as 900 in Fig. 9), however given the 1.0 mm OD of the central post, the inherent fragility of the design made it impractical outside of a laboratory setting. Thus, the design was structurally fortified with four 1.0mm support posts traversing the axial length of the mixing element, positioned at 90° intervals around the static mixer. These mixers are called ribbon mixers.

[0224] Three different designs were experimentally evaluated to ascertain the performance sensitivity towards the optimised substrate transport mode of operation. In all cases the entire length of the mixer was covered with ribbons, which provided improved the performance over the SKI mixer. Our three ribbon mixers are denoted RB0 (1000 in Fig. 10), RB2 (1100 in Fig. 11) and RB4 (1200 in Fig. 12).

[0225] The performance of the five static mixer electrodes that were experimentally tested - benchmark mixer, SKI, RB0, RB2 and RB4 was compared. The ‘transport to substrate’ fitness value, as calculated by the Lattice Boltzmann method, was calculated as the percentage of tracer particles achieving impact with the substrate. The ‘bulk mixing’ fitness value, as calculated by the Lattice Boltzmann method, was calculated as a measure of the mixing in the bulk of the liquid phase as the tracers traverse the length of the mixing element. It can be clearly seen that the benchmark mixer has an extremely low substrate transport, which is reflected in the 55 ppm Cu²⁺ ion removal rate after 4hrs of operation.

[0226] Despite having a 20% lower surface area than the reference, the SKI mixer performance exceed that of the reference, which has been ascribed to the improve substrate transport over the reference. Unlike SKI, the ribbon mixers had a substantially higher surface area (-70%) than the reference mixer, due to the utilisation of the ribbon motif across the entire length of the mixing element. This was also coupled with improved substrate transport characteristics over the reference and SKI, which also corresponded with enhanced Cu²⁺ ion removal during after 4hrs of operation.

[0227] In one embodiment, the surface area change is calculated with respect to the reference mixing element, * denotes linear interpolation between available data points and is an estimation.

Bulk Copper ion

Mixer Substrate Area Surface area mixing removal at 4hrs reference transport (%) (mm²) change (%) (%) (ppm)

Benchmark 3 45 2126 - 55

(Reference)

Tree (SKI) 37 48 1699 -20 61*

Ribbon (RBO) 46 53 3672 73 80

Ribbon (RB2) 57 38 3715 75 77

Ribbon (RB4) 48 44 3587 69 76

[0228] Figure 18 is a graph illustrating the chronoamperometric response of the experimentally evaluated static mixers in a electrochemical flow reactor, according to an embodiment. Figure 19 is a graph illustrating the corresponding copper ion removal rate as determined by ICP-OES, for the static mixers featured in Figure 18, according to an embodiment.

[0229] The corresponding chronoamperometric response of each static mixer is presented in graph 1800 of Figure 18, the benchmark mixer is depicted in black. It can be clearly seen that all ribbon mixers supported a relatively higher steady state current than the benchmark mixer, in the first 4 hours of testing. SKI was observed to outperform the benchmark mixer, with a cross-over point occurring at approximately 1800s where the steady state current is lower than the reference.

[0230] In addition to the electrochemical reduction of copper, the current depicted in Figure 18 is also a function of the electrolysis of water. Hence, it would be inappropriate to directly attribute an increased current with increased copper plating performance. Thus, in order to verify the performance of each static-mixer, the removal of copper ions from solution as a function of time was employed as a conclusive measure of electrochemical performance. This was achieved through the removal of an aliquot of reticulated testing solution for analysis via ICP-OES against known standards. In this set of experiments the electrochemical flow reactor was configured to minimise the electrolysis of water e.g. the evolution of hydrogen and oxygen gas. However, the reactor could be reconfigured to promote the formation of hydrogen gas.

[0231] The copper ion removal performance of the evaluated mixers is depicted in Fig. 19. Over the first four hours, the performance of the benchmark mixer recovers the least amount of copper from solution of any static mixer evaluated, removing 55 ppm Cu²⁺ from solution. Interestingly the SKI mixer performs marginally better than the benchmark mixer while the three ribbon mixers all perform approximately the same, extracting approximately 80 ppm after four hours. Referring to Figure 19, the evolved structural motif of SKI mixer does not extend the entire length of static mixer, but rather is separated by a single central support post, this relative underutilisation of the mixer has been ascribed to the lower performance. Ultimately, the ribbon mixers were found to be approximately 45% better at removing Cu²⁺ from solution than the benchmark mixer, under identical electrochemical flow reactor conditions.

[0232] All static mixers were found to effectively remove copper from the testing solution within a 24hr testing period.

[0233] The operation of the coupled workflow may be computationally expensive. Accordingly, in one embodiment, the workflow is parallelized to run on multiple central processing units (CPUs), concurrently. In one embodiment, the workflow is implemented on High-Performance Computer (HPC) clusters (CSIRO’s cluster, NCI Gadi and Pawsey) so as to maximize the number of different computer experiments that can be run and also the number of different families of geometries that can be tested.

Example static mixers

[0234] The static mixer designs, as designed by the design system 100, may be configured as an integral module, which means that the static mixer can be manufactured as a single piece of material without joining multiple pieces together. To achieve this, the static mixer design may be formed of an elongated integral support structure, such as scaffold, wherein the scaffold comprises a radially arranged network or a spiral ribbon of repetitions of a template shape component, such as polytope projections, to define a plurality of passages configured for deflection and therefore mixing one or more fluidic reactants during flow along the fluid flow path and reaction thereof through the mixer, and at least one elongated support member, wherein at least a portion of the projections are in connection with the elongated support element. The integral static mixer may be further configured for insertion into the fluid flow path to deflect the fluid. This means that the static mixer design has an outer diameter that fits within the inner diameter of the mixing tube so that it possible to slide the static mixer into the mixing tube. As a result, the fluid that flows through the mixing tube is deflected by the elements of the static mixer. This can occur through the use of planar structures, like plates or vanes, or other structures such as rods and cylinders.

[0235] In some embodiments, the projections may extend radially to form an outer perimeter of the static mixer element. The outer perimeter is smaller than the inner perimeter of the mixing tube so that the static mixer can be inserted into the mixing tube. In some embodiments, the projections may form a continuous network of passages arranged in multiple orientations relative to one another. The projections may be polytope structures repeated periodically along the longitudinal axis of the elongated support member. In some embodiments, the projections are the same polytope structures or are selected from at least two different types of polytope structures. Ribbon mixers

[0236] The static mixer designs, as designed by the design system 100, may be formed of an elongated support structure, such as an integral scaffold, wherein the scaffold comprises an interconnected network of repetitions of a template shape component, such as spiral ribbon projections of polytope structures that form a plurality of passages configured for mixing one or more fluidic reactants during flow and reaction thereof through the mixer, and at least one elongated support member, wherein at least a portion of the projections are in connection with the elongated support element.

[0237] In some embodiments, the scaffold may comprise at least two spaced apart elongated support members that are structurally connected via the interconnected network of projections. The scaffold may comprise at least three spaced apart elongated support members. For example, the scaffold may comprise at least four spaced apart elongated support members.

Tree-shaped mixers

[0238] The static mixer designs, as designed by the design system 100, may comprise static mixer element be formed of an elongated support structure, such as an integral scaffold, wherein the scaffold comprises repetitions of a template shape component, such as two or more sets of projections, wherein each set of projections are spaced apart from each other along the longitudinal axis of the mixer and extend radially from the centrally located elongated support structure to define a plurality of passages configured for mixing one or more fluidic reactants during flow and reaction thereof through the mixer. In some embodiments, the projections extend radially to form an outer perimeter of the static mixer element.

Projections

[0239] In some embodiments, the repetitions, such as the projections, may extend radially from the elongated support members to form an outer perimeter of the element. The outer perimeter is less than the inner radius of the mixing tube so that the mixer can be inserted into the fluid flow path through mixing tube. [0240] In some embodiments, the projections may be a polytope structure. As described herein, a polytope structure may be defined as a polygon or a polyhedron. The proj ections may be polytope structures repeated periodically along the longitudinal axis of the elongated support member, as configured by the form parameters. In some embodiments, the projections are the same polytope structures or are selected from at least two different types of polytope structures.

[0241] In some embodiments, the projections may be a polytope structure. As described herein, a polytope structure may be defined as a polygon or a polyhedron.

[0242] In some embodiments, the polytope structure may be a polygonal or polyhedral structure. In some embodiments, the polytope structure may be a regular or irregular triangular shaped polytope, preferably an irregular shaped polytope. In some embodiments, the polytope structure may be a scalene triangle, isosceles triangle, or equilateral triangle, preferably the polytope structure is a scalene or isosceles triangle.

[0243] In some embodiments, the polytope structure may be a 2-dimensional polygon structure or a 3 -dimensional polyhedron structure. The 3 -dimensional polyhedron structure may comprise triangular prisms, square based pyramids or triangle -based pyramids.

[0244] In some embodiments, the projections may be connected to each other via at least a portion of at least one surface of a projection to form a continuous interconnected network of projections. In some embodiments, the projections may be connected to each other via at least a portion of at least one surface of a projection to form a continuous interconnected network of projections, wherein at least a portion of the interconnected network of projections are structurally connected to at least one elongated support member. In some embodiments, the projections may be connected to each other via at least a portion of at least one surface of a projection to form a continuous interconnected network of projections, wherein at least a portion of the interconnected network of projections are structurally connected to at least two elongated support members, preferably at least three elongated projections, even more preferably at least four elongated support members. Multi-stage static mixers

[0245] In some embodiments, it may be beneficial to couple a plurality of static mixers in series to provide additional performance, or additional functionality. For example, a processing component may comprise three static mixers which form a three-stage mixer, with stage 1 mixing to enhance substrate to transport, stage 2 coated section for a catalytic reaction, and stage 3 enabling bulk mixing.

[0246] In another example, a combination of two or more mixers may be implemented in order to achieve a complex multi-stage chemical reaction.

[0247] Examples described herein refer to particular fluid flow applications; however, methods and systems described herein may be applied for the determination of static mixer designs for applications other than the applications described herein as examples.

[0248] It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. Furthermore, it will be appreciated by persons skilled in the art that embodiments disclosed herein can be combined with one or more other embodiment disclosed herein, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

[0249] Throughout this disclosure, unless specifically stated otherwise or the context requires otherwise, reference to a single step, composition of matter, group of steps or group of compositions of matter shall be taken to encompass one and a plurality (i.e., one or more) of those steps, compositions of matter, groups of steps or groups of compositions of matter. Thus, as used herein, the singular forms “a”, “an” and “the” include plural aspects unless the context clearly dictates otherwise. For example, reference to “a” includes a single as well as two or more; reference to “an” includes a single as well as two or more; reference to “the” includes a single as well as two or more and so forth.

[0250] The term “and/or”, e.g., “X and/or Y” shall be understood to mean either “X and Y” or “X or Y” and shall be taken to provide explicit support for both meanings or for either meaning. [0251] Unless otherwise indicated, the terms “first,” “second,” etc. are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the items to which these terms refer. Moreover, reference to a “second” item does not require or preclude the existence of lower-numbered item (e.g., a “first” item) and/or a higher-numbered item (e.g., a “third” item).

[0252] As used herein, the phrase “at least one of’, when used with a list of items, means different combinations of one or more of the listed items may be used and only one of the items in the list may be needed. The item may be a particular object, thing, or category. In other words, “at least one of’ means any combination of items or number of items may be used from the list, but not all of the items in the list may be required. For example, “at least one of item A, item B, and item C” may mean item A; item A and item B; item B; item A, item B, and item C; or item B and item C. In some cases, “at least one of item A, item B, and item C” may mean, for example and without limitation, two of item A, one of item B, and ten of item C; four of item B and seven of item C; or some other suitable combination.

[0253] It is to be appreciated that certain features that are, for clarity, described herein in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features that are, for brevity, described in the context of a single embodiment, may also be provided separately or in any sub-combination.

[0254] Throughout the present specification, various aspects and components of the invention can be presented in a range format. The range format is included for convenience and should not be interpreted as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible sub-ranges as well as individual numerical values within that range, unless specifically indicated. For example, description of a range such as from 1 to 5 should be considered to have specifically disclosed sub-ranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 5, from 3 to 5 etc., as well as individual and partial numbers within the recited range, for example, 1, 2, 3, 4, 5, 5.5 and 6, unless where integers are required or implicit from context. This applies regardless of the breadth of the disclosed range. Where specific values are required, these will be indicated in the specification. [0255] References herein to software or executable instructions are to be understood as referring to executable instructions stored in volatile or non-volatile memory. The memory can include any data storage device that can store data which can thereafter be read by a processor. Examples of memory include read-only memory (ROM), randomaccess memory (RAM), magnetic tape, optical data storage device, flash storage devices, or any other suitable storage devices.

References

[0256] The content of the following references are incorporated herein by reference.

[0257] Bayatsarmadi, B, Home, M, Rodopoulos, T, Gunesegaram, D, Intensifying diffusion-limited reactions by using static-mixer electrodes in a novel electrochemical flow cell, vl67, 063502, (2020).

[0258] Cheney N, MacCurdy R, Clune J and Lipson, H (2013, July) Unshackling evolution: evolving soft robots with multiple materials and a powerful generative encoding', In Proceedings of the 15th annual conference on Genetic and evolutionary computation, pp. 167-174. ACM.

[0259] Deb, Kalyanmoy, et al. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. International conference on parallel problem solving from nature. Springer, Berlin, Heidelberg, 2000.

[0260] Eiben AE and Smith JE (2003) Introduction to evolutionary computing, Springer, Heidelberg.

[0261] Faber M (1995) Fluid dynamics for physicists, Cambridge University Press, Cambridge.

[0262] Kruger T, Kusumaatmaja H, Kuzmin A, Shardt O, Silva G, Magnus Viggen E (2017) The Lattice Boltzmann method: Principles and practice, Springer, Switzerland.

[0263] Press WH, Teukolsky, SA, Vettering, WT and Flannery, BP (1996) Numerical recipes in Fortran90, Cambridge University Press, Cambridge.

Claims

CLAIMS:

1. A method of designing a static mixer for mixing a fluid along a fluid flow path, the method comprising: determining, one or more design parameters comprising: one or more form parameters defining a form of at least one design component; and one or more dimension parameters defining a dimension associated with the at least one design component; determining, by a design algorithm executing on a first processing device: a form parameter value associated with the one or more form parameters; and a dimension parameter value associated with the one or more dimension parameters; determining, by a shape generator, a candidate static mixer design based on the form parameter value and the dimension parameter value, the candidate static mixer design being configured as an integral module for insertion into the fluid flow path to deflect the fluid; apply a computational fluid dynamics algorithm, executing on a second processing device, to the candidate static mixer design to determine a fitness value; iteratively optimising the design parameters by repeatedly performing the steps of (i) determining the candidate static mixer design and (ii) determining the fitness value, wherein optimising the design parameters improves the fitness value; and in response to the fitness value satisfying a fitness threshold, selecting the candidate static mixer design.

2. The method of claim 1, further comprising: generating a design description of the candidate static mixer design; and

RECTIFIED SHEET (RULE 91) controlling an additive printing machine, in accordance with the design description, to manufacture a static mixer.

3. The method of claim 1 or 2, wherein determining the candidate static mixer design comprises replicating a template shape component to generate multiple repetitions of the template shape component to generate a plurality of shape components.

4. The method of claim 3, wherein generating the multiple repetitions is configured by the design parameters.

5. The method of claim 3 or 4, wherein the multiple repetitions are arranged along a longitudinal axis of the static mixer.

6. The method of any one of claims 3 to 5, wherein determining the candidate static mixer design comprises virtually connecting the plurality of shape components.

7. The method of any one of the preceding claims, wherein the one or more form parameters further comprise one or more recursive relationship parameters to define a relationship between the plurality of shape components.

8. The method of claim 7, wherein the method comprises determining, by the design algorithm a recursion parameter value associated with the one or more recursive relationship parameters and determining, by the shape generator, the candidate static mixer design is further based on the recursive relationship parameter.

9. The method of claim 7 or 8, wherein the one or more recursive relationship parameters define how a template shape is generated multiple times in each of the multiple repetitions.

10. The method of any one of claims 3 to 9, wherein the form parameters comprise at least one angle parameter that defines an angle of one of the multiple repetitions of the template shape in relation to the static mixer.

11. The method of any one of claims 3 to 9, wherein determining the candidate static mixer design comprises adding one or more support structures to support the plurality of shape components.

RECTIFIED SHEET (RULE 91)

12. The method of claim 12, wherein the method further comprises virtually connecting the plurality of shape components to the support structures.

13. The method of any one of claims 3 to 12, wherein determining the candidate static mixer design comprises determining intersections of the plurality of shape components.

14. The method of any one of claims 3 to 13, wherein the template shape comprises a branch configured by the one or more dimension parameters and determining the candidate static mixer design comprises replicating the branch to generate a plurality of branches along the longitudinal shape of the static mixer and arranged according to the one or more form parameters.

15. The method of claim 14, wherein generating each of the plurality of branches comprises for each branch, one or more twigs originating from that branch as configured by the one or more form parameters.

16. The method of any one of claims 3 to 15, wherein the template shape comprises a triangle, the triangle is configured by three points and each point is a form parameter, and determining the candidate static mixer design comprises replicating the triangle to generate a plurality of triangles along the longitudinal shape of the static mixer and arranged according to the one or more form parameters.

17. The method of claim 16, wherein the template shape comprises two triangles, the two triangles share two points to define a connection line between the two triangles.

18. The method of any one of claims 1 to 17, wherein the design parameters comprise, one or more of: manufacturing constraints; or parameters related to the specific intended purpose for the static mixer.

19. The method of any one of claims 1 to 18, wherein the fitness value comprises an indication of one or more of: a surface area of a substrate; a substrate adsorption rate;

RECTIFIED SHEET (RULE 91) a cumulative adsorption level; a transport-to-substrate measure; an electric field of the static mixer; a pressure drop caused by the static mixer; an indication of fluid flow; an indication of fluid turbulence; a flow impediment measure; a stagnant flow region; a bulk mixing level; a measure of adsorption uniformity; a measure of shear; heat transfer; temperature gradients; temperature homogeneity; and/or a residence time distribution.

20. The method of any one of claims 1 to 19, further comprising: in response to the fitness value not satisfying the fitness threshold: determining, by the design algorithm, a second candidate static mixer design based on the candidate static mixer design; applying the computational fluid dynamics algorithm, to the second candidate static mixer design to determine a second fitness value; and in response to the second fitness value satisfying a second fitness threshold, selecting the second candidate static mixer design to be manufactured.

21. The method of claim 20, further comprising determining the second fitness threshold based on the fitness value.

RECTIFIED SHEET (RULE 91)

22. The method of any one of claims 1 to 21, wherein the design algorithm comprises an evolutionary design algorithm.

23. The method of claim 22, wherein determining a second candidate static mixer design comprises, determining a second candidate static mixer design based on the candidate static mixer design and the fitness value.

24. The method of claim 22 or 23, wherein the evolutionary design algorithm comprises a shape generator algorithm and a grid generator algorithm.

25. The method of claim 24, wherein determining a candidate static mixer design comprises: determining a set of genes defining the candidate static mixer design; determining, using the shape generator algorithm, a candidate static mixer shape based on the set of genes; and determining, using the grid generator algorithm, a candidate static mixer volume based on the candidate static mixer shape.

26. The method of claim 25, wherein determining a set of genes comprises determining a set of genes based on the design parameters.

27. The method of any one of claims 1 to 26, wherein determining a candidate static mixer design comprises determining a plurality of candidate static mixer designs.

28. The method of claim 27, wherein applying a computational fluid dynamics algorithm comprises: for each candidate static mixer design of the plurality of candidate static mixer designs, apply a computational fluid dynamics algorithm, executing on the processing device, to the candidate static mixer design to determine a respective fitness value.

29. The method of claim 27 or 28, wherein the method further comprises selecting one of the plurality of static mixer designs, based on the plurality of respective fitness values.

RECTIFIED SHEET (RULE 91)

30. The method of any one of claims 1 to 29, wherein the computational fluid dynamics algorithm comprises a numerical module configured to calculate the velocity field of fluid flowing through the candidate static mixer design.

31. The method of any one of claims 1 to 30, wherein the computational fluid dynamics algorithm applies a Lattice Boltzmann method.

32. The method of any one of claims 1 to 31, wherein the design parameters define a least one post configured to extend along the length of the static mixer.

33. The method of any one of claims 1 to 32, further comprising: amending the candidate static mixer design to include a post configured to extend along the length of the static mixer.

34. The method of any one of claims 1 to 33, wherein the static mixer design is constrained to be insertable into a mixer tube.

35. The method of any one of claims 1 to 34, wherein the method comprises generating a design description comprising a stereolithographic file.

36. The method of any one of claims 1 to 35, wherein the first processing device comprises the second processing device.

37. A system comprising: one or more processors; and memory comprising computer executable instructions, which when executed by the one or more processors, cause the system to perform the method of any one of the preceding claims.

38. A machine-readable storage medium storing instructions which, when executed by one or more processors, cause the one or more processors to perform the method of any one of claims 1 to 36.

39. A static mixer made from methods described in any one of claims 1 to 36.

40. A catalytic static mixer comprising the static mixer of claim 39 and a catalytic coating.

RECTIFIED SHEET (RULE 91)