CN119940051B - Prediction method of particle distribution characteristics inside valve under wet solid conditions - Google Patents
Prediction method of particle distribution characteristics inside valve under wet solid conditionsInfo
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Abstract
本发明涉及数值模拟技术领域，公开了一种湿气固条件下阀门内部颗粒分布特征预测方法。方法包括建立阀门三维模型，对模型进行网格划分，结合湿气固条件下颗粒碰撞反弹特性，修正切向恢复系数和法向恢复系数，利用修正后的碰撞反弹模型开展数值模拟，获取模拟数据。通过数据提取和图像处理，生成阀门内部流动分布特征图和颗粒分布特征图，依据特征图判断颗粒积聚区域，并提取颗粒数密度，量化分析阀门内部高浓度颗粒分布。基于量化分析结果，提取颗粒捕集率参数，获得湿气固条件下由壁面液膜引起的颗粒捕集特征。本方法能够有效预测阀门内部颗粒分布及积聚特性，为阀门设计与优化提供依据。
The present invention relates to the field of numerical simulation technology, and discloses a method for predicting the particle distribution characteristics inside a valve under wet solid conditions. The method comprises establishing a three-dimensional model of the valve, meshing the model, combining the particle collision and rebound characteristics under wet solid conditions, correcting the tangential restitution coefficient and the normal restitution coefficient, and using the corrected collision and rebound model to carry out numerical simulation and obtain simulation data. Through data extraction and image processing, a flow distribution characteristic map and a particle distribution characteristic map inside the valve are generated, the particle accumulation area is judged based on the characteristic map, and the particle number density is extracted to quantitatively analyze the distribution of high-concentration particles inside the valve. Based on the quantitative analysis results, the particle capture rate parameter is extracted to obtain the particle capture characteristics caused by the wall liquid film under wet solid conditions. This method can effectively predict the particle distribution and accumulation characteristics inside the valve, and provide a basis for valve design and optimization.
Description
Technical Field
The application relates to the technical field of numerical simulation, in particular to a valve internal particle distribution characteristic prediction method under a wet gas-solid condition.
Background
The valve is used for regulating and controlling medium flow in industrial production, and is widely applied to the fields of chemical industry, petroleum, electric power and the like. With the development of industrial technology, the application of gas-solid two-phase flow is increasing, for example, when industrial gas containing solid particles is conveyed under high temperature and high pressure, the particles may be accumulated or aggregated due to the wetting action of the wall surface, and the stability of fluid flow and valve performance are affected.
Currently, two-phase flow under wet solids conditions is under relatively limited investigation. The existing research is mainly aimed at dry environments, and the influence of a liquid film on particle collision and aggregation behaviors is difficult to accurately describe by a related model, so that the prediction accuracy of particle distribution characteristics is insufficient. In addition, the existing numerical simulation method has low applicability under the moisture-solid condition, and is difficult to meet the requirements of valve design and maintenance on particle distribution characteristic prediction.
Therefore, research is conducted on particle distribution characteristics under the moisture-solid condition, effective data support can be provided for optimizing valve performance, and the method has important significance in improving the efficiency and safety of industrial processes.
Disclosure of Invention
The embodiment of the application aims to provide a method for predicting the internal particle distribution characteristics of a valve under a wet gas-solid condition, so as to solve the problem that the collision rebound and accumulation behaviors of particles are difficult to accurately predict under the wet gas-solid condition in the prior art, and particularly, the prediction accuracy of the particle accumulation occurrence area and the capture rate is limited under the influence of a wall liquid film. The method effectively makes up the defects and provides a reliable basis for the optimal design of the valve.
According to the embodiment of the application, a method for predicting the distribution characteristics of particles in a valve under a wet gas-solid condition is provided, which comprises the following steps:
s1, establishing a valve three-dimensional model;
s2, carrying out grid division on the valve three-dimensional model;
S3, correcting tangential recovery coefficients and normal recovery coefficients in the particle collision rebound model by combining the three-dimensional valve model subjected to grid division with particle collision rebound characteristics under the moisture-solid condition, and carrying out numerical simulation on the corrected particle collision rebound model to obtain simulation data;
s4, carrying out data extraction on the simulation data, and then carrying out image processing to obtain a flow distribution characteristic diagram and a particle distribution characteristic diagram;
S5, judging a particle accumulation occurrence area according to the flow distribution characteristic diagram and the particle distribution characteristic diagram;
s6, extracting particle number density according to the particle accumulation occurrence area, and quantitatively analyzing the distribution of high-concentration particles in the valve under the moisture-solid condition by adopting a particle number density analysis method;
s7, extracting particle trapping rate parameters according to the quantitative analysis result, and further obtaining particle trapping characteristics caused by the wall liquid film under the moisture-solid condition;
The tangential recovery coefficient The expression of (2) is as follows:
;
The normal recovery coefficient The expression of (2) is as follows:
;
Wherein, the In order to fit the coefficients of the coefficients,At the critical angle of the beam,The impact angle is inclined for the particles.
The technical scheme provided by the embodiment of the application can comprise the following beneficial effects:
According to the embodiment, the three-dimensional model construction, the grid division and the corrected particle collision rebound model are adopted, the tangential recovery coefficient and the normal recovery coefficient are corrected by combining the particle motion characteristics under the moisture-solid condition, the technical problem that the traditional model under the dry wall surface can not accurately reflect the particle collision rebound and accumulation behaviors under the moisture-solid condition is solved, and the particle distribution prediction accuracy under the moisture-solid condition is improved. By introducing the quantitative analysis method of particle number density, the problem of insufficient analysis precision of particle accumulation areas and trapping rate in the prior art is solved, and accurate identification and quantitative analysis of the particle accumulation areas are further realized. Finally, the influence characteristics of the wetting wall on particle distribution are further obtained by extracting the particle trapping rate parameters, so that a more accurate technical basis is provided for valve design optimization.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
FIG. 1 is a flow chart illustrating a method for predicting internal particle distribution characteristics of a valve under wet gas-solid conditions, according to an exemplary embodiment.
FIG. 2 is a three-dimensional model diagram of a ball valve, according to an example embodiment.
FIG. 3 is a flow chart illustrating meshing of a ball valve according to an exemplary embodiment.
FIG. 4 is a schematic diagram illustrating a ball valve internal flow path calculation region, according to an example embodiment.
FIG. 5 is a partial mesh encryption schematic of a three-dimensional model of a ball valve, according to an example embodiment.
Fig. 6 is a schematic diagram illustrating particle-wall collision bounce according to an exemplary embodiment.
Fig. 7 is a flow chart illustrating a particle impact rebound model boundary condition UDF file under wet conditions, according to an exemplary embodiment.
FIG. 8 is a grid cell arrangement illustrating a particle density solution according to an exemplary embodiment.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the application.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
FIG. 1 is a flow chart illustrating a method for predicting internal particle distribution characteristics of a valve under moisture solids conditions, according to an exemplary embodiment, as shown in FIG. 1, the method comprising the steps of:
in the implementation of step S1, a valve three-dimensional model is established;
Specifically, a three-dimensional model is built according to the actual geometric dimensions of the valve through operations such as stretching, array, mirror image, cutting, rotation and the like of a three-dimensional modeling software SOLIDOORKS, and as shown in fig. 2, the valve rod 1, the bracket 2, the valve cover 3, the ball 4, the valve seat 5 and the valve body 6 are respectively modeled and assembled into a complete ball valve model. And exporting the assembled ball valve three-dimensional model into STEP format, so that the subsequent model is conveniently imported into ANSYS SPACECLAIM software for model pretreatment.
In the implementation of the step S2, grid division is carried out on the valve three-dimensional model;
Specifically, the three-dimensional model of the valve is led into ANSYS SPACECLAIM software for model pretreatment, then grid division is carried out in FLUENT MESHING software, the number of grids is set, local grid encryption treatment is carried out on the valve cavity area inside the valve, and high-precision grids of the interaction area of fluid and particles are ensured so as to reflect the flow characteristics more accurately.
The flow chart of the grid division is shown in figure 3 and comprises the steps of importing a model and preprocessing, defining a grid area, generating a grid, checking the quality of the grid and the flow coefficientRefinement of grid and flow coefficientComparing flow coefficients, comparing minimum mesh sizeAnd particle diameterAnd solving the numerical value in the next step.
In the process of importing a model and preprocessing, in order to reduce the calculation amount of subsequent grid division and improve the grid precision, the valve three-dimensional model is simplified in ANSYS SPACECLAIM software, only parts related to a flow channel are reserved, irrelevant parts such as a bracket are deleted, holes and gaps irrelevant to the flow channel are filled, chamfers and fillets are deleted, concave-convex areas are filled and the like. In order to ensure that the gaseous medium in the ball valve pipeline and the solid particles in the medium are fully mixed, the length of the upstream pipeline of the ball valve is prolonged to 10 times of the diameter of the pipeline by a pulling function, the length of the downstream pipeline is prolonged to 10 times of the diameter of the pipeline,
In the defined grid area, the wall surface, the inlet and the outlet of the valve and the valve cavity area inside the valve to be grid encrypted are named, then the named inlet surface and outlet surface are selected through volume extraction in the preparation tab to extract the fluid area inside the valve and named fluid, and finally the conversion to FLUENT MESHING software is selected in the Workbench tab.
In the process of generating grids, the workflow of 'WATERTIGHT GEOMETRY' is selected in 'FLUENT MESHING' software, after a geometric model is imported, local dimensions are added to the inner surface of a named valve to be encrypted by the grids, so that the local grids are encrypted, then, a surface grid is generated, when the geometric structure is described, the 'geometric model is checked to be composed of only fluid areas without gaps', boundary conditions are updated to be a pressure outlet and a pressure inlet, a boundary layer is added, finally, a polyhedral grid 'poly-hexcore' generator grid is selected, a domain diagram is calculated for the internal flow channel of the ball valve in a dotted line frame of fig. 4, and fig. 5 is a schematic diagram for encrypting the local grids in the valve.
In checking the grid quality, clicking "execute grid check" in the "grid" tab, the grid quality parameters are visible on the underlying console, with emphasis on whether there is a negative volume and an orthogonal quality, and if there is a negative volume or an orthogonal quality below 0.5, it is necessary to return to the "model import and pre-process" step for re-modification.
After the grid quality inspection is completed, the flow coefficient is usedAs a target variable, grid independence verification starts. Specifically, an initial grid is used for carrying out numerical solution to obtain a flow coefficient. Then, by adjusting the minimum size of the gridTo refine the number of grids, and re-performing numerical solution to obtain flow coefficient. Comparing the errors of the two flow coefficients, if the errors are more than 5%, continuously refining grids and solving again, gradually optimizing grid division until the errors of the flow coefficients are less than 5%, and if the errors are less than 5%, indicating that the numerical solution is basically irrelevant to the grid division. Next, the minimum dimensions of the grid are comparedAnd particle diameter. If it isThe current grid division passes the independence verification and can be used for subsequent numerical solution, ifReturning to the "grid generation" step, the grid density is readjusted to ensure grid independence and accuracy of the particle distribution characteristics.
The grid quality of the exemplary embodiment in the disclosure finally reaches more than 0.7, meets the requirement of numerical simulation calculation, and can be solved in the next step.
In the implementation of step S3, the three-dimensional valve model after meshing is combined with the particle collision rebound characteristic under the moisture-solid condition, and the tangential recovery coefficient in the particle collision rebound model is calculatedAnd normal coefficient of restitutionCarrying out correction, carrying out numerical simulation on the corrected particle collision rebound model, and obtaining simulation data;
in particular, when the gas-solid two-phase flow calculation is directly performed, stable convergence of the calculation or ideal calculation accuracy is often difficult to achieve due to the strong coupling action of particles and gas in the flow field and the complexity of particle movement. Therefore, in order to improve the calculation efficiency and the accuracy of the result, the method is required to be carried out in two steps, namely, firstly, a stable gas flow field is established through numerical simulation, the basic characteristics of the gas flow are ensured to reach a stable state, then, on the basis, particles are introduced, and the movement track, the distribution characteristic and the interaction of the particles with the wall surface of the gas flow field are further calculated.
More specifically, firstly, a three-dimensional valve model after grid division is imported into FLUENT software, and unified grid units are set in a grid scaling tab, a single-phase gas flow field is established, steady state and gravity acceleration are set in a universal tab, energy and viscosity are opened in a model tab, and the flow field is setSST turbulence model and wall function, setting single-phase gas as 'air' in a 'materials' tab, setting fluid domain material as 'air' in a 'unit area condition' tab, defining boundary conditions of 'outlet' and 'inlet' as pressure in a 'boundary condition' tab, setting calculation method as Coupled and control method as defaults in a 'solving' tab, setting convergence residual value in a 'calculation monitoring' tab, setting an initialization method as 'standard initialization' in an 'initialization' tab, clicking an 'initialization' button to finish initialization setting, setting iteration times and time steps in a 'calculation setting' tab, and clicking 'start calculation'.
Next, by the experiment of collision and rebound between particles and wall with liquid film and analyzing the normal component and tangential component of the velocity of particles during collision, as shown in FIG. 6, the tangential recovery coefficient is obtainedAnd normal coefficient of restitutionAnd the tangential recovery coefficient and the normal recovery coefficient of the particle impact rebound model under the moisture-solid condition are used for correcting;
Finally, after the stable flow field is obtained after the calculation is completed, setting ' transient ' and ' gravity acceleration ' in a ' universal ' tab, opening ' discrete phase ' in a ' model ' tab, checking ' interaction with a continuous phase ', creating ' injection source ', selecting ' particle type ' as ' inertia ', selecting ' injection source type ' as ' file ', wherein ' file ' is an externally imported user-defined particle package file, selecting ' function ' in the ' user-defined ' tab, loading a reflection boundary condition UDF function of a particle impact rebound model under the condition of moisture solid containing correction, setting ' discrete phase boundary type ' in DPM of all wall surfaces in the ' boundary condition ' tab as ' user-defined ', setting ' discrete phase BC function ' as a user-defined file ' bc_reflection: libduf ', setting the iteration times and time step in a ' running calculation ' tab, clicking ' to start calculation, and obtaining data of CASE files and DATE files after the calculation.
By constructing the gas flow field in advance before particle calculation, the problems that two-phase flow is difficult to converge and the error is large in the traditional method when two-phase flow is directly calculated are effectively solved. The numerical calculation method of the embodiment of the application obviously improves the accuracy and the reliability of the result, and simultaneously provides a more reliable and innovative solution for the numerical simulation of the two-phase flow.
In numerical computation, the residual is one of the key indicators for measuring whether the computation converges, and the judgment condition for the termination of the computation generally includes the residual and the number of iteration steps. When the residual reaches a preset threshold or the iteration number reaches an upper limit, the calculation is automatically ended. In order to improve the accuracy of flow field simulation as much as possible, the residual error convergence standard is set to 10 -20 times and the iteration number is 2000 at this time, so as to ensure the reliability and accuracy of the calculation result.
A flow chart for compiling a reflection boundary condition UDF function of a particle impact rebound model under modified moisture-solid conditions is shown in fig. 7, and the specific steps are as follows:
(1) Initializing variables including the angle between the particle velocity and the normal vector of the wall Angle of reflectionNormal direction of particlesCritical speed of particleCoefficient of normal recoveryCoefficient of tangential recovery;
(2) Calculating a vector, judging whether the rotation condition is axisymmetric according to the value of rp_axi_ swirl, wherein rp_axi_ swirl is a global variable in Fluent and is used for identifying whether an axisymmetric rotation flow model is started, if so, calculating a three-dimensional vector to avoid numerical instability, and if not, directly using a two-dimensional vector;
(3) Checking the particle type, judging whether the particle is an inert particle, if yes, continuing the next processing, if not, skipping the particle processing, wherein the particle type is set to be inert in the exemplary embodiment of the application, so that the next processing can be directly performed;
(4) Comparing the normal velocity of the particles And critical speedThe particle velocity and the normal vector algorithm are multiplied by the velocityCalculating critical velocity of particles using empirical formula;
(5) If it isThe particle velocity is determined to be 0, and the particle velocity of 0 is set, meaning that the particles are trapped by the wall liquid film;
If it is Then entering wall reflection logic, firstly calculating a reflection angle, and calculating a tangential recovery coefficient according to the size of the reflection angle and a fitting coefficient and a formula obtained by combining experimentsAnd normal coefficient of restitutionFinally, the particle speed is readjusted by using two recovery coefficients, and the initial particle speed is updated to continue moving.
The impact rebound speed and angle of the particles and the wall surface with the liquid film are changed under the influence of the liquid film, and meanwhile, the existence of the liquid film is equivalent to the addition of a protective layer on the wall surface, so that the impact speed of the particles and the wall surface is reduced, and the movement track of the particles is changed.
Therefore, the fitting coefficient and the formula obtained by the experiment are obtained by collision and rebound experiments of particles and a wall surface with a liquid film, and the normal component and the tangential component of the velocity of the particles during collision are analyzed to obtain the tangential recovery coefficientAnd normal coefficient of restitutionAnd the method is used for writing a reflection boundary condition UDF function of the particle impact rebound model under the modified moisture-solid condition in the subsequent numerical simulation so as to simulate the particle impact rebound behavior more truly.
Through the obtained experimental data, tangential recovery coefficients can be obtained by fitting in Origin softwareAnd normal coefficient of restitutionAngle of impact with particle inclinationThe changing functional relation:
(1) Tangential recovery coefficient
(2) Normal coefficient of restitution
Wherein, the In order to fit the coefficients of the coefficients,Is a critical angle.
In an exemplary embodiment of the present application, the fitting coefficients after fitting by experimental data are:
In the implementation of step S4, the flow distribution feature map and the particle distribution feature map are obtained after the data extraction is performed on the analog data and then the image processing is performed.
Specifically, the calculated analog data is subjected to graphic processing, and a characteristic section is required to be created for displaying an internal flow field distribution characteristic diagram better. Selecting "cloud" in the "results" tab in FLUENT and clicking on "new face" to create an appropriate feature section, sequentially selecting "visibility" and "Velocity Magnitude" in the "coloring variables" tab, and then clicking on "save/display"; likewise, a cloud image is created again on the created feature section with respect to the internal Pressure distribution, and "Pressure" and "Static Pressure" are selected in sequence in the "coloring variable" tab, and then "save/display" is clicked;
the "coloring variables" in the "particle track" tab select "Particle Variables" and "Particle Velocity Magnitude" in sequence and then click "track" and "save/display" so that a map of the movement track of the interior particle can be obtained.
In order to better display the movement of particles in the valve or the distribution condition of particles trapped by the wetted wall surface, the valve grid and the particle track are displayed in a graph, the transparency of the valve grid is properly set, namely, the grids are checked in a scene option tab, the grid is Particle Velocity, the grid transparency is 60%, and finally the particle distribution characteristic graph is obtained.
In the implementation of step S5, the particle accumulation occurrence area is determined according to the flow distribution feature map and the particle distribution feature map.
Specifically, the flow distribution characteristic diagram and the particle distribution characteristic diagram are utilized to visually display the flow field condition in the valve, the interaction condition of particles and a wall liquid film under the moisture-solid condition is observed, and the locking speed is reduced to the area where the particles are located. By analyzing the particle mass concentration distribution and the volume concentration distribution of these regions, a specific region where particle accumulation occurs is labeled.
In the implementation of step S6, the particle number density is extracted according to the particle accumulation occurrence area, and the quantitative analysis of the high-concentration particle distribution inside the valve under the moisture-solid condition is performed by adopting a particle number density analysis method.
The particle number density is used as a characterization parameter, the particle number density of a particle accumulation occurrence area is obtained by calculating the equivalent particle number in each grid unit and summing up the probability fractions of each particle reaching the grid unit according to the particle number density result, the spatial distribution characteristics of the particles under the moisture-curing condition are further quantified according to the particle number density result, the quantification standard comprises the sum of the particle numbers in each grid unit and the distribution uniformity among the grid units, the concentration gradient and the accumulation characteristics of the particles on the spatial distribution are evaluated according to the spatial distribution characteristics of the particles under the moisture-curing condition by counting the equivalent number of the particles in the grid units and combining the probability distribution of the particles reaching the grid units, and the distribution range and the position of the particles with high concentration are further confirmed, wherein the concentration of the particles in the accumulation area is larger than that of the particles at an inlet. The particle number density is defined as the number of equivalent particles in a given grid (s×s), the grid cell arrangement to be used is shown in fig. 8, and the probability score calculation formula is as follows:
Wherein, the For each probability score that a particle falls on a respective grid,AndIs the coordinates of the particles and,AndFor the coordinates of the center points of the respective grids,AndAt the center point of two adjacent gridsShaft and method for producing the sameDistance in the axial direction.
By the method, the distribution density degree of the particles in different areas can be intuitively quantified. Areas of high particle count density are often closely related to particle accumulation and these areas are often critical sites for valve operation that are susceptible to wear or clogging. Based on analysis of particle number density, a reference basis can be provided for optimizing a flow field under a moisture-solid condition, and a new thought is provided for researching particle distribution characteristics.
In the implementation of step S7, the particle capturing rate parameter is extracted according to the result of the quantitative analysis, so as to further obtain the particle capturing characteristic caused by the wall liquid film under the moisture-solid condition.
Specifically, the particle trapping rate is defined as the trapping probability fraction of particles in the wall liquid film area, and the trapping characteristic of the particles in the valve is obtained by calculating the trapping rate difference of the particles in different wetting wall areas and constructing a particle trapping distribution model. The calculation formula of the particle trapping rate is as follows:
Wherein, the In order to achieve the particle trapping rate, the particle size distribution,In order for the number of particles to be trapped by the wall,The total particle number in the flow field is calculated.
The capture distribution characteristics of the particles in different wetted wall areas were analyzed by numerical simulation and data extraction. In certain specific areas inside the valve, the wall liquid film may lead to higher particle trapping rates due to flow characteristics or geometry effects. For these regions, potential particle accumulation regions can be identified by spatially distributed features of the trapping rate, thereby optimizing the valve cavity shape design and reducing the risk of particle deposition during operation.
As can be seen from the above embodiments, the embodiment of the present application adopts three-dimensional model construction, meshing and modified particle impact rebound model, and combines particle motion characteristics under moisture-solid condition to tangential recovery coefficientAnd normal coefficient of restitutionThe method solves the technical problem that the model under the traditional drying wall surface can not accurately reflect the collision rebound and accumulation behaviors of the moisture-solid condition on the particles, and further improves the accuracy of particle distribution prediction under the moisture-solid condition. By introducing the quantitative analysis method of particle number density, the problem of insufficient analysis precision of particle accumulation areas and trapping rate in the prior art is solved, and accurate identification and quantitative analysis of the particle accumulation areas are further realized. Finally, the influence characteristics of the wetting wall on particle distribution are further obtained by extracting the particle trapping rate parameters, so that a more accurate technical basis is provided for valve design optimization.
Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of the application following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
It is to be understood that the application is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be effected without departing from the scope thereof. The scope of the application is limited only by the appended claims.
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| CN102460527A (en) * | 2009-05-01 | 2012-05-16 | 爱克斯崔里斯科技有限公司 | Improvements to Particle Detectors |
| CN116884883A (en) * | 2023-09-01 | 2023-10-13 | 山西创芯光电科技有限公司 | A method for reducing air bubbles in the bottom filling of infrared detectors |
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| CN102460527A (en) * | 2009-05-01 | 2012-05-16 | 爱克斯崔里斯科技有限公司 | Improvements to Particle Detectors |
| CN116884883A (en) * | 2023-09-01 | 2023-10-13 | 山西创芯光电科技有限公司 | A method for reducing air bubbles in the bottom filling of infrared detectors |
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