CN116772013A - Rectangular air pipe low-resistance rectifying tee joint and design method thereof - Google Patents

Abstract

The invention belongs to the technical field of wind system energy saving and consumption reduction. It discloses a rectangular air duct low-resistance rectifier tee and a design method thereof, which includes a Y-shaped tee body, two guide plates and flanges penetrating the tee; Y The outlets on both sides of the Y-shaped tee body have the same size. The inner cavity of the Y-shaped tee body is provided with guide plates on both sides. The guide plates are connected to the upper and lower walls of the Y-shaped tee body; the tee of the Y-shaped tee body The outer ends of the inlet and tee outlet are connected with flanges. In the present invention, when the airflow enters the tee, the airflow is divided into two parts through the diversion effect of the deflector plate, flowing from the upper and lower parts of the deflector to the straight pipe section of the tee outlet respectively. The reasonable curvature design of the deflector can make the lower airflow flow along the The guide plate flows without generating eddy currents, reducing the resistance loss of the air flow in the tee. The air volume in the upper and upper parts of the guide plate is roughly equal, making the air flow velocity distribution above and below the branch pipe section more uniform, improving the efficiency of the air flow. Uniformity to achieve the purpose of rectification.

Description

A rectangular air duct low-resistance rectifier tee and its design method

Technical field

The invention belongs to the technical field of energy saving and consumption reduction in wind systems, and in particular relates to a rectangular air duct low-resistance rectifier tee and a design method thereof.

Background technique

The energy consumption of the HVAC system accounts for about 40% to 60% of the building energy consumption. An important component of the energy consumption of the HVAC system operation is the energy consumption of the wind system. In the wind system energy consumption, the energy consumption caused by overcoming the resistance of local components accounts for more than 40% of the total resistance energy consumption of the wind system. Tee is a common local component of the wind system. In a wind system with more tees, the local resistance loss of the tees can reach more than 50%. Therefore, the resistance optimization design of the tees is very important in terms of energy saving and consumption reduction of the wind system. .

At the same time, due to the change in flow direction, after the airflow flows through the tee, it is easy to generate eddy currents at the outlet of the tee, which in turn leads to uniformity of outlet airflow distribution. When there are other local components downstream of the tee, the uneven airflow organization will become more unstable after flowing through the local components and increase the resistance of the local components.

In order to reduce the resistance loss of air flow at the tee and improve the flow state of the air flow, we propose a rectangular air duct low-resistance rectifying tee.

Through the above analysis, the problems and defects existing in the existing technology are:

1. High resistance loss: The existing tee will cause a large resistance loss when the air flows through, leading to an increase in energy consumption. The local resistance loss of the tee accounts for a large proportion in the wind system, and can even reach more than 50%.

2. Uneven flow: Since the tee changes the flow direction of the airflow, the airflow easily generates eddies and turbulence after passing through the tee, resulting in uneven flow of airflow. Uneven air flow will further affect the flow stability of downstream local components and increase the resistance of local components.

3. Increased energy consumption: Since the existing tee design cannot effectively reduce resistance loss and improve the air flow state, the energy consumption of the wind system increases. This issue is particularly significant given the important proportion of ventilation and air conditioning systems in building energy consumption.

To sum up, the tee used in the prior art causes problems and shortcomings such as resistance loss, uneven flow, and increased energy consumption when air flows through. In response to these problems, a design scheme for a rectangular air duct low-resistance rectifier tee was proposed, aiming to reduce resistance loss and improve the air flow state, thereby improving the efficiency and energy-saving performance of the wind system.

Contents of the invention

In view of the problems existing in the prior art, the present invention provides a rectangular air duct low-resistance rectifier tee and a design method thereof.

The invention is implemented in this way. A rectangular air duct low-resistance rectifier tee includes:

Y-shaped tee body, two deflectors and flanges running through the tee;

The outlets on both sides of the Y-shaped tee body have the same size, and guide plates are provided on both sides of the inner cavity of the Y-shaped tee body, and the guide plates are connected to the upper and lower walls of the Y-shaped tee body;

The outer ends of the tee inlet and the tee outlet of the Y-shaped tee body are connected with flanges.

Furthermore, the inlet and outlet heights of the Y-shaped tee body are equal.

Furthermore, the Y-shaped tee body, flange, and guide plate are all made of steel plates.

Further, the starting end of the baffle is located at the tee inlet, and the end is located at the tee outlet.

Further, the Y-shaped tee body and the deflector plate have a symmetrical structure along the center line of the Y-shaped tee.

Furthermore, the surfaces of the Y-shaped tee body, flange, and guide plate are all provided with anti-rust paint.

Another object of the present invention is to provide a design method for a rectangular air duct low-resistance rectifier tee. The method includes:

Step 1. Determine the fluid flow field state in the low-resistance rectifier tee of the rectangular air duct. According to the size of the inlet and outlet of the tee and the fluid velocity in the tee, use the Reynolds stress model to simulate the velocity field distribution and pressure field distribution in the tee. , obtain the pressure loss of the tee and the airflow unevenness at the outlet section of the tee;

Step 2: List the possible optimal relative positions of the deflector within the tee, simulate the tee with the addition of the deflector, and calculate the resistance loss of the tee under the conditions of adding deflectors at each relative position and The airflow unevenness in the tee outlet cross section;

Step 3: Calculate the drag reduction rate of each deflector, compare the drag reduction rate and air flow unevenness of each deflector, and select the drag reduction rate and air flow unevenness that are better than those without adding the deflector. Parameters of the deflector, the selected position of the deflector is the optimal drag reduction and rectification position of the deflector within the tee.

Further, in the step 1 of the step 1, the fluid flow field state in the low-resistance rectifying tee of the rectangular air duct is determined. The established tee model adds straight pipe sections at the inlet and outlet to simulate the air flow before and through the tee. The flow state after passing through.

Furthermore, based on the inlet size and outlet size and the pipeline inlet fluid velocity, the RSM model was used to simulate the tee without and with the baffle added, and the velocity distribution of the airflow flowing through the tee and after flowing through the tee was simulated. and pressure distribution, and calculate the local resistance and airflow unevenness of the tee.

Furthermore, the calculation method of the airflow unevenness of the tee outlet cross-section in step one is as follows:

Select n measuring points on the air duct section, measure the partial velocity of each point in the flow direction, and obtain the arithmetic average:

Then the unevenness is:

The airflow unevenness k is a dimensionless number. The smaller the k value, the better the airflow uniformity.

Furthermore, after obtaining the local resistance of the tee (denoted as ΔP) in steps one and two, the local resistance coefficient is calculated:

Among them, ΔP is the local resistance of the tee, Pa; ρ is the air density, kg/m ³ , v is the exit velocity of the tee, m/s.

The drag reduction rate η is:

Among them, eta is the drag reduction rate of the deflector, ξ _{is now} the local resistance coefficient of the tee with the deflector added, and ξ _{was originally} the local resistance coefficient of the tee without the deflector.

Combined with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are:

First, in the present invention, when the airflow enters the tee, the airflow is divided into two parts through the diverting effect of the deflector plate, and flows from the upper and lower parts of the deflector to the straight pipe section of the tee outlet respectively. The reasonable curvature design of the baffle can make the airflow below flow along the baffle without generating eddy currents, and reduce the resistance loss of the airflow in the tee. At the same time, the air volume in the upper and lower parts of the baffle is roughly equal, so that the air flow velocity distribution above and below the branch pipe section is more even, improving the uniformity of the air flow and achieving the purpose of rectification.

The invention guides the air flow through the guide plate and changes the distribution of the air flow inside the tee and the downstream straight pipe section, thereby achieving the purpose of reducing resistance loss and rectifying the flow.

Second, the rectangular air duct low-resistance rectifying tee of the present invention uses baffles to guide and distribute the air flow, which can reduce the eddy currents generated by the air flow in the tee, reduce the local resistance of the wind system, save energy consumption, and at the same time change the The air flow distribution in the tee and outlet straight pipe section improves the uniformity of air flow and achieves the purpose of rectification.

Third, the application of the present invention can reduce the resistance loss of air flow at the tee. For a wind system containing multiple tee components, the energy consumption of the entire wind system can be reduced, and the operating cost of the wind system can be reduced; at the same time, for wind systems containing multiple tee components, In scenarios where air flow uniformity is required, the present invention can improve the air flow uniformity downstream of the tee; when the downstream pipe section is connected to other local components, the present invention can improve the air flow uniformity within a short distance and reduce local resistance components. interactions between.

Fourth, in the existing research on tees, most scholars focus on drag reduction, and there are few studies on reducing drag while improving airflow uniformity. During the actual operation of the wind system, the tee will change the flow direction of the air flow, making the air flow unstable. When there are other local components connected downstream of the tee, the unstable air flow at the entrance will flow through the local components. It is more unstable and will increase local resistance. This is a technical problem that people have been eager to solve but have never been successful. The significance of the present invention is to reduce local resistance while improving airflow uniformity, improve airflow uniformity within a short distance after the tee, and reduce the impact of uneven airflow organization on downstream straight pipe sections or local components.

Description of drawings

Figure 1 is a schematic structural diagram of a rectangular air duct low-resistance rectifier tee provided by an embodiment of the present invention;

Figure 2 is a schematic structural diagram of a flange provided by an embodiment of the present invention;

Figure 3 is a schematic diagram of the relative positions of the deflectors provided by the embodiment of the present invention;

Figure 4 is a schematic diagram of the drag reduction rate of adding different deflectors to the tee provided by the embodiment of the present invention;

FIG. 5 is a schematic diagram of the airflow unevenness with and without the addition of a guide plate according to an embodiment of the present invention.

In the picture: 1. Y-shaped tee body; 2. deflector; 3. flange; 4. screw hole; 5. tee inlet; 6. tee outlet.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with examples. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention.

The specific solution of the rectangular air duct low-resistance rectifier tee provided by the embodiment of the present invention is as follows:

When the airflow enters the tee body from the tee inlet, the airflow will be affected by the deflector, which can guide the airflow in the appropriate direction and reduce the turbulence and resistance of the airflow. The baffle is connected to the upper and lower walls of the Y-shaped tee body, which can limit the lateral flow of the air flow, thereby reducing the turbulence and resistance of the air flow.

When the airflow passes through the baffle, it will enter the inner cavity of the tee body. The baffles on both sides of the inner cavity can further guide the airflow in the appropriate direction and reduce the turbulence and resistance of the airflow. Since the outlets on both sides of the Y-shaped tee body have the same size, the airflow can flow out smoothly from the outlets on both sides, reducing the turbulence and resistance of the airflow.

Finally, the outer ends of the tee inlet and tee outlet are connected with flanges, which can be easily connected to other pipes and equipment.

The rectangular air duct low-resistance rectifier tee can reduce the turbulence and resistance of the air flow and improve the smoothness and efficiency of the air flow by setting the deflector and optimizing the inner cavity structure.

The rectangular air duct low-resistance rectifier tee provided by the embodiment of the present invention has the following advantages:

1) Through the symmetrical structural design of the baffle, the airflow entering the tee is evenly divided into two parts, thereby reducing the vortex generated by the airflow at the outlet, improving the uniform fluidity of the airflow, thereby reducing the airflow in the tee resistance loss at.

2) The design of a rectangular air duct low-resistance rectifying tee is used to flow the air along the predetermined streamline, thereby reducing the flow resistance and turbulence, and improving the flow efficiency and stability of the air flow.

3) By using advanced manufacturing technology and intelligent control technology, and considering various air flow conditions and practical application scenarios, the optimized design and application of low-resistance rectifying tees for rectangular air ducts are achieved, thereby improving the efficiency of the wind system and stability, and meets the requirements of energy saving and environmental protection.

In the embodiment of the present invention, when the airflow enters the inlet of the rectangular air duct low-resistance rectifying tee, the airflow will be affected by the deflector and be evenly divided into two parts, flowing from the top and bottom of the deflector to the outlet of the tee respectively. The symmetrical structure design of the baffle and the shape of the streamlined baffle make the air flow along the predetermined streamline when flowing through the tee, reducing the degree of bending and vortex of the air flow, thereby reducing the air flow at the tee resistance loss and energy loss. In addition, the position and shape of the baffle can also be optimized and designed according to specific air flow conditions and application requirements to achieve the best flow effect and energy saving effect.

Therefore, the rectangular air duct low-resistance rectifying tee provided by the embodiment of the present invention has excellent air flow performance and energy-saving effect, and is suitable for the construction and renovation of various wind systems.

The following is further explained with reference to the accompanying drawings:

As shown in Figure 1, the rectangular air duct low-resistance rectifying tee provided by the embodiment of the present invention includes a Y-shaped tee body 1, a guide plate 2 and a flange 3. The deflector 3 has a symmetrical structure inside the tee, and can be connected to the upper and lower walls by welding or gluing. The schematic diagram of the position of the deflector within the tee is shown in Figure 3. Both the tee inlet 5 and the outlet 6 are provided with flanges 5 and screw holes 4. Among them, the number and diameter of the screw holes 4 need to be determined according to the size of the tee inlet 5 and outlet 6. When the airflow enters the tee, the guide plate 2 evenly divides the airflow on one side into two parts, and the airflow flows from the top and bottom of the guide plate to the tee outlet respectively.

As shown in Figure 2, the number and diameter of the screw holes 4 on the flange 3 of the tee inlet and outlet in the embodiment of the present invention need to be determined based on the actual size of the tee.

The present invention obtains the velocity distribution and pressure distribution of the fluid after flowing through the rectangular air duct low-resistance rectifying tee through RSM model simulation. According to the local resistance of the rectangular air duct low-resistance rectifying tee and the airflow organization after flowing through the tee The non-uniformity determines the relative position of the baffles.

Working principle of the present invention: The design method of the rectangular air duct low-resistance rectifier tee in the embodiment of the present invention includes the following steps:

Step 1: Determine the fluid flow field state in the low-resistance rectifier tee of the rectangular air duct. The established tee model can add straight pipe sections at the inlet and outlet, so that the flow state of the air flow before and after flowing through the tee can be simulated. According to the inlet size and outlet size and the pipeline inlet fluid velocity, the RSM model is used to simulate the tee without a baffle, simulate the velocity distribution and pressure distribution of the air flow through the tee and after flowing through the tee, and calculate the tee local resistance and airflow unevenness.

Step 2: List the possible optimal relative positions of the deflector within the tee, simulate the tee with the addition of the deflector, and calculate the local resistance and airflow unevenness of the tee.

Step 3: Calculate the drag reduction rate, the drag reduction rate and airflow unevenness of the tee with different deflectors added, and select the guide whose drag reduction rate and airflow unevenness are better than the corresponding parameters without adding deflectors. In this case, the relative position of the flow plate is the optimal drag reduction and rectification position of the flow plate in the tee.

Taking the position determination process of the deflector plate of the low-resistance rectifying tee of the rectangular air duct as an example, first determine the size of each part of the duct, in which the size of the tee inlet is 400mm × 320mm, the size of the tee outlet is 320mm × 320mm, and the size of the tee The radius of curvature is 320mm, the length of the inlet straight pipe section is 5m, and the length of the outlet straight pipe section is 10m.

In the table, b ₁ , b ₂ , and b ₃ are the distances between the first and middle end of the deflector and the inner wall surface respectively, and B ₁ and B ₂ are the widths of the tee inlet and outlet respectively.

Use the RSM model to perform simulation solutions to obtain the drag reduction rates of different deflectors; obtain the airflow non-uniformity k at the 1D, 2D, 3D...18D cross-sections from the tee outlet. (D is the width of the tee outlet).

The calculation method of the above three-way air flow unevenness is as follows:

Select n measuring points on the air duct section, measure the partial velocity u _i of each point in the flow direction, and obtain the arithmetic mean value:

Then the unevenness is:

The airflow unevenness k is a dimensionless number. The smaller the k value, the better the airflow uniformity. In the example, 25 measuring points are selected for each section, and the partial velocities along the flow direction at 25 points are measured. Substitute into the above formula to obtain the airflow unevenness of each section.

The airflow parameters in the tee are sorted to obtain the drag reduction rate of the baffle plate shown in Figure 4. Since the drag reduction rate of baffle plate E is negative, baffle E is eliminated and only the baffle plate with positive drag reduction rate is evaluated. Stream board for comparison. Comparing the drag reduction rate of the three-way, it is determined that the deflector with the best drag reduction effect is H.

Figure 5 shows the airflow unevenness distribution diagram. Comparing the airflow unevenness between the baffle H and the airflow non-uniformity without adding the baffle I, it is concluded that the air flow of the baffle H in the straight pipe section of the tee outlet 0~4D The non-uniformity is smaller than that without adding the guide plate I, that is, the guide plate H has the effect of improving the uniformity of the airflow organization.

According to the above results, it can be seen that the drag reduction and rectification effects of the deflector H are better. Therefore, for a tee with an inlet size of 400mm×320mm, an outlet size of 320mm×320mm, and a curvature radius of 320mm, the relative position of the deflector is 0.6 -0.5-0.6 is the optimal deflector position.

In this example, the best position of the deflector is only relative to the listed deflectors. When determining the best position of the three-way deflector of different sizes, you need to select the simulated deflector according to the actual situation. The number of relative positions, the location of measuring points and the number of measuring points.

The detailed working principle of this rectangular duct low-resistance rectifier tee:

1) Structural description: The rectangular air duct low-resistance rectifier tee includes a Y-shaped tee body 1, a deflector 2 and a flange 3. The deflector 2 has a symmetrical structure inside the tee, and is welded or glued to the upper and lower walls. Both the inlet 5 and the outlet 6 of the tee are provided with flanges 3 and screw holes 4.

2) Air flow diversion: When the air flow enters the rectangular air duct low-resistance rectifying tee, the deflector 2 evenly divides the air flow on one side into two parts, which flow from the top and bottom of the deflector to the outlet of the tee respectively. This design can effectively reduce airflow resistance and tissue unevenness.

3) Position of the deflector: Based on the local resistance of the rectangular duct low-resistance rectifier tee and the unevenness of the airflow organization after flowing through the tee, the relative position of the deflector needs to be determined based on the simulation results of the RSM model. The RSM model can be used to simulate the velocity distribution and pressure distribution of the fluid to guide the installation location of the baffle.

4) Flange design: The number and diameter of the screw holes 4 on the inlet and outlet flange 3 of the tee need to be determined based on the actual size to ensure connection and installation with other air ducts or equipment.

Through the reasonable design and adjustment of the baffle, the rectangular air duct low-resistance rectifying tee can achieve uniform air flow distribution and reduce resistance, thereby improving the efficiency and performance of the air duct system. The application of the RSM model can guide the optimization of the position of the deflector to ensure a more even distribution of airflow inside the tee. This design can reduce wind resistance, reduce noise generation, and improve the efficiency of the entire air duct system.

The signal and data processing process in the design method of this rectangular air duct low-resistance rectifier tee is as follows:

Step 1: Determine the flow field state

Determine the inlet and outlet dimensions and fluid velocity of the rectangular duct low-resistance rectifier tee.

Use the Reynolds stress model or other applicable numerical simulation methods to simulate the velocity field distribution and pressure field distribution within the tee.

Based on the simulation results, calculate the pressure loss of the tee and the air flow unevenness of the tee outlet section.

Step 2: Deflector optimization simulation

Based on the existing tee simulation, consider adding the deflector and determine the possible optimal relative position of the deflector.

Simulate the tee with a deflector to calculate the resistance loss under the deflector at different relative positions and the airflow unevenness at the outlet section of the tee.

Step 3: Determination of baffle selection and location

Calculate the drag reduction rate of each deflector, that is, the ratio of the drag loss after adding the deflector to the drag loss without adding the deflector.

Compare the drag reduction rate and airflow unevenness of each deflector, and select a deflector whose drag reduction rate and airflow unevenness are better than the corresponding parameters without adding a deflector.

Determine the position of the deflector, which is the best drag reduction and rectification position of the deflector within the tee.

During the signal and data processing process, numerical simulation methods are used to simulate the flow field in the tee. By calculating and comparing the resistance loss and airflow unevenness under different relative positions of the deflector, the optimal deflector is finally determined. Location. This process involves the processing of simulation data, parameter calculation and comparative analysis to obtain the optimal design solution.

In the description of the present invention, unless otherwise stated, "plurality" means two or more; the terms "upper", "lower", "left", "right", "inner", "outer" , "front end", "rear end", "head", "tail", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than Any indication or implication that the referred device or element must have a specific orientation, be constructed and operate in a specific orientation should not be construed as a limitation on the invention. Furthermore, the terms "first," "second," "third," etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field shall, within the technical scope disclosed in the present invention, be within the spirit and principles of the present invention. Any modifications, equivalent substitutions and improvements made within the above shall be included in the protection scope of the present invention.

Claims (10)

1. A rectangular air duct low-resistance rectifier tee, characterized in that the tee includes: Y-shaped tee body, two deflectors and flanges running through the tee; The outlets on both sides of the Y-shaped tee body have the same size, and guide plates are provided on both sides of the inner cavity of the Y-shaped tee body, and the guide plates are connected to the upper and lower walls of the Y-shaped tee body; The outer ends of the tee inlet and the tee outlet of the Y-shaped tee body are connected with flanges. 2. The rectangular air duct low-resistance rectifying tee according to claim 1, characterized in that the inlet and outlet heights of the Y-shaped tee body are equal. 3. The rectangular air duct low-resistance rectifying tee according to claim 1, characterized in that the Y-shaped tee body, flange and deflector are all made of steel plates. 4. The rectangular air duct low-resistance rectifying tee according to claim 1, characterized in that the starting end of the deflector is located at the tee inlet and the end is located at the tee outlet. 5. The rectangular air duct low-resistance rectifying tee according to claim 1, characterized in that the Y-shaped tee body and the deflector have a symmetrical structure along the center line of the Y-shaped tee. 6. The rectangular air duct low-resistance rectifying tee according to claim 1, characterized in that the Y-shaped tee body, flange, and baffle surface are all provided with anti-rust paint. 7. A design method for the rectangular air duct low-resistance rectifier tee used in any one of claims 1 to 6, characterized in that the design method includes: Step 1. Determine the fluid flow field state in the low-resistance rectifier tee of the rectangular air duct. According to the size of the inlet and outlet of the tee and the fluid velocity in the tee, use the Reynolds stress model to simulate the velocity field distribution and pressure field distribution in the tee. , obtain the pressure loss of the tee and the airflow unevenness at the outlet section of the tee; Step 2: List the possible optimal relative positions of the deflector within the tee, simulate the tee with the addition of the deflector, and calculate the resistance loss of the tee under the conditions of adding deflectors at each relative position and The airflow unevenness in the tee outlet cross section; Step 3: Calculate the drag reduction rate of each deflector, compare the drag reduction rate and air flow unevenness of each deflector, and select the drag reduction rate and air flow unevenness that are better than those without adding the deflector. Parameters of the deflector, the selected position of the deflector is the optimal drag reduction and rectification position of the deflector within the tee. 8. The design method of the rectangular air duct low-resistance rectifying tee as claimed in claim 7, characterized in that the step one determines the fluid flow field state in the rectangular air duct low-resistance rectifying tee, and the three established The pass model adds straight pipe sections at the inlet and outlet to simulate the flow state before and after the air flows through the tee. 9. The design method of the low-resistance rectifying tee for rectangular air ducts as claimed in claim 8, characterized in that, according to the inlet size and outlet size and the pipeline inlet fluid velocity, the RSM model is used to design the unadded baffle and the added baffle. Simulate the tee of the flow plate, simulate the velocity distribution and pressure distribution of the air flowing through the tee and after flowing through the tee, and calculate the local resistance and air flow unevenness of the tee. 10. The design method of the low-resistance rectifying tee of the rectangular air duct as claimed in claim 7, characterized in that the calculation method of the air flow unevenness of the tee outlet cross-section in the step one is as follows: Select n measuring points on the air duct section, measure the partial velocity of each point in the flow direction, and obtain the arithmetic average: Then the unevenness is: The airflow unevenness k is a dimensionless number. The smaller the k value, the better the airflow uniformity; After obtaining the local resistance of the tee (denoted as ΔP) in steps 1 and 2, calculate the local resistance coefficient: Among them, ΔP is the local resistance of the tee, Pa; ρ is the air density, kg/m ³ , v is the exit velocity of the tee, m/s; The drag reduction rate η is: Among them, eta is the drag reduction rate of the deflector, ξ _{is now} the local resistance coefficient of the tee with the deflector added, and ξ _{was originally} the local resistance coefficient of the tee without the deflector.