A concomitant method, ejector optimization and jet centrifugal pump optimization design method

Abstract

The present application relates to an adjoint method, an ejector optimization and an optimization design method for a jet centrifugal pump. The present application relates to the technical field of a jet centrifugal pump, and includes the following steps: step 1, establishing a geometric model of a jet centrifugal pump and producing a grid; step 2, calculating the flow field of the jet centrifugal pump; step 3, performing adjoint calculations on the jet centrifugal pump by an adjoint method; step 4, analyzing the sensitivity of the jet centrifugal pump; step 5, establishing an ejector geometric model and generating a grid; step 6, ejector flow field calculation and adjoint calculation; step 7, ejector sensitivity analysis and grid deformation; step 8, simulating and analyzing again, performing a new round of flow field simulation on the updated design, confirming the correctness of the optimization direction and analyzing the optimization effect, and repeating steps 6 to 7 until a suitable solution is obtained. The present application has the advantage of saving experimental time and cost through the adjoint algorithm.

Description

Technical Field

[0001] The present application relates to the technical field of jet centrifugal pumps, and in particular to an accompanying method, ejector optimization, and an optimization design method for jet centrifugal pumps. Background Art

[0002] Compared with traditional centrifugal pumps, jet centrifugal pumps are combined with self-circulating ejectors to form a low-pressure area at the nozzle outlet through the high-speed fluid behind the jet nozzle, thus achieving self-priming function. Jet centrifugal pumps are widely used in floor pipe pressurization, irrigation and other fields due to their strong self-priming ability. However, due to the large number of flow-through components, they have the disadvantage of low efficiency. The existing algorithms require a large number of simulation calculations and are inefficient. Summary of the invention

[0003] In view of the shortcomings of the prior art, one of the purposes of the present application is to provide a concomitant method, an ejector optimization and an optimization design method of a jet centrifugal pump, which has the advantage of saving test time and cost through a concomitant algorithm.

[0004] The above-mentioned purpose of the present application is achieved through the following technical solutions:

[0005] An adjoint method, characterized in that: an objective function J and an optimization design parameter c are defined, and the head formula of the jet centrifugal pump is: Where P out is the outlet pressure of the jet centrifugal pump, P in is the inlet pressure of the jet centrifugal pump. Using the head formula of the jet centrifugal pump, the optimization function is established to increase the pressure difference between the outlet and inlet of the jet centrifugal pump: J = P out -P in , the value of c defines all parameter vectors, including the structural parameters of the jet centrifugal pump. At the same time, the establishment of the objective function depends not only on the design parameter c, but also on the flow condition q(c): q(c) = [v x ,v y ,v z ,p,T], J=J(q(c),c), the application of the adjoint method in the flow field depends on q(c) and c, so the flow field is a constraint in the optimization problem, and the control equation is: R(q(c),c)=0. When the flow condition q(c) and the state of the control variable c change, the selected optimization objective will also change: The optimization should be performed between defined flow limits, which result in zero change in R: Through the Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem: L(q,c,λ)=J(q,c)-λ T R(q,c), where the parameter λ is the vector of adjoint variables: Combining the above formulas, we can get: The value of λ is chosen to eliminate the influence of flow variables. The adjoint equation that needs to be solved, that is, the gradient of the objective function is: Therefore, the relationship between the objective function and the design variables is: Initializes the adjoint solver and then performs adjoint calculations.

[0006] The present application also discloses an ejector optimization design method: including the above-mentioned accompanying method, and also including the following steps, step 1, establishing an ejector geometric model and generating a grid, step 2, ejector flow field calculation and accompanying calculation, step 3, ejector sensitivity analysis and grid deformation, step 4, simulate and analyze again, perform a new round of flow field simulation on the updated design, confirm the correctness of the optimization direction and analyze the optimization effect, repeat steps 2 to 3 until a suitable solution is obtained.

[0007] In a preferred example, the present application can be further configured as follows: in step 3, the ejector is divided into different areas, and control points are provided in different directions within a given area, and the number of control points is between 20 and 80.

[0008] In a preferred example, the present application can be further configured as follows: when the given area is a sensitive area, the numbers of control points in the three directions of xyz are 20, 20, and 20 respectively.

[0009] In a preferred example, the present application can be further configured as follows: when the given area is an ejector, the numbers of control points in the three directions of xyz are 80, 20, and 20 respectively.

[0010] The present application also discloses a jet centrifugal pump optimization design method: including the above-mentioned ejector optimization design method, and also including the following steps, step a, establishing a geometric model of the jet centrifugal pump and producing a grid, step b, calculating the flow field of the jet centrifugal pump, step c, performing adjoint calculation on the jet centrifugal pump through an adjoint method, and step d, analyzing the sensitivity of the jet centrifugal pump.

[0011] In a preferred example, the present application can be further configured as follows: in step b, a Realizable ke model is used to perform steady-state calculations on the flow field.

[0012] In a preferred example, the present application can be further configured as follows: in step c, in the initial stage of solving the adjoint of the jet centrifugal pump, the value of the Courant number is smaller than the value of the Courant number after the adjoint operation is stable.

[0013] This application has the following advantages: The adjoint method can help designers identify the most sensitive areas of the optimization target, thereby accurately improving the key parts of the jet centrifugal pump to provide a higher head. Compared with other optimization design methods, the adjoint method has the outstanding advantage of being based on overall sensitivity analysis, ensuring the comprehensiveness of the results, and a simple and fast operation method, which can greatly save test time and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart for implementing the optimization design method of the jet centrifugal pump of this application.

[0015] Figure 2 It is a schematic diagram of the pump body structure of this application.

[0016] Figure 3 It is a schematic diagram of a shape-sensitive cross section of the jet centrifugal pump of the present application.

[0017] Figure 4 It is a schematic diagram of the three-dimensional model structure of the ejector of this application.

[0018] Figure 5 It is a sensitivity analysis diagram of the ejector of this application based on shape.

[0019] Figure 6 This is a schematic diagram of the sensitive area of ​​this application as a control area.

[0020] Figure 7 This is a schematic diagram of the control area of ​​this application as a whole.

[0021] Figure 8 It is a schematic diagram of the pressure change and prediction diagram of the sensitive area of ​​this application.

[0022] Fig. 9 It is a schematic diagram of the pressure change and prediction diagram for the overall area of ​​this application. DETAILED DESCRIPTION

[0023] The following is combined with Figure 1-9 This application is described in further detail.

[0024] The present application discloses an adjoint method, defines an objective function J, and optimizes a design parameter c. The head formula of a jet centrifugal pump is: Where P out is the outlet pressure of the jet centrifugal pump, in Pascal (Pa), P in is the inlet pressure of the jet centrifugal pump, in Pascal (Pa), and ρ is the density of the liquid, in kg / m3 (kg / m 3 ); g is the acceleration due to gravity, usually 9.8m / s 2Using the head formula of the jet centrifugal pump, the optimization function is established to increase the pressure difference between the outlet and inlet of the jet centrifugal pump: J = P out -P in , the value of c defines all parameter vectors, q(c) corresponds to the flow field variables, including velocity, pressure, temperature, etc., including the structural parameters of the jet centrifugal pump. At the same time, the establishment of the objective function depends not only on the design parameter c, but also on the following, v x , v y , v z is the velocity component in each axis, in m / s, p is the pressure, in Pa, T is the temperature, in °C, and also includes the flow field condition q(c): q(c) = [v x ,v y ,v z ,p,T]

[0025] J=J(q(c),c)

[0026] The equations describing heat and mass transfer in the flow field can be written in simplified form, with numerical residuals as:

[0027] R(q(c),c)=0

[0028] When the flow field condition q(c) and the state of the design parameter c change, the selected optimization objective will also change:

[0029]

[0030] The optimization should be performed between defined flow constraints (e.g. flow rate and design variables), so that the residual variable δR should remain zero when the flow field changes:

[0031]

[0032] By using the Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem:

[0033] L(q,c,λ)=J(q,c)-λ T R(q,c)

[0034] The parameter λ is the vector of accompanying variables, v x * , v y * , v z * , p * and T * is the adjoint variable vector of the flow field variable:

[0035]

[0036] Combining the above formulas, we can get:

[0037]

[0038] The value of λ is chosen to eliminate the influence of flow variables. The adjoint equation that needs to be solved, that is, the gradient of the objective function is:

[0039]

[0040] Therefore, the relationship between the objective function and the design variables is:

[0041] Initializes the adjoint solver and then performs adjoint calculations.

[0042] The present application also discloses an ejector optimization design method, which adopts the above-mentioned adjoint method and includes the following steps: step 1, establishing an ejector geometric model and generating a grid, step 2, ejector flow field calculation and adjoint calculation, step 3, ejector sensitivity analysis and grid deformation, step 4, re-simulation and analysis, performing a new round of flow field simulation on the updated design, confirming the correctness of the optimization direction and analyzing the optimization effect, repeating steps 2 to 3 until a suitable solution is obtained. In the present application, the suitable solution can be a solution that the experimenter believes achieves the purpose of the experiment, or it can be a solution until the design can no longer be improved.

[0043] In step 3, the ejector is divided into different areas, and control points are set in different directions within the given area. The number of control points is between 20 and 80. When the given area is a sensitive area, the number of control points in the three directions of xyz are 20, 20, and 20 respectively. When the given area is an ejector, the number of control points in the three directions of xyz are 80, 20, and 20 respectively.

[0044] The present application also discloses a jet centrifugal pump optimization design method, comprising the following steps:

[0045] Step 1: Geometric modeling and mesh generation of jet centrifugal pump:

[0046] When establishing the geometric model of the jet centrifugal pump, accurate measurement and modeling are performed to ensure that the geometric model meets the design requirements and actual engineering needs. After modeling, the model is meshed. Figure 2 As shown, in this application, a certain type of jet centrifugal pump is taken as an example, and its performance parameter is flow rate = 2.964m 3 / h, speed = 2849r / min, head = 28.51m, number of impeller blades = 6.

[0047] Step 2: Calculation of flow field of jet centrifugal pump:

[0048] Through analysis, compared with other turbulence models, the Realizable ke model predicts the experimental results best and the internal flow field structure is more accurate, so the Realizable ke model is selected for steady-state calculation of the flow field.

[0049] Set the inlet boundary condition to mass flow inlet and the outlet boundary condition to pressure outlet.

[0050] The momentum term, turbulent kinetic energy and turbulent kinetic energy dissipation rate of the jet centrifugal pump are all discretized using the second-order upwind scheme. The pressure-velocity coupling scheme adopts the coupled scheme.

[0051] The residual term of the model and the calculated inlet and outlet pressures are stabilized as the convergence criterion.

[0052] Step 3: Calculation of jet centrifugal pump:

[0053] After the flow field calculation, define the objective function J, and optimize the design parameter c. Head is one of the important indicators to measure pump performance, indicating the net increase in energy per unit mass of fluid passing through the pump. Pump design is usually based on a specific head and flow rate. The head formula of a jet centrifugal pump is:

[0054]

[0055] Where P out is the outlet pressure of the jet centrifugal pump, P in is the inlet pressure of the jet centrifugal pump. Using the head formula of the jet centrifugal pump, the optimization function is established to increase the pressure difference between the outlet and inlet of the jet centrifugal pump:

[0056] J=P out -P in

[0057] The value of c defines all parameter vectors, including the structural parameters of the jet centrifugal pump. At the same time, the establishment of the objective function depends not only on the design parameter c, but also on the flow condition q(c):

[0058] q(c)=[v x ,v y ,v z ,p,T]

[0059] J=J(q(c),c)

[0060] The equations describing heat and mass transfer in the flow field can be written in simplified form, with numerical residuals as:

[0061] R(q(c),c)=0

[0062] When the flow field condition q(c) and the state of the design parameter c change, the selected optimization objective will also change:

[0063]

[0064] The optimization should be performed between defined flow constraints (e.g. flow rate and design variables), so that the residual variable δR should remain zero when the flow field changes:

[0065]

[0066] Through the Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem: L(q,c,λ)=J(q,c)-λ T R(q,c)

[0067] The parameter λ is the vector of adjoint variables:

[0068]

[0069] Combining the above formulas, we can get:

[0070]

[0071] The value of λ is chosen to eliminate the influence of flow variables. The adjoint equation that needs to be solved, that is, the gradient of the objective function is:

[0072]

[0073] Therefore, the relationship between the objective function and the design variables is:

[0074] The adjoint solver is initialized and then the adjoint calculation is performed. This step mainly calculates the sensitivity of the jet centrifugal pump to the objective function.

[0075] The discretization scheme affects the accuracy of the adjoint solution. Compared with the first-order upwind discretization scheme, the second-order upwind scheme can achieve a higher level of accuracy by incorporating more information about the flow field.

[0076] At the same time, matching the fluid discretization method with the adjoint discretization method can obtain the best prediction. Therefore, as with the flow solution, a second-order upwind scheme is used for the momentum equation.

[0077] The parameters are usually adjusted to improve the stability and convergence of the adjoint solution under comprehensive consideration.

[0078] The Courant number is a dimensionless number used to evaluate the relationship between the time step and the size of the spatial discrete grid. It is a physical quantity that measures the stability of numerical calculations. The larger the Courant number, the faster the convergence speed, but at the same time it may lead to instability in the calculation process, which is manifested as oscillation or even divergence of the calculated solution. In the initial stage of solving the adjoint of the jet centrifugal pump, the value of the Courant number can be relatively small, preferably 1. When the adjoint operation is stable, the Courant number can be increased to increase the convergence speed. The Courant number is selected as 3 for subsequent iterations. The artificial compression value affects the continuity and momentum equations. The value is usually 0 to 1. It needs to be comprehensively considered based on stability and convergence speed. The preferred value is 0.1.

[0079] Step 4: Sensitivity analysis of jet centrifugal pump:

[0080] By analyzing the shape-sensitive section of a jet centrifugal pump with the goal of increasing the pressure difference between the outlet and the inlet ( Figure 3 ), which can comprehensively reflect the sensitivity of the defined observable quantity to the geometry. According to the sensitivity distribution, the deformation optimization area is selected. Through observation, it can be seen that compared with other structures, the pressure difference between the ejector inlet and outlet has the greatest impact and needs to be considered. Considering that the calculation amount of the concomitant optimization of the entire jet centrifugal pump is large, and the sensitivity of other parts is low, the present invention proposes a method of first performing concomitant optimization on the ejector, and then putting the optimized ejector back into the jet centrifugal pump for verification.

[0081] Step 5: Ejector geometry modeling and mesh generation

[0082] The three-dimensional model of the ejector is as follows Figure 4 As shown, the main geometric structure is throat diameter = 15mm, nozzle diameter = 9mm, and area ratio is 2.78, which is defined as the ratio of the ejector throat area to the nozzle outlet area. There is a large velocity gradient at the entrance of the primary and secondary flows, and the grid is encrypted.

[0083] Step 6: Ejector flow field calculation and adjoint calculation

[0084] Similar to the jet centrifugal pump, the Realizable ke model is used to simulate and analyze the flow field. The inlet boundary adjustment is set to the mainstream inlet and the secondary flow inlet, both of which are mass flow inlets, and the outlet boundary condition is set to the pressure outlet. The specific setting values ​​of these boundary conditions are extracted from the overall calculation results of the jet centrifugal pump above. By creating sections for the mainstream, secondary flow and outlet of the ejector, the corresponding mass flow and pressure information are obtained to ensure the authenticity of the boundary conditions. After the flow field calculation, the optimization goal is defined as increasing the outlet pressure and performing an accompanying solution.

[0085] Step 7: Ejector sensitivity analysis and mesh deformation

[0086] Figure 5 This is a sensitivity analysis diagram of the ejector based on its shape. It can be seen from the figure that the ejector's main flow inlet, the thickness of the main nozzle, and the front of the main and secondary flow mixing area are very sensitive to pressure. Based on the sensitivity analysis, two different control areas are set, such as Figure 6 , 7 As shown, Figure 6 Use sensitive areas as control areas. Figure 7 The whole is taken as the control area. Control points are evenly set in different directions within the control area, and the control points can be used to smooth the mesh deformation. The number of control points has an important influence on the deformation of the mesh. If there are too few control points, the mesh deformation degree will be too low, which will lead to an increase in the number of iterations and it will be difficult to obtain the desired target value. If the control point is too large, the quality of the mesh will be reduced. Usually, the number of control points is between 20 and 80. When the control area is a sensitive area, the number of control points in the three directions of xyz is 20, 20, and 20 respectively. When the control area is the whole ejector, the number of control points in the three directions of xyz is 80, 20, and 20 respectively. The optimization goal is to increase the pressure at the outlet, and each iteration aims to increase the pressure difference by 2%. At the same time, the deformation factor determines the distance that each control point moves along the optimal direction. The value range is usually 0 to 1. The larger the value, the greater the degree of mesh change. For areas with high sensitivity, the deformation factor should be preferably 0.1. This is because these areas are extremely sensitive to pressure changes, and a smaller deformation factor can avoid significant performance fluctuations due to excessive structural adjustments. At the same time, using smaller displacements for smooth deformation can maintain the mesh quality during the deformation process, ensuring that these key areas are more finely adjusted during the optimization process to improve the optimization accuracy.

[0087] For the overall area of ​​the ejector, a larger deformation factor of 1 is set due to the presence of areas with lower sensitivity. Considering that the area has a smaller response to pressure changes, a larger deformation factor can speed up the optimization process, reduce the number of iterations, and thus improve computational efficiency. This strategy helps balance optimization accuracy and computational efficiency, ensuring that while fine optimization is achieved in key areas, the overall optimization process does not consume too much time and resources due to a large number of iterations. Before deforming the mesh, the expected pressure change can be obtained through predictive analysis.

[0088] Step 8: Simulate and analyze again:

[0089] Perform a new round of flow field simulation on the updated design to confirm the correctness of the optimization direction and analyze the optimization effect. Repeat steps 6 to 7 until the design cannot be improved any further. Figure 8 The pressure change and prediction diagram of the sensitive area, Fig. 9The pressure change and prediction diagram of the overall area. It can be seen from the figure that after multiple iterations, the pressure gradually stabilizes and conforms to the predicted pressure change trend. Figure 6 , 8 For sensitive areas, the deformation factor is small and the number of iterations is small, but due to the high sensitivity, a small grid change will lead to a drastic change in pressure. When a certain number of iterations is reached, the pressure drops. Figure 7 , 9 ,In contrast to the sensitive area, the overall area has a large deformation factor and a large number of iterations, but the pressure changes smoothly and has a high degree of coincidence with the predicted pressure changes.

[0090] Step 9: Overall Verification

[0091] The optimal solution mesh after the two iterations was exported, and a new solid domain was established based on the mesh to replace the initial ejector area of ​​the jet centrifugal pump. After meshing, the flow field of the optimized jet centrifugal pump was recalculated. It was verified that the head of the two jet centrifugal pumps (i.e., the jet pump based on the sensitive area as the control area and the jet pump based on the overall area as the control area) increased by 12% and 15% respectively, both of which were significantly improved.

[0092] The implementation principle of this embodiment is: the adjoint method can help designers identify the most sensitive areas of the optimization target, so as to accurately improve the key parts of the jet centrifugal pump to provide a higher head. Compared with other optimization design methods, the outstanding advantage of the adjoint method is that it is based on overall sensitivity analysis, ensuring the comprehensiveness of the results and the simple and fast operation method, which can save a lot of test time and cost.

[0093] The embodiments of this specific implementation method are all preferred embodiments of the present application, and are not intended to limit the protection scope of the present application. Therefore, all equivalent changes made based on the structure, shape, and principle of the present application should be included in the protection scope of the present application.

Claims

1. A companion method, characterized in that: Define the objective function J, and optimize the design parameter c, the head formula of the jet centrifugal pump is: Where P out is the outlet pressure of the jet centrifugal pump, P in is the inlet pressure of the jet centrifugal pump. Using the head formula of the jet centrifugal pump, the optimization function is established to increase the pressure difference between the outlet and inlet of the jet centrifugal pump: J = P out -P in , the value of c defines all parameter vectors, including the structural parameters of the jet centrifugal pump. At the same time, the establishment of the objective function depends not only on the design parameter c, but also on the flow condition q(c): q(c) = [v x ,v y ,v z ,p,T], J=J(q(c),c), the application of the adjoint method in the flow field depends on q(c) and c, so the flow field is a constraint in the optimization problem, and the control equation is: R(q(c),c)=0. When the flow condition q(c) and the state of the control variable c change, the selected optimization objective will also change: The optimization should be performed between defined flow limits, which result in zero change in R: Through the Lagrange multiplier method, the constrained optimization problem is transformed into an unconstrained optimization problem: L(q,c,λ)=J(q,c)-λ T R(q,c), where the parameter λ is the vector of adjoint variables: Combining the above formulas, we can get: The value of λ is chosen to eliminate the influence of flow variables. The adjoint equation that needs to be solved, that is, the gradient of the objective function is: Therefore, the relationship between the objective function and the design variables is: Initializes the adjoint solver and then performs adjoint calculations.

2. An ejector optimization design method, characterized in that: The accompanying method as claimed in claim 1 also includes the following steps: step 1, establishing an ejector geometric model and generating a mesh, step 2, ejector flow field calculation and accompanying calculation, step 3, ejector sensitivity analysis and mesh deformation, step 4, simulating and analyzing again, performing a new round of flow field simulation on the updated design, confirming the correctness of the optimization direction and analyzing the optimization effect, and repeating steps 2 to 3 until a suitable solution is obtained.

3. The method for optimizing the design of an ejector according to claim 2, characterized in that: In step 3, the ejector is divided into different regions, and control points are set in different directions within a given region, and the number of control points is between 20 and 80.

4. The method for optimizing the design of an ejector according to claim 3, characterized in that: When the given area is a sensitive area, the number of control points in the xyz directions are 20, 20, and 20 respectively.

5. The method for optimizing the design of an ejector according to claim 3, characterized in that: When the given area is an ejector, the number of control points in the xyz directions is 80, 20, and 20, respectively.

6. A jet centrifugal pump optimization design method, characterized in that: It includes an ejector optimization design method as described in claim 2 or 3 or 4, and also includes the following steps: step a, establishing a geometric model of the jet centrifugal pump and producing a grid, step b, calculating the flow field of the jet centrifugal pump, step c, performing adjoint calculation on the jet centrifugal pump by an adjoint method, and step d, analyzing the sensitivity of the jet centrifugal pump.

7. The method for optimizing the design of a jet centrifugal pump according to claim 6, characterized in that: In step b, the Realizable ke model is used to perform steady-state calculations on the flow field.

8. The method for optimizing the design of a jet centrifugal pump according to claim 6, characterized in that: In step c, at the initial stage of solving the adjoint of the jet centrifugal pump, the value of the Courant number is smaller than the value of the Courant number after the adjoint operation is stable.

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