Optimization method of turbine nozzle shock wave and loss based on entropy generation rate regulation

Abstract

The present invention discloses a method for optimizing the shock wave and loss of a turbine nozzle based on entropy production rate regulation. The present invention adopts a shock wave and loss quantification method based on entropy production rate, integrates blade parameterization and gradient variation hybrid optimization algorithm to implement multi-objective optimization of turbine nozzles, takes minimization of shock wave intensity (characterized by shock wave entropy production) and total loss (characterized by total flow channel entropy production) as optimization goals, takes mass flow change and leakage flow loss (characterized by leakage flow entropy production) not exceeding a limit value as constraint conditions, and finally achieves the goal of reducing shock wave intensity and aerodynamic losses at the same time. This method more accurately identifies and quantifies shock waves and losses, can more clearly analyze the optimization mechanism of blade profile changes, and provides a new idea and direction for the coupled regulation of shock waves and losses in turbine nozzles.

Description

Technical Field

[0001] The present invention relates to the field of turbine optimization design, and more specifically, to a variable cross-section turbine nozzle shock wave and loss optimization method. Background Art

[0002] In a variable-geometry turbocharger, the turbine mass flow and expansion ratio can be controlled by adjusting the nozzle opening to achieve better engine matching and generate more turbine work. When the vehicle starts, the nozzle is closed to provide the engine with greater boost pressure; when braking, the nozzle is also closed to assist engine braking. In both cases, the nozzle expansion ratio will become larger and may generate shock waves near the trailing edge. This shock wave will lose turbine efficiency and induce periodic vibrations at the leading edge of the turbine rotor blades, resulting in fatigue fracture. Therefore, weakening the nozzle blade trailing edge shock wave is one of the key issues in the design of a variable-geometry turbine.

[0003] In order to weaken the nozzle shock wave, relevant staff have proposed some modification plans for the blade shape and structure of the nozzle blades. However, most of these plans have the disadvantages of low robustness and unclear mechanism, and some will even damage the aerodynamic performance of the turbine. Due to the particularity of the variable-section turbine geometry and the limitations of the understanding of the shock wave weakening mechanism, a control method that can simultaneously improve the aerodynamic performance of the turbine and weaken the shock wave and has strong universality has not yet been found. Summary of the invention

[0004] The present invention aims to characterize shock wave intensity and aerodynamic loss by integrating entropy production rate, and to provide an optimization method for unified regulation of shock wave intensity and aerodynamic loss, so as to ultimately achieve the goal of simultaneously reducing shock wave intensity and aerodynamic loss.

[0005] The turbine nozzle shock wave and loss optimization method based on entropy production rate regulation of the present invention is carried out according to the following steps:

[0006] (1) According to the geometry of the turbine nozzle and the location of the shock wave, and considering the impact on the turbine flow, the parameterized modeling method and range are determined; the part after the nozzle suction throat is selected as the blade modification area; the Hicks-Henne type function is used to parameterize the nozzle blade, and parameterization is achieved by setting the number and distribution of basis functions; the nozzle profile is modified by changing the coefficient size of the basis function; the coefficient of the basis function is the design variable;

[0007] (2) Given different upper and lower limits of the design variables, a design space is formed. The criteria for selecting the upper and lower limits are: under the extreme value conditions, the nozzle geometry does not suffer from severe distortion and the trailing edge does not become too thin;

[0008] (3) Perform optimal Latin hypercube sampling in the design space to generate an initial sample set so that the sample points are evenly distributed in the entire design space;

[0009] (4) For the original turbine, the maximum expansion ratio and minimum nozzle opening conditions are selected as the optimized conditions. The steady Reynolds-Averaged Navier-Stokes (RANS) equations are used for numerical simulation. The RANS equations are discretized based on the finite volume method. The SST (shear stress transport) model is selected as the turbulence model. The total temperature and total pressure conditions are given at the inlet boundary, and the static pressure (usually atmospheric pressure) is given at the outlet boundary to obtain the steady flow field of the nozzle.

[0010] (5) A shock wave quantification method is used to quantify the shock wave of the steady flow field of the original blade nozzle under the working conditions described in step (4). First, the shock wave is identified by the projection of the density gradient on the normalized velocity vector (referred to as density gradient). When the density gradient is greater than a limit value, it is identified as a shock wave region, and additional circumferential angle and turbulence dissipation rate restriction conditions are added to eliminate the throat shock wave and the weaker trailing edge shock wave as well as the boundary layer loss, secondary flow loss and leakage flow loss region that may cross the shock wave region; then, the entropy production rate of the region is integrated, and the entropy production value obtained is used as a quantitative evaluation index of the shock wave intensity. The shock wave intensity of the original blade is set to J0;

[0011] (6) Quantitatively analyzing the leakage flow of the steady flow field of the original blade nozzle under the working conditions described in step (4), firstly identifying the leakage flow by the Q criterion, and when Q>0, identifying it as the leakage flow area, and adding density gradient, turbulent kinetic energy, turbulent dissipation rate, and wall distance restriction conditions to eliminate shock wave loss, boundary layer loss, and secondary flow loss areas; then integrating the entropy production rate of the area, and obtaining the entropy production value as a quantitative evaluation index of the leakage flow loss; let the leakage flow loss of the original blade be X0;

[0012] (7) Integrate the entropy generation rate of the original blade nozzle flow channel to obtain the total entropy generation value of the flow channel, which is used as an evaluation index of the total loss of the nozzle; let the total loss of the original blade be Y0;

[0013] (8) Integrate the infinitesimal flow rate of the volute inlet cross section (equal to the product of velocity, density and area infinitesimal) to obtain the nozzle mass flow rate; let the mass flow rate of the original blade be M0;

[0014] (9) For each design scheme in the initial sample set generated in step (3), numerical simulation is performed given the boundary conditions of the working condition described in step (4), and the shock wave quantification method of the original blade profile in step (5) is used to obtain the shock wave intensity J of the sample blade profile. i ; The leakage flow loss quantification method in step (6) is used to obtain the leakage flow loss X of the sample blade i ; Use the method in step (7) to obtain the total loss Y i; Using the method in step (8), the mass flow rate M is obtained i ;

[0015] (10) RBF (Radial Basis Function) model is constructed to obtain the mapping relationship between shock wave intensity, leakage flow loss, total loss and mass flow rate and the design variables in step (2). The gradient mutation optimization algorithm is used to implement the optimization. The objective function is to minimize the shock wave intensity and total loss. The constraint condition is that the mass flow rate change does not exceed the mass flow upper limit M. c , the leakage flow loss does not exceed the leakage upper limit X c , and finally a design with smaller shock wave intensity and total loss is obtained.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] The present invention discloses a method for optimizing turbine nozzle shock waves and losses based on entropy production rate regulation, which adopts a shock wave and loss quantification method based on entropy production rate, and unifies the evaluation indexes of shock wave intensity and loss size. The optimization targets in the traditional method are replaced by shock wave entropy production and total flow channel entropy production instead of density gradient and total pressure loss. Taking shock wave entropy production as the optimization target can not only quantify the shock wave intensity, but also capture the three-dimensional characteristics of the shock wave, thereby improving the pertinence of shock wave optimization; taking total flow channel entropy production as the optimization target can get rid of the dependence on the nozzle inlet and outlet boundary conditions, and can more objectively quantify the total nozzle loss. The present invention provides a new idea and direction for the coupled regulation of turbine nozzle shock waves and losses. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Shown is the blade profile modification range, i.e., the nozzle distribution schematic diagram;

[0019] Figure 2 Shown is a schematic diagram of the entropy generation rate of the nozzle at 50% blade height, the shock wave identification window, and the circumferential angle;

[0020] Figure 3 Shown is a schematic diagram of the shock wave region identified in the flow channel;

[0021] Figure 4 Shown is a schematic diagram of the leakage flow area identified in the flow channel;

[0022] Figure 5 Shown is the distribution diagram of the 50% blade height shock wave entropy generation rate of the nozzle before and after optimization;

[0023] Figure 6 Shown is a comparison of turbine performance curves before and after optimization. DETAILED DESCRIPTION

[0024] The turbine nozzle shock wave and loss optimization method based on entropy production rate regulation of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0025] The specific process of the present invention is as follows:

[0026] (1) According to the geometry of the turbine nozzle and the location of the shock wave, and considering the impact on the turbine flow, the parameterized modeling method and range are determined; the part after the nozzle suction throat is selected as the blade modification area; the Hicks-Henne type function is used to parameterize the nozzle blade, and parameterization is achieved by setting the number and distribution of basis functions; the nozzle profile is modified by changing the coefficient size of the basis function; the coefficient of the basis function is the design variable;

[0027] (2) Given different upper and lower limits of the design variables, a design space is formed. The criteria for selecting the upper and lower limits are: under the extreme value conditions, the nozzle geometry does not suffer from severe distortion and the trailing edge does not become too thin;

[0028] (3) Perform optimal Latin hypercube sampling in the design space to generate an initial sample set so that the sample points are evenly distributed in the entire design space. The number of initial samples in the sample set is generally related to the number of design variables, and 10 times the number of design variables can be selected;

[0029] (4) For the original turbine, the maximum expansion ratio and minimum nozzle opening conditions are selected as the optimized conditions. The steady Reynolds-Averaged Navier-Stokes (RANS) equations are used for numerical simulation. The RANS equations are discretized based on the finite volume method. The SST (shear stress transport) model is selected as the turbulence model. The total temperature and total pressure conditions are given at the inlet boundary, and the static pressure (usually atmospheric pressure) is given at the outlet boundary to obtain the steady flow field of the nozzle.

[0030] (5) A shock wave quantification method is used to quantify the shock wave of the steady flow field of the original blade nozzle under the working conditions described in step (4). First, the shock wave is identified by the projection of the density gradient on the normalized velocity vector (referred to as density gradient). When the density gradient is greater than a limit value, it is identified as a shock wave region, and additional circumferential angle and turbulence dissipation rate restriction conditions are added to eliminate the throat shock wave and the weaker trailing edge shock wave as well as the boundary layer loss, secondary flow loss and leakage flow loss region that may cross the shock wave region; then, the entropy production rate of the region is integrated, and the entropy production value obtained is used as a quantitative evaluation index of the shock wave intensity. The shock wave intensity of the original blade is set to J0;

[0031] (6) Quantitatively analyze the leakage flow of the steady flow field of the original blade nozzle under the working conditions described in step (4), first identify the leakage flow by the Q criterion, and when Q>0, identify it as a leakage flow area, and add density gradient, turbulent kinetic energy, turbulent dissipation rate, and wall distance restriction conditions to eliminate shock wave loss, boundary layer loss, and secondary flow loss areas (such as shock wave areas); then integrate the entropy production rate of the area, and use the entropy production value obtained as a quantitative evaluation index of the leakage flow loss; let the leakage flow loss of the original blade be X0;

[0032] (7) Integrate the entropy generation rate of the original blade nozzle flow channel to obtain the total entropy generation value of the flow channel, which is used as an evaluation index of the total loss of the nozzle; let the total loss of the original blade be Y0;

[0033] (8) Integrate the infinitesimal flow rate of the volute inlet cross section (equal to the product of velocity, density and area infinitesimal) to obtain the nozzle mass flow rate; let the mass flow rate of the original blade be M0;

[0034] (9) For each design scheme in the initial sample set generated in step (3), numerical simulation is performed given the boundary conditions of the working condition described in step (4), and the shock wave quantification method of the original blade profile in step (5) is used to obtain the shock wave intensity J of the sample blade profile. i ; The leakage flow loss quantification method in step (6) is used to obtain the leakage flow loss X of the sample blade i ; Use the method in step (7) to obtain the total loss Y i ; Using the method in step (8), the mass flow rate M is obtained i ;

[0035] (10) RBF (Radial Basis Function) model is constructed to obtain the mapping relationship between shock wave intensity, leakage flow loss, total loss and mass flow rate and the design variables in step (2). The gradient mutation optimization algorithm is used to implement the optimization. The objective function is to minimize the shock wave intensity and total loss. The constraint condition is that the mass flow rate change does not exceed the mass flow upper limit M. c , the leakage flow loss does not exceed the leakage flow upper limit X c , and finally a design with smaller shock wave intensity and total loss is obtained.

[0036] Example:

[0037] 1) This embodiment is a turbocharger turbine. Figure 1 The shape and distribution of the turbine nozzle on a two-dimensional plane are given, and the blade modification area is marked; it can be seen that the blade modification area in the figure covers the suction surface line behind the blade throat; according to the geometric shape of the blade modification area, the Hicks-Henne type function stacking method is used to realize the parameterization of the nozzle blade.

[0038] 2) Given different upper and lower limits of design variables, a design space is formed, and the criteria for selecting the upper and lower limits are: under extreme value conditions, the nozzle geometry does not suffer from severe distortion and the trailing edge does not become too thin; the design variables include Hicks-Henne type function basis function coefficients: c1, c2, c3, c4, c5, and the value ranges are: c1: 0-0.0014, c2: 0-0.0017, c3: 0-0.0017, c4: 0-0.0017, c5: 0-0.0022.

[0039] 3) Using the method introduced in step (3) to generate 50 samples in the design space can ensure that the sample points are evenly distributed in the design space.

[0040] 4) Perform steady-state numerical simulation on the original blade profile according to the method and boundary conditions introduced in step (4) to obtain the steady-state flow field of the nozzle.

[0041] 5) The method in step (5) is used to quantitatively analyze the shock wave of the steady flow field of the original blade nozzle to obtain the shock wave intensity J0 of the original blade; the quantitative analysis of the shock wave includes the following operations:

[0042] First, the shock wave in the nozzle flow channel is identified by the projection of the density gradient on the normalized velocity vector (referred to as density gradient). The calculation formula of the density gradient is as follows:

[0043]

[0044] In the formula, is the Hamiltonian operator, ρ is the density, u is the velocity vector, α<0 indicates expansion, and α>0 indicates compression. By setting the limit of α, non-isentropic compression waves can be filtered out from the flow field, and areas larger than this limit will be identified as shock wave areas; however, there are throat shock waves and weaker trailing edge shock wave areas in the nozzle flow channel, as well as boundary layer losses, secondary flow losses, and leakage flow loss areas that may cross in the shock wave area. Therefore, it is necessary to limit the circumferential angle and turbulent dissipation rate to eliminate these areas. The identification condition of the shock wave in this embodiment: α>60kg / m 4 , θ0<θ<θ0+4°(θ0∈(272°,286°)), ε<2×10 7 m 2 / s 3 , where α is the projection of the density gradient on the normalized velocity vector, θ is the circumferential angle, θ0 is the starting circumferential angle of the identification window, which should be adjusted according to the position of the shock wave, and ε is the turbulent dissipation rate. The circumferential angle and identification window are as follows: Figure 2 The shock wave region obtained under this condition is shown in Figure 3 shown.

[0045] Afterwards, the entropy production rate is integrated for the identified area, and the entropy production rate formula is as follows:

[0046]

[0047] Where μ is the fluid dynamic viscosity, unit is Pa·s; u, v, w are velocity components, unit is m / s; T is temperature, unit is K. The entropy generation in the shock wave region, i.e., the shock wave intensity J0, is calculated.

[0048] 6) The method in step (6) is used to quantitatively analyze the leakage flow of the steady flow field of the original blade nozzle to obtain the leakage flow loss X0 of the blade; the quantitative analysis of the leakage flow includes the following operations:

[0049] First, the leakage flow is identified by the Q criterion, which is formulated as follows:

[0050]

[0051] Where Ω is the vorticity tensor, S is the strain rate tensor, and Q>0 indicates the presence of vortices. Since the Q criterion is essentially to identify vortices in the flow channel, its ability to identify leakage flow is limited. The identification area is mixed with shock wave loss, boundary layer loss, and secondary flow loss areas, so it is also necessary to limit density gradient, turbulent kinetic energy, turbulent dissipation rate, and wall distance to eliminate them. The identification condition of leakage flow in this embodiment is: α<60kg / m 4 ,ε<5×10 8 m 2 / s 3 , κ>1000J / kg, w>0.00023m, where α is the projection of the density gradient on the normalized velocity vector, ε is the turbulent dissipation rate, κ is the turbulent kinetic energy, and w is the distance to the wall, where the wall is the nozzle blade surface. Under this condition, the leakage flow area identified is as follows: Figure 4 shown.

[0052] Afterwards, the entropy production rate is integrated for the identified area, and the entropy production rate formula is as follows:

[0053]

[0054] Where, μ is the fluid dynamic viscosity, unit: Pags; u, v, w are velocity components, unit: m / s; T is the temperature, unit: K; ρ is the density, unit: kg / m 3 ; ε is the turbulent dissipation rate. The entropy generation in the leakage flow area, i.e., the leakage flow loss X0, is calculated.

[0055] 7) Integrate the entropy generation rate of the original blade nozzle flow channel to obtain the total entropy generation value of the flow channel, that is, the total loss Y0;

[0056] 8) Integrate the flow rate microelement of the volute inlet section (equal to the product of velocity, density and area microelement) to obtain the nozzle mass flow rate; obtain the original blade mass flow rate M0;

[0057] 9) For each design scheme in the initial sample set generated in step (3), numerical simulation is performed given the boundary conditions of the working condition described in step (4), and the shock wave quantification method of the original blade profile in step (5) is used to obtain the shock wave intensity J of the sample blade profile. i ; The leakage flow loss quantification method in step (6) is used to obtain the leakage flow loss X of the sample blade i ; Use the method in step (7) to obtain the total loss Y i ; Using the method in step (8), the mass flow rate M is obtained i ;

[0058] 10) After completing the calculation of all samples, the RBF model is constructed to obtain the mapping relationship between shock wave intensity, leakage flow loss, total loss, mass flow and design variables. The cross-validation method is used to check the accuracy of the proxy model. The predicted values ​​of the performance indicators (shock wave intensity, leakage flow loss, total loss, mass flow) are well compared with the calculated values, and the root mean square error (RMSE, Root Mean Square Error) is less than 0.1. It can be considered that the proxy model in this example has a high mapping accuracy and can be used for subsequent optimization.

[0059] 11) The multi-objective optimization of the nozzle is implemented by using the gradient variation hybrid optimization algorithm. The objective function is to minimize the shock wave intensity and the total loss. The constraint condition is that the mass flow rate does not exceed M c =1.04M0 and leakage flow loss does not exceed X c =0.02W / K, obtain the Pareto frontier solution set, select the nozzle blade profiles corresponding to some optimal solutions for numerical simulation calculation, and find the shock wave intensity J i and the total loss Y i Finally, the performance curve of the optimized blade shape is calculated to check the impact on turbine performance.

[0060] The design variables of the optimal nozzle are: c1=0.00140653, c2=0.000787016, c3=0.000947656, c4=0.000540575, c5=0.000242088. Table 2 shows the changes in the nozzle objective function before and after optimization.

[0061] Table 2

[0062] J Y original <![CDATA[1.90611×10 -5 ]]> 1.31641 optimization <![CDATA[2.23229×10 -6 ]]> 1.08754 Increase -88.29％ -17.39％

[0063] It can be seen from the table that both objective functions have been weakened, and the shock wave intensity has been weakened by 88.29%, with significant optimization effects; leakage flow loss and mass flow rate changes are also within the specified range. Figure 5 This is a comparison of the entropy generation rate distribution of the 50% blade height plane nozzle before and after optimization. From the figure, it can be clearly seen that the trailing edge shock wave of the original blade shape basically disappears after optimization, and the overall high entropy generation area is also reduced. Figure 6 This is a comparison of the performance index (efficiency) calculated under different working conditions of the optimized nozzle and the original blade profile. As can be seen from the figure, the efficiency of the optimized turbine is also improved under all working conditions, and the improvement is greater under large expansion ratios. Ultimately, the goal of reducing shock wave intensity and aerodynamic losses at the same time was achieved.

[0064] The above is only an introduction to the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several modifications and substitutions can be made without departing from the principle of the present invention, and these modifications and substitutions should also be regarded as the protection scope of the present invention.

Claims

1. A turbine nozzle shock wave and loss optimization method based on entropy production rate regulation, characterized in that: The following steps are involved: (1) According to the geometry of the turbine nozzle and the location of the shock wave, and considering the impact on the turbine flow, the parameterized modeling method and range are determined; the part after the nozzle suction throat is selected as the blade modification area; the Hicks-Henne type function is used to parameterize the nozzle blade, and parameterization is achieved by setting the number and distribution of basis functions; the nozzle profile is modified by changing the coefficient size of the basis function; the coefficient of the basis function is the design variable; (2) Given different upper and lower limits of the design variables, a design space is formed. The criteria for selecting the upper and lower limits are: under the extreme value conditions, the nozzle geometry does not suffer from severe distortion and the trailing edge does not become too thin; (3) Perform optimal Latin hypercube sampling in the design space to generate an initial sample set so that the sample points are evenly distributed in the entire design space; (4) For the original turbine, the maximum expansion ratio and minimum nozzle opening condition are selected as the optimized condition; The steady Reynolds-averaged Navier-Stokes RANS equations are used for numerical simulation. The RANS equations are discretized based on the finite volume method. The SST model is selected as the turbulence model. The total temperature and total pressure conditions are given at the inlet boundary and the static pressure is given at the outlet boundary to obtain the steady flow field of the nozzle. (5) A shock wave quantification method is used to quantitatively analyze the shock wave of the steady flow field of the original blade nozzle under the working conditions described in step (4). First, the shock wave is identified by the projection of the density gradient on the normalized velocity vector. When the density gradient is greater than a limit value, it is identified as a shock wave region, and additional circumferential angle and turbulence dissipation rate restriction conditions are added to eliminate the throat shock wave and the weaker trailing edge shock wave as well as the boundary layer loss, secondary flow loss and leakage flow loss region crossing the shock wave region; then, the entropy production rate of the region is integrated, and the entropy production value obtained is used as a quantitative evaluation index of the shock wave intensity; (6) quantitatively analyzing the leakage flow of the steady flow field of the original blade nozzle under the working conditions described in step (4), firstly identifying the leakage flow by the Q criterion, and when Q>0, identifying it as the leakage flow area, and adding density gradient, turbulent kinetic energy, turbulent dissipation rate, and wall distance restriction conditions to eliminate shock wave loss, boundary layer loss, and secondary flow loss areas; then integrating the entropy production rate of the area, and obtaining the entropy production value as a quantitative evaluation index of the leakage flow loss; (7) Integrate the entropy generation rate of the original blade nozzle flow channel to obtain the total entropy generation value of the flow channel, which is used as an evaluation index of the total nozzle loss; (8) Integrate the infinitesimal cross-sectional flow rate at the volute inlet, which is equal to the product of velocity, density and area, to obtain the nozzle mass flow rate; (9) For each design scheme in the initial sample set generated in step (3), numerical simulation is performed given the boundary conditions of the operating condition described in step (4), and the shock wave quantification method of the original blade profile in step (5) is used to obtain the shock wave intensity of the sample blade profile; the leakage flow loss quantification method of step (6) is used to obtain the leakage flow loss of the sample blade profile; the total loss is obtained by the method in step (7); and the mass flow rate is obtained by the method in step (8); (10) RBF model is constructed to obtain the mapping relationship between shock wave intensity, leakage flow loss, total loss and mass flow rate and the design variables in step (2). The gradient mutation optimization algorithm is used to implement the optimization. The objective function is to minimize the shock wave intensity and total loss. The constraint condition is that the mass flow rate change does not exceed the upper limit of the mass flow rate M. c , the leakage flow loss does not exceed the leakage upper limit X c , and finally a design with smaller shock wave intensity and total loss is obtained.

2. The turbine nozzle shock wave and loss optimization method based on entropy production rate regulation according to claim 1 is characterized in that: The outlet boundary is given a static pressure of atmospheric pressure.

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