Turbulence modeling method suitable for complex flow of compression system of aerospace vehicle

Abstract

The invention relates to a turbulence modeling method suitable for complex flow of an aerospace vehicle compression system, and belongs to the field of aerospace vehicle turbulence modeling. According to the distribution rule of the normalized velocity helicities of the LES flow field at the blade tip of the gas compressor rotor in the aerospace vehicle, constructing a normalized velocity helicities model, namely an h model; according to an LES flow field at the root of a stator of a gas compressor in an aerospace vehicle, a second-order explicit anisotropic Reynolds stress model, namely a Q model, is constructed; according to the h model and the Q model, a novel RANS turbulence model, namely a Wilcox2006k-omega-h-Q model, for reasonably capturing blade tip gap leakage flow and corner separation flow is constructed, and turbulence modeling suitable for complex flow of an aerospace vehicle compression system is completed; according to the method, the novel RANS turbulence model capable of reasonably capturing the blade tip clearance leakage flow and the corner separation flow is constructed, and high-fidelity numerical simulation solution of the internal flow of the compression system of the aerospace vehicle is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of turbulence modeling of aerospace vehicles and relates to a turbulence modeling method suitable for complex flows in a compression system of an aerospace vehicle. Background Art

[0002] Currently, designers in aerospace vehicle compression system design and development generally use RANS-based three-dimensional computational fluid dynamics (RANS CFD) simulation software to evaluate the design performance of various compression systems and use the evaluation results to improve compression system designs. RANS CFD has become a key component of compression system design, integrating iterative feedback with design to continuously improve designs before physical manufacturing tests.

[0003] However, under off-design conditions, the flow within the compression system often becomes extremely complex, exhibiting a series of complex flow phenomena, including large separation, strong mixing between secondary flow / wake and the primary flow, strong turbulent dissipation of secondary flow, and strong unsteady interactions between the rotor and stator. The RANS turbulence model is insufficiently capable of capturing the physical complexity of the flow within the compression system. This results in CFD simulation results under off-design conditions often deviating significantly from reality, severely distorting the simulation results and severely restricting the depth and breadth of simulation software applications in aerospace vehicle design systems. Improving the turbulence model's ability to predict complex flows within compression systems, and thereby improving the simulation accuracy of three-dimensional numerical simulation software, has become a difficult problem that must be overcome. Summary of the Invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the existing technology, propose a turbulence modeling method suitable for the complex flow of the compression system of an aerospace vehicle, construct a new RANS turbulence model that can reasonably capture the tip gap leakage flow and corner separation flow, and realize high-fidelity numerical simulation solution of the internal flow of the compression system of an aerospace vehicle.

[0005] The solution of the present invention is:

[0006] A turbulence modeling method suitable for complex flows in aerospace vehicle compression systems includes:

[0007] According to the distribution law of the normalized velocity helicity of the LES flow field at the tip of the compressor rotor in the aerospace vehicle, a normalized velocity helicity model, namely the h-model, is constructed.

[0008] According to the LES flow field at the root of the compressor stator in aerospace vehicles, a second-order explicit anisotropic Reynolds stress model, namely the Q model, is constructed.

[0009] Based on the h-model and Q-model, a new RANS turbulence model, namely the Wilcox2006 k-ω-hQ model, is constructed to reasonably capture the tip gap leakage flow and corner separation flow, completing the turbulence modeling suitable for the complex flow of the compression system of aerospace vehicles.

[0010] In the above-mentioned turbulence modeling method applicable to complex flows in the compression system of an aerospace vehicle, the method for constructing h is:

[0011] Set the turbulent kinetic energy generation term to P k , construct P k Functional relationship with h:

[0012]

[0013] Where τ is the Reynolds stress tensor;

[0014] u is the velocity vector;

[0015] τ: It is the combination of the Reynolds stress tensor and the velocity gradient tensor;

[0016] is the gradient operator;

[0017] β(h) is the function of the h model.

[0018] In the above-mentioned turbulence modeling method applicable to complex flows in the compression system of an aerospace vehicle, the function β(h) is:

[0019]

[0020] Where c h1 、c h2 、c h3 are all calibration coefficients; among them, c h1 Control the upper limit of β(h); c h2 Control the growth rate and upper limit of β(h); c h3 Controls the growth rate of β(h).

[0021] In the above-mentioned turbulence modeling method applicable to the complex flow of the compression system of aerospace vehicles, the LES flow field results at the blade tips of two typical compressor rotors, Rotor37 and Rotor67, are used to verify the c h1 、c h2 、c h3 The coefficient value of .

[0022] In the above-mentioned turbulence modeling method applicable to the complex flow of the compression system of aerospace vehicles, the functional relationship between the Reynolds stress tensor τ and the strain tensor S and the vorticity tensor Ω is established, which is the Q model:

[0023]

[0024] Where τ is the Reynolds stress tensor;

[0025] S is the strain tensor;

[0026] Ω is the vorticity tensor;

[0027] k is the turbulent kinetic energy;

[0028] I is the unit tensor;

[0029] ν t is eddy viscosity;

[0030] ω is the turbulence specific dissipation rate;

[0031] C corner is the turbulence anisotropy intensity coefficient.

[0032] In the above-mentioned turbulence modeling method applicable to the complex flow of the compression system of an aerospace vehicle, the SΩ and ΩS represent the interaction terms of the strain tensor and the vorticity tensor, which are second-order nonlinear tensors.

[0033] In the above-mentioned turbulence modeling method applicable to the complex flow of the compression system of aerospace vehicles, the C corner The coefficient value of .

[0034] In the above-mentioned turbulence modeling method suitable for the complex flow of the compression system of aerospace vehicles, the Q model takes into account the anisotropic behavior of turbulence in the corner area and induces counter-rotating flow vortices in the corner area; the counter-rotating flow vortices draw in high-momentum fluid from the mainstream, enhance the three-dimensional shear between the corner area flow and the mainstream, and then suppress the non-physical excessive separation in the corner area.

[0035] In the above-mentioned turbulence modeling method applicable to complex flows in the compression system of aerospace vehicles, the Wilcox2006 k-ω-hQ model is constructed as follows:

[0036] Taking the Wilcox2006 k-ω turbulence model as the benchmark model, the h model is introduced to correct the k and ω terms in the benchmark model, and then the Q model is introduced to correct the Reynolds stress-strain constitutive relation in the benchmark model to complete the construction of the Wilcox2006k-ω-hQ model.

[0037] In the above-mentioned turbulence modeling method applicable to the complex flow of the compression system of aerospace vehicles, the expansion of the Wilcox2006k-ω-hQ model is:

[0038]

[0039] Where ρ is density;

[0040] k is the turbulent kinetic energy;

[0041] t is time;

[0042] u is the velocity vector;

[0043] ω is the turbulence specific dissipation rate;

[0044] is the gradient operator;

[0045] is the divergence operator;

[0046] β(h) is the function of the h model;

[0047] μ is the molecular dynamic viscosity;

[0048] τ is the Reynolds stress tensor;

[0049] β * , β, σ k , σ ω , σ d , γ are both constants;

[0050] is the cross diffusion term;

[0051] τ: It is the contraction of the Reynolds stress tensor and the velocity gradient tensor.

[0052] The beneficial effects of the present invention compared with the prior art are:

[0053] (1) The Wilcox2006 k-ω-hQ model of the present invention more reasonably characterizes the variation of the rotor tip gap leakage flow and the stator root corner separation flow with increasing back pressure, and the flow field blockage prediction is more accurate, thereby providing characteristic prediction results that are highly consistent with the experimental results, demonstrating the effectiveness of the two improved models, the h model and the Q model, in capturing typical complex flows in compression systems;

[0054] (2) Compared with the Wilcox2006 k-ω model, the Wilcox2006 k-ω-hQ model provides a root blade surface pressure distribution that is consistent with the experimental results, and then provides an accurate inter-stage matching result;

[0055] (3) The Wilcox2006 k-ω-hQ model of the present invention suppresses excessive separation in the angular region, and the predicted flow field is very close to the actual flow field, which makes the evaluation of the compressor aerodynamic performance more accurate and avoids misleading designers due to CFD errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the helicity distribution of the LES flow field at the blade tip of the compressor rotor of the present invention;

[0057] Figure 2 Schematic diagram of eddy viscosity distribution of LES flow field at the blade tip of the compressor rotor of the present invention;

[0058] Figure 3 The present invention is β (h) with c h1 Schematic diagram of the coefficient change curve;

[0059] Figure 4 The present invention is β (h) with c h2 Schematic diagram of the coefficient change curve;

[0060] Figure 5 The present invention is β (h) with c h3 Schematic diagram of the coefficient change curve;

[0061] Figure 6 Schematic diagram of the vorticity distribution of the LES flow field at the root of the compressor stator of the present invention;

[0062] Figure 7 Schematic diagram of LES turbulence anisotropy distribution of the present invention;

[0063] Figure 8 Schematic diagram of the Wilcox2006 k-ω turbulence anisotropy distribution of the present invention;

[0064] Figure 9 Schematic diagram of the vortex field at the stator corner area of ​​the compressor of the present invention;

[0065] Figure 10 Schematic diagram of the calculation domain of a certain half-stage compressor of the present invention

[0066] Figure 11 It is the total pressure ratio characteristic curve diagram of the present invention;

[0067] Figure 12 This is the isentropic efficiency characteristic curve of the present invention;

[0068] Figure 13 This is a schematic diagram of the calculation domain of a three-and-a-half-stage compressor of the present invention;

[0069] Figure 14 Schematic diagram of the pressure distribution on the stator surface of the present invention;

[0070] Figure 15 Schematic diagram of Mach number distribution on the S1 flow surface of the S3 stator of the present invention;

[0071] Figure 16 This is a flow chart of turbulence modeling applicable to complex flows in aerospace vehicle compression systems according to the present invention. DETAILED DESCRIPTION

[0072] The present invention will be further described below with reference to the embodiments.

[0073] This paper provides a turbulence modeling method suitable for complex flows in aerospace vehicle compression systems. It constructs a Reynolds-averaged (RANS) turbulence model for high-fidelity prediction of complex flows in aerospace vehicle compression systems, including tip gap leakage and corner separation. This method has direct application in the field of computational fluid dynamics (CFD) numerical simulation technology.

[0074] The present invention aims to construct a new RANS turbulence model (Wilcox2006 k-ω-helicity-QCR model) that can reasonably capture the tip gap leakage flow and corner separation flow, develop the model program code, and package it in the form of a solver core functional component and integrate it into the self-developed CFD numerical simulation software Cipher1.0, so as to realize high-fidelity numerical simulation solution of the internal flow of the aerospace vehicle compression system.

[0075] The development of the Wilcox2006 k-ω-helicity-QCR model was completed in three steps: constructing a normalized velocity helicity (helicity, hereinafter abbreviated as h) model, constructing a second-order explicit anisotropic Reynolds stress (QCR, hereinafter abbreviated as Q) model, and finally constructing the Wilcox2006 k-ω-hQ model that integrates these two models. The technical solutions for each step are detailed below.

[0076] Turbulence modeling methods suitable for complex flows in aerospace vehicle compression systems, such as Figure 16 As shown, the specific steps include:

[0077] According to the distribution law of the normalized velocity helicity of the LES flow field at the tip of the compressor rotor in an aerospace vehicle, a normalized velocity helicity model, namely the h-model, is constructed.

[0078] h Model construction: Analyze the helicity distribution of the LES flow field at the compressor rotor tip (see Figure 1 ) found that the helicity value in the core area of ​​the tip leakage vortex is very large, approaching the maximum value of 1.0. According to the definition of helicity, the larger the h value, The bigger ( is the velocity vector, is the vorticity vector), and The two vectors tend to be parallel, the tip leakage vortex is stretched to a large extent, and there is a strong three-dimensional shear between the leakage flow and the mainstream.

[0079] like Figure 1 、 Figure 2As shown in the figure, by comparing the helicity distribution and eddy viscosity (eddy viscosity ratio) distribution at the blade tip, it can be seen that the eddy viscosity is large in the area with large h, which indicates that h is related to the turbulent kinetic energy generation term P in the k-ω model. k is positively correlated; when h approaches 0, P k Degenerates to the original k-ω model P k Form. Construct P k The functional relationship between η and h is used to characterize the non-equilibrium turbulent transport process of the tip leakage flow, which can significantly improve the prediction accuracy of the turbulence model for the development of the tip leakage vortex.

[0080] The construction method of h is:

[0081] Set the turbulent kinetic energy generation term to P k , construct P k Functional relationship with h:

[0082]

[0083] Where τ is the Reynolds stress tensor;

[0084] u is the velocity vector;

[0085] τ: It is the combination of the Reynolds stress tensor and the velocity gradient tensor;

[0086] is the gradient operator;

[0087] β(h) is the function of the h model.

[0088] Wherein, the function β(h) is:

[0089]

[0090] Where c h1 、c h2 、c h3 are all calibration coefficients; among them, c h1 Control the upper limit of β(h); c h2 Control the growth rate and upper limit of β(h); c h3 Controls the growth rate of β(h).

[0091] β(h) varies with c h2 Changes Figure 4 , when c h2 When it is above 2.0, the upper limit of β(h) function tends to be consistent; c h3 Control the growth rate of β(h) function, β(h) changes with c h3 Changes Figure 5 .

[0092] According to the LES flow field results at the blade tip of two typical compressor rotors, Rotor37 and Rotor67, the calibration of c h1 、c h2 、c h3 The coefficient value of .

[0093] According to the LES flow field at the root of the stator of the compressor in the aerospace vehicle, a second-order explicit anisotropic Reynolds stress model, namely the Q model, is constructed.

[0094] Analysis of the LES flow field at the root of the compressor stator (see Figure 6 ) found that the flow in the corner separation zone has strong turbulent anisotropy. The turbulent scale structure in the separation zone has different shapes due to three-dimensional shear, which is reflected in the discrete distribution of turbulent state points in the Lumley triangle (see Figure 7 The Wilcox2006 k-ω model underestimates the anisotropic behavior of turbulence in the angular separation region (see Figure 8 ), the predicted three-dimensional shear is weak, resulting in large deviations in the prediction of angular separation. Constructing a functional relationship between the Reynolds stress tensor τ and the strain, vorticity tensors S, and Ω to characterize the anisotropic state of turbulence in angular separation flows can significantly improve the accuracy of turbulence models for predicting angular separation.

[0095] The functional relationship between the Reynolds stress tensor τ and the strain tensor S and vorticity tensor Ω is established, which is the Q model:

[0096]

[0097] Where τ is the Reynolds stress tensor;

[0098] S is the strain tensor;

[0099] Ω is the vorticity tensor;

[0100] k is the turbulent kinetic energy;

[0101] I is the unit tensor;

[0102] ν t is eddy viscosity;

[0103] ω is the turbulence specific dissipation rate;

[0104] C corner is the turbulence anisotropy intensity coefficient.

[0105] SΩ and ΩS represent the interaction terms between the strain tensor and the vorticity tensor, and are second-order nonlinear tensors.

[0106] According to the experimental measurement results of flat plate flow boundary layer and three-dimensional diffuser pipe flow under typical zero pressure / adverse pressure gradient conditions, C corner The coefficient value of .

[0107] The Q model takes into account the anisotropic behavior of turbulence in the corner area and induces counter-rotating streamwise vortices in the corner area; the counter-rotating streamwise vortices draw in high-momentum fluid from the mainstream, enhance the three-dimensional shear between the corner area flow and the mainstream, and then suppress the non-physical excessive separation in the corner area.

[0108] The flow field results at the corner area of ​​the compressor stator root predicted by the Wilcox2006 k-ω model and the Wilcox2006 k-ω-Q model combined with the Q model are shown in the figure. Figure 9 As shown in Figure 2, the Q model can account for the anisotropic behavior of turbulent flow in the corners, inducing counter-rotating streamwise vortices in the corners. These counter-rotating streamwise vortices draw in high-momentum fluid from the mainstream, enhancing the three-dimensional shear between the corner and mainstream flows, thereby suppressing unphysical excessive separation in the corners.

[0109] Based on the h model and Q model, a new RANS turbulence model, namely the Wilcox2006 k-ω-hQ model, is constructed to reasonably capture the tip gap leakage flow and corner separation flow, completing the turbulence modeling suitable for the complex flow of the compression system of aerospace vehicles.

[0110] The Wilcox2006 k-ω-hQ model is constructed as follows:

[0111] Taking the Wilcox2006 k-ω turbulence model as the benchmark model, the h model is introduced to correct the k and ω terms in the benchmark model, and then the Q model is introduced to correct the Reynolds stress-strain constitutive relation in the benchmark model to complete the construction of the Wilcox2006k-ω-hQ model.

[0112] The expansion of the Wilcox2006 k-ω-hQ model is:

[0113]

[0114] Where ρ is density;

[0115] k is the turbulent kinetic energy;

[0116] t is time;

[0117] u is the velocity vector;

[0118] ω is the turbulence specific dissipation rate;

[0119] is the gradient operator;

[0120] is the divergence operator;

[0121] β(h) is the function of the h model;

[0122] μ is the molecular dynamic viscosity;

[0123] τ is the Reynolds stress tensor;

[0124] β * , β, σ k , σ ω , σ d , γ are both constants;

[0125] is the cross diffusion term;

[0126] τ: It is the contraction of the Reynolds stress tensor and the velocity gradient tensor.

[0127] Example

[0128] The computational domain of a certain stage semi-axial compressor is as follows Figure 10 As shown, the RANS CFD performance characteristics prediction results show (see Figure 11 、 Figure 12 ), the characteristic variation trends given by both models are in good agreement with the experimental results. The instability margin predicted by the Wilcox2006 k-ω-hQ model (20.9%) is more than twice that of the Wilcox2006 k-ω model (8.71%) and is close to the experimental result (24.81%). The results of this example demonstrate that the Wilcox2006 k-ω-hQ model more reasonably characterizes the variations of the rotor tip gap leakage flow and the stator root corner separation flow with increasing backpressure, and more accurately predicts flow field blockage, thereby providing characteristic predictions that are highly consistent with experimental results. This demonstrates the effectiveness of the two improved h-model and Q-model in capturing typical complex flows within compression systems.

[0129] The computational domain of a three-stage semi-axial compressor is as follows Figure 13 As shown in the figure, the predicted results of the pressure distribution on the blade surface of each stator (S1, S2, S3) at the highest efficiency point are shown (see Figure 14 ), the Wilcox2006 k-ω model predicts an "excessively long" suction surface "pressure plateau" at the S3 root, implying that the angular separation predicted by the Wilcox2006 k-ω model is too large at the S3 root. Compared to the Wilcox2006 k-ω model, the Wilcox2006 k-ω-hQ model provides a pressure distribution on the blade surface at the S3 root that is consistent with the experimental results, thereby providing accurate interstage matching results.

[0130] The flow field results of the near-end wall S1 are as follows Figure 15As shown in the figure, the Wilcox2006 k-ω model predicts excessive angular separation at the third-stage stator blade tip, whereas no angular separation was observed in the experimental results. The Wilcox2006 k-ω-hQ model suppresses excessive angular separation, resulting in a flow field that closely approximates the actual flow field, providing a more accurate assessment of compressor aerodynamic performance and preventing designers from being misled by CFD errors.

[0131] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A turbulence modeling method suitable for complex flows in aerospace vehicle compression systems, characterized by: include: According to the distribution law of the normalized velocity helicity of the LES flow field at the tip of the compressor rotor in the aerospace vehicle, a normalized velocity helicity model, namely the h-model, is constructed. According to the LES flow field at the root of the compressor stator in aerospace vehicles, a second-order explicit anisotropic Reynolds stress model, namely the Q model, is constructed. Based on the h-model and Q-model, a new RANS turbulence model, namely the Wilcox2006 k-ω-hQ model, is constructed to reasonably capture the tip gap leakage flow and corner separation flow, completing the turbulence modeling suitable for the complex flow of the compression system of aerospace vehicles.

2. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 1, characterized in that: The construction method of h is: Set the turbulent kinetic energy generation term to P k , construct P k Functional relationship with h: Where τ is the Reynolds stress tensor; u is the velocity vector; τ: It is the combination of the Reynolds stress tensor and the velocity gradient tensor; is the gradient operator; β(h) is the function of the h model.

3. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 2, characterized in that: The function β(h) is: Where c h1 、c h2 、c h3 All are calibration coefficients; Among them, c h1 Control the upper limit of β(h); c h2 Control the growth rate and upper limit of β(h); c h3 Controls the growth rate of β(h).

4. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 3, characterized in that: According to the LES flow field results at the blade tip of two typical compressor rotors, Rotor37 and Rotor67, the calibration of c h1 、c h2 、c h3 The coefficient value of .

5. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 1, characterized in that: The functional relationship between the Reynolds stress tensor τ and the strain tensor S and vorticity tensor Ω is established, which is the Q model: Where τ is the Reynolds stress tensor; S is the strain tensor; Ω is the vorticity tensor; k is the turbulent kinetic energy; I is the unit tensor; ν t is eddy viscosity; ω is the turbulence specific dissipation rate; C corner is the turbulence anisotropy intensity coefficient.

6. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 5, characterized in that: The SΩ and ΩS represent the interaction terms of the strain tensor and the vorticity tensor, and are second-order nonlinear tensors.

7. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 5, characterized in that: According to the experimental measurement results of flat plate flow boundary layer and three-dimensional diffuser pipe flow under typical zero pressure / adverse pressure gradient conditions, C corner The coefficient value of .

8. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 5, characterized in that: The Q model takes into account the anisotropic behavior of turbulence in the corner area and induces counter-rotating streamwise vortices in the corner area; the counter-rotating streamwise vortices draw in high-momentum fluid from the mainstream, enhance the three-dimensional shear between the corner area flow and the mainstream, and then suppress the non-physical excessive separation in the corner area.

9. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 5, characterized in that: The Wilcox2006 k-ω-hQ model is constructed as follows: Taking the Wilcox2006 k-ω turbulence model as the benchmark model, the h model is introduced to correct the k and ω terms in the benchmark model, and then the Q model is introduced to correct the Reynolds stress-strain constitutive relation in the benchmark model to complete the construction of the Wilcox2006k-ω-hQ model.

10. The turbulence modeling method for complex flows in aerospace vehicle compression systems according to claim 9, characterized in that: The expansion of the Wilcox2006 k-ω-hQ model is: Where ρ is density; k is the turbulent kinetic energy; t is time; u is the velocity vector; ω is the turbulence specific dissipation rate; is the gradient operator; is the divergence operator; β(h) is the function of the h model; μ is the molecular dynamic viscosity; τ is the Reynolds stress tensor; β * , β, σ k , σ ω , σ d , and γ are all constants; is the cross diffusion term; τ: It is the contraction of the Reynolds stress tensor and the velocity gradient tensor.

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