Transition measurement and correction method based on laminar flow kinetic energy transport equation model

Abstract

The invention discloses a transition measurement and correction method based on a laminar flow kinetic energy transport equation model.Based on a laminar flow kinetic energy model, a modeling function containing incoming flow turbulivity and reverse pressure gradient influence is introduced so as to achieve modification, and the method comprises the following steps that A, modeling and correction are introduced into constant coefficients in source items of the laminar flow kinetic energy model; b, modeling and correction are introduced into a constant coefficient in a source item of the laminar flow kinetic energy model; c, calculating transition of the flow field according to the laminar flow kinetic energy model modified in the step A and the step B; d, a result obtained after calculation in the step C is compared with Samp; and comparing the K panel experiment data with the panel experiment data given by the ERCOFTAC experiment database. A modeling function including incoming flow turbulivity and reverse pressure gradient influence is introduced, and the problems that transition prediction of a laminar flow energy model in a flow field with low turbulivity is advanced and transition prediction of the laminar flow energy model in a flow field with reverse pressure gradient is lagged can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of transition measurement and correction, and in particular to a transition measurement and correction method based on a laminar kinetic energy transport equation model. Background Art

[0002] Fluid mechanics is a discipline that studies fluid motion, involving various complex flow phenomena. Among them, turbulent transition is an important and difficult problem in fluid mechanics. Transition refers to the process of fluid changing from laminar flow to turbulent flow. In laminar flow, fluid particles move smoothly in a straight line parallel to the tube axis, while in turbulent flow, fluid particles move irregularly.

[0003] Existing high-precision measurement methods, such as direct numerical simulation (DNS) and large eddy simulation (LES) methods, can measure relatively reliable flow field data, but require large computing resources and a long time period. There is also a transition model based on the Reynolds average method (RANS), which reduces the demand for computing resources while ensuring a certain accuracy. Due to its high cost-effectiveness, it is widely accepted and used. Therefore, many transition research works have been carried out based on the RANS method, among which the laminar kinetic energy model has also emerged and been widely used.

[0004] However, at present, the calculation results of the laminar kinetic energy layer model are compared with the S&K flat plate experimental data and the flat plate experimental data given by the ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) database. The measurement and correction methods of the laminar kinetic energy model have the following problems and limitations:

[0005] 1. No modeling and calibration were performed for the examples with different incoming flow turbulence. In the example with low incoming flow turbulence, the transition prediction was significantly advanced.

[0006] 2. The promoting effect of adverse pressure gradient on boundary layer transition is not considered, and no modeling and calibration are performed for the above-mentioned influence. In the calculation examples with the above-mentioned flow field structure, the transition prediction is obviously delayed. Summary of the invention

[0007] The purpose of the present invention is to provide a transition measurement and correction method based on the laminar kinetic energy transport equation model to address the above-mentioned problems, hoping to improve the existing laminar kinetic energy model measurement and correction method, which does not model and calibrate examples for different incoming flow turbulence degrees and does not consider the problem of the promoting effect of the adverse pressure gradient on the boundary layer transition.

[0008] The technical solution adopted by the present invention is as follows:

[0009] A transition measurement and correction method based on a laminar kinetic energy transport equation model is provided. The method is based on the laminar kinetic energy model and introduces a modeling function including the influence of the incoming flow turbulence and the adverse pressure gradient, thereby realizing the modification. The method comprises the following steps: Step A: BP The constant coefficients in are introduced into the modeling and correction; Step B: The source term R of the laminar kinetic energy model NAT Introduce the constant coefficients in the modeling and correction; Step C: calculate the transition of the flow field according to the laminar kinetic energy model modified by Step A and Step B; Step D: compare the results calculated in Step C with the S&K flat plate experimental data and the flat plate experimental data given by the ERCOFTAC experimental database to draw conclusions.

[0010] It should be noted that the method is modified and optimized based on the laminar kinetic energy model, and its calculation basis is still based on the laminar kinetic energy model.

[0011] A further technical solution is that the source term R of the flow energy model in step A is BP The construction is as follows:

[0012] R BP =C R β BP k L ωf W (1)

[0013]

[0014] λ eff =min(Cλd n ,λ T )(6)

[0015] Among them, k L is the laminar kinetic energy, ν is the laminar kinematic viscosity coefficient, ω is the specific dissipation rate, k T is the turbulent kinetic energy, Ω is the modulus of the rotation rate tensor, d n is the wall distance; where the constant coefficient is C R =0.12, A BP =0.6, C BP,crit =1.2, C λ =2.495; where β BP 、f W ,φ BP , eff , T It is an intermediate function completely defined by the above physical quantities, which plays a comprehensive role in controlling the boundary layer transition.

[0016] It should be noted that the source term R of the laminar kinetic energy model is BPConstructed as existing formula technology.

[0017] A further technical solution is that the modeling and correction of step A includes the following steps: Step a: Using a modeling method to correct the source term R BP C BP,crit After correction, we get the modular function f BP,threshold , f BP,threshold is a threshold function based on the local turbulence, with f BP,threshold Function replaces the constant coefficient C in equation (3) BP,crit ;

[0018] The modeling method is:

[0019]

[0020] f BP,threshold =min{2.11,max[1.31,(k BP,threshold Tu local +b BP,threshold )]} (8)

[0022]

[0023] Where, ν is the laminar kinematic viscosity coefficient, k T is the turbulent kinetic energy, u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, Ω is the modulus of the rotation rate tensor, Tu local is the local turbulence, U s is the local combined velocity, constant coefficient k BP,threshold =-53.33, b BP,threshold =2.643.

[0024] A further technical solution is that the source term R of the flow energy model in step B is NAT The construction is as follows:

[0025] R NAT =C R,NAT β NAT k L Ω(11)

[0026]

[0027] Among them, k L is the laminar kinetic energy, ν is the laminar viscosity coefficient, Ω is the modulus of the rotation rate tensor, and d n is the distance to the wall, constant coefficient C R,NAT =0.22, A NAT =200, C NAT,crit =1250, C NC=0.1; where β NAT ,φ NAT 、f NAT,crit It is an intermediate function completely defined by the above physical quantities, which plays a comprehensive role in controlling the boundary layer transition.

[0028] It should be noted that the source term R of the laminar kinetic energy model is NAT Constructed as existing formula technology.

[0029] A further technical solution is that the modeling and correction of step B includes the following steps:

[0030] Step b: Modeling the source term R NAT A NAT After correction, we get the modular function f NAT , use f NAT Substitute the constant coefficient A in equation (12) NAT ;

[0031] The modeling method is:

[0032]

[0033] f NAT =k NAT λ P +b NAT (16)

[0034]

[0035] Where u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, Ω is the modulus of the rotation rate tensor, and λ P is the pressure gradient parameter, f NAT is the pressure gradient parameter λ around P The modular function constructed, where the constant coefficient k NAT =1.5×10 5 , b NT =350.00.

[0036] A further technical solution is that the modeling and correction in step B further includes the following steps:

[0037] Step c: Modeling the source term R NAT C NAT,crit After correction, we get the modular function f NAT,threshold , use f NAT,threshold Substitute the constant coefficient C in equation (13) NAT,crit ;

[0038] The modeling method is:

[0039]

[0040] f NAT,threshold =(k NAT,shreshold λ P +b NAT,shreshold )L weight

[0041] +C NAT,crit (1.00-L weight )(20)

[0042]

[0043] Where, ν is the laminar kinematic viscosity coefficient, U s is the local combined velocity, Ω is the modulus of the rotation rate tensor, and λ P is the pressure gradient parameter, f NAT,threshold is the pressure gradient parameter λ around P The constructed modular function, d n is the wall distance; L weight is a weight function used to ensure that the correction process starts at the correct position, with a constant coefficient k NAT,shreshold =1.2×10 6 , b NAT,shreshold =2450.00, k weight =5.56, b weight =-0.67 constant coefficient C NAT,crit = 1250, ξ is the length scale 1, λ T The length scale is 2.

[0044] A further technical solution is that the modeling and correction in step B further includes the following steps:

[0045] Step d: Modeling the source term R NAT C NC After correction, we get the modular function f NC , use f NC Substitute the constant coefficient C in equation (14) NC ;

[0046] The modeling method is:

[0047]

[0048] f NC =k NC λ P +b NC (twenty four)

[0049] Among them, k L is the laminar kinetic energy, d n is the wall distance, ν is the laminar flow viscosity coefficient, λP is the pressure gradient parameter, f NC is the pressure gradient parameter λ around P Constructed modular function with constant coefficient k NC =-86.22, b NC =-0.072.

[0050] A further technical solution is that the step D compares the result calculated in the step C with the S&K plate experimental data and the ERCOFTAC zero pressure gradient and reverse pressure gradient experimental data.

[0051] A further technical solution is that, under the condition of zero pressure gradient, experiments are carried out based on the S&K flat plate and the ERCOFTACT3 series flat plate: wherein, S&K, T3AM, T3A, and T3B are all boundary layer transition experiments of flat plates without pressure gradient, and the difference is that the turbulence at the leading edge of the flat plate increases successively, which is used to verify the calculation reliability of the correction work under variable turbulence conditions; under the condition of adverse pressure gradient, experiments are carried out based on the ERCOFTAC T3 series flat plates: wherein, T3C2~5 measure the change law of the transition position of the flat plate boundary layer in the presence of a pressure gradient; the boundary layer transition of the T3C2~4 flat plates is affected by the adverse pressure gradient, which is used to verify the calculation reliability of the correction work under the presence of an adverse pressure gradient, and the boundary layer transition position of T3C5 is located in the forward pressure gradient area, which is used to ensure that the correction work does not have adverse effects in other areas.

[0052] A further technical solution is that the condition for starting the correction of step c is: when L weight =1, f NAT,threshold =k NAT,shreshold λ P +b NAT,shreshold , fully open the correction; when L weight = 0, f NAT,threshold Will be restored to a constant coefficient C NAT,crit , turn off the correction completely.

[0053] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0054] The present invention aims at the existing laminar kinetic energy model and obtains a modeling function through a modeling method, thereby using the modeling function to modify multiple constant coefficients in the original laminar kinetic energy model, so that the modified laminar kinetic energy model can be applied to transition prediction and correction technology of various flow fields; at the same time, the modified laminar kinetic energy model can propose a more universal transition modeling scheme for the problem of obvious errors in transition prediction under some working conditions.

[0055] Compared with the existing laminar kinetic energy model, the present invention can improve the problem of early transition prediction of the laminar kinetic energy model in the flow field with low turbulence and delayed transition prediction of the laminar kinetic energy model in the flow field with adverse pressure gradient to a certain extent by introducing the influence of the incoming flow turbulence and adverse pressure gradient on the boundary layer transition. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of the method of the present invention;

[0057] Figure 2 This is a comparison chart of the calculation results of the zero-pressure gradient plate of the present invention;

[0058] in, Figure 2 (a) S&K Tu leading edge =0.18%;

[0059] Figure 2 (b) T3AM Tu leading edge =0.90%;

[0060] Figure 2 (c) is T3A Tu leading edge =3.00%;

[0061] Figure 2 (d) is T3B Tu leading edge =6.00%;

[0062] Figure 3 This is a comparison diagram of the pressure gradient plate calculation results of the present invention;

[0063] in, Figure 3 (a) is the transition of T3C2 reverse pressure stage;

[0064] Figure 3 (b) is the transition of T3C3 reverse pressure stage;

[0065] Figure 3 (c) is the transition of T3C4 reverse pressure stage;

[0066] Figure 3 (d) is the transition of T3C5 forward pressure segment. DETAILED DESCRIPTION

[0067] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0068] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0069] Example 1.

[0070] like Figure 1 As shown, one embodiment of the present invention is a transition measurement and correction method based on the laminar kinetic energy transport equation model. The reason for the transition is that in a flow field with high incoming flow turbulence, the source term R BP First, it starts to grow, so that the turbulent kinetic energy k T It grows in the stream direction, causing a transition. In the flow field with low incoming turbulence, the source term R NAT First it starts to grow, further leading to the source term R BP growth, so that the turbulent kinetic energy k T Growth in the flow direction triggers a turning point.

[0071] The problem with the existing laminar kinetic energy model is that the source term R BP and the source term R NAT The existing structure of is not applicable to the transition calculation of various flow fields, and the growth position does not match the experimental data. In order to solve this problem, the source term R BP and the source term R NAT By introducing appropriate modeling and correction, the transition prediction correction technology described in this embodiment can be implemented.

[0072] The method sets the incoming flow turbulence and adverse pressure gradient functions based on the laminar kinetic energy model to modify the original laminar kinetic energy model. The method comprises the following steps:

[0073] Step A: Source term R of laminar kinetic energy model BP C BP,crit Correction is made by changing the constant coefficient C BP,crit Replaced by a threshold function f based on the local turbulence BP,threshold ;

[0074] Step B: Source term R of the laminar kinetic energy model NAT Introduce multiple constant coefficients in the modeling and correction, and also form multiple new modular functions; specifically, the source term R is corrected by the modeling method. NAT A NAT After correction, we get the modular function f NAT , use f NAT Substitution constant coefficient A NAT ; The source term R is modeled by NAT C NAT,crit After correction, we get the modular function f NAT,threshold , use f NAT,threshold Substitution constant coefficient C NAT,crit ; The source term R is modeled by NAT C NC After correction, we get the modular function f NC , use f NC Substitution constant coefficient CNC ;

[0075] Step C: calculating the transition of the flow field according to the laminar kinetic energy model modified in step A and step B;

[0076] Step D: Compare the result calculated in step C with the S&K flat plate experimental data and the flat plate experimental data provided by the ERCOFTAC experimental database to draw a conclusion.

[0077] This embodiment targets the existing laminar kinetic energy model and obtains a modeling function through a modeling method, thereby using the modeling function to modify multiple constant coefficients in the original laminar kinetic energy model, so that the modified laminar kinetic energy model can be applied to transition prediction and correction technology of various flow fields; at the same time, the modified laminar kinetic energy model can propose a more universal transition modeling solution for the problem of obvious errors in transition prediction under some working conditions.

[0078] Example 2.

[0079] In one embodiment of the present invention, the step a uses a modeling method to model the source term R BP φ BP The function is modified to obtain the modular function f BP,threshold , f BP,threshold is a threshold function based on the local turbulence, with f BP,threshold Function substitution constant coefficient C BP,crit ;

[0080] The modeling method is:

[0081]

[0082] f BP,threshold =min{2.11,max[1.31,(k BP,threshold Tu local +b BP,threshold )]}

[0083]

[0084] Where, ν is the laminar kinematic viscosity coefficient, k T is the turbulent kinetic energy, u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, Ω is the modulus of the rotation rate tensor, Tu local is the local turbulence, U s is the local combined velocity, constant coefficient k BP,threshold =-53.33, b BP,threshold =2.643.

[0085] The difference from the original laminar flow energy model is that the newly constructed threshold function f BP,thresholdReplaced the constant coefficient threshold C BP,crit , f BP,threshold Contains Tu local , that is, the effect of turbulence on transition is introduced, so that the model has better performance in the calculation of different incoming flow turbulence conditions.

[0086] Example 3.

[0087] In one embodiment of the present invention, the step b uses a modeling method to model the source term R NAT A NAT After correction, we get the modular function f NAT , use f NAT Substitution constant coefficient A NAT ;

[0088] The modeling method is:

[0089]

[0090] f NAT =k NAT λ P +b NAT

[0091]

[0092] Where u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, and λ P is the pressure gradient parameter, f NAT is the pressure gradient parameter λ around P The constructed modular function, Ω is the modulus of the rotation rate tensor, f NAT is the pressure gradient parameter λ around P Constructed modular function with constant coefficient k NAT =1.5×10 5 , b NT =350.00.

[0093] The difference from the original laminar flow energy model is that the modeling function f NAT Substitution constant coefficient A NAT , and the effects of pressure gradient and separation on transition are introduced, so that the model has better performance in the calculation of the working conditions.

[0094] Example 4.

[0095] In one embodiment of the present invention, the step c uses a modeling method to model the source term R NAT C NAT,crit After correction, we get the modular function f NAT,threshold , use f NAT,threshold Substitution constant coefficient CNAT,crit ;

[0096] The modeling method is:

[0097]

[0098] f NAT,threshold =(k NAT,shreshold λ P +b NAT,shreshold )L weight +C NAT,crit (1.00-L weight )

[0099]

[0100]

[0101] Where, ν is the laminar kinematic viscosity coefficient, U s is the local combined velocity, Ω is the modulus of the rotation rate tensor, and λ P is the pressure gradient parameter, f NAT,threshold is the pressure gradient parameter λ around P The constructed modular function, d n is the wall distance; L weight is a weight function used to ensure that the correction process starts at the correct position, k NAT,shreshold 、b NAT,shreshold , k weight and b weight is a constant coefficient, constant coefficient C NAT,crit = 1250, ξ is the length scale 1, λ T The length scale is 2.

[0102] The conditions for starting the correction of step c are:

[0103] When L weight =1, f NAT,threshold =k NAT,shreshold λ P +b NAT,shreshold , fully enable correction;

[0104] When L weight = 0, f NAT,threshold Will be restored to a constant coefficient C NAT,crit , turn off the correction completely.

[0105] The difference from the original laminar flow energy model is that the modeling function f NAT,threshold Substitution constant coefficient C NAT,crit , and the effects of pressure gradient and separation on transition are introduced, so that the model has better performance in the calculation of the working conditions.

[0106] Example 5.

[0107] In one embodiment of the present invention, the step d uses a modeling method to model the source term R NAT C NC After correction, we get the modular function f NC , use f NC Substitution constant coefficient C NC ;

[0108] The modeling method is:

[0109]

[0110] f NC =k NC λ P +b NC

[0111] Among them, k L is the laminar kinetic energy, d n is the wall distance, ν is the laminar flow viscosity coefficient, λ P is the pressure gradient parameter, f NC is the pressure gradient parameter λ around P Constructed modular function with constant coefficient k NC =-86.22, b NC =-0.072.

[0112] The difference from the original laminar flow energy model is that the modeling function f NC Substitution constant coefficient C NC , and the effects of pressure gradient and separation on transition are introduced, so that the model has better performance in the calculation of the working conditions.

[0113] Example 6.

[0114] like Figure 2 As shown, one embodiment of the present invention is that, in order to more intuitively demonstrate the advantages of the method of the present invention compared with the existing laminar kinetic energy model, the result calculated in step C is compared with the S&K flat plate experimental data and the ERCOFTAC zero pressure gradient flat plate experimental data. S&K, T3AM, T3A, and T3B are all boundary layer transition experiments of flat plates without pressure gradient. The difference is that the turbulence at the leading edge of the flat plate increases successively, which is used to verify the calculation reliability of the correction work under variable turbulence conditions; the S&K flat plate refers to a flat plate boundary layer transition experiment with low incoming flow turbulence conducted by Schubauer and Klebanoff, and the turbulence at the leading edge of the flat plate is about 0.18%. And the free incoming flow turbulence Tu at the leading edge of the S&K, T3AM, T3A, and T3B flat plates is set leading edgeThey are 0.18%, 0.90%, 3.00% and 6.00% respectively, among which the leading edge turbulence of T3AM, T3A and T3B flat plates increases successively. Figure 2 (a), 2(b), 2(c), and 2(d) correspond to the S&K, T3AM, T3A, and T3B plates, respectively.

[0115] Comparing the calculation results of the original layer flow energy model (black line, original model) and the current layer flow energy model (red line, present model) after adding the transition prediction correction method of the present invention, it can be seen that the C f The transition is determined by the rise of the curve. In the transition prediction of four flat plates with different turbulence intensities, the C f The curve change trend is more consistent with the experimental data.

[0116] Example 7.

[0117] like Figure 3 As shown, one embodiment of the present invention is to compare the result calculated in step C with the result calculated by the ERCOFTAC pressure gradient plate in order to more intuitively demonstrate the advantages of the method of the present invention over the existing laminar kinetic energy model. Figure 3 (a), 3(b), 3(c), and 3(d) correspond to the T3C2, T3C3, T3C4, and T3C5 plates, respectively. T3C2-5 measured the changing law of the transition position of the flat plate boundary layer in the presence of a pressure gradient. The T3C2, T3C3, T3C4, and T3C5 plates have a pressure gradient. There is an adverse pressure gradient at the transition position of the T3C2, T3C3, and T3C4 plates, and a favorable pressure gradient at the transition position of T3C5. The boundary layer transition of the T3C2-4 plates is affected by the adverse pressure gradient, which is used to verify the calculation reliability of the correction work under the condition of an adverse pressure gradient. The boundary layer transition position of T3C5 is located in the favorable pressure gradient area, which is used to ensure that the correction work does not have adverse effects in other areas.

[0118] Comparing the calculation results of the original model and the current model, it can be seen that due to the lack of adverse pressure gradient modeling in the original model, the transition predictions of the T3C2, T3C3, and T3C4 plates all have obvious lags. The current model completely improves this defect, and the prediction results are basically consistent with the experimental data.

[0119] Therefore, the method adopted in this embodiment can improve the problem of early transition prediction of the laminar kinetic energy model in a flow field with low turbulence and delayed transition prediction of the laminar kinetic energy model in a flow field with adverse pressure gradient to a certain extent.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A transition measurement and correction method based on a laminar kinetic energy transport equation model, the method is based on the laminar kinetic energy model, introduces a modeling function including the influence of the incoming flow turbulence and the adverse pressure gradient, modifies the original laminar kinetic energy model, and is characterized in that: The method comprises the following steps: Step A: Source term R of laminar kinetic energy model BP The constant coefficients in are introduced into modeling and correction; Step B: Source term R of the laminar kinetic energy model NAT The constant coefficients in are introduced into modeling and correction; Step C: calculating the transition of the flow field according to the laminar kinetic energy model modified in steps A and B; Step D: Compare the result calculated in step C with the S&K flat plate experimental data and the flat plate experimental data provided by the ERCOFTAC experimental database to draw a conclusion.

2. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 1 is characterized in that: The source term R of the laminar flow energy model in step A BP The construction is as follows: R BP =C R b BP k L ω / f W (1) l eff =min(C λ d n ,l T ) (6) Among them, k L is the laminar kinetic energy, ν is the laminar kinematic viscosity coefficient, ω is the specific dissipation rate, k T is the turbulent kinetic energy, Ω is the modulus of the rotation rate tensor, d n is the wall distance; where C R , A BP , C BP,crit , C λ is a constant coefficient; among them, β BP 、f W ,φ BP , eff , T It is an intermediate function completely defined by the above physical quantities, which plays a comprehensive role in controlling the boundary layer transition.

3. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 2 is characterized in that: The modeling and correction of step A includes the following steps: Step a: Modeling the source term R BP C BP,crit After correction, we get the modular function f BP,threshold , f BP,threshold is a threshold function based on the local turbulence, with f BP,threshold Function replaces the constant coefficient C in equation (3) BP,crit ; The modeling method is: f BP,threshold =min{2.11,max[1.31,(k BP,threshold You local +b BP,threshold )]} (8) Where, ν is the laminar kinematic viscosity coefficient, k T is the turbulent kinetic energy, u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, Ω is the modulus of the rotation rate tensor, Tu local is the local turbulence, U s is the local combined velocity, where k BP,threshold and b BP,threshold is a constant coefficient.

4. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 1 is characterized in that: The source term R of the laminar flow energy model in step B NAT The construction is as follows: R NAT =C R,NAT b NAT k L Oh(11) Among them, k L is the laminar kinetic energy, ν is the laminar viscosity coefficient, Ω is the modulus of the rotation rate tensor, and d n is the wall distance, where C R,NAT , A NAT , C NAT,crit and C NC is a constant coefficient, where β NAT ,φ NAT 、f NAT,crit It is an intermediate function completely defined by the above physical quantities, which plays a comprehensive role in controlling the boundary layer transition.

5. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 4 is characterized in that: The modeling and correction of step B includes the following steps: Step b: Modeling the source term R NAT A in NAT After correction, we get the modular function f NAT , use f NAT Substitute the constant coefficient A in equation (12) NAT ; The modeling method is: f NAT =k NAT l P +b NAT (16) Where u is the local velocity in the x direction, v is the local velocity in the y direction, w is the local velocity in the z direction, and λ P is the pressure gradient parameter, f NAT is the pressure gradient parameter λ around P The modular function constructed, Ω is the modulus of the rotation rate tensor, where k NAT and b NT is a constant coefficient.

6. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 4 is characterized in that: The modeling and correction of step B includes the following steps: Step c: Modeling the source term R NAT C NAT,crit After correction, we get the modular function f NAT,threshold , use f NAT,threshold Substitute the constant coefficient C in equation (13) NAT,crit ; The modeling method is: f NAT,threshold =(k NAT,shreshold l P +b NAT,shreshold )L weight +C NAT,crit (1.00-L weight ) (20) Where, ν is the laminar kinematic viscosity coefficient, U s is the local combined velocity, Ω is the modulus of the rotation rate tensor, and λ P is the pressure gradient parameter, f NAT,threshold is the pressure gradient parameter λ around P The constructed modular function, d n is the wall distance; L weight is a weight function used to ensure that the correction process starts at the correct position, k NAT,shreshold , b NAT,shreshold , k weight and b weight is a constant coefficient, C NAT,crit is a constant coefficient, ξ is the length scale 1, λ T The length scale is 2.

7. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 4 is characterized in that: The modeling and correction of step B includes the following steps: Step d: Modeling the source term R NAT C NC After correction, we get the modular function f NC , use f NC Substitute the constant coefficient C in equation (14) NC ; The modeling method is: f NC =k NC l P +b NC (24) Among them, k L is the laminar kinetic energy, d n is the wall distance, ν is the laminar flow viscosity coefficient, λ P is the pressure gradient parameter, f NC is the pressure gradient parameter λ around P The constructed modular function, k NC and b NC is a constant coefficient.

8. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 1 is characterized in that: The step D compares the result calculated in step C with the S&K plate experimental data and the ERCOFTAC zero pressure gradient and reverse pressure gradient experimental data.

9. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 8, characterized in that: Under the condition of zero pressure gradient, experiments were conducted based on the S&K flat plate and the ERCOFTACT3 series flat plate: S&K, T3AM, T3A, and T3B are all boundary layer transition experiments of flat plates without pressure gradient. The difference is that the turbulence at the leading edge of the flat plate increases successively, which is used to verify the calculation reliability of the correction work under variable turbulence conditions; Under the adverse pressure gradient conditions, experiments were conducted using the ERCOFTAC T3 series flat plates: T3C2 to 5 measured the changing pattern of the transition position of the flat plate boundary layer in the presence of a pressure gradient; the boundary layer transition of the T3C2 to 4 flat plates was affected by the adverse pressure gradient, which was used to verify the calculation reliability of the correction work in the presence of an adverse pressure gradient; the boundary layer transition position of T3C5 was located in the favorable pressure gradient region, which was used to ensure that the correction work did not have adverse effects in other regions.

10. The transition measurement and correction method based on the laminar kinetic energy transport equation model according to claim 6, characterized in that: The conditions for starting the correction of step c are: When L weight =1, f NAT,threshold =k NAT,shreshold λ P +b NAT,shreshold , fully turn on the correction; When L weight = 0, f NAT,threshold Will be restored to a constant coefficient C NAT,crit , turn off the correction completely.

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