A modeling method for the natural transition of the boundary layer at the bow of an underwater rotating body

Abstract

The present invention relates to a modeling method for the natural transition of the bow boundary layer of an underwater rotating body, comprising the following steps: calculating the laminar basic flow of the bow boundary layer of the underwater rotating body to obtain the tangential velocity distribution of the bow boundary layer of the rotating body; calculating the parameters required for modeling the critical instability position of the bow boundary layer of the underwater rotating body, including the outer edge velocity of the boundary layer, the momentum thickness, the boat length Reynolds number, and the velocity gradient factor; calculating the critical instability position of the underwater rotating body boundary layer by using the modeling function about the critical instability position; calculating the local momentum thickness Reynolds number critical instability value by using the modeling function about the critical instability position; calculating the parameters required for modeling the transition position of the bow boundary layer of the underwater rotating body, and calculating the average velocity gradient factor from the instability position to the downstream along the wall; and calculating the transition position by using the modeling function of the transition of the bow boundary layer of the underwater rotating body.

Description

[Technical field]

[0001] The present invention relates to the technical field of hydrodynamic research, and in particular to a modeling method for the natural transition of the boundary layer at the bow of an underwater rotating body. [Background technology]

[0002] Underwater vehicles, such as submarines and torpedoes, are mostly rotating bodies. The boundary layer at the bow of the rotating body usually goes through three stages: laminar zone, transition zone and turbulent zone. Studies have shown that both the transition zone and the turbulent zone will radiate strong noise outward, affecting the work of the bow sonar of the underwater rotating body. How to reduce noise interference has always been a concern of science and engineering. If we want to control these noises, we first need to know where the transition position of the boundary layer at the bow of the rotating body is under different head shapes and different sailing speeds, and then reduce the noise by affecting the transition position.

[0003] For the transition prediction of the boundary layer at the bow of an underwater rotating body, the commonly used research methods include four categories: experimental method, direct numerical simulation, semi-empirical method and empirical method. Among them, the transition position can be accurately measured by experimental method, but the measurement of large-scale real boats is very difficult; the direct numerical simulation method has too much calculation, and engineering application is not realistic at present; the most representative eN method among the semi-empirical methods requires stability analysis of the flow field, and the calculation amount is also large. Among the empirical methods, the transition modeling method does not require stability analysis of the flow field, and the transition prediction accuracy meets the requirements of engineering use, so it has become a more popular transition prediction method in engineering practice.

[0004] Existing modeling studies on natural transitions in boundary layers can be divided into two categories: transition modeling methods based on laminar flow characteristics and transition modeling methods based on turbulence models. The former focuses on the process developed from laminar flow, calculates the laminar basic flow of the boundary layer, explores the correlation between the transition position and the characteristic parameters of the flow field, and models the transition process; the latter models the transition process through parameters with turbulent characteristics in the transition, such as intermittent factors, turbulent kinetic energy, etc. Among them, there are two common transition modeling methods based on laminar flow characteristics, namely the one-step method (Michle method) and the two-step method (Granville method). The existing Michle method and Granville method, in which the modeling functions are given based on the experimental data of the boundary layer of flat plates and two-dimensional wings, are not suitable for the transition prediction of underwater rotating bodies. Therefore, it is urgent to propose a modeling method for the natural transition of the boundary layer at the bow of underwater rotating bodies. [Summary of the invention]

[0005] The present invention provides a method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body, which is simple and fast in calculation and has a transition prediction accuracy that meets engineering requirements. The technical solution of the present invention is as follows:

[0006] A method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body comprises the following steps:

[0007] Step 1, calculating the laminar basic flow of the boundary layer of the bow of the underwater rotating body, and obtaining the tangential velocity u distribution of the boundary layer of the bow of the rotating body;

[0008] Step 2: Calculate the parameters required for modeling the critical instability position of the boundary layer of the bow of the underwater rotating body, including the velocity at the outer edge of the boundary layer, the momentum thickness, the Reynolds number of the boat length, and the velocity gradient factor;

[0009] Step 3: Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position. The method is as follows:

[0010] (1) Obtain the modular function about the critical instability position

[0011] According to the results of stability analysis under different working conditions, the critical instability position under each working condition is obtained, and then the critical instability value Re of momentum thickness Reynolds number under each working condition is obtained. θcr , the underwater rotating body length Reynolds number Re is known L , velocity gradient factor κ and momentum thickness Reynolds number critical instability value Re θcr , using rational functions, the discrete data (Re L κ, Re θcr ) to perform function fitting and establish a modeling function about the critical instability position;

[0012] (2) Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position

[0013] Calculate along the wall from the leading edge point downstream and determine the momentum thickness Reynolds number Re at each wall position θ and the critical instability value of the momentum thickness Reynolds number at this location θcr , using the boundary layer outer edge velocity U at each wall position obtained in step 2 e and momentum thickness θ, calculate the local momentum thickness Reynolds number Re θ ;

[0014] Using the boat length Reynolds number Re obtained in step 2 L and velocity gradient factor κ, and calculate the local momentum thickness Reynolds number critical instability value Re by modulo function about the critical instability position θcr ;

[0015] Look downstream from the leading edge of the rotating body until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical instability value of the momentum thickness Reynolds number at this locationθcr is equal, which is the instability position, and the corresponding wall arc length coordinate value is recorded as s cr ;

[0016] Step 4: Calculate the parameters required for modeling the transition position of the boundary layer at the bow of the underwater rotating body. According to formula (3), calculate the average velocity gradient factor along the wall from the unstable position to the downstream:

[0017] Step 5, calculating the transition position using the transition modeling function of the boundary layer at the bow of the underwater rotating body;

[0018] (1) Obtaining the boundary layer transition modeling function of the underwater rotating body

[0019] According to e N The method is used to calculate the transition position under different working conditions and obtain the critical transition value of momentum thickness Reynolds number Re θtr , and then obtain the momentum thickness Reynolds number difference ΔRe θ =Re θtr -Re θcr , the underwater rotating body length Reynolds number Re is known L , average velocity gradient factor and the momentum thickness Reynolds number difference ΔRe θ , using rational functions, and using the least squares method to solve discrete data Perform function fitting and establish the boundary layer transition modeling function of the bow of underwater rotating body;

[0020] (2) Calculate the transition position using the boundary layer transition modeling function of the underwater rotating body bow

[0021] Using the boat length Reynolds number Re obtained in step 2 L and the average velocity gradient factor obtained in step 4 Calculate along the wall from the unstable position to the downstream and calculate the critical transition value of momentum thickness Reynolds number Re at each location θtr ;

[0022] Look downstream from the instability position until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical transition value of momentum thickness Reynolds number Re θtr is equal, which is the transition position, and the corresponding wall arc length coordinate value is recorded as s tr .

[0023] Furthermore, step 2 is specifically as follows:

[0024] 1) According to step 1, the velocity distribution of the outer edge of the boundary layer of the rotating body is obtained, and the maximum tangential velocity of the boundary layer at the head of the rotating body is defined as the outer edge position of the local boundary layer, and the tangential velocity at this location is the outer edge velocity of the boundary layer Ue ;

[0025] 2) According to step 1, the nominal thickness and momentum thickness of the boundary layer of the rotating body are obtained, and the distance from the outer edge of the boundary layer at the head of the rotating body to the wall of the rotating body is defined as the local nominal thickness of the boundary layer δ. The momentum thickness of the boundary layer θ is further calculated by integrating formula (1):

[0026]

[0027] Where y is the coordinate perpendicular to the wall;

[0028] 3) Obtain the underwater rotating body length Reynolds number Re L , given by formula (2):

[0029]

[0030] Among them, U ∞ is the navigation speed of the underwater rotating body, L is the length of the underwater rotating body, ν is the kinematic viscosity coefficient of the fluid;

[0031] 4) Obtain the distribution of the velocity gradient factor κ along the wall coordinate s, which is given by formula (3):

[0032]

[0033] Furthermore, in step 3, the modulus function of the critical instability position is given by formula (4):

[0034]

[0035] Among them, f(Re L ,κ) is the critical instability position modulus function; p i , p j are the coefficients in the modular function.

[0036] Furthermore, in step three, the coefficients of the modular function regarding the critical instability position are p1=192, p2=1184, p3=3201, p4=393.4, p5=0.11, q0=1, q1=066, q2=1297, q3=73.7, q4=9.746, q5=0.2024.

[0037] Furthermore, in step 3, the local momentum thickness Reynolds number Re is calculated by equation (5): θ :

[0038]

[0039] Furthermore, in step 5, the transition modeling function of the boundary layer at the bow of the underwater rotating body is given by formula (6):

[0040]

[0041] in, is the transition modulization function; a i , b j The coefficients in the modulo function.

[0042] Furthermore, the coefficient of the transition modeling function of the boundary layer at the bow of the underwater rotating body in step 5 is

[0043] a1=1.139×10 10 , a2=8.246×10 8 , a3=2.383×10 7 , a4=6.035×10 6 , a5=6.912×10 6 ,

[0044] b0=1, b1=3.327×10 7 , b2=-1.662×10 7 , b3=2.886×10 6 , b4=-3.299×10 5 ,

[0045] b5=1.695×10 4 ;

[0046] The modeling method for the natural transition of the boundary layer at the bow of an underwater rotating body is characterized in that in step 5, the critical transition value of the momentum thickness Reynolds number at each location is calculated by formula (7): θtr :

[0047] Re θtr =ΔRe θ +Re θcr (7)

[0048] Compared with the prior art, the present invention has at least the following beneficial effects:

[0049] The natural transition modeling method described in the present invention is established for the boundary layer of an underwater rotating body. Compared with existing methods, it can be more conveniently applied to practical engineering problems and is of great significance for reducing drag and noise of underwater rotating bodies.

[0050] The natural transition modeling method described in the present invention does not require stability analysis of the flow field. Compared with existing methods, the amount of calculation is small, the calculation results are reliable, and the transition prediction accuracy meets the requirements of engineering use.

[0051] In summary, the present invention provides a method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body, which is simple and fast in calculation and has a transition prediction accuracy that meets the requirements of engineering use.

Brief Description of the Drawings

[0052] Figure 1 This is a structural diagram of the steps of the present invention

[0053] Figure 2 This is a schematic diagram of the result of calculating the unstable position.

[0054] Figure 3 This is a schematic diagram of the result of calculating the transition position. [Specific implementation method]

[0055] The present invention is further described in detail below in conjunction with the accompanying drawings and Examples. In the following description, for the purpose of explanation and not limitation, specific details are explained to help fully understand the present invention. However, it is obvious to those skilled in the art that the present invention can also be practiced in other examples that are separated from these specific details.

[0056] It should be noted that in order to avoid obscuring the present invention due to unnecessary details, only the device structure and / or processing steps closely related to the solution according to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0057] The embodiment of the present invention provides a method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body, such as Figure 1 As shown, the method comprises the following steps:

[0058] Step 1: Calculate the laminar basic flow of the boundary layer at the bow of the underwater rotating body to obtain the tangential velocity u distribution of the boundary layer at the bow of the rotating body.

[0059] In this step, the calculated bow line shape of the underwater rotating body is determined to be a linear curve in the literature (the bow line shape is shown in the literature, Lauchle GC, Eisenhuth JJ, Gurney G B. Boundary-layer transition on a body of revolution [J]. Journal of Hydronautics, 1980, 14 (4): 117-121.)

[0060] In this step, the laminar basic flow of the boundary layer of the bow of the underwater rotating body is calculated by the solver in Ansys Fluent; the working condition of this embodiment is zero angle of attack and the sailing speed U ∞ is 4.62 m / s, the length of the rotating boat L is 3.05 m, and the kinematic viscosity coefficient ν of the fluid is 1.0067×10 -6 m2 / s.

[0061] Step 2: Calculate the parameters required for modeling the critical instability position of the boundary layer at the bow of the underwater rotating body, namely, the velocity at the outer edge of the boundary layer, the momentum thickness, the boat length Reynolds number, and the velocity gradient factor, as follows:

[0062] 1) According to step 1, obtain the velocity distribution of the outer edge of the boundary layer of the rotating body. Define the maximum tangential velocity of the boundary layer at the front of the rotating body as the outer edge of the local boundary layer, and the tangential velocity at this location is the boundary layer outer edge velocity U e .

[0063] 2) According to step 1, the nominal thickness and momentum thickness of the boundary layer of the rotating body are obtained. The distance from the outer edge of the boundary layer at the head of the rotating body to the wall of the rotating body is defined as the local nominal thickness of the boundary layer δ, and the momentum thickness of the boundary layer θ is further calculated by integrating formula (1):

[0064]

[0065] in, y is the coordinate perpendicular to the wall.

[0066] 3) Obtain the underwater rotating body length Reynolds number Re L , given by formula (2):

[0067]

[0068] Among them, U ∞ is the navigation speed of the underwater rotating body, L is the length of the underwater rotating body, and ν is the kinematic viscosity coefficient of the fluid.

[0069] 4) Obtain the distribution of the velocity gradient factor κ along the wall coordinate s, which is given by formula (3):

[0070]

[0071] Step 3: Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position, as follows:

[0072] (1) Obtain the modular function about the critical instability position

[0073] In order to obtain the modular function of the critical instability position, this step selects 8 different line types, 7 boat length Reynolds numbers, and a total of 56 working conditions. According to the results of the stability analysis of the 56 working conditions, the critical instability position under each working condition is obtained, and then the momentum thickness Reynolds number critical instability value Re under each working condition is obtained. θcr The velocity gradient factor κ and the critical instability value Re of momentum thickness Re under 56 working conditions θcr Discrete data (κ, Reθcr ), as shown in Table (1)

[0074] Table (1) Critical instability values ​​of velocity gradient factors and momentum thickness Reynolds numbers in the 56 working conditions selected in this step

[0075]

[0076] (Continued Table (1))

[0077]

[0078] The Reynolds number of the underwater rotating body is known. L , velocity gradient factor κ and momentum thickness Reynolds number critical instability value Re θcr , using rational functions, the discrete data (Re L κ, Re θcr ) is used to perform function fitting and establish the modeling function about the critical instability position, which is given by formula (4):

[0079]

[0080] Among them, f(Re L ,κ) is the modulo function of the critical instability position; the coefficients in the modulo function are p1=192, p2=1184, p3=3201, p4=393.4, p5=0.11, q0=1, q1=066, q2=1297, q3=73.7, q4=9.746, q5=0.2024.

[0081] (2) Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position

[0082] Calculate along the wall from the leading edge point downstream and determine the momentum thickness Reynolds number Re at each wall position θ and the critical instability value of the momentum thickness Reynolds number at this location θcr Using the boundary layer outer edge velocity U at each wall position obtained in step 2 e and momentum thickness θ, the local momentum thickness Reynolds number Re is calculated by equation (5): θ :

[0083]

[0084] Using the boat length Reynolds number Re obtained in step 2 L and velocity gradient factor κ, and calculate the local momentum thickness Reynolds number critical instability value Re by modulo function about the critical instability position θcr .

[0085] Look downstream from the leading edge of the rotating body until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical instability value of the momentum thickness Reynolds number at this location θcr equal, this is the unstable position, see Figure 2 As shown, the corresponding arc length coordinate value s cr It is 0.11288m.

[0086] Step 4: Calculate the parameters required for modeling the transition position of the boundary layer at the bow of the underwater rotating body. According to formula (3), calculate the average velocity gradient factor along the wall from the unstable position to the downstream:

[0087] Step 5: Calculate the transition position using the transition modeling function of the underwater rotating body bow boundary layer

[0088] (1) Obtaining the boundary layer transition modeling function of the underwater rotating body

[0089] In order to obtain the transition modeling function of the boundary layer at the bow of the underwater rotating body, this step selects 8 different line types (line types see the literature, Liu J, Liu J, Zhang Y. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies [J]. Physics of Fluids, 2023, 35 (4).), 7 boat length Reynolds numbers, a total of 56 working conditions, according to e N Method, calculate the transition position of the 56 working conditions (the e N The method is shown in the literature Liu J, Liu J, Zhang Y. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies [J]. Physics of Fluids, 2023, 35 (4).) to obtain the critical transition value of momentum thickness Reynolds number Re θtr , and then obtain the momentum thickness Reynolds number difference ΔRe θ =Re θtr -Re θcr The average velocity gradient factor under 56 working conditions Discrete data of the difference between momentum thickness and Reynolds number As shown in Table (2)

[0090] Table (2) Average velocity gradient factor and momentum thickness Reynolds number difference in the 56 working conditions selected in this step

[0091]

[0092] (Continued Table (2))

[0093]

[0094] The Reynolds number of the underwater rotating body is known. L , average velocity gradient factor and the momentum thickness Reynolds number difference ΔRe θ , using rational functions, and using the least squares method to solve discrete data Function fitting is performed to establish the boundary layer transition modeling function of the bow of the underwater rotating body, which is given by formula (6):

[0095]

[0096] in, is the transition modulo function; the coefficient in the modulo function is a1 = 1.139 × 10 10 , a2=8.246×10 8 ,

[0097] a3=2.383×10 7 , a4=6.035×10 6 , a5=6.912×10 6 , b0=1,b1=3.327×10 7 , b2=-1.662×10 7 ,

[0098] b3=2.886×10 6 , b4=-3.299×10 5 , b5=1.695×10 4 .

[0099] (2) Calculate the transition position using the boundary layer transition modeling function of the underwater rotating body bow

[0100] Using the boat length Reynolds number Re obtained in step 2 L and the average velocity gradient factor obtained in step 4 Calculate along the wall from the instability position to the downstream, and calculate the critical transition value of momentum thickness Reynolds number Re at each location by formula (10): θtr :

[0101] Re θtr =ΔRe θ +Re θcr (10)

[0102] Look downstream from the instability position until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical transition value of momentum thickness Reynolds number Re θtr Equal, this is the turning point, see Figure 3 As shown, the corresponding arc length coordinate value s tr It is 0.53046m.

[0103] Features described and / or illustrated above for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with features in other embodiments or used in place of features in other embodiments.

[0104] It should be emphasized that the term “include / comprises” when used herein refers to the presence of features, integers, steps or components, but does not exclude the presence or addition of one or more other features, integers, steps or components.

[0105] The above devices and methods of the present invention can be implemented by hardware, or by hardware combined with software. The present invention relates to such a computer-readable program, which, when executed by a logic component, enables the logic component to implement the above-mentioned devices or components, or enables the logic component to implement the above-mentioned various methods or steps. The present invention also relates to a storage medium for storing the above-mentioned program, such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, etc.

[0106] The many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, the embodiments of the present invention are not intended to be limited to the exact structure and operation illustrated and described, but are intended to cover all suitable modifications and equivalents that fall within the scope thereof.

[0107] Parts of the present invention that are not described in detail are well known to those skilled in the art.

Claims

1. A method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body, comprising the following steps: Step 1, calculating the laminar basic flow of the boundary layer of the bow of the underwater rotating body, and obtaining the tangential velocity u distribution of the boundary layer of the bow of the rotating body; Step 2: Calculate the parameters required for modeling the critical instability position of the boundary layer of the bow of the underwater rotating body, including the velocity at the outer edge of the boundary layer, the momentum thickness, the Reynolds number of the boat length, and the velocity gradient factor; Step 3: Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position. The method is as follows: (1) Obtain the modular function about the critical instability position According to the results of stability analysis under different working conditions, the critical instability position under each working condition is obtained, and then the critical instability value Re of momentum thickness Reynolds number under each working condition is obtained. θcr , the underwater rotating body length Reynolds number Re is known L , velocity gradient factor κ and momentum thickness Reynolds number critical instability value Re θcr , using rational functions, the discrete data (Re L κ, Re θcr ) to perform function fitting and establish a modeling function about the critical instability position; (2) Calculate the critical instability position of the boundary layer of the underwater rotating body using the modeling function of the critical instability position Calculate along the wall from the leading edge point downstream and determine the momentum thickness Reynolds number Re at each wall position θ and the critical instability value of the momentum thickness Reynolds number at this location θcr , using the boundary layer outer edge velocity U at each wall position obtained in step 2 e and momentum thickness θ, calculate the local momentum thickness Reynolds number Re θ ; Using the boat length Reynolds number Re obtained in step 2 L and velocity gradient factor κ, and calculate the local momentum thickness Reynolds number critical instability value Re by modulo function about the critical instability position θcr ; Look downstream from the leading edge of the rotating body until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical instability value of the momentum thickness Reynolds number at this location θcr is equal, which is the instability position, and the corresponding wall arc length coordinate value is recorded as s cr ; Step 4: Calculate the parameters required for modeling the transition position of the boundary layer at the bow of the underwater rotating body, and calculate the average velocity gradient factor along the wall from the unstable position to the downstream. Step 5, calculating the transition position using the transition modeling function of the boundary layer at the bow of the underwater rotating body; (1) Obtaining the boundary layer transition modeling function of the underwater rotating body According to e N The method is used to calculate the transition position under different working conditions and obtain the critical transition value of momentum thickness Reynolds number Re θtr , and then obtain the momentum thickness Reynolds number difference ΔRe θ =Re θtr -Re θcr , the underwater rotating body length Reynolds number Re is known L , average velocity gradient factor and the momentum thickness Reynolds number difference ΔRe θ , using rational functions, and using the least squares method to solve discrete data Perform function fitting and establish the boundary layer transition modeling function of the bow of underwater rotating body; (2) Calculate the transition position using the boundary layer transition modeling function of the underwater rotating body bow Using the boat length Reynolds number Re obtained in step 2 L and the average velocity gradient factor obtained in step 4 Calculate along the wall from the unstable position to the downstream and calculate the critical transition value of momentum thickness Reynolds number Re at each location θtr ; Look downstream from the instability position until you reach a certain flow position where the local momentum thickness Reynolds number Re θ and the critical transition value of momentum thickness Reynolds number Re θtr is equal, which is the transition position, and the corresponding wall arc length coordinate value is recorded as s tr .

2. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 1, characterized in that: Step 2 is as follows: 1) According to step 1, the velocity distribution of the outer edge of the boundary layer of the rotating body is obtained, and the maximum tangential velocity of the boundary layer at the head of the rotating body is defined as the outer edge position of the local boundary layer. The tangential velocity at this location is the outer edge velocity of the boundary layer U e ; 2) According to step 1, the nominal thickness and momentum thickness of the boundary layer of the rotating body are obtained, and the distance from the outer edge of the boundary layer at the head of the rotating body to the wall of the rotating body is defined as the local nominal thickness of the boundary layer δ. The momentum thickness of the boundary layer θ is further calculated by integrating formula (1): Where y is the coordinate perpendicular to the wall; 3) Obtain the underwater rotating body length Reynolds number Re L , given by formula (2): Among them, U ∞ is the navigation speed of the underwater rotating body, L is the length of the underwater rotating body, ν is the kinematic viscosity coefficient of the fluid; 4) Obtain the distribution of the velocity gradient factor κ along the wall coordinate s, which is given by formula (3):

3. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 2, characterized in that: In step 3, the modulus function of the critical instability position is given by equation (4): Among them, f(Re L ,κ) is the critical instability position modulus function; p i , p j are the coefficients in the modular function.

4. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 3, characterized in that: In step three, the coefficients of the modular function about the critical instability position are p1=192, p2=1184, p3=3201, p4=393.4, p5=0.11, q0=1, q1=066, q2=1297, q3=73.7, q4=9.746, q5=0.2024.

5. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 2, characterized in that: In step 3, the local momentum thickness Reynolds number Re is calculated by equation (5): θ :

6. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 1, characterized in that: In step 5, the transition modeling function of the boundary layer at the bow of the underwater rotating body is given by formula (6): in, is the transition modulization function; a i , b j The coefficients in the modulo function.

7. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 6, characterized in that: The coefficient of the transition modeling function of the boundary layer at the bow of the underwater rotating body in step 5 is a1=1.139×10 10 , a2=8.246×10 8 , a3=2.383×10 7 , a4=6.035×10 6 , a5=6.912×10 6 , b0=1,b1=3.327×10 7 , b2=-1.662×10 7 , b3=2.886×10 6 , b4=-3.299×10 5 , b5=1.695×10 4 .

8. The method for modeling the natural transition of the boundary layer at the bow of an underwater rotating body according to claim 1, characterized in that: In step 5, the critical transition value of the momentum thickness Reynolds number at each location is calculated by equation (7): θtr : Re θtr =ΔRe θ +Re θcr (7)。

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