Integrated Modeling Method for Boundary Layer Transition of Underwater Vehicles at Different Turbulence Intensities

Abstract

The present invention provides an integrated modeling method for the boundary layer transition of an underwater vehicle under different turbulence intensities, including the following steps: determining the oncoming flow conditions, including the oncoming flow turbulence intensity, the oncoming flow velocity, and the head shape of the underwater vehicle; solving the laminar flow field of the boundary layer at the head of the underwater vehicle according to the oncoming flow conditions determined in S1; extracting key modeling parameters and calculating the critical instability position; extracting integrated modeling parameters, obtaining an integrated modeling function, and predicting the bypass transition or natural transition position; given the oncoming flow conditions at the position where the bypass transition / natural transition needs to be predicted, predicting the bypass transition / natural transition position.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic research, and specifically, to an integrated modeling method for the boundary layer transition at the head of an underwater body of revolution.

Background Art

[0002] The prediction of boundary layer transition is an important link in the design of underwater vehicles, mainly because the position and characteristics of boundary layer transition are directly related to the resistance and noise of underwater vehicles. By predicting the transition position and then realizing transition control, it is ultimately possible to achieve the purpose of reducing resistance and noise in the design of the head of an underwater vehicle, and improve the propulsion efficiency and concealment of the underwater vehicle. When designing a vehicle, it is not only necessary to accurately predict the transition position, but also to obtain the result as soon as possible. Therefore, it is very important to accurately and quickly predict the position of the boundary layer of an underwater vehicle.

[0003] The existing boundary layer transition prediction methods mainly include empirical and semi-empirical methods. Among them, the transition modeling method in the empirical method does not require a stability analysis of the flow field, has a small amount of calculation, and the transition prediction accuracy meets the requirements of engineering applications, and can meet both the requirements of accuracy and speed, so it is very suitable for current engineering applications.

[0004] The incoming flow turbulence intensity is the ratio of the root mean square of the pulsating velocity to the time-averaged velocity in the incoming flow, indicating the intensity of the turbulent pulsation in the incoming flow. Affected by the incoming flow turbulence intensity, the boundary layer transition types at the head of an underwater vehicle from laminar to turbulent can generally be divided into two categories: natural transition and bypass transition. In the case of a relatively low incoming flow turbulence intensity (Tu ≤ 0.15%), the boundary layer flow will successively go through the receptivity stage, the small disturbance linear growth stage, the non-linear action stage, and finally undergo transition. This type of transition is called natural transition; in the case of a relatively high incoming flow turbulence intensity (Tu > 0.15%), it will directly cause large-amplitude disturbances to appear in the boundary layer and quickly trigger transition. This type of transition is called bypass transition. Regarding the modeling method for the natural transition of the boundary layer at the head of an underwater vehicle under low incoming flow turbulence intensity, there has been research in this area (Tianjin University. "A Modeling Method for the Natural Transition of the Boundary Layer at the Head of an Underwater Body of Revolution.", CN118690678A); regarding the modeling method for the bypass transition of the boundary layer at the head of an underwater vehicle under high incoming flow turbulence intensity, no public research has been seen so far.

[0005] Due to the complexity of the marine environment, the incoming flow turbulence intensity during the navigation of an underwater vehicle is not constant. There are significant differences in the incoming flow turbulence intensity in different sea areas, water depths, and time periods. Therefore, it is very necessary to develop an integrated transition modeling method for different incoming flow turbulence intensities, which can not only predict the bypass transition position but also predict the natural transition position. No relevant research work has been seen so far.

Summary of the Invention

[0006] The invention provides an integrated modeling method for the transition of the leading-edge boundary layer of an underwater vehicle with different oncoming flow turbulence intensities, which is simple to calculate and has a transition prediction accuracy meeting the engineering requirements. This method considers the influence of the oncoming flow turbulence intensity on the transition type, uses numerical simulation to calculate the laminar flow field, explores the relationship between flow field characteristic parameters such as the transition position and the oncoming flow turbulence intensity, and establishes an integrated modeling function. The present invention adopts the following technical solutions:

[0007] An integrated modeling method for the boundary layer transition of an underwater vehicle with different turbulence intensities includes the following steps:

[0008] S1. Determine the oncoming flow conditions, including the oncoming flow turbulence intensity, the oncoming flow velocity, and the leading-edge line type of the underwater vehicle;

[0009] S2. According to the oncoming flow conditions determined in S1, solve the laminar flow field of the leading-edge boundary layer of the underwater vehicle;

[0010] S3. Extract the key modeling parameters and calculate the critical instability position;

[0011] S4. Extract the integrated modeling parameters, obtain the integrated modeling function, and predict the bypass transition or natural transition position;

[0012] S41. Extract the integrated modeling parameters:

[0013] Extract the integrated modeling parameters, that is, the oncoming flow turbulence intensity Tu and the mean velocity gradient factor

[0014] S42. Obtain the integrated modeling function:

[0015] For the bypass transition under high oncoming flow turbulence intensity with Tu > 0.15%, calculate the critical instability position according to the above steps S1 to S3 to obtain the critical instability value Re θcr of the momentum thickness Reynolds number; obtain the critical transition calibration value Re θtr-c of the momentum thickness Reynolds number according to the bypass transition position measured by the water tunnel experiment, and then obtain the difference ΔRe θ = Re θtr-c - Re θcr between the momentum thickness Reynolds number of the bypass transition position and the Reynolds number of the critical instability position; measure the oncoming flow turbulence intensity when the bypass transition occurs through the water tunnel experiment; and then obtain a set of discrete data L about the oncoming flow turbulence intensity Tu, the hull length Reynolds number Re and the mean velocity gradient factor θ and the difference ΔRe

[0016] For natural transition under low oncoming flow turbulence intensity Tu ≤ 0.15%, calculate the critical instability position according to the above steps S1 to S3 to obtain the critical instability value Re of the momentum thickness Reynolds number θcr ; According to the natural transition position given by the e N method, obtain the critical transition calibration value Re of the momentum thickness Reynolds number θtr-c , and then obtain the difference ΔRe between the momentum thickness Reynolds number at the natural transition position and the Reynolds number at the critical instability position θ = Re θtr-c - Re θcr ; Furthermore, obtain a set of discrete data on the oncoming flow turbulence intensity Tu, the hull length Reynolds number Re L , the average velocity gradient factor and the difference ΔRe of the momentum thickness Reynolds number θ

[0017] Considering the influence of the oncoming flow turbulence intensity, establish a scaling function of the difference in the momentum thickness Reynolds number with the oncoming flow turbulence intensity, the hull length Reynolds number, and the average velocity gradient factor. Fit the above discrete data by the least squares method to establish an integrated scaling function for the transition position under different oncoming flow turbulence intensities;

[0018] S5, Given the oncoming flow conditions at the position where bypass transition / natural transition needs to be predicted, predict the position of bypass transition / natural transition.

[0019] Further, the method of step S3 is as follows:

[0020] S31, Extract key scaling parameters:

[0021] Calculate according to the laminar flow field distribution obtained in S2, and extract the key scaling parameters in the boundary layer at the head of the underwater vehicle, including: the velocity U at the outer edge of the boundary layer e , the hull length Reynolds number Re L , the velocity gradient factor κ, the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m ;

[0022] S32, Calculate the critical instability position:

[0023] Calculate the ratio of the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m at each location from the leading edge of the vehicle downstream. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this location is the critical instability position.

[0024] Further, in step 42, the integrated scaling function for the transition position under different oncoming flow turbulence intensities. :

[0025]

[0026] Further, in step S42: in the modularization function, the coefficients are a = 28.34, b = 5.839, c = -7.847×10^8, d = 1.901×10^-3, f = -1408, g = 56.24.

[0027] Further, the method of step S5 is as follows:

[0028] Given the oncoming flow conditions for predicting the position of bypass transition / natural transition, according to the method of steps S2 - S3, solve the laminar flow field of the boundary layer at the head of the underwater vehicle, extract the key modularization parameters, calculate the critical instability position; extract the integrated modularization parameters, apply the integrated modularization function of the transition position under different oncoming flow turbulence intensities determined in step S42, and obtain the integrated modularization function of the transition position at the specified oncoming flow turbulence intensity; use this modularization function to calculate the critical transition modularization value Re of the momentum thickness Reynolds number at each location downstream along the wall surface from the instability position θtr-m ;

[0029] Calculate the local momentum thickness Reynolds number Re at each location downstream from the instability position of the vehicle boundary layer θ and the ratio of the critical transition modularization value Re of the momentum thickness Reynolds number at this location. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this is the transition position. θtr-m Compared with the prior art (Patent CN118690678A), the essential difference of the present invention is that: this patent (Patent CN118690678A) only considers natural transition and can only be used at low oncoming flow turbulence intensities. The present invention simultaneously considers the experimental results of bypass transition and natural transition and establishes an integrated modularization function for the transition position under different oncoming flow turbulence intensities.

[0030] Compared with the prior art, it has the following beneficial effects:

[0031] The present invention provides a feasible and reliable integrated modularization method for the transition of the boundary layer at the head of an underwater vehicle under different oncoming flow turbulence intensities, which is applicable to predicting the transition positions of both bypass transition and natural transition. The present invention provides a convenient method for predicting the transition of the boundary layer at the head of an underwater vehicle, and further provides theoretical support for drag reduction and noise reduction during the head design of an underwater vehicle. The present invention does not require a stability analysis of the flow field, has a small computational amount, and the transition prediction accuracy meets the requirements of engineering applications.

[0032]

Description of the Drawings

Description of the Drawings

[0033] The accompanying drawings are used to provide a further understanding of the present invention and form a part of the specification. Together with the following specific embodiments, they are used to explain the present invention, but do not constitute a limitation to the present invention. In the accompanying drawings:

[0034] Figure 1 is the block diagram of the step structure of the present invention

[0035] Figure 2 is the schematic diagram of the result of calculating the critical instability position in the natural transition example

[0036] Figure 3 is the schematic diagram of the result of calculating the transition position in the natural transition example

[0037] Figure 4 is the schematic diagram of the result of calculating the critical instability position in the bypass transition example

[0038] Figure 5 is the schematic diagram of the result of calculating the transition position in the bypass transition example

Specific Embodiments

[0039] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the relevant content and do not limit the present invention. In addition, it should be noted that only the parts related to the present invention are shown in the accompanying drawings for the convenience of description.

[0040] The embodiment of the present invention provides an integrated modeling method for the leading-edge boundary layer transition of an underwater vehicle under different oncoming flow turbulence intensities, as Figure 1 shown. This method includes the following steps:

[0041] S1. Determine the oncoming flow conditions, including the oncoming flow turbulence intensity, the oncoming flow velocity, and the leading-edge shape of the underwater vehicle;

[0042] S2. Solve the laminar flow field of the leading-edge boundary layer of the underwater vehicle according to the calculation conditions determined in S1;

[0043] S3. Extract the key modeling parameters and calculate the critical instability position;

[0044] S4. Extract the integrated modeling parameters, obtain the integrated modeling function, and predict the bypass transition or natural transition position.

[0045] Further, the method of S3 is as follows:

[0046] S31. Extract the key modeling parameters:

[0047] According to the calculation of the laminar flow field distribution obtained in S2, extract the key modeling parameters in the leading-edge boundary layer of the underwater vehicle, including: the outer edge velocity U of the boundary layer e , the local momentum thickness Reynolds number Reθ , the hull length Reynolds number Re L , the velocity gradient factor κ and the critical instability modal value Re of the momentum thickness Reynolds number θcr-m .

[0048] S32, calculate the critical instability position:

[0049] Calculate the local momentum thickness Reynolds number Re at each location downstream from the leading edge of the vehicle θ and the ratio of the critical instability modal value Re of the momentum thickness Reynolds number θcr-m . As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio equals 1, this location is the critical instability position.

[0050] S4, extract the integrated modal parameters. Further, the method of S4 is as follows:

[0051] S41, extract the integrated modal parameters:

[0052] Extract the integrated modal parameters, that is, the incoming flow turbulence intensity Tu and the average velocity gradient factor

[0053] S42, obtain the integrated modal function:

[0054] For bypass transition under high incoming flow turbulence intensity with Tu > 0.15%, calculate the critical instability position according to the above steps S1 to S3, and obtain the critical instability value Re of the momentum thickness Reynolds number θcr ; obtain the critical transition calibration value Re of the momentum thickness Reynolds number according to the bypass transition position measured by the water tunnel experiment θtr-c , and then obtain the difference ΔRe between the momentum thickness Reynolds number at the bypass transition position and the Reynolds number at the critical instability position θ = Re θtr-c - Re θcr . Measure the incoming flow turbulence intensity when bypass transition occurs through the water tunnel experiment. Then obtain a set of discrete data on the incoming flow turbulence intensity Tu, the hull length Reynolds number Re L , the average velocity gradient factor and the difference ΔRe of the momentum thickness Reynolds number θ as shown in Table (1). Table (1) Discrete data in the bypass transition conditions selected in this step

[0055]

[0056] For natural transition under low incoming flow turbulence intensity with Tu ≤ 0.15%, calculate the critical instability position according to the above steps S1 to S3, and obtain the critical instability value Re of the momentum thickness Reynolds number θcr ; according to e​N The natural transition position given by the method is used to obtain the critical transition calibration value Re of the momentum thickness Reynolds number θtr-c , and then the difference ΔRe between the momentum thickness Reynolds number at the natural transition position and the Reynolds number at the critical instability position is obtained θ = Re θtr-c - Re θcr . Existing research results generally believe that natural transition occurs when the oncoming flow turbulence intensity is about lower than 0.15%. Therefore, three values of the oncoming flow turbulence intensity not higher than 0.15%, namely 0.05%, 0.1%, and 0.15%, are selected during modeling. A set of discrete data on the oncoming flow turbulence intensity Tu, the hull length Reynolds number Re L , the average velocity gradient factor and the difference ΔRe of the momentum thickness Reynolds number θ are as shown in the following Tables (2), (3), and (4). As shown in Tables (2), (3), and (4) below

[0057] Table (2) Discrete data with an oncoming flow turbulence intensity of 0.05% in the natural transition conditions selected in this step

[0058]

[0059] Table (3) Discrete data with an oncoming flow turbulence intensity of 0.10% in the natural transition conditions selected in this step

[0060]

[0061] Table (4) Discrete data with an oncoming flow turbulence intensity of 0.15% in the natural transition conditions selected in this step

[0062]

[0063]

[0064] Considering the influence of the oncoming flow turbulence intensity, a modeling function of the difference in the momentum thickness Reynolds number and the oncoming flow turbulence intensity, the hull length Reynolds number, and the average velocity gradient factor is established. Therefore, the above discrete data is fitted by the least squares method to establish an integrated modeling function for the transition position under different oncoming flow turbulence intensities

[0065]

[0066] Among them, the coefficients in the modeling function are a = 28.34, b = 5.839, c = -7.847×10 8 , d = 1.901×10 -3 , f = -1408, g = 56.24

[0067] S5. Given the oncoming flow conditions for predicting the location of bypass transition / natural transition, predict the location of bypass transition / natural transition:

[0068] Given the oncoming flow conditions for predicting the location of bypass transition / natural transition, according to the methods in steps S2 - S3, solve the laminar flow field of the boundary layer at the head of the underwater vehicle, extract the key scaling parameters, and calculate the critical instability location; extract the integrated scaling parameters, and apply the integrated scaling function for the transition location under different oncoming flow turbulence intensities determined in step S42 to obtain the integrated scaling function for the transition location at the specified oncoming flow turbulence intensity. Using this scaling function, calculate the critical transition scaling value of the momentum thickness Reynolds number Re θtr-m .

[0069] Calculate the local momentum thickness Reynolds number Re θ at each location downstream from the instability location of the vehicle boundary layer and the critical transition scaling value of the momentum thickness Reynolds number Re θtr-m . As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this location is the transition location.

[0070] To describe the objectives, technical solutions, and advantages of the embodiments of the present invention more clearly, the following will, in conjunction with the accompanying drawings in the embodiments of the present invention, clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components described and shown in the accompanying drawings here can be arranged and designed in different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0071] The following gives two embodiments calculated by using the integrated scaling method for the transition of the boundary layer at the head of the underwater vehicle obtained by the method of the present invention:

[0072] In the first embodiment, calculate the natural transition location of the boundary layer at the head of the underwater vehicle under low oncoming flow turbulence intensity.

[0073] S1. Determine the oncoming flow conditions, including the oncoming flow turbulence intensity, oncoming flow velocity, and the head shape of the underwater vehicle;

[0074] In this step, it is determined that the oncoming flow turbulence intensity Tu is 0.1034%, and the oncoming flow velocity U ∞ is 9.9 m / s, and natural transition occurs.

[0075] In this step, the head shape of the underwater vehicle to be calculated is determined as an external shape curve with an exact mathematical expression (the form values are public, Lauchle G C, Eisenhuth J J, Gurney G B. Boundary-layer transition on a body of revolution[J]. Journal of Hydronautics, 1980, 14(4): 117-121.).

[0076] S2. According to the calculation conditions determined in S1, solve the laminar flow field of the boundary layer at the head of the underwater vehicle.

[0077] In this step, use Fluent software to calculate the laminar flow field of the boundary layer at the head of the underwater body of revolution, and obtain the tangential velocity u distribution of the boundary layer at the head of the body of revolution.

[0078] S3. Extract key scaling parameters, including: the outer edge velocity U of the boundary layer e , the Reynolds number Re based on the vehicle length L , the velocity gradient factor κ, the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m , and calculate the critical instability position.

[0079] In this step, the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m is calculated through the critical instability position scaling function (see the patent "A scaling method for natural transition of the boundary layer at the head of an underwater body of revolution.", CN118690678A).

[0080] In this step, calculate the ratio of the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m at each location from the leading edge of the vehicle downstream. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this is the critical instability position, as shown in Figure 2 . The corresponding arc length coordinate s cr is 0.0609 m.

[0081] S4. Extract the integrated scaling parameters, obtain the integrated scaling function, and predict the natural transition position.

[0082] In this step, extract the integrated scaling parameters. Determine that Tu is 0.1034%. Calculate the average velocity gradient factor cr downstream along the wall from the instability position s

[0083] In this step, the integrated scaling function is given by Equation (1)

[0084]

[0085] Among them, the coefficients in the modularization function are a = 28.34, b = 5.839, c = -7.847×10 8 , d = 1.901×10⁻³, f = -1408, g = 56.24.

[0086] In this step, the value of the incoming flow turbulence intensity 0.1034% is substituted into the integrated modularization function to obtain the modularization function of the transition position at this turbulence intensity, which is given by (2)

[0087]

[0088] In this step, using the modularization function of the transition position at this turbulence intensity, the critical transition modularization value Re of the momentum thickness Reynolds number at each wall position is calculated downstream along the wall from the instability position θtr-m , which is given by Equation (3)

[0089] Re θtr-m = VRe θ + Re θcr-m (3)

[0090] The local momentum thickness Reynolds number Re at each position is calculated downstream from the instability position of the boundary layer of the vehicle θ and the ratio of the critical transition modularization value Re of the momentum thickness Reynolds number at this position is calculated. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this is the transition position of the natural transition example, as shown in θtr-m , and the corresponding arc length coordinate s Figure 3 is 0.2722 m. The transition position measured by the Lauchle water tunnel experiment is between 0.2637 m and 0.4018 m, and the prediction result of this modularization method is consistent with the experimental result. tr In the second embodiment, the bypass transition position of the boundary layer at the head of the underwater vehicle is calculated under high incoming flow turbulence intensity.

[0091] S1. Determine the incoming flow conditions, including the incoming flow turbulence intensity, the incoming flow velocity, and the head shape of the underwater vehicle;

[0092] In this step, it is determined that the incoming flow turbulence intensity Tu is 0.5533%, the incoming flow velocity U

[0093] is 2 m / s, and bypass transition occurs. ∞

[0094] In this step, the head shape of the underwater body of revolution for calculation is determined to be the SUBOFF shape (Groves, N.C., Huang, T.T., and Chang, M.S., Geometric characteristics of DARPA (Defense Advanced Research Projects Agency) SUBOFF Models (DTRC Model Numbers 5470 and 5471) [R], Technical Report No. DTRC / SHD-1298–01, 1989.)

[0095] S2. According to the calculation conditions determined in S1, solve the laminar flow field of the boundary layer at the head of the underwater vehicle.

[0096] In this step, use Fluent software to calculate the laminar flow field of the boundary layer at the head of the underwater body of revolution, and obtain the distribution of the tangential velocity u of the boundary layer at the head of the body of revolution.

[0097] S3. Extract the scaling parameters, including: the velocity U at the outer edge of the boundary layer e , the Reynolds number Re based on the vehicle length L , the velocity gradient factor κ, the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m , and calculate the critical instability position.

[0098] In this step, the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m is obtained by calculating through the critical instability position scaling function (the critical instability position scaling function can be seen in the patent "A Scaling Method for Natural Transition of the Boundary Layer at the Head of an Underwater Body of Revolution.", CN118690678A).

[0099] In this step, calculate the ratio of the local momentum thickness Reynolds number Re θ and the critical instability scaling value Re of the momentum thickness Reynolds number θcr-m at each location from the leading edge of the vehicle downstream. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this location is the critical instability position, as shown in Figure 4 , and the corresponding arc length coordinate s cr is 0.1564 m.

[0100] S4. Extract the integrated scaling parameters, obtain the integrated scaling function, and predict the natural transition / bypass transition position.

[0101] In this step, extract the integrated scaling parameters. Determine that Tu is 0.5533%. Along the wall from the instability position s crCalculate the average velocity gradient factor downstream

[0102] In this step, the integrated modeling function is given by Equation (3)

[0103]

[0104] where the coefficients in the modeling function are a = 28.34, b = 5.839, c = -7.847×10 8 , d = 1.901×10 -3 , f = -1408, g = 56.24.

[0105] In this step, the value of the incoming flow turbulence intensity 0.5533% is substituted into the integrated modeling function to obtain the transition position modeling function at this turbulence intensity, which is given by (4)

[0106]

[0107] In this step, using the transition position modeling function at this turbulence intensity, the critical transition modeling value Re θtr-m of the momentum thickness Reynolds number at each wall position is calculated downstream along the wall from the instability position, as shown in Equation (5).

[0108] Re θtr-m = VRe θ + Re θcr-m (5)

[0109] Calculate the local momentum thickness Reynolds number Re θ at each location downstream from the instability position of the vehicle boundary layer and the ratio of the critical transition modeling value Re θtr-m of the momentum thickness Reynolds number at this location. As the local momentum thickness Reynolds number increases, the ratio gradually increases. When the ratio is equal to 1, this is the transition position of the bypass transition example, as shown in Figure 5 The corresponding arc length coordinate s tr is 0.2088 m. The transition position measured in the bypass water tunnel experiment is 0.20 m. Comparing the prediction result of this modeling method with the experimental result, the relative error is 4.43%, which is in agreement with the experimental result.

[0110] The present invention provides an integrated modeling method for the transition of the leading-edge boundary layer of an underwater vehicle with different incoming flow turbulence intensities, which is simple to calculate and has a transition prediction accuracy meeting engineering requirements. This method considers the influence of the incoming flow turbulence intensity on the transition type, uses numerical simulation to calculate the laminar flow field, explores the relationship between flow field characteristic parameters such as the transition position and the incoming flow turbulence intensity, establishes an integrated modeling function, and is applicable to predicting both the natural transition position and the bypass transition position.

[0111] Through two embodiments of different transition types, many of their features and advantages are clear from the above 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. In addition, since many modifications and changes are readily envisioned by those skilled in the art, the embodiments of the present invention are not limited to the exact structures and operations illustrated and described, but rather may cover all suitable modifications and equivalents that fall within its scope.

[0112] The parts not detailed in the present invention are well-known to those skilled in the art.

Claims

1. An integrated modeling method for the transition of the boundary layer of an underwater vehicle under different turbulence intensities, comprising the following steps: S1. Determine the oncoming flow conditions, including the oncoming flow turbulence intensity, the oncoming flow velocity, and the head shape of the underwater vehicle; S2. Solve the laminar flow field of the boundary layer at the head of the underwater vehicle according to the oncoming flow conditions determined in S1; S3. Extract the key modeling parameters and calculate the critical instability position; S4. Extract the integrated modeling parameters, obtain the integrated modeling function, and predict the bypass transition or natural transition position; S41. Extract the integrated modeling parameters: Extract the integrated modular parameters, namely the incoming flow turbulence intensity Tu and the mean velocity gradient factor S42. Obtain the integrated modeling function: For bypass transition under high incoming flow turbulence intensity with Tu > 0.15%, calculate the critical instability position according to the above steps S1 to S3 to obtain the critical instability value of the momentum thickness Reynolds number Re θcr ; Obtain the critical transition calibration value Re θtr-c of the momentum thickness Reynolds number according to the bypass transition position measured by the water tunnel experiment, and then obtain the difference ΔRe θ = Re θtr-c - Re θcr ; Measure the incoming flow turbulence intensity at the time of bypass transition through the water tunnel experiment; and then obtain a set of discrete data L about the incoming flow turbulence intensity Tu, the hull length Reynolds number Re , the average velocity gradient factor θ and the difference ΔRe For natural transition under low incoming flow turbulence intensity with Tu ≤ 0.15%, calculate the critical instability position according to the above steps S1 to S3 to obtain the critical instability value of the momentum thickness Reynolds number Re θcr ; According to the natural transition position given by the e N method, obtain the critical transition calibration value of the momentum thickness Reynolds number Re θtr-c , and then obtain the difference ΔRe θ = Re θtr-c - Re θcr ; Furthermore, obtain a set of discrete data L about the incoming flow turbulence intensity Tu, the hull length Reynolds number Re , the average velocity gradient factor θ and the difference in momentum thickness Reynolds number ΔRe Considering the influence of the oncoming flow turbulence intensity, establish a modeling function of the difference in Reynolds number of momentum thickness and the oncoming flow turbulence intensity, the Reynolds number of the vehicle length, and the average velocity gradient factor. Fit the above discrete data by the least squares method to establish an integrated modeling function for the transition position under different oncoming flow turbulence intensities; Wherein, a, b, c, d, f, and g are coefficients of the integrated modular function; S5. Given the oncoming flow conditions at the position where the bypass transition / natural transition needs to be predicted, predict the bypass transition / natural transition position.

2. The integrated modeling method for the transition of the boundary layer of an underwater vehicle under different turbulence intensities according to claim 1, characterized in that The method of step S3 is as follows: S31. Extract the key modeling parameters: According to the calculation of the laminar flow field distribution obtained in S2, key modeling parameters within the boundary layer at the head of the underwater vehicle are extracted, including: the velocity U at the outer edge of the boundary layer e , the hull length Reynolds number Re L , the velocity gradient factor κ, the local momentum thickness Reynolds number Re θ and the critical instability modeling value Re of the momentum thickness Reynolds number θcr-m ; S32. Calculate the critical instability position: Calculate the local momentum thickness Reynolds number Re at each location downstream from the leading edge of the vehicle θ and the critical instability modal value Re of the momentum thickness Reynolds number θcr-m The ratio increases gradually as the local momentum thickness Reynolds number increases. When the ratio equals 1, this is the critical instability position.

3. The integrated modeling method for the transition of the boundary layer of an underwater vehicle under different turbulence intensities according to claim 1, wherein In step S42: The coefficients in the modeling function are a = 28.34, b = 5.839, c = -7.847×10^8, d = 1.901×10^-3, f = -1408, g = 56.

24.

4. The integrated modeling method for the boundary layer transition of an underwater vehicle under different turbulence intensities according to claim 1, characterized in that The method of step S5 is as follows: Given the oncoming flow conditions for predicting the position of bypass transition / natural transition, according to the methods in steps S2 - S3, solve the laminar flow field of the boundary layer at the head of the underwater vehicle, extract the key modeling parameters, and calculate the critical instability position; extract the integrated modeling parameters, apply the integrated modeling function of the transition position under different oncoming flow turbulence intensities determined in step S42 to obtain the integrated modeling function of the transition position under the specified oncoming flow turbulence intensity; use this modeling function to calculate the critical transition modeling value of the momentum thickness Reynolds number Re at each location downstream along the wall surface from the instability position θtr-m ; Calculate the local momentum thickness Reynolds number Re at each location downstream from the instability position of the vehicle boundary layer θ and the critical transition modeling value Re of the momentum thickness Reynolds number at that location θtr-m The ratio of them gradually increases as the local momentum thickness Reynolds number increases. When the ratio equals 1, this location is the transition position.

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