A three-dimensional boundary layer transition line prediction method for an underwater vehicle

Abstract

The present invention relates to a method for predicting the three-dimensional boundary layer transition line of an underwater vehicle, comprising the following steps: determining the shape and navigation conditions of the underwater vehicle, and calculating the three-dimensional laminar basic flow field of the underwater vehicle; analyzing and determining the propagation direction of small disturbances in the three-dimensional boundary layer of the underwater vehicle; determining the set of frequency points to be calculated, for an input frequency in the set of frequency points, after calculating the dimensionless circular frequency, analyzing the amplitude growth rate of three-dimensional small disturbances at each station of the underwater vehicle and calculating the critical instability line at this input frequency; after inputting a meridian plane, calculating the amplitude amplification factor of three-dimensional small disturbances of the underwater vehicle at the input frequency; traversing all the meridian planes to be calculated; obtaining the amplitude amplification factors of small disturbances at each station of the underwater vehicle at the input frequency; traversing all the frequencies to be calculated; and predicting the three-dimensional boundary layer transition line of the underwater vehicle.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic research, and particularly relates to a method for predicting the three-dimensional boundary layer transition line of an underwater vehicle. Background Art

[0002] The boundary layer flow on the head surface of an underwater vehicle can be divided into three stages: the laminar stage, the transition stage, and the turbulent stage. Among them, the laminar stage is relatively quiet, the wall pulsating pressure is weak, and the interference to the head sonar is weak; the turbulent stage is relatively noisy, the wall pulsating pressure is strong, and the interference to the head sonar is relatively obvious; while the noise in the transition stage is very strong, and the interference to the head sonar is very significant. If the position of the transition section can be delayed and the range of the quiet laminar section can be expanded, the total flow noise interference received by the head sonar can be reduced, thereby improving its detection ability. Therefore, controlling the transition of the boundary layer is an important issue to be considered in the design of underwater vehicles. To achieve the control of transition, the transition position needs to be predicted first. When the head of the underwater vehicle is a three-dimensional surface, or when the two-dimensional rotating body surface is floating, diving, turning, encountering ocean currents, etc., the boundary layer at the head is three-dimensional, and the existing stability analysis and transition prediction methods for the two-dimensional surface boundary layer in water medium are no longer applicable.

[0003] Currently, there is no research on the method for predicting the three-dimensional boundary layer transition of an underwater vehicle in the publicly published literature. The related research that has been published is mainly on the prediction of the two-dimensional surface boundary layer transition of an underwater vehicle. Liu et al. (2021) used the eN method based on linear stability analysis to analyze the flow stability and transition characteristics of the two-dimensional surface boundary layer of an underwater rotating body, and further studied the influence of different bow shapes and oncoming flow velocities on the flow stability and transition characteristics.

[0004] In summary, it is of great guiding significance to explore a feasible and reasonable prediction technology and method for the transition position of the three-dimensional boundary layer of an underwater vehicle. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the three-dimensional boundary layer transition line of an underwater vehicle with high accuracy and applicable to engineering. The technical solution of the present invention is as follows:

[0006] A method for predicting the three-dimensional boundary layer transition line of an underwater vehicle, comprising the following steps:

[0007] Step 1: Determine the shape and navigation conditions of the underwater vehicle, and calculate the three-dimensional laminar basic flow field of the underwater vehicle;

[0008] Step 2: Analyze and determine the propagation direction of small disturbances in the three-dimensional boundary layer of the underwater vehicle, including the following steps:

[0009] 1) Calculate the distribution of the basic flow energy on the wall normal, find the first maximum value of the basic flow energy, and the distance from the first maximum point to the vehicle wall is the boundary layer thickness, and the position of the maximum point is the outer edge position of the boundary layer;

[0010] 2) Analyze the velocity at the outer edge position of the boundary layer, calculate the tangential velocity at the outer edge position of the boundary layer in step 1), take its velocity direction as the potential flow direction, and take the potential flow direction as the small perturbation propagation direction;

[0011] Step 3: Determine the set of frequency points to be calculated. For an input frequency f in the set of frequency points, after calculating the dimensionless circular frequency ω, analyze the amplitude growth rate of the three-dimensional small perturbations at each station of the underwater vehicle and calculate the critical instability line at this input frequency, including the following:

[0012] 1) Establish a linearized perturbation equation for the dimensionless three-dimensional flow;

[0013] 2) Use the approximate parallel flow assumption in the potential flow direction of the surface boundary layer to obtain a perturbation expansion in the form of a traveling wave; substitute the perturbation expansion into the linearized perturbation equation to obtain the linear stability equation;

[0014] 3) From the linear stability equation, using numerical calculation methods, obtain the characteristic relationship between the wave numbers α and β and the circular frequency ω at different stations on the wall of the underwater vehicle; at a certain circular frequency ω, take the potential flow direction as the small perturbation propagation direction at each station, and use the saddle point method to determine the amplitude growth rate of the small perturbations at each station, that is, use the characteristic relationship to find all β that satisfy and the corresponding growth rate σ = -α r , and consider the local most dangerous situation, that is, the situation with the largest growth rate, to obtain the small perturbation amplitude growth rate σ i ,; g ;

[0015] 4) For each input frequency f in the set of frequency points, starting from an input meridian plane of the underwater vehicle, find the point where the first small perturbation amplitude growth rate is zero, so as to determine the critical instability curve of the underwater vehicle at the input frequency f;

[0016] Step 4: After inputting a meridian plane, calculate the three-dimensional small perturbation amplitude amplification factor of the underwater vehicle at the input frequency f, including the following:

[0017] It is considered that the small perturbations in the boundary layer at the frequency f can continue to grow to the transition position. The small perturbations with the circular frequency ω start from the intersection point S 0 of the input meridian plane and the critical instability curve obtained in step 3), and propagate along the small perturbation propagation direction to the amplification coefficient at the station S, that is, the small perturbation amplitude amplification factor N;

[0018] At the input frequency f, at the intersection point S of the critical instability curve obtained from the input meridional plane and step three 0 starting from this point, calculate the disturbance amplitude amplification factor N at each point on the disturbance propagation curve by integrating according to formula (4);

[0019] Traverse all the meridional planes that need to be calculated;

[0020] Obtain the small disturbance amplitude amplification factor N(q 1 ,q 3 ,f) at each station of the underwater vehicle at the input frequency f;

[0021] Change the frequency f, and then perform the calculations in steps 4) of step three and step four until all the frequencies f that need to be calculated are traversed and then enter step five;

[0022] Step five: Predict the three-dimensional boundary layer transition line of the underwater vehicle, including the following:

[0023] 1) Calculate the maximum value of the small disturbance amplitude amplification factor at each station of the underwater vehicle in step four, that is

[0024] 2) When the amplitude of the small disturbance reaches times the initial amplitude, the laminar flow develops into turbulent flow; take the curve determined by N max (q 1 ,q 3 ) = N T as the three-dimensional boundary layer transition line of the underwater vehicle.

[0025] Furthermore, the basic flow energy is where u is the velocity in the potential flow direction, v is the normal velocity, and w is the velocity perpendicular to the potential flow direction.

[0026] Furthermore, in 1) of step three, the linearized perturbation equation (1) of the dimensionless three-dimensional flow is:

[0027]

[0028] where t is time, q 1 , q 2 and q 3 are the coordinates parallel to the wall in the potential flow direction, normal to the wall, and parallel to the wall and perpendicular to the potential flow direction respectively, Γ′, A′, B′, C′, D′, V′ 11 , V′ 22 , V′ 33 , V′ 12 , V′ 13 , V′ 23 are coefficient matrices, and φ′ = (u′, v′, w′, p′) Tis the perturbation vector, and φ′ is a function of t, q 1 , q 2 , q 3 , where u′ is the perturbation of the velocity in the potential flow direction, v′ is the perturbation of the normal velocity, w′ is the perturbation of the velocity perpendicular to the potential flow direction, and p′ is the perturbation of the pressure.

[0029] Furthermore, in step 3), 2), the perturbation expansion (2) in the form of a traveling wave is obtained as:

[0030]

[0031] where is the eigenfunction vector of the perturbation, ω is the circular frequency, α is the wave number in the potential flow direction, β is the wave number perpendicular to the potential flow direction, c.c. is the complex conjugate. For the spatial mode problem, α = α r + iα i is a complex number, and β = β r is a real number.

[0032] Furthermore, the linear stability equation is:

[0033]

[0034] where is the coefficient matrix, which includes the basic flow, the curvature C s in the potential flow direction of the wall, and the curvature C g perpendicular to the potential flow direction, the circular frequency ω, the wave numbers α and β, and the Reynolds number Re.

[0035] Furthermore, the amplification factor N of the small perturbation amplitude is given by equation (4):

[0036]

[0037] where A represents the amplitude of the small perturbation at station S, A 0 represents the amplitude of the small perturbation at station S 0 , and S 0 S represents the perturbation propagation curve that propagates from station S 0 to station S.

[0038] Furthermore, the method in step 5) is:

[0039] 1) Calculate the maximum value of the amplification factor of the small perturbation amplitude at each station of the underwater vehicle in step 4), i.e.,

[0040] 2) When the amplitude of the small perturbation reaches times the initial amplitude, the laminar flow develops into turbulent flow; set N max (q 1 , q 3) = N T The determined curve is used as the three-dimensional boundary layer transition line of the underwater vehicle.

[0041] Furthermore, the transition criterion N T takes 7.

[0042] Furthermore, the method for determining the set of frequency points is as follows: Set the initial value of frequency calculation to 5000 Hz. For the current calculated frequency f, after calculating the circular frequency ω, calculate the growth rate σ of the small disturbance propagation amplitude at each station of the underwater vehicle g , if the growth rates of the small disturbance propagation amplitudes at all stations are less than 0, then reduce the frequency and recalculate until the growth rate σ of the small disturbance propagation amplitude at a certain station of the underwater vehicle g is greater than 0. At this time, the frequency f is the upper bound of the set of frequency points to be calculated, and frequency points are selected between 0 Hz and this upper bound to form the set of frequency points to be calculated.

[0043] Furthermore, the curvature in the potential flow direction and the curvature perpendicular to the potential flow direction in step three are determined by the second fundamental form of the surface in differential geometry.

[0044] Advantages of the present invention compared with the prior art:

[0045] (1) The present invention establishes a prediction method for the transition line of three-dimensional surface boundary layer flow applicable to underwater vehicles, with curvature in the potential flow direction and curvature perpendicular to the potential flow direction;

[0046] (2) The present invention uses an analysis method based on the theory of flow stability to predict the transition line of the three-dimensional boundary layer of underwater vehicles under complex working conditions. It has a small amount of calculation, is simple, relatively accurate, has strong universality, and is applicable to engineering. Description of the Drawings

[0047] Figure 1 is the flow chart of the steps of the present invention

[0048] Figure 2 is the axial velocity profile within the boundary layer at the selected station

[0049] Figure 3 is the circumferential velocity profile within the boundary layer at the selected station

[0050] Figure 4 is the growth rate σ = -α i and the relationship diagram of the spanwise wave number β r

[0051] Figure 5 is the critical instability curve (purple curve) at f = 385.1 Hz and the corresponding growth rate σ g contour plot

[0052] Figure 6 ​The critical instability curve (purple curve) with f = 270.7 Hz and the corresponding growth rate σ g Contour plot

[0053] Figure 7 The critical instability curve (purple curve) with f = 98.5 Hz and the corresponding growth rate σ g Contour plot

[0054] Figure 8 The small perturbation amplitude amplification factor N(q 1 , q 3 , f) contour plot for f = 385.1 Hz

[0055] Figure 9 The small perturbation amplitude amplification factor N(q 1 , q 3 , f) contour plot for f = 270.7 Hz

[0056] Figure 10 The small perturbation amplitude amplification factor N(q 1 , q 3 , f) contour plot for f = 98.5 Hz

[0057] Figure 11 The maximum value N of the small perturbation amplitude amplification factor max (q 1 , q 3 ) contour plot and transition line (black curve) Specific embodiments

[0058] The present invention will be described in detail below in conjunction with specific embodiments and the accompanying drawings. In the following description, for purposes of explanation and not limitation, specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details.

[0059] It should be noted here that in order to avoid obscuring the present invention with unnecessary details, only the device structures and / or processing steps closely related to the solution according to the present invention are shown in the drawings, while other details less relevant to the present invention are omitted.

[0060] An embodiment of the present invention provides a method for predicting the three-dimensional boundary layer transition line of an underwater vehicle, as Figure 1 shown, including the following steps:

[0061] Step 1: Determine the shape and navigation conditions of the underwater vehicle, and calculate the three-dimensional laminar basic flow field of the underwater vehicle. The three-dimensional laminar basic flow field is obtained by solving the steady incompressible Navier-Stokes equations.

[0062] In this step, the calculation object is the flow of the boundary layer around the axisymmetric body SUBOFF model (the geometric values are disclosed in Groves, NC, Huang, TT, Chang, MS. Geometric characteristics of DARPA SUBOFF Models (DTRC Model Numbers 5470 and 5471). DTRC / SHD-1298-01, David Taylor Research Center, Maryland, (1989).);

[0063] The calculation condition is an angle of attack of 1°, and the sailing speed U ∞ = 5 m / s. In this step, a sufficient number of grids need to be ensured within the boundary layer of the laminar basic flow to meet the requirements of subsequent stability analysis. The calculated axial position is x = 0.26 m. The velocity profile results of the laminar basic flow boundary layer of the 30° meridian plane starting from the leeward side are as Figure 2 、 Figure 3 shown. In the figure, q 2 represents the normal coordinate, respectively represent the dimensionless axial velocity and the dimensionless circumferential velocity. In this embodiment, the Fluent software is used to calculate the flow field distribution of the laminar basic flow of the underwater vehicle at the angle of attack;

[0064] Step 2: Analyze and determine the propagation direction of small disturbances in the three-dimensional boundary layer of the underwater vehicle, including the following:

[0065] 1) Calculate the distribution of the basic flow energy on the wall normal (where u is the velocity in the potential flow direction, v is the normal velocity, and w is the velocity perpendicular to the potential flow direction), find the first maximum value of the basic flow energy. The distance from the first maximum value point to the wall of the underwater vehicle is the boundary layer thickness, and the position of the maximum value point is the outer position of the boundary layer;

[0066] 2) Analyze the velocity at the outer position of the boundary layer, calculate the tangential velocity at the outer position of the boundary layer in step 1), take its velocity direction as the potential flow direction, and use the potential flow direction as the propagation direction of small disturbances;

[0067] Step 3: Determine the set of frequency points to be calculated. After inputting a frequency f in the set of frequency points and calculating the dimensionless circular frequency ω, analyze the amplitude growth rate of three-dimensional small disturbances at each station of the underwater vehicle and calculate the critical instability line at this frequency, including the following:

[0068] 1) Establish the linearized perturbation equation (1) of the dimensionless three-dimensional flow

[0069]

[0070] where t is time, q 1 , q 2 and q 3 are the potential flow direction parallel to the wall, the normal direction of the wall, and the coordinates parallel to the wall and perpendicular to the potential flow direction respectively. Γ′, A′, B′, C′, D′, V′ 11 , V′ 22 , V′ 33 , V′ 12 , V′ 13 , V′ 23 are coefficient matrices, φ′ = (u′, v′, w′, p′) T is the perturbation vector, and φ′ is a function of t, q 1 , q 2 , q 3 . u′ is the perturbation of the velocity in the potential flow direction, v′ is the perturbation of the normal velocity, w′ is the perturbation of the velocity perpendicular to the potential flow direction, and p′ is the perturbation of the pressure;

[0071] 2) Using the approximate parallel flow assumption in the potential flow direction of the curved surface boundary layer, the perturbation expansion (2) in the form of a traveling wave is obtained

[0072]

[0073] where is the eigenfunction vector of the perturbation, ω is the circular frequency, α is the wave number in the potential flow direction, β is the wave number perpendicular to the potential flow direction, c.c. is the complex conjugate. For the spatial mode problem, α = α r + iα i is a complex number, β = β r is a real number. Substituting the perturbation expansion (2) into the linearized perturbation equation (1), the linear stability equation (3) is obtained

[0074]

[0075] where is the coefficient matrix, which includes the basic flow, the curvature C s in the potential flow direction of the wall and the curvature C g perpendicular to the potential flow direction, the circular frequency ω, the wave numbers α and β, and the Reynolds number Re;

[0076] 3) From the linear stability equation (3), using numerical calculation methods, the characteristic relationships of the wave numbers α, β and the circular frequency ω at different stations on the wall of the underwater vehicle can be obtained. At a certain circular frequency ω, taking the potential flow direction as the propagation direction of small perturbations at each station, the growth rate of the propagation amplitude of small perturbations at each station can be determined using the saddle point method, that is, all β satisfying r and the corresponding growth rate σ = -α i, and considering the most dangerous situation locally, i.e., the situation with the largest growth rate, the growth rate σ of the small disturbance amplitude is obtained g . Starting from the initial value of the higher frequency f (for an underwater vehicle, the initial value of the general frequency f is 5000 Hz), after calculating the circular frequency ω, calculate the growth rate σ of the small disturbance propagation amplitude at each station of the underwater vehicle g . If the growth rates of the small disturbance propagation amplitudes at all stations are less than 0, then reduce the frequency f and recalculate until the growth rate σ of the small disturbance propagation amplitude at a certain station of the underwater vehicle g is greater than 0. At this time, the frequency f is the upper bound of the set of frequency points to be calculated, and 20 - 60 frequencies are evenly selected between 0 Hz and this upper bound to form the set of frequency points to be calculated;

[0077] 4) Input a frequency f in the set of frequency points to be calculated. Starting from each meridian plane of the underwater vehicle in step one, find the point where the growth rate of the small disturbance amplitude is zero for the first time, so as to determine the critical instability curve of the underwater vehicle at the input frequency f;

[0078] In this step, the method for establishing the linear perturbation equation of the dimensionless three-dimensional flow and the eigenvalue analysis method of the stability equation can adopt the means well-known in the art. For details, see "Flow Stability", Zhou Heng et al., National Defense Industry Press;

[0079] In this step, the growth rate σ = -α i and the relationship with the spanwise wave number β r is as shown in Figure 4 . It can be seen that there are three points A, B, and C for the spanwise wave number β that satisfies . Take the maximum value of the growth rate σ = -α r as the growth rate σ of the small disturbance propagation amplitude i , that is, point C; g

[0080] In this step, the critical instability curves and the corresponding growth rate nephograms obtained at the frequencies f = 385.1 Hz, 270.7 Hz, and 98.5 Hz are respectively as shown in Figure 5 , Figure 6 , Figure 7 . The purple curve in the figure is the critical instability curve, and the black curve is the disturbance propagation curve;

[0081] Step four: After inputting the meridian plane, calculate the three-dimensional small disturbance amplitude amplification factor of the underwater vehicle at the frequency f input in step three, including the following:

[0082] It is considered that the small disturbance within the boundary layer at the frequency f can continuously grow to the transition position, and the small disturbance of the circular frequency ω starts from the intersection point S of the input meridian plane and the critical instability curve obtained in step three 0The amplification factor that starts from a certain point and propagates along the small perturbation propagation direction to station S, that is, the small perturbation amplitude amplification factor N, is given by Equation (4):

[0083]

[0084] where A represents the amplitude of the small perturbation at station S, A 0 represents the amplitude of the small perturbation at station S 0 ; S 0 S represents the perturbation propagation curve that starts from station S 0 and propagates to station S

[0085] At the input frequency f, starting from the intersection point S of the critical instability curve obtained from the input meridional plane and step 3 0 , the perturbation amplitude amplification factor N at each point on the perturbation propagation curve is calculated by integrating according to Equation (4);

[0086] Traverse all the meridional planes to be calculated, and obtain the small perturbation amplitude amplification factor N(q 1 , q 3 , f) of each station of the underwater vehicle at the input frequency f in step 3; change the frequency f, and then perform the calculations in steps 4) and 5 in step 3 until all the frequencies f to be calculated are traversed and then enter step 5;

[0087] In this step, the upper bound of the set of frequency points to be calculated is 417.0 Hz;

[0088] In this step, 53 frequencies are evenly calculated between the frequency f = 2.9 Hz and the upper bound 417.0 Hz;

[0089] In this step, the cloud diagrams of the small perturbation amplitude amplification factor N(q 1 , q 3 , f) at the frequencies f = 385.1 Hz, 270.7 Hz, and 98.5 Hz are respectively as shown in Figure 8 , Figure 9 , Figure 10 ; the purple curve in the figure is the critical instability curve, and the black curve is the perturbation propagation curve;

[0090] Step 5: Predict the three-dimensional boundary layer transition line of the underwater vehicle, including the following:

[0091] 1) Calculate the maximum value of the small perturbation amplitude amplification factor of each station of the underwater vehicle in step 4, that is

[0092] 2) When the amplitude of the small perturbation reaches times the initial amplitude, the laminar flow develops into turbulent flow; let N max (q 1 , q 3) = N T The determined curve serves as the three-dimensional boundary layer transition line of the underwater vehicle.

[0093] In this step, based on the understanding of the natural transition of the boundary layer, it can be considered that as long as the amplitude of the small disturbance wave of a certain frequency reaches the initial amplitude times during the development along the flow direction, the laminar flow develops into turbulent flow.

[0094] In this step, N T used as the transition criterion T The value of is calibrated by experiments, and the transition criterion is taken as N max

[0095] In this step, the maximum value N max (q 1 , q 3 ) cloud diagram is as Figure 11 shown.

[0096] In this step, the obtained transition line is as shown by the black curve in Figure 11 . It can be seen that the transition position on the leeward side is forward, and the transition position on the windward side is backward.

[0097] The features described and / or illustrated above for one embodiment can be used in the same or similar manner in one or more other embodiments, and / or combined with the features in other embodiments or replace the features in other embodiments.

[0098] It should be emphasized that the term "including / comprising" when used herein refers to the presence of features, whole things, steps or components, but does not exclude the presence or addition of one or more other features, whole things, steps, components or their combinations. 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 that when executed by a logic component, can enable the logic component to implement the devices or components described above, or enable the logic component to implement the various methods or steps described above. The present invention also relates to a storage medium for storing the above program, such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, etc.

[0099] Many features and advantages of these embodiments are clear from this detailed description, so 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 easily conceivable 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 can cover all suitable modifications and equivalents falling within their scope.

[0100] The parts not detailed in the present invention are well-known technologies to those skilled in the art.

Claims

1. A method for predicting a three-dimensional boundary layer transition line of an underwater vehicle, comprising the following steps: Step 1: Determine the shape and navigation conditions of the underwater vehicle, and calculate the three-dimensional laminar basic flow field of the underwater vehicle; Step 2: Analyze and determine the propagation direction of small disturbances in the three-dimensional boundary layer of the underwater vehicle, including the following steps: 1) Calculate the distribution of basic flow energy on the wall normal line and find the first maximum value of basic flow energy. The distance from the first maximum point to the wall of the navigation body is the boundary layer thickness, and the position of the maximum point is the outer edge of the boundary layer; 2) Analyze the velocity at the outer edge of the boundary layer, calculate the tangential velocity at the outer edge of the boundary layer in step 1), take its velocity direction as the potential flow direction, and take the potential flow direction as the propagation direction of the small disturbance; Step 3: Determine the frequency point set to be calculated. For an input frequency f in the frequency point set, after calculating the dimensionless circular frequency ω, analyze the amplitude growth rate of the three-dimensional small disturbance at each station of the underwater vehicle at this input frequency and calculate the critical instability line, including the following: 1) Establish the linearized perturbation equation of dimensionless three-dimensional flow; 2) using the approximate parallel flow assumption in the direction of the potential flow of the curved boundary layer to obtain a disturbance expansion in the form of a traveling wave; substituting the disturbance expansion into the linearized disturbance equation to obtain a linear stability equation; 3) Using the linear stability equation and numerical calculation method, the characteristic relationship between the wave numbers α, β and the circular frequency ω at different positions on the wall of the underwater vehicle is obtained; At a certain circular frequency ω, the potential flow direction is taken as the propagation direction of small disturbances at each station, and the saddle point method is used to determine the growth rate of the propagation amplitude of small disturbances at each station, that is, the characteristic relationship is used to obtain all the conditions that satisfy Beta r And the corresponding growth rate σ=-α i , and considering the most dangerous local situation with the largest growth rate, the small disturbance amplitude growth rate σ is obtained g ; 4) For each input frequency f in the frequency point set, starting from an input meridian plane of the underwater vehicle, find the first point where the small disturbance amplitude growth rate is zero, thereby determining the critical instability curve of the underwater vehicle at the input frequency f; Step 4: After inputting a meridian plane, the three-dimensional small disturbance amplitude amplification factor of the underwater vehicle is calculated at the input frequency f, including the following: It is assumed that the small disturbance at the frequency f in the boundary layer can continue to grow to the transition position. The small disturbance of circular frequency ω starts from the intersection S0 of the input meridian plane and the critical instability curve obtained in step 3 and propagates along the propagation direction of the small disturbance to the station S. The amplification factor is the small disturbance amplitude amplification factor N. At the input frequency f, starting from the intersection S0 of the input meridian plane and the critical instability curve obtained in step 3, the disturbance amplitude amplification factor N of each point on the disturbance propagation curve is calculated by integrating formula (4); Traverse all meridian planes that need to be calculated; Obtain the small disturbance amplitude amplification factor N(q1,q3,f) of each station of the underwater vehicle at the input frequency f; Change the frequency f, and then perform the calculations in step 3 (4) and step 4, until all the frequencies f that need to be calculated are traversed and then proceed to step 5; Step 5: Predict the three-dimensional boundary layer transition line of the underwater vehicle.

2. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 1, characterized in that: The basic flow energy is Where u is the velocity in the potential flow direction, v is the normal velocity, and w is the velocity in the direction perpendicular to the potential flow.

3. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 1, characterized in that: In step 3, the linearized perturbation equation (1) of the dimensionless three-dimensional flow is established as follows: Where t is the time, q1, q2 and q3 are the potential flow direction parallel to the wall, the normal to the wall, and the coordinates parallel to the wall and perpendicular to the potential flow direction, Γ′, A′, B′, C′, D′, V′ 11 , V′ 22 , V′ 33 , V′ 12 , V′ 13 , V′ 23 is the coefficient matrix, φ′=(u′,v′,w′,p′) T is the disturbance vector, and φ′ is a function of t, q1, q2, q3, u′ is the velocity disturbance in the potential flow direction, v′ is the normal velocity disturbance, w′ is the velocity disturbance in the direction perpendicular to the potential flow, and p′ is the pressure disturbance.

4. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 3, characterized in that: 2) in step 3, the disturbance expansion (2) in the form of traveling wave is obtained as follows: in is the characteristic function vector of the disturbance, ω is the circular frequency, α is the wave number in the potential flow direction, β is the wave number in the perpendicular potential flow direction, cc is the complex conjugate, for the spatial mode problem, α=α r +iα i is a complex number, β=β r is a real number.

5. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 4, characterized in that: The linear stability equation is: in, is a coefficient matrix, which contains the basic flow, the potential flow direction curvature C of the wall s and the curvature C in the direction perpendicular to the potential flow g , circular frequency ω, wave numbers α and β, and Reynolds number Re.

6. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 5, characterized in that: The small disturbance amplitude amplification factor N is given by formula (4): Where A represents the amplitude of the small disturbance at station S, A0 represents the amplitude of the small disturbance at station S0, and S0S represents the disturbance propagation curve from station S0 to station S.

7. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 1, characterized in that: The method of step five is: 1) Calculate the maximum value of the small disturbance amplitude amplification factor of each station of the underwater vehicle in step 4, that is, 2) When the amplitude of the small disturbance reaches the initial amplitude times, the laminar flow develops into turbulent flow; max (q1,q3)=N T The determined curve is taken as the three-dimensional boundary layer transition line of the underwater vehicle.

8. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 7, characterized in that: Transition criterion N T Take 7.

9. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 1, characterized in that: The method for determining the frequency point set is as follows: the initial value of the frequency calculation is set to 5000 Hz. For the current calculation frequency f, after calculating the circular frequency ω, the growth rate σ of the propagation amplitude of small disturbances at each station of the underwater vehicle is calculated. g If the growth rate of the propagation amplitude of small disturbances at each station is less than 0, then reduce the frequency and recalculate until the growth rate of the propagation amplitude of small disturbances at a station of the underwater vehicle is σ g If it is greater than 0, the frequency f at this time is the upper limit of the frequency point set to be calculated, and the frequency points are selected between 0 Hz and this upper limit to form the frequency point set to be calculated.

10. The method for predicting the three-dimensional boundary layer transition line of an underwater vehicle according to claim 1, characterized in that: The curvature in the potential flow direction and the curvature in the perpendicular potential flow direction in step three are determined by the second fundamental form of the surface in differential geometry.

Images