A method for predicting the transition position of the boundary layer of a hydrofoil

Abstract

The present invention relates to a method for predicting the transition position of a hydrofoil boundary layer, and belongs to the technical field of hydrodynamic research. The method for predicting the transition position of a hydrofoil boundary layer comprises the following steps: S1, obtaining a hydrofoil discrete grid; S2, solving the hydrofoil laminar flow field; S3, calculating the local wall tangential velocity; S4, obtaining the growth rate of the instability frequency disturbance; S5, obtaining the amplification factor cloud map of small disturbances of different frequencies; S6, predicting the transition position of the hydrofoil boundary layer. The method for predicting the transition position of a hydrofoil boundary layer can draw a vertical grid with a curved surface shape of a leading edge and a trailing edge through the curved surface adaptive vertical grid technology, thereby improving the prediction accuracy of the transition position; by respectively analyzing and calculating the data of the suction surface and the pressure surface, the transition positions of the suction surface and the pressure surface are obtained, which is suitable for asymmetric airfoils and airfoils with an angle of attack, and can accurately predict the transition position of the hydrofoil under complex conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of hydrodynamics research, and in particular relates to a method for predicting the transition position of a hydrofoil boundary layer. Background Art

[0002] In recent years, with the increase in speed, the flow noise problem of underwater vehicles has gradually become prominent. Flow noise is the sound caused by the relative movement of the fluid and the vehicle causing the fluctuation of fluid pressure, among which the airfoil appendages of the vehicle (hull, rudder, stern wing) are one of the important sources. At high flow rates, the airfoil flow noise even increases at the 10th power of the flow velocity. Therefore, suppressing the flow noise of the airfoil is one of the keys to improving the concealment capability of underwater vehicles, which is also an important technical bottleneck facing the development of underwater vehicles in my country. On the airfoil surface, the flow state of the boundary layer will go through a stage from laminar flow to turbulent flow, that is, transition. Strong nonlinear interactions will occur in the transition zone, which is physically manifested as a local surge in pulsating pressure and noise, which is stronger than both laminar flow and turbulent flow. From the source of noise, it can be seen that in order to suppress the airfoil flow noise, it is first necessary to accurately predict the transition position of the boundary layer, and then achieve the purpose of noise reduction by affecting the transition position.

[0003] In the prior art, Chinese invention patent application CN118673593A discloses a method for predicting the transition line of the three-dimensional boundary layer of an underwater vehicle, which is used to predict the transition line of the boundary layer of the bow surface of an underwater vehicle. However, the hydrofoil structure has both a leading edge and a trailing edge, which is different from the boundary layer of the bow surface of an underwater vehicle; and sometimes the airfoil geometry is not symmetrical, or the incoming flow has an angle of attack, which will result in the absence of a similarity solution for the flow field, and the flow becomes more complex and non-steady. Therefore, the method provided by the patent is not suitable for predicting the transition position of the airfoil.

[0004] Therefore, how to provide a method to predict the transition position of the hydrofoil boundary layer is a technical problem that urgently needs to be solved. Summary of the invention

[0005] In view of the shortcomings in the prior art, the present invention provides a method for predicting the transition position of the hydrofoil boundary layer, which can accurately predict the transition position of the hydrofoil under complex conditions, and provide a theoretical basis and technical support for reducing the flow noise of underwater airfoil structures in engineering.

[0006] The present invention provides a method for predicting the transition position of a hydrofoil boundary layer, comprising the following steps:

[0007] S1, obtain the hydrofoil discrete grid: divide the computational domain of the hydrofoil, and use the surface adaptive vertical grid technology to draw the discrete grid wrapping the hydrofoil perpendicular to the wall;

[0008] S2, solve the laminar flow field of the hydrofoil: according to the hydrofoil discrete grid, set the boundary conditions that meet the physical reality at the boundary of the computational domain, solve the Navier-Stokes equations satisfied by the fluid motion on each discrete grid, and obtain the The flow field pressure and velocity of the hydrofoil discrete grid at time t;

[0009] S3, calculate the local wall tangential velocity: transform the flow field velocity into the local orthogonal body-fitting coordinate system, calculate the wall tangential velocity of each discrete grid, and then obtain the change of the wall tangential velocity along the wall normal, and use the finite difference method to obtain the first-order derivative and second-order derivative of the wall tangential velocity along the normal;

[0010] S4, obtain the growth rate of the instability frequency disturbance: decompose the instantaneous quantity of the hydrofoil flow into the basic flow and the disturbance quantity, derive the nonlinear disturbance equation satisfied by the disturbance quantity, and obtain the linearized disturbance equation after ignoring the high-order small quantity of the small disturbance; based on the parallel flow assumption, obtain the linear stability equation, and obtain the growth rate of all instability frequency disturbances according to the linear stability equation;

[0011] S5, obtaining the cloud map of amplification factors of small disturbances of different frequencies: according to the growth rate of small disturbances of different frequencies during propagation, respectively calculate the growth rate of small disturbance amplitudes of different frequencies on the suction surface and the pressure surface at each grid along the hydrofoil surface, obtain the amplification factors of small disturbances of different frequencies, and obtain the cloud map of amplification factors;

[0012] S6, predict the transition position of the hydrofoil boundary layer: according to the cloud diagram of the amplification factor of small disturbances of different frequencies, use the solution form of small disturbances to determine the amplification factor of small disturbances, so as to obtain the growth factor of small disturbances ; Take the envelope of all small disturbances of instability frequency on the suction surface and pressure surface respectively, and draw the envelope line. When the growth multiple of a certain unstable small disturbance reaches the growth threshold, it is considered that the flow direction position of the small disturbance corresponding to the growth threshold at this time is the transition position of the hydrofoil boundary layer, and then the transition positions of the suction surface and pressure surface are obtained respectively.

[0013] In some of the embodiments, a size of three times the chord length of the hydrofoil is selected as the size of the calculation domain.

[0014] In some embodiments, in step S2, according to formula (1), The flow field pressure and velocity of the discrete grid at the moment, where the flow field velocity includes the stream velocity and the normal velocity; the flow direction of the fluid motion on each discrete grid is recorded as Axis, normal to Axis, spanwise axis, the expression of formula (1) is:

[0015] (1);

[0016] In formula (1), is the flow field pressure, is the flow velocity, is the normal velocity, is the fluid density, is the kinematic viscosity coefficient of the fluid.

[0017] In some of the embodiments, the incoming flow velocity is given as the inlet condition at the entrance of the computational domain, and the free outflow boundary condition is adopted in the far field of the computational domain, the diffusion flux satisfying all flow variables is 0, and the time step of the unsteady solution is 0.0002 seconds; when the flow in the boundary layer no longer changes with time, it is considered that the laminar boundary layer flow reaches a steady state, and at this time, the pressure and velocity of the hydrofoil laminar flow field are obtained according to formula (1).

[0018] In some embodiments, in step S3, the wall tangential velocity of each discrete grid is calculated according to formula (2), and the expression of formula (2) is:

[0019] (2);

[0020] In formula (2), is the wall tangential velocity, is the wall tangent inclination angle.

[0021] In some of the embodiments, after the wall tangential velocity is calculated, a five-point fourth-order difference format is used to solve the first-order derivative and the second-order derivative of the wall tangential velocity, wherein the difference format is reduced in order near the wall.

[0022] In some embodiments, in step S4, the linear stability equation is expressed as shown in equation (3):

[0023] (3);

[0024] In formula (3), is the characteristic function, , used to describe the profile information of small disturbances in the form of traveling waves; represents the normal direction of fluid motion in the local orthogonal body-fitting coordinate system; , , is the coefficient matrix containing the streamwise wavenumbers of small perturbations and circular frequency , also includes the first-order derivative and second-order derivative of the wall tangential velocity obtained in step S3; in the spatial mode, is a plural number, represented by , the imaginary part of the wave number is the spatial growth rate of the disturbance, is the streamwise wave number in real form.

[0025] In some of the embodiments, according to the physical condition that small perturbations tend to zero at the wall and at infinity, there are boundary conditions when applying equation (3), and the boundary conditions are as follows:

[0026] (4);

[0027] In formula (4), For small disturbances The distance between the axis and the hydrofoil boundary layer, the flow direction of the fluid motion in the local orthogonal body-fitting coordinate system is recorded as , the extension direction is , The small disturbance edge The speed in the axis direction.

[0028] In some of the embodiments, in step S5, the growth rate of the small disturbance amplitude of different frequencies on the suction surface at each grid along the hydrofoil surface is calculated using formula (5), and the expression of formula (5) is:

[0029] (5);

[0030] In formula (5), is the magnification factor, is the frequency, and are two adjacent grids, From the grid To Grid The arc length at For Grid The growth rate at For Grid The growth rate at .

[0031] In some embodiments, in step S6, the growth threshold is .

[0032] Based on the above scheme, the prediction method of the transition position of the hydrofoil boundary layer in the embodiment of the present invention can draw a vertical grid with a curved surface shape having a leading edge and a trailing edge through the surface adaptive vertical grid technology, and can avoid errors caused by the interpolation process after introducing the local orthogonal body-fitting coordinate system in subsequent steps. At the same time, the grid is more conducive to the stability of numerical calculations, and the unsteady calculation process is less likely to diverge, which can improve the prediction accuracy of the transition position; by separately analyzing and calculating the data of the suction surface and the pressure surface, the transition position of the suction surface and the pressure surface is obtained. It is suitable for asymmetric airfoils and airfoils with an angle of attack, and can accurately predict the transition position of the hydrofoil under complex conditions, providing a theoretical basis and technical support for reducing the flow noise of underwater airfoil structures in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0034] Figure 1 A flow chart of a method for predicting the transition position of the hydrofoil boundary layer;

[0035] Figure 2 is the geometric shape of the NACA16 hydrofoil in Example 1 of the present invention;

[0036] Figure 3 is the discrete grid of the NACA16 hydrofoil in Example 1 of the present invention;

[0037] Figure 4 is a flow field pressure cloud diagram of a NACA16 hydrofoil in Example 1 of the present invention;

[0038] Figure 5 : is a flow field and flow direction velocity cloud diagram of the NACA16 hydrofoil in Example 1 of the present invention;

[0039] Figure 6 is a cloud diagram of the normal velocity of the flow field of the NACA16 hydrofoil in Example 1 of the present invention;

[0040] Figure 7 is the tangential velocity distribution of the inner wall surface of the boundary layer at 0.78 m on the suction surface of the NACA16 hydrofoil in Example 1 of the present invention;

[0041] Figure 8 is a distribution cloud diagram of the growth rate of the instability disturbance of the suction surface of the NACA16 hydrofoil in Example 1 of the present invention;

[0042] Fig. 9 is a cloud diagram of the amplification factor of the instability disturbance of the suction surface of the NACA16 hydrofoil in Example 1 of the present invention;

[0043] Fig.10 is the envelope of the amplification factor of the instability disturbances of different frequencies on the suction surface of the NACA16 hydrofoil in Example 1 of the present invention;

[0044] Fig.11 It is the boundary layer transition position of the suction surface and the pressure surface of the NACA16 hydrofoil in Example 1 of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0046] In the description of the present invention, it should be understood that the terms "center", "lateral", "longitudinal", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0047] like Figure 1 As shown, in one embodiment of the method for predicting the transition position of the hydrofoil boundary layer of the present invention, the method for predicting the transition position of the hydrofoil boundary layer comprises the following steps:

[0048] S1, obtain the hydrofoil discrete grid: divide the computational domain of the hydrofoil, and use the surface adaptive vertical grid technology to draw the discrete grid wrapping the hydrofoil perpendicular to the wall;

[0049] S2, solve the laminar flow field of the hydrofoil: according to the hydrofoil discrete grid, set the boundary conditions that meet the physical reality at the boundary of the computational domain, solve the Navier-Stokes equations satisfied by the fluid motion on each discrete grid, and obtain the The flow field pressure and velocity of the hydrofoil discrete grid at time t;

[0050] S3, calculate the local wall tangential velocity: transform the flow field velocity into the local orthogonal body-fitting coordinate system, calculate the wall tangential velocity of each discrete grid, and then obtain the change of the wall tangential velocity along the wall normal, and use the finite difference method to obtain the first-order derivative and second-order derivative of the wall tangential velocity along the normal;

[0051] S4, obtain the growth rate of the instability frequency disturbance: decompose the instantaneous quantity of the hydrofoil flow into the basic flow and the disturbance quantity, derive the nonlinear disturbance equation satisfied by the disturbance quantity, and obtain the linearized disturbance equation after ignoring the high-order small quantity of the small disturbance; based on the parallel flow assumption, obtain the linear stability equation, and obtain the growth rate of all instability frequency disturbances according to the linear stability equation;

[0052] S5, obtaining the cloud map of amplification factors of small disturbances of different frequencies: according to the growth rate of small disturbances of different frequencies during propagation, respectively calculate the growth rate of small disturbance amplitudes of different frequencies on the suction surface and the pressure surface at each grid along the hydrofoil surface, obtain the amplification factors of small disturbances of different frequencies, and obtain the cloud map of amplification factors;

[0053] S6, predict the transition position of the hydrofoil boundary layer: according to the cloud diagram of the amplification factor of small disturbances of different frequencies, use the solution form of small disturbances to determine the amplification factor of small disturbances, so as to obtain the growth factor of small disturbances ; Take the envelope of all small disturbances of instability frequency on the suction surface and pressure surface respectively, and draw the envelope line. When the growth multiple of a certain unstable small disturbance reaches the growth threshold, it is considered that the flow direction position of the small disturbance corresponding to the growth threshold at this time is the transition position of the hydrofoil boundary layer, and then the transition positions of the suction surface and pressure surface are obtained respectively.

[0054] In the above-mentioned schematic embodiment, the prediction method of the transition position of the hydrofoil boundary layer utilizes the surface adaptive vertical grid technology, which can draw a vertical grid with a curved surface shape having a leading edge and a trailing edge, and can avoid errors in the interpolation process after introducing the local orthogonal body-fitting coordinate system in the subsequent steps. At the same time, the grid is more conducive to the stability of numerical calculations, and the unsteady calculation process is less likely to diverge, which can improve the prediction accuracy of the transition position; by separately analyzing and calculating the data of the suction surface and the pressure surface, the transition position of the suction surface and the pressure surface is obtained, which is suitable for asymmetric airfoils and airfoils with an angle of attack, and can accurately predict the transition position of the hydrofoil under complex conditions, providing a theoretical basis and technical support for reducing the flow noise of underwater airfoil structures in engineering.

[0055] In step S2, it should be noted that the finite volume method is used to solve the Navier-Stokes equations. The Navier-Stokes equations are unsteady motion equations. When the flow in the boundary layer no longer changes with time, it is considered that the laminar boundary layer flow has reached a steady state, and the flow field pressure and velocity can be calculated.

[0056] In some embodiments, 3 times the hydrofoil chord length is selected as the size of the computational domain. By selecting 3 times the hydrofoil chord length as the size of the computational domain, it is possible to ensure that the computational region is large enough to capture the flow characteristics and interference effects near the hydrofoil, while reducing the impact of the computational boundary on the flow field, thereby improving the accuracy and reliability of the computational results.

[0057] It should also be noted that the surface adaptive vertical grid program is written based on FORTRAN language to automatically generate discrete grids. Among them, in the normal calculation domain close to the wall 20 times the boundary layer, the grid (including the leading and trailing edges of the hydrofoil) is vertical to the wall, such as Figure 3As shown in the figure, the orthogonal quality coefficient of such a grid is very close to 1. In addition, the flow direction and normal distribution of the grid follow the following principles: the hydrofoil flow direction grid first changes from dense to sparse, and then changes from sparse to dense; the hydrofoil normal grid is very dense near the wall, so that the grid can capture the complex boundary layer flow near the wall, and becomes increasingly sparse away from the wall.

[0058] In some embodiments, in step S2, according to formula (1), The flow field pressure and velocity of the discrete grid at the moment, where the flow field velocity includes the stream velocity and the normal velocity; the flow direction of the fluid motion on each discrete grid is recorded as Axis, normal to Axis, spanwise axis, the expression of formula (1) is:

[0059] (1);

[0060] In formula (1), is the flow field pressure, is the flow velocity, is the normal velocity, is the fluid density, is the kinematic viscosity coefficient of the fluid.

[0061] In some embodiments, the incoming flow velocity is given as the inlet condition at the entrance of the computational domain, and the free outflow boundary condition is adopted in the far field of the computational domain, the diffusion flux satisfying all flow variables is 0, and the time step of the unsteady solution is 0.0002 seconds; when the flow in the boundary layer no longer changes with time, it is considered that the laminar boundary layer flow reaches a steady state, and at this time, the pressure and velocity of the hydrofoil laminar flow field are obtained according to formula (1).

[0062] In some embodiments, in step S3, the wall tangential velocity of each discrete grid is calculated according to formula (2), and the expression of formula (2) is:

[0063] (2);

[0064] In formula (2), is the wall tangential velocity, is the wall tangent inclination angle.

[0065] In some embodiments, after the wall tangential velocity is calculated, a five-point fourth-order difference format is used to solve the first-order derivative and the second-order derivative of the wall tangential velocity, wherein the difference format is reduced in order near the wall.

[0066] In some embodiments, in step S4, the linear stability equation is expressed as shown in equation (3):

[0067] (3);

[0068] In formula (3), is the characteristic function, , used to describe the profile information of small disturbances in the form of traveling waves; represents the normal direction of fluid motion in the local orthogonal body-fitting coordinate system; , , is the coefficient matrix containing the streamwise wavenumbers of small perturbations and circular frequency , also includes the first-order derivative and second-order derivative of the wall tangential velocity obtained in step S3; in the spatial mode, is a plural number, represented by , the imaginary part of the wave number is the spatial growth rate of the disturbance, is the streamwise wave number in real form.

[0069] In some embodiments, according to the physical condition that small perturbations tend to zero at the wall and at infinity, there are boundary conditions when applying equation (3), and the boundary conditions are as follows:

[0070] (4);

[0071] In formula (4), For small disturbances The distance between the axis and the hydrofoil boundary layer, the flow direction of the fluid motion in the local orthogonal body-fitting coordinate system is recorded as , the extension direction is , The small disturbance edge The speed in the axis direction.

[0072] In some embodiments, in step S5, the growth rate of the small disturbance amplitude of different frequencies on the suction surface at each grid along the hydrofoil surface is calculated using formula (5), and the expression of formula (5) is:

[0073] (5);

[0074] In formula (5), is the magnification factor, is the frequency, and are two adjacent grids, From the grid To Grid The arc length at For Grid The growth rate at For Grid The growth rate at .

[0075] In some embodiments, in step S6, the growth threshold is .

[0076] Example 1

[0077] Example 1: The NACA16 hydrofoil was used to predict the transition position using the prediction method in the embodiment of the present invention, and the geometric shape of the NACA16 hydrofoil was as follows: Figure 2 As shown, Embodiment 1 is described below in conjunction with the accompanying drawings. The method for predicting the transition position of the hydrofoil boundary layer includes the following steps:

[0078] S1, obtain the hydrofoil discrete grid: select 3 times the hydrofoil chord length as the size of the calculation domain, divide the calculation domain of the hydrofoil, use the surface adaptive vertical grid technology, write the surface adaptive vertical grid program based on FORTRAN language, and draw the discrete grid wrapping the hydrofoil perpendicular to the wall; among them, in the normal calculation domain close to the wall 20 times the boundary layer, the grid (including the leading edge and trailing edge position of the hydrofoil) is perpendicular to the wall, such as Figure 3 As shown, the orthogonal quality coefficient of such a grid is very close to 1.

[0079] S2, solve the laminar flow field of the hydrofoil: according to the hydrofoil discrete grid, the incoming flow velocity is given as the inlet condition at the entrance of the computational domain, and the free outflow boundary condition is adopted in the far field of the computational domain, satisfying the diffusion flux of all flow variables to be 0, and the time step of the unsteady solution is 0.0002 seconds; solve the Navier-Stokes equations satisfied by the fluid motion on each discrete grid. When the flow in the boundary layer no longer changes with time, it is considered that the laminar boundary layer flow reaches a steady state. At this time, according to formula (1), The flow field pressure and velocity of the hydrofoil discrete grid at time , where the flow field velocity includes the stream velocity and the normal velocity; the flow direction of the fluid motion on each discrete grid is recorded as Axis, normal to Axis, spanwise axis, the expression of formula (1) is:

[0080] (1);

[0081] In formula (1), is the flow field pressure, is the flow velocity, is the normal velocity, is the fluid density, is the fluid kinematic viscosity coefficient. The flow field pressure cloud diagram obtained in this embodiment is as follows Figure 4 As shown, the flow velocity cloud diagram is as follows Figure 5 As shown, the normal velocity cloud diagram is as follows Figure 6 shown.

[0082] S3, calculate the local wall tangential velocity: transform the flow field velocity into the local orthogonal body-fitting coordinate system, calculate the wall tangential velocity of each discrete grid according to formula (2), and then obtain the change of the wall tangential velocity along the wall normal. Use the five-point fourth-order difference format to solve the first-order derivative and second-order derivative of the wall tangential velocity, where the difference format near the wall is reduced in order; the expression of formula (2) is:

[0083] (2);

[0084] In formula (2), is the wall tangential velocity, such as Figure 2 As shown, is the wall tangent inclination angle, which is obtained by using the three-point non-equally spaced difference format; in this embodiment, taking the suction surface as an example, the tangential velocity of the wall surface in the boundary layer at 0.78 m on the suction surface is along the direction perpendicular to the wall surface h (see Figure 2 ) is distributed as Figure 7 As shown, the velocity magnitude near the hydrofoil suction surface wall was also measured in the experiment. By comparison, it is found that the calculated results are consistent with the experimental measurement results, which verifies the accuracy of the laminar boundary layer velocity profile calculated by the present invention.

[0085] S4, obtain the growth rate of the destabilizing frequency disturbance: decompose the instantaneous quantity of the hydrofoil flow into the basic flow and the disturbance quantity, derive the nonlinear disturbance equation satisfied by the disturbance quantity, and obtain the linearized disturbance equation after ignoring the high-order small quantity of the small disturbance; based on the parallel flow assumption, obtain the linear stability equation (3), and obtain the growth rate of all destabilizing frequency disturbances according to the linear stability equation; the expression of the linear stability equation is shown in equation (3):

[0086] (3);

[0087] In formula (3), is the characteristic function, , used to describe the profile information of small disturbances in the form of traveling waves; represents the normal direction of fluid motion in the local orthogonal body-fitting coordinate system; , , is the coefficient matrix containing the streamwise wavenumbers of small perturbations and circular frequency , also includes the first-order derivative and second-order derivative of the wall tangential velocity obtained in step S3; in the spatial mode, is a plural number, represented by , the imaginary part of the wave number is the spatial growth rate of the disturbance, is the streamwise wave number in real form;

[0088] According to the physical condition that small disturbances tend to zero at the wall and at infinity, there are boundary conditions when applying equation (3), which are as follows:

[0089] (4);

[0090] In formula (4), For small disturbances The distance between the axis and the hydrofoil boundary layer, the flow direction of the fluid motion in the local orthogonal body-fitting coordinate system is recorded as , the extension direction is , The small disturbance edge In this embodiment, taking the suction surface as an example, the growth rate distribution cloud diagram of the instability disturbance of the suction surface is as follows: Figure 8 shown.

[0091] S5, obtain the amplification factor cloud map of small disturbances of different frequencies: according to the growth rate of small disturbances of different frequencies during propagation, calculate the growth rate of small disturbance amplitudes of different frequencies on the suction surface and pressure surface at each grid along the hydrofoil surface, obtain the amplification factor of small disturbances of different frequencies, and obtain the amplification factor cloud map; taking the suction surface as an example, use formula (5) to calculate the growth rate of small disturbance amplitudes of different frequencies on the suction surface at each grid along the hydrofoil surface. The expression of formula (5) is:

[0092] (5);

[0093] In formula (5), is the magnification factor, is the frequency, and are two adjacent grids, From the grid To Grid The arc length at For Grid The growth rate at For Grid In this embodiment, the amplification factor cloud diagram of the suction surface instability disturbance is as follows: Fig. 9 shown.

[0094] S6, predict the transition position of the hydrofoil boundary layer: according to the cloud diagram of the amplification factor of small disturbances of different frequencies, use the solution form of small disturbances to determine the amplification factor of small disturbances, so as to obtain the growth factor of small disturbances ; Take the envelope of all small disturbances of instability frequency on the suction surface and pressure surface respectively, draw the envelope line, when the growth multiple of a small instability disturbance reaches the growth threshold When The corresponding small disturbance flow position is the transition position of the hydrofoil boundary layer, and then the transition positions of the suction surface and the pressure surface are obtained respectively. In this embodiment, the envelope of the amplification factor of the instability disturbance of different frequencies on the suction surface is as follows: Fig.10 As shown in Figure 2, the boundary layer transition positions of the suction side and the pressure side are as follows: Fig.11 As shown in the figure, it can be analyzed that the transition position of the suction surface of the hydrofoil is 1.14 m, the experimentally measured transition position of the suction surface is 1.04 m, and the calculated relative error is about 8.7%, with a high prediction accuracy; the predicted transition position of the pressure surface is 0.45 m, and the experimentally measured transition position of the pressure surface is 0.46 m, with a relative error of about 2.2%, and a high prediction accuracy.

[0095] Through the description of multiple embodiments of the method for predicting the transition position of the hydrofoil boundary layer of the present invention, it can be seen that the embodiment of the method for predicting the transition position of the hydrofoil boundary layer of the present invention has at least one or more of the following advantages:

[0096] 1. The method for predicting the transition position of the hydrofoil boundary layer provided by the present invention utilizes the surface adaptive vertical grid technology to draw a vertical grid with a curved surface shape of the leading edge and the trailing edge, and can avoid errors caused by the interpolation process after introducing the local orthogonal body-fitting coordinate system in the subsequent steps. At the same time, the grid is more conducive to the stability of numerical calculation, and the unsteady calculation process is less likely to diverge, which can improve the prediction accuracy of the transition position;

[0097] 2. The method for predicting the transition position of the hydrofoil boundary layer provided by the present invention obtains the transition positions of the suction surface and the pressure surface by respectively analyzing and calculating the data of the suction surface and the pressure surface. It is applicable to asymmetric airfoils and airfoils with an angle of attack, and can accurately predict the transition position of the hydrofoil under complex conditions, providing a theoretical basis and technical support for reducing the flow noise of underwater airfoil structures in engineering.

[0098] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0099] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A method for predicting the transition position of a hydrofoil boundary layer, characterized in that: The following steps are involved: S1, obtain the hydrofoil discrete grid: divide the computational domain of the hydrofoil, and use the surface adaptive vertical grid technology to draw the discrete grid wrapping the hydrofoil perpendicular to the wall; S2, solve the laminar flow field of the hydrofoil: according to the hydrofoil discrete grid, set the boundary conditions that meet the physical reality at the boundary of the computational domain, solve the Navier-Stokes equations satisfied by the fluid motion on each discrete grid, and obtain the The flow field pressure and velocity of the hydrofoil discrete grid at time t; S3, calculate the local wall tangential velocity: transform the flow field velocity into the local orthogonal body-fitting coordinate system, calculate the wall tangential velocity of each discrete grid, and then obtain the change of the wall tangential velocity along the wall normal, and use the finite difference method to obtain the first-order derivative and second-order derivative of the wall tangential velocity along the normal; S4, obtain the growth rate of the instability frequency disturbance: decompose the instantaneous quantity of the hydrofoil flow into the basic flow and the disturbance quantity, derive the nonlinear disturbance equation satisfied by the disturbance quantity, and obtain the linearized disturbance equation after ignoring the high-order small quantity of the small disturbance; based on the parallel flow assumption, obtain the linear stability equation, and obtain the growth rate of all instability frequency disturbances according to the linear stability equation; S5, obtaining the cloud map of amplification factors of small disturbances of different frequencies: according to the growth rate of small disturbances of different frequencies during propagation, respectively calculate the growth rate of small disturbance amplitudes of different frequencies on the suction surface and the pressure surface at each grid along the hydrofoil surface, obtain the amplification factors of small disturbances of different frequencies, and obtain the cloud map of amplification factors; S6, predict the transition position of the hydrofoil boundary layer: according to the cloud diagram of the amplification factor of small disturbances of different frequencies, use the solution form of small disturbances to determine the amplification factor of small disturbances, so as to obtain the growth factor of small disturbances ; Take the envelope of all small disturbances of instability frequency on the suction surface and pressure surface respectively, and draw the envelope line. When the growth multiple of a certain unstable small disturbance reaches the growth threshold, it is considered that the flow direction position of the small disturbance corresponding to the growth threshold at this time is the transition position of the hydrofoil boundary layer, and then the transition positions of the suction surface and pressure surface are obtained respectively.

2. The method for predicting the transition position of the hydrofoil boundary layer according to claim 1, characterized in that: The size of 3 times the chord length of the hydrofoil is selected as the size of the calculation domain.

3. The method for predicting the transition position of the hydrofoil boundary layer according to claim 1, characterized in that: In step S2, according to formula (1), The flow field pressure and velocity of the discrete grid at the moment, where the flow field velocity includes the stream velocity and the normal velocity; the flow direction of the fluid motion on each discrete grid is recorded as Axis, normal to Axis, span direction axis, the expression of formula (1) is: （1）； In formula (1), is the flow field pressure, is the flow velocity, is the normal velocity, is the fluid density, is the kinematic viscosity coefficient of the fluid.

4. The method for predicting the transition position of the hydrofoil boundary layer according to claim 3, characterized in that: The incoming flow velocity is given as the inlet condition at the entrance of the computational domain, and the free outflow boundary condition is adopted in the far field of the computational domain. The diffusion flux of all flow variables is 0, and the time step of the unsteady solution is 0.0002 seconds. When the flow in the boundary layer no longer changes with time, the laminar boundary layer flow is considered to have reached a steady state. At this time, the pressure and velocity of the laminar flow field of the hydrofoil are obtained according to formula (1).

5. The method for predicting the transition position of the hydrofoil boundary layer according to claim 3, characterized in that: In step S3, the wall tangential velocity of each discrete grid is calculated according to formula (2), and the expression of formula (2) is: （2）； In formula (2), is the wall tangential velocity, is the wall tangent inclination angle.

6. The method for predicting the transition position of the hydrofoil boundary layer according to claim 5, characterized in that: After the wall tangential velocity is calculated, the five-point fourth-order difference format is used to solve the first-order derivative and second-order derivative of the wall tangential velocity, in which the difference format is reduced in order near the wall.

7. The method for predicting the transition position of the hydrofoil boundary layer according to claim 5 or 6, characterized in that: In step S4, the expression of the linear stability equation is shown in formula (3): （3）； In formula (3), is the characteristic function, , used to describe the profile information of small disturbances in the form of traveling waves; represents the normal direction of fluid motion in the local orthogonal body-fitting coordinate system; , , is the coefficient matrix containing the streamwise wavenumbers of small perturbations and circular frequency , also includes the first-order derivative and second-order derivative of the wall tangential velocity obtained in step S3; in the spatial mode, is a plural number, represented by , the imaginary part of the wave number is the spatial growth rate of the disturbance, is the streamwise wave number in real form.

8. The method for predicting the transition position of the hydrofoil boundary layer according to claim 7, characterized in that: According to the physical condition that small disturbances tend to zero at the wall and at infinity, there are boundary conditions when applying equation (3), which are as follows: （4）； In formula (4), For small disturbances The distance between the axis and the hydrofoil boundary layer, the flow direction of the fluid motion in the local orthogonal body-fitting coordinate system is recorded as , the extension direction is , The small disturbance edge The speed in the axis direction.

9. The method for predicting the transition position of the hydrofoil boundary layer according to claim 8, characterized in that: In step S5, the growth rate of the small disturbance amplitude of different frequencies on the suction surface at each grid along the hydrofoil surface is calculated using formula (5). The expression of formula (5) is: （5）； In formula (5), is the magnification factor, is the frequency, and are two adjacent grids, From the grid To Grid The arc length at For Grid The growth rate at For Grid The growth rate at .

10. The method for predicting the transition position of the hydrofoil boundary layer according to claim 1, characterized in that: In step S6, the growth threshold is .

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