Transition prediction method for boundary layer of underwater rotary body with rough element surface

Abstract

The invention relates to a transition prediction method for an underwater revolved body boundary layer aiming at a rough element surface, which comprises the following steps of: 1, acquiring a geometric shape of a wall surface rough element, and arranging the rough element on an original smooth revolved body surface; step 2, aiming at an underwater revolving body boundary layer of the rough element surface, generating a computational domain grid to calculate a laminar flow basic flow; in order to calculate flow field distribution of a boundary layer capable of being used for stability analysis, using a dense grid in the normal direction close to the wall surface; a grid perpendicular to the wall surface is used in the area without the roughness elements, and a grid not perpendicular to the wall surface is used in the area with the roughness elements; 3, basic flow of a laminar flow boundary layer of the underwater rotary body with the roughness elements is calculated; 4, calculating small perturbation evolution in the boundary layer of the underwater rotary body according to the rough element surface; solving a harmonic linearized N-S equation to obtain small perturbation evolution of a rough element boundary layer; and 5, predicting the natural transition position of the boundary layer of the underwater rotary body.

Description

Technical Field

[0001] The invention relates to the technical field of hydrodynamics research, and in particular to a transition prediction method for an underwater rotating body boundary layer with a rough element surface. Technical Background

[0002] In engineering practice, the surface of underwater vehicles is not completely smooth, and there will be some roughness, such as roughness caused by inaccurate wall processing, gaps at the joints of plates, and uneven wall surfaces caused by the attachment and corrosion of aquatic organisms. According to experience in the flat plate boundary layer, the roughness of the wall will advance the transition position, which is not conducive to reducing the noise interference of the bow sonar. The problem of roughness on the surface of underwater vehicles is inevitable in practice, so it is of great engineering significance to study the influence of wall roughness elements on the transition position of the boundary layer of underwater rotating bodies.

[0003] The question of how wall roughness elements affect the transition position of the boundary layer of underwater rotating bodies is at the forefront of boundary layer stability and transition research, and therefore has important scientific significance. People started studying the effect of wall roughness elements on transition in flat plate boundary layers relatively early, and the research results are relatively rich. Some people have also studied the effect of wall roughness elements on the transition position in supersonic / hypersonic rotating bodies and non-rotating bodies. From the currently published literature, before the 1990s, some preliminary studies on the effect of wall roughness elements on transition in the boundary layer of underwater rotating bodies were reported; since then, it has been difficult to see relevant research results published. It can be seen that in-depth research on the effect of wall roughness elements on the transition position of the boundary layer of underwater rotating bodies is of great significance to deepening people's understanding of related issues.

[0004] To study the influence of wall roughness elements on the transition position, an accurate and engineering feasible transition prediction method is needed. However, the relatively accurate transition prediction methods currently available in engineering, such as the traditional eN method, are all for smooth surfaces and cannot be directly used on rough element surfaces because the approximate parallel flow assumption in stability theory cannot be used at the rough element. Therefore, it is necessary to develop a natural transition prediction method for the boundary layer of underwater rotating bodies with wall roughness elements. Summary of the invention

[0005] The purpose of the present invention is to consider the influence of wall roughness elements on the transition position and provide a more accurate boundary layer transition prediction method. The technical solution is as follows:

[0006] A method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface comprises the following steps:

[0007] Step 1: obtain the geometric shape of the wall rough element and arrange the rough element on the surface of the original smooth rotating body;

[0008] Step 2: Generate a computational domain grid to calculate the laminar basic flow for the boundary layer of the underwater rotating body on the surface of the rough element; use a dense grid in the normal direction near the wall to calculate the flow field distribution of the boundary layer that can be used for stability analysis; use a grid perpendicular to the wall in the area without rough elements, and use a grid that is not perpendicular to the wall in the area with rough elements;

[0009] Step 3, calculate the basic flow of the laminar boundary layer of the underwater rotating body with rough elements;

[0010] Step 4: Calculate the evolution of small disturbances in the boundary layer of the underwater rotating body for the rough element surface; solve the harmonic linearized NS equations to obtain the evolution of small disturbances in the rough element boundary layer;

[0011] Step 5: predict the natural transition position of the boundary layer of the underwater rotating body on the rough surface.

[0012] Furthermore, in step 2, an isolated rough element in the form of a cosine function is selected, and its expression is shown in formula (1):

[0013]

[0014] where h(ξ) is the normal coordinate of the point on the rough element at the streamwise position ξ, c is the flow coordinate of the center line of the rough element, H is the height of the rough element, and L is the width of the rough element.

[0015] Further, the method of step 4 is as follows:

[0016] Small perturbations are given in the form of harmonic traveling waves, namely

[0017]

[0018] Among them, u'(r,t), v'(r,t), w'(r,t) and p'(r,t) are the disturbances of stream velocity, normal velocity, circumferential velocity and pressure respectively; r = (ξ,η,ζ) is the radius vector of any spatial point in the flow field, ξ, η and ζ are the stream coordinate, normal coordinate and circumferential coordinate in the body-fitting coordinate system respectively; and is the characteristic function of a small disturbance; α0 is the reference streamwise wave number, β is the circumferential wave number, f is the frequency; cc is the complex conjugate;

[0019] The characteristic function of small perturbations satisfies the harmonic linearized NS equation:

[0020]

[0021] in, is a differential operator; are coefficient matrices, which contain the basic flow information obtained in step 2;

[0022] By solving equation (3), the disturbance evolution of the boundary layer of the underwater rotating body with rough elements is obtained, that is, the amplitude distribution Au of the streamwise velocity disturbance of a single frequency in the streamwise direction;

[0023] According to formula (4), the growth rate σ of a single frequency disturbance along the flow direction is obtained: i , multiple disturbances of different frequencies are calculated to obtain the growth rate σ of disturbances of different frequencies along the flow direction;

[0024]

[0025] Among them, ΔAu i is the disturbance at a certain flow position ξ i The amplitude change at i is the growth rate of the disturbance at this streamwise location.

[0026] Furthermore, the method of step five is as follows:

[0027] According to formula (5), the growth rate σ of small disturbances of different frequencies is integrated along the arc length of the wall, and the distribution of the disturbance amplification factor can be obtained:

[0028]

[0029] Where N(f,x) is the amplification factor of a small disturbance of frequency f at axial position x; x0 is the axial position of the critical instability at the wall;

[0030] Take the envelope of the amplification factor N(f,x) of different frequencies to obtain the maximum amplification factor curve N of the disturbance max (x), that is Set the transition threshold N T , when N max (x) = N T When the boundary layer undergoes a natural transition, x at this time is the predicted axial position where the transition occurs, and the transition threshold N T The value of is obtained by experimental calibration.

[0031] The beneficial effects of the present invention compared with the prior art are as follows:

[0032] (1) The present invention takes into account the basic flow distortion caused by the rough surface, better considers the actual physical situation, and thus more accurately realizes the boundary layer transition prediction with rough elements.

[0033] (2) The present invention can provide a reliable technical means for studying the transition effect of roughness elements on the boundary layer of underwater rotating bodies.

[0034] (3) The present invention can be applied to the prediction of boundary layer transition of non-smooth surfaces that are widely present in actual engineering, and then calculate the length of the laminar flow region, providing technical support for drag reduction and noise reduction in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] (1) Figure 1 It is a flowchart of the steps of the present invention

[0036] (2) Figure 2 This is a rough element shape diagram

[0037] (3) Figure 3 This is a schematic diagram of the grid distribution at the coarse element.

[0038] (4) Figure 4 It is the growth rate cloud chart

[0039] (5) Figure 5 Is the amplification factor N value cloud map

[0040] (6) Figure 6 is the maximum magnification factor N max curve DETAILED DESCRIPTION

[0041] The present invention is described in detail below in conjunction with specific embodiments and accompanying drawings. In the following description, for the purpose of explanation and not limitation, specific details are set forth to help fully understand the present invention. However, it is apparent to those skilled in the art that the present invention may also be practiced in other embodiments that depart from these specific details.

[0042] It should be noted that, in order to avoid obscuring the present invention due to unnecessary details, only the device structure and / or processing steps closely related to the solution according to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0043] The embodiment of the present invention provides a method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface. Figure 1 As shown, the following steps are included:

[0044] Step 1: Get the geometric shape of the wall rough element. Arrange the rough element on the surface of the original smooth rotating body, and in order to better reflect the flow field information at the rough element, the flow direction grid points at the rough element are not less than 20.

[0045] In this step, the smooth shape of the underwater rotating body is selected as the SUBOFF standard model without appendages (for specific parameters, see reference (Groves N., Huang T., and Chang M.. Geometric characteristics of DARPA Suboff models. DTRC / SHD-1298-01. David Taylor Research Center-ShipHydromechanics Department, Department of the Navy. 1989), and the model diameter is 0.06m. The present invention selects an isolated rough element in the form of a cosine function, and its expression is shown in formula (1). The axial distance from the center line of the rough element to the stationary point of the rotating body is 0.06m.

[0046]

[0047] where h(ξ) is the normal coordinate of the point on the rough element at the streamwise position ξ, c is the flow coordinate of the center line of the rough element, H is the height of the rough element, and L is the width of the rough element.

[0048] The rough element height selected in the present invention is H = 0.2δ 99 , width L = 2δ 99 , where δ 99 is the local dimensionless nominal thickness of the boundary layer at the smooth wall.

[0049] The geometric shape of the wall rough element obtained in this step is as follows Figure 2 shown.

[0050] Step 2: For the underwater rotating body boundary layer with rough element surface, generate the computational domain grid to calculate the basic flow of the laminar boundary layer of the underwater rotating body considering the non-parallelism.

[0051] In this step, in order to calculate the flow field distribution of the boundary layer that can be used for stability analysis, a dense grid is used in the normal direction near the wall; a grid perpendicular to the wall is used in the area without rough elements, and a non-vertical grid is used in the area with rough elements. The schematic diagram of the grid distribution at the rough element is shown in the figure. Figure 3 shown.

[0052] Step 3: Calculate the basic flow of the laminar boundary layer of the underwater rotating body with rough elements.

[0053] In this step, the incoming flow velocity is selected as 7.0 m / s, the fluid medium is water, the angle of attack of the rotating body is 0°, and the flow field is uniform in the circumferential direction, so it can be simplified to a two-dimensional flow field.

[0054] In this step, the Ansys Fluent solver is used to calculate the laminar boundary layer flow field. For detailed boundary condition settings, please refer to the literature (Liu, J., Chu, X., and Zhang, Y.. Numerical investigation of natural transitions of bow boundary layers over underwater axisymmetricbodies. Phys. Fluids 33, 074101, 2021).

[0055] Step 4: Calculate the evolution of small disturbances in the boundary layer of the underwater rotating body for the rough element surface. The basic flow of the underwater rotating body of the rough element will be distorted at the rough element, so it has strong non-parallelism. Therefore, the present invention solves the harmonic linearized Navier-Stokes (NS) equations to obtain the evolution of small disturbances in the boundary layer of the rough element.

[0056] In this step, the small perturbation is given in the form of a harmonic traveling wave, that is,

[0057]

[0058] Among them, u'(r,t), v'(r,t), w'(r,t) and p'(r,t) are the disturbances of stream velocity, normal velocity, circumferential velocity and pressure respectively. r = (ξ,η,ζ) is the radius vector of any spatial point in the flow field, ξ, η and ζ are the stream coordinate, normal coordinate and circumferential coordinate in the body-fitting coordinate system respectively. and is the characteristic function of a small perturbation. α0 is the reference streamwise wave number, β is the circumferential wave number, and f is the frequency. cc is the complex conjugate.

[0059] The characteristic function of small perturbations satisfies the harmonic linearized NS equation:

[0060]

[0061] in, is a differential operator. are coefficient matrices, which contain the basic flow information obtained in step 2.

[0062] For more information about the harmonic linearized NS equations (2), including the derivation of the equations and the setting of boundary conditions, see the literature (Zhang Yongming, Liu Di, Kong Chenhao, Lv Junbo, Liu Jianhua, Zhao Lei. "A transition prediction method for the boundary layer of an underwater rotating body considering non-parallelism." CN202410557269.3.2024).

[0063] By solving equation (2), we can obtain the disturbance evolution of the boundary layer of the underwater rotating body with rough elements, that is, the amplitude distribution Au of the single-frequency streamwise velocity disturbance in the streamwise direction. Furthermore, according to formula (3), we can obtain the growth rate, that is, the growth rate σ of the single-frequency disturbance along the streamwise direction: i , by calculating multiple disturbances of different frequencies, the growth rate σ of disturbances of different frequencies along the flow direction can be obtained.

[0064]

[0065] Among them, σ i is the disturbance at a certain flow position ξ i The growth rate at .

[0066] The growth rate σ cloud diagram of different frequency disturbances along the flow direction obtained in this step is as follows Figure 4 shown.

[0067] Step 5: predict the natural transition position of the boundary layer of the underwater rotating body on the rough surface.

[0068] The present invention adopts the natural transition prediction method suitable for the boundary layer of underwater rotating bodies developed in the literature (Liu, J., Liu, J., and Zhang, Y.. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies. Phys. Fluids 35, 044107, 2023), and its main process is as follows.

[0069] (1) Based on the growth rate distribution σ obtained in step 3, the growth rates of disturbances of different frequencies are integrated along the arc length of the wall according to formula (4), and the distribution of the disturbance amplification factor can be obtained:

[0070]

[0071] where N(f,x) is the amplification factor of a small disturbance of frequency f at axial position x. x0 is the axial position of the critical instability at the wall.

[0072] The cloud diagram of the disturbance amplification factor N obtained in this step is as follows Figure 5 shown.

[0073] (2) Taking the envelope of the amplification factor N(f,x) of different frequencies, we can get the maximum amplification factor curve N of the disturbance max (x), that is The maximum amplification factor curve N of the disturbance obtained in this step max (x) Figure 6 shown.

[0074] (3) When N max (x) = N T When the boundary layer undergoes a natural transition, x at this time is the transition position predicted by the present invention, where the transition threshold N T It is obtained based on experimental calibration. The present invention selects the value N calibrated in the literature (Liu, J., Liu, J., and Zhang, Y.. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies. Phys. Fluids 35, 044107, 2023) T =7. According to Figure 6 It can be obtained that when the axial position x = 2.01, N max The value reaches the transition threshold N T =7, which is the axial position where the boundary layer transition of the underwater rotating body with a rough surface occurs, and the dimensioned position is 0.1206m.

[0075] Features described and / or illustrated above for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or used in place of features in other embodiments.

[0076] It should be emphasized that the term "include / comprises" when used herein refers to the presence of features, integers, steps or components, but does not exclude the presence or addition of one or more other features, integers, steps, components or combinations thereof.

[0077] The above devices and methods of the present invention can be implemented by hardware, or by hardware combined with software. The present invention relates to such a computer-readable program, which, when executed by a logic component, enables the logic component to implement the above-mentioned devices or components, or enables the logic component to implement the above-mentioned various methods or steps. The present invention also relates to a storage medium for storing the above-mentioned program, such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, etc.

[0078] The many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, it is not intended that the embodiments of the invention be limited to the exact construction and operation illustrated and described, but rather all suitable modifications and equivalents falling within the scope thereof are intended to be covered.

[0079] Parts of the present invention that are not described in detail are well known to those skilled in the art.

Claims

1. A method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface, comprising the following steps: Step 1: obtain the geometric shape of the wall rough element and arrange the rough element on the surface of the original smooth rotating body; Step 2: Generate a computational domain grid to calculate the laminar basic flow for the boundary layer of the underwater rotating body on the rough element surface; use a dense grid in the normal direction near the wall to calculate the flow field distribution of the boundary layer that can be used for stability analysis; In the area without coarse elements, a grid perpendicular to the wall is used, and in the area with coarse elements, a grid not perpendicular to the wall is used; Step 3, calculate the basic flow of the laminar boundary layer of the underwater rotating body with rough elements; Step 4: Calculate the evolution of small disturbances in the boundary layer of the underwater rotating body for the rough element surface; solve the harmonic linearized NS equations to obtain the evolution of small disturbances in the rough element boundary layer; Step 5: predict the natural transition position of the boundary layer of the underwater rotating body on the rough surface.

2. The method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface according to claim 1, characterized in that: In step 2, an isolated rough element in the form of a cosine function is selected, and its expression is shown in formula (1): where h(ξ) is the normal coordinate of the point on the rough element at the streamwise position ξ, c is the flow coordinate of the center line of the rough element, H is the height of the rough element, and L is the width of the rough element.

3. The method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface according to claim 1, characterized in that: The method of step 4 is as follows: Small perturbations are given in the form of harmonic traveling waves, namely Among them, u'(r,t), v'(r,t), w'(r,t) and p'(r,t) are the disturbances of stream velocity, normal velocity, circumferential velocity and pressure respectively; r = (ξ,η,ζ) is the radius vector of any spatial point in the flow field, ξ, η and ζ are the stream coordinate, normal coordinate and circumferential coordinate in the body-fitting coordinate system respectively; and is the characteristic function of a small disturbance; α0 is the reference streamwise wave number, β is the circumferential wave number, f is the frequency; cc is the complex conjugate; The characteristic function of small perturbations satisfies the harmonic linearized NS equation: in, is a differential operator; are coefficient matrices, which contain the basic flow information obtained in step 2; By solving equation (3), the disturbance evolution of the boundary layer of the underwater rotating body with rough elements is obtained, that is, the amplitude distribution Au of the streamwise velocity disturbance of a single frequency in the streamwise direction; According to formula (4), the growth rate σ of a single frequency disturbance along the flow direction is obtained: i , multiple disturbances of different frequencies are calculated to obtain the growth rate σ of disturbances of different frequencies along the flow direction; Among them, ΔAu i is the disturbance at a certain flow position ξ i The amplitude change at i is the growth rate of the disturbance at this streamwise location.

4. The method for predicting the transition of the boundary layer of an underwater rotating body with a rough surface according to claim 1, characterized in that: The method for step five is as follows: According to formula (5), the growth rate σ of small disturbances of different frequencies is integrated along the arc length of the wall, and the distribution of the disturbance amplification factor can be obtained: Where N(f,x) is the amplification factor of a small disturbance of frequency f at axial position x; x0 is the axial position of the critical instability at the wall; Take the envelope of the amplification factor N(f,x) of different frequencies to obtain the maximum amplification factor curve N of the disturbance max (x), that is Set the transition threshold N T , when N max (x) = N T When the boundary layer undergoes a natural transition, x at this time is the predicted axial position where the transition occurs, and the transition threshold N T The value of is obtained by experimental calibration.

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