CN115146383A - Method for forecasting transition position of curved surface boundary layer of super-hydrophobic surface - Google Patents

Method for forecasting transition position of curved surface boundary layer of super-hydrophobic surface Download PDF

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CN115146383A
CN115146383A CN202210769703.5A CN202210769703A CN115146383A CN 115146383 A CN115146383 A CN 115146383A CN 202210769703 A CN202210769703 A CN 202210769703A CN 115146383 A CN115146383 A CN 115146383A
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张永明
刘斌
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Abstract

The invention relates to a method for forecasting a transition position of a curved surface boundary layer of a super-hydrophobic surface, which comprises the following steps: dividing a computational domain mesh, wherein one or more layers of meshes of vertical curved surfaces are drawn in a near-wall area of the wall surface of the curved surface geometric solid; simulating a super-hydrophobic surface of a wall surface of the curved surface geometric body, and listing wall surface sliding speed boundary conditions; solving an NS equation on a calculation domain grid, calculating a flow field of a curved surface boundary layer of the super-hydrophobic surface, and interpolating the flow field to a grid orthorhombic to the surface of the curved surface geometry along the normal direction to obtain wall surface tangential velocity component profiles at all positions; analyzing the flow stability of a flow field of a curved surface boundary layer of the super-hydrophobic surface based on a linear stability theory to obtain the growth rate of each frequency disturbance wave amplitude along the flow direction; and calculating the maximum growth multiple of the super-hydrophobic surface curved surface boundary layer, and forecasting the natural transition position of the super-hydrophobic surface curved surface boundary layer.

Description

Method for forecasting transition position of curved surface boundary layer of super-hydrophobic surface
Technical Field
The invention belongs to the technical field of hydrodynamics research, and particularly relates to a method for forecasting a transition position of a curved surface boundary layer of a super-hydrophobic surface.
Background
The slip characteristics of superhydrophobic surfaces have attracted extensive attention and research since this century. The super-hydrophobic coating is prepared on the surface of the shell material of the underwater vehicle, so that the shear stress state of the wall surface can be directly influenced, the wall surface speed is greater than zero, and finally, a turbulence transition point moves downstream, and the super-hydrophobic coating also has attractive application prospects in the aspects of resistance reduction, noise reduction and the like. The revolution body/hydrofoil is taken as a typical underwater curved surface aircraft, and is closely related to actual problems of submarine motion in water, ship navigation on the water surface, torpedo launching and the like, so how to predict the transition position of the super-hydrophobic surface curved surface boundary layer is feasible and reasonable, and the method is particularly critical to development and application of the super-hydrophobic coating technology of the underwater curved surface aircraft.
Because the curved surface boundary layer flow is more complicated than the plane boundary layer flow, the related transition forecasting research is relatively less, and the curved surface boundary layer of the super-hydrophobic surface is more complicated than the curved surface boundary layer of the common surface, so that the related transition forecasting research work is not seen at present. For the reason, the transition forecasting technology for the problem mainly has two difficulties: firstly, simulating a super-hydrophobic surface on a curved surface, and calculating a flow field of a curved surface boundary layer; secondly, how to analyze the flow stability of the curved surface boundary layer of the super-hydrophobic surface and forecast the transition position. In recent years, some related technologies and methods have been developed to lay a foundation for solving the first difficulty. The calculation of the boundary layer of an ultra-hydrophobic surface plate is relatively simple and corresponding calculation methods have been proposed (Liu, B.and Zhang, Y.. A Numerical study on the natural transition locations in the flat-plate layers on super-hydrophilic surfaces. Phys. Fluids 32,124103,2020, liu, B.and Zhang, Y.. Numerical information of the natural transition in the flat-plate layers on super-hydrophilic surfaces conditioning the information of the guiding region AIP Advances 12,035140, 2022). The second difficulty is the need to consider both the wall slip velocity condition and the wall curvature, and no such work has been published. However, work solely considering the wall surface slip velocity condition has been done, for which is directed the superhydrophobic surface plate boundary layer (Liu, b.and Zhang, y. A Numerical study on the natural transition location in the flat-plate layers on super-hydrophobic surfaces. Properties. Fluids 32,124103,2020, liu, b.and Zhang, y. Numerical induction of the natural transition in the flat-plate layers on super-hydrophobic surfaces conditioning the flexibility of the leading region. Aip advance 12, 510340, 2022); work has also been published on the curvature of walls alone, for ordinary surface curved boundary layers without slip conditions, complex surface profiles, and both flow direction and circumferential curvature of the wall taken into account (Liu, j., chu, x., and Zhang, y. Although these works do not consider the super-hydrophobic surface slip velocity condition and the wall curvature at the same time, a foundation is laid for solving the second difficulty.
In conclusion, the method has important guiding significance for exploring a feasible and reasonable forecasting technology and method aiming at the transition position of the curved surface boundary layer of the super-hydrophobic surface.
Disclosure of Invention
The invention aims to provide a feasible and reasonable method for forecasting the transition position of a curved surface boundary layer of a super-hydrophobic surface. The method not only provides an effective method for accurately forecasting the transition of the curved surface boundary layer of the underwater vehicle such as a revolving body/hydrofoil, but also provides a feasible modeling mode for realizing the boundary condition of the curved surface sliding speed of the super-hydrophobic surface. In order to achieve the purpose, the invention adopts the following technical scheme:
a method for forecasting a transition position of a curved surface boundary layer of a super-hydrophobic surface comprises the following steps:
firstly, dividing a computational domain mesh, wherein one or more layers of meshes of a vertical curved surface are drawn in a near-wall area of a wall surface of a curved surface geometric solid.
Secondly, simulating the super-hydrophobic surface of the wall surface of the curved surface geometric body according to the computational domain mesh divided in the first step, and listing the boundary conditions of the wall surface sliding speed, wherein the method comprises the following steps:
using the data of the grid points of the wall surface of the curved surface geometric body in the first step, obtaining the tangential direction of the surface at any position of the curved surface geometric body through calculation, and setting the direction as the local sliding speed direction of the super-hydrophobic surface;
calculating the velocity gradient of the normal direction of the local wall surface in the near-wall area grid unit of each vertical curved surface; using linear slip velocity boundary condition assumptions, as shown in equation (1), the wall slip velocity boundary conditions of the superhydrophobic surface geometry are listed:
Figure BDA0003726901200000021
in the formula
Figure BDA0003726901200000022
Is the sliding speed of the curved surface geometry of the super-hydrophobic surface along the tangential direction of the wall surface, U * In the case of a tangential velocity, the velocity, y is * Is wall normal, λ * For the slip length, the superscript "@" indicates a dimensional physical quantity.
And thirdly, solving an NS equation on the calculation domain grid in the first step according to the wall surface slip speed boundary condition set in the second step, calculating the flow field of the curved surface boundary layer of the super-hydrophobic surface, and interpolating the flow field to an orthogonalized grid of the surface of the curved geometric body along the normal direction to obtain wall surface tangential speed component profiles of all parts.
Fourthly, analyzing the flow stability of the flow field of the curved surface boundary layer of the superhydrophobic surface in the third step based on a linear stability theory to obtain the growth rate of each frequency disturbance wave amplitude along the flow direction, wherein the method comprises the following steps:
from the dimensionless NS equation for incompressible flows, the instantaneous amount of flow is decomposed into the sum of the basic flow and the disturbance, i.e.
Figure BDA0003726901200000031
Wherein phi = (v) 1 ,v 2 ,v 3 ,p) T In the form of a vector of instantaneous quantities,
Figure BDA0003726901200000033
is a basic flow vector, phi '= (v' 1 ,v' 2 ,v' 3 ,p') T As disturbance vector, v 1 ,v 2 ,v 3 Velocity components in the flow, normal and circumferential directions, respectively, p is pressure, the prime symbol "-" represents the basic flow, the prime symbol "' represents the disturbance amount. Through the linear stability analysis of the flow direction of the aqueous medium and the flow of the curved surface boundary layer with the curvature in the circumferential direction, a disturbed linear stability equation is obtained, namely:
Figure BDA0003726901200000034
in the formula (I), the compound is shown in the specification,
Figure BDA0003726901200000035
representing the vector of the characteristic function after writing the perturbation phi' in the form of a travelling wave, i.e.
Figure BDA0003726901200000036
Figure BDA0003726901200000037
Wherein t is time, q 1 ,q 2 And q is 3 Local flow direction, normal direction and circumferential space coordinates under an orthogonal curve coordinate system are respectively, omega is circular frequency, alpha is flow direction wave number, beta is circumferential wave number, and c.c. is complex conjugate; in the spatial mode, α is a complex number, denoted α = α r +iα i Wherein, -a i For the spatial growth rate of the disturbance, α r Flow direction wave number in real number form;
Figure BDA0003726901200000038
the coefficient matrix comprises a basic flow, a flow direction curvature drx and a circumferential curvature drz of a wall surface, disturbance circle frequency, wave number and Reynolds number parameters;
the disturbance flows to a velocity component v 'when propagating in a curved surface boundary layer of the super-hydrophobic surface' 1 And a circumferential velocity component v' 3 Applying the slip velocity boundary conditions listed in the second step, at the wall, of the linear stability equation (2) at q 2 The wall boundary conditions at =0 are:
Figure BDA0003726901200000039
based on the flow field of the curved surface boundary layer of the super-hydrophobic surface obtained in the third step, solving a linear stability equation (2) at each flow direction position to obtain the spatial growth rate-alpha of each frequency disturbance wave amplitude value in the boundary layer of the super-hydrophobic surface along the flow direction i 。
Fifthly, calculating the maximum growth multiple of the growth rate of the disturbance wave amplitude values with different frequencies obtained in the fourth step, and forecasting the natural transition position of the curved surface boundary layer of the super-hydrophobic surface, wherein the method comprises the following steps:
spatial growth rate-alpha of amplitude along flow direction obtained in the fourth step i Integrating along the flow direction to obtain a certain flow direction position q 1 The amplification factor N of the amplitude of the disturbance wave, namely:
Figure BDA00037269012000000310
wherein f is the frequency of a disturbance and q 10 And taking the flow direction position where the frequency disturbance starts to be instable as the initial position of the integration.
Calculating the maximum increase multiple of the disturbance wave with different frequencies at each flow direction position
Figure BDA00037269012000000311
Wherein N is max For all frequency disturbances in the local q 1 At the maximum value of the N value, i.e. satisfy
Figure BDA0003726901200000041
When maximum increase multiple
Figure BDA0003726901200000042
Critical value given by transition criterion
Figure BDA0003726901200000043
When the layer flow is transited to turbulent flow, at the moment
Figure BDA0003726901200000044
Corresponding flow direction position q 1 Is where the transition occurs.
Further, the near-wall region vertical meshing in the first step is used to calculate the velocity gradient of the wall surface normal at each position.
Further, the transition criterion in the fifth step is taken
Figure BDA0003726901200000045
And further, setting the flow direction curvature and the circumferential curvature in the fourth step to be zero, and forecasting the transition position of the boundary layer of the super-hydrophobic surface plane.
Compared with the prior art, the invention at least has the following beneficial effects:
the invention provides a method for simulating a super-hydrophobic surface of a curved surface wall, which can set the sliding speed direction of the surface of a complex curved surface geometry and realize the boundary condition of the sliding speed of the wall surface.
The invention provides a method for calculating a flow field of a curved surface boundary layer of a super-hydrophobic surface.
The invention establishes a linear stability analysis method for the flow of the curved surface boundary layer of the super-hydrophobic surface.
The transition position forecasting method established by the invention is not limited to forecasting the curved surface boundary layer of the super-hydrophobic surface, and can forecast the transition positions of the plane boundary layer of the super-hydrophobic surface and the curved surface boundary layer of the common surface.
The predicted transition position of the super-hydrophobic surface curved surface boundary layer provides theoretical basis and support for further developing technologies of resistance reduction, noise reduction and the like of the underwater curved surface vehicle.
In summary, the invention provides a feasible and reasonable method for predicting the transition position of the boundary layer of the superhydrophobic surface curved surface.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a method for predicting a transition position of a curved surface boundary layer of a superhydrophobic surface according to the present invention;
FIG. 2 is a schematic diagram of a near-wall region grid of a SUBOFF model of a superhydrophobic surface according to an embodiment of the invention;
FIG. 3 is a schematic diagram of slip velocity boundary conditions at a SUBOFF model wall of a superhydrophobic surface according to an embodiment of the invention;
FIG. 4 is a slip velocity at a SUBOFF model wall of a superhydrophobic surface according to an embodiment of the invention;
FIG. 5 is a wall tangential velocity component profile of a SUBOFF model of a superhydrophobic surface 0.1m from the leading edge according to an embodiment of the invention;
FIG. 6 is a contour plot of the growth rate distribution of the perturbation amplitude within the boundary layer of the SUBOFF model of the superhydrophobic surface according to one embodiment of the invention;
FIG. 7 is an N-value distribution contour plot of the perturbation amplitude within the boundary layer of the SUBOFF model of the superhydrophobic surface according to one embodiment of the invention;
FIG. 8 is a graph of maximum increase times of the perturbation amplitude value in the boundary layer of the SUBOFF model of the superhydrophobic surface according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An application example of the method for predicting a transition position of a boundary layer of a superhydrophobic surface according to the present invention is described below with reference to the accompanying drawings, as shown in fig. 1, including the following steps:
the model of the embodiment is an unaffiliated SUBOFF model (Groves N., huang T., and Chang M., geological engineering of DARPA Suboff models, DTRC/SHD-1298-01.David Taylor Research Center-Ship hydro mechanics Department, department of the Navy.1989), which is one of the standard models for researching the curved surface flow of an underwater vehicle, and the axisymmetric Geometric structure mainly comprises a blunt head and a cylindrical intermediate; the working condition is zero attack angle and the sailing speed is 10m/s.
1. The first step, dividing the computational domain mesh, wherein one or more layers of meshes of the vertical curved surface are drawn near the wall surface of the complex curved surface geometry. The grids far away from the wall surface do not have the special requirement and can be divided according to specific conditions.
Firstly, setting the radial computational domain of the SUBOFF model of the super-hydrophobic surface to be 5 times of the length of the model, and then dividing the computational domain grid by using a FORTRAN writing program, wherein the grid of the near-wall region needs a vertical curved surface, as shown in FIG. 2. The near-wall region vertical grid is used for conveniently calculating the velocity gradient of the wall surface normal direction at each position in the second step and realizing the boundary condition of the super-hydrophobic surface curved surface sliding velocity.
2. And step two, simulating a super-hydrophobic surface of the curved wall according to the calculation domain grid divided in the step one, and realizing the boundary condition of the wall surface sliding speed.
Firstly, using data of the surface grid points of the SUBOFF model of the superhydrophobic surface in the first step, calculating by a FORTRAN writing program to obtain the tangential direction of the surface of the SUBOFF model at any position, and setting the tangential direction as the local slip velocity direction of the superhydrophobic surface. Then, the vertical distance between the center of the cell and the wall can be obtained by using the data of the wall surface grid cells, and the local wall surface normal velocity gradient is calculated in the near-wall area grid cell of each vertical curved surface by using a user-defined function in ANSYS Fluent software. Finally, using the linear slip velocity boundary condition assumption proposed by Navier in 1823 (the assumption is the existing public knowledge, specifically see the references (Navier, c.l.m.h. m. moire sur les lois du mouvement des fluids m.acad.r. sci.inst.6,389-440, 1823)), as shown in formula (1), the wall slip velocity boundary condition of the superhydrophobic surface curved geometry as shown in fig. 3 is achieved:
Figure BDA0003726901200000061
in the formula
Figure BDA0003726901200000062
Is the sliding speed of the curved surface geometry body of the super-hydrophobic surface along the tangential direction of the wall surface, U * Is the tangential velocity, y * Is wall normal, λ * For the slip length, the superscript "@" indicates a dimensional physical quantity. The slip length in this application example was taken from measurements in the experiment and was constant in size of 21 microns (Ou J., perot b., and rotostein J p., lamilar drag reduction in microchannel using ultra-hydrophilic surfaces 16,4635, 2004).
3. And thirdly, solving an NS equation on the calculation domain grid in the first step according to the boundary condition of the wall surface slip velocity set in the second step, calculating a flow field of the super-hydrophobic surface curved surface boundary layer, and obtaining the section of the wall surface tangential velocity component at each position.
Firstly, configuring the boundary conditions of the wall surface slip speed of the SuBOFF model of the super-hydrophobic surface in the second step in ANSYS Fluent software. Then, an NS equation solver in ANSYS Fluent software is used for solving an NS equation on the calculation domain grid in the first step, and a flow field of the surface boundary layer of the super-hydrophobic surface is obtained, wherein the slip speed of the surface SUBOFF model wall of the super-hydrophobic surface is shown as a black solid line in FIG. 4. In order to verify that the boundary condition of the surface slip speed of the superhydrophobic surface is realized, the black dots in fig. 4 plot the slip speed obtained by multiplying the slip length by the speed gradient in the normal direction of the local wall surface, and it can be seen that the two are completely consistent. And finally, interpolating the flow field of the boundary layer to the orthogonal grid of the surface of the curved surface geometric body along the normal direction, and finally obtaining wall surface tangential velocity component sections at all positions, wherein a wall surface tangential velocity component section at a position 0.1m away from the front edge of the model is shown in the figure 5.
4. And fourthly, analyzing the flow stability of the flow field of the curved surface boundary layer of the superhydrophobic surface in the third step based on a linear stability theory to obtain the growth rate of each frequency disturbance wave amplitude along the flow direction.
First, starting from the dimensionless NS equation for incompressible flows, the instantaneous amount of flow is decomposed into the sum of the basic flow and the disturbance, i.e. the sum
Figure BDA0003726901200000063
Wherein the vector phi = (v) 1 ,v 2 ,v 3 ,p) T In the form of a vector of instantaneous quantities,
Figure BDA0003726901200000064
is a basic flow vector, phi '= (v' 1 ,v' 2 ,v' 3 ,p') T As disturbance vector, v 1 ,v 2 ,v 3 The velocity components in the flow direction, normal direction and circumferential direction, respectively, p is the pressure, the prime symbol "-" represents the base flow, and the prime symbol "" represents the disturbance amount. Then, a linear stability analysis method suitable for the flow direction and the curved boundary layer flow with curvature in the circumferential direction of the aqueous medium, which is established by Liu et al (Liu, J., chu, X., and Zhang, Y.. Numerical interpretation of physical transitions of a bow boundary layer over an underster axial systematic boundary materials. Phys. Fluids 33,074101, 2021), can be used to obtain a disturbed linear stability equation, namely:
Figure BDA0003726901200000071
in the formula
Figure BDA0003726901200000072
After writing the disturbance phi' in the form of a travelling waveFeature function vectors, i.e.
Figure BDA0003726901200000073
Figure BDA0003726901200000074
Wherein t is time, q 1 ,q 2 And q is 3 Flow direction, normal and circumferential spatial coordinates, respectively, ω is the circular frequency, α is the flow direction wave number, β is the circumferential wave number, c.c. is the complex conjugate, in spatial mode α is complex, i.e. α = α r +iα i In which-alpha i Is the spatial growth rate of the perturbation;
Figure BDA0003726901200000075
the coefficient matrix comprises basic flow, flow direction curvature drx and circumferential direction curvature drz of the wall surface, disturbance circle frequency, wave number, reynolds number and other parameters.
It is then noted that the perturbation flows towards a velocity component v 'as it propagates through the boundary layer of the curved surface of the superhydrophobic surface' 1 And a circumferential velocity component v' 3 Also using slip velocity boundary conditions at the wall where the slip length is also 21 microns, then the linear stability equation (2) at q 2 The wall boundary conditions at =0 are:
Figure BDA0003726901200000076
and finally, based on the flow field of the curved surface boundary layer of the superhydrophobic surface obtained in the third step, solving a linear stability equation (2) at each flow direction position by adopting a numerical method to obtain a contour map with dimensional growth rate distribution of each frequency disturbance wave amplitude value in the boundary layer of the superhydrophobic surface SUBOFF model along the flow direction, as shown in FIG. 6. The numerical method is a well-known means in the art, and is specifically described in flow stability, zhongheng and Zhao Tuo Fu, national defense industry Press.
5. And fifthly, calculating the maximum growth multiple of the growth rate of the disturbance wave amplitude values with different frequencies obtained in the fourth step, and forecasting the natural transition position of the curved surface boundary layer of the super-hydrophobic surface.
Firstly, considering that disturbance waves with different frequencies in a boundary layer with low incoming flow turbulence can continuously grow to a turbulence transition point, then integrating the growth rate-alpha obtained in the fourth step of the flow direction i An amplification factor N value distribution contour map of the disturbance wave amplitude can be obtained, as shown in fig. 7, where the magnitude of N is given by the equation (4):
Figure BDA0003726901200000077
where f is the frequency of a disturbance and q 10 Is the location of the destabilization of the disturbance wave.
Then, envelope is taken for the amplification factor N values at different frequencies, so that the maximum amplification factor Nmax of the disturbance wave at different frequencies at each streaming direction position can be obtained, namely:
Figure BDA0003726901200000081
finally, the maximum increase multiple e of the boundary layer disturbance amplitude of the SUBOFF model of the super-hydrophobic surface can be obtained Nmax The curves are shown in fig. 8. When the maximum growth multiple e Nmax E given by criterion of transition for the first time Ntr When the layer flow is to be transitioned into the turbulent flow, as can be seen from the figure, the corresponding flow direction position is 0.17m, and then the transition position of the SUBOFF model boundary layer on the superhydrophobic surface is 0.17m. In order to clearly see the influence of the super-hydrophobic surface on the transition position of the boundary layer of the SUBOFF model, the slip lengths in the second step and the fourth step are set to be zero, and the transition position of the boundary layer of the SUBOFF model on the common surface is 0.12m. The transition position result shows that the influence of the super-hydrophobic surface on the transition position of the SUBOFF model boundary layer can be well considered.
The forecasting method for the transition position of the curved surface boundary layer of the super-hydrophobic surface not only provides an effective method for accurately forecasting the transition of the curved surface boundary layer of the underwater navigation body such as a revolving body/hydrofoil, but also provides a feasible modeling mode for realizing the boundary condition of the sliding speed of the curved surface of the super-hydrophobic surface.
It will be understood by those skilled in the art that the foregoing embodiments are merely for clarity of description and are not intended to limit the scope of the invention. It will be apparent to those skilled in the art that other variations or modifications may be made on the above invention and still be within the scope of the invention.
The invention has not been described in detail and is in part known to those of skill in the art.

Claims (4)

1. A method for forecasting a transition position of a curved surface boundary layer of a super-hydrophobic surface comprises the following steps:
firstly, dividing a computational domain mesh, wherein one or more layers of meshes of a vertical curved surface are drawn in a near-wall area of a wall surface of a curved surface geometric solid;
secondly, simulating a super-hydrophobic surface of the wall surface of the curved surface geometric body according to the computational domain grid divided in the first step, and listing boundary conditions of wall surface slip speed, wherein the method comprises the following steps:
using the data of the grid points of the wall surface of the curved surface geometric body in the first step, obtaining the tangential direction of the surface at any position of the curved surface geometric body through calculation, and setting the direction as the local sliding speed direction of the super-hydrophobic surface;
calculating the velocity gradient of the normal direction of the local wall surface in the near-wall area grid unit of each vertical curved surface; using linear slip velocity boundary condition assumptions, as shown in equation (1), the wall slip velocity boundary conditions of the superhydrophobic surface geometry are listed:
Figure FDA0003726901190000011
in the formula
Figure FDA0003726901190000012
The sliding speed of the super-hydrophobic surface curved surface geometric body along the tangential direction of the wall surface，U * Is the tangential velocity, y * Is wall normal, λ * For the slip length, the superscript "-" indicates a physical quantity with dimensions;
thirdly, solving an NS equation on a calculation domain grid in the first step according to the wall surface slip speed boundary condition set in the second step, calculating a flow field of a curved surface boundary layer of the super-hydrophobic surface, and interpolating the flow field to an orthogonalized grid of the surface of the curved geometric body along the normal direction to obtain wall surface tangential speed component profiles of all parts;
fourthly, analyzing the flow stability of the flow field of the curved surface boundary layer of the superhydrophobic surface in the third step based on a linear stability theory to obtain the growth rate of each frequency disturbance wave amplitude along the flow direction, wherein the method comprises the following steps:
from the dimensionless NS equation for incompressible flows, the instantaneous amount of flow is decomposed into the sum of the basic flow and the disturbance, i.e.
Figure FDA0003726901190000013
Wherein phi = (v) 1 ,v 2 ,v 3 ,p) T In the form of a vector of instantaneous quantities,
Figure FDA0003726901190000014
is the elementary stream vector, φ '= (v' 1 ,v' 2 ,v' 3 ,p') T As disturbance vector, v 1 ,v 2 ,v 3 Velocity components of the flow direction, the normal direction and the circumferential direction are respectively, p is pressure, a prime mark represents a basic flow, and an upper prime mark represents disturbance quantity; through the linear stability analysis of the flow direction of the aqueous medium and the flow of the curved surface boundary layer with the curvature in the circumferential direction, a disturbed linear stability equation is obtained, namely:
Figure FDA0003726901190000015
in the formula (I), the compound is shown in the specification,
Figure FDA0003726901190000016
representing writing of perturbations phiThe vector of the characteristic function after the form of a travelling wave, i.e.
Figure FDA0003726901190000021
Wherein t is time, q 1 ,q 2 And q is 3 Local flow direction, normal direction and circumferential space coordinates under an orthogonal curve coordinate system are respectively, omega is circular frequency, alpha is flow direction wave number, beta is circumferential wave number, and c.c. is complex conjugate; in the spatial mode, α is a complex number, denoted α = α r +iα i Wherein, - α i For spatial growth rate of the disturbance, α r Flow direction wave number in real number form;
Figure FDA0003726901190000022
Figure FDA0003726901190000023
the coefficient matrix comprises a basic flow, a flow direction curvature drx and a circumferential curvature drz of a wall surface, disturbance circle frequency, wave number and Reynolds number parameters;
the disturbance flows to a velocity component v 'when propagating through the curved boundary layer of the superhydrophobic surface' 1 And a circumferential velocity component v' 3 Applying the slip velocity boundary conditions listed in the second step, at the wall, of the linear stability equation (2) at q 2 The wall boundary conditions at =0 are:
Figure FDA0003726901190000024
based on the flow field of the curved surface boundary layer of the super-hydrophobic surface obtained in the third step, solving a linear stability equation (2) at each flow direction position to obtain a spatial growth rate-alpha of each frequency disturbance wave amplitude value in the boundary layer of the super-hydrophobic surface along the flow direction i ；
Fifthly, calculating the maximum growth multiple of the growth rate of the disturbance wave amplitude values with different frequencies obtained in the fourth step, and forecasting the natural transition position of the curved surface boundary layer of the super-hydrophobic surface, wherein the method comprises the following steps:
for the one obtained in the fourth stepIs measured by a spatial rate-alpha of increase of the amplitude of the wave in the direction of flow i Integrating along the flow direction to obtain an amplification factor N of the disturbance wave amplitude at a certain flow direction position q1, namely:
Figure FDA0003726901190000025
in the formula, f is the frequency of a certain disturbance, q10 is the initial position of integration, and the flow direction position of the frequency disturbance beginning instability is taken;
calculating the maximum increase multiple of the disturbance wave with different frequencies at each flow direction position
Figure FDA0003726901190000026
Wherein N is max For all frequency disturbances in the local q 1 At the maximum value of the N value, i.e. satisfy
Figure FDA0003726901190000027
When maximum increase multiple
Figure FDA0003726901190000028
Critical value given by criterion of transition
Figure FDA0003726901190000029
At this time, the layer flow is considered to be turbulent flow, and at this time
Figure FDA00037269011900000210
The corresponding flow direction position q1 is a position where transition occurs.
2. The method for predicting the transition point of the superhydrophobic surface boundary layer according to claim 1, wherein the step of obtaining the transition point of the superhydrophobic surface boundary layer, the near-wall region vertical meshing in the first step is used to calculate the wall normal velocity gradient at each location.
3. The method for forecasting the transition position of the superhydrophobic surface boundary layer according to claim 1, wherein the transition criterion in the fifth step is taken
Figure FDA0003726901190000031
4. The method for predicting the transition position of the curved boundary layer of the superhydrophobic surface according to claim 1, wherein the flow curvature and the circumferential curvature in the fourth step are set to be zero, so as to predict the transition position of the boundary layer of the superhydrophobic surface.
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