Evaluation device, rough surface, evaluation method and program

Abstract

This evaluation device is for performing evaluation for a specific section where a fluid changes from a laminar flow to a turbulent flow, in a rough surface which is the surface on which the fluid flows, and comprises: an acquisition unit that acquires the thickness of a laminar flow boundary layer at the entrance of the specific section; a calculation unit that calculates turbulent flow energy at the rough surface and a flow direction distribution of a frictional resistance coefficient value by performing direct numerical value calculation based on the acquired thickness of the laminar flow boundary layer; and an output unit that outputs information based on the calculated result.

Description

[Technical field]

[0001] The present invention relates to an evaluation device, a rough surface, an evaluation method, and a program. [Background technology]

[0002] Conventionally, a technique for reducing the frictional resistance of a fluid is known in which riblet processing is performed along the direction of the fluid flow. By performing riblet processing, it is possible to reduce the frictional resistance of a fluid flowing in a predetermined direction, but if the direction of the fluid flow and the direction of the riblet processing deviate by a predetermined angle or more, the frictional resistance will increase instead. In addition, a technique is known in which protrusions having small wavy roughness are used to delay the natural transition and reduce frictional resistance. Thus, the relationship between the shape of the surface through which the fluid flows and the increase in frictional resistance has been actively studied (for example, see Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Y.Kuwata and R.Nagura, Direct numerical simulation on the effects of surface slope and skewness on rough-wall turbulence, “Physics of Fluids”, USA, AIP Publishing, October 8, 2020, 32, 105113-1-15 Summary of the Invention [Problem to be solved by the invention]

[0004] However, according to previous studies, there has been little research on rough surfaces to reduce frictional resistance.

[0005] The present invention has been made in view of the above circumstances, and aims to provide an evaluation device, an evaluation method, and a program that can clarify the mechanism by which frictional resistance is reduced by fine distribution roughness. Another aim of the present invention is to provide a rough surface that can reduce frictional resistance by using the evaluation device, evaluation method, and program. [Means for solving the problem]

[0006] [1] One aspect of the present invention is an evaluation device that performs evaluation of a specific section of a rough surface over which a fluid flows, where the flow transitions from laminar to turbulent, and includes an acquisition unit that acquires the thickness of the laminar boundary layer at the inlet of the specific section, a calculation unit that calculates the turbulent energy on the rough surface and the flow direction distribution of the friction resistance coefficient value by performing direct numerical calculation based on the acquired thickness of the laminar boundary layer, and an output unit that outputs information based on the calculated results.

[0007] [2] In one aspect of the present invention, in the evaluation device described in [1] above, the calculation unit calculates the turbulent energy and the flow direction distribution of the friction coefficient value on the rough surface by using the VP method (Volume Penalization Method) and the Zonal Method.

[0008] [3] In one aspect of the present invention, in the evaluation device described in [1] or [2] above, the acquisition unit acquires the thickness of the laminar boundary layer at the inlet of the specific section based on an image of the rough surface.

[0009] [4] In one aspect of the present invention, in the evaluation device described in any one of [1] to [3] above, the evaluation device further includes an identification unit that identifies a transition position from laminar flow to turbulent flow based on the calculated turbulent energy on the rough surface and the flow direction distribution of the friction resistance coefficient value, and the output unit outputs the identified transition position.

[0010] [5] In one aspect of the present invention, in the evaluation device described in any of [1] to [4] above, the acquisition unit acquires laminar boundary layer thicknesses at the inlet of the specific section for the plurality of rough surfaces, and the calculation unit performs direct numerical calculation based on the acquired thicknesses of the plurality of laminar boundary layers to calculate a flow direction distribution of turbulent energy and friction coefficient values ​​for each of the plurality of rough surfaces, and the evaluation device further includes a selection unit that selects the rough surfaces that can suppress the growth of vortices and destroy the generated vortices based on the calculated flow direction distribution of turbulent energy and friction coefficient values ​​for each of the plurality of rough surfaces.

[0011] [6] In one aspect of the present invention, in the evaluation device described in [5] above, the selection unit decomposes the variables of the Navier-Stokes equations into time-invariant variables and time-varying variables, and selects the rough surface that can suppress the growth of a vortex and promote neutralization by destroying the generated vortex based on the wavelength of the vortex that is amplified when a random number is given as a disturbance.

[0013] [ 7 One aspect of the present invention is the [5] or [6] Described in Selected by the evaluation device On rough surfaces, A rough surface over which a fluid flows, The surface has first protrusions based on a first wavelength, which is a wavelength that can suppress the growth of vortices, and second protrusions based on a second wavelength, which is a wavelength different from the first wavelength and can promote the destruction of generated vortices, and has the first protrusions and the second protrusions in both a first direction that is parallel to the rough surface and is the advection direction of the vortex, and a second direction that is parallel to the rough surface and is perpendicular to the first direction.

[0014] [ 8One aspect of the present invention is an evaluation method for evaluating a specific section of a rough surface over which a fluid flows, where the flow transitions from laminar to turbulent, the evaluation method including an acquisition step of acquiring the thickness of the laminar boundary layer at the inlet of the specific section, a calculation step of calculating the turbulent energy on the rough surface and the flow direction distribution of friction resistance coefficient values ​​by performing direct numerical calculation based on the acquired thickness of the laminar boundary layer, and an output step of outputting information based on the calculated results.

[0015] [ 9 One aspect of the present invention is a program for causing a computer to perform an evaluation of a specific section of a rough surface over which a fluid flows, where the flow transitions from laminar to turbulent, the program comprising: an acquisition step of acquiring the thickness of the laminar boundary layer at the inlet of the specific section; a calculation step of calculating the turbulent energy and the flow direction distribution of friction resistance coefficient values ​​on the rough surface by performing direct numerical calculation based on the acquired thickness of the laminar boundary layer; and an output step of outputting information based on the calculated results. Effect of the Invention

[0016] According to the present invention, it is possible to provide an evaluation device, an evaluation method, and a program that can clarify the mechanism of frictional resistance reduction caused by fine distribution roughness. Furthermore, the present invention can provide a rough surface that can reduce frictional resistance by using the evaluation device, evaluation method, and program. [Brief description of the drawings]

[0017] [Figure 1] 1 is a diagram for explaining a specific section that is an evaluation target of an evaluation device in an embodiment. FIG. [Diagram 2] FIG. 11 is a diagram for explaining a boundary condition in the embodiment. [Diagram 3] 11A and 11B are diagrams illustrating an example of a mask function shape near a wall and a grid resolution in the embodiment. [Figure 4]FIG. 2 is a diagram showing an example of a zonal grid used by the evaluation device according to the embodiment. [Diagram 5] FIG. 2 illustrates the geometry of a roughened surface according to an embodiment. [Figure 6] FIG. 13 is a diagram illustrating an example of a visualization of a simulation result obtained by the evaluation device according to the embodiment. [Figure 7] 11 is a contour map for explaining a comparison of turbulent kinetic energy for each type of rough surface according to an embodiment. [Figure 8] FIG. 13 is a diagram showing the maximum value of turbulent kinetic energy along the x direction for each type of rough surface according to the embodiment. [Figure 9] FIG. 13 is a diagram showing changes in the decomposition integral value of turbulent kinetic energy in the Z direction and the frictional resistance coefficient value along the X direction according to the embodiment. [Figure 10] FIG. 13 illustrates a number of snapshots taken at different times for different types of rough surfaces according to an embodiment. [Figure 11] 13 is a contour map of phase, time, and span-averaged turbulent kinetic energy in a TS wave component according to an embodiment. [Figure 12] 13 is a contour map of phase-, time-, and span-averaged turbulent kinetic energy in a three-dimensional structure of a TS wave component according to an embodiment. [Figure 13] FIG. 2 is a functional configuration diagram illustrating an example of a functional configuration of an evaluation device according to an embodiment. [Figure 14] 1 is a flowchart illustrating an example of an evaluation device method according to an embodiment. [Figure 15] 1 is a block diagram showing an example of an internal configuration of an evaluation device 10 according to the present embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] [Embodiment] The evaluation device, rough surface, evaluation method, and program according to the aspects of the present invention will be described in detail below with reference to the accompanying drawings, with preferred embodiments presented. The aspects of the present invention are not limited to these embodiments, and include various modifications or improvements. In other words, the components described below include those that a person skilled in the art can easily imagine, and those that are substantially the same, and the components described below can be appropriately combined. In addition, various omissions, substitutions, or modifications of the components can be made without departing from the gist of the present invention. In addition, in the following drawings, the scale and number of each structure may be different from the scale and number of the actual structure in order to make each structure easier to understand.

[0019] FIG. 1 is a diagram for explaining a specific section to be evaluated by the evaluation device in the embodiment. The figure shows a boundary layer developed on a flat plate. More specifically, the figure shows a laminar boundary layer composed of laminar flow. It is known that the boundary layer is strongly affected by viscosity. In the illustrated example, the fluid flows from upstream to downstream, with the left direction being the upstream direction and the right direction being the downstream direction. As it flows from upstream to downstream, it transitions from laminar flow (a state in which the flow is gentle and has low friction resistance) to turbulent flow (a state in which the flow is turbulent and has high friction resistance). Further downstream (not shown) from the laminar boundary layer as illustrated, it passes through a transition region and becomes a turbulent boundary layer. By using the evaluation device according to the present embodiment, it is possible to reduce the overall friction resistance by providing a rough surface that can suppress and destroy the growth of vortices related to the transition.

[0020] Whether a flow is laminar or turbulent can be determined by the magnitude of turbulent energy. An increase in turbulent energy downstream means that a transition from laminar to turbulent flow has occurred. Friction resistance itself is evaluated more directly by Reynolds stress than by turbulent energy. It is generally known that turbulent energy and Reynolds stress are highly correlated.

[0021] In general, it is known that a surface with riblet processing has an effect on a flow that has already developed into a turbulent flow. The evaluation device according to the present embodiment aims to obtain an effect in the region including the transition region from laminar flow to turbulent flow and the turbulent flow region by performing an evaluation in the region. In other words, it can be said that the conventional technology such as riblets and the rough surface provided by the evaluation device according to the present embodiment have different unstable modes. In the following description, the section that is the target of evaluation by the evaluation device according to the present embodiment may be referred to as a specific section (Test Section). The specific section can also be said to be the section between the transition from laminar flow to turbulent flow and the turbulent flow region of the rough surface on which the fluid flows.

[0022] The figure also shows the velocity distribution of the fluid at the entrance of a particular section. Generally speaking, due to the viscosity of the fluid, the closer to the object surface, the slower the fluid velocity is, and the velocity is zero at the surface, and the further away from the surface, the faster the fluid velocity is. In a laminar boundary layer, the upper and lower layers are less intermixed, so separation is likely to occur, but because there is less intermixing, frictional resistance is small. In other words, since frictional resistance is small in a laminar boundary layer, the velocity distribution has a gradual decrease in velocity depending on the distance from the object surface. In a turbulent boundary layer, the region near the object surface where the fluid velocity is slow is called the viscous sublayer or inner layer. In addition, the region far from the object surface where the fluid velocity is fast is called the turbulent layer or outer layer. Furthermore, the region between the viscous sublayer and the turbulent layer is called the buffer layer.

[0023] In addition, the thickness of the laminar boundary layer at the inlet of a specific section is indicated as δs in the figure. The evaluation device according to this embodiment performs direct numerical calculation (Direct Numerical Simulation, DNS) based on δs to calculate the turbulent energy on the rough surface and the flow direction distribution of the friction coefficient value.

[0024] Fluids to be evaluated by the evaluation device according to this embodiment include water, oil, air, and the like. The width of the boundary layer (including the viscous sublayer in the turbulent state) is determined by the composition of the fluid. The rough surface provided by the evaluation device according to this embodiment can reduce frictional resistance even if the roughness height is equivalent to the width of the viscous sublayer in the turbulent state or smaller. According to the rough surface provided by the evaluation device according to this embodiment, the kinetic energy that brings about laminar-turbulent transition can be reduced, and frictional resistance can be reduced by delaying the transition and suppressing turbulent regeneration. In addition, in a turbulent state, the kinetic energy of the fluid is stably consumed in the surface very near region by the micro-rough surface distributed in a sand-like shape with a size equivalent to or smaller than the viscous sublayer. It can also be said that the rough surface provided by the evaluation device according to this embodiment has a structure that can obtain such effects.

[0025] FIG. 2 is a diagram for explaining boundary conditions in the embodiment. The figure shows a rough surface to be evaluated by the evaluation device according to the embodiment. As shown in the figure, the rough surface is arranged along the xy plane. The direction perpendicular to the rough surface is described as the z direction. Since a finite calculation area is handled in the numerical calculation, it is preferable to give appropriate boundary conditions. In addition, since a boundary layer is formed in the flow on the rough surface, the grid spacing may be arranged denser closer to the rough surface. In addition, since the flow field becomes closer to a steady main flow from the rough surface to the distance, the grid spacing may be arranged gradually wider. In other words, grid stretching may be performed.

[0026] The boundary conditions used in the calculation by the evaluation device according to this embodiment will be described. According to this embodiment, the turbulent transition process is analyzed by performing three-dimensional direct numerical calculation, so it is preferable to reduce the calculation cost and set the calculation domain efficiently. The Reynolds number based on the thickness δs of the laminar boundary layer at the inlet is set to 3535. In order to obtain a sufficiently large time step within a range in which the compressibility effect can be ignored, the Mach number is set to 0.2. In addition, the displacement is non-dimensionalized by the boundary layer thickness at the inlet boundary, and the calculation domain in the flow direction is 56.6.

[0027] The inlet boundary condition gives the streamwise velocity and wall-normal velocity obtained by the Blasius laminar flow solution, and the density and pressure are the same as those of the main flow. The inlet boundary condition adds an artificial disturbance to the wall-normal velocity to induce Tollmien-Schlichting (TS) waves. Note that a rough surface may be placed away from the inlet boundary in order to analyze the effect of the rough surface after the artificial disturbance is accepted by the boundary layer. The computational domain in the spanwise direction may be determined based on a two-point correlation of ω dash (fluctuation component of the height direction velocity). Periodic conditions are applied to the boundaries in the spanwise direction.

[0028] At the exit boundary, velocity and pressure are allowed to be free. At the far boundary in the wall-normal direction, pressure and velocity are fixed, and wall-normal and spanwise velocities are allowed to be free. At the exit boundary, density, velocity, and pressure are allowed to be free conditions (Dirichlet boundary conditions). At the far boundary in the wall-normal direction, pressure and streamwise velocity are fixed to free-stream values, and wall-normal and spanwise velocities are allowed to be free conditions. At the wall boundary, a no-slip condition is applied, and velocities in all directions are fixed to zero. Adiabatic wall conditions are also assumed, and density and pressure have zero gradients in the wall-normal direction.

[0029] The evaluation device according to this embodiment reproduces rough surfaces of three-dimensional shapes using the VP method (Volume Penalization Method). The VP method for compressible flows can impose a no-slip condition on any fixed wall shape by adding a penalty term to the governing equation, the Navier-Stokes equation. By using the VP method, it is not necessary to generate a grid that fits the solid wall, and walls of any shape can be analyzed.

[0030] The Navier-Stokes equations with the penalty term added are expressed by the following equations (1) to (3).

[0031]

number

[0032]

number

[0033]

number

[0034] where ρ is the density of the fluid, u i is the flow velocity, U 0,i is the solid wall velocity, which is set to 0 to impose the no-slip condition. φ is the porosity, which is set to 1.0. κ is the thermal conductivity, τ ij is the viscous stress, and ν is the permeability, both of which are assumed to be sufficiently small. T is the thermal effusivity, which is assumed to be the same as ν. Also, e is the total energy, p is the pressure, T is the temperature, and T0 is the solid wall temperature. According to this embodiment, since temperature changes can be ignored in low Mach number flows, the solid wall temperature is assumed to be the same as the mainstream. Also, χ is a mask function, and since the VP method does not require the generation of a boundary-fitted mesh, it is possible to reproduce a solid wall of any shape by defining the mask function by the following equation (4).

[0035]

number

[0036] 3 is a diagram showing an example of a mask function shape near a wall and a grid resolution in the embodiment. The line W1 shown in the figure indicates the roughness height of the fluid, and the dashed line indicates the average roughness height h m As the mask function is defined on an orthogonal grid in this way, in order to reproduce the shape of the fixed wall, it is preferable to resolve the roughness with a sufficient number of grid points in both the flow direction and the wall normal direction. The resolution should be about 20 points or more per wavelength of roughness.

[0037] In addition, the VP method ensures the number of grid points inside the wall by offsetting the origin in the wall normal direction from the edge of the computational grid. In other words, the area below the line W1 in the figure is defined as a solid wall, and the area above is calculated as a fluid region.

[0038] Here, in order to reproduce the shape of the rough surface with an orthogonal grid, it is preferable to use a sufficiently fine grid resolution. However, if such a calculation is performed for the entire calculation domain, it will require a huge calculation cost. Therefore, in this embodiment, an overset grid method (Zonal method) is applied to capture turbulence with high accuracy while suppressing the calculation cost. The Zonal method is a method of performing numerical calculations using two or more calculation grids. By applying the Zonal method, it is possible to perform calculations of complex shapes that are difficult to perform with a single calculation grid, or to perform calculations by locally increasing the grid resolution. For example, the Zonal method is used for detailed flow field analysis of the internal flow of the intake of a supersonic aircraft in the main wing of an aircraft, and for analysis of the area around a plasma actuator installed on the leading edge of the main wing.

[0039] FIG. 4 is a diagram showing an example of a zonal grid used by the evaluation device according to the embodiment. In the evaluation device according to the embodiment, it is preferable to set a locally high grid resolution near the wall in order to reproduce the shape of the wall surface. The area shown by the line W2 in the figure is the local zone, and the area shown by the line W3 is the global zone. The local zone has a grid resolution in the flow direction that is twice that of the global zone. The height of the local zone is expressed as Lz + ≈50, which includes the viscous sublayer and buffer layer in the turbulent boundary layer.

[0040] The resolution of the global zone is specifically (Nx, Ny, Nz) = (1454, 151, 284). The computational domain length is (Lx, Ly, Lz) = (56.6, 11.3, 28.3) in the flow direction, span direction, and wall normal, respectively. On the other hand, the resolution of the local zone is specifically (Nx, Ny, Nz) = (2843, 201, 137). The computational domain is (Lx, Ly, Lz) = (50.9, 11.3, 0.59). However, in the smooth surface and the wavy rough surface as comparative examples, Ny = 201 and Ly = 14.1 in the span direction, but in the calculation of the sandy rough surface as an example, Ly = 11.3 was used. This is because a high resolution is required to reproduce the fine unevenness of the rough surface, so it is preferable to reduce the computational domain in the span direction.

[0041] The evaluation device according to this embodiment may analyze a sandy rough surface based on data obtained by laser measurement of an actual sandpaper. Conventionally, it has been known that the friction coefficient value in a fully developed turbulent flow depends on the height of the roughness. In recent years, it has been noted that the friction coefficient value in a fully developed turbulent flow depends on the effective slope ES, which is a parameter that determines the shape of the roughness, and the skewness Sk. The effective slope ES and skewness Sk of the rough surface provided by the evaluation device according to this embodiment are calculated by the following equations (5) and (6).

[0042]

number

[0043]

number

[0044] The skewness Sk, also known as the degree of deviation, is a parameter that indicates the deviation in the distribution of peaks and valleys on a rough surface. For example, when considering the distribution of the probability of existence for each roughness height, if Sk=0, the roughness distribution is symmetrical, if Sk>0, the proportion of peaks is high, and if Sk<0, the proportion of valleys is high. The effective gradient ES is defined as the average value of the inclination. It can also be said that the effective gradient ES is the ratio of the roughness height to the roughness interval. For a wavy rough surface, the effective gradient ES can be expressed as ES=h / λ, where h is the roughness height and λ is the roughness wavelength.

[0045] In this embodiment, specifically, the skewness Sk = -0.097, and the effective gradient ES = 0.130. It is known that when the effective gradient ES is relatively small, the difference in δU+ due to the value of the skewness Sk is small, suggesting that the difference in the skewness Sk is not so important.

[0046] Specifically, the inventors used a sandpaper roughness of grit size 1000, scaled to a height of 0.092. Having found that this rough surface was effective, they next artificially simulated it using a Gaussian function, and found that a similar effect could be obtained. In the case of sandpaper roughness, it is preferable to use a repeating pattern, since a single sand-like roughness data cannot completely cover the entire calculation area. Note that when simulating using a Gaussian function, it is not necessary to use a repeating pattern.

[0047] FIG. 5 is a diagram showing the geometric shape of a rough surface according to an embodiment. An example of a repeating pattern will be described with reference to the figure. A rectangle surrounded by a dashed line in the figure indicates one unit tile. By continuously arranging the unit tiles, the entire calculation area can be completely covered. As shown in the figure, it can be seen that the repeating boundaries of the rough surface are smoothly connected. In addition, the unit tiles are not limited to an example of being continuously arranged in one direction as shown in the figure, but may be continuously arranged in two-dimensional directions.

[0048] Here, it is not easy to determine the viscosity unit precisely in the transition process. However, it is possible to convert the viscosity scale to a viscosity scale by calculating the viscosity scale from the flow field data on the smooth surface and assuming that the calculated viscosity scale is the same turbulent scale on the rough surface. In this case, the average height in this embodiment is h+m=15.5.

[0049] 6 is a diagram showing an example of a visualization of the results of a simulation performed by the evaluation device according to the embodiment. The left side of the figure shows the upstream flow, and the right side shows the downstream flow. As shown in the figure, the TS wave in the form of a two-dimensional roll vortex induced at the inlet boundary is advected downstream, and eventually distorts while rippling in the orthogonal span depth direction, and then breaks down into turbulent flow.

[0050] FIG. 7 is a contour map for explaining a comparison of turbulent kinetic energy for each type of rough surface according to the embodiment. In the figure, vortices are visualized by Q values ​​in the instantaneous field in three rough surfaces. The left side of the figure shows the upstream of the flow, and the right side shows the downstream. FIG. 7(a) is an example of a sandy rough surface (sandy roughness, sandpaper roughness, or sand-grind roughness), and is a diagram of a case where a rough surface provided by the evaluation device according to the present embodiment is used. FIG. 7(b) is an example of wavy roughness (VP ​​method), and is a comparative example. FIG. 7(c) is an example of wavy roughness (Body Fitted grid), and is a comparative example. FIG. 7(c) is an example of a flat plate (smooth surface), and is a comparative example.

[0051] FIG. 8 is a diagram showing the maximum value of turbulent kinetic energy along the x direction for each type of rough surface according to the embodiment. As an example of a case where a rough surface provided by the evaluation device according to the embodiment is used, a sandy rough surface is shown. In addition, wavy roughness (VP), wavy roughness (BF), and smooth (flat plate or smooth surface) are shown as comparative examples. It is clear from the figure that, in the sandy rough surface, the TS wave collapses early, suppressing the generation of disturbances that occur when the TS wave collapses after it grows. In other words, it is found from the figure that the sandy rough surface suppresses the turbulent kinetic energy TKE (turbulent kinetic energy) the most.

[0052] FIG. 9 is a diagram showing the change along the X direction for the decomposition integral value of the turbulent kinetic energy in the Z direction and the frictional resistance coefficient value according to the embodiment. FIG. 9(a) and FIG. 9(b) show the change along the X direction for the decomposition integral value of the turbulent kinetic energy in the Z direction. FIG. 9(c) and FIG. 9(d) show the change along the X direction for the frictional resistance coefficient value. FIG. 9(a) and FIG. 9(c) are an example of a flat plate (smooth surface) and are comparative examples. FIG. 9(b) and FIG. 9(d) are an example of a sandy rough surface, and are diagrams showing the case where a rough surface provided by the evaluation device according to the embodiment is used. As can be seen from the diagram, in the sandy rough surface, the decomposition integral value of the turbulent kinetic energy in the Z direction and the frictional resistance coefficient value are both kept low compared to the flat plate (smooth surface).

[0053] FIG. 10 is a diagram showing a plurality of snapshots at different times for each type of rough surface according to the embodiment. FIG. 10(A) is an example of a flat plate (smooth surface) and is a comparative example. FIG. 10(B) is an example of a sandy rough surface, and is a diagram showing a case where a rough surface provided by the evaluation device according to the embodiment is used. FIG. 10(C) is an example of wavy roughness and is a comparative example. These snapshots show how TS waves are induced at the inlet boundary, propagate in the flow direction, and eventually break down into a three-dimensional structure. Comparing the positions at which the roll vortex breaks down, it can be seen that the breakup occurs most quickly in the case where the rough surface provided by the evaluation device according to the embodiment is used among the three cases shown in the figure.

[0054] Here, according to the present embodiment, in order to clarify the difference in the transition process based on the TS wave period, phase average decomposition is applied. Specifically, the turbulent kinetic energy k is divided into k tilde, which indicates the TS wave component, and k dash, which indicates the three-dimensional component, as shown in the following equation (7).

[0055]

number

[0056] Furthermore, the turbulent kinetic energy k can be divided into a time-varying term and a time-invariant term, as shown in the following equation (8).

[0057]

number

[0058] k bar is a time average (a term that does not vary with time). k tilde and k two dashes are terms that vary with time. More specifically, k tilde indicates a TS wave component, and k two dashes indicates a three-dimensional component. k tilde is a term that contributes to the roll vortex not growing, and k two dashes is a term that contributes to crushing the roll vortex. According to this embodiment, by decomposing the turbulent kinetic energy k into three terms in this way, the roll vortex is not allowed to grow, and even if the roll vortex does grow, it can be crushed.

[0059] FIG. 11 is a contour map of turbulent kinetic energy averaged over phase, time, and span in a TS wave component according to an embodiment. FIG. 12 is a contour map of turbulent kinetic energy averaged over phase, time, and span in a three-dimensional structure of a TS wave component according to an embodiment. FIG. 11(a) and FIG. 12(a) are an example of a smooth surface (flat plate, or smooth surface) and are comparative examples. FIG. 11(b) and FIG. 12(b) are an example of a sandy rough surface, and are diagrams of a case where a rough surface provided by the evaluation device according to the present embodiment is used. FIG. 11(c) and FIG. 12(c) are an example of wavy roughness and are comparative examples.

[0060] Comparing the turbulent kinetic energy k on the three rough surfaces, the sandy rough surface is found to be the smallest on the downstream side. From the decomposition statistics, it can be seen that the sandy rough surface reduces the TS wave kinetic energy more than the other two rough surfaces. Also, it can be seen that the three-dimensional kinetic energy increases the most on the upstream side, but decreases on the downstream side. In the instantaneous visualization, the sandy rough surface is the one where three-dimensionalization occurs the fastest. However, the break weakens the TS wave motion, and as a result, the total turbulent kinetic energy is smaller on the downstream side. In addition, the wavy roughness also suppresses the TS wave kinetic energy, but the total turbulent kinetic energy is larger than that of the sandy rough surface. This is due to the vortex generated at the top of the wavy roughness.

[0061] As explained above, we found that TS waves are weakened on a sandy rough surface. We also found that the decomposition of TS waves is promoted on a sandy rough surface, but the total turbulent kinetic energy and the friction coefficient value are suppressed.

[0062] Next, an example of a specific implementation of the evaluation device described above will be described with reference to FIGS.

[0063] FIG. 13 is a functional configuration diagram showing an example of the functional configuration of an evaluation device according to an embodiment. With reference to the same figure, an example of the functional configuration of the evaluation device 10 will be described. The evaluation device 10 includes an acquisition unit 11, a calculation unit 12, a storage unit 13, an identification unit 14, a selection unit 15, and an output unit 16. Each of these functional units is realized, for example, by using an electronic circuit. Furthermore, each functional unit may include a storage means such as a semiconductor memory or a magnetic hard disk device inside as necessary. Furthermore, each function may be realized by a computer having a CPU (Central Processing Unit) and software.

[0064] The acquisition unit 11 acquires the thickness δs of the laminar boundary layer at the entrance of a specific section for the rough surface to be evaluated by the evaluation device 10. In this embodiment, for example, the rough surface to be evaluated is imaged by the imaging device 20, and the acquisition unit 11 may acquire the thickness δs of the laminar boundary layer by image processing of image information of the rough surface. The imaging device 20 may be a CCD camera using a CCD (Charge Coupled Devices) image sensor, or a CMOS camera using a CMOS (Complementary Metal Oxide Semiconductor) image sensor. In addition, the image captured by the imaging device 20 may be a color image or a monochrome image. When evaluating a plurality of rough surfaces, the acquisition unit 11 may acquire the thickness δs of the laminar boundary layer for the plurality of rough surfaces.

[0065] The calculation unit 12 calculates the turbulent energy and the flow direction distribution of the friction coefficient value at the rough surface by performing a direct numerical simulation (DNS) based on the acquired laminar boundary layer thickness δs. Specifically, the calculation unit 12 calculates the turbulent energy and the flow direction distribution of the friction coefficient value at the rough surface by using the above-mentioned VP method (Volume Penalization Method) and oval grid method (Zonal Method). When evaluating a plurality of rough surfaces, the calculation unit 12 may calculate the turbulent energy and the flow direction distribution of the friction coefficient value at each of the plurality of rough surfaces by performing a direct numerical simulation based on the acquired thicknesses δs of the plurality of laminar boundary layers.

[0066] The storage unit 13 includes, for example, a hard disk drive (HDD), a solid state drive (SSD), a flash memory, a read only memory (ROM), etc. The storage unit 13 stores parameters and the like used in the calculation.

[0067] The identifying unit 14 identifies the transition position from laminar flow to turbulent flow based on the turbulent energy on the rough surface calculated by the calculation unit 12 and the flow direction distribution of the friction resistance coefficient values.

[0068] The selection unit 15 selects a rough surface capable of suppressing the growth of a vortex and destroying a generated vortex based on the turbulent energy of each of the multiple rough surfaces calculated by the calculation unit 12 and the flow direction distribution of the friction coefficient value. The selection unit 15 decomposes the variables of the Navier-Stokes equation into a variable that does not vary with time (e.g., a time-averaged variable) and a variable that varies with time, identifies a wavelength that is amplified when a random number is given as a disturbance, and selects a rough surface capable of suppressing the growth of a vortex and destroying a generated vortex based on the identified wavelength. The selection unit 15 may decompose the turbulent kinetic energy k into a variable that does not vary with time and a variable that varies with time, for example, as shown in equations (7) and (8).

[0069] The output unit 16 outputs information based on the result of the calculation by the calculation unit 12. The output unit 16 may also output the transition position identified by the identification unit 14. Furthermore, the output unit 16 may output information about the rough surface selected by the selection unit 15.

[0070] The rough surface provided by the evaluation device 10 is a rough surface on which a fluid flows, and is a sandy rough surface having a plurality of sandy protrusions. The rough surface provided by the evaluation device 10 has at least a first protrusion and a second protrusion as protrusions constituting the sandy rough surface. The first protrusion is based on a first wavelength that is a wavelength that can suppress the growth of vortices. The second protrusion is based on a second wavelength that is a wavelength different from the first wavelength and is a wavelength that can destroy the generated vortex. The rough surface provided by the evaluation device 10 is not effective only in a predetermined direction like a riblet, but is effective in various directions. That is, the first protrusion and the second protrusion are provided in both the first direction that is parallel to the rough surface and is the direction in which vortices are advected, and the second direction that is parallel to the rough surface and perpendicular to the first direction.

[0071] FIG. 14 is a flowchart showing an example of an evaluation method using the evaluation device 10 according to the embodiment. With reference to the same figure, an example of an evaluation method using the evaluation device 10 according to the present embodiment will be described. First, the evaluation device 10 acquires the thickness δs of the laminar boundary layer (step S11). Next, the evaluation device 10 calculates the turbulent energy and the flow direction distribution of the friction resistance coefficient value by performing direct numerical calculation based on the acquired thickness δs of the laminar boundary layer (step S13). Next, the evaluation device 10 identifies the transition position from laminar flow to turbulent flow based on the calculation result (step S15). In addition, the evaluation device 10 selects, from among the multiple rough surfaces, a rough surface that can suppress the growth of vortices and destroy the generated vortex (step S17). Finally, the evaluation device 10 outputs the calculation result (step S19).

[0072] FIG. 15 is a block diagram showing an example of the internal configuration of the evaluation device 10 according to the present embodiment. At least some of the functions of the evaluation device 10 can be realized using a computer. As shown in the figure, the computer includes a central processing unit 901, a RAM 902, an input / output port 903, input / output devices 904 and 905, and a bus 906. The computer itself can be realized using existing technology. The central processing unit 901 executes instructions included in a program read from the RAM 902 or the like. The central processing unit 901 writes data to the RAM 902, reads data from the RAM 902, and performs arithmetic and logical operations according to each instruction. The RAM 902 stores data and programs. Each element included in the RAM 902 has an address and can be accessed using the address. Note that RAM is an abbreviation for "random access memory." The input / output port 903 is a port through which the central processing unit 901 exchanges data with an external input / output device or the like. The input / output devices 904 and 905 are input / output devices. Input / output devices 904 and 905 exchange data with the central processing unit 901 via an input / output port 903. A bus 906 is a common communication path used within the computer. For example, the central processing unit 901 reads and writes data from and to a RAM 902 via the bus 906. Also, for example, the central processing unit 901 accesses the input / output port via the bus 906.

[0073] [Summary of the embodiment] As described above, the evaluation device 10 performs evaluation of a specific section of a rough surface over which a fluid flows, where the flow transitions from laminar to turbulent. The evaluation device 10 includes an acquisition unit 11 to acquire the thickness δs of the laminar boundary layer at the inlet of the specific section, a calculation unit 12 to perform direct numerical calculation based on the acquired thickness δs of the laminar boundary layer, calculates the turbulent energy on the rough surface and the flow direction distribution of the frictional resistance coefficient value, and an output unit 16 to output information based on the calculated results. By adopting such a configuration, the evaluation device 10 can clarify the mechanism by which frictional resistance is reduced by fine distribution roughness.

[0074] According to the above-mentioned embodiment, the calculation unit 12 calculates the turbulent energy and the flow direction distribution of the friction coefficient value on the rough surface by using the VP method (Volume Penalization Method) and the Zonal Method. Therefore, according to the present embodiment, the calculation can be performed by direct numerical calculation.

[0075] According to the above-described embodiment, the acquisition unit 11 acquires the thickness δs of the laminar boundary layer at the inlet of the specific section based on an image of the rough surface. That is, according to the present embodiment, the evaluation device 10 performs evaluation based on image information of the rough surface through which the fluid flows. Therefore, according to the present embodiment, the rough surface can be easily evaluated.

[0076] According to the above-described embodiment, the identifying unit 14 is further provided, and identifies the transition position from laminar flow to turbulent flow based on the calculated turbulent energy on the rough surface and the flow direction distribution of the friction resistance coefficient value. Therefore, according to the present embodiment, the evaluation device 10 can identify the transition position from laminar flow to turbulent flow.

[0077] According to the above-described embodiment, the acquisition unit 11 acquires the thickness δs of the laminar boundary layer for the plurality of rough surfaces, and the calculation unit 12 performs direct numerical calculation based on the acquired thickness δs of the laminar boundary layer to calculate the turbulent energy and the flow direction distribution of the friction coefficient value for each of the plurality of rough surfaces. Furthermore, the evaluation device 10 includes the selection unit 15, and selects a rough surface that can suppress the growth of vortices and destroy the generated vortex based on the calculated turbulent energy and the flow direction distribution of the friction coefficient value for each of the plurality of rough surfaces. Therefore, according to the present embodiment, a rough surface that can efficiently reduce friction resistance can be selected.

[0078] According to the embodiment described above, the selection unit 15 decomposes the variables of the Navier-Stokes equations into time-invariant variables and time-variant variables, identifies a wavelength that is amplified when a random number is applied as a disturbance to each of the rough surfaces, and selects a rough surface that can suppress the growth of vortices and destroy the generated vortices based on the identified wavelength. Therefore, according to the embodiment, it is possible to select a rough surface that can efficiently reduce frictional resistance by direct numerical calculation.

[0079] Furthermore, according to the above-described embodiment, it is possible to provide a rough surface on which a fluid flows and which is selected using the above-described evaluation device 10. Therefore, according to the present embodiment, it is possible to provide a rough surface that is capable of reducing frictional resistance.

[0080] According to the above-mentioned embodiment, the rough surface according to this embodiment has first protrusions based on a first wavelength that is a wavelength capable of suppressing the growth of vortices, and second protrusions based on a second wavelength that is a wavelength different from the first wavelength and capable of destroying the generated vortices, and has the first protrusions and the second protrusions in both a first direction parallel to the rough surface and a second direction parallel to the rough surface and perpendicular to the first direction. By having such protrusions, the rough surface according to this embodiment can reduce frictional resistance in any direction without specifying a direction in which it is effective.

[0081] The above describes the form for carrying out the present invention using an embodiment, but the present invention is not limited to such an embodiment, and various modifications and substitutions can be made within the scope that does not deviate from the spirit of the present invention.

[0082] In addition, a computer program for implementing the functions of each of the above-mentioned devices may be recorded on a computer-readable recording medium, and the program recorded on the recording medium may be read into a computer system and executed. Note that the "computer system" referred to here may include hardware such as an OS and peripheral devices. In addition, the term "computer-readable recording medium" refers to writable non-volatile memory such as a flexible disk, an optical magnetic disk, a ROM, or a flash memory, a portable medium such as a DVD (Digital Versatile Disc), or a storage device such as a hard disk built into a computer system.

[0083] Furthermore, the term "computer-readable recording medium" includes a memory that holds a program for a certain period of time, such as a volatile memory (e.g., DRAM (Dynamic Random Access Memory)) inside a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. The above-mentioned program may be transmitted from a computer system that stores the program in a storage device or the like to another computer system via a transmission medium, or by a transmission wave in the transmission medium. Here, the "transmission medium" that transmits the program refers to a medium that has a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. The above-mentioned program may be a program for realizing part of the above-mentioned functions. Furthermore, the above-mentioned function may be realized in combination with a program already recorded in the computer system, that is, a so-called difference file (difference program). [Explanation of symbols]

[0084] 1... evaluation system, 10... evaluation device, 11... acquisition unit, 12... calculation unit, 13... storage unit, 14... identification unit, 15... selection unit, 16... output unit, 20... imaging device

Claims

1. An evaluation device for evaluating a specific section of a rough surface where a fluid flows over the surface and transitions from laminar flow to turbulent flow, comprising: an acquisition unit that acquires a thickness of a laminar boundary layer at an inlet of the specific section; a calculation unit that calculates a flow direction distribution of turbulent energy and a flow direction distribution of a friction coefficient value on the rough surface by performing a direct numerical calculation based on the obtained thickness of the laminar boundary layer; an output unit that outputs information based on the calculated result; An evaluation device comprising:

2. The calculation unit calculates the turbulent energy and the flow direction distribution of the friction coefficient value on the rough surface by using a volume penalization method (VP method) and a zonal method. The evaluation device according to claim 1 .

3. The acquisition unit acquires a thickness of a laminar boundary layer at an inlet of the specific section based on an image of the rough surface. The evaluation device according to claim 1 or 2.

4. and a determination unit that determines a transition position from a laminar flow to a turbulent flow based on the calculated turbulent energy on the rough surface and a flow direction distribution of the friction resistance coefficient value, The output unit outputs the identified transition position. The evaluation device according to claim 1 or 2.

5. The acquisition unit acquires a thickness of a laminar boundary layer at an inlet of the specific section for the plurality of rough surfaces, the calculation unit calculates a flow direction distribution of turbulent energy and a flow direction distribution of a friction coefficient value for each of the plurality of rough surfaces by performing a direct numerical calculation based on the thicknesses of the plurality of laminar boundary layers obtained; The present invention further includes a selection unit that selects the rough surfaces capable of suppressing the growth of vortices and destroying generated vortices based on the calculated turbulence energy for each of the rough surfaces and the flow direction distribution of the friction resistance coefficient value. The evaluation device according to claim 1 .

6. The selection unit decomposes the variables of the Navier-Stokes equations into time-invariant variables and time-variant variables, and selects the rough surface that can suppress the growth of a vortex and promote neutralization by destroying the generated vortex based on the wavelength of the vortex that is amplified when a random number is given as a disturbance. The evaluation device according to claim 5 .

7. A rough surface over which a fluid may flow, comprising: The light source has a first protrusion based on a first wavelength that is a wavelength capable of suppressing the growth of a vortex, and a second protrusion based on a second wavelength that is a wavelength different from the first wavelength and that is capable of promoting the destruction of a generated vortex, The first protrusion and the second protrusion are provided in both a first direction that is parallel to the rough surface and is a direction of vortex advection, and a second direction that is parallel to the rough surface and is perpendicular to the first direction. A rough surface selected by the evaluation device according to claim 5 or 6.

8. 1. An evaluation method for evaluating a specific section of a rough surface where a fluid flows over the surface and transitions from laminar flow to turbulent flow, comprising the steps of: acquiring a thickness of the laminar boundary layer at an inlet of the specific section; a calculation step of calculating a flow direction distribution of turbulent energy and a flow direction distribution of a friction coefficient value on the rough surface by performing a direct numerical calculation based on the obtained thickness of the laminar boundary layer; an output step of outputting information based on the calculated result; An evaluation method having the following:

9. On the computer, A program for evaluating a specific section of a rough surface where a fluid flows over the surface and transitions from laminar flow to turbulent flow, comprising: acquiring a thickness of a laminar boundary layer at an inlet of the specific section; a calculation step of calculating a flow direction distribution of turbulent energy and a flow direction distribution of a friction coefficient value on the rough surface by performing a direct numerical calculation based on the obtained thickness of the laminar boundary layer; an output step for outputting information based on the calculated result; A program that executes the following.

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