CN114004175B - Method for quickly searching global wall surface distance and dimensionless wall surface distance - Google Patents
Method for quickly searching global wall surface distance and dimensionless wall surface distance Download PDFInfo
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Abstract
The invention provides a method for quickly searching a global wall surface distance and a dimensionless wall surface distance, which comprises the following steps: s1, obtaining the surface element information of the wall surface by calculating a domain grid, and constructing a K-D tree based on the space coordinates of all surface element surface centers of the wall surface; s2, performing quick search based on the K-D tree, determining the nearest distance between the grid center and the surface center of the surface element, and recording the corresponding relation between the grid and the surface element; s3, judging whether the grid is a first layer of grid of the wall surface, and correcting the nearest distance of the first layer of grid of the wall surface to obtain the final wall surface distance; and S4, solving the dimensionless wall surface distance by adopting a dichotomy based on the final wall surface distance and the Reichardt formula obtained in the step S3. The invention has the advantages of high searching speed and high accuracy in calculating the wall distance; and the method does not depend on physical quantities such as turbulent energy and the like, the obtained result is more accurate, and the applicability is also strong.
Description
Technical Field
The invention relates to the field of computational fluid mechanics, in particular to a method for quickly searching a global wall surface distance and a dimensionless wall surface distance.
Background
Turbulence phenomena are typical of extreme weather such as sand storm, typhoon and tsunami in nature, complex flow environments in which large civil airliners and passenger ships are located, and internal flow of engines involved in autonomous development of aeroengines. Turbulence is a complex flow phenomenon with irregular spatial and temporal distribution, and is characterized by strong nonlinearity, randomness, multiscale and the like.
The turbulence model is always one research focus in the field of computational fluid mechanics, and as a k-epsilon model commonly used for the turbulence model, only the wall distance and the dimensionless wall distance of a first layer of wall grid need to be calculated in early application to perform the related processing of a wall function. In recent years, the widely used SSTk- ω model requires calculation of the wall distance of the entire calculation domain, and based on this, the k- ω model suitable for wall flow is used in the vicinity of the near wall, and the k- ε model suitable for free shear flow is used in the far wall. Recently, attention has been given to WMLES (Wall-Modeled LES) models, which take Wall effects into account, are often used for high-precision simulation of engineering turbulence, which model requires Wall processing in addition to global Wall distances, which also requires global dimensionless Wall distances.
At present, the method for calculating the total wall distance has the problems of long time consumption or inaccurate result, and in addition, the dimensionless wall distance is often calculated by turbulent energy, but cannot be calculated according to the method in large vortex simulation. In summary, a set of fast and general methods for calculating the global wall distance and the dimensionless wall distance have not been developed.
Disclosure of Invention
The invention aims at least solving the technical problems in the prior art, and particularly creatively provides a method for quickly searching the distance between the whole domain wall and the dimensionless wall.
In order to achieve the above object of the present invention, the present invention provides a method for quickly searching for a global wall distance and a dimensionless wall distance, comprising the steps of:
s1, obtaining the surface element information of the wall surface by calculating a domain grid, and constructing a K-D tree based on the space coordinates of all surface element surface centers of the wall surface;
s2, performing quick search based on the K-D tree, determining the nearest distance between the grid center and the surface center of the surface element, and recording the corresponding relation between the grid and the surface element;
s3, judging whether the grid is a first layer of grid of the wall surface, and correcting the nearest distance of the first layer of grid of the wall surface to obtain the final wall surface distance;
and S4, solving the dimensionless wall surface distance by adopting a dichotomy based on the final wall surface distance and the Reichardt formula obtained in the step S3.
In a preferred embodiment of the present invention, the step S1 includes the steps of:
all wall surface elements are found by the existing grid data, and the face center coordinate information (x 1 i ,x2 i ,x3 i ),i∈{1,2,...,M}，x1 i Coordinate value of the centroid in x direction of the ith bin, x2 i Coordinate value of the centroid in y direction of the ith bin, x3 i Representing the coordinate value of the centroid of the ith bin in the z direction, wherein the bins corresponding to M bins form a point set;
constructing a K-D tree based on the point set, wherein the process of constructing the K-D tree is as follows:
s1-1, the centroid coordinates (x 1) 1 ,x2 1 ,x3 1 ) As the root node of the tree, let i=2, then get the face-center coordinates of the second face element (x 1 2 ,x2 2 ,x3 2 )；
S1-2, for the centroid coordinates (x 1) of the ith bin i ,x2 i ,x3 i ) Sequentially comparing with xk values of nodes of an nth layer of the K-D tree, wherein N is N+, k=mod (N-1, 3) +1, K values are 1,2 and 3 respectively refer to three directions of x, y and z, mod is a residual function, and if xk of a face center of an ith face element is calculated i If the value is smaller than xk value of the n-th layer node, entering a left subtree of the n-th layer node, otherwise, entering a right subtree until the subtree is a null tree, judging whether i is greater than M, if so, executing the step S1-3, and if not, determining the face center coordinate (x 1 i ,x2 i ,x3 i ) As the tree node, let i=i+1, execute step S1-2; wherein k has values of 1,2 and 3 respectively representing three directions of x, y and z, and M is the total number of the surface elements;
s1-3, and constructing the K-D tree.
In a preferred embodiment of the present invention, the step S2 includes the steps of:
traversing all grid cores, and determining the shortest distance from each grid core to the surface of the face element by using a K-D treeThe process of searching the K-D tree is as follows:
s2-1, entering a root node;
s2-2, at layer n, let k=mod (n-1, 3) +1, where mod is a remainder function; comparing the lattice center xk value with the node xk value, entering a left subtree if the lattice center xk value is smaller than the node xk value, otherwise, entering a right subtree; xk is a unified expression form of x1, x2 and x3, k can be 1,2 and 3, and x1, x2 and x3 respectively refer to x, y and z;
s2-3, repeatedly executing the step S2-2 until a leaf node appears, marking the leaf node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than a minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current leaf node; if L is greater than the minimum distance variable d, executing the next step;
s2-4, if the current node is the root node, ending the process, otherwise, executing the step S2-5;
s2-5, entering a father node, if the father node is accessed, executing the step S2-5, otherwise, executing the step S2-6;
s2-6, marking the node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than the minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current node;
s2-7, calculating the absolute value of the difference between the grid center xk value and the current node xk value, if the absolute value is larger than d, executing the step S2-4, otherwise, entering another subtree of the current node, and executing the step S2-2.
Furthermore, the correspondence between the mesh and the bin is: the information of the face center of the face element forms a KD tree, the information of the grid center is the input of the KD tree, the face center nearest to a certain grid center can be obtained by searching the KD tree for the grid center, and the face numbers are updated finally by S2-3 and S2-6, and have a corresponding relation with the grid center.
In a preferred embodiment of the present invention, the correction in S3 includes:
for a pair ofProjecting in the normal direction of the wall surface to obtain a vector representation of the corrected nearest distance +.> wherein ,/>For the current vector representation of the nearest distance, +.> Is the normal direction of the plane.
In a preferred embodiment of the present invention, the Reichardt formula in S4 is:
where κ is von Karman constant, ln (·) is the natural logarithm, exp (·) represents an exponential function based on the natural constant e, y + Is the non-dimensional wall surface distance, u + Is a dimensionless speed.
In a preferred embodiment of the present invention, the solving the dimensionless wall distance in S4 by using a dichotomy includes:
F(y + ) To be about y + Monotonically increasing function of y + Is the non-dimensional wall surface distance, u + For dimensionless speed, y is the wall distance, u is the speed component parallel to the wall, and v is the motion viscosity coefficient;
then let F (y) + ) =0, solving by dichotomy to obtain a dimensionless wall distance y + 。
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows: the method is suitable for an SSTk-omega model, a WMLES (Wall-modulated LES) model and the like in turbulence CFD simulation, and can realize rapid calculation of the whole-domain Wall distance and the dimensionless Wall distance. The specific steps are as follows:
1. the invention calculates the wall surface distance, and the K-D tree is used for accelerating the search, reducing the calculated amount, saving the calculation time, correcting the first layer of grid on the wall surface and improving the accuracy.
2. The invention calculates the non-dimensional wall surface distance, does not depend on physical quantities such as turbulence energy and the like, and obtains more accurate results from the basic definition of the physical quantities, thereby being a solving method with very wide applicability.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic view of the process of the first layer of grid wall distance of the wall surface of the present invention.
FIG. 2 is a flow chart of the K-D tree construction of the present invention.
FIG. 3 is a flowchart of the K-D tree search of the present invention.
FIG. 4 is a flow chart of the dimensionless wall distance calculation of the present invention.
FIG. 5 is a flow chart of the overall calculation of the global wall distance and dimensionless wall distance of the present invention.
Fig. 6 is a wall distance cloud of the present invention.
Fig. 7 is a dimensionless wall distance cloud of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
The technical scheme of the invention is as follows:
s1, obtaining the surface element information of the wall surface by calculating a domain grid, and constructing a K-D tree based on the space coordinates of all surface element surface centers of the wall surface;
s2, performing quick search based on the K-D tree, determining the nearest distance between the grid center and the surface center of the surface element, and recording the corresponding relation between the grid and the surface element;
s3, judging whether the grid is a first layer of grid of the wall surface, and correcting the nearest distance to obtain the final wall surface distance;
s4, solving the dimensionless wall surface distance by adopting a dichotomy based on the calculated wall surface distance and the Reichardt formula, and selecting a Newton mountain-down method to calculate besides the dichotomy, wherein the dichotomy is faster.
When the method is applied to the engine, an alarm is sent out when the calculated result exceeds a threshold value, and the terminal is uploaded.
The S1 finds all wall surface elements through the existing grid data, and determines the surface center coordinate information (x 1 i ,x2 i ,x3 i ) A set of points is formed in which the total number of bins is M. Based on the point set, a K-D tree is constructed, and the implementation flow is as follows, as shown in FIG. 2:
1. the coordinates of the centroid of the first bin (x 1 1 ,x2 1 ,x3 1 ) As the root node of the tree, i.e., the first layer, let i=2;
2. the centroid coordinates (x 1) for the i-th bin i ,x2 i ,x3 i ) Comparing with xk values of nodes of the nth layer in turn, wherein k=mod (n-1, 3) +1, wherein n=1, 2, …, k values of 1,2 and 3 respectively refer to three directions of x, y and z, mod is a remainder function, if xk of the ith bin is i If the value is smaller than the xk value of the node of the nth layer, entering a left subtree of the node of the nth layer, otherwise, entering a right subtree until the subtree is a null tree, and obtaining the face center coordinate (x 1 i ,x2 i ,x3 i ) As the tree node, let i=i+1;
3. repeating the step 2 until i > M, namely the face center coordinates of all the face elements are inserted into the tree structure, and completing the construction of the K-D tree.
S2, traversing all grid cores, and determining the shortest distance from each grid core to the surface element surface core by using a K-D treeThe flow of searching the K-D tree is as follows, as shown in FIG. 3:
n=1, entering the root node, i.e. the first layer;
2. at layer n, let k=mod (n-1, 3) +1, where mod is a remainder function, such as mod (10, 3) =1; and comparing the check center xk value with the node xk value, which is smaller than the entering left subtree, otherwise, entering the right subtree. x1, x2, x3 refer to three directions x, y and z, respectively;
3. repeating the step 2 until a leaf node appears, marking the leaf node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than the minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current leaf node;
4. if the current node is the root node, ending the process, otherwise, entering a step 5;
5. entering a father node, if the node is accessed, entering a step 5, otherwise, entering a step 6;
6. marking the node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than the minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current node;
7. and (3) calculating the absolute value of the difference between the grid center xk value and the current node xk value, if the absolute value is larger than d, entering the step 4, otherwise, entering another subtree of the current node, and entering the step 2.
S3, judging whether the grid is a first layer of the wall surface grid according to whether the surface element belongs to the grid, if so, the method needs to be carried out onProjection is carried out in the normal direction of the wall surface, and the final correction distance is obtained>As shown in fig. 1, P is a grid core, and f is a face core, which respectively belong to grids and face elements in space; if the mesh is not the first layer mesh of the wall surface, no correction is needed, and +.> I.e. the wall distance.
The S4 is a dimensionless wall distance y + And dimensionless speed u + The definition is as follows:
wherein y is the wall distance S2u τ For wall friction speed, v is the kinematic viscosity coefficient and u is the velocity component parallel to the wall.
The Reichardt formula is:
where κ is von Karman constant, usually 0.41.
In FIG. 4Original meaning lower limit value of Left in dichotomy, < >>The original means the upper limit value of Right in the dichotomy.
From the formulas (1), (2) and (3), the relation y can be obtained + Is a function of (a), i.e., equation (4), F (y + ) Is a monotonically increasing function, F (y + ) Root, dimensionless wall distance y =0 + Can be solved by using dichotomy, fromThereby obtaining the dimensionless wall distance y + 。
For the back step flow calculation, the calculation parameters are shown in table 1. The invention is adopted to solve the calculation example, and calculate the distance between the whole domain wall surface and the dimensionless wall surface.
TABLE 1 Back step flow calculation parameters
| Parameters (parameters) | Value of |
| Reynolds number | Re＝389 |
| Coefficient of hydrodynamic viscosity | μ＝1.85508E-5kg/(m·s) |
| Density of fluid | ρ＝1.1842kg/m 3 |
| Grid number | N＝658056 |
| Wall surface element number | M＝185220 |
The results obtained by the invention are shown in fig. 6 and 7, the wall distance cloud image is shown in fig. 6, the dimensionless wall distance cloud image is shown in fig. 7, and good results can be seen.
In the invention, the time complexity of the common searching method is O (N.M), wherein N grid number is multiplied symbol, M wall surface element number; the time complexity of the K-D tree searching method is as follows:table 2 shows the calculation time comparison result of the K-D tree searching method and the common searching method, and the acceleration effect of the K-D tree searching method is obvious.
TABLE 2 wall distance calculation time consuming
| Method | Time-consuming(s) |
| Ordinary searching method | 2212 |
| K-D number search method | 48 |
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
Claims (5)
1. The method for quickly searching the global wall surface distance and the dimensionless wall surface distance is characterized by comprising the following steps of:
s1, obtaining the surface element information of the wall surface by calculating a domain grid, and constructing a K-D tree based on the space coordinates of all surface element surface centers of the wall surface;
s2, performing quick search based on the K-D tree, determining the nearest distance between the grid center and the surface center of the surface element, and recording the corresponding relation between the grid and the surface element;
s2-1, entering a root node;
s2-2, at layer n, let k=mod (n-1, 3) +1, where mod is a remainder function; comparing the lattice center xk value with the node xk value, entering a left subtree if the lattice center xk value is smaller than the node xk value, otherwise, entering a right subtree; xk is a unified expression form of x1, x2 and x3, k can be 1,2 and 3, and x1, x2 and x3 respectively refer to x, y and z;
s2-3, repeatedly executing the step S2-2 until a leaf node appears, marking the leaf node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than a minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current leaf node; if L is greater than the minimum distance variable d, executing the next step;
s2-4, if the current node is the root node, ending the process, otherwise, executing the step S2-5;
s2-5, entering a father node, if the father node is accessed, executing the step S2-5, otherwise, executing the step S2-6;
s2-6, marking the node as accessed, calculating the distance L between the grid center and the face center of the node, if L is smaller than the minimum distance variable d, enabling d to be equal to L, and recording the face center number of the current node;
s2-7, calculating the absolute value of the difference between the grid center xk value and the current node xk value, if the absolute value is larger than d, executing the step S2-4, otherwise, entering another subtree of the current node, and executing the step S2-2;
s3, judging whether the grid is a first layer of grid of the wall surface, and correcting the nearest distance of the first layer of grid of the wall surface to obtain the final wall surface distance;
and S4, solving the dimensionless wall surface distance by adopting a dichotomy based on the final wall surface distance and the Reichardt formula obtained in the step S3.
2. The method for quickly searching for the global wall distance and the dimensionless wall distance according to claim 1, wherein the step S1 comprises the following steps:
s1-1, the centroid coordinates (x 1) 1 ,x2 1 ,x3 1 ) As the root node of the tree, let i=2, then get the face-center coordinates of the second face element (x 1 2 ,x2 2 ,x3 2 )；
S1-2, for the centroid coordinates (x 1) of the ith bin i ,x2 i ,x3 i ) Sequentially comparing with xk values of nodes of the nth layer of the K-D tree, if xk of the surface center of the ith surface element i If the value is smaller than xk value of the n-th layer node, entering a left subtree of the n-th layer node, otherwise, entering a right subtree until the subtree is a null tree, judging whether i is greater than M, if so, executing the step S1-3, and if not, determining the face center coordinate (x 1 i ,x2 i ,x3 i ) As a tree node, let i=i+1, execute step S1-2; wherein k has values of 1,2 and 3 respectively representing three directions of x, y and z, and M is the total number of the surface elements;
s1-3, and constructing the K-D tree.
3. The method for quickly searching for the global wall distance and the dimensionless wall distance according to claim 1, wherein the correcting in S3 includes:
for a pair ofProjecting in the normal direction of the wall surface to obtain a vector representation of the corrected nearest distance +.> wherein ,for the current vector representation of the nearest distance, +.>Is the normal direction of the plane.
4. The method for quickly searching for the global wall distance and the dimensionless wall distance according to claim 1, wherein the Reichardt formula in S4 is as follows:
where κ is von Karman constant, ln (·) is the natural logarithm, exp (·) represents an exponential function based on the natural constant e, y + Is the non-dimensional wall surface distance, u + Is a dimensionless speed.
5. The method for quickly searching for the global wall distance and the dimensionless wall distance according to claim 1, wherein the step of solving the dimensionless wall distance by using a dichotomy in S4 comprises:
F(y + ) Y+ is a non-dimensional wall distance, u+ is a non-dimensional velocity, y is a wall distance, u is a velocity component parallel to the wall, and v is a motion viscosity coefficient;
then let F (y) + ) =0, solved by dichotomy to obtain the dimensionless wall distance y+.
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| CN109948002A (en) * | 2019-03-14 | 2019-06-28 | 空气动力学国家重点实验室 | The nearest wall surface of unstrctured grid based on balance KD tree is apart from method for solving |
| CN112052512A (en) * | 2020-07-23 | 2020-12-08 | 中国空气动力研究与发展中心计算空气动力研究所 | Method for judging layering of turbulent boundary layer |
| CN112181991A (en) * | 2020-10-15 | 2021-01-05 | 中国人民解放军国防科技大学 | Earth simulation system grid remapping method based on rapid construction of KD tree |
| CN113158338A (en) * | 2021-04-13 | 2021-07-23 | 中国空气动力研究与发展中心计算空气动力研究所 | Rapid turbulence wall function aerodynamic force prediction method based on coarse grid |
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| CN109948002A (en) * | 2019-03-14 | 2019-06-28 | 空气动力学国家重点实验室 | The nearest wall surface of unstrctured grid based on balance KD tree is apart from method for solving |
| CN112052512A (en) * | 2020-07-23 | 2020-12-08 | 中国空气动力研究与发展中心计算空气动力研究所 | Method for judging layering of turbulent boundary layer |
| CN112181991A (en) * | 2020-10-15 | 2021-01-05 | 中国人民解放军国防科技大学 | Earth simulation system grid remapping method based on rapid construction of KD tree |
| CN113158338A (en) * | 2021-04-13 | 2021-07-23 | 中国空气动力研究与发展中心计算空气动力研究所 | Rapid turbulence wall function aerodynamic force prediction method based on coarse grid |
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