CN119246005A - A method, device, equipment and medium for determining vorticity and velocity in large eddy simulation - Google Patents
A method, device, equipment and medium for determining vorticity and velocity in large eddy simulation Download PDFInfo
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Abstract
The application discloses a large vortex simulated vortex quantity and speed determining method, device, equipment and medium, which are applied to the technical field of vortex dynamics and comprise the steps of obtaining a target flow field speed and a target vortex quantity at the previous moment, wherein the target flow field speed comprises a flow field speed obtained by using a grid filter and a test filter, the target vortex quantity comprises a vortex quantity obtained by using the grid filter and the test filter, calculating an analytic vortex quantity flux based on the target flow field speed and the target vortex quantity, calculating a target first physical quantity based on the target vortex quantity, calculating a vortex viscosity coefficient based on the analytic vortex quantity flux and the target first physical quantity, determining a target vortex quantity at the next moment based on the vortex viscosity coefficient and based on a vortex transport equation, and calculating the target flow field speed at the next moment based on the flow field speed obtained by filtering of the grid filter at the previous moment and the vortex quantity obtained by filtering of the grid filter at the next moment. Therefore, the vortex viscosity coefficient can be calculated in a self-adaptive mode, and therefore the vortex quantity and the speed of the flow field can be accurately determined.
Description
Technical Field
The application relates to the technical field of vortex dynamics, in particular to a method, a device, equipment and a medium for determining vortex quantity and speed of large vortex simulation.
Background
Research finds that the core physical process of the evolution of the multi-scale turbulence is the dynamic evolution of the multi-scale vortex structure, so that the vortex dynamics is more and more focused in recent years, and at present, how to accurately determine the vorticity and the speed of a flow field in a large vortex simulation scene is a problem to be solved.
Disclosure of Invention
In view of the above, the present application aims to provide a method, a device, equipment and a medium for determining the vortex quantity and the speed of a large vortex simulation, which can accurately determine the vortex quantity and the speed of a flow field. The specific scheme is as follows:
in a first aspect, the application discloses a method for determining vortex quantity and speed of large vortex simulation, which comprises the following steps:
The method comprises the steps of obtaining a target flow field speed at the last moment and a target vorticity at the last moment, wherein the target flow field speed comprises a flow field speed obtained by filtering with a grid filter of large vortex simulation and a flow field speed obtained by filtering with a test filter, the target vorticity comprises a vorticity obtained by filtering with the grid filter of large vortex simulation and a vorticity obtained by filtering with the test filter, and the test filter is a filter with grid size larger than that of the grid filter;
calculating analytic vorticity flux based on the target flow field speed and the target vorticity, wherein the analytic vorticity flux characterizes contribution of a flow structure with a scale between a filtering width of the grid filter and a filtering width of the test filter to vorticity transportation;
Calculating a target first physical quantity based on the target vorticity, wherein the target first physical quantity comprises a first physical quantity obtained by filtering through the grid filter and a first physical quantity obtained by filtering through the test filter, and the first physical quantity is a symmetrical tensor representing spatial variation of a vorticity field;
Calculating a vortex viscosity coefficient based on the analytic vortex flux and the target first physical quantity by using a vortex viscosity coefficient calculation formula, wherein the vortex viscosity coefficient calculation formula is established based on a quasi-vortex energy power conservation relation of a flow structure with a scale between the filtering width of the grid filter and the filtering width of the test filter;
Closing a vortex quantity transportation equation based on the vortex viscosity coefficient, and determining a target vortex quantity at the next moment corresponding to the previous moment based on the vortex quantity transportation equation;
and calculating the target flow field speed at the next moment corresponding to the previous moment based on the flow field speed obtained by filtering the grid filter at the previous moment by using the large vortex simulation and the vortex quantity obtained by filtering the grid filter at the next moment corresponding to the previous moment by using the large vortex simulation.
Optionally, the vortex viscosity coefficient calculation formula is:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,In order to test the filter width of the filter,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filter processing of the test filter.
Optionally, when a preset flow field uniformity condition is satisfied, the vortex viscosity coefficient calculation formula is:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,To represent the filter width of the lattice filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filtering process of the test filter.
Optionally, the calculating the resolved vorticity flux based on the target flow field speed and the target vorticity includes:
and calculating the analytic vortex flux based on the target flow field speed and the target vortex by using an analytic vortex flux calculation formula, wherein the analytic vortex flux calculation formula is as follows:
;
Wherein, In order to resolve the vorticity flux,、To filter the resulting flow field velocities using a grid filter of large vortex simulations,、To filter the resulting flow field velocity using a test filter,、To filter the resulting vorticity using a grid filter of large vortex simulations,、To filter the resulting vorticity using a test filter,Representing the filtering process of the test filter, i, j represent different directions.
Optionally, the calculating the target first physical quantity based on the target vorticity includes:
determining a first physical quantity based on the target vortex quantity by using a preset first physical quantity calculation formula, wherein the preset first physical quantity calculation formula is as follows:
、;
Wherein, Representing the first physical quantity after filtering by the grid filter,、Indicating the vorticity obtained by filtering using a grid filter,Representing the first physical quantity after filtering by the test filter,、Indicating the vorticity obtained by filtering using the test filter,、For the distance vector i, j denote different directions.
Optionally, the vorticity transport equation is:
;
Wherein, To filter the resulting vorticity using a grid filter of large vortex simulations,To filter the resulting flow field velocities using a grid filter of large vortex simulations,Is the vortex-induced viscosity coefficient, t is the time,As a result of the distance vector,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the first physical quantity after filtering by the grid filter,The coefficient of motion viscosity is represented by the equation,、Indicating vorticity obtained by filtering with a grid filter, i, j indicating different directions.
Optionally, the calculating the target flow field speed at the next moment corresponding to the previous moment based on the flow field speed obtained by filtering with the grid filter of the large vortex simulation at the previous moment and the vortex amount obtained by filtering with the grid filter of the large vortex simulation at the next moment corresponding to the previous moment includes:
Updating a flow function vector by using a first preset formula based on vorticity obtained by filtering a grid filter using large vortex simulation at the next moment corresponding to the previous moment, wherein the first preset formula is as follows:
;
Wherein, As a vector of the flow function,As a result of the distance vector,For the vorticity obtained by filtering by using a grid filter of large vortex simulation, i and j represent different directions;
Updating a speed potential function according to a flow field speed obtained by filtering by using a grid filter of large vortex simulation at the previous moment by using a second preset formula, wherein the second preset formula is as follows:
;
Wherein, As a function of the velocity potential of the object,Filtering the flow field speed obtained by using a grid filter of large vortex simulation at the previous moment;
Calculating a flow field speed obtained by filtering a grid filter using large vortex simulation at the next moment corresponding to the previous moment based on the updated flow function vector and the speed potential function by using a third preset formula, wherein the third preset formula is as follows:
;
Wherein, In order to replace the symbol,As a vector of the flow function,As a result of the distance vector,Filtering the flow field speed obtained by using a grid filter of large vortex simulation at the next moment;
And calculating the flow field speed obtained by filtering the flow field by using the test filter at the next moment based on the flow field speed obtained by filtering the flow field by using the grid filter of the large vortex simulation at the next moment.
In a second aspect, the application discloses a device for determining the vortex quantity and speed of large vortex simulation, which comprises:
The speed and vorticity acquisition module is used for acquiring a target flow field speed at the last moment and a target vorticity at the last moment, wherein the target flow field speed comprises a flow field speed obtained by filtering by using a grid filter of large vortex simulation and a flow field speed obtained by filtering by using a test filter, the target vorticity comprises a vorticity obtained by filtering by using the grid filter of large vortex simulation and a vorticity obtained by filtering by using the test filter, and the test filter is a filter with a grid size larger than that of the grid filter;
The analytic vortex flux calculation module is used for calculating analytic vortex flux based on the target flow field speed and the target vortex, wherein the analytic vortex flux represents contribution of a flow structure with a scale between the filtering width of the grid filter and the filtering width of the test filter to vortex transportation;
the first physical quantity calculating module is used for calculating a target first physical quantity based on the target vortex quantity, wherein the target first physical quantity comprises a first physical quantity obtained by filtering through the grid filter and a first physical quantity obtained by filtering through the test filter, and the first physical quantity is a symmetrical tensor representing the spatial variation of a vortex field;
The vortex viscosity coefficient calculation module is used for calculating a vortex viscosity coefficient based on the analysis vortex flux and the target first physical quantity and by utilizing a vortex viscosity coefficient calculation formula, wherein the vortex viscosity coefficient calculation formula is established based on a quasi-vortex energy power conservation relation of a flow structure with a scale between the filtering width of the grid filter and the filtering width of the test filter;
The target vortex quantity calculation module is used for closing a vortex quantity transportation equation based on the vortex viscosity coefficient and determining the target vortex quantity of the next moment corresponding to the previous moment based on the vortex quantity transportation equation;
and the flow field speed calculation module is used for calculating the target flow field speed at the next moment corresponding to the previous moment based on the flow field speed obtained by filtering the grid filter using the large vortex simulation at the previous moment and the vortex quantity obtained by filtering the grid filter using the large vortex simulation at the next moment corresponding to the previous moment.
In a third aspect, the application discloses an electronic device comprising a memory and a processor, wherein:
the memory is used for storing a computer program;
The processor is used for executing the computer program to realize the method for determining the vortex quantity and the speed of the large vortex simulation.
In a fourth aspect, the present application discloses a computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the aforementioned large vortex simulation vortex size and speed determination method.
According to the scheme, the method for determining the vortex quantity and the speed of the large vortex simulation comprises the steps of obtaining a target flow field speed at the previous moment and a target vortex quantity at the previous moment, wherein the target flow field speed comprises a flow field speed obtained by filtering with a grid filter of the large vortex simulation and a flow field speed obtained by filtering with a test filter, the target vortex quantity comprises a vortex quantity obtained by filtering with the grid filter of the large vortex simulation and a vortex quantity obtained by filtering with the test filter, and the test filter is a filter with a grid size larger than that of the grid filter; calculating an analytic vortex flux based on the target flow field speed and the target vortex, wherein the analytic vortex flux characterizes a contribution of a flow structure with a scale between a filtering width of the grid filter and a filtering width of the test filter to vortex transportation, calculating a target first physical quantity based on the target vortex, the target first physical quantity comprising a first physical quantity obtained by filtering with the grid filter and a first physical quantity obtained by filtering with the test filter, wherein the first physical quantity is a symmetric tensor representing the spatial variation of the vortex field, calculating a vortex viscosity coefficient based on the analytic vortex flux, the target first physical quantity and using a vortex viscosity coefficient calculation formula, wherein the vortex viscosity coefficient calculation formula is established based on a quasi-vortex energy power conservation relation of the flow structure with the scale between the filtering width of the grid filter and the filtering width of the test filter, closing the vortex transportation equation based on the vortex viscosity coefficient, and calculating the target flow field speed at the next moment corresponding to the previous moment based on the flow field speed obtained by filtering the grid filter which uses the large vortex simulation at the previous moment and the vortex quantity obtained by filtering the grid filter which uses the large vortex simulation at the next moment corresponding to the previous moment.
Therefore, the vortex-induced viscosity coefficient can be calculated in a self-adaptive manner according to the local flow characteristic of the flow field based on the quasi-vortex energy power conservation relation of the flow structure with the scale between the filtering width of the grid filter and the filtering width of the test filter, so that the vortex quantity and the speed of the flow field can be determined accurately.
Correspondingly, the large-vortex simulated vortex quantity and speed device, the device and the readable storage medium have the same technical effects.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present application, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining vortex quantity and speed of large vortex simulation provided by an embodiment of the application;
FIG. 2 is a schematic diagram of a grid according to an embodiment of the present application;
FIG. 3 is a schematic diagram of determining a vortex quantity transportation equation according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a large vortex simulated vortex and velocity determination apparatus according to an embodiment of the present application;
Fig. 5 is a block diagram of an electronic device according to an embodiment of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Currently, the autonomous development of fluid industry software is urgent. For the problem of industrial scale hydrodynamic simulation, large vortex simulation is a common technology, which can ensure the accurate depiction of multi-scale turbulence by a fluid solver, can greatly reduce the calculated amount, and is an important technology of modern fluid simulation software. However, the traditional large vortex simulation method is based on Navier-Stokes (namely Navier-Stokes) equation, and the large vortex simulation method developed by the embodiment of the application is based on vortex dynamics equation, so that a multi-scale turbulence vortex structure can be better depicted.
Dynamics have received increasing attention in recent years because research has found that the core physical process of the evolution of multi-scale turbulence is the dynamic evolution of multi-scale vortex structures. Therefore, the application further derives a large vortex simulation basic equation based on the vortex dynamics equation on the basis of the direct numerical simulation solver of the vortex dynamics, and obtains the self-adaptive vortex dynamics large vortex simulation vortex viscosity coefficient expression through the energy conservation principle. Based on the method, a vortex dynamics large vortex simulation solver is developed and is used for multi-scale turbulence numerical simulation of industrial scale.
Referring to fig. 1, the embodiment of the application discloses a method for determining vortex quantity and speed of large vortex simulation, which comprises the following steps:
Step S11, obtaining a target flow field speed at the last moment and a target vorticity at the last moment, wherein the target flow field speed comprises a flow field speed obtained by filtering by using a grid filter of large vortex simulation and a flow field speed obtained by filtering by using a test filter, the target vorticity comprises a vorticity obtained by filtering by using the grid filter of large vortex simulation and a vorticity obtained by filtering by using the test filter, and the test filter is a filter with a grid size larger than that of the grid filter.
And step S12, calculating analysis vortex flux based on the target flow field speed and the target vortex, wherein the analysis vortex flux represents the contribution of a flow structure with a scale between the filtering width of the grid filter and the filtering width of the test filter to vortex transportation.
In this embodiment, an analytic vorticity flux calculation formula may be used, and the analytic vorticity flux may be calculated based on the target flow field speed and the target vorticity, where the analytic vorticity flux calculation formula is:
;
Wherein, In order to resolve the vorticity flux,、To filter the resulting flow field velocities using a grid filter of large vortex simulations,、To filter the resulting flow field velocity using a test filter,、To filter the resulting vorticity using a grid filter of large vortex simulations,、To filter the resulting vorticity using a test filter,Representing the filtering process of the test filter, i, j represent different directions.
And S13, calculating a target first physical quantity based on the target vortex quantity, wherein the target first physical quantity comprises a first physical quantity obtained by filtering through the grid filter and a first physical quantity obtained by filtering through the test filter, and the first physical quantity is a symmetrical tensor representing the spatial variation of a vortex field.
In this embodiment, a preset first physical quantity calculation formula may be used, and the first physical quantity may be determined based on the target vortex quantity, where the preset first physical quantity calculation formula is:
、;
Wherein, Representing the first physical quantity after filtering by the grid filter,、Indicating the vorticity obtained by filtering using a grid filter,Representing the first physical quantity after filtering by the test filter,、Indicating the vorticity obtained by filtering using the test filter,、For the distance vector i, j denote different directions.
And S14, calculating a vortex viscosity coefficient based on the analysis vortex flux and the target first physical quantity and by using a vortex viscosity coefficient calculation formula, wherein the vortex viscosity coefficient calculation formula is established based on a quasi-vortex energy power conservation relation of a flow structure with a scale between the filtering width of the grid filter and the filtering width of the test filter.
In this embodiment, the vortex viscosity coefficient calculation formula is:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,In order to test the filter width of the filter,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filter processing of the test filter. The present embodiment uses the form of an einstein index to represent the first physical quantity, which in an einstein summing convention means that if one index (which may be a subscript or a superscript) occurs twice in the same term, then the index is summed in a traversal. Such indicators are called dummy indicators because their specific names are not important, it is important that they represent the operation of summing. Instead, the indices that occur only once are called free indices, which are not summed but remain as indices in the final expression. The physical quantities with mn, pq subscripts and the physical quantities with subscripts ij are one meaning.,。
Further, when a preset flow field uniformity condition is satisfied, the vortex viscosity coefficient calculation formula is:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,To represent the filter width of the lattice filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filtering process of the test filter.
That is, the present embodiment can take a uniform grid for the problem of uniform flow field and simple geometry, and take a filter width of the test filter twice that of the grid filter. The eddy current viscosity coefficient calculation formula can be simplified into the formula, so that the calculation amount is reduced. Uniform grids, i.e., grids of uniform size. The uniform flow field can be understood as no large speed gradient and no drastic change of the flow field, and a solver determines a grid division mode according to experience and a specific problem.
And S15, sealing a vortex quantity transportation equation based on the vortex viscosity coefficient, and determining a target vortex quantity at the next moment corresponding to the previous moment based on the vortex quantity transportation equation.
In this embodiment, the vorticity transport equation is:
;
Wherein, To filter the resulting vorticity using a grid filter of large vortex simulations,To filter the resulting flow field velocities using a grid filter of large vortex simulations,Is the vortex-induced viscosity coefficient, t is the time,As a result of the distance vector,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the first physical quantity after filtering by the grid filter,The coefficient of motion viscosity is represented by the equation,、Indicating vorticity obtained by filtering with a grid filter, i, j indicating different directions.
And S16, calculating the target flow field speed at the next moment corresponding to the previous moment based on the flow field speed obtained by filtering by using the grid filter of the large vortex simulation at the previous moment and the vortex quantity obtained by filtering by using the grid filter of the large vortex simulation at the next moment corresponding to the previous moment.
The embodiment can update the flow function vector by using a first preset formula based on vorticity obtained by filtering the grid filter using large vortex simulation at the next moment corresponding to the previous moment, wherein the first preset formula is as follows:
;
Wherein, As a vector of the flow function,As a result of the distance vector,For the vorticity obtained by filtering by using a grid filter of large vortex simulation, i and j represent different directions;
Updating a speed potential function according to a flow field speed obtained by filtering by using a grid filter of large vortex simulation at the previous moment by using a second preset formula, wherein the second preset formula is as follows:
;
Wherein, As a function of the velocity potential of the object,Filtering the flow field speed obtained by using a grid filter of large vortex simulation at the previous moment;
Calculating a flow field speed obtained by filtering a grid filter using large vortex simulation at the next moment corresponding to the previous moment based on the updated flow function vector and the speed potential function by using a third preset formula, wherein the third preset formula is as follows:
;
Wherein, In order to replace the symbol,As a vector of the flow function,As a result of the distance vector,The resulting flow field velocity is filtered for the next instant using a grid filter of large vortex simulation.
And calculating the flow field speed obtained by filtering the flow field by using the test filter at the next moment based on the flow field speed obtained by filtering the flow field by using the grid filter of the large vortex simulation at the next moment. Specifically, a test filter is used for filtering the flow field speed obtained by filtering the grid filter using the large vortex simulation at the next moment, and the flow field speed obtained by filtering the grid filter at the next moment is obtained.
It is noted that the core idea of Large Eddy Simulation (LES) is to split the flow into Large-scale resolvable flows and small-scale flows that need to be approximated by a model by spatial filtering. Where large and small scale are relative concepts, there are no absolute values related to the problem of the solution requirements, the part of interest, the size of the computational domain, etc. The size scale depends on the size of the filter function. The filtering function is small-scale, and the filtering function is large-scale. Spatial filtering is typically implemented using convolution operations, using a filter function (filter)And physical quantityPerforming convolution calculation to obtain physical quantity on coarser grid:
(1);
The filter function in large vortex simulation is a tool used to separate large scale vortices (the part that is desired to be directly simulated) from small scale vortices (the part that is desired to be simulated by a sub-lattice model) in a fluid field. The filtering function is typically a local operation, which may be a box filter, gaussian filter, or hat filter, etc. Wherein the physical quantity is a general concept, and any physical quantity can obtain a large-scale part through a filtering method. Wherein the mesh size of the coarser mesh is controlled by the size of the filter based on the particular problem to be solved.
The vorticity transport equation for incompressible viscous flow is:
(2);
Wherein the method comprises the steps of Is the vorticity, t is the time,The coefficient of motion viscosity is represented by the equation,In order to be able to achieve a speed,Is a gradient operator. The above equation is rewritten as the tensor form:
(3);
Wherein, The speed is indicated by the velocity of the light,For the distance vector i, j denote different directions. In this embodiment, the vectors are all expressed in terms of einstein index, and the subscripts j=1, 2,3 represent three different directions, and the conservation form of the vorticity transport equation is further deduced below. The left side of the above equal sign can be written as:
(4);
for the vorticity field, it is a tubular vector field, satisfying:
(5);
and, for non-compressible flows, satisfy:
(6);
the third and fifth terms on the right side of the equal sign in equation (4) are therefore zero. The nonlinear term (i.e., second, third term) to the left of the equal sign of the final equation (3) can be written in a conservation form and yields the conservation form of the vortex transport equation for incompressible viscous flow as follows:
(7);
Using a grid filter (GRID FILTER) Filtering the equation (7) to obtain the following filtering equation:
(8);
in the above formula, the physical quantity with the upper horizontal line represents the filtered large-scale flow result and can be directly calculated. Vortex flow Speed and velocityIs decomposed into resolvable large-scale partsAnd) And unresolved small scale partAnd):
(9);
(10);
Thus the second term in equation (8)Can be developed into the following form:
(11);
when the operator of the filter function (filter) is a Reynolds operator (Reynolds operator), the following is satisfied WhereinIs any unresolved small-scale physical quantity.
The Reynolds operator satisfies the operation rule:、、 is a calculation operator of (a). Wherein the method comprises the steps of 、The upper horizontal line represents the operator action result for any physical quantity.
The second and third terms on the right side of the medium number above therefore satisfy:
(12);
(13);
At this time, the formula (11) can be simplified as:
(14);
The same principle is as follows:
(15);
Definition of the definition The method comprises the following steps:
(16);
When the operator of the filter is a Reynolds operator, the last equal sign of the above type is established. Will be Substituting the filtered vortex quantity into a filtering equation (8) to obtain a filtered vortex quantity transportation equation as follows:
(17);
Moving the third term to the right of the equation and expanding, we get:
(18);
from equation (5), the third term on the right side of the upper equal sign is zero. Finally, a simplified filtered vorticity transport equation is obtained as follows:
(19);
The effect of small scale structures smaller than the filter scale on vortex transport is shown. Large vortex simulations can only directly calculate large scale flow, so a model needs to be introduced to approximate the contribution of small scale flow structures. The analogy Smagorinsky (i.e., simaroubrin Style) model here takes a form pair similar to viscous stress based on the vortex viscosity assumption Modeling is carried out, and the mathematical expression is as follows:
(20);
Wherein, For the width of the filter to be the same,,,Is the vortex viscosity coefficient. The dimensional analysis was performed on both sides of the above equal sign to verify its correctness, with the following results:
(21);
L represents distance, T represents time, and formula (21) represents alignment of the equal-sign two-side dimensions of formula (19). In order to seal the obtained filtering vorticity transport equation, the vortex viscosity coefficient needs to be given . The method derives eddy current coefficients based on the model proposed by Germano (i.e., jeer Ma Nuo) in 1991The method can adaptively calculate. A specific procedure for adaptively calculating the vortex viscosity coefficient will be given below.
Embodiments of the application except for the use of a mesh filter (GRID FILTER)In addition, a test filter (TEST FILTER) is introduced. The grid size of the test filter is larger than that of the grid filter, and the selection of the filters can be the same or different, so that the expression of the formula is not influenced. Final definition:。
The direct numerical simulation (DNS, direct Numerical Simulation) grid, the large vortex simulation (LES) grid filter (GRID FILTER) and the test filter (TEST FILTER) grid are shown in fig. 2. Fig. 2 is a schematic diagram of a grid provided in an embodiment of the present application, where a gray grid represents a DNS grid and can resolve all scale structures in a flow, and a blue grid represents a grid filter grid of LES, which is larger than the DNS grid in size, so that only large scale structures in a flow field can be resolved. The grid of the test filter is shown as a red dashed line (here the test filter has a filter size of 2 times the filter size of the grid filter is taken as an example). The result after the test filter processing can be obtained by averaging the result after the grid filter processing. For example, the magnitude of the test filter contribution at the red node in the figure may be derived based on a weighted average of the results at the nine grid point locations defined by the red dashed line.
Similarly, use is made ofFiltering the vorticity transport equation to obtain the following equation:
(22);
In the present application, physical quantities with upper transverse lines and upper wavy lines, e.g (F is any physical quantity) representing the large scale flow result after filtering by the test filter. Wherein the method comprises the steps ofThe expression is as follows:
(23);
Similarly, when the operator of the filter is a Reynolds operator, the last equal sign of the above equation is established. Definition of the definition The method comprises the following steps:
(24);
The term represents a dimension between the filter width of the lattice filter (GRID FILTER) And testing the filter width of the filter (TEST FILTER)The contribution of the flow structure in between to vortex transport. And is also provided withThe expression of (2) contains only the filtered physical quantity.
Using the foregoing model, equation (20), pairAndThe modeling was as follows:
(25);
(26);
Substituting equations (25) (26) into equation (24) yields:
(27);
the dimensional analysis is carried out on the two sides of the upper type equal sign:
(28);
The dimensions on both sides of the above equal sign are pseudo-vortex energy power, which indicates that, on a physical level, the formula (27) reflects a dimension between the filter width of the grid filter (GRID FILTER) And testing the filter width of the filter (TEST FILTER)Quasi-vortex energy conservation of the flow structure.
Finally obtain vortex viscosity coefficientThe expression of (2) is:
(29);
The expression contains only the filtered physical quantity, so equation (19) is closed. And the vortex viscosity coefficient calculated by the method The self-adaptive adjustment can be carried out according to the local flow characteristic of the flow field, so that the adaptability of the model to different flow conditions is improved.
For three-dimensional problems, if the flow field is uniform (e.g. uniform velocity, no large velocity gradient), and the geometry is simple, a uniform grid is taken, i.e,Taking the filter width of the test filter (TEST FILTER) to be twice that of the grid filter (GRID FILTER), namelyWhere the subscript i denotes the grid direction, there are:
(30);
(31);
Thus vortex viscosity coefficient And can be expressed as:
(32);
The filtered vorticity transport equation can ultimately be expressed as:
(33);
For example, referring to fig. 3, fig. 3 is a schematic diagram illustrating a scroll transportation equation determination according to an embodiment of the present application.
Further, in determining vorticity and speed, each iterative calculation process is as follows (upper right label indicates time step):
First, the flow field speed at the last moment is obtained 、Vortex quantity、;
Calculated from equation (24)、、;
Calculating the vortex viscosity coefficient according to formula (29);
Solving equation (33) and calculating the vorticity at the next moment;
According to the vorticity at the next momentUpdating stream function vectors;
;
Updating the velocity potential function according to the velocity at the last moment;
;
Updating flow field speed at next moment;
;
By aligningFiltering using a test filter is further obtained.
In the embodiment, based on a model proposed in Germano in 1991, a control equation for solving the simulation numerical value of the large vortex of vortex quantity transportation is deduced, and the vortex viscosity coefficient of the large vortex simulation of vortex dynamics is self-adaptive and does not need to be given in advance. Based on the development of the vortex dynamics large vortex simulation numerical simulation autonomous source code simulation software, autonomous control of the autonomous source code software is realized, and the source code software can be subjected to CPU (i.e. Central Processing Unit, central processing unit) parallel computation.
The application realizes the breakthrough from 0 to 1, and develops a large vortex simulation numerical solver for incompressible fluid of vortex dynamics. The traditional large vortex simulation solver is based on a Navier-Stokes equation, and the application is based on a vortex dynamics equation. The large vortex simulation solver based on the vortex dynamics equation can better describe the vortex system structure of the turbulence. Meanwhile, by adopting the vortex dynamics large vortex simulation solver, the computational complexity is greatly reduced while the analysis of multi-scale turbulence is ensured, and the solving of the industrial-scale turbulence problem is realized.
Therefore, the embodiment of the application can adaptively calculate the vortex viscosity coefficient according to the local flow characteristic of the flow field based on the quasi-vortex energy power conservation relation of the flow structure with the scale between the filtering width of the grid filter and the filtering width of the test filter, thereby accurately determining the vortex quantity and speed of the flow field.
Referring to fig. 4, the embodiment of the application discloses a device for determining vortex quantity and speed of large vortex simulation, which comprises the following steps:
A speed and vorticity acquisition module 11, configured to acquire a target flow field speed at a previous time and a target vorticity at a previous time, where the target flow field speed includes a flow field speed obtained by filtering with a grid filter of large vortex simulation and a flow field speed obtained by filtering with a test filter, and the target vorticity includes a vorticity obtained by filtering with a grid filter of large vortex simulation and a vorticity obtained by filtering with a test filter, and the test filter is a filter with a grid size larger than that of the grid filter;
A resolved vorticity flux calculation module 12 configured to calculate a resolved vorticity flux based on the target flow field speed and the target vorticity, wherein the resolved vorticity flux characterizes a contribution of a flow structure having a scale between a filtering width of the grid filter and a filtering width of the test filter to vorticity transport;
A first physical quantity calculating module 13, configured to calculate a target first physical quantity based on the target vortex quantity, where the target first physical quantity includes a first physical quantity obtained by filtering with the grid filter and a first physical quantity obtained by filtering with the test filter, and the first physical quantity is a symmetric tensor that represents a spatial variation of a vortex field;
A vortex viscosity coefficient calculation module 14, configured to calculate a vortex viscosity coefficient based on the resolved vortex flux, the target first physical quantity, and using a vortex viscosity coefficient calculation formula, where the vortex viscosity coefficient calculation formula is established based on a quasi-vortex energy power conservation relationship of a flow structure with a scale between a filtering width of the grid filter and a filtering width of the test filter;
The target vortex quantity calculation module 15 is used for closing a vortex quantity transportation equation based on the vortex viscosity coefficient and determining the target vortex quantity of the next moment corresponding to the previous moment based on the vortex quantity transportation equation;
The flow field speed calculating module 16 is configured to calculate a target flow field speed at a next time corresponding to the previous time based on the flow field speed obtained by filtering with the grid filter of the large vortex simulation at the previous time and the vortex amount obtained by filtering with the grid filter of the large vortex simulation at the next time corresponding to the previous time.
In an alternative embodiment, the vortex viscosity coefficient calculation module 14 is specifically configured to:
Calculating a vortex viscosity coefficient based on the resolved vortex flux and the target first physical quantity by using a vortex viscosity coefficient calculation formula, wherein in the embodiment, the vortex viscosity coefficient calculation formula is as follows:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,In order to test the filter width of the filter,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filter processing of the test filter.
When the preset flow field uniformity condition is met, the vortex viscosity coefficient calculation formula is as follows:
;
Wherein, Is the vortex-induced viscosity coefficient of the material,In order to resolve the vorticity flux,、、Representing a first physical quantity filtered using the lattice filter,To represent the filter width of the lattice filter,Represents a norm of a first physical quantity filtered using the test filter,Representing a first physical quantity filtered using the test filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the filtering process of the test filter.
In an alternative embodiment, the analytical vortex flux calculation module 12 is specifically configured to:
and calculating the analytic vortex flux based on the target flow field speed and the target vortex by using an analytic vortex flux calculation formula, wherein the analytic vortex flux calculation formula is as follows:
;
Wherein, In order to resolve the vorticity flux,、To filter the resulting flow field velocities using a grid filter of large vortex simulations,、To filter the resulting flow field velocity using a test filter,、To filter the resulting vorticity using a grid filter of large vortex simulations,、To filter the resulting vorticity using a test filter,Representing the filtering process of the test filter, i, j represent different directions.
In an alternative embodiment, the first physical quantity calculation module 13 is specifically configured to:
determining a first physical quantity based on the target vortex quantity by using a preset first physical quantity calculation formula, wherein the preset first physical quantity calculation formula is as follows:
、;
Wherein, Representing the first physical quantity after filtering by the grid filter,、Indicating the vorticity obtained by filtering using a grid filter,Representing the first physical quantity after filtering by the test filter,、Indicating the vorticity obtained by filtering using the test filter,、For the distance vector i, j denote different directions.
The vorticity transport equation is:
;
Wherein, To filter the resulting vorticity using a grid filter of large vortex simulations,To filter the resulting flow field velocities using a grid filter of large vortex simulations,Is the vortex-induced viscosity coefficient, t is the time,As a result of the distance vector,Is the filter width of the grid filter,Represents a norm of a first physical quantity filtered using the lattice filter,Representing the first physical quantity after filtering by the grid filter,The coefficient of motion viscosity is represented by the equation,、Indicating vorticity obtained by filtering with a grid filter, i, j indicating different directions.
The flow field speed calculation module 16 specifically uses a first preset formula, and updates a flow function vector based on the vorticity obtained by filtering the grid filter using the large vortex simulation at the next moment corresponding to the previous moment, where the first preset formula is:
;
Wherein, As a vector of the flow function,As a result of the distance vector,For the vorticity obtained by filtering by using a grid filter of large vortex simulation, i and j represent different directions;
Updating a speed potential function according to a flow field speed obtained by filtering by using a grid filter of large vortex simulation at the previous moment by using a second preset formula, wherein the second preset formula is as follows:
;
Wherein, As a function of the velocity potential of the object,Filtering the flow field speed obtained by using a grid filter of large vortex simulation at the previous moment;
Calculating a flow field speed obtained by filtering a grid filter using large vortex simulation at the next moment corresponding to the previous moment based on the updated flow function vector and the speed potential function by using a third preset formula, wherein the third preset formula is as follows:
;
Wherein, In order to replace the symbol,As a vector of the flow function,As a result of the distance vector,Filtering the flow field speed obtained by using a grid filter of large vortex simulation at the next moment;
And calculating the flow field speed obtained by filtering the flow field by using the test filter at the next moment based on the flow field speed obtained by filtering the flow field by using the grid filter of the large vortex simulation at the next moment.
Therefore, the embodiment of the application can adaptively calculate the vortex viscosity coefficient according to the local flow characteristic of the flow field based on the quasi-vortex energy power conservation relation of the flow structure with the scale between the filtering width of the grid filter and the filtering width of the test filter, thereby accurately determining the vortex quantity and speed of the flow field.
Referring to fig. 5, an embodiment of the present application discloses an electronic device 20, which includes a processor 21 and a memory 22, wherein the memory 22 is used for storing a computer program, and the processor 21 is used for executing the computer program, and the large vortex simulated vortex quantity and speed method disclosed in the previous embodiment is disclosed.
For specific procedures of the large vortex simulation vortex amount and speed method, reference may be made to the corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
The memory 22 may be a carrier for storing resources, such as a read-only memory, a random access memory, a magnetic disk or an optical disk, and the storage mode may be transient storage or permanent storage.
In addition, the electronic device 20 further includes a power supply 23, a communication interface 24, an input/output interface 25, and a communication bus 26, where the power supply 23 is configured to provide working voltages for each hardware device on the electronic device 20, the communication interface 24 is capable of creating a data transmission channel between the electronic device 20 and an external device, and the communication protocol to be followed by the communication interface is any communication protocol applicable to the technical solution of the present application, and is not specifically limited herein, and the input/output interface 25 is configured to obtain external input data or output data to the external device, and a specific interface type thereof may be selected according to specific application needs and is not specifically limited herein.
Further, the embodiment of the application also discloses a computer readable storage medium for storing a computer program, wherein the computer program realizes the large vortex simulated vortex quantity and speed method disclosed in the previous embodiment when being executed by a processor.
For specific procedures of the large vortex simulation vortex amount and speed method, reference may be made to the corresponding contents disclosed in the foregoing embodiments, and details are not repeated here.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, so that the same or similar parts between the embodiments are referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above detailed description of the method, device, equipment and medium for determining the vortex quantity and speed of large vortex simulation provided by the application applies specific examples to illustrate the principle and implementation of the application, and the above examples are only used for helping to understand the method and core idea of the application; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present application, the present description should not be construed as limiting the present application in view of the above.
Claims (10)
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