CN112163381B - Lateral boundary condition setting method suitable for complex terrain wind field flow numerical simulation - Google Patents
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Abstract
The invention provides a lateral boundary condition setting method suitable for complex terrain wind field flow numerical simulation, which is based on a finite volume method for solving an incompressible fluid control equation in computational fluid mechanics simulation, and judges the inflow or outflow condition of airflow at each surface element according to the airflow flux direction of the finite volume unit body center corresponding to each surface element in a computational domain lateral boundary surface (namely, a computational domain boundary arranged in parallel with the main flow direction), so as to establish corresponding speed and pressure coupling boundary conditions. The invention considers the macroscopic steering effect of the complicated ground surface on the wind direction and the ground steering force on the airflow, can simulate the real physical phenomenon of coexistence of the inflow and outflow of the atmosphere at different spatial positions on the same lateral boundary surface, well overcomes the limitations of the existing unidirectional and simplified lateral boundary conditions, establishes the composite lateral boundary conditions which are more consistent with the actual flowing condition of the wind field, are suitable for various common turbulence modes and can keep the stability and convergence of numerical calculation.
Description
Technical Field
The invention belongs to the technical field of computational fluid mechanics, and particularly relates to a lateral boundary condition setting method suitable for flow numerical simulation of a wind field in complex terrains.
Background
The inland topography of China is complex, and the large-scale land wind farm of potential and active service is mostly located in wind resource gathering areas of mountains, plateaus, hills, basins and other areas, and a numerical simulation method based on computational fluid dynamics (Computational Fluid Dynamics, CFD) has become an important tool for researching wind resource assessment of wind farms of complex topography. In general, the wind field calculation range is selected by taking the subsurface mat surface as a reference surface, and extending vertically upwards to the height of an atmospheric boundary layer (one kilometer level) to form a hexahedral region, and in numerical calculation, boundary conditions of variables such as wind speed, pressure and the like need to be reasonably selected and set on different boundaries, so that the solvability of a flow control equation in the calculation region is ensured. The study shows that the boundary condition setting method of the wind field calculation area is used as a key factor in numerical simulation, directly influences the convergence and stability of the whole operation process, and further determines the feasibility and accuracy of a numerical solution algorithm.
Currently, research on complex terrain wind field CFD numerical simulation boundary conditions is mainly focused on two directions of processing of inlet boundary generation and surface boundary. Because of the sensitivity of the lateral boundary conditions to the spatial discrete format of numerical simulation, the degree of irregularity of the underlying surface edge, and the wind speed-pressure coupling algorithm, the optimization setting thereof has been an open research topic in the CFD field. At present, selection and setting of wind speed and pressure conditions on lateral boundaries in CFD numerical simulation of wind fields at home and abroad are generally based on two main types of boundary conditions for solving a hydrodynamic partial differential (PARTIAL DEFERENTIAL Equation, PDE) control equation set (i.e. Navier-Stokes equation set), and direct selection, correction or combination use is carried out on a first type of Dirichlet boundary condition (i.e. a value of a to-be-solved variable on a boundary surface is directly given) and a second type of Neumann boundary condition (i.e. a directional derivative of the to-be-solved variable on an external normal of the boundary surface is specified).
For example Churchfield m.j. Et al simulate the flow of the atmosphere boundary over the wind field terrain where hills and valleys are combined, on the lateral boundary surface using a continuity period (Periodic) boundary condition established based on the Dirichlet boundary condition, i.e. all variable values on two (a pair of) lateral boundaries are correspondingly equal. However, the periodic boundary condition requires that the source boundary and the target boundary in the two lateral boundaries must be completely consistent in geometry and mesh division, so that complete mapping of the flow variable from the source interface to the target interface is realized, which makes the boundary condition only suitable for simulation verification of the flow field under a typical two-dimensional topography, and cannot be applied to actual three-dimensional complex topography. Peralta C et al simulate the flow of wind fields of independent hills of scarps sitting in the sea by using a Slip (Slip) boundary condition based on Neumann boundary condition on the lateral boundary surface, namely that the normal velocity of fluid on the lateral boundary surface is zero, and the tangential velocity is equal to that of a first layer of grids on the inner side of the boundary surface. However, slip boundary conditions do not mechanically allow fluid to pass through the boundary surface, and do not reflect actual fluid flux exchanges, resulting in inaccuracy of flow field simulation at the boundary region. Balogh M and the like simulate wind fields around independent hills of gentle slopes by adopting symmetrical boundary conditions of Dirichlet and Neumann on lateral boundary surfaces, so that the calculated amount is reduced to a certain extent, but the actual flowing condition is simplified correspondingly and the actual state of the airflow at the boundary can not be reflected.
In summary, the above-mentioned common lateral boundary conditions are simpler in implementation of the calculation program, but when encountering irregular geometric boundaries (such as complex terrains of mountain areas and hilly areas), there are problems that the solution is inapplicable, resulting in divergence, or the actual flow state of the wind field at the boundary cannot be accurately simulated after use, so that the accuracy of the solution of the whole calculation domain is affected.
Disclosure of Invention
The invention aims to provide a lateral boundary condition setting method suitable for flow numerical simulation of a wind field of complex terrains, which ensures operation stability and convergence when solving air flow on the terrains of complex terrains such as mountain areas and hills, and overcomes the influence of boundary effect generated by the conventional simplified lateral boundary condition on calculation accuracy.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a lateral boundary condition setting method suitable for complex terrain wind field flow numerical simulation, which comprises the following steps:
Step 1, selecting a hexahedral calculation domain of numerical simulation according to a target wind power plant area, and determining the positions of boundary surfaces of the calculation domain: taking the complex topography of the target area as a surface boundary surface, arranging the inlet and outlet boundary surfaces perpendicular to the main wind direction of the area, arranging the top boundary along the horizontal direction and ensuring the minimum ground clearance to be kilometer level, and arranging the lateral boundary surfaces parallel to the main wind direction
Step2, space grid division is carried out on the hexahedral computation domain obtained in the step 1, and a plurality of limited volume units are obtained;
step 3, setting a turbulence mode of atmospheric flow numerical simulation, and calculating the fluid volume flux corresponding to the previous time step of the current solving time step at the center of the finite volume unit corresponding to each grid surface element on the lateral boundary surface according to the selected turbulence mode
Step 4, according to the fluid volume flux corresponding to the previous time step (m-1) of each grid surface element obtained in the step 3The wind speed and pressure conditions at the centers of each grid bin are set.
Preferably, in step 3, the turbulence modes of the atmospheric flow numerical simulation include a reynolds average mode and a large vortex simulation mode.
Preferably, if a Reynolds average pattern is used, the fluid volume flux corresponding to the previous time step for each grid cell is calculated by
Wherein,Obtaining a wind speed vector of a previous time step for the limited volume unit body center corresponding to each grid surface element on the lateral boundary surface; /(I)Is the face vector of the mesh bin.
Preferably, if a large vortex simulation mode is adopted, the fluid volume flux corresponding to the previous time step of each grid element is calculated by the following formula
Wherein, subscript i is the finite volume element number; n is the number of adjacent mesh bins surrounding the target mesh bin.
Preferably, in step 4, the wind speed and pressure conditions at the face center of each grid bin are set, in particular:
If it is The speed-pressure coupling boundary condition at the target mesh bin centroid is set to:
If it is The speed-pressure coupling boundary condition at the target mesh bin centroid is set to:
In the method, in the process of the invention, Wind speed vector at current time step for target grid bin centroid,/>For its tangential wind velocity component,/>For its normal wind velocity component; /(I)And/>Tangential and normal wind speed components at the center of the unit body of the limited volume corresponding to the target surface element obtained in the previous time step respectively; /(I)For the pressure of the target grid bin centroid at the current time step,/>And (3) obtaining the pressure at the center of the finite volume unit corresponding to the target grid surface element obtained in the previous time step, wherein p atm is the atmospheric pressure corresponding to the altitude at which the surface center of the target grid surface element is located.
Compared with the prior art, the method has the beneficial effects that:
The lateral boundary condition setting method suitable for the complex terrain wind field flow numerical simulation provided by the invention can fully consider the local change effect of complex terrain on the atmosphere flow direction of the near stratum region, and the flow field characteristics obtained by simulation are more in line with the actual atmosphere flow state near the lateral boundary surface;
furthermore, the boundary condition of the coupling of the speed and the pressure can simulate the real physical phenomenon of coexistence of the inflow and the outflow of the atmosphere on the same lateral boundary surface;
Furthermore, the speed-pressure coupling type lateral boundary condition provided by the invention is suitable for two common atmospheric turbulence modes (Reynolds average mode and large vortex simulation mode), and can overcome the problems of numerical solution divergence and oscillation caused by rugged topography.
Drawings
FIG. 1 is a flow chart of a lateral boundary condition setting method suitable for complex terrain wind field flow numerical simulation in accordance with the present invention;
FIG. 2 is a schematic diagram of the boundaries of a computational domain;
FIG. 3 is a schematic diagram of mesh cells and their centers, corresponding finite volume elements and their centers, in a dominant wind left side lateral boundary surface;
FIG. 4 is a simulated cloud of lateral wind velocity components of the main wind to the right lateral boundary surface using the lateral boundary conditions of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in FIG. 1, the method for setting the lateral boundary conditions suitable for the flow numerical simulation of the wind field of the complex terrain provided by the invention comprises the following steps:
step1, determining hexahedral calculation domains of complex terrain wind field flow numerical simulation in a target wind field area, and determining the positions of all boundary surfaces;
Selecting a hexahedral calculation domain of the wind field of the numerical simulation complex terrain according to the dimension of the horizontal direction of the target wind field: taking the complex topography of the target area as a surface boundary surface, the inlet and outlet boundary surfaces are arranged perpendicular to the main (prevailing) wind direction of the area, the top surface boundary is arranged in a horizontal direction and ensures a minimum ground clearance of the order of 1 km, and the lateral boundary surfaces are arranged parallel to the main (prevailing) wind direction, as shown in fig. 2.
Step 2, setting a turbulence mode of atmospheric flow numerical simulation, and calculating the fluid volume flux corresponding to the previous time step (m-1) of the current solving time step (m) at the positions of the finite volume unit body centers corresponding to each grid surface element on the lateral boundary surface determined in the step 1 according to the selected turbulence mode
The turbulence modes of the atmospheric flow numerical Simulation are generally divided into two main types according to resolution accuracy, namely Reynolds-AVERAGED NAVIER-Stokes (RANS) mode and Large vortex Simulation (LES) mode;
Calculating the fluid volume flux corresponding to the previous time step (m-1) of the current solving time step (m) at the finite volume unit body center corresponding to each grid surface element on the lateral boundary surface determined in the step 1 Specifically:
(a) If the RANS mode is used, the calculation is performed by the following formula Is a combination of the above:
Wherein, Obtaining a wind speed vector of a previous time step for the limited volume unit body center corresponding to each grid surface element on the lateral boundary surface; /(I)Is a face vector of the grid bin, wherein/>S b is the area of the bin,/>Is a unit normal vector of the bin whose direction is perpendicular to the bin and points outside the computational domain.
(B) If LES mode is used, then the calculation is performed by
Wherein, subscript i is a finite volume element number, i=0 represents a finite volume element where the target mesh element is located, n=2-4 represents the number of adjacent mesh elements around the target mesh element, and n=2 when the target mesh element is located at the vertex angle, as shown in fig. 3; when the target mesh bin is at the edge, n=3; when the target mesh bin is located at the rest position, n=4; here at the target mesh binThe non-steady state flux analyzed by the LES mode is subjected to numerical averaging in a near space range, and the purpose of the method is to enhance the robustness of boundary conditions.
Step 3, obtaining according to each bin in the lateral boundarySetting the wind speed and pressure conditions at the centers of the grid cells:
(a) If it is It is stated that there is an airflow at the mesh bin flowing into the computational domain, and the corresponding speed-pressure coupling boundary condition is set to:
In the method, in the process of the invention, A tangential velocity component of a wind velocity vector at a current time step (m) for a target grid bin centroidTangential velocity component obtained in previous time step at the center of limited volume unit corresponding to target grid surface elementIts normal velocity component/>By/>, obtained in step 2)Obtaining the ratio of the grid surface element area S b; pressure/>, at the current time step, of the target mesh bin centroidThe pressure value/>, which is obtained in the previous time step, is set at the position of the center of the finite volume unit corresponding to the target grid surface element
(B) If it isIt is stated that there is an airflow flowing out of the computational domain at that bin, and the corresponding speed-pressure coupling boundary condition is set to:
In which the tangential velocity component of the target mesh bin centroid at the current time step The tangential velocity component/>, which is obtained in the previous time step, is set at the center of the unit body of the finite volume corresponding to the surface elementNormal velocity component/>, of target grid bin centroid at current time stepThe method is set as the method phase velocity component/>, which is obtained in the previous time step, at the center of the unit body of the finite volume corresponding to the surface elementPressure/>, at the centroid of a target mesh binThe atmospheric pressure p atm corresponding to the altitude where the centroid is located is set.
Examples
The invention provides a lateral boundary condition setting method suitable for complex terrain wind field flow numerical simulation, which comprises the following steps:
Step (1), selecting a hexahedral calculation domain of numerical simulation according to a target wind power plant area, and determining the position of each boundary surface of the calculation domain;
In the embodiment, a wind power plant in a mountain area is taken as a research object, and a digital terrain elevation model of the area is obtained in an online database through Shuttle Radar Topography Mission (SRTM).
The horizontal dimension of the calculation domain required by the numerical simulation can be selected according to the actual occupation area of the target wind power plant (8 km×5km in the example), and the vertical dimension is selected to be the common kilometer-level air boundary layer height (1 km in the example). The selected numerical simulation domain includes a main ridge (with an altitude drop of about 400 meters) and 8 anemometers (denoted by the letter "SM" plus a number), as shown in fig. 2.
The surface boundary of the calculation domain is the complex subsurface of the target wind field, the inlet and outlet boundaries of the calculation domain are arranged perpendicular to the main (prevailing) wind direction of the region, the lateral boundaries (two) of the calculation domain are arranged parallel to the main (prevailing) wind direction, and the top boundary of the calculation domain is arranged along the horizontal direction, so that the hexahedral calculation domain is obtained, as shown in fig. 2.
Step (2), carrying out space grid division on the hexahedral calculation domain obtained in the step (1);
In order to ensure the calculation accuracy of numerical simulation, the hexahedral calculation domain obtained in the step (2) is divided by adopting a hexahedral structured grid unit, and the resolution of the grid unit is required to analyze the change characteristics of the complex topography in the horizontal and vertical directions in principle;
aiming at the topography of the example, the spatial resolution of the grid unit in the horizontal direction is 15m; the spatial resolution in the vertical direction is encrypted near the ground, the height of the bottom layer grid is 4m, the bottom layer grid extends vertically in a tanh function relationship, and the height of the top layer grid is 40m.
Step (3), according to a turbulence mode adopted in the atmospheric flow numerical simulation, boundary conditions of an inlet, an outlet, a top and a surface boundary of a calculation domain are respectively set;
The calculation example carries out numerical simulation on the atmospheric flow of a wind field with complex terrain by selecting an LES mode, takes the average wind speed of the highest measuring layer on a reference wind measuring tower (in the calculation example, the southwest wind direction of the wind measuring tower SM03 at the position of 57 m) in the main wind direction as the drive based on the inlet boundary condition of the LES mode, and adopts a full-period (full period) preamble (Precursor) method to generate;
The outlet boundary condition is a general CFD pressure outlet boundary condition, namely the pressure condition is standard atmospheric pressure, and the wind speed condition is zero gradient change;
The top surface boundary condition adopts a common free Slip boundary (Slip) condition;
surface boundary condition adaptation for LES mode Shear stress wall model.
Step (4), setting boundary conditions of the lateral boundary surface according to a turbulence mode adopted in the atmospheric flow numerical simulation:
(4-a) based on the LES pattern employed in the atmospheric flow numerical simulation, at the finite volume cell centers corresponding to the respective mesh bins on the lateral boundary surface, the fluid volume flux corresponding to the previous time step (m-1) relative to the current solving time step (m) And (3) performing calculation:
Wherein, Wind speed vectors obtained based on the previous time step are used for the positions of the centers of the limited volume units corresponding to each grid surface element on the lateral boundary surface; /(I)Is a face vector of the grid bin, wherein/>S is the area of the bin,/>Is a unit normal vector of a bin, whose direction is perpendicular to the bin and points outside the computational domain; the subscript i is the finite volume element number, and as shown in fig. 3, i=0 represents the finite volume element in which the target mesh bin is located, n=2-4 represents the number of adjacent bins around the target mesh bin, n=2 when the target mesh bin is located at the vertex angle, and n=3 when the target mesh bin is located at the edge; when the target mesh bin is located at the rest position, n=4; here/>, at the target mesh binThe non-steady state flux analyzed by the LES mode is subjected to numerical averaging in a near space range, and the purpose of the method is to enhance the robustness of boundary conditions.
(4-B) by determination ofAnd sets the wind speed and pressure conditions at the target grid bin centroid in the lateral boundary surface:
If it is It is stated that there is an airflow at this bin flowing into the calculation domain, the corresponding wind speed-pressure coupling boundary condition is set as:
In the method, in the process of the invention, A tangential velocity component of a wind velocity vector at a current time step (m) for a target grid bin centroidTangential velocity component obtained in previous time step at the center of limited volume unit corresponding to target grid surface elementIts normal velocity component/>By/>, obtained in step 2)Obtaining the ratio of the surface area S b to the surface area S b; pressure/>, at the current time step, of the target mesh bin centroidThe pressure value/>, which is obtained in the previous time step, is set at the position of the center of the finite volume unit corresponding to the target grid surface element
If it isIt is stated that there is an airflow flowing out of the computational domain at that bin, and the corresponding speed-pressure coupling boundary condition is set to:
In which the tangential velocity component of the target mesh bin centroid at the current time step The tangential velocity component/>, which is obtained in the previous time step, is set at the center of the unit body of the finite volume corresponding to the surface elementNormal velocity component/>, of target grid bin centroid at current time stepThe method is set as the method phase velocity component/>, which is obtained in the previous time step, at the center of the unit body of the finite volume corresponding to the surface elementPressure/>, at the centroid of a target mesh binThe atmospheric pressure p atm corresponding to the altitude where the centroid is located is set.
And (5) carrying out CFD numerical solution on the speed and the pressure of the atmospheric flow in the whole calculation domain range under the lateral boundary condition set in the method:
The numerical simulation of the invention is developed based on an open-source CFD field operation and processing software OpenFOAM (Open Source Field Operation and Manipulation) as a platform, the computing platform is based on a finite volume method (Finite Volume Method, FVM), an incompressible fluid Navier-Stokes equation set describing the movement of atmospheric turbulence is subjected to numerical solution, and the Pressure and speed coupling adopts a PISO (Pressure IMPLICIT WITH SPLITTING of Operators) algorithm. Wherein the gradient is And Laplace operator/>The term adopts Gauss linear space discrete format, which is equivalent to the common second-order center differential format; the convection item adopts Gamma format which is biased to the second order windward characteristic, so as to approach the second order precision to the maximum extent under the condition of keeping the numerical stability; the time discrete format adopts an implicit second-order backward differential format (implicit 2-order backward scheme), and the self-adaptive time step is in the range of 0.1 to 0.5 seconds on the premise that the Ke Lang number (CFL) is not more than 0.7.
And (6) qualitative and quantitative analysis of the numerical simulation result:
Qualitatively, the simulated cloud of the transverse wind velocity component (Uy) at the lateral boundary of the main wind to the right is shown in fig. 4, and it can be seen that, using the lateral boundary condition of velocity and pressure coupling according to the present invention, the local change effect of the air flow direction in the region near the lateral boundary surface of the complex terrain can be fully considered, and the macroscopic steering effect of the ground steering force generated by the earth rotation on the air flow over the whole wind field is considered, so that the simulation of the real physical phenomenon that the air inflow (Uy positive) and the air outflow (Uy negative) are simultaneously allowed on the side boundary is realized.
To further verify the rationality of the lateral boundary condition setting method of the present invention, the simulated wind statistics (i.e., average wind speed and standard deviation of wind speed) at the 8 anemometer tower locations in the target area may be quantitatively compared with the measured data, as shown in table 1. The simulation shows that the variation trend of the wind speed average value and the fluctuation condition in space is basically consistent with the measured data; meanwhile, the simulation and actual measurement wind data errors at each point are also within an acceptable range (10%).
The above description is merely illustrative of the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any substitution of the computing platform (e.g. OpenFOAM, fluent, CFX, etc.), turbulence patterns (RANS, LES, DNS), and other simulation parameters, based on the lateral boundary conditions, as will be readily appreciated by those skilled in the art, is within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
TABLE 1
Claims (5)
1. The lateral boundary condition setting method suitable for the complex terrain wind field flow numerical simulation is characterized by comprising the following steps of:
Step 1, selecting a hexahedral calculation domain of numerical simulation according to a target wind power plant area, and determining the positions of boundary surfaces of the calculation domain: taking the complex topography of the target area as a ground surface boundary surface, arranging an inlet boundary surface and an outlet boundary surface perpendicular to the main wind direction of the area, arranging a top surface boundary along the horizontal direction and ensuring the minimum ground clearance to be kilometer level, and arranging a lateral boundary surface parallel to the main wind direction;
step2, space grid division is carried out on the hexahedral computation domain obtained in the step 1, and a plurality of limited volume units are obtained;
Step 3, setting a turbulence mode of atmospheric flow numerical simulation, and calculating fluid volume flux corresponding to the previous time step of the current solving time step at the position of the finite volume unit body center corresponding to each grid surface element on the lateral boundary surface according to the selected turbulence mode;
and 4, setting the wind speed and pressure conditions at the surface centers of the grid cells according to the fluid volume flux corresponding to the previous time step of each grid cell obtained in the step 3.
2. A method of setting lateral boundary conditions suitable for use in complex terrain wind farm flow numerical simulation according to claim 1, wherein in step 3, the turbulence modes of the atmospheric flow numerical simulation include a reynolds average mode and a large vortex simulation mode.
3. A method for setting lateral boundary conditions suitable for flow numerical simulation of a wind farm of complex terrain according to claim 2, wherein if a reynolds average pattern is adopted, the fluid volume flux corresponding to the previous time step of each grid cell is calculated by the following formula
Wherein,Obtaining a wind speed vector of a previous time step for the limited volume unit body center corresponding to each grid surface element on the lateral boundary surface; /(I)Is the face vector of the mesh bin.
4. The method for setting lateral boundary conditions suitable for flow numerical simulation of a wind field of complex terrain according to claim 2, wherein if a large vortex simulation mode is adopted, the fluid volume flux corresponding to the previous time step of each grid cell is calculated by the following formula
Wherein, subscript i is the finite volume element number; n is the number of adjacent grid cells around the target grid cell; obtaining a wind speed vector of a previous time step for the limited volume unit body center corresponding to each grid surface element i on the lateral boundary surface; /(I) Is the face vector corresponding to each grid face element i on the lateral boundary surface.
5. The method for setting lateral boundary conditions suitable for complex terrain wind field flow numerical simulation according to claim 1, wherein in step 4, wind speed and pressure conditions at the face center of each grid face element are set, specifically:
If it is The speed-pressure coupling boundary condition at the target mesh bin centroid is set to:
If it is The speed-pressure coupling boundary condition at the target mesh bin centroid is set to:
In the method, in the process of the invention, Wind speed vector at current time step for target grid bin centroid,/>For its tangential wind velocity component,For its normal wind velocity component; /(I)And/>Tangential and normal wind speed components at the center of the unit body of the limited volume corresponding to the target surface element obtained in the previous time step respectively; /(I)For the pressure of the target grid bin centroid at the current time step,/>The pressure at the center of the finite volume unit corresponding to the target grid surface element obtained in the previous time step is p atm, and the atmospheric pressure corresponding to the altitude at which the surface center of the target grid surface element is located; s b is the area of the target grid surface element; /(I)The fluid volume flux corresponding to the previous time step of the target grid bin.
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