CN117875221B - Novel fan wake coupling method - Google Patents
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Abstract
The invention discloses a novel fan wake coupling method, which belongs to fan engineering calculation; the method is characterized in that the near wake field of the fan is simulated based on CFD values of an actuation line method to obtain aerodynamic performance such as thrust and power of the fan and wake key information, the dynamic wake winding model DWM method is used for calculating the far wake field of the fan, the coupling method reflects wake distribution conditions of the fan more truly than a medium-precision wake model, the aerodynamic performance precision is higher than that of the high-precision wake model, and the calculation efficiency is higher than that of the high-precision wake model, so that the method is more suitable for quick preliminary calculation.
Description
Technical Field
The invention relates to the technical field of fan engineering calculation, in particular to a novel fan wake coupling method.
Background
The maximum power generation capacity is obtained in a limited wind farm, and the consideration of the fan wake effect is an essential design core problem. With the increasing maturity of wind power generation, people even begin to pay attention to the influence among wind farms, so-called "wind theft" effect is proposed, and the large-scale wake evolution among wind farms can lead to significant reduction of the power generated by fans downstream of the wind farms, which indicates that the current engineering wake model far underestimates the influence of the fan wake. The influence of the fan wake on the downstream fan is not negligible. Although CFD (Computational Fluid Dynamic, computational fluid dynamics) methods are widely used for numerical simulation of fan wake with the development and improvement of computer technology, CFD methods require a large amount of computational resources to face the fan wake computation of extremely long distances from field to field, and are impractical in engineering applications
Thus, a novel fan wake coupling method is provided.
Disclosure of Invention
The invention aims to provide a novel fan wake coupling method, which is used for simulating a near wake field of a fan based on CFD values of an actuation line method to obtain aerodynamic performances such as thrust and power of the fan and wake key information, and calculating a far wake field of the fan by using a DWM method, wherein the calculation time is in hours and days (days) and is suitable for engineering design.
In order to achieve the above purpose, the invention provides a novel fan wake coupling method, which comprises the following steps:
S1: calculating the wake flow of the fan, wherein the wake flow calculation is divided into three areas in sequence, including a near wake flow area Z1 of the fan, a coupling area Z2 and a far wake flow area Z3 of the fan, setting the time step as T, and initializing the speed fields of the three areas (V d,0,0),Vd is uniform wind speed, and V z1、Vz2 and V z3 respectively represent the speed fields of different areas;
S2: for a near-wake zone Z1 of the fan, a fan actuation line model is established, a source item is added in an average Reynolds equation to replace a real fan blade, and the average Reynolds equation is solved to obtain a near-wake zone velocity field V z1 of the fan;
S3: adding an exponential relaxation factor for the coupling zone Z2, and performing coupling calculation to obtain a coupling zone velocity field V z2;
S4: dividing a fan far wake zone Z3 into a plurality of radial equidistant circular rings, solving a dynamic wake meandering model DWM by using a catch-up method, inputting a fan near wake zone speed field V z1, acquiring an inlet boundary condition of the DWM, and then calculating an axial speed V x and a tangential speed V r of the far wake field to obtain a fan far wake speed field V z3;
S5: updating the coupling area again by adopting the method in the step S3, and outputting a new coupling area speed field V z2;
S6: steps S4 and S5 are repeated until the required velocity field V z3 of the fan' S far wake zone is calculated.
Preferably, in the step S2, the specific process of calculating the speed field of the near wake area of the fan is as follows:
Setting the length of a calculation domain of a near-wake zone Z1 of a fan to be x c1, dividing the calculation domain of the near-wake zone Z1 of the fan into a plurality of grids, solving a speed field V z1 of the near-wake zone of the fan by adopting an average Reynolds equation, and adding a source term to replace a real fan blade in the NS equation by utilizing a fan actuation line model, wherein the formula is as follows:
In the above formula, ρ is the fluid density, u is the near wake velocity vector, i=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, j=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, p is the pressure, g i is the gravitational acceleration, τ ij and τ tij are the viscous and turbulent stresses, F σi is the surface tension, and F is the source term modeling the blade effect on the fluid, i.e., the vector sum of lift and drag;
In the fan near-wake field, the wind turbine blade is divided into tens of airfoil segments by means of a fan actuation line model, each airfoil segment is replaced with a physical force calculated from the local reynolds number and airfoil aerodynamic parameter table using an actuation point, each actuation point force is denoted by f k, and the aerodynamic formulas generated at (x, y, z, t) for all blade segments are as follows:
In the above formula, F (x, y, z, t) is the vector sum of lift force and resistance force of each pneumatic point, x, y, z, t is the three-dimensional coordinate point and the current calculation time, k is the actuation point index, N is the total number of actuation point segments, d k is the distance between the (x, y, z) and the ith actuator point, and ε is a constant that determines the width of the projection area;
the velocity field formula of the near wake area of the fan is obtained as follows:
Vz1＝(u1,u2,u3)
When the time steps When the calculation of the velocity field of the near wake region of the fan is completed, V d is the average axial wind speed of the calculation domain x c1, u 1 represents the x coordinate axis direction velocity in the Cartesian coordinate system, u 2 represents the y coordinate axis direction velocity in the Cartesian coordinate system, and u 3 represents the z coordinate axis direction velocity in the Cartesian coordinate system.
Preferably, in the step S3, the coupling calculation is performed as follows:
The formula of the coupling calculation is as follows:
VZ2＝VZ1w+VZ3(1-w)
In the above formula, w is a weight factor:
In the above equation, β is the dimensionless length or the relative length of the coupling zone Z2.
Preferably, in the step S4, the process of obtaining the entry boundary condition of the DWM is as follows:
The radial velocity profile V r|P＝0 (r) at the boundary of the equation entry is given by:
Vr|P＝0(r)＝0
In the above formula, P represents a P-th section at the coupling zone Z2, and r is the radial distance from the calculated point to the origin in the coordinate system;
the axial wake velocity of the equation entry boundary is calculated using the following equation for the boundary conditions:
Vx|P＝0(r)＝u1(r)
In the above formula, P represents the P-th section at the coupling zone Z2, r is the radial distance from the calculated point to the origin in the coordinate system, and u 1 represents the x coordinate axis direction speed in the cartesian coordinate system.
Preferably, in the step S4, the process of calculating the velocity field V z3 of the fan far wake area is as follows:
The formula of the fan far wake zone velocity field V z3 is as follows:
Vz3＝(Vx,Vr，0)
The axial velocity V x and tangential velocity V r in the cylindrical coordinate system are calculated as follows:
In the above-mentioned method, the step of, Is the axial velocity axial gradient in the cylindrical coordinate system,/>Is the axial velocity radial gradient in the cylindrical coordinate system, r is the radial distance from the calculated point to the origin in the coordinate system, V T-1 is the vortex viscosity in the previous time period, and the current vortex viscosity V T is calculated by using the axial velocity V x and the radial velocity V r in the cylindrical coordinate system, and the formula is as follows:
In the above-mentioned method, the step of, For the filter function related to the turbulence of the environment,/>For wake-shear layer dependent filter function,/>And/>The filter function of (2) represents the retardation of the turbulence stress generated by the environmental turbulence and the development of the turbulence stress generated by the wake shear layer respectively,/>Is the influence of environmental turbulence on vortex viscosity,/>Is the effect of wake shear layer on vortex viscosity, R wake is wake half width, V x-1 (x, R) is axial velocity at last time step, min| r{Vx-1 (x, R) } represents minimum of V x-1 along radius given downstream distance, I Amb is turbulence intensity at hub center.
Therefore, the novel fan wake coupling method has the following advantages that:
(1) In the invention, the advantages of accurate calculation of the aerodynamic performance of the fan based on the actuating line method of computational fluid mechanics and the advantages of analytic wake vortex details and the characteristics of rapid calculation of the fan wake by a dynamic wake meandering model (DYNAMIC WAKE MEANDERING (DWM) model) and saving of calculation resources are effectively combined, so that the precision and the efficiency of a calculation result are improved by one grade, and the coupling model belongs to a quasi-high-precision wake model, but the calculation efficiency is far higher than that of the high-precision wake model.
(2) According to the invention, the problem of speed backflow can be avoided even if a smaller calculation domain is used by CFD through a numerical relaxation method, and the stability of speed-pressure coupling calculation in the calculation domain is ensured.
(3) In the invention, the speed distribution of the near-wake field of the CFD is adopted as the entrance boundary of the DWM, so that the defect of large prediction error of the DWM model on the near-wake field is overcome, and the characteristic of high efficiency of the DWM is fully exerted.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of a novel fan wake coupling method of the present invention;
FIG. 2 is an experimental process layout diagram of a novel fan wake coupling method of the present invention;
FIG. 3 is a graph of average axial wake distributions predicted by different methods of a novel fan wake coupling method of the present invention;
FIG. 4 is a graph showing calculation time of different calculation models in a novel fan wake coupling method of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. The specific model specification needs to be determined by selecting the model according to the actual specification and the like of the device, and the specific model selection calculation method adopts the prior art in the field, so detailed description is omitted.
Examples
As shown in FIG. 1, the invention provides a novel fan wake coupling method, which comprises the following steps:
S1: calculating the wake flow of the fan, wherein the wake flow calculation is divided into three areas sequentially, including a near wake flow area Z1 of the fan, a coupling area Z2 and a far wake flow area Z3 of the fan, setting the time step as T, and initializing the speed fields of the three areas, wherein the initialization result is that V d,0,0),Vd is uniform wind speed, and V z1、Vz2 and V z3 respectively represent the speed fields of different areas;
S2: for a near-wake zone Z1 of a fan, a fan actuation line model is established, a source item is added in an average Reynolds equation to replace a real fan blade, the average Reynolds equation is solved, a near-wake zone speed field V z1 of the fan is obtained, and the specific process of calculating the near-wake zone speed field V z1 of the fan is as follows:
Setting the length of a calculation domain of a near-wake zone Z1 of a fan to be x c1, dividing the calculation domain of the near-wake zone Z1 of the fan into a plurality of grids, solving a speed field V z1 of the near-wake zone of the fan by adopting an average Reynolds equation, and adding a source term to replace a real fan blade in the NS equation by utilizing a fan actuation line model, wherein the formula is as follows:
In the above formula, ρ is the fluid density, u is the near wake velocity vector, i=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, j=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, p is the pressure, g i is the gravitational acceleration, τ ij and τ tij are the viscous and turbulent stresses, F σi is the surface tension, and F is the source term modeling the blade effect on the fluid, i.e., the vector sum of lift and drag;
In the fan near-wake field, the wind turbine blade is divided into tens of airfoil segments by means of a fan actuation line model, each airfoil segment is replaced with a physical force calculated from the local reynolds number and airfoil aerodynamic parameter table using an actuation point, each actuation point force is denoted by f k, and the aerodynamic formulas generated at (x, y, z, t) for all blade segments are as follows:
In the above formula, F (x, y, z, t) is the vector sum of lift force and resistance force of each pneumatic point, x, y, z, t is the three-dimensional coordinate point and the current calculation time, k is the actuation point index, N is the total number of actuation point segments, d k is the distance between the (x, y, z) and the ith actuator point, and ε is a constant that determines the width of the projection area;
the velocity field formula of the near wake area of the fan is obtained as follows:
Vz1＝(u1,u2,u3)
When the time steps When the calculation of the velocity field of the near wake region of the fan is completed, V d is the average axial wind speed of the calculation domain x c1, u 1 represents the x coordinate axis direction velocity in the Cartesian coordinate system, u 2 represents the y coordinate axis direction velocity in the Cartesian coordinate system, and u 3 represents the z coordinate axis direction velocity in the Cartesian coordinate system.
S3: adding an exponential relaxation factor for the coupling zone Z2, and performing coupling calculation to obtain a coupling zone velocity field V z2;
The formula of the coupling calculation is as follows:
VZ2＝VZ1w+VZ3(1-w)
In the above formula, w is a weight factor:
In the above equation, β is the dimensionless length or the relative length of the coupling zone Z2.
S4: for a fan far wake zone Z3, dividing the fan far wake zone Z3 into a plurality of radial equidistant circular rings, solving a dynamic wake winding model DWM by using a catch-up method, inputting a fan near wake zone speed field V z1, and acquiring an inlet boundary condition of the DWM, wherein the process is as follows:
The radial velocity profile of the equation entry boundary is given by:
Vr|P＝0(r)＝0
In the above formula, P represents a P-th section at the coupling zone Z2, and r is the radial distance from the calculated point to the origin in the coordinate system;
the axial wake velocity of the equation entry boundary is calculated using the following equation for the boundary conditions:
Vx|P＝0(r)＝u1(r)
In the above formula, P represents the P-th section at the coupling zone Z2, r is the radial distance from the calculated point to the origin in the coordinate system, and u 1 represents the x coordinate axis direction speed in the cartesian coordinate system.
The formula of the fan far wake zone velocity field V z3 is as follows:
Vz3＝(Vx,Vr，0)
The axial velocity V x and tangential velocity V r in the cylindrical coordinate system of the far-wake field are calculated as follows:
In the above-mentioned method, the step of, Is the axial velocity axial gradient in the cylindrical coordinate system,/>Is the axial velocity radial gradient in the cylindrical coordinate system, V T-1 is the vortex viscosity in the previous time period, and the axial velocity V x and the radial velocity V r in the cylindrical coordinate system are used to calculate the vortex viscosity V T of this time, and the formula is as follows:
In the above-mentioned method, the step of, For the filter function related to the turbulence of the environment,/>For wake-shear layer dependent filter function,/>And/>The filter function of (2) represents the retardation of the turbulence stress generated by the environmental turbulence and the development of the turbulence stress generated by the wake shear layer respectively,/>Is the influence of environmental turbulence on vortex viscosity,/>Is the effect of wake shear layer on vortex viscosity, R wake is wake half width, V x-1 (x, R) is axial velocity at last time step, min| r{Vx-1 (x, R) } represents minimum of V x-1 along radius given downstream distance, I Amb is turbulence intensity at hub center.
S5: updating the coupling area again by adopting the method in the step S3, and outputting a new coupling area speed field V z2;
S6: steps S4 and S5 are repeated until the required velocity field V z3 of the fan' S far wake zone is calculated.
The specific experimental process is as follows, wind tunnel test is carried out, as shown in fig. 2, a wind tunnel test layout diagram is shown, model-level fans are installed on front and rear rotary tables of a wind tunnel, and yaw of the fans can be achieved by rotating the rotary tables. The two fans are spaced by 10 meters, the front fan is positioned at a position 3.0 meters away from the wind tunnel inlet, and the hub center of the front fan is positioned at a position 1.15 meters above the wind tunnel floor. The second fan hub has a height of 1.08m. Three wake measurement profiles were designed between two fans, each profile being parallel to the fan plane of rotation. These sections are located at distances of 3.6 meters, 5.4 meters and 7.2 meters, respectively, from the front fan rotation plane.
The number of test working conditions is 4, and as shown in table 1, the error between the calculated result of the coupling model and the result acquired by the test value fan 1 and the fan 2 is controlled within 10%.
TABLE 1 mean aerodynamic coefficient
FIG. 3 compares the average axial wake distributions predicted using different methods, in FIG. 3, the solid line is the experimental value; the round line is a high-precision model, and the dotted line is a medium-precision model; the x-dotted line is the coupling model of the application, and from the figure, it can be seen that according to the solid line of the test result, the fitting result of the coupling model provided by the application is better than the middle-precision model and slightly worse than the high-precision model;
Fig. 4 shows the calculation time required by the three calculation methods to calculate the 4 schemes, from which it can be seen that the time of the coupling model proposed by the present application is the shortest, and therefore, the time is the fastest using the coupling model proposed by the present application.
Therefore, the novel fan wake coupling method is adopted, the near-wake field of the fan is simulated based on the CFD value of the actuation line method, and the aerodynamic performance such as the thrust and the power of the fan and wake key information are obtained. The far wake field of the fan is calculated by using the DWM method, the wake distribution situation of the fan is reflected more truly by the coupling method relative to a medium-precision wake model, the pneumatic performance precision is higher, and the calculation efficiency is higher relative to a high-precision wake model.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (4)
1. A novel fan wake coupling method is characterized in that: the method comprises the following steps:
S1: calculating the wake flow of the fan, wherein the wake flow calculation is divided into three areas in sequence, including a near wake flow area Z1 of the fan, a coupling area Z2 and a far wake flow area Z3 of the fan, setting the time step as T, and initializing the speed fields of the three areas (V d,0,0),Vd is uniform wind speed, and V z1、Vz2 and V z3 respectively represent the speed fields of different areas;
S2: for a near-wake zone Z1 of the fan, a fan actuation line model is established, a source item is added in an average Reynolds equation to replace a real fan blade, and the average Reynolds equation is solved to obtain a near-wake zone velocity field V z1 of the fan;
S3: adding an exponential relaxation factor for the coupling zone Z2, and performing coupling calculation to obtain a coupling zone velocity field V z2;
S4: dividing a fan far wake zone Z3 into a plurality of radial equidistant circular rings, solving a dynamic wake meandering model DWM by using a catch-up method, inputting a fan near wake zone speed field V z1, acquiring an inlet boundary condition of the DWM, and then calculating an axial speed V x and a tangential speed V r of the far wake field to obtain a fan far wake speed field V z3;
The process of calculating the fan far wake zone velocity field V z3 is as follows:
The formula of the fan far wake zone velocity field V z3 is as follows:
Vz3＝(Vx,Vr，0)
The axial velocity V x and tangential velocity V r in the cylindrical coordinate system are calculated as follows:
In the above-mentioned method, the step of, Is the axial velocity axial gradient in the cylindrical coordinate system,/>Is the axial velocity radial gradient in the cylindrical coordinate system, r is the radial distance from the calculated point to the origin in the coordinate system, V T-1 is the vortex viscosity in the previous time period, and the current vortex viscosity V T is calculated by using the axial velocity V x and the radial velocity V r in the cylindrical coordinate system, and the formula is as follows:
In the above-mentioned method, the step of, For the filter function related to the turbulence of the environment,/>For wake-shear layer dependent filter function,/>And/>The filter function of (2) represents the retardation of the turbulence stress generated by the environmental turbulence and the development of the turbulence stress generated by the wake shear layer respectively,/>Is the influence of environmental turbulence on vortex viscosity,/>Is the effect of wake shear layer on vortex viscosity, R wake is wake half width, V x-1 (x, R) is axial velocity at last time step, min| r{Vx-1 (x, R) } represents minimum of V x-1 along radius given downstream distance, I Amb is turbulence intensity at hub center;
S5: updating the coupling area again by adopting the method in the step S3, and outputting a new coupling area speed field V z2;
S6: steps S4 and S5 are repeated until the required velocity field V z3 of the fan' S far wake zone is calculated.
2. The novel fan wake coupling method of claim 1, wherein: in the step S2, the specific process of calculating the speed field of the near wake area of the fan is as follows:
Setting the length of a calculation domain of a near-wake zone Z1 of a fan to be x c1, dividing the calculation domain of the near-wake zone Z1 of the fan into a plurality of grids, solving a speed field V z1 of the near-wake zone of the fan by adopting an average Reynolds equation, and adding a source term to replace a real fan blade in the NS equation by utilizing a fan actuation line model, wherein the formula is as follows:
In the above formula, ρ is the fluid density, u is the near wake velocity vector, i=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, j=1, 2,3 respectively represent the three coordinate axis directions of xyz in the cartesian coordinate system, p is the pressure, g i is the gravitational acceleration, τ ij and τ tij are the viscous and turbulent stresses, F σi is the surface tension, and F is the source term modeling the blade effect on the fluid, i.e., the vector sum of lift and drag;
In the fan near-wake field, the wind turbine blade is divided into tens of airfoil segments by means of a fan actuation line model, each airfoil segment is replaced with a physical force calculated from the local reynolds number and airfoil aerodynamic parameter table using an actuation point, each actuation point force is denoted by f k, and the aerodynamic formulas generated at (x, y, z, t) for all blade segments are as follows:
In the above formula, F (x, y, z, t) is the vector sum of lift force and resistance force of each pneumatic point, x, y, z, t is the three-dimensional coordinate point and the current calculation time, k is the actuation point index, N is the total number of actuation point segments, d k is the distance between the (x, y, z) and the ith actuator point, and ε is a constant that determines the width of the projection area;
the velocity field formula of the near wake area of the fan is obtained as follows:
Vz1＝(u1,u2,u3)
When the time steps When the calculation of the velocity field of the near wake region of the fan is completed, V d is the average axial wind speed of the calculation domain x c1, u 1 represents the x coordinate axis direction velocity in the Cartesian coordinate system, u 2 represents the y coordinate axis direction velocity in the Cartesian coordinate system, and u 3 represents the z coordinate axis direction velocity in the Cartesian coordinate system.
3. The novel fan wake coupling method of claim 2, wherein: in the step S3, the coupling calculation process is as follows:
The formula of the coupling calculation is as follows:
VZ2＝VZ1w+VZ3(1-w)
In the above formula, w is a weight factor:
In the above equation, β is the dimensionless length or the relative length of the coupling zone Z2.
4. A novel fan wake coupling method as defined in claim 3 wherein: in the step S4, the process of obtaining the entry boundary condition of the DWM is as follows:
The radial velocity profile V r|P＝0 (r) at the boundary of the equation entry is given by:
Vr|P＝0(r)＝0
In the above formula, P represents a P-th section at the coupling zone Z2, and r is the radial distance from the calculated point to the origin in the coordinate system;
The axial wake velocity V x|P＝0 (r) of the equation entry boundary is calculated using the following equation for the boundary conditions:
Vx|P＝0(r)＝u1(r)
In the above formula, P represents the P-th section at the coupling zone Z2, r is the radial distance from the calculated point to the origin in the coordinate system, and u 1 represents the x coordinate axis direction speed in the cartesian coordinate system.
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| CN209910946U (en) * | 2019-06-20 | 2020-01-07 | 国家海洋技术中心 | Tidal current energy power generation device wake field measurement system |
| CN115017731A (en) * | 2022-06-29 | 2022-09-06 | 华能集团技术创新中心有限公司 | Offshore wind farm dynamic wake flow modeling method and device |
| CN117592388A (en) * | 2023-11-09 | 2024-02-23 | 重庆大学 | CFD-based wind farm multi-machine wake simulation method |
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| US6963291B2 (en) * | 2002-05-17 | 2005-11-08 | The Board Of Trustees Of The Leland Stanford Junior University | Dynamic wake prediction and visualization with uncertainty analysis |
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| CN209910946U (en) * | 2019-06-20 | 2020-01-07 | 国家海洋技术中心 | Tidal current energy power generation device wake field measurement system |
| CN115017731A (en) * | 2022-06-29 | 2022-09-06 | 华能集团技术创新中心有限公司 | Offshore wind farm dynamic wake flow modeling method and device |
| CN117592388A (en) * | 2023-11-09 | 2024-02-23 | 重庆大学 | CFD-based wind farm multi-machine wake simulation method |
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