CN114398843B - Three-dimensional wake wind speed distribution calculation method suitable for various terrains - Google Patents
Three-dimensional wake wind speed distribution calculation method suitable for various terrains Download PDFInfo
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Abstract
The invention relates to a three-dimensional wake wind speed distribution calculation method suitable for various terrains, which considers the influence on the inflow wind speed of a fan under the coupling effect of a terrain acceleration effect and a wind shear effect and the influence on the wake center settlement height caused by the change of the terrain of a leeward slope, combines wind speed and turbulence data measured by a foundation laser radar to correct an inflow wind profile model, a turbulence intensity model and a wake settlement theoretical model, ensures the accuracy of the model, finally establishes a wake wind speed distribution calculation method suitable for various terrains, and provides accuracy guarantee for the power prediction, layout optimization and microscopic site selection of a complex terrain wind power plant.
Description
Technical Field
The invention relates to the technical field of wind power generation, in particular to a three-dimensional wake wind speed distribution calculation method suitable for various terrains.
Background
The wake effect of the wind turbine is an important influencing factor for influencing the flow of the flow field in the wind farm, and is formed because the upstream wind turbine absorbs energy from wind, and the energy acquired by the downstream wind turbine is reduced according to the principle of conservation of energy. Under the influence of wake effect, the generating capacity of the downwind wind turbine is reduced, and the load of the wind turbine is exponentially increased along with the increase of the turbulence intensity in the wake. After the landing flat terrain wind power plant is developed successively, the complex terrain area with rich wind energy resources is gradually called as a target for wind power plant site selection. The wind power plant with complex topography is influenced by wind shear effect (the phenomenon that the wind speed of the front inflow of the wind turbine changes along with the altitude), topography fluctuation and other factors, so that the wake field in the wind power plant is intricate, and the power prediction and microscopic site selection precision of the wind power plant are seriously influenced.
The existing advanced wake wind speed calculation method is mainly a three-dimensional wake model, the inflow wind speed is assumed to be a fixed value, wake flow is linearly expanded, wake flow area wind speed distribution is Gaussian distribution, a wake flow area wind speed distribution model is deduced and established according to the mass/energy conservation law, the method can accurately predict the wake flow distribution characteristics of a flat terrain or an offshore wind farm, and for a wind farm with complex terrain, the phenomena that the inflow wind profile is unevenly distributed due to the terrain, the lee tail of slope flows down, the wake flow expansion is greatly influenced by the turbulence intensity distribution and the like exist, and the phenomena have great influence on the wake flow wind speed distribution curve. In the prior art, the inflow wind speed distribution characteristic under the coupling influence of wind shear and a terrain acceleration effect and the influence of the subsidence of the terrain on wake flow are not applied to wake flow distribution method calculation, and an empirical value is adopted by a wake flow area turbulence intensity correction model, and advanced laser radar is not combined for data source acquisition and correction, so that the conventional wake flow wind speed calculation method is worth the assessment in the aspect of predicting the wake flow distribution accuracy of a wind power plant with complex terrain. Therefore, the establishment of the three-dimensional wake distribution calculation method suitable for various terrains is an important problem of urgent need of attack of quality improvement and efficiency enhancement of wind power generation.
Disclosure of Invention
Aiming at the situation, the invention aims to overcome the defects of the prior art and provide a three-dimensional wake wind speed distribution calculation method suitable for various terrains.
The technical scheme of the invention is as follows:
a three-dimensional wake wind speed distribution calculation method suitable for various terrains comprises the following steps:
Step 1, building a three-dimensional mountain model
Describing the mountain by adopting a cosine mountain model, as shown in a formula (1):
Wherein C is a constant representing the three-dimensional shape of the mountain, h is the height of the mountain, and L is the horizontal distance from the mountain top to the h/2 height;
step 2, building a complex topography inflow wind profile model
In combination with a three-dimensional mountain terrain model, when the inflow wind moves from flat terrain to three-dimensional mountain terrain, corresponding terrain fluctuation changes have a certain acceleration amplification effect on wind speed under different wind directions, the wind speed v (x, theta) at the height h 0 of the terrain corresponding to the wind direction theta can be represented by a formula (2), v 0 is the wind speed corresponding to the flat terrain, s is the gradient, a is a position parameter, and the wind speed v is determined by the following formula (3):
v(z,x,y,θ)＝(1+4as)v0·f(θ) (2)
Wherein, when x <0 on the windward side, l=l 1; on lee side x >0, l=l 2;
In flat terrain, due to the friction of the ground to the incoming wind, the wind speed presents an exponential variation law along with the increase of the height from the ground, and the wind speed v 0 of the flat terrain in the formula (2) is corrected by considering the influence of the wind shear effect, as shown in the following formula (4), wherein alpha is the wind shear index determined by a foundation-based vertical wind profile linear radar arranged in front of a fan, and v n corresponds to the wind speed at the height z n;
v0＝vn(z/zn)α (4)
Finally, the simultaneous formulas (2) - (4) can establish a complex topography inflow wind profile model under the coupling effect of wind shear and topography acceleration under different inflow wind direction angles:
v(z,x,y,θ)＝vn(1+4as)·(z/zn)α·f(θ) (5)
Step 3, wake expansion coefficient correction
And correcting the wake expansion coefficient on the basis of a wake area turbulence intensity model by utilizing the accurate turbulence information acquired by the three-dimensional scanning laser radar arranged in the downwind direction of the fan, wherein the wake expansion coefficient is as shown in the following formula:
Wherein k n, n1, n2 and n3 are determined by a data source acquired by a laser radar, C T is a thrust coefficient of the wind turbine, I 0 is inflow turbulence intensity, x/D is a dimensionless downwind direction distance, and D is a diameter of a rotor of the wind turbine;
Step 4, establishing a three-dimensional wake wind speed distribution calculation method
In the process of establishing the three-dimensional model in the step, the lee slope is assumed to be flat terrain, the wake wind speed distribution is three-dimensional Gaussian distribution, and the three-dimensional wake model without considering wake sinking is established based on the law of conservation of fluid momentum by combining the incoming wind profile model and the wake expansion coefficient correction model established in the steps 2 and 3:
a) Three-dimensional Gaussian distribution hypothesis
According to the characteristic that the inflow wind profile model and the wake distribution established in the step 2 show three-dimensional Gaussian distribution, establishing three-dimensional Gaussian distribution construction, and determining parameters in the model according to wake radius expansion characteristics, gaussian distribution density function curve properties and characteristics that wind speed at wake boundaries is equal to inflow natural wind, wherein sigma is a standard deviation in Gaussian distribution, c is an empirical coefficient, and r w is the wake radius at a downwind direction position x;
b) Law derivation of conservation of momentum
The momentum conservation law considers that mass flux in the same wake radius cross section range at any two positions x1 and x2 of the wake area is the same, and the mass flux is shown as the following formula (8), wherein a is an axial induction factor and is determined by the thrust coefficient of the wind turbine;
c) Three-dimensional wake wind speed calculation method establishment
According to the parameters determined in the steps, a three-dimensional wake wind speed calculation method without considering influence of wake sinking is initially established, and is shown in the following formula (9):
(5) Three-dimensional wake flow wind speed distribution calculation method establishment taking wake flow sinking effect into consideration
The wake center sinking height model is established to correct the three-dimensional wake wind speed distribution method:
In the formula, z 0 is the initial height position of the wake center, and gamma (z) & f (theta) is the sinking height of the lower wake center corresponding to different wind directions theta, so the corrected three-dimensional wake wind speed distribution calculating method is shown in the following formula (11):
After the three-dimensional wake flow wind speed distribution calculation method model is established, wake flow field wind speed distribution conditions faced by the rear exhaust fan under flat terrain or complex terrain can be rapidly and accurately predicted, so that power output of the rear exhaust fan can be effectively predicted, and the purpose of improving whole-field generated energy can be achieved by accurately predicting wake flow field three-dimensional wind speed distribution conditions of complex terrain in advance, so that accurate data source support is provided for follow-up wind field layout optimization and field level cooperative control.
The method considers the influence of the terrain acceleration effect and the wind shear effect on the inflow wind speed of the fan and the influence of the change of the terrain of the leeward slope on the settlement height of the wake center, combines the wind speed and the turbulence data measured by the foundation laser radar to correct the inflow wind profile model, the turbulence intensity model and the wake settlement theoretical model, ensures the precision of the model, finally establishes a wake wind speed distribution calculation method suitable for various terrains, and provides precision guarantee for the power prediction, the layout optimization and the microscopic site selection of the complex terrains. Compared with the prior art, the invention has the following advantages:
1. In the prior art, a fixed value or a single wind shear model is mainly adopted in the description of the inflow wind profile, the distribution attention degree of the inflow wind profile under the coupling effect of the terrain and the wind shear is insufficient, the inflow wind profile is used as the input end of a wake calculation method, the accuracy of the inflow wind profile directly influences the wake wind speed distribution shape and the wind speed prediction value, and based on the fact, the coupling effect of the wind shear effect and the terrain acceleration effect is considered, and based on the support of laser radar measured data, the wind profile model is established, the accuracy of the input end of the wake calculation method is effectively improved, and therefore the improvement of the wake prediction accuracy is realized;
2. The prior wake wind speed prediction technology defaults that the topography is mostly flat, ignores the influence of the topography effect on wake development trend and distribution shape, establishes a wake sinking model based on a three-dimensional mountain model by considering the influence of different wind direction angles, and applies the model to the correction of a three-dimensional wake wind speed calculation method, thereby improving the model prediction accuracy and effectively improving the applicability of the wake calculation method on various topography;
3. The wake zone turbulence intensity has a significant impact on the wake expansion coefficient. In the invention, the parameters of the turbulence intensity model are calculated and valued by using rich data sources acquired by a laser radar, so that the accuracy of correction of the wake intensity model and the wake expansion coefficient is improved, and the aim of improving the wake wind speed prediction accuracy is indirectly realized.
Drawings
FIG. 1 is a schematic flow chart established by the three-dimensional wake wind speed distribution calculation method of the invention.
FIG. 2 is a flow chart illustrating the three-dimensional wake wind speed distribution calculation method according to the present invention.
FIG. 3 is a schematic diagram of the three-dimensional wake wind speed distribution calculation method established by the invention applied to complex terrains.
FIG. 4 is a graph comparing an inflow profile model with measured data.
Fig. 5 is a cloud image of actual measurement data of wake flow of a laser radar complex terrain.
FIG. 6 is a comparison of the predicted wake center height of the model with measured data.
FIG. 7 is a comparison of the predicted wind speed results with measured data for a three-dimensional wake calculation method.
Detailed Description
The following describes the embodiments of the present invention in further detail with reference to the drawings.
1-3, The invention discloses a three-dimensional wake wind speed distribution calculating method suitable for various terrains, which comprises the following steps:
Step 1, building a three-dimensional mountain model
Describing the mountain by adopting a cosine mountain model, as shown in a formula (1):
Wherein, C is a constant representing the three-dimensional shape of the mountain, h is the height of the mountain, L is the horizontal distance from the mountain top to the h/2 height, and the parameters can be obtained by means of Google Earth data, wind field research design data and the like;
In the prior art, most of wind speeds at the center of the height of a hub of a wind turbine are adopted in the inflow wind speed determination, the partial method considers that wind shear effect corrects the inflow wind speed distribution, but for complex terrains, the inflow wind speed is influenced by the wind shear effect and the terrain acceleration effect, so that the inflow wind profile is accurately described, and the method firstly adopts a cosine mountain model to describe a mountain;
step 2, building a complex topography inflow wind profile model
Further, in combination with the three-dimensional mountain terrain model, when the inflow wind moves from the flat terrain to the three-dimensional mountain terrain, the corresponding terrain fluctuation has a certain acceleration amplification effect on the wind speed under different wind directions, the wind speed v (x, θ) at the height h 0 of the wind direction θ corresponding to the terrain can be represented by a formula (2), v 0 is the corresponding wind speed under the flat terrain, s is the gradient, a is the position parameter, and the following formula (3) is used for determining:
v(z,x,y,θ)＝(1+4as)v0·f(θ) (2)
Wherein, when x <0 on the windward side, l=l 1; on lee side x >0, l=l 2;
In flat terrain, due to the friction of the ground to the incoming wind, the wind speed presents an exponential variation law along with the increase of the height from the ground, and the wind speed v 0 of the flat terrain in the formula (2) is corrected by considering the influence of the wind shear effect, as shown in the following formula (4), wherein alpha is the wind shear index determined by a foundation-based vertical wind profile linear radar arranged in front of a fan, and v n corresponds to the wind speed at the height z n;
v0＝vn(z/zn)α (4)
Finally, the simultaneous formulas (2) - (4) can establish a complex topography inflow wind profile model under the coupling effect of wind shear and topography acceleration under different inflow wind direction angles:
v(z,x,y,θ)＝vn(1+4as)·(z/zn)α·f(θ) (5)
Step 3, wake expansion coefficient correction
And correcting the wake expansion coefficient on the basis of a wake area turbulence intensity model by utilizing the accurate turbulence information acquired by the three-dimensional scanning laser radar arranged in the downwind direction of the fan, wherein the wake expansion coefficient is as shown in the following formula:
Wherein k n, n1, n2 and n3 are determined by a data source acquired by a laser radar, C T is a thrust coefficient of the wind turbine, I 0 is inflow turbulence intensity, x/D is a dimensionless downwind direction distance, and D is a diameter of a rotor of the wind turbine;
The development of the wake zone of the wind turbine is influenced by the shear turbulence caused by the wind speed gradient between wake and free air flow and the additional mechanical turbulence caused by the blade tip vortex caused by disturbance flows such as impellers, cabins, towers and the like besides the influence of the intensity of the environmental turbulence; the existence of the turbulence in the wake region accelerates the free incoming wind speed outside the wake region to exchange with the momentum of the wake, gradually eliminates the speed loss of the wake region along with the diffusion of the momentum mixing region to the wake center, namely the wake depth becomes shallower, and simultaneously, the diffusion to the wake boundary increases the width of the wake region. In another sense, turbulence also affects the velocity of movement of the wake center, and thus, the turbulence intensity has a significant impact on wake development. The classical Frandsen model takes the empirical value of each parameter in the turbulence distribution, and the wake expansion coefficient is corrected on the basis of the wake area turbulence intensity model by utilizing the accurate turbulence information acquired by the three-dimensional scanning laser radar arranged in the downwind direction of the fan.
Step 4, establishing a three-dimensional wake wind speed distribution calculation method
In the process of establishing the three-dimensional model in the step, the lee slope is assumed to be flat terrain, the wake wind speed distribution is three-dimensional Gaussian distribution, and the three-dimensional wake model without considering wake sinking is established based on the law of conservation of fluid momentum by combining the incoming wind profile model and the wake expansion coefficient correction model established in the steps 2 and 3:
d) Three-dimensional Gaussian distribution hypothesis
According to the characteristic that the inflow wind profile model and the wake distribution established in the step 2 show three-dimensional Gaussian distribution, establishing three-dimensional Gaussian distribution construction, and determining parameters in the model according to wake radius expansion characteristics, gaussian distribution density function curve properties and characteristics that wind speed at wake boundaries is equal to inflow natural wind, wherein sigma is a standard deviation in Gaussian distribution, c is an empirical coefficient (determined by actual running conditions of a fan, combined with Gaussian distribution characteristics, a typical value is 2.58), and r w is wake radius at a downwind position x;
e) Law derivation of conservation of momentum
The momentum conservation law considers that mass flux in the same wake radius cross section range at any two positions x1 and x2 of the wake area is the same, and the mass flux is shown as the following formula (8), wherein a is an axial induction factor and is determined by the thrust coefficient of the wind turbine;
f) Three-dimensional wake wind speed calculation method establishment
According to the parameters determined in the steps, a three-dimensional wake wind speed calculation method without considering influence of wake sinking is initially established, and is shown in the following formula (9):
(5) Three-dimensional wake flow wind speed distribution calculation method establishment taking wake flow sinking effect into consideration
The movement of the wind turbine wake center is mainly at the height position of the hub center in flat terrain, but in the complex terrain, the wake can correspondingly sink downwards from the hub height in the process of moving forwards from the mountain top along the leeward slope, wind tunnel tests and numerical simulation prove that the phenomenon exists, the laser radar measurement data adopted by the invention show that the sinking height of the wake center is consistent with the fluctuation height of the terrain, the phenomenon can lead to the corresponding change of the wake distribution curve, the current wake distribution calculation method technology ignores the influence caused by the phenomenon, the applicability of the wake calculation method can be reduced, and the three-dimensional wake wind speed distribution method is modified by establishing the wake center sinking height model in the step to improve the applicability of the wake distribution calculation method:
In the formula, z 0 is the initial height position of the wake center, and gamma (z) & f (theta) is the sinking height of the lower wake center corresponding to different wind directions theta, so the corrected three-dimensional wake wind speed distribution calculating method is shown in the following formula (11):
After the three-dimensional wake wind speed distribution calculation method model is established, the wake field wind speed distribution situation faced by the rear exhaust fan under flat terrain or complex terrain can be rapidly and accurately predicted by combining the terrain situation and utilizing the wake flow sinking model to correct after the information such as the inflow wind direction, the wind speed, the turbulence, the terrain and the fan parameters and the like of the front exhaust fan are input into the model, so that the power output of the rear exhaust fan can be effectively predicted, and the purpose of improving the whole-field generated energy can be realized by accurately predicting the wake field three-dimensional wind speed distribution situation of the complex terrain in advance.
In order to verify the prediction precision of the model, the invention combines the wind measurement experimental data of two laser radars on complex terrains to respectively verify an incoming flow wind profile model, a wake sinking model and a three-dimensional wake wind speed distribution calculation method model:
FIG. 4 is a comparison of an inflow profile model with measured data. The measured data in the figure are obtained by a vertical wind profile type laser radar arranged in front of a fan, and the figure shows that the inflow wind profile model which is established by the invention and takes the coupling effect of the terrain acceleration and the wind shear into consideration has higher coincidence degree with the measured data, the model predicts the development trend of the inflow wind profile to be basically consistent with the development trend of the measured data, and the error of each measuring point is 0.15m/s;
fig. 5 is a cloud image of actual measurement data of wake flow of a laser radar complex terrain. The data cloud image is obtained by a three-dimensional scanning laser radar arranged in the downwind direction of a fan, a triangular blank area in the image is a mountain, the development of wake flow of complex terrain can be clearly seen from the image, the wake flow is not carried out along the height plane of the hub of the fan, the wake flow is sunk along the ridge line, the movement trend of the center of the wake flow in the image is approximately parallel to the ridge line, and the actual measurement data cloud image effectively proves the development trend of the wake flow sunk phenomenon in the complex terrain.
FIG. 6 is a comparison of the predicted wake center height of the model with measured data. In combination with fig. 5, to further quantify the development trend of the wake in complex terrain, the wake center heights of 5 typical positions in the wake of the wind turbine are intercepted, and the result shows that the development trend of the wake center does not follow the hub center height of the wind turbine, but has higher consistency with the wake sinking model established by the invention.
FIG. 7 is a comparison of the predicted wind speed results with measured data for a three-dimensional wake calculation method. In the figure, the comparison of measured data at typical positions of two working conditions of the downwind direction of the fan is shown, and the data result shows that the wind speed of a wake area is asymmetrically distributed due to the influence of wind shear and a topographic effect, the height of the center of the wake is not at the center height position of the hub of the fan, and in addition, the wake prediction method established by the invention can be clearly seen to have higher anastomosis degree with the measured data at different working conditions and different downwind positions.
The verification result shows that the model has higher prediction precision, can be suitable for wake wind speed distribution prediction under different topography conditions, and can provide powerful precision guarantee for fan layout optimization and wind power prediction of wind fields.
Claims (1)
1. The three-dimensional wake wind speed distribution calculating method suitable for various terrains is characterized by comprising the following steps of:
Step 1, building a three-dimensional mountain model
Describing the mountain by adopting a cosine mountain model, as shown in a formula (1):
Wherein C is a constant representing the three-dimensional shape of the mountain, h is the height of the mountain, and L is the horizontal distance from the mountain top to the h/2 height;
step 2, building a complex topography inflow wind profile model
When the three-dimensional mountain terrain model is combined, and the inflow wind moves from flat terrain to three-dimensional mountain terrain, the corresponding terrain fluctuation has a certain acceleration amplification effect on wind speed under different wind directions, the wind speed v (z, y, x, theta) at the height h 0 of the terrain corresponding to the wind direction theta is expressed by a formula (2), v 0 is the corresponding wind speed under the flat terrain, s is the gradient, a is a position parameter, and the wind speed v is determined by the following formula (3):
v(z,x,y,θ)＝(1+4as)v0·f(θ) (2)
Wherein, when x <0 on the windward side, l=l 1; on lee side x >0, l=l 2;
In flat terrain, due to the friction of the ground to the incoming wind, the wind speed presents an exponential variation law along with the increase of the height from the ground, and the wind speed v 0 of the flat terrain in the formula (2) is corrected by considering the influence of the wind shear effect, as shown in the following formula (4), wherein alpha is the wind shear index determined by a foundation-based vertical wind profile linear radar arranged in front of a fan, and v n corresponds to the wind speed at the height z n;
v0＝vn(z/zn)α (4)
Finally, the simultaneous formulas (2) - (4) can establish a complex topography inflow wind profile model under the coupling effect of wind shear and topography acceleration under different inflow wind direction angles:
v(z,x,y,θ)＝vn(1+4as)·(z/zn)α·f(θ) (5)
Step 3, wake expansion coefficient correction
And correcting the wake expansion coefficient on the basis of a wake area turbulence intensity model by utilizing the accurate turbulence information acquired by the three-dimensional scanning laser radar arranged in the downwind direction of the fan, wherein the wake expansion coefficient is as shown in the following formula:
Wherein k n, n1, n2 and n3 are determined by a data source acquired by a laser radar, C T is a thrust coefficient of the wind turbine, I 0 is inflow turbulence intensity, x/D is a dimensionless downwind direction distance, and D is a diameter of a rotor of the wind turbine;
Step 4, establishing a three-dimensional wake wind speed distribution calculation method
In the process of establishing the three-dimensional model in the step, the lee slope is assumed to be flat terrain, the wake wind speed distribution is three-dimensional Gaussian distribution, and the three-dimensional wake model without considering wake sinking is established based on the law of conservation of fluid momentum by combining the incoming wind profile model and the wake expansion coefficient correction model established in the steps 2 and 3:
a) Three-dimensional Gaussian distribution hypothesis
According to the characteristic that the inflow wind profile model and the wake distribution established in the step 2 show three-dimensional Gaussian distribution, establishing three-dimensional Gaussian distribution construction, and determining parameters in the model according to wake radius expansion characteristics, gaussian distribution density function curve properties and characteristics that wind speed at wake boundaries is equal to inflow natural wind, wherein sigma is a standard deviation in Gaussian distribution, c is an empirical coefficient, and r w is the wake radius at a downwind direction position x;
b) Law derivation of conservation of momentum
The momentum conservation law considers that mass flux in the same wake radius cross section range at any two positions x1 and x2 of the wake area is the same, and the mass flux is shown as the following formula (8), wherein a is an axial induction factor and is determined by the thrust coefficient of the wind turbine;
c) Three-dimensional wake wind speed calculation method establishment
According to the parameters determined in the steps, a three-dimensional wake wind speed calculation method without considering influence of wake sinking is initially established, and is shown in the following formula (9):
(5) Three-dimensional wake flow wind speed distribution calculation method establishment taking wake flow sinking effect into consideration
The wake center sinking height model is established to correct the three-dimensional wake wind speed distribution method:
In the formula, z 0 is the initial height position of the wake center, and gamma (z) & f (theta) is the sinking height of the lower wake center corresponding to different wind directions theta, so the corrected three-dimensional wake wind speed distribution calculating method is shown in the following formula (11):
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