WO2022033490A1 - 一种通过添加k源项来校正标准k-ε模型的方法 - Google Patents

一种通过添加k源项来校正标准k-ε模型的方法 Download PDF

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WO2022033490A1
WO2022033490A1 PCT/CN2021/111902 CN2021111902W WO2022033490A1 WO 2022033490 A1 WO2022033490 A1 WO 2022033490A1 CN 2021111902 W CN2021111902 W CN 2021111902W WO 2022033490 A1 WO2022033490 A1 WO 2022033490A1
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model
wind
standard
hill
source term
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闫姝
王绍民
许世森
郭小江
王晓东
叶昭良
张波
曾崇济
史绍平
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中国华能集团有限公司
中国华能集团清洁能源技术研究院有限公司
华能海上风电科学技术研究有限公司
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  • the invention belongs to the field of wind power generation, and relates to a method for correcting a standard k- ⁇ model by adding a k source term.
  • Wind energy is a clean and renewable resource. Therefore, wind power generation technology has developed rapidly in my country in recent years, and has promoted the construction of a large number of wind farms. Most of the early wind farms were built in places with abundant wind resources and relatively flat terrain. However, as the scale of wind farms increased and the number of wind farms increased, wind farms began to be built in areas with complex terrain. Therefore, the use of standard linear models to simulate wind farm conditions cannot reproduce wind resource conditions in complex terrains well. The use of CFD technology for simulation is becoming more and more common and has good application prospects. Considering the conditions of calculation accuracy, operation time, and calculation resources, the Reynolds time-averaged method is still the most economical and common calculation method at present. Considering the influence of surface roughness, the standard k- ⁇ turbulence model with wall function is widely used in engineering calculation.
  • the most prominent feature of the flow in hilly terrain is the separation flow, which is very different from the attached flow in the flat terrain.
  • Some methods can model the atmospheric boundary layer of flat topography well, but cannot model the separation zone well. Therefore, it is not suitable to directly apply the method of slab terrain to hilly terrain. It is necessary to select appropriate boundary conditions and add appropriate source terms to keep the generation rate and dissipation rate of turbulence in harmony.
  • the purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art, and to provide a method for calibrating the standard k- ⁇ model by adding a k source term, which can effectively improve the accuracy of the k- ⁇ model for simulating the wind resources of hill topography .
  • the method for calibrating the standard k- ⁇ model by adding k source terms includes the following steps:
  • step 3 Analyze the error between the calculation result of step 2) and the actual wind measurement data, and set the k source term according to the analysis result, then use the k source term to correct the k- ⁇ turbulence model, and finally use the corrected k- ⁇ turbulence model for complex terrain wind resource calculation.
  • step 1) The specific operations of step 1) are:
  • Step 2) also includes: determining the value range of the variable in the entry condition. .
  • the k source term is set, and then the k source term is used to correct the k- ⁇ turbulence model, and finally the corrected k
  • the - ⁇ turbulence model is used to calculate the wind resources of complex terrain to make up for the inaccuracy of traditional correction methods, and to qualitatively observe the influence of different inflow conditions and terrain on the flow.
  • lidars can complete the monitoring of wind resources in hilly terrain, which greatly saves human and material resources.
  • Figure 1 is the layout point map of the wind farm
  • Figure 2a is the wind rose diagram of lidar387
  • Figure 2b is the wind rose diagram of lidar 366
  • Fig. 3a is the selection diagram of computational domain
  • Fig. 3b is a grid division diagram of the computational domain
  • Figure 4 is the plane velocity cloud map where the two radars are imported at 100°;
  • Figure 5a shows the comparison between the wind speed profile of lidar387 and the measured data
  • Figure 5b shows the comparison between the wind speed profile of lidar366 and the measured data.
  • the method for calibrating the standard k- ⁇ model by adding k source terms comprises the following steps:
  • step 3 Analyze the error between the calculation result of step 2) and the actual wind measurement data, and set the k source term according to the analysis result, then use the k source term to correct the k- ⁇ turbulence model, and finally use the corrected k- ⁇ turbulence model for complex terrain wind resource calculation.
  • step 1) determine the hill topography to be studied, select the installation positions of two lidars, install the lidar, and then use the lidar to measure the wind measurement data of the hill topography.
  • Step 2) also includes: determining the value range of the variable in the entry condition.
  • the present invention only takes a complex terrain wind field in Hebei as an example to illustrate the applicability of the method, and the methods for other types of complex terrain are similar.
  • a wind farm in Huailai is located between 115°33'E-115°38'E and 40°22'N-40°26'N.
  • Figure 1 shows the layout of the wind farm.
  • each wind lidar measured local wind data for 36 days from April 1, 2019 to May 6, 2019, including wind direction, wind speed, maximum and minimum wind speed, availability, etc., covering The height ranges from 40m to 230m from the ground. According to the wind measurement data of the two wind lidars, a rose diagram of the wind direction of the 16 sectors was made, as shown in Figure 2a and Figure 2b.
  • the wind farm lidar387, the main wind direction at 90m height is ESE, accounting for 13.72% of the total wind direction frequency
  • the secondary main wind direction is WNW, accounting for 12.84% of the total wind direction frequency.
  • the main wind direction at 90m height is WNW, accounting for 13.11% of the total wind direction frequency
  • the secondary main wind direction ESE accounting for 12.08% of the total wind direction frequency.
  • the main wind direction and the secondary main wind direction are more obvious. It is beneficial to the layout of the fan, and the concentration of the wind direction is beneficial to the stable operation of the fan.
  • u is the incoming flow velocity
  • Z is the corresponding height
  • Z 0 is the surface roughness length, which can be determined according to the type of the underlying surface of the wind farm
  • ⁇ is the Karman constant, which is 0.4 by default
  • u * is the friction speed.
  • the size of the computational domain is 23500m ⁇ 10500m ⁇ 2500m
  • the number of grid nodes is 285 ⁇ 145 ⁇ 205
  • the X and Y directions are evenly distributed
  • the first layer in the Z direction The grid height is 0.05m
  • the extension ratio is 1.06
  • the total number of grids is 8.47 million.
  • the east and south sides of the computational domain are the inlet boundary conditions
  • the west and north sides are the outlet boundary conditions
  • the bottom is a non-slip solid wall
  • the top is a non-slip solid wall.
  • Symmetrical boundary numerical calculation using ANSYS-Fluent software, using standard k- ⁇ turbulence model.
  • the two main wind directions are calculated respectively, and it is found that when a direction in the corresponding sector is given at the entrance, the airflow will deflect to a certain extent when passing through the undulating terrain in the flow field.
  • the speed direction Compared with the direction at the entrance, they are all deflected clockwise by about 20°. Therefore, the incoming flow direction of the WNW sector is set as 280°, and the incoming flow direction of the ESE sector is set as 100°.
  • lidar366 When the inlet is 100°, the velocity direction of the airflow to lidar366 is 116°, and the velocity direction to lidar387 is 118°.
  • lidar366 is based on 116°, and two sets of ranges with amplitudes of 2° and 5° are selected; lidar387 is based on 118°, and two sets of ranges with amplitudes of 5° and 10° are selected. Calculate the average speed at different heights in each range.
  • Figure 4 is the cloud diagram of the calculation result, intercepted
  • the plane is the plane where the two radars are located, the yellow line on the left is the position of lidar387, the yellow line on the right is the position of lidar366, and the flow direction is from right to left.
  • step 3 Analyze the error between the calculation result in step 2) and the measured data, and correct it by adding an appropriate source term to improve the accuracy of the numerical simulation.
  • the adjustment of the inlet parameters cannot solve the problem that the thickness of the boundary layer is too large, by adding the source term Sk to the calculation example, To improve the near-wall velocity, it is confirmed by calculation that the most suitable source term is as follows:
  • Table 1 and Table 2 are the error comparison between the simulation results of lidar387 and lidar366 and the wind measurement data respectively.
  • the height represents the height measured by the wind measurement radar, which is not equidistantly distributed from 40m to 230m.
  • the measured wind speed represents the corresponding height
  • lidar387 takes 118° ⁇ 10°
  • lidar366 takes the average speed within the range of 116° ⁇ 5° wind direction
  • Z 0 0.05m
  • Z 0 0.05m
  • Z0 0.05m plus the source term Sk
  • the standard error and the improved error are the errors between the respective wind speeds and the measured wind speeds respectively
  • the calculation method is the standard The wind speed (improved wind speed) is subtracted from the measured wind speed, and then the absolute value is calculated.
  • the improved method with the source term is generally better than that without the source term.
  • the total error of each height of wind speed 0.28 at lidar387 is 217.13%
  • the total error of each height of wind speed 0.33 is 64.28%
  • the total error after improvement is 28.76%.
  • the improved error is also 0.6% smaller than the wind speed 0.33 error.
  • the total error of each height with a wind speed of 0.28 at lidar366 is 249.64%
  • the total error of each height with a wind speed of 0.33 is 91.62%, while the improved total error is 29.89%.
  • the improved error is 4.23% smaller than the standard error. Therefore, the use of the improved model after adding the source term improves the accuracy of the simulation both in key parts and the whole, and helps to better analyze the wind resources of the wind farm.

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Abstract

一种通过添加k源项来校正标准k-ε模型的方法，包括以下步骤：1）获取山丘地形的测风数据；2）构建山丘地形模型，并对山丘地形模型进行网格划分，然后利用标准k-ε湍流模型计算；3）分析步骤2）的计算结果与实际测风数据之间的误差，并根据分析结果设定k源项，然后利用k源项对k-ε湍流模型进行修正，最后利用修正后的k-ε湍流模型进行复杂地形风资源计算，该方法能够有效提高k-ε模型模拟山丘地形风资源的准确性。

Description

一种通过添加k源项来校正标准k-ε模型的方法 技术领域
本发明属于风力发电领域，涉及一种通过添加k源项来校正标准k-ε模型的方法。
背景技术
风能是一种清洁的可再生资源，因此，风力发电技术近几年来在我国得到了快速发展，并推动了风电场的大量建设。早起的风电厂大多建设在风力资源丰富、地形较为平坦的地方，但是随着风电场的规模越来越大、数量越来越多、风电场开始建设在复杂地形区域。因此，采用标准线性模型模拟风电场条件，不能很好地再现复杂地形的风资源条件。而采用CFD技术进行模拟则变得越来越常见并且有良好的应用前景。综合考虑计算精度，运算时长，以及计算资源等条件，雷诺时均法仍是目前最经济最普遍的计算方法。考虑地表粗糙度的影响，采用带有壁面函数的标准k-ε湍流模型是目前工程计算中普遍采用的方法。
山丘地形流动最显著的特征是分离流动，与平板地形下的附着流动有很大区别。有些可以较好模拟平板地形大气边界层的方法，却不能很好地模拟分离区。因此，直接将平板地形的方法运用到山丘地形中是不合适的，需要选择合适的边界条件，并增加合适的源项，以使湍流的产生率和耗散率保持协调。
发明内容
本发明的目的在于克服上述现有技术的缺点，提供了一种通过添加k源项来校正标准k-ε模型的方法，该方法能够有效提高k-ε模型模拟山丘地形风资源的准确性。
为达到上述目的，本发明所述的通过添加k源项来校正标准k-ε模型的方法包括以下步骤：
1)获取山丘地形的测风数据；
2)构建山丘地形模型，并对山丘地形模型进行网格划分，然后利用标准k-ε湍流模型计算；
3)分析步骤2)的计算结果与实际测风数据之间的误差，并根据分析结果设定k源项，然后利用k源项对k-ε湍流模型进行修正，最后利用修正后的k-ε湍流模型进行复杂地形风资源计算。
步骤1)的具体操作为：
确定待研究的山丘地形，再选取两个激光雷达的安装位置，然后再安装激光雷达，再利用激光雷达测量山丘地形的测风数据。
选取两个激光雷达的安装位置的具体过程为：
确定当地主风向方向，然后在山丘迎风面的山脚位置处放置第一个激光雷达来确定入口边界条件，在山丘背风面的山脚位置处放置第二个激光雷达。
步骤2)中还包括：确定入口条件中变量的取值范围。。
本发明具有以下有益效果：
本发明所述的通过添加k源项来校正标准k-ε模型的方法在具体操作时，设定k源项，然后利用k源项对k-ε湍流模型进行修正，最后利用修正后的k-ε湍流模型进行复杂地形风资源计算，以弥补采用传统修正方法计算不准确的不足，以定性的观测不同来流条件和不同地形对流动的影响。
进一步，两个激光雷达即可完成对山丘地形风资源的监测，极大的节约人力物力资源。
附图说明
图1为风电场布机点位图；
图2a为lidar387的风向玫瑰图；
图2b为lidar 366的风向玫瑰图；
图3a为计算域的选取图；
图3b为计算域的网格划分图；
图4为100°进口两雷达所在平面速度云图；
图5a为lidar387的风速廓线与实测数据对比图；
图5b为lidar366的风速廓线与实测数据对比图。
具体实施方式
这下面结合附图对本发明做进一步详细描述：
本发明所述的通过添加k源项来校正标准k-ε模型的方法包括以下步骤：
1)获取山丘地形的测风数据；
2)构建山丘地形模型，并对山丘地形模型进行网格划分，然后利用标准k-ε湍流模型计算；
3)分析步骤2)的计算结果与实际测风数据之间的误差，并根据分析结果设定k源项，然后利用k源项对k-ε湍流模型进行修正，最后利用修正后的k-ε湍流模型进行复杂地形风资源计算。
步骤1)的具体操作为：确定待研究的山丘地形，再选取两个激光雷达的安装位置，然后再安装激光雷达，再利用激光雷达测量山丘地形的测风数据。
选取两个激光雷达的安装位置的具体过程为：
确定当地主风向方向，然后在山丘迎风面的山脚位置处放置第一个激光雷达来确定入口边界条件，在山丘背风面的山脚位置处放置第二个激光雷达。
步骤2)中还包括：确定入口条件中变量的取值范围。
实施例一
本实施例的具体过程为：
1)确定复杂地形，选取安装两个测风激光雷达的位置，并安装测风激光雷达，再获取实际地形下的测风数据；
由于复杂地形包含的种类繁多，不能一一枚举，本发明仅以河北某复杂地形风场为例，说明方法的适用性，其他种类的复杂地形方法类似。
怀来某风电场位于115°33’E-115°38’E、40°22’N-40°26’N之间，图1为风电场布机点位图。
在风电场左下区域布置有两个测风激光雷达，分别为lidar387和lidar366，两测风激光雷达的直线距离为551.4m，二者连线与X轴正方向夹角约为160.2°。每个测风激光雷达都测量了从2019年4月1日到2019年5月6日为期36天的当地测风数据，包括风向、风速、风速最大值最小值、可利用率等，涵盖了从距地面40m到230m间距不等的高度范围。根据两测风激光雷达的测风数据，制作16扇区的风向玫瑰图，如图2a及图2b所示。
由风向玫瑰图可得，该风电场lidar387处，90m高度主风向为ESE,占总风向频率的13.72％，次主风向为WNW，占总风向频率的12.84％。lidar366处，90m高度主风向为WNW,占总风向频率的13.11％，次主风向ESE，占总风向频率的12.08％。主风向和次主风向方向较明显。对风机的布置有利，同时风向的集中有利于风机的稳定运行。
利用如下公式确定入口速度廓线：
Figure PCTCN2021111902-appb-000001
其中，u表示来流速度，Z表示对应高度，Z 0为地表粗糙长度，可根据风电场下垫面种类确定，κ为卡门常数，默认取0.4，u *为摩擦速度。
2)构建地形模型，并对地形木星进行网格划分，利用CFD软件中的标准k-ε湍流模型进行计算，计算域按照正南正北方向设置，计算域的选取原则为尽量使lidar387和lidar366的位置在所选计算域的中间，同时计算域的入口边界尽平整，方便设置来流边界条件。
其中，如图3a及图3b所示，ESE扇区下，计算域的尺寸为23500m×10500m×2500m，网格节点 数为285×145×205，X、Y方向均匀分布，Z方向第一层网格高度为0.05m，延展比为1.06，网格总数为847万，计算域的东、南两面为进口边界条件，西、北两面为出口边界条件，底面为无滑移固壁，顶部为对称边界，数值计算采用ANSYS-Fluent软件，采用标准k-ε湍流模型。
对两个主风向分别进行计算，发现在入口处给定对应扇区内的一个方向，气流在流场中经过起伏的地形均会发生一定偏转，等到流经lidar387和lidar366位置处时，速度方向都比入口处方向沿顺时针偏转了约20°左右，因此，将WNW扇区的来流方向定为280°，将ESE扇区的来流方向定为100°。
当进口为100°时，气流流动到lidar366处的速度方向为116°，而到lidar387处速度方向为118°。根据现有的测风数据，lidar366处以116°为基准，选取振幅分别为2°和5°的两组范围；lidar387处以118°为基准，选取振幅分别为5°和10°的两组范围，求得每个范围内不同高度各自的平均速度，根据测风数据随高度变化的规律，选择摩擦速度u*＝0.33m/s，粗糙长度Z 0＝0.05m，图4为计算结果云图，截取的平面为两雷达所在平面，左侧黄线为lidar387位置，右侧黄线为lidar366位置，流动方向从右向左。
由云图可看出，两测风激光雷达都在山坡后背风侧，流动发展到两测风雷达处，基本保持均匀大气边界层的流动，流动状态整体相似，区别在于lidar387比lidar366位置更加靠后，因此逆压梯度更大，导致近壁面边界层更厚，速度廓线对比如图5a及图5b所示。
3)对步骤2)的计算结果与实测数据之间的误差进行分析，通过添加合适的源项来进行修正，以提高数值模拟的准确度，图中横坐标代表风速，纵坐标代表距地面高度，观察发现默认设置下，计算u*＝0.33m/s，Z 0＝0.05m在100m以上拟合相对较好，在100m以下比测风数据偏小，调整参数为u*＝0.28m/s，Z 0＝0.05m进行计算，发现在整个计算范围内，速度均比测量结果要偏小很多，在调整入口参数无法解决边界层厚度偏大的情况下，通过对算例添加源项Sk，改进近壁面速度，经过计算确认，最合适的源项如下：
S k(z)＝0.001
计算结果u*＝0.28m/s，Z 0＝0.05m，k如图5a及图5b所示，在添加源项Sk之后，增大了流场内整体的湍动能，使得整个计算域内速度都有所提高，尤其在近壁面处更加明显，近壁面初速度相对不加源项增大，而上部的主流速度基本不变，对lidar387和lidar366都有较好的改善作用。
表1及表2分别为lidar387和lidar366处模拟结果与测风数据的误差对比，其中，高度表示测风雷达测量的高度，从40m到230m不等距分布，实测风速表示对应高度处，lidar387取118°±10°，lidar366取116°±5°风向范围内的平均速度，风速0.28为算例u*＝0.28m/s，Z 0＝0.05m，风速0.33为算例u*＝0.33m/s，Z 0＝0.05m，改进风速为算例u*＝0.28m/s，Z0＝0.05m加源项Sk，标准误差和改进误差分别是各自风速与实测风速间的误差，计算方法为标准风速(改进风速)减去实测风速，然后求绝对值，最后在除实测风速，由结果可以得到，无论lidar387还是lidar366，加源项改进后的方法整体上都要比不加源项的要好。其中，lidar387处风速0.28各个高度的总误差为217.13％，风速0.33各个高度的总误差为64.28％，改进后总误差为28.76％。在轮毂高度90m处，改进误差也比风速0.33误差小0.6％。lidar366处风速0.28各个高度的总误差为249.64％，风速0.33各个高度的总误差为91.62％，而改进后总误差为29.89％，同样在轮毂高度90m处，改进误差比标准误差小4.23％。因此采用添加源项后的改进模型不论是在关键局部还是整体都提高了模拟的准确性，有助于更好地进行风电场风资源分析。
表1
Figure PCTCN2021111902-appb-000002
Figure PCTCN2021111902-appb-000003
表2
Figure PCTCN2021111902-appb-000004
此实施例仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。在不脱离本发明主旨和范围的前提下，本发明还会有进一步的改进，所作改进仍在要求保护的本发明范围内，因此，本发明的保护范围应该以权利要求的保护范围为准。

Claims (4)

  1. 一种通过添加k源项来校正标准k-ε模型的方法，其特征在于，包括以下步骤：
    1)获取山丘地形的测风数据；
    2)构建山丘地形模型，并对山丘地形模型进行网格划分，然后利用标准k-ε湍流模型计算；
    3)分析步骤2)的计算结果与实际测风数据之间的误差，并根据分析结果设定k源项，然后利用k源项对k-ε湍流模型进行修正，最后利用修正后的k-ε湍流模型进行复杂地形风资源计算。
  2. 根据权利要求1所述的通过添加k源项来校正标准k-ε模型的方法，其特征在于，步骤1)的具体操作为：
    确定待研究的山丘地形，再选取两个激光雷达的安装位置，然后再安装激光雷达，再利用激光雷达测量山丘地形的测风数据。
  3. 根据权利要求1所述的通过添加k源项来校正标准k-ε模型的方法，其特征在于，选取两个激光雷达的安装位置的具体过程为：
    确定当地主风向方向，然后在山丘迎风面的山脚位置处放置第一个激光雷达来确定入口边界条件，在山丘背风面的山脚位置处放置第二个激光雷达。
  4. 根据权利要求1所述的通过添加k源项来校正标准k-ε模型的方法，其特征在于，步骤2)中还包括：确定入口条件中变量的取值范围。
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