﻿ 带旋转孔容腔瞬态演化与建模方法研究<sup>*</sup>
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Research on transient evolvement and modeling method of cavity with rotating orifices
DING Shuiting, PU Junyu, QIU Tian, YU Hang
School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-08-29; Accepted: 2016-12-09; Published online: 2016-12-13 18:16
Foundation item: Innovation Plan of Aero Engine Complex System Safety by the Ministry of Education Chang Jiang Scholars of China(IRT0905); China Postdoctoral Science Foundation (2016M591047)
Corresponding author. QIU Tian, E-mail: qiutian@buaa.edu.cn
Abstract: Rotating orifices and cavity are important parts of the air system of gas turbine engine, and their transient response might induce dangerous instantaneous transient load. To investigate the transient evolvement of the cavity with rotating orifices, a CFD model of the cavity with rotating orifices was built to research the cavity in front of the rotating orifices. Based on the steady flow characteristic of the rotating orifices, a transient one-dimensional model was built to simulate the transient process. The comparison of the results between the one-dimensional model and the CFD model shows that the former can conduct the transient process simulation satisfactorily and satisfy the elementary engineering needs. Finally, the analysis of the reason for the result errors of one-dimensional model is presented in this paper.
Key words: air system     cavity with rotating orifice     one-dimensional model     transient evolvement     discharge coefficient

1 孔特性处理方法

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2 物理模型与计算工况

 图 1 CFD计算模型几何结构示意图 Fig. 1 Schematic diagram of geometric structure of CFD model
 图 2 网格划分示意图 Fig. 2 Schematic diagram of mesh generation

CFD计算采用ANSYS CFX进行，湍流模型选择CFX中的k-Omega模型，在该湍流模型下，计算可取得较好的收敛性，稳态计算残差基本可到10-5以下，部分稳态算例的残差在10-4以下。稳态计算设定计算总步长为2 000步，计算完成时，模型中的流量等计算参数基本不变。瞬态计算采用自适应步长方法求解，初始步长为10-7 s，自适应最大步长设为10-5 s，最小步长设为10-9 s，瞬态计算过程中，单步计算循环超过5次时，下一时间步长为前一步长的0.8倍，当单步计算循环低于2次时，下一时间步长为前一步长的1.06倍，瞬态计算的收敛残差为10-5

CFD计算模型采用六面体网格进行划分，并进行了网格无关性验证，验证过程中分别采用20万、60万、100万3个量级的网格进行对比，图 3给出了距离进口10 cm处一径向线上的切向速度随半径位置r的分布。可见，采用60万网格的结果与采用100万网格的结果比较接近，本文中的CFD计算最终所用网格为667 460。

 图 3 网格无关性验证 Fig. 3 Grid independence verification

 图 4 CFD计算模型与Dittmann等[7]试验流量系数结果对比 Fig. 4 Comparison of discharge coefficient between CFD model and test of Dittmann[7]

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 图 5 稳态工况流量系数结果与拟合 Fig. 5 Discharge coefficient results and fitting under steady working condition
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2个瞬态工况的计算过程中，旋转孔转速始终保持为10 000 r/min，控制进出口边界压比πm随时间变化，初始时刻，压比πm=1.05。

1) 斜坡工况，πm在0.02 s内由1.05线性上升至2.0后保持恒定。

2) 光滑工况，πm在0.02 s内上升至2.0后保持恒定，压比变化率呈梯形分布，其表达式见式(12)。

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 图 6 瞬态工况压比随时间变化 Fig. 6 Change of pressure ratio with time under transient working condition
3 瞬态1-D模型计算方法

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4 瞬态1-D模型与CFD计算模型结果对比 4.1 腔内平均总压

 图 7 瞬态工况腔内平均总压结果 Fig. 7 Average total pressure results in cavity under transient working condition
4.2 进口流量

 图 8 瞬态工况进口流量结果 Fig. 8 Inlet flow rate results under transient working condition
4.3 出口流量

 图 9 瞬态工况出口流量结果 Fig. 9 Outlet flow rate results under transient working condition
4.4 腔内平均总温

 图 10 瞬态工况腔内平均总温结果 Fig. 10 Average total temperature results in cavity under transient working condition
5 结果分析

1) 稳态工况下自身的非均匀性造成的误差。图 11为模型进出口边界压比为1.65条件下，CFD计算得到的腔内总温的分布云图。可见，高半径处的总温明显高于低半径处，实际条件下，进入孔的流体总温略低于腔内平均总温。瞬态1-D模型假设稳态条件下腔室为各项参数均匀的节点，忽略了腔内温度的分布特性，采用该假设已经引入了一定的误差。

 图 11 稳态工况下腔内总温分布云图 Fig. 11 Distribution contour of total temperature in cavity under steady working condition

2) 瞬态过程偏离稳态结果的误差。瞬态1-D模型的旋转孔特性来源于稳态计算结果，但是实际的瞬态过程中，由于内部流动与稳态有非常明显的差异，可能使得直接采用稳态条件下的特性曲线无法准确计算当前的瞬态过程，从而导致瞬态1-D模型预测失准。

5.1 流量结果误差分析

 图 12 瞬态与稳态工况下流量系数对比 Fig. 12 Comparison of discharge coefficient under transient and steady working conditions

 图 13 稳态工况下腔内角速度云图 Fig. 13 Contour of angular velocity in cavity under steady working condition

 图 14 斜坡工况下腔内角速度演化过程 Fig. 14 Evolvement of angular velocity in cavity under slope working condition
 图 15 斜坡工况下0.007 s时刻腔内径向速度云图 Fig. 15 Contour of radial velocity in cavity at 0.007 s under slope working condition

 图 16 斜坡工况下孔前截面角速度演化 Fig. 16 Evolvement of angular velocity in cross section in front of orifice under slope working condition
5.2 温度结果误差分析

 图 17 斜坡工况下腔内总温分布云图 Fig. 17 Distribution contour of total temperature in cavity under slope working condition
 图 18 斜坡工况下腔内总温与孔进口总温对比 Fig. 18 Comparison of total temperature between cavity and inlet of orifice under slope working condition
6 瞬态1-D模型工程评价思路

 图 19 光滑工况下进出口流量误差变化 Fig. 19 Variation of inlet and outlet flow rate errors under smooth working condition

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 图 20 不同分辨率下光滑工况的出口流量误差 Fig. 20 Outlet flow rate errors under smooth working condition with different resolution
7 结论

1) 以稳态孔特性为基础，考虑容腔在瞬态过程中的容积效应，建立瞬态1-D模型，对于较强的瞬态过程，能够从整体上反映流量和压力的演化。瞬态过程中，进口流量快速上升和快速下降的过程都能较好的模拟。

2) 较强瞬态过程中，细节的流动过程无法通过瞬态1-D模型进行模拟，采用集总方式建立的瞬态1-D模型无法在瞬态过程中为旋转孔提供准确的进气边界条件，可能使模拟结果出现较大的误差，因此需要对瞬态过程的流动细节加以更充分的研究，从机理层面对瞬态1-D模型进行修正。

3) 腔内温度有较强的不均匀性，且出口焓比较明显地受到温度分布和进口流量的影响，而当前瞬态1-D模型均匀性的假设，导致瞬态1-D模型得到的温度结果有明显偏差。目前认为，进口流量对旋转孔进口总温有明显影响，因此进一步的温度修正中，应当将进口流量的影响加以考虑。

4) 低维瞬态模型的精度要求，不考虑误差随时间的动态变化是不合理的，本文提出了带时间分辨率的误差分析思路，将低维瞬态模型的误差分析限定在满足工程需要的时间分辨率下，可用于研究瞬态低维模型的适用性。

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文章信息

DING Shuiting, PU Junyu, QIU Tian, YU Hang

Research on transient evolvement and modeling method of cavity with rotating orifices

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(9): 1721-1731
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0689