Uncertainty of measuring isentropic efficiency of compressor by temperature rise method
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摘要:
基于Rotor37单转子压气机性能试验数据，分别使用蒙特卡洛法与不确定度传播率法对温升法测量压气机等熵效率的不确定度进行评定，对不同转速、流量工况下等熵效率的测量不确定度进行分析，对等熵效率测量不确定度分配方法进行研究。结果表明，两种方法评定的最佳估计值、标准不确定度基本相同，但蒙特卡洛法评定的95%包含概率的最短包含区间比不确定度传播率法更窄，在输入量为非正态分布时差距更大，因此在输入量为非正态分布时应慎重使用不确定度传播率法。同一转速下，随着流量增大，等熵效率测量不确定度增大；不同转速下，随着转速降低，等熵效率测量不确定度增大，低转速时温升法测得高精度压气机等熵效率的难度大大增加。等熵效率测量不确定度分配方法研究结果表明，等作用分配方法对总温测量精度要求比等精度分配方法高，更难以实现。所研究的压气机在70%设计转速最大流量工况下，给定等熵效率测量相对不确定度为0.5%。按等精度分配方法分配总压、总温测量不确定度需分别达到35 Pa和0.083 K。通过增加径向测点数、采用铂电阻总温探针和气流总温校准方法可以提高总温测量精度，进而提高等熵效率的测量精度。
Abstract:Based on Rotor37 single rotor compressor performance experiment data, Monte Carlo method and guide to the uncertainty in measurement method were used for uncertainty evaluation of measuring the compressor isentropic efficiency by temperature rise method, the measurement uncertainty of isentropic efficiency under different rotational speed and flow rate conditions were analyzed, and the allocation scheme of isentropic efficiency measurement uncertainty was studied. Results showed that the best estimate value and standard uncertainty evaluated by these two kinds of methods were basically the same, but the shortest inclusion interval of 95% inclusion probability evaluated by Monte Carlo method was narrower than that evaluated by guide to the uncertainty in measurement method, and the gap was bigger in case of non-normal distribution of input, so guide to the uncertainty in measurement method should be carefully used in such case. At the same speed, the measurement uncertainty of isentropic efficiency increased with the increase of flow rate. At different rotational speeds, the measurement uncertainty of isentropic efficiency increased with the decrease of rotational speed. It became a lot more difficult to measure the compressor isentropic efficiency of high accuracy by temperature rise method at low rotational speed. The results of isentropic efficiency measurement uncertainty allocation showed that higher accuracy of total temperature measurement was required for equal action allocation, making it more difficult for realization. Under the maximum flow condition of 70% designed rotational speed of the compressor studied, given that the relative measurement uncertainty of isentropic efficiency was 0.5%, the measurement uncertainty of total pressure and total temperature should reach 35 Pa and 0.083 K, respectively, according to equal accuracy allocation. Increasing radial measurement points, and using platinum resistance total temperature probe and gas flow total temperature calibration method can improve the measurement accuracy of both total temperature and isentropic efficiency.
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图 1 MCM评定等熵效率测量不确定度的流程
Figure 1. Evaluation process of measurement uncertainties for isentropic efficiency based on MCM
图 3 输入量不同分布下的等熵效率概率分布直方图
Figure 3. Probability distribution histogram of isentropic efficiency with different input distributions
图 4 不同转速下评定的总压比测量不确定度
Figure 4. Evaluated measurement uncertainty of total pressure ratio at different rotational speeds
图 5 不同转速下评定的总温比测量不确定度
Figure 5. Evaluated measurement uncertainty of total temperature ratio at different rotational speeds
图 6 不同转速下评定的等熵效率测量不确定度
Figure 6. Evaluated measurement uncertainty of isentropic efficiency at different rotational speeds
图 7 测点数对要求的单点测量不确定度的影响
Figure 7. Influence of the number of measuring points on the required single point measurement uncertainty
表 1 输入量为正态分布时的包含因子
Table 1. Inclusion factor of normally distributed inputs
P 0.68 0.90 0.95 0.9545 0.99 0.9973 k 1 1.645 1.960 2 2.576 3 
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表 2 输入量为其他分布时的包含因子
Table 2. Inclusion factor of other distributed inputs
分布类别 P k 三角 1 $ \sqrt 6 $ 均匀 1 $ \sqrt 3 $ 反正弦 1 $ \sqrt 2 $ 两点 1 1
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表 3 参数测量最大误差限
Table 3. Maximum error limit of parameter measurement results
流场参数 最大误差限 总温/K ±0.6 进口总压/Pa ±100 出口总压/Pa ±1700
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表 4 输入量不同分布下估计的标准不确定度
Table 4. Estimated standard uncertainty under different distribution of inputs
输入分布 进口总压/Pa 出口总压/Pa 总温/K 均匀分布 58 981 0.35 正态分布 50 850 0.30 三角分布 41 694 0.25
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表 5 等熵效率最佳估计值及标准不确定度
Table 5. Best estimate value and standard uncertainty of isentropic efficiency
输入
分布MCM-最佳
估计值/%MCM-标准
不确定度/%GUM-最佳
估计值/%GUM-标准
不确定度/%均匀分布 87.02 0.91 87.03 0.91 正态分布 0.79 87.03 0.79 三角分布 0.64 87.02 0.64
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表 6 等熵效率95%包含概率的最短包含区间
Table 6. Shortest inclusion interval of 95% inclusion probability of isentropic efficiency
输入量
分布95%概率最短包含区间/% MCM GUM 均匀分布 （85.29, 88.79） （85.20, 88.84） 正态分布 （85.46, 88.56） （85.45, 88.60） 三角分布 （85.77, 88.26） （85.74, 88.31）
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表 7 等熵效率概率分布的峰态与偏态系数
Table 7. Kurtosis and skewness coefficients of probability distribution of isentropic efficiency
输入量分布 峰态系数 偏态系数 均匀分布 2.5529 0.0288 正态分布 2.9968 0.0124 三角分布 2.7753 0.0220
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表 8 等熵效率测量不确定度的等精度分配
Table 8. Equal accuracy allocation of measurement uncertainty of isentropic efficiency
等熵效率相对
不确定度/
%总压相对
不确定度/
%总压
不确定度/
Pa总温相对
不确定度/
%总温
不确定度/
K0.5 0.027 35 0.027 0.083 1.0 0.053 70 0.053 0.167 1.5 0.080 105 0.080 0.250 2.0 0.107 141 0.107 0.334
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表 9 等熵效率测量不确定度的等作用分配
Table 9. Equal action allocation of measurement uncertainty of isentropic efficiency
等熵效率相对不确定度/% 总压相对不确定度/% 总压不确定度/Pa 总温相对不确定度/% 总温不确定度/K 0.5 0.063 83 0.020 0.062 1.0 0.126 166 0.040 0.124 1.5 0.189 249 0.059 0.186 2.0 0.253 333 0.079 0.247
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表 10 不同径向测点数量下等熵效率测量不确定度的分配
Table 10. Allocation of measurement uncertainty of isentropic efficiency at different radial measuring points
径向测
点数总压相对
不确定度/%总压
不确定度/Pa总温相对
不确定度/%总温
不确定度/K5 0.060 79 0.060 0.187 7 0.071 93 0.071 0.221 9 0.080 105 0.080 0.250 11 0.089 117 0.089 0.277
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