Adaptability of high-frequency response characteristic model for micro probe-transducer system
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摘要:
为了拓宽微型探头-传感系统的可用频带,满足高频压力信号的测量需求,需对系统的频率响应特性进行研究,并分析现有数学模型对不同结构微型探头-传感系统的适用性及预测精度。对5种典型结构的微型探头-传感系统进行了判定和划分,综述了现有微型探头-传感系统的频响预测模型、假设条件及模型修正方法。为对理论数学模型进行定量评价,计算得到了不同结构微型探头-传感系统的谐振频率、截止频率和工作频带(幅值误差±5%),并与数值仿真和实验结果进行了对比。结果表明:对于引压管较短的谐振腔,利用Panton模型计算其谐振频率,误差可控制在1%以内;对于引压管较长及带有测压孔的结构,B-T模型的预测精度最高。对实验用微型探头-传感系统进行了优化设计,并用于超声速凝结自激振荡现象的研究。结果表明:优化的微型探头-传感系统频响特性可满足高频(约10 kHz)压力波动信号的动态测量需求。
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关键词:
- 瞬态压力测量 /
- 微型探头-传感系统 /
- 计算流体力学(CFD) /
- 系统参数辨识 /
- 高频响应特性
Abstract:To broaden the available bandwidth of micro probe transducer system and improve the measurement accuracy of high-frequency pressure signal, it is important to study the frequency response characteristic and analyze the application scope and prediction accuracy of the mathematic models for different probe-transducer system structures. In this study, the probe-transducer system structure was divided into five typical types. Then, the frequency response prediction models, and assumed conditions and updating methods of the existing probe-transducer system were summarized. To evaluate the theoretical mathematic models' prediction accuracy quantitatively, the resonant frequency, cut-off frequency and working band (amplitude error ±5%) for probe-transducer system with different structures were extracted by mathematic models and compared with the CFD and experimental results. For the resonator whose probe is shorter, the Panton model can be used and the error can be controlled within 1%. For the structure whose probe is longer and the structure with pressure hole, the B-T model is the most accurate. Finally, the probe-transducer system was optimized to study the self-excited oscillation phenomenon in supersonic condensation. The results show that the frequency response characteristic of the optimized probe-transducer system can meet the requirement of dynamic measurement for the high-frequency (about 10 kHz) fluctuating pressure signal.
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表 1 微型探头-传感系统典型结构
Table 1. Typical structures of micro probe-transducer system
结构 特征 示意图 ωn/(rad·s-1) Ⅰ 谐振腔模型,引压管长度非常小 Ⅱ 腔室终端十分小,与引压管相比,终端腔室的影响可忽略 Ⅲ 腔室长度远小于引压管长度,可将终端腔室作为集中参数处理 Ⅳ 与引压管相比,腔室长度较长,不能忽略腔室长度影响 Ⅴ 引压管与待测管路连接时,有一定的测压孔节流 表 2 微型探头-传感系统数学模型
Table 2. Mathematical models of micro probe-transducer system
表 3 微型探头-传感系统尺寸
Table 3. Size of micro probe-transducer systems
结构 l0/mm r0/mm l/mm r/mm L/mm R/mm Ⅱ 25 1 Ⅲ 25 1 1 1.5 Ⅳ 25 1 10 1.5 Ⅴ 20 1 20 2 1 2.5 表 4 4种预测模型的截止频率计算结果及误差
Table 4. Cut-off frequency computational result and error of four prediction models
类型 结构 fb0/Hz fb1/Hz fb2/Hz fb3/Hz fb4/Hz σf1/% σf2/% σf3/% σf4/% CFD Ⅱ 5742.5 4251.3 6932.5 6939.8 6701.0 25.97 20.72 20.85 16.69 Ⅲ 5108.7 3845.7 5900.1 5881.3 5579.6 24.72 15.49 15.12 9.22 Ⅳ 2947.1 2852.9 3018.3 2980.2 2611.4 3.20 2.42 1.12 11.39 Ⅴ 1741.1 1761.1 1.15 实验 Ⅱ[22] 24.25 21.17 22.06 22.21 23.02 12.70 9.03 8.41 5.07 Ⅲ[14] 116.54 157.72 156.61 152.95 146.10 35.34 34.38 31.24 25.36 Ⅴ[14] 170.92 179.53 5.04 表 5 4种预测模型的工作频带计算结果及误差
Table 5. Working frequency band computational result and error of four prediction models
类型 结构 fg0/Hz fg1/Hz fg2/Hz fg3/Hz fg4/Hz σf1/% σf2/% σf3/% σf4/% CFD Ⅱ 666.4 656.0 684.8 684.8 684.7 1.56 2.76 2.76 2.75 Ⅲ 622.5 593.4 630.4 627.3 611.8 4.67 1.27 0.77 1.72 Ⅳ 383.4 440.2 408.6 398.3 364.1 14.81 6.57 3.89 5.03 Ⅴ 250.8 240.8 3.99 实验 Ⅱ[22] 3.43 3.34 3.50 3.50 3.50 2.62 2.04 2.04 2.04 Ⅲ[14] 24.51 29.37 29.91 28.81 20.37 19.83 22.03 17.54 16.89 Ⅴ[14] 16.14 14.01 13.20 表 6 Panton模型谐振频率实验与预测结果对比[24]
Table 6. Comparison of measured and predicted resonant frequencies with Panton model[24]
l/d fexp/Hz f1/Hz f2/Hz f3/Hz σf1/% σf2/% σf3/% 0.31 1319 1320 1357 1951 0.08 2.88 47.92 2552 2557 2626 3775 0.20 2.90 47.92 4434 4439 4562 6558 0.11 2.89 47.90 0.42 980 990 989 1191 1.02 0.92 21.53 2775 2780 2803 3371 0.18 1.01 21.48 3666 3691 3701 4451 0.68 0.95 21.41 0.63 252 254 252 268 0.79 0 6.35 3238 3228 3242 3443 0.31 0.12 6.33 4845 4824 4851 5153 0.43 0.12 6.36 表 7 微型探头-传感系统不同结构对各模型的适应性
Table 7. Adaptability of different micro probe-transducer system structures to various models
结构 适用模型 Ⅰ 对引压管长进行修正后,用Panton模型计算其谐振频率。工程实际中,可利用模型简化后的经典公式或改进公式,但当l/d < 0.42,即管长较短时,经典公式的误差较大。如果需要精确计算,则使用模型的原始公式 Ⅱ 在工程中,可利用四分之一波长理论公式计算其谐振频率;如果精确计算其频率特性,可选择B-T模型 Ⅲ 当粗略估算最低阶共振频率时,可选择不可压缩二阶系统模型;而当精确计算时,可选择线性摩擦模型、耗散模型和B-T模型。其中,线性摩擦模型适用于低频扰动情况,B-T模型精度最高 Ⅳ、Ⅴ 结构IV可看作结构V腔室体积为0时的一种特殊情况,利用B-T模型计算 表 8 微型探头-传感系统尺寸及闭环截止频率
Table 8. Size and closed-loop cut-off frequency of micro probe-transducer system
r0/mm l0/mm r/mm l/mm V/mm3 fb/Hz 0.3 4 0.5 2.5 0.23 12860 0.3 5 0.5 1.5 0.23 13958 0.3 5 0.4 1.5 0.23 16441 0.3 6 0.5 0.5 0.23 17125 0.3 6 0.5 0.5 0.11 18271 0.6 4 0.8 2.5 1.57 15024 0.6 5 0.8 1.5 1.57 15661 0.6 5 0.9 1.5 1.57 14547 0.6 5 0.9 1.5 0.94 15374 0.6 5 0.9 1.5 0 16870 0.6 6 0.9 0.5 0.90 18287 0.9 4 1.1 2.5 1.23 17857 0.9 4 1.3 2.5 1.23 15343 0.9 5 1.1 1.5 1.23 18844 0.9 5 1.1 1.5 2.46 17571 -
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