Band limited correlation estimates for A(ξω/U) and B(ηω/U) using Beresh et. al. 2013 data sets
Band limited correlation estimates for A(ξω/U) and B(ηω/U) using Beresh et. al. 2013 data sets
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使用 Beresh 等人的 2013 年数据集对 A(xiω/U) 和 B(ηω/U) 进行频带限制相关性估计。
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发表时间：
2014
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通讯作者：
Justin A. Smith
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作者：
L. Dechant;Justin A. Smith
在这里，我们讨论利用零压力梯度、超音速（Beresh 等人（2013））数据集改进的 Corcos（Corcos（1963），（1963））样式交叉谱密度。利用窄带测量与宽带互谱密度之间的联系，即 Г(ψ ,η ,ω )= Φ (ω) A(ωη/U )exp (-i ωψ/U)，我们重点估计以下形式的相干表达式：A (ψω nb/U) 和 B (ηω nb/ U)，其中 ωnb 表示窄带频率，即频段中心频率值，ψ 和 η 分别为传感器分别沿流向/纵向和横流/横向方向间隔。一种估计参数的方法，保留了 Corcos 指数函数形式，A(xiω/U)=exp(-klat ηω/U)，但确定了与 Beresh 等人一致的新参数（常数）。等人。讨论了数据集。 Corcos 结果要求数据可以通过自相似变量 ψω/U 和 ηω/U 正确解释。纵向（流向）变量 xiω/U 倾向于提供更好的数据折叠，而与文献一致，横向 ηω/U 仅在较高频段中心频率下成功。假设相似性变量提供了数据的有用描述，则使用 Beresh 等人得出的纵向相干衰减常数结果。等人。数据集得出的纵向常数 klong≈0.36-0.28 的值大约比“传统”（低速、大雷诺数和零压力梯度）klong≈0.11 大 3 倍。我们认为最可能的原因是 Beresh 等人。等人。数据集会导致纵向衰减增加，从而导致相干长度减少，这是由于壁剪切引起的压缩导致不利的压力梯度。关注频率相关相似变量适用的较高频带中心频率测量，横向或横向相干衰减常数 klat≈0.7 与“传统”（低速、大雷诺数和零压力梯度）一致。值得注意的是，纵向/流向相干衰减与其他研究人员观察到的值存在偏差，而横向/横向相干性衰减与其他研究人员观察到的值一致。我们认为，虽然用于获得新的衰减常数估计值的测量来自内部风洞测试，但它们可能提供了预期再入流行为的有用估计，因此建议使用。这些数据还可用于确定不确定性量化 (UQ) 分析的相关长度的不确定性。« less
Here we discuss an improved Corcos (Corcos (1963), (1963)) style cross spectral density utilizing zero pressure gradient, supersonic (Beresh et. al. (2013)) data sets. Using the connection between narrow band measurements with broadband cross-spectral density, i.e. Γ(ξ ,η ,ω )= Φ (ω) A(ωη/U )exp (-i ωξ/U) we focus on estimating coherence expressions of the form: A (ξω nb/U) and B (ηω nb/ U) where ωnb denotes the narrow band frequency, i.e. the band center frequency value and ξ and η are sensors spacing in streamwise/longitudinal and cross-stream/lateral directions, respectively. A methodology to estimate the parameters which retains the Corcos exponential functional form, A(ξω/U)=exp(-klat ηω/U) but identifies new parameters (constants) consistent with the Beresh et. al. data sets is discussed. The Corcos result requires that the data be properly explained by self-similar variable: ξω/U and ηω/U. The longitudinal (streamwise) variable ξω/U tends to provide a better data collapse, while, consistent with the literature the lateral ηω/U is only successful for higher band center frequencies. Assuming the similarity variables provide a useful description of the data, the longitudinal coherence decay constant result using the Beresh et. al. data sets yields a value for the longitudinal constant klong≈0.36-0.28 that is approximately 3x largermore » than the “traditional” (low speed, large Reynolds number and zero pressure gradient) of klong≈0.11. We suggest that the most likely reason that the Beresh et. al. data sets incur increased longitudinal decay which results in reduced coherence lengths is due to wall shear induced compression causing an adverse pressure gradient. Focusing on the higher band center frequency measurements where the frequency dependent similarity variables are applicable, the lateral or transverse coherence decay constant klat≈0.7 is consistent with the “traditional” (low speed, large Reynolds number and zero pressure gradient). It should be noted, that the longitudinal/streamwise coherence decay deviates from the value observed by other researchers while the lateral/ cross-stream value is consistent has been observed by other researchers. We believe that while the measurements used to obtain new decay constant estimates are from internal wind tunnel tests, they likely provide a useful estimate expected reentry flow behavior and are therefore recommended for use. These data could also be useful in determining the uncertainty of correlation length for a uncertainty quantification (UQ) analysis.« less