热粘性孔隙中非线性声波的耗散
Dissipation of nonlinear acoustic waves in thermoviscous pores
AI总结：
本文推导了非线性声波传播模型，用于分析波浪壁面狭窄孔隙中的热粘性耗散，并通过二维激波解析DNS验证，发现增加壁面波纹可降低壁面热流和剪切对声波强度的依赖。
摘要：
我们推导了一个非线性声波传播模型，用于分析具有波浪壁面的狭窄孔隙中的热粘性耗散。当非线性波在热粘性孔隙中传播时，波陡效应与体耗散，以及来自孔壁的热粘性传热和剪切作用相互竞争。因此，波的长度尺度被改变。我们利用特征非线性波厚度尺度，得到了控制非定常激波-壁面相互作用的线性和非线性波动方程。我们还进行了孔隙内波传播的二维激波解析 DNS，并将结果与模型方程进行了比较。我们表明，对于平直壁面和激波强度参数 $ε$，量纲壁面热流和剪切按 $ε$ 缩放。对于波浪壁面，缩放变为 $ε^{3/2 - n(k)}$，其中 $k$ 是壁面波纹波数，指数 $n$ 从 $k=0$ 时的 $0.5$ 增加到 $k=10$ 时的 $n(k)\approx0.65$，$k=20$ 时的 $n(k)\approx 0.75$，以及 $k=40$ 时的 $n(k)\approx0.85$。因此，增加壁面波纹会降低壁面热流和剪切对非线性声波强度的依赖性。
英文摘要：
We derive a nonlinear acoustic wave propagation model for analysing the thermoviscous dissipation in narrow pores with wavy walls. As the nonlinear waves propagate in the thermoviscous pores, the wave-steepening effect competes with the bulk dissipation, as well as the thermoviscous heat transfer and shear from the pore walls. Consequently, the length scale of the wave is modified. We use the characteristic nonlinear wave thickness scale to obtain linear and nonlinear wave equations governing the unsteady shock-wall interaction. We also perform two-dimensional shock-resolved DNS of the wave propagation inside the pores and compare the results with model equations. We show that for flat-walls and shock strength parameter $ε$, the dimensional wall heat-flux and shear scale as $ε$. For wavy walls, the scaling becomes $ε^{3/2 - n(k)}$ where $k$ is the wall-waviness wavenumber and the exponent $n$ increases from $0.5$ for $k=0$ to $n(k)\approx0.65$ for $k=10$, $n(k)\approx 0.75$ for $k=20$, and $n(k)\approx0.85$ for $k=40$. Hence, increasing the wall waviness reduces the dependence of the wall heat-flux and shear on nonlinear acoustic wave strength.
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