On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows

Abstract

The near-wall structures and statistics of fluctuating pressure (p′) in compressible turbulent channel flows (CTCF) with isothermal walls have been investigated by direct numerical simulations. Two typical cases for high bulk Mach number Ma = 3.83 and low one Ma = 1.56 are considered. A novel type of near-wall pressure structures named “alternating positive and negative structures (APNS)” is found in the high-Ma case based on the comprehensive analysis of spectra and dynamic mode decomposition of p′. These APNS of p′ are identified to have the streamwise and spanwise length scales of (λx/h, λz/h) ≈ (0.9, 1.5), where h is the channel half-height, and prefer to inhabit the low-speed wall streaks. It is also verified via a pressure splitting method that the APNS of p′ are dominated by the compressibility effects. Based on the linear stability analysis, the APNS of p′ can be intimately related to a linear stability eigenmode of the high-Ma CTCF and are sustained by the transient growth mechanism as the disturbances of the APNS length scales. Furthermore, these APNS of p′ offer an extra mechanism to generate the near-wall p′ for the high-Ma case. Moreover, it is found that the APNS of p′ have a dominating effect on the pressure-dilatation correlation and the production of Reynolds shear stress. The present study may provide a reliable way to achieve a better understanding and modeling of compressibility effects in the wall-bounded turbulence of high Ma.

Statistical properties of pressure-Hessian tensor in a turbulent channel flow

“…Standard isothermal, no-slip boundary conditions are applied at the channel walls. More details of the numerical procedures and validation can be found in Tang et al (2020). In the present channel flow, the turbulent Mach number is less than 0.3, and the relative dilatation, which measures the local compressibility according to Suman & Girimaji (2013), is close to zero across the entire channel.…”

“…To study the statistical properties of the pressure-Hessian tensor in wall turbulence, including the anisotropic and inhomogeneous effects, we adopted the flow fields of a weakly compressible turbulent channel flow with a bulk Mach number of Ma B = 1.56 and a Reynolds number of Re B = 7813 based on the bulk-averaged velocity (Gerolymos & Vallet 2014) in our previous paper (Tang et al 2020). The corresponding frictional Reynolds number is Re τ = 532.…”

“…However, it is unclear whether the inhomogeneity and anisotropy originate directly from the mean shear flow or the inhomogeneous and anisotropic fluctuating flow. The method of pressure decomposition (Tang et al 2020) provides a chance to achieve more physical understanding. In our previous study (Tang et al 2020), with the purpose of investigating the statistical characteristics of pressure fluctuations in compressible channel turbulence, we decomposed the pressure fluctuations into the fast pressure p r , slow pressure p s , Stokes pressure p τ and compressible pressure p c .…”

“…The method of pressure decomposition (Tang et al 2020) provides a chance to achieve more physical understanding. In our previous study (Tang et al 2020), with the purpose of investigating the statistical characteristics of pressure fluctuations in compressible channel turbulence, we decomposed the pressure fluctuations into the fast pressure p r , slow pressure p s , Stokes pressure p τ and compressible pressure p c . The fast pressure represents the pressure fluctuations generated by the interaction between turbulent fluctuations and the mean flow.…”

“…Firstly, the instantaneous pressure is split in terms of the mean pressure and the fluctuation. Then the fluctuating pressure is decomposed following the method in Tang et al (2020). In turn, the derivatives of each pressure part are computed to obtain the corresponding pressure-Hessian part.…”