# zbMATH — the first resource for mathematics

Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows. (English) Zbl 1225.76168
Summary: The interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows (TCF) are studied using direct numerical simulations (DNS). DNS of three isothermal-wall TCF for Mach number $$Ma = 0.2, 0.7, \text{and} 1.5$$, respectively are performed using a discontinuous Galerkin method (DGM). The Reynolds numbers of these three cases are $$\approx 2800$$, based on the bulk velocity, bulk density, half channel width and dynamic viscosity at the wall. A high cross-correlation between density and spanwise vorticity occurs at $$y^{+}\approx 4$$, which is coincident with the peak mean spanwise baroclinicity. The relationship between the spanwise baroclinicity and the correlation is analysed. The difference between the evolution of density and spanwise vorticity very near the wall is discussed. The transport equation for the mean product of density and vorticity fluctuations $$\langle \rho^{\prime}\omega^{\prime}_{i}\rangle$$; is presented and the distributions of terms in the $$\langle \rho^{\prime}\omega^{\prime}_{z}\rangle$$; transport equation indicate that the minima and maxima of the profiles are located around $$y^{+}\approx 5$$. The connection between pressure gradients and vorticity fluxes for compressible turbulent flows with variable viscosity has been formulated and verified. High correlations (0.7-1.0) between pressure gradient and vorticity flux are found very close to the wall $$(y^{+} < 5)$$. The correlation coefficients are significantly influenced by $$Ma$$ and viscosity in this region. Turbulence advection plays an important role in destroying the high correlations between pressure gradient and vorticity flux in the region away from the wall $$(y^{+} > 5)$$.

##### MSC:
 76F50 Compressibility effects in turbulence 76F40 Turbulent boundary layers 76F65 Direct numerical and large eddy simulation of turbulence
Full Text:
##### References:
 [1] Lighthill, Laminar Boundary Layers (1963) [2] DOI: 10.1063/1.1454997 · Zbl 1185.76221 · doi:10.1063/1.1454997 [3] DOI: 10.1063/1.869874 · Zbl 1147.76436 · doi:10.1063/1.869874 [4] DOI: 10.1093/acprof:oso/9780198528692.001.0001 · Zbl 1116.76002 · doi:10.1093/acprof:oso/9780198528692.001.0001 [5] DOI: 10.2514/3.25250 · doi:10.2514/3.25250 [6] DOI: 10.1063/1.858819 · Zbl 0781.76030 · doi:10.1063/1.858819 [7] DOI: 10.1063/1.869966 · Zbl 1147.76463 · doi:10.1063/1.869966 [8] DOI: 10.1016/0169-5983(88)90066-4 · doi:10.1016/0169-5983(88)90066-4 [9] Cockburn, Discontinuous Galerkin Methods – Theory, Computation and Applications (2000) · doi:10.1007/978-3-642-59721-3 [10] DOI: 10.1007/s001620050077 · Zbl 0913.76030 · doi:10.1007/s001620050077 [11] DOI: 10.1017/S0022112096001553 · doi:10.1017/S0022112096001553 [12] Schlichting, Boundary-Layer Theory (1979) [13] Panton, Incompressible Flows (1984) [14] DOI: 10.1017/S0022112095004587 · Zbl 0960.76517 · doi:10.1017/S0022112095004587
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.