Using data from direct numerical simulation (DNS) of incompressible and compressible channel flow, we develop a method of sub-ensemble decomposition to investigate the pressure gradient effect on the Karman constant and the additive constant B characterizing the mean velocity profile (MVP). The sub-ensemble decomposition is defined according to the magnitude of vertical fluctuation velocity, which mimics coherent motions like ejection and sweep. DNS data analysis shows that each sub-ensemble displays a distinct Karman constant, with a variation which mimics effects of pressure gradient. The latter is demonstrated by a relation between sub-ensembles' m and Bm similar to empirical data under various pressure gradients. A set of global parameters, 0-pg=0.39 & B0-pg=5.5, are then derived for interpreting two constants observed by Nagib et al.
An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected for two flow conditions at convective Mach numbers Mc=0.11 and 0.47.The coherent vortices,braids and eruptions in the mixing zone were observed,interpreted as evidence of multi-scale,three-dimensional structures at a high Reynolds number.The mixing layers with a large visualized range present two stages along the streamwise direction,corresponding to the initial mixing and the well-developed stage.A new method,the gray level ensemble average method(GLEAM),by virtue of the similarity of the mixing layer,was applied to measure the growth rate of the CML thickness.New evidence for a nonlinear growth of CML is reported,providing an interpretation of previous observations of the scattering of the growth rate.
A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expression and is easy for use in CFD codes.Compared with the original second-order or third-order MUSCL scheme,the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves.This new scheme has been tested through a set of one-dimensional and two-dimensional tests,including the Shu-Osher problem,the Sod problem,the Lax problem,the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test.All numerical tests show that,compared with the original MUSCL schemes,the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.
A direct numerical simulation of the shock/turbulent boundary layer interaction flow in a supersonic 24-degree compression ramp is conducted with the free stream Mach number 2.9.The blow-and-suction disturbance in the upstream wall boundary is used to trigger the transition.Both the mean wall pressure and the velocity profiles agree with those of the experimental data,which validates the simulation.The turbulent kinetic energy budget in the separation region is analyzed.Results show that the turbulent production term increases fast in the separation region,while the turbulent dissipation term reaches its peak in the near-wall region.The turbulent transport term contributes to the balance of the turbulent conduction and turbulent dissipation.Based on the analysis of instantaneous pressure in the downstream region of the mean shock and that in the separation bubble,the authors suggest that the low frequency oscillation of the shock is not caused by the upstream turbulent disturbance,but rather the instability of separation bubble.
LI XinLiang1,FU DeXun2,MA YanWen2 & LIANG Xian1 1 Key Laboratory of High Temperature Gas Dynamics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China
In this paper,direct numerical simulation(DNS)is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma∞=2.25,5,6,8.When Ma∞=8,two cases with the ratio of wall-to-reference temperature T_(w)/T_(∞)=1.9 and 10.03 are considered respectively.The wall temperature approaches recovery temperatures for other cases.The characteristics of compressible turbulent boundary layer(CTBL)affected by freestream Mach number and wall temperature are investigated.It focuses on assessing compressibility effects and the validity of Morkovin’s hypothesis through computing and analyzing the mean velocity profile,turbulent intensity,the strong Reynolds analogy(SRA)and possibility density function of dilatation term.The results show that,when the wall temperature approaches recovery temperature,the effects of Mach number on compressibility is insignificant.As a result,the compressibility effect is very weak and the Morkovin’s hypothesis is still valid for Mach number even up to 8.However,when Mach number equal to 8,the wall temperature effect on the compressibility is sensitive.In this case,when T_(w)/T_(∞)=1.9,the Morkovin’s hypothesis is not fully valid.The validity of classical SRA depends on wall temperature directly.A new modified SRA is proposed to eliminate such negative factor in near wall region.Finally the effects of Mach number and wall temperature on streaks are also studied.
