This is the first part of direct numerical simulation(DNS)of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients.We consider the case with the thermal Rayleigh number of 105,the Pradtle number of 1,the Lewis number of 2,the buoyancy ratio of composition to temperature being in the range of[0,1],and height-to-width aspect ration of 4.A new 7thorder upwind compact scheme was developed for approximation of convective terms,and a three-stage third-order Runge-Kutta method was employed for time advancement.Our DNS suggests that with the buoyancy ratio increasing form 0 to 1,the flow of transition is a complex series changing from the steady to periodic,chaotic,periodic,quasi-periodic,and finally back to periodic.There are two types of periodic flow,one is simple periodic flow with single fundamental frequency(FF),and another is complex periodic flow with multiple FFs.This process is illustrated by using time-velocity histories,Fourier frequency spectrum analysis and the phase-space trajectories.
Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh- order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent en-ergy budget is studied. The computed results show that the effect of circumferen-tial curvature on turbulence characteristics is not obvious.
A high-order shock-fitting finite difference scheme is studied and used to do direc-tion numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone.
