J. H. Agui

Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields

The unsteady interaction of a moving shock wave with nearly homogeneous and isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock tube facility. Rectangular grids of various mesh sizes were used to generate turbulence with Reynolds numbers based on Taylors microscale ranging from 260 to 1300. The interaction has been investigated by measuring the three-dimensional velocity and vorticity vectors, the full velocity gradient and rate-of-strain tensors with instrumentation of high temporal and spatial resolution. This allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause. Fluctuations of all velocity gradients in the longitudinal direction are amplified significantly downstream of the interaction. Fluctuations of the velocity gradients in the lateral directions show no change or a minor reduction through the interaction. Root mean square values of the lateral vorticity components indicate a 25% amplification on average, which appears to be very weakly dependent on the shock strength. The transmission of the longitudinal vorticity fluctuations through the shock appears to be less affected by the interaction than the fluctuations of the lateral components. Non-dissipative vortex tubes and irrotational dissipative motions are more intense in the region downstream of the shock. There is also a significant increase in the number of events with intense rotational and dissipative motions. Integral length scales and Taylors microscales were reduced after the interaction with the shock in all investigated flow cases. The integral length scales in the lateral direction increase at low Mach numbers and decrease during strong interactions. It appears that in the weakest of the present interactions, turbulent eddies are compressed drastically in the longitudinal direction while their extent in the normal direction remains relatively the same. As the shock strength increases the lateral integral length scales increase while the longitudinal ones decrease. At the strongest interaction of the present flow cases turbulent eddies are compressed in both directions. However, even at the highest Mach number the issue is more complicated since amplification of the lateral scales has been observed in flows with fine grids. Thus the outcome of the interaction strongly depends on the initial conditions.

Wall-vorticity flux dynamics in a two-dimensional turbulent boundary layer

Four high-frequency-response pressure transducers with 10 viscous units resolution each have been used to obtain simultaneously the fluctuating pressure gradients at the wall of a zero-pressure-gradient boundary layer and then to compute the vorticity flux away from the wall. Since the viscous force on an element of incompressible fluid is determined by the local vorticity gradients, understanding of their dynamical characteristics is essential in identifying the turbulent structure. Extremely high and low amplitudes of both vorticity gradients have been observed which contribute significantly to their statistics although they have low probability of appearance. The r.m.s. of the vorticity flux when scaled with inner wall variables depends very strongly on the Reynolds number, indicating a breakdown of this type of scaling. The application of a small threshold to the data indicated two preferential directions of the vorticity flux vector. An attempt has been made to identify these high- and low-amplitude signals with physical phenomena associated with bursting-sweep processes. Vortical structures carrying bipolar vorticity are the dominant wall structures which are associated with the violent events characterized by large fluctuations of vorticity flux.

Experimental investigation of a three dimensional boundary layer flow in the vicinity of an upright wall mounted cylinder

The flow of a three-dimensional boundary layer approaching an upright wall mounted circular cylinder has been experimentally investigated by means of instantaneous flow visualisation techniques using a laser sheet and time resolved measurements of the wall pressure, the gradients of which are related to the vorticity flux away from the wall. The mean separation point of the oncoming boundary layer is located on the plane of symmetry, 0.76 and 0.82 diameters upstream of the cylinder for the two investigated Reynolds numbers, based on the cylinder diameter, of 1.0x105 and 2.2x105, respectively. The present flow visualisation studies have shown that there is always a primary vortex present in the flow which induces an eruption of wall fluid. Very often, this eruption results in the formation of counter rotating or mushroom vortices. A secondary vortex further upstream has been observed occasionally. This vortex, as well as the vortices formed by the fast eruption of wall fluid evolve quickly in time and space and therefore cannot be obtained from time-average measurements. The primary vortex consists of several large scale structures which have originated in the oncoming boundary layer and which have acquired substantial additional vorticity. Point measurements indicate that the r.m.s. pressure fluctuations increase as separation is approached and reach a maximum near reattachment. A low degree of space-time correlation and longer integral time scales were also observed downstream of separation. A bimodal probability density function of the fluctuating pressure was observed in the vicinity of the mean separation point, close to the corner region and in the wake of the cylinder. Quasi periodic vortex shedding from the cylinder with a Strouhal number 0.13 was also observed.

Vorticity dynamics in interactions of shock or expansion waves with turbulence and vortices

The interaction of planar shock waves or expansion waves with homogeneous and isotropic turbulence and induced longitudinal and spanwise vortices generated by a wing have been investigated experimentally in the CCNY Shock Tube Research Facility at several Reynolds numbers. A custom made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three dimensional velocity and vorticity vectors, and associated total temperature, in nonisothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. These results indicate that the outcome of the interaction depends strongly on the upstream turbulence of the flow.