Direct numerical simulation of compressible free shear flows

Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified

Relations between two-point correlations and pressure strain terms

The structure of the two-point spatial correlations (velocity-velocity, velocity-scalar, and scalar-scalar) were studied with a view to improve turbulence closure models. The linear model for the two-point correlations proposed by Naot provides a method of including the information about the turbulence structure in the turbulence models. The assumptions and adequacy of this model were tested against the homogeneous shear flow simulation data base. The model performs poorly in some details and it is suggested how it may be improved. The models were also tested for rapid pressure-strain terms in a variety of flows including axisymmetric expansion and contraction flows, homogeneous shear flow, channel flow, and boundary layer

Evolution of isolated turbulent trailing vortices

In this work, the temporal evolution of a low swirl-number turbulent Batchelor vortex is studied using pseudospectral direct numerical simulations. The solution of the governing equations in the vorticity-velocity form allows for accurate application of boundary conditions. The physics of the evolution is investigated with an emphasis on the mechanisms that influence the transport of axial and angular momentum. Excitation of normal mode instabilities gives rise to coherent large scale helical structures inside the vortical core. The radial growth of these helical structures and the action of axial shear and differential rotation results in the creation of a polarized vortex layer. This vortex layer evolves into a series of hairpin-shaped structures that subsequently breakdown into elongated fine scale vortices. Ultimately, the radially outward propagation of these structures results in the relaxation of the flow towards a stable high-swirl configuration. Two conserved quantities, based on the deviation from the laminar solution, are derived and these prove to be useful in characterizing the polarized vortex layer and enhancing the understanding of the transport process. The generation and evolution of the Reynolds stresses is also addressed

The Sound Generated by a Two-Dimensional Shear Layer: The Far Field Directivity from Computations and Acoustic Analogies

The sound generated by vortex pairing in a two- dimensional mixing layer is studied by direct numerical simulation of the Navier-Stokes equations (DNS) for the layer and a portion of its acoustic field, and by solving Lilley's equation (with source terms determined from the DNS) for the entire acoustic field. Predictions for the acoustic field based on Lilley's equation are in good agreement with the DNS results. The radiated acoustic field at the pairing frequencies is highly directive and cannot be produced by point quadrupole sources. Instead, it is of the superdirective character considered by Crighton and Huerre (1990, J. Fluid Mech., 220), where the magnitude of the pressure varies like the exponential of the cosine of the angle between the observation point and the downstream axis. By making modifications to this basic directivity, we account, in part, for shear in the mean velocity and the convection of the acoustic waves by the different freestream velocities on either side of the layer, and obtain a good overall agreement between the theory and the computations

Boundary Conditions for Direct Computation of Aerodynamic Sound Generation

Accurate computation of the far-field sound along with the near-field source terms associated with a free shear flow requires that the Navier-Stokes equations be solved using accurate numerical differentiation and time-marching schemes, with nonreflecting boundary conditions. Nonreflecting boundary conditions have been developed for two-dimensional linearized Euler equations by Giles. These conditions are modified for use with nonlinear Navier-Stokes computations of open flow problems. At an outflow, vortical structures are found to produce large reflections due to nonlinear effects; these reflection errors cannot be improved by increasing the accuracy of the linear boundary conditions. An exit zone just upstream of an outflow where disturbances are significantly attenuated through grid stretching and filtering is developed for use with the nonreflecting boundary conditions; reflections from vortical structures are decreased by 3 orders of magnitude. The accuracy and stability of the boundary conditions are investigated in several model flows that include sound radiation by an energy source in a uniformly sheared viscous flow, the propagation of vortices in a uniform flow, and the spatial evolution of a compressible mixing layer

The Sound Generated by a Two-Dimensional Shear Layer: A Comparison of Direct Computations and Acoustic Analogies

The sound generated by vortex pairing in a two-dimensional mixing layer is studied by solving the Navier-Stokes equations (DNS) for the layer and a portion of its acoustic field, and by solving acoustic analogies with source terms determined from the DNS. Predictions for the acoustic field based on Lilley’s equation are in excellent agreement with the DNS results giving detailed verification of Lilley’s acoustic analogy for the first time. We show that parts of the full source term which arise when the left-hand-side of Lilley’s equation is linearized should not be neglected solely because they are attributable to refraction and scattering, nor because they are proportional to the dilatation. Lilley’s source, -2u_(i,j)u_(j,k)u_(k,i), appears to be mainly responsible for the overall directivity of the acoustic field produced by the vortex pairings, which is highly focused at shallow angles to the streamwise axis. Scattering of the waves by the flow appears also to be significant, causing the directivity to be more omnidirectional than the Lilley source alone would predict. We also show how small errors in determining the sources, especially those due to scattering, can sometimes lead to large errors in the predictions