M. Y. Hussaini

The analysis and modelling of dilatational terms in compressible turbulence

It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Enhancement of thermal and electrical properties of carbon nanotube polymer composites by magnetic field processing

We show that the thermal and electrical properties of single wall carbon nanotube (CNT)-polymer composites are significantly enhanced by magnetic alignment during processing. The electrical transport properties of the composites are mainly governed by the hopping conduction with localization lengths comparable to bundle diameters. The bundling of nanotubes during the composite processing is an important factor for electrical, and in particular, for thermal transport properties. Better CNT isolation will be needed to reach the theoretical thermal conductivity limit for CNT composites.

The subgrid‐scale modeling of compressible turbulence

A subgrid‐scale model recently derived by Yoshizawa [Phys. Fluids 29, 2152 (1986)] for use in the large‐eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is only applicable to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre‐filtered fields, is suggested which appears to reduce these limitations.

Numerical computations of turbulence amplification in shock-wave interactions

Numerical computations are presented which illustrate and test various effects pertinent to the amplification and generation of turbulence in shock wave-turbulent boundary layer interactions. Several fundamental physical mechanisms are identified. Idealizations of these processes are examined by nonlinear numerical calculations. The results enable some limits to be placed on the range of validity of existing linear theories. Additional results are given which are of a fundamentally nonlinear nature.

The analysis and simulation of compressible turbulence

This paper considers compressible turbulent flows at low turbulent Mach numbers. Contrary to the general belief that such flows are almost incompressible (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a nondimensional time scale which is the order of the fluctuating Mach number. An asymptotic theory which enables a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

A spectral collocation method for the Navier-Stokes equations

Abstract A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection, and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

INTERACTION OF A SHOCK WITH A LONGITUDINAL VORTEX

In this paper we study the shock/longitudinal vortex interaction problem in axisymmetric geometry. Linearized analysis for small vortex strength is performed, and compared with results from a high order axisymmetric shock-fitted Euler solution obtained for this purpose. It is confirmed that for weak vortices, predictions from linear theory agree well with results from nonlinear numerical simulations at the shock location. To handle very strong longitudinal vortices, which may ultimately break the shock, we use an axisymmetric high order essentially non-oscillatory (ENO) shock capturing scheme. Comparison of shock-captured and shock-fitted results are performed in their regions of common validity. We also study the vortex breakdown as a function of Mach number ranging from 1.3 to 10, thus extending the range of existing results. For vortex strengths above a critical value, a triple point forms on the shock and a secondary shock forms to provide the necessary deceleration so that the fluid velocity can adjust to downstream conditions at the shock.

Spectral multigrid methods for elliptic equations II

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Lagrangian-Eulerian advection of noise and dye textures for unsteady flow visualization

A new hybrid scheme, called Lagrangian-Eulerian advection (LEA), that combines the advantages of the Eulerian and Lagrangian frameworks is applied to the visualization of dense representations of time-dependent vector fields. The algorithm encodes the particles into a texture that is then advected. By treating every particle equally, we can handle texture advection and dye advection within a single framework. High temporal and spatial correlation is achieved through the blending of successive frames. A combination of particle and dye advection enables the simultaneous visualization of streamlines, particle paths and streak-lines. We demonstrate various experimental techniques on several physical flow fields. The simplicity of both the resulting data structures and the implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

Mixing augmentation technique for hypervelocity scramjets

The paper discusses mixing problems in hypervelocity scramjet combustors. Techniques for providing turbulence and/or mixing enhancement are described. One such technique, the oscillating shock interaction, is studied numerically and options for producing oscillatory shock waves for mixing augmentation in scramjet combustors are discussed.