Michele G. Macaraeg

Spectral multi-domain for large-scale fluid dynamic simulations

A number of successful applications of a spectral collocation method extended by a multi-domain patching technique are shown. The multi-domain technique can be used to improve resolution for problems with widely disparate scales, and to reduce the ill-conditioning of the spectral operators for problems in which a large number of points are required for distributed resolution. A new nonreflecting outflow boundary treatment for unsteady transition-to-turbulence simulations is also presented, which relies on the multi-domain technique. The role of multi-domain in improving the efficiency of such calculations is discussed.

Improvements in spectral collocation discretization through a multiple domain technique

Abstract A new parallel solver for ODEs implementing a “parallelism across the steps” has been recently proposed in (Amodio and Brugnano, 1997; Brugnano and Trigiante, 1998), where it is shown that it is able to obtain an almost perfect speed-up on linear problems, and given mesh. A possible way to adapt this algorithm to efficiently handle nonlinear initial value problems has been studied in the companion paper (Brugnano and Trigiante, this issue). The corresponding algorithm is here analyzed in details, in order to show its parallel efficiency. Numerical tests on a distributed memory parallel computer are also included.

Ignition and Structure of a Laminar Diffusion Flame in the Field of a Vortex

Abstract The distortion of flames in flows with vortical motion is examined via asymptotic analysis and numerical simulation. The model consists of a constant-density. one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are then allowed to mix and react in the presence of a vortex. The evolution in time of the temperature and mass-fraction fields is followed. Emphasis is placed on the ignition time and location as a function of vortex Reynolds number and initial temperature differences of the reacting species. The study brings out the influence of the vortex on the chemical reaction. In all phases, good agreement is observed between asymptotic analysis and the full numerical solution of the model equations.

New instability modes for bounded, free shear flows

A class of highly amplified supersonic disturbances are found for high‐speed, bounded mixing layers at high values of streamwise wavenumber. Their amplification is an order of magnitude greater than the most amplified modes, which occur at 60°–65° at low streamwise wavenumber. These disturbances are stabilized by increasing Mach number, viscosity, and sweep; however, the effect of sweep on the most amplified mode is not significant until the wave propagation angle reaches 30°. The maximum growth rate of the unstable disturbances decreases as the temperature of the higher Mach number stream is increased. The structure of these disturbances is such that the phase speed with respect to the mean flow is subsonic in a small region in the center of the shear layer, and supersonic on either side of this region.

Linear stability of high-speed mixing layers

Abstract A newly developed spectral compressible linear stability code (SPECLS) is presented for analysis of shear flow stability and applied to high-speed boundary layers and free shear flows. The formulation utilizes the first application of a staggered mesh for a compressible flow analysis by a spectral technique and a multi-domain spectral discretization (MDSPD) option to resolve highly irregular structures. An order of magnitude less number of points is needed for equivalent accuracy in disturbance growth rates compared to calculations by a finite difference formulation, and a factor of three fewer points is required by the MDSPD relative to a single-domain spectral discretization (SPSPD). The mean flow in this study consists of two parallel gases, one of which is quiescent. A sudden appearance of multiple supersonic modes is found to occur near Mach 3. Their existence has not been observed in past studies. This occurence is attributed to the boundary conditions which impose zero perturbations (reflecting boundary conditions) of all disturbances in the far field. The condition is imposed sufficiently far that subsonic disturbances are unaffected (i.e., results match the case of an unbounded free shear layer). However, at approximately Mach 2 there are radiating solutions (supersonic disturbances) both above and below the shear region. The imposed “wall” far-field condition causes a multiplicity of higher supersonic modes at Mach numbers exceeding two. The issue of relevance in studying the stability of a free shear flow is the impact of transition on fuel-air mixing efficiency in scramjet combustors. The bounded free shear layer in this study is the proper analogue of this situation. In particular the observation of a pronounced drop in mixing efficiency as Mach number is increased may be related to these multiple modes which have very low growth rates relative to the subsonic disturbances which predominate at low Mach numbers. At M ∞ = 3 it is found that increasing the temperature of the quiescent gas relative to the injected gas in the mixing layer inhibits the development of these supersonic modes for low streamwise wave numbers. Verification of the method will be given for the case of boundary layers using an existing finite difference compressible stability code, and by comparison with analytical results obtained for free shear flows.

Role of Acoustics in Flame/Vortex Interactions

The role of acoustics in flame/vortex interactions is examined via asymptotic analysis and numerical simulation. The model consists of a one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are allowed to mix and react by convection and diffusion in the presence of an acoustic field or a time-varying pressure field of small amplitude. The main emphasis is on the influence of the acoustics on the ignition time and flame structure as a function of vortex Reynolds number and initial temperature differences of the reactants.

Analysis of artificial viscosity effects on reacting flows using a spectral multidomain technique

Standard techniques used to model chemically-reacting flows require an artificial viscosity for stability in the presence of strong shocks. The resulting shock is smeared over at least three computational cells, so that the thickness of the shock is dictated by the structure of the overall mesh and not the shock physics. A gas passing through a strong shock is thrown into a nonequilibrium state and subsequently relaxes down over some finite distance to an equilibrium end state. The artificial smearing of the shock envelops this relaxation zone which causes the chemical kinetics of the flow to be altered. A method is presented which can investigate these issues by following the chemical kinetics and flow kinetics of a gas passing through a fully resolved shock wave at hypersonic Mach numbers. A nonequilibrium chemistry model for air is incorporated into a spectral multidomain Navier-Stokes solution method. Since no artificial viscosity is needed for stability of the multidomain technique, the precise effect of this artifice on the chemical kinetics and relevant flow features can be determined.

Investigation of supersonic modes and three-dimensionality in bounded, free shear flows

Abstract It is found through two-dimensional temporal simulations of high-speed free shear layers that mean flow distortion is significantly increased when supersonic disturbances are introduced as initial conditions. The shear layer exhibits no subharmonic growth or roll-up, but rather a spectral broadening as energy is distributed into higher harmonics. Increasing the velocity of one side of the mixing layer ( u 2 ) to roughly 1 5 the speed of the high speed side ( u 1 ), allows a slight subharmonic growth at a very slow rate for two-dimensional modes. A first look at three-dimensional free shear flows is also presented for M =2. No effect is seen for incompressible flow; however, stabilization is seen with respect to maximum temporal growth rates as the transverse velocity is increased. A much stronger, but similar effect is seen if u 2 is increased. The wave direction of maximum growth for u 2 > 0.4 is found to be the direction of the faster stream ( u 1 ) over a broad range of transverse velocities.

Spectral solution of the incompressible Navier-Stokes equations on the Connection Machine 2

The authors address the issue of solving the time-dependent incompressible Navier-Stokes equations on the Connection Machine 2, for the problem of transition to turbulence on the steady flow in a channel. The spectral algorithm used serially requires O(N/sup 4/) operations; using the massive parallelism of the CM it becomes an O(N/sup 2/) problem, then solving the equations on an N*N*N grid. Preliminary timings of the code, written in Lisp, are included and compared with a corresponding code optimized for the Cray-2 for a 128*128*101 grid.<<ETX>>

Numerical studies of transverse curvature effects on transonic flow stability

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary‐layer profile and a nonsimilar axisymmetric boundary‐layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1–1.4) and aerodynamically relevant Reynolds numbers (5000–10 000 based on displacement thickness), the maximum growth rate is found to increase with curvature—the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.