Embedded cavity drag in steady and unsteady flows

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thicknesses deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and iso-vorticity contours. The dominant physics in the overall drag characteristics of the flow is examined by an analysis of the pressure and wall shear stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The flow dynamics of the boundary-layer flow over an embedded cavity is summarized. Finally, the relevance of the results to the control of flow separation in such flows is discussed

Inviscid spatial stability of a compressible mixing layer. Part 2: The flame sheet model

The results of an inviscid spatial calculation for a compressible reacting mixing layer are reported. The limit of infinitive activation energy is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the moving stream, the Mach number of the moving streams, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding nonreacting mixing layer. We show that the addition of combustion has important, and complex effects on the flow stability

A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented

Zero wavenumber modes of a compressible supersonic mixing layer

It is shown that there exists a family of supersonic neutral modes for a compressible mixing layer in an unbounded domain. These modes have zero wavenumber and frequency with nonzero phase speed. They are analogous to the supersonic neutral modes of the compressible vortex sheet found by Miles. The results presented give a more complete picture of the spectrum of the disturbances in this flow

Absolute/convective instabilities and the convective Mach number in a compressible mixing layer

Two aspects of the stability of a compressible mixing layer: Absolute/Convective instability and the convective Mach number were considered. It was shown that, for Mach numbers less than one, the compressible mixing layer is convectively unstable unless there is an appreciable amount of backflow. Also presented was a rigorous derivation of a convective Mach number based on linear stability theory for the flow of a multi-species gas in a mixing layer. The result is compared with the heuristic definitions of others and to selected experimental results

Inviscid spatial stability of a compressible mixing layer. Part 3: Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantative features of the stability characteristics are quite similiar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number

Effect of heat release on the spatial stability of a supersonic reacting mixing layer

A numerical study of the stability of compressible mixing layers in which a diffusion flame is embedded is described. The mean velocity profile has been approximated by a hyperbolic tangent profile and the limit of infinite activation energy taken, which reduces the diffusion flame to a flame sheet. The addition of combustion in the form of a flame sheet was found to have important, and complex, effects on the flow stability

Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry

The ignition and structure of a reacting compressible mixing layer is considered using finite rate chemistry lying between two streams of reactants with different freestream speeds and temperatures. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. An analysis of both the ignition a diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows to analyze the behavior of these regimes as a function of the parameters of the problem

A general purpose subroutine for fast fourier transform on a distributed memory parallel machine

One issue which is central in developing a general purpose Fast Fourier Transform (FFT) subroutine on a distributed memory parallel machine is the data distribution. It is possible that different users would like to use the FFT routine with different data distributions. Thus, there is a need to design FFT schemes on distributed memory parallel machines which can support a variety of data distributions. An FFT implementation on a distributed memory parallel machine which works for a number of data distributions commonly encountered in scientific applications is presented. The problem of rearranging the data after computing the FFT is also addressed. The performance of the implementation on a distributed memory parallel machine Intel iPSC/860 is evaluated