H. A. Hassan

Euler calculations for multielement airfoils using Cartesian grids

A finite volume formulation for the Euler equations using Cartesian grids is presented and used to study complex two-dimensional configurations. The formulation extends methods developed for the potential equation to the Euler equations. Results using this approach for single-element airfoils are shown to be competitive with, and as accurate as, other methods that employ mapped grids. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.

Hybrid Simulation Approach for Cavity Flows: Blending, Algorithm, and Boundary Treatment Issues

The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the difficulty of formulating a single set of closure coefficients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modifications to common second-order accurate Reynolds averaged Navier-Stokes algorithms are proposed to enhance the capturing of large eddy motions

Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods

A planar Couette flow is simulated using several different interface conditions in a hybrid technique in which the direct simulation Monte Carlo (DSMC) method and the Navier-Stokes equations are coupled. Comparison of computational times and accuracy of the different methods are made to determine the best approach for further study. It is concluded that the Marshak condition, in which the properties at the interfaces between the continuum and rarefied regions are determined from flux conservation equations, is the best technique in terms of accuracy and run-time performance. When coupling NavierStokes and DSMC solvers, the use of a Maxwellian distribution to represent the particle velocity distribution hi the Navier-Stokes region yields unacceptable errors.

Rates of thermal relaxation in direct simulation Monte Carlo methods

For internal energy relaxation in rarefied gas mixtures, exact relationships are derived between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans’ equation. These expressions apply to the Borgnakke–Larsen model for internal energy exchange mechanics and are not limited to the assumption of constant Z. Although Jeans’ equation leads to adiabatic relaxation curves, which coalesce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke–Larsen selection probabilities depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, simulation results show that the common assumption P=1/Z is invalid, in general, and leads to considerably slower relaxation than stipulated by Z in Jeans’ equation. Moreover, inconsistent definitions of collision rates appearing in the literature can...

A generalized hard‐sphere model for Monte Carlo simulation

A new molecular model, called the generalized hard‐sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard‐sphere (VHS) model of Bird [Rarefied Gas Dynamics, edited by S. S. Fisher (AIAA, New York, 1981), Part 1, p. 239] and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo (DSMC) methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier–Stokes calculations.

Inflow boundary conditions for hybrid large eddy/Reynolds averaged Navier-Stokes simulations

Inflow boundary conditions are developed for hybrid large-eddy simulation (LES)/Reynolds-averaged Navier-Stokes approaches. They are based on an extension of the rescaling-reintroducing method developed for LES to a hybrid scheme. A blending function is used to shift the turbulence closure from a κ-ζ model near the wall to a κ-Δ subgrid-scale model away from the wall. The approach was tested for a flat plate and then applied to the study of a 25-deg compression-expansion ramp for a Mach number of 2.88 and a Reynolds number of 3.24 × 10 7 /m. In general, improvements over the κ-ζ model were noted in the recovery region. The significance of this work is that it provides a way for LES methods to address flows at a high Reynolds number

Calculation of supersonic turbulent reacting coaxial jets

The mixing and subsequent combustion within turbulent reacting shear layers is examined. To conduct this study, a computer program has been written to solve the axisymmetric Reynolds-averaged, Navier-Stokes equations. Turbulence is modeled using three algebraic turbulence models, and the chemical kinetics is modeled using a seven-species, seven-reaction, finite-rate chemistry model. Three separate flowfields are investigated. The effect of turbulent mixing upon the extent of combustion is demonstrated. No single turbulence model considered accurately predicted the degree of mixing for all three cases.

A Transition Closure Model for Predicting Transition Onset

A unified approach which makes it possible to determine the extent and onset of transition in one calculation is presented. It treats the laminar fluctuations in a manner similar to that used in describing turbulence. As a result, the complete flowfield can be calculated using existing CFD codes and without the use of stability codes. The method is validated by comparing the results for flat plates, airfoils, and infinite swept wings with available experiments. In general, good agreement is indicated.

Unified turbulence closure model for axisymmetric and planar free shear flows

A new two-equation turbulence model based on the exact turbulent kinetic energy and the variance of vorticity or enstrophy equations is developed and used to calculate planar and axisymmetric free shear flows. It is shown that one set of model constants reproduces available growth rates and similarity profiles of velocity and shear stress. In general, agreement is well within the scatter of experimental data.

Assumed Joint Probability Density Function Approach for Supersonic Turbulent Combustion

In a recent experiment, Cheng et al. used UV spontaneous vibrational Raman scattering and laser-induced predissociative fluorescence techniques for simultaneous measurements of temperature and concentrations of O2, H2, H2O, OH, and N2 (and the rms of their fluctuations) in supersonic turbulent reacting shear layers. Because present computational techniques are not suited for the prediction of all of the above measurements, a new approach has been developed and is being used to predict all relevant flow properties and the rms of their fluctuations (where appropriate). The approach explores the use of a multivariate Beta PDF for concentrations. In particular, a version developed by Girimaji to model scalar mixing in turbulent flows is employed. Predictions using this model were, in general, satisfactory in regions preceding ignition, but not in regions downstream of ignition. Part of the discrepancy is a result of our current inability to relate Favre and time averages. 10 refs.