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Publications and source records attributed to Hsu, Andrew T..
Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.
In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.
Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
The accurate prediction of turbulent combustion is still beyond reach for today's computation techniques. It is the consensus of the combustion profession that the predictions of chemically reacting flow were poor if conventional turbulence models were used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature, pressure, and density produces excessively large errors. The probability density function (PDF) method is the only alternative at the present time that uses local instant values of the temperature, density, etc. in predicting chemical reaction rate, and thus it is the only viable approach for turbulent combustion calculations.
In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.
Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.
The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.
An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence.
The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.
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An unsteady TVD Navier-Stokes solver was developed and applied to the problem of shock reflection on a circular cylinder. The obtained numerical results were compared with the Schlieren photos from an experimental study. These results show that the present computer code has the ability of capturing moving shocks.
Previous calculations of jet-in-crossflow problems have been sensitive to the turbulence and artificial viscosity models and to the grid. Consequently, the eddy viscosity model in the PARC3D code was modified to consider the turbulent jet by switching from the Baldwin-Lomax (1978) model to an axisymmetric jet model. A modified artificial viscosity model has been utilized and evaluated in this study as well. The new model includes cell size scaling and a directional dependence in the coefficients. Computational results from PARC3D demonstrate the effects of the viscosity models on the pressure distribution fore and aft of the jet and the ability of the adaptive grid scheme to adjust to the three-dimensional gradients around the jet.
Adaptive grid has been applied to the numerical study of generic hypersonic nozzles for the NASP vehicle to evaluate the effect of adaptive grid on solution accuracy. Several cases are calculated with and without adaptive grids; the numerical results are compared with experimental data wherever available, and with numerical results from other researchers. The present work shows that in most situations, especially when free shear layers and shocks exist in the flowfield, adaptive grid is essential in improving solution accuracy.
An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented which provides high flowfield resolution when applied to two-dimensional and three-dimensional flow problems. The present scheme locally adjusts the grid density using gradients of selected flow variables from either finite difference or finite volume calculations, and it can specify user-prescribed grid stretching such that control of the grid spacing can be maintained in areas of known flowfield behavior. A robust and efficient grid smoothing technique has been incorporated into the adaptive grid routine.
A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.
An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.
Underexpanded axisymmetric jets are studied numerically using a full Navier-Stokes solver. Emphasis has been given to supersonic and hypersonic jets in supersonic and hypersonic ambient flows, a phenomenon previously overlooked. It is demonstrated that the shear layers and shock patterns in a jet plume can be captured without complicated viscous/inviscid and subsonic/supersonic coupling schemes. In addition, a supersonic pressure relief effect has been identified for underexpanded jets in supersonic ambient flows. While it is well known that an underexpanded jet in a quiescent ambience (or subsonic ambience) contains multiple shock cells, the present study shows that because of the supersonic pressure relief effect, an underexpanded jet in a supersonic or hypersonic ambience contains only one major shock cell.