@article{xiao_hassan_baurle_2007, title={Modeling scramjet flows with variable turbulent Prandtl and Schmidt numbers}, volume={45}, ISSN={["1533-385X"]}, DOI={10.2514/1.26382}, abstractNote={A complete turbulence model, where the turbulent Prandtl and Schmidt numbers are calculated as part of the solution and where averages involving chemical source terms are modeled, is presented. The ability of avoiding the use of assumed or evolution Probability Distribution Functions (PDF’s) results in a highly ecient algorithm for reacting flows. The predictions of the model are compared with two sets of experiments involving supersonic mixing and one involving supersonic combustion. The results demonstrate the need for consideration of turbulence/chemistry interactions in supersonic combustion. In general, good agreement with experiment is indicated.}, number={6}, journal={AIAA JOURNAL}, author={Xiao, X. and Hassan, H. A. and Baurle, R. A.}, year={2007}, month={Jun}, pages={1415–1423} }
 @article{xiao_hassan_edwards_gaffney_2007, title={Role of turbulent Prandtl numbers on heat flux at hypersonic Mach numbers}, volume={45}, DOI={10.2514/1.2144}, number={4}, journal={AIAA Journal}, author={Xiao, X. and Hassan, H. A. and Edwards, J. R. and Gaffney, R. L.}, year={2007}, pages={806–813} }
 @article{xiao_edwards_hassan_cutler_2006, title={Variable turbulent Schmidt-number formulation for scramjet applications}, volume={44}, ISSN={["0001-1452"]}, DOI={10.2514/1.15450}, abstractNote={In high speed engines, thorough turbulent mixing of fuel and air is required to obtain high performance and high efficiency. Thus, the ability to predict turbulent mixing is crucial in obtaining accurate numerical simulation of an engine and its performance. Current state of the art in CFD simulation is to assume both turbulent Prandtl number and Schmidt numbers to be constants. However, since the mixing of fuel and air is inversely proportional to the Schmidt number, a value of 0.45 for the Schmidt number will produce twice as much diffusion as that with a value of 0.9. Because of this, current CFD tools and models have not been able to provide the needed guidance required for the efficient design of a scramjet engine. The goal of this investigation is to develop the framework needed to calculate turbulent Prandtl and Schmidt numbers as part of the solution. This requires four additional equations: two for the temperature variance and its dissipation rate and two for the concentration variance and its dissipation rate. In the current investigation emphasis will be placed on studying mixing without reactions. For such flows, variable Prandtl number does not play a major role in determining the flow. This, however, will have to be addressed when combustion is present. The approach to be used is similar to that used to develop the k-zeta model. In this approach, relevant equations are derived from the exact Navier-Stokes equations and each individual correlation is modeled. This ensures that relevant physics is incorporated into the model equations. This task has been accomplished. The final set of equations have no wall or damping functions. Moreover, they are tensorially consistent and Galilean invariant. The derivation of the model equations is rather lengthy and thus will not be incorporated into this abstract, but will be included in the final paper. As a preliminary to formulating the proposed model, the original k-zeta model with constant turbulent Prandtl and Schmidt numbers is used to model the supersonic coaxial jet mixing experiments involving He, O2 and air.}, number={3}, journal={AIAA JOURNAL}, author={Xiao, X and Edwards, JR and Hassan, HA and Cutler, AD}, year={2006}, month={Mar}, pages={593–599} }
 @article{fan_xiao_edwards_hassan_2004, title={Hybrid large-eddy/Reynolds-averaged Navier-Stokes simulations of shock-separated flows}, volume={41}, ISSN={["1533-6794"]}, DOI={10.2514/1.3735}, abstractNote={Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.}, number={6}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={Fan, CC and Xiao, XD and Edwards, JR and Hassan, HA}, year={2004}, pages={897–906} }
 @article{xiao_edwards_hassan_baurle_2003, title={Inflow boundary conditions for hybrid large eddy/Reynolds averaged Navier-Stokes simulations}, volume={41}, ISSN={["0001-1452"]}, DOI={10.2514/2.2130}, abstractNote={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}, number={8}, journal={AIAA JOURNAL}, author={Xiao, XD and Edwards, JR and Hassan, HA and Baurle, RA}, year={2003}, month={Aug}, pages={1481–1489} }
 @article{xiao_edwards_hassan_2001, title={Transitional flow over an elliptic cone at Mach 8}, volume={38}, ISSN={["0022-4650"]}, DOI={10.2514/2.3767}, abstractNote={Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.}, number={6}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={Xiao, XD and Edwards, JR and Hassan, HA}, year={2001}, pages={941–945} }