@article{rodio_xiao_hassan_rumsey_2015, title={NASA Trapezoidal-Wing Simulation Using Stress-omega, and One- and Two-Equation Turbulence Models}, volume={52}, ISSN={["1533-3868"]}, DOI={10.2514/1.c032848}, abstractNote={The Wilcox 2006 stress-ω model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley Research Center code CFL3D, and used to study a variety of two-dimensional and three-dimensional configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent-stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than the experiment, similar to the results of a two-equation model.}, number={4}, journal={JOURNAL OF AIRCRAFT}, author={Rodio, J. J. and Xiao, X. and Hassan, H. A. and Rumsey, C. L.}, year={2015}, pages={1189–1200} }
 @article{thompson_hassan_2015, title={Simulation of a Variety of Wings Using a Reynolds Stress Model}, volume={52}, ISSN={["1533-3868"]}, DOI={10.2514/1.c033046}, abstractNote={The Wilcox 2006 stress-ω model, a Reynolds stress model, implemented in both the NASA Langley codes FUN3D and CFL3D, has been used to study a number of 2-D and 3-D cases. This study continues the assessments of the stress-ω model by simulating the flow over two wings: the DPW-W1 and the DLR-F11 wings. Using FUN3D, which uses unstructured grids, and CFL3D, which uses structured grids, the results were compared to solvers employing one- and two-equation turbulence models and experimental data. In general, in situations where experimental data is available, the stress-ω model performs as well or better than one- and two-equation models.}, number={5}, journal={JOURNAL OF AIRCRAFT}, author={Thompson, K. B. and Hassan, H. A.}, year={2015}, pages={1668–1680} }
 @article{fulton_edwards_hassan_mcdaniel_goyne_rockwell_cutler_johansen_danehy_2014, title={Large-Eddy/Reynolds-Averaged Navier-Stokes Simulations of Reactive Flow in Dual-Mode Scramjet Combustor}, volume={30}, ISSN={["1533-3876"]}, DOI={10.2514/1.b34929}, abstractNote={Numerical simulations of the turbulent reactive flow within a model scramjet combustor configuration, experimentally mapped at the University of Virginia’s Scramjet Combustion Facility at an equivalence ratio of 0.17, are described in this paper. A hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes method is used, with special attention focused on capturing facility-specific effects, such as asymmetric inflow temperature distributions, on flow development within the combustor. Predictions obtained using two nine-species hydrogen oxidation models are compared with experimental data obtained using coherent anti-Stokes Raman spectroscopy, hydroxyl radical planar laser-induced fluorescence, stereoscopic particle image velocimetry, and focusing schlieren techniques. The large-eddy simulation/Reynolds-averaged Navier–Stokes models accurately capture the mean structure of the fully developed flame but tend to overpredict fluctuation levels toward the outer edge of the reactive plume. Model predictions ...}, number={3}, journal={JOURNAL OF PROPULSION AND POWER}, author={Fulton, Jesse A. and Edwards, Jack R. and Hassan, Hassan A. and McDaniel, James C. and Goyne, Christopher P. and Rockwell, Robert D. and Cutler, Andrew D. and Johansen, Craig T. and Danehy, Paul M.}, year={2014}, pages={558–575} }
 @article{gieseking_choi_edwards_hassan_2011, title={Compressible-Flow Simulations Using a New Large-Eddy Simulation/Reynolds-Averaged Navier-Stokes Model}, volume={49}, ISSN={["1533-385X"]}, DOI={10.2514/1.j051001}, abstractNote={A new hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes simulation (LES/RANS) method is presented in this work. In this approach, the resolved turbulence kinetic energy, ensemble-averaged modeled turbulence kinetic energy and turbulence frequency, and time-resolved turbulence frequency are used to form an estimate of an outer-layer turbulence length scale that is nearly Reynolds-number-independent. The ratio of this outer-layer scale with an inner-layer length scale (proportional to the wall distance) is used to construct a blending function that facilitates the shift between an unsteady RANS formulation near solid surfaces and a LES formulation away from the wall. The new model is tested through simulations of compressible flat-plate boundary layers over a widerangeofReynoldsnumbersandMach2.86 flowoverasmoothcompressionramp.Theresultsshowthatthenew modelpredicts mean andsecond-moment statistics that arein goodagreement withexperiment andare comparable with those obtained using an earlier model (Edwards, J. R., Choi, J-I., and Boles, J. A., “Hybrid Large-Eddy/ Reynolds-Averaged Navier–Stokes Simulation of a Mach-5 Compression Corner Interaction,” AIAA Journal, Vol. 464, 2008, pp. 977–991.) which required a case-by-case calibration of a model constant.}, number={10}, journal={AIAA JOURNAL}, author={Gieseking, Daniel A. and Choi, Jung-Il and Edwards, Jack R. and Hassan, Hassan A.}, year={2011}, month={Oct}, pages={2194–2209} }
 @article{keistler_hassan_2010, title={Simulation of Supersonic Combustion Involving H-2/Air and C2H4/Air}, volume={48}, ISSN={["1533-385X"]}, DOI={10.2514/1.43213}, abstractNote={A turbulence model that calculates the turbulent Prandtl and Schmidt numbers as part of the solution is presented. This model also accounts for compressibility effects, and addresses turbulence/chemistry interaction. Its predictions are compared with two experiments: an axisymmetric case involving mixing, hydrogen combustion, and ethylene combustion; and a three-dimensional ethylene mixing experiment. Fair to good agreement is indicated in the cases where data is available. Chemical mechanisms are found to have an influence on autoignition for hydrogen combustion cases, and on ignition location and flame size for hydrogen/ethylene combustion cases using reduced mechanisms.}, number={1}, journal={AIAA JOURNAL}, author={Keistler, P. G. and Hassan, H. A.}, year={2010}, month={Jan}, pages={166–173} }
 @article{bynum_hollis_hassan_xiao_2008, title={Turbulent aeroheating on the mars science laboratory entry vehicle}, volume={22}, ISSN={["1533-6808"]}, DOI={10.2514/1.33281}, abstractNote={A series of calculations are carried out for a Mars Science Laboratory entry vehicle heat shield and compared with tests carried out in the Arnold Engineering Development Center for Mach 8 and 10 and a range of Reynolds numbers. Three turbulence models are employed that are implemented in the LAURA code: the Cebeci-Smith algebraic model, the 98 Wilcox k − ω model, and the k − ζ model. In general, good agreement is indicated with turbulent predictions. Because the flow is attached, the algebraic model performs as well as other models.}, number={2}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Bynum, Michael D. and Hollis, Brian R. and Hassan, H. A. and Xiao, X.}, year={2008}, pages={306–309} }
 @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{xiao_edwards_hassan_2004, title={Blending functions in hybrid large-eddy/Reynolds-averaged Navier-Stokes simulations}, volume={42}, ISSN={["0001-1452"]}, DOI={10.2514/1.2094}, abstractNote={Several blending functions for use in hybrid large-eddy simulation (LES)/Reynolds-averaged Navier-Stokes (RANS) simulations of shock-separated flows are tested. The blending functions shift the turbulence closure from a k-ζ turbulence model near solid surfaces to a k − ∆ subgrid closure away from the wall. Three distinct forms for the blending function are developed: one that depends on the ratio of the von Karman length scale and the Taylor microscale, another that depends on the ratio of the RANS eddy viscosity to the subgrid eddy viscosity, and a third which replaces the von Karman length scale in the first form with the distance to the nearest wall. Comparisons are made for two cases: Mach 2.79 flow over a 20-deg compression corner and Mach 2.88 flow over a 25-deg compression/expansion corner. Inflow boundary conditions for all calculations employ the rescaling/reintroducing procedure developed by Xiao et al. (Xiao, X., Edwards, J. R., Hassan, H. A., and Baurle, R. A., "Inflow Boundary Conditions for Hybrid Large Eddy/Reynolds Averaged Navier-Stokes Simulations," AIAA Journal ,V ol. 41, No. 8, 2003, pp. 1481-1489) for hybrid LES/RANS simulations of wall-bounded flows. In general, the blending function based on the von Karman length scale gives the best results when compared with measured data. The skin friction predictions show the highest sensitivity to the various blending functions.}, number={12}, journal={AIAA JOURNAL}, author={Xiao, X and Edwards, JR and Hassan, HA}, year={2004}, month={Dec}, pages={2508–2515} }
 @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={An assessment of a hybrid large-eddy/Reynolds-averaged simulation (LES/RANS) procedure for high-speed, shock-separated flows is reported. A distance-dependent blending function is used to shift the turbulence closure fromMenter's k-w shear-stress-transport model near solid surfaces to a k-Δ subgrid closure away from solid surfaces and in free-shear regions. A modified recycling/rescaling procedure is used to generate time-dependent fluctuation data that are fed into the inflow plane for some calculations, with the goal being to replace the incoming boundary layer with a hybrid LES/RANS boundary layer that maintains nearly the same levels of fluctuation energy. Simulations of Mach 3 flow over a ramped-cavity configuration highlight the effects of grid refinement and choice of hybridization strategy, while simulations of Mach 3 flow over a 20-deg compression corner illustrate the effects of the choice of model constants and the inclusion of boundary-layer recycling on the mean-flow solutions.}, 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{baurle_tam_edwards_hassan_2003, title={Hybrid simulation approach for cavity flows: Blending, algorithm, and boundary treatment issues}, volume={41}, ISSN={["0001-1452"]}, DOI={10.2514/2.2129}, abstractNote={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}, number={8}, journal={AIAA JOURNAL}, author={Baurle, RA and Tam, CJ and Edwards, JR and Hassan, HA}, year={2003}, month={Aug}, pages={1463–1480} }
 @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{edwards_roy_blottner_hassan_2001, title={Development of a one-equation Transition/Turbulence model}, volume={39}, ISSN={["1533-385X"]}, DOI={10.2514/2.1526}, abstractNote={This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.}, number={9}, journal={AIAA JOURNAL}, author={Edwards, JR and Roy, CJ and Blottner, FG and Hassan, HA}, year={2001}, month={Sep}, pages={1691–1698} }
 @article{mcdaniel_hassan_2001, title={Study of transition in a high-disturbance environment}, volume={38}, ISSN={["0021-8669"]}, DOI={10.2514/2.2892}, abstractNote={A theory is developed for a form of bypass transition that is induced by a high-disturbance environment and is used to study transitional e ows at low speeds. It employs an approach similar to that developed for natural transition. In this approach, transitional e ows are treated in a turbulencelike manner, and transition onset and extentaredeterminedaspartofthesolution.Itisshownthatthisform ofbypasstransitionisaresultofareceptivity mechanism, where the disturbance is characterized by a scale different from that of Tollmien ‐Schlichting waves. The theory is calibrated and validated by considering a range of low-speed e ows, with high freestream turbulence intensities, in the presence and absence of pressure gradients, referred to as the T3 test cases. Excellent agreement with measurements is indicated. It is suggested that transition in one of the test cases, T3C4, is a result of the bursting of a laminar separation bubble.}, number={6}, journal={JOURNAL OF AIRCRAFT}, author={McDaniel, RD and Hassan, HA}, year={2001}, pages={1051–1055} }
 @article{mcdaniel_hassan_2001, title={Transition mechanisms in conventional hypersonic wind tunnels}, volume={38}, ISSN={["0022-4650"]}, DOI={10.2514/2.3691}, abstractNote={A recently developed theory that addresses bypass transition is used to study mechanisms responsible for transition in two-dimensional/axisymmetric e ows in conventional hypersonic wind tunnels. It is shown that transition in such facilities, where the intensity is in excess of 1%, is a result of a combined bypass/second-mode mechanism. This mechanism is validated by comparing predictions of the theory with heat transfer measurements carried out for straight and e ared sharp cones at zero angle of attack, a Mach number of 7.93, and unit Reynolds numbers of 1.6‐8.2 £ 10 6 /m. In general, good agreement with experiment is indicated. Nomenclature a = model constants (e rst-mode) a1‐a3 = model constants dee ned in Eq. (6) b = model constants (second-mode ) cπ = constant, 0.09 k = turbulent kinetic energy, m 2 /s 2 M = Mach number Q m = rms of mass e ux, kg/m 2 ¢s N m = mean mass e ux, kg/m 2 ¢s P = pressure, Pa qw = heat e ux at the wall, W/m 2 Re = Reynolds number}, number={2}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={McDaniel, RD and Hassan, HA}, year={2001}, pages={180–184} }
 @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={The k‐‡ transitional/turbulence model is used to study the transitional e ow over an elliptic cone of aspect ratio of 2:1 at Mach 8 and a range of Reynolds numbers. Although the cone guration has been the subject of detailed experimental and computational investigations, it has not been possible to determine with certainty the instability mechanisms responsible for transition. The present analysis suggests that none of the obvious mechanisms, i.e., second-mode or crosse ow, are responsible for the transition. Instead, a form of bypass transition resulting from large-amplitudedisturbancesappearsto reproducequitewell theexperimentally measured heat-transferdata and the onset and the extent of transition over a wide range of Reynolds numbers.}, number={6}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={Xiao, XD and Edwards, JR and Hassan, HA}, year={2001}, pages={941–945} }
 @article{czerwiec_edwards_rumsey_bertelrud_hassan_2000, title={Study of high-lift configurations using k-zeta transition/turbulence model}, volume={37}, ISSN={["0021-8669"]}, DOI={10.2514/2.2728}, abstractNote={The flow over the multi-element McDonnell Douglas configuration is computed using the κ-ζ transition/turbulence model. The model is capable of calculating transition onset as part of the solution at a cost comparable to Navier-Stokes solvers that employ two-equation models. The model is first incorporated into CFL3D and then used to calculate flows for two angles of attack, 8 and 19 deg, at a freestream Mach number of 0.2 and a Reynolds number of 9 x 10 6 . In general, good agreement is indicated for predicting transition onset and velocity profiles over sections of the main airfoil and flap. Most of the differences between computation and experiment are in the prediction of the extent and penetration of the slat wake at the 19-deg angle-of-attack case. Even for this case relative differences were less than 5%}, number={6}, journal={JOURNAL OF AIRCRAFT}, author={Czerwiec, R and Edwards, JR and Rumsey, CL and Bertelrud, A and Hassan, HA}, year={2000}, pages={1008–1016} }
 @article{mcdaniel_nance_hassan_2000, title={Transition onset prediction for high-speed flow}, volume={37}, ISSN={["0022-4650"]}, DOI={10.2514/2.3579}, abstractNote={An approach that treats nonturbulent e uctuations in a turbulencelike manner and determines onset and extent of transition as part of a e ow calculation isused to study transition athigh Mach numbers. Threesetsof previously obtained experimental data involving straight and e ared cones at zero angle of attack are used to calibrate and validate the model. Two sets, at Mach numbers 3.5 and 6, were carried out in quiet tunnels, and the third set was carried out at a Mach number of 8 in a conventional tunnel. The results suggest that the second mode is not the only mode responsible for transition at high Mach numbers. In general, fair to good agreement with measured recovery factors, adiabatic wall temperatures, and heat-transfer rates is indicated.}, number={3}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={McDaniel, RD and Nance, RP and Hassan, HA}, year={2000}, pages={304–309} }
 @article{nance_hollis_horvath_alter_hassan_1999, title={Computational study of hypersonic transitional wake flow}, volume={13}, ISSN={["1533-6808"]}, DOI={10.2514/2.6441}, abstractNote={A study of transition and turbulence in hypersonic blunt-body wake flows is presented. The current approach combines the A>£ turbulence closure model with a newly developed transition prediction method. This method utilizes results from linear stability theory and treats transitional flows in a turbulence-like manner. As a result, the onset and extent of transition are determined as part of the solution. The model is used to study flows past two spherically blunted 70-deg cone geometries at Mach 6 and 10. Two mechanisms of instability are examined. Comparison between computation and experiment suggests that for the cases considered, transition is a result of the instability of the free shear layer emanating from the shoulder region.}, number={2}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Nance, RP and Hollis, BR and Horvath, TJ and Alter, SJ and Hassan, HA}, year={1999}, pages={236–242} }
 @article{warren_hassan_1998, title={Alternative to the e(n) method for determining onset of transition}, volume={36}, ISSN={["0001-1452"]}, DOI={10.2514/2.361}, abstractNote={We employ a two-equation model similar to that employed in turbulent calculations. It is based on the premise that, if a flow quantity can be written as the sum of a mean and a fluctuating quantity, then the exact equations that govern the fluctuations and their averages are identical irrespective of the nature of the oscillations, i.e., laminar, transitional, or turbulent}, number={1}, journal={AIAA JOURNAL}, author={Warren, EW and Hassan, HA}, year={1998}, month={Jan}, pages={111–113} }
 @article{robinson_hassan_1998, title={Further development of the k-zeta (enstrophy) turbulence closure model}, volume={36}, ISSN={["0001-1452"]}, DOI={10.2514/2.298}, abstractNote={The k‐‡ model is extended to the study of two-dimensional and three-dimensional separated external e ows where Morkovin’ s hypothesis is expected to hold. The resulting model is free of damping and wall functions and is coordinate independent. Further, all modeled correlations are tensorially consistent and Galilean invariant. Applications include a variety of separated e ows over airfoils and a cylinder/offset e are juncture. Comparisons are made with other turbulence models and experiment. In general, good agreement with experiment is indicated. The results demonstrate that it is possible to develop a two-equation turbulence model that is capable of predicting separated e ows without sacrie cing performance for free shear layers.}, number={10}, journal={AIAA JOURNAL}, author={Robinson, DF and Hassan, HA}, year={1998}, month={Oct}, pages={1825–1833} }
 @article{rao_hassan_1998, title={Modeling turbulence in the presence of adverse pressure gradients}, volume={35}, ISSN={["0021-8669"]}, DOI={10.2514/2.2328}, abstractNote={In an attempt to model a recent set of experiments by Sknre and Krogstad dealing with equilibrium boundary layers near separation, it became clear that the traditional k-co model was unable to reproduce the data. Careful investigation of the data suggested that the diffusion term in the k equation behaves differently in the presence and absence of unfavorable pressure gradients. This led to the conclusion that an important diffusion mechanism was missing from the k equation and a new diffusion model was proposed. The results of the new theory indicate marked improvement when compared with the data for strong adverse pressure gradient flows. Moreover, the new theory reproduces Strafford's limit of velocity in a region of vanishing shear sn'ess. However, because subsonic and supersonic boundary layers act differently in the presence of an adverse pressure gradient, no adjustments in the diffusion term is recommended for supersonic flows in the presence of mild adverse pressure gradients. It is a known fact that traditional turbulence models are somewhat inadequate when it comes to predicting flows with an adverse pressure gradient I. This is a result of prevailing modeling practices. Whether we deal with one-equation, two-equation, or a su'ess model, current modeling does not address situations where adverse pressure gradients play a role. Thus, we use results from the decay of homogeneous turbulence, the log-law region, and asymptotic expansions along turbolent-nonturbulent boundaries to determine model constants 1. There is no reason to expect that such practices will produce turbulence models that are valid in the presence of unfavorable pressure gradients. * Research Assistant, Mechanical and Aerospace Engineering, Student Member AIAA. t Professor. Mechanical and Aerospace Engineering, Associate Fellow AIAA. Copyright © 1996 American lnstitum of Aeronautics and Aslxonautics, Inc. All rights reserved. The situation has changed recently with the availability of well documented incompressible experiments describing equilibrium boundary layers near separation 2"3. As is shown in Ref. 3, the diffusion term in the k equation behaves differently in the presence and absence of pressure gradients. This led us to the conclusion that an important diffusion mechanism is missing from the k equation. The objective of this investigation is to show that there is indeed a missing term resulting from the traditional neglect of the term _ , where p'and u[are the pressure and velocity fluctuations. Moreover, it results in improved agreement between theory and experiment for low speed flows. However, subsonic and supersonic boundary layers are known 4 to behave differently in the presence of adverse pressure gradients. As a result, a modification like the one suggested here is not expected to apply for all Mach numbers. It has been suggested that compt_sion associated with an adverse pressure gradi_ is associated with an increase in skin friction and a decrease in boundary layer thickness at supenmnic speeds. This would suggest that some modification of the proposed turbulence model is required. While examining the experiment of Fernando and Stairs 5, we discovered that a traditional k-co model was quite satisfactory. As a result, it is concluded that adjustment in the diffusion term is only required for subsonic flows. The application of an adverse pressure gradient on a wall bounded flow promotes separation of the boundary layer. Thus, we use the theoretical behavior of turbulent boundary layers near separation to investigate current modeling practice. The only term that requires modeling in the k equation is the diffusion term 1. Traditionally, it is modeled as 1 ' ' ' = -_tO "*_k _puiuiu j + p'u/ ' Oxj (D 1 American Institute of Aeronautics and Astronautics wherei3is thedensity, k is the turbulent kinetic energy, I-t is the turbulent viscosity, and c" is a model constant. The applicability of this model near separation is evaluated for an incompressible flow. In the near wail region, the Wilcox k-co model reduces to c3P Oz o = -_+_(2) ox oy r at1 (au): 13,coi o = ÷v,t _ (3) a F am-1 (av_ 2 _ 2 (4) where the turbulent viscosity is defined as k v, = -, (5) 0} P is the pressure, x is the shear stress, k is the turbulent kinetic energy, and co is the specific dissipation rate. The values of the model constants are 5 3 13" 9 a = ,_, 13= _, = y-_ (6) 1 1 o" = 5., a= 5. (7) Integration of Eq. (2) gives aP au z = ,_,, +y_ = _t,_ (8) where "c,, is the wall shear stress. In regions where "¢w_ O, Stratford 6 showed that U has the form u = 2 (J-P_)/go' P' = la._.e pi_x (9) where K o is typically a constant of about 0.5. Equation (9) was later confirmed by Townsend 7 using the data of Sehubauer and Klebanof-f 8. The velocity gradient given by Eq. (9) is}, number={3}, journal={JOURNAL OF AIRCRAFT}, author={Rao, MS and Hassan, HA}, year={1998}, pages={500–502} }
 @article{nance_hash_hassan_1998, title={Role of boundary conditions in Monte Carlo simulation of microelectromechanical systems}, volume={12}, ISSN={["0887-8722"]}, DOI={10.2514/2.6358}, number={3}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Nance, RP and Hash, DB and Hassan, HA}, year={1998}, pages={447–449} }
 @article{warren_hassan_1998, title={Transition closure model for predicting transition onset}, volume={35}, ISSN={["0021-8669"]}, DOI={10.2514/2.2368}, number={5}, journal={JOURNAL OF AIRCRAFT}, author={Warren, ES and Hassan, HA}, year={1998}, pages={769–775} }
 @article{robinson_hassan_1998, title={Two-equation turbulence closure model for wall bounded and free shear flows}, volume={36}, ISSN={["0001-1452"]}, DOI={10.2514/2.360}, abstractNote={The κ-ζ model can be used for both wall bounded and free shear flows using one set of model constants}, number={1}, journal={AIAA JOURNAL}, author={Robinson, DF and Hassan, HA}, year={1998}, month={Jan}, pages={109–111} }
 @article{brauns_hassan_1997, title={Novel approach for calculating equilibrium radiating flows}, volume={11}, ISSN={["1533-6808"]}, DOI={10.2514/2.6200}, number={1}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Brauns, FJ and Hassan, HA}, year={1997}, pages={52–58} }
 @article{alexopoulos_hassan_1997, title={k-zeta (enstrophy) compressible turbulence model for mixing layers and wall bounded flows}, volume={35}, ISSN={["0001-1452"]}, DOI={10.2514/2.219}, abstractNote={We extend the κ-ζ model of Robinson et al. to compressible turbulent flows. The success of the κ-ζ in reproducing a variety of incompressible flows should provide a good basis for the current model. As in the incompressible model, the current model will be based on the exact compressible equations to ensure that the correct physics is incorporated.}, number={7}, journal={AIAA JOURNAL}, author={Alexopoulos, GA and Hassan, HA}, year={1997}, month={Jul}, pages={1221–1224} }