Search

This paper develops a new approach for analysis of subgrid closures for turbulent combustion as modeled using direct quadrature (finite-rate chemistry) techniques. The approach, termed multiresolut...

The suction force at the leading edge of a round-nosed aerofoil is an important indicator of the state of the flow over the leading edge and, often, the entire aerofoil. The leading-edge suction parameter (LESP) is a non-dimensional version of this force. In recent works, the LESP was calculated with good accuracy for attached flows at low Reynolds numbers (10 000–100 000) from unsteady aerofoil theory. In contrast to this ‘inviscid’ LESP, results from viscous computations and experiments are used here to calculate the ‘viscous’ LESP on aerofoils undergoing pitching motions at low subsonic speeds. The LESP formulation is also updated to account for the net velocity of the aerofoil. Spanning multiple aerofoils, Reynolds numbers and kinematics, the cases include motions in which dynamic stall occurs with or without leading-edge vortex (LEV) formation. Inflections in the surface pressure and skin-friction distributions near the leading edge are shown to be reliable indicators of LEV initiation. Critical LESP, which is the LESP value at LEV initiation, was found to be nearly independent of pivot location, weakly dependent on pitch rate and strongly dependent on Reynolds number. The viscous LESP was seen to drop to near-zero values when the flow is separated at the leading edge, irrespective of LEV formation. This behaviour was shown to correlate well with the loss of streamline curvature at the leading edge due to flow separation. These findings serve to improve our understanding and extend the applicability of the leading-edge suction behaviour gained from earlier works.

This work summarizes the development and testing of a new family of chemical closure models for large-eddy simulation (LES) of turbulent combustion using finite-rate chemistry. The goal of this research is to provide a simple, yet effective model that provides a correction to the ‘laminar chemistry’ prediction formed by evaluating chemical production terms using filtered-mean data. The general model takes the form $\overline {\dot {{\omega }}_{s} (q)} =f(\overline {{q}},{\Delta } ,{\ldots } )\dot {{\omega }}_{s} (\overline {{q}})$ , where the enhancement factor, f, accounts for the effects of the subgrid fluctuations on apparent reactivity as expressed at a given mesh level. A form for the enhancement factor is derived by least-squares minimization (LSM) of a ‘reactivity functional’ connecting information at different mesh levels. A modified a priori analysis, in which simultaneous large-eddy simulations are performed on fine and coarse mesh levels, is used to identify candidate modeled forms for the enhancement factor. In the modified a priori analysis, coarse-mesh realizations are constrained by the filtered fine-mesh velocity, allowing eddy structures to be highly correlated. Several LSM variants are described and tested through comparisons with experimental data. The test cases include three experiments conducted at the University of Virginia’s supersonic combustion facility involving non-premixed hydrogen and partially-premixed ethylene combustion as well as a premixed propane-air flame in the Volvo Validation Rig. The results demonstrate the capability of the models to provide a consistent (if modest in some cases) improvement in predictive capability, relative to ‘laminar chemistry’, in a cost-effective manner.

Reynolds-averaged Navier–Stokes and hybrid large-eddy/Reynolds-averaged Navier–Stokes simulations of turbulent flow past an Aerospatiale A-Airfoil near stall at Rec=2.1×106, M=0.15, α=13.3 and a NA...

A hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes turbulence model is applied to compute the wave-front aberrations in an optical beam passing through a supersonic open cavity flow. Th...

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.

A large-eddy simulation/Reynolds-averaged Navier–Stokes model is applied to three high-speed mixing layers and three sonic injection flows to generate data suitable for evaluating two current Reynolds-averaged Navier–Stokes models for turbulent mass diffusivity. These models solve transport equations for concentration variance and dissipation rate and differ in the constitutive relation for the turbulent mass diffusivity and the form of the evolution equation for the dissipation rate. The predictive capability of the large-eddy simulation/Reynolds-averaged Navier–Stokes model is assessed through simulations of an air–air mixing-layer experiment and a sonic ethylene injection into a Mach 2.0 airstream. This model provides good predictions of the mean velocity, turbulence intensity, and rms temperature fluctuation throughout the shear layer flowfield but slightly over-predicts the spreading rate of the mixing layer. The simulation of the sonic injection is in generally good agreement with the experiment but...

A hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes turbulence model is used to simulate the Mach 6 flow around a scaled model similar to NASA’s Orion multipurpose crew vehicle. The results for surface pressure and heat transfer are compared with experimental data from previous base flow experiments conducted at the Calspan—University at Buffalo Research Center. Using the highest Reynolds number test case (11×106 based on capsule diameter), different numerical aspects of the hybrid approach are addressed, such as use of a low-dissipation scheme, a modification to the eddy-viscosity blending function, time-averaging results, filtering computational results, and sensitivity to grid resolution. In addition, results are compared with Reynolds-Averaged Navier–Stokes using Menter’s two-equation baseline model and to detached-eddy simulation predictions. By introducing a new modification to the blending from Reynolds-averaged Navier–Stokes to large-eddy simulation within boundary layers, very good agr...

The reactive flow through a model scramjet combustor is simulated using a hybrid large-eddy/Reynolds-averaged Navier–Stokes technique. The scramjet configuration considered is similar to the one investigated at the Institute for Chemical Propulsion of the DLR, German Aerospace Center. The model scramjet consists of 15 fuel-injecting holes, located on the base of a wedge-shaped fuel injector, through which hydrogen is injected at sonic conditions. In the present study, only five of the 15 fuel-injecting holes are considered, and periodicity is assumed in the spanwise direction. Several parametric studies are conducted with a view toward determining the sensitivities of the predictions to modeling and algorithmic variations. Different grids (two different topologies), flux reconstruction methods (total variation diminishing and piecewise parabolic method), reaction mechanisms, and inflow boundary conditions (uniform and nonuniform) are used. To enhance fuel–air mixing, a synthetic eddy method is used to gen...

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 ...

An inviscid theoretical method that is applicable to non-periodic motions and that accounts for large amplitudes and non-planar wakes (large-angle unsteady thin airfoil theory) is developed. A pitch-up, hold, pitch-down motion for a flat plate at Reynolds number 10,000 is studied using this theoretical method and also using computational (immersed boundary method) and experimental (water tunnel) methods. Results from theory are compared against those from computation and experiment which are also compared with each other. The variation of circulatory and apparent-mass loads as a function of pivot location for this motion is examined. The flow phenomena leading up to leading-edge vortex shedding and the limit of validity of the inviscid theory in the face of vortex-dominated flows are investigated. Also, the effect of pitch amplitude on leading-edge vortex shedding is examined, and two distinctly different vortex-dominated flows are studied using dye flow visualizations from experiment and vorticity plots from computation.

A hybrid Large Eddy simulation / Reynolds-Averaged Navier-Stokes turbulence model is applied to compute the wavefront aberrations in an optical beam passing through a supersonic open cavity flow. The turbulence model blends a RANS-type closure near solid walls with a subgrid model in the free-stream based on the ratios of estimated inner and outer turbulent length scales. The cavity geometry is modeled using an immersed boundary method, and an auxiliary flat plate simulation is performed to replicate the effects of the wind-tunnel boundary layer on the computed optical path difference. Two-dimensional proper orthogonal decomposition modes of the optical wavefront are computed; these compare favorably with wind tunnel data despite uncertainties about inflow turbulence levels and boundary layer thicknesses over the wind tunnel window. Dynamic mode decomposition of a planar wavefront spanning the entire cavity reveals that wavefront distortions are driven by shear layer oscillation at the Rossiter frequencies; these disturbances create eddy shocklets that propagate into the free-stream and create additional optical path disturbances.

Two large-eddy simulation/Reynolds-averaged Navier–Stokes models are applied to a shock/boundary interaction generated by a 20 deg compression corner. The models are designed to transition from unsteady Reynolds-averaged Navier–Stokes to large-eddy simulation as the boundary layer shifts from its logarithmic behavior to its wakelike response, but they differ in that one model requires a preselection of a model constant for each problem, while the other computes this constant as a function of local and ensemble-averaged turbulence properties. Predictions are compared with mean-flow and second-moment experimental data obtained at Princeton University. In general, calculatedmean-flow velocity, surface-pressure, and surface skin-friction distributions agree well with the experiment, with the most noticeable discrepancy being a slight overprediction of the level of upstream influence induced by the shock wave. Comparisons with mass-flux fluctuation intensity, Reynolds axial stress, and Reynolds shear-stress profiles are also presented. These show generally good agreement with experimental trends relating to Reynolds stress amplification and anisotropy modulation. The calculations also predict the existence of a low-frequency motion of the separation shock that is probably associated with the motion of the backflow region. Higher-frequency modulations of the shock front as induced by the passage of coherent, streaklike structures through the shock also appear to contribute to the measurable intermittency effects.

This work presents results from large-eddy/Reynolds-averaged Navier–Stokes (LES/RANS) simulations of the well-known Burrows–Kurkov supersonic reacting wall-jet experiment. Generally good agreement with experimental mole fraction, stagnation temperature, and Pitot pressure profiles is obtained for non-reactive mixing of the hydrogen jet with a non-vitiated air stream. A lifted flame, stabilized between 15 and 20 cm downstream of the hydrogen jet, is formed for hydrogen injected into a vitiated air stream. Flame stabilization occurs closer to the hydrogen injection location when a three-dimensional combustor geometry (with boundary layer development resolved on all walls) is considered. Volumetric expansion of the reactive shear layer is accompanied by the formation of large eddies which interact strongly with the reaction zone. Time averaged predictions of the reaction zone structure show an under-prediction of the peak water concentration and stagnation temperature, relative to experimental data, but display generally good agreement with the extent of the reaction zone. Reactive scalar scatter plots indicate that the flame exhibits a transition from a partially-premixed flame structure, characterized by intermittent heat release, to a diffusion-flame structure that could probably be described by a strained laminar flamelet model.

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.

SUMMARY This paper first applies a flux vector-type splitting method based on the numerical speed of sound for computing incompressible single and multifluid flows. Here, a preconditioning matrix based on Chorin's artificial compressibility concept is used to modify the incompressible multifluid Navier–Stokes equations to be hyperbolic and density or volume fraction-independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratios and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially nonoscillatory-type primitive variable extrapolations coupled with monotone upstream-centered schemes for conservation laws-type volume fraction recompressed reconstruction is used to maintain the preservation of sharp interface evolutions in multifluid flow simulations. Benchmark tests including a solid rotation test of a notched two-dimensional cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, and the Rayleigh–Taylor instability were chosen to validate the current incompressible multifluid methodology. An incompressible driven cavity was also chosen to check the robustness of the proposed method on the computation of single fluid incompressible flow problems. Copyright © 2011 John Wiley & Sons, Ltd.

The limits of linear superposition in two-dimensional high-rate low-Reynolds-number aerodynamics are examined by comparing the lift-coefficient history and flowfield evolution for airfoils undergoing harmonic motions in pure pitch, pure plunge, and pitch―plunge combinations. Using quasi-steady airfoil theory and Theodorsen's formula as predictive tools, pitching motions are sought that produce lift histories identical to those of prescribed plunging motions. It follows that a suitable phasing of pitch and plunge in a combined motion should identically produce zero lift, canceling either the circulatory contribution (with quasi-steady theory) or the combination of circulatory and noncirculatory contributions (with Theodorsen's formula). Lift history is measured experimentally in a water tunnel using a force balance and is compared with two-dimensional Reynolds-averaged Navier―Stokes computations and Theodorsen's theory; computed vorticity contours are compared with dye injection in the water tunnel. Theodorsen's method evinces considerable, and perhaps surprising, resilience in finding pitch-to-plunge equivalence of lift-coefficient―time history, despite its present application to cases in which its mathematical assumptions are demonstrably violated. A combination of pitch and plunge motions can be found such that net lift coefficient is nearly identically zero for arbitrarily high reduced frequency, provided that amplitude is small. Conversely, cancellation is possible at large motion amplitude, provided that reduced frequency is moderate. The product of Strouhal number and nondimensional amplitude is therefore suggested as the upper bound for when superposition and linear predictions remain valid in massively unsteady two-dimensional problems.

Computational predictions of transverse injection of air, helium, and ethylene into a Mach 1.98 crossflow of air are presented. A hybrid large-eddy simulation/Reynolds-averaged Navier―Stokes turbulence model is used. A blending function, dependent on modeled turbulence variables, is used to shift the turbulence closure from the Menter t-ω model near solid surfaces to a Smagorinsky subgrid model in the outer part of the incoming boundary layer and in the jet mixing zone. The results show reasonably good agreement with time-averaged Mie-scattering images of the plume structure for both helium and air injection and with experimental surface pressure distributions, even though the penetration of the jet into the crossflow is slightly overpredicted. Predictions of ethylene mole fraction at several transverse stations within the plume are in good agreement with time-averaged Raman-scattering mole-fraction data. The model results are used to examine the validity of the commonly used assumption of the constant turbulent Schmidt number in the intense mixing zone downstream of the injection location. The assumption of a constant turbulent Schmidt is shown to be inadequate for jet mixing dominated by large-scale entrainment.

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scramjet combustors. The experiment used either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state of the art for each modeling approach and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an overprediction of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/largeeddy simulations also overpredicted the mixing layer spreading rate for the helium case, while underpredicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared with their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure assumptions.

This work utilizes an immersed boundary (IB) method to simulate the effects of arrays of discrete bleed ports in controlling shock wave / turbulent boundary layer inter actions . Both Reynolds averaged Navier -Stokes (RANS) and hybrid large -eddy / Reynolds -averaged Navier -Stokes (LES/RANS) turbulence closures are used with the IB technique. The approach is validated by conducting simulations of Mach 2.5 flow over a perfo rated plate containing 18 individual bleed holes. Predictions of discharge coefficient as a function of bleed plenum pressure are compared with experimental data. Simulations of an impinging oblique shock / boundary layer interaction at Mach 2.45 with an d without active bleed control are also performed. The 68 -hole bleed plate is rendered as an immersed object in the computational domain. Wall pressure predictions show that, in general, the LES/RANS technique under -estimate s the upstream extent of axi al separation that occurs in the absence of bleed. Good agreement with P itot -pressure surveys throughout the interaction region is obtained, however. Active suction completely removes the separation region and induces local disturbances in the wall pres sure distributions that are associated with the expansion of the boundary layer fluid into the bleed port and its subsequ ent re -compression. Predicted Pitot -pressure distributions are in good agreement with experiment for the case with bleed. Swirl stre ngth probability -density distributions are used to estimate the evolution of turbulence length -sca les throughout the interaction, and the effects of bleed on the amplification of Reynolds stresses are highlighted. Finally, simple improvements to engineerin g-level bleed models are proposed based on the computational results.

This work presents an immersed-boundary technique for compressible, turbulent flows and applies the technique to simulate the effects of micro vortex generators in controlling oblique-shock/turbulent boundary-layer interactions. The Reynolds-averaged Navier-Stokes equations, closed using the Menter k-ω turbulence model, are solved in conjunction with the immersed-boundary technique. The approach is validated by comparing solutions obtained using the immersed-boundary technique with solutions obtained on a body-fitted mesh and with experimental laser Doppler anemometry data collected at Cambridge University for Mach 2.5 flow over single micro vortex generators. Simulations of an impinging oblique-shock boundary-layer interaction at Mach 2.5 with and without micro vortex-generator flow control are also performed, considering the development of the flow in the entire wind tunnel. Comparisons are made with experimental laser Doppler anemometry data and surface-pressure measurements from Cambridge University and an analysis of the flow structure is performed. The results show that three dimensional effects initiated by the interaction of the oblique shock with the sidewall boundary layers significantly influence the flow patterns in the actual experiment. The general features of the interactions with and without the micro vortex-generator array are predicted to good accord by the Reynolds-averaged Navier-Stokes/ immersed-boundary model.

Simulations of compressible boundary-layer flow at three different Reynolds numbers (Re δ = 5.59 × 10 4 , 1.78 × 10 5 , and 1.58 x 10 6 ) are performed using a hybrid large-eddy simulation/Reynolds-averaged Navier-Stokes method. Variations in the recycling/rescaling method, the higher order extension, the choice of primitive variables, the Reynolds-averaged Navier-Stokes to large eddy simulation transition parameters, and the mesh resolution are considered in order to assess the model. The results indicate that the present model can provide good predictions of the mean-flow properties, second-moment statistics, and structural features of the boundary layers considered. Normalized turbulent statistics in the outer layer are found to be independent of Reynolds number, similar to incompressible turbulent boundary layers.

We seek to extend the literature on sinusoidal pure-plunge of 2D airfoils at high reduced frequency and low Reynolds number, by including effects of camber and nonzero mean incidence angle. We compare experimental results in a water tunnel using dye injection and 2D particle image velocimetry, with a set of computations in 2D – Immersed Boundary Method and unsteady Reynolds-Averaged Navier Stokes. The Re range is from 10,000 to 60,000, based on free stream velocity and airfoil chord, chosen to cover cases where transition in attached boundary layers would be of some importance, and where transition would only occur in the wake. Generally at high reduced frequency there is no Reynolds number effect. Mean angle of attack has significance, notionally, depending on whether it is below or above static stall. Computations were found to agree well with experimentally-derived velocity contours, vorticity contours and momentum in the wake. As found previously for the NACA0012, varying Strouhal number is found to control the topology of the wake, while varying reduced amplitude and reduced frequency together, but keeping Strouhal number constant, causes wake vortical structures to scale with the reduced amplitude of plunge. Flowfield periodicity – as evinced from comparison of instantaneous and time-averaged particle image velocimetry – is generally attained after two periods of oscillation from motion onset.

Simulations of Mach 5 turbulent flow over a 28-deg compression corner are performed using a hybrid large-eddy/ Reynolds-averaged Navier-Stokes method. The model captures the mean-flow structure of the interaction reasonably well, with observed deficiencies relating to an underprediction of the displacement effects of the shock-induced separation region. The computational results provide some support for a recent theory concerning the underlying causes of low-frequency shock-wave oscillation. In the simulations, the sustained presence of a collection of streaks of fluid with lower/higher momentum than the average induces a low-frequency undulation of the separation front. Power spectra obtained at different streamwise stations are in good agreement with experimental results. Downstream of reattachment, the simulations capture a three-dimensional mean-flow structure, dominated by counter-rotating vortices that produce wide variations in the surface skin friction. Predictions of the structure of the reattaching boundary layer agree well with experimental pitot pressure measurements. In comparison with Reynolds-averaged model predictions, the hybrid large-eddy/Reynolds-averaged Navier-Stokes model predicts more amplification of the Reynolds stresses and a broadening of the Reynolds stress distribution within the boundary layer that is probably due to reattachment-shock motion.

This work focuses on the development of a complete particle tracking code, capable of coupling with the existing CFD code REACTMB, developed at NCSU and used for a variety of flow simulations using both LES and RANS methods. A complete framework has been developed, capable of finding the location of particles in multi-block curvilinear grids, interpolating solution values to exact particle location and advecting the particles under the influence of drag and other forces. The code has been parallelized using OpenMPI, and the algorithm accounts for particle information exchanged between various blocks and processors to successfully track a large number of particles. The drag forces are calculated based on the solution data generated by the REACTMB code, at every time step. To account for turbulence, the code uses a Discrete Random Walk (DRW) model, allowing for stochastic particle tracking to account for turbulent effects. The code is highly modular and flexible, thereby allowing addition of modules to account for higher complexities, in terms of force models and stochastic particle tracking.

An immersed boundary method for time-dependent, three-dimensional, incompressible flows is presented in this paper. The incompressible Navier-Stokes equations are discretized using a low-diffusion flux splitting method for the inviscid fluxes and second-order central-differences for the viscous components. Higher-order accuracy achieved by using weighted essentially non-oscillatory (WENO) or total variation diminishing (TVD) schemes. An implicit method based on artificial compressibility and dual-time stepping is used for time advancement. The immersed boundary surfaces are defined as clouds of points, which may be structured or unstructured. Immersed-boundary objects are rendered as level sets in the computational domain, and concepts from computational geometry are used to classify points as being outside, near, or inside the immersed boundary. The velocity field near an immersed surface is determined from separate interpolations of the components tangent and normal to the surface. The tangential velocity near the surface is constructed as a power-law function of the local wall normal distance. Appropriate choices of the power law enable the method to approximate the energizing effects of a turbulent boundary layer for higher Reynolds number flows. Five different flow problems (flow over a circular cylinder, an in-line oscillating cylinder, a NACA0012 airfoil, a sphere, and a stationary mannequin) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational and experimental results. Finally, the flow induced by realistic human walking motion is simulated as an example of a problem involving multiple moving immersed objects.

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. Because of the high Reynolds numbers involved, a formulation based on the Reynolds-averaged Navier-Stokes equations is developed. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study three cases involving shockwave/boundary-layer interaction at Mach numbers of 9.22, 8.18, and 5.0. In general, heat transfer prediction for separated flows showed improvement over traditional turbulence models in which the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is a key to bridging the gap between theory and experiment for hypersonic flows dominated by strong shock-wave/boundary-layer interactions.

An approach for assimilating trusted-source data as a potential means of reducing uncertainties in large-eddy simulations is presented in this paper. The approach is based on an interpretation of ensemble Kalman filtering as applied to statistically-stationary flows. The technique leads to a spatially and temporally varying source term that serves to steer a large-eddy simulation in the direction of trusted-source data without significantly affecting resolved-turbulence structural content. The approach has been tested for a reacting 2D hydrogen-air shear layer (with trusted-source data obtained from a concurrent fine-mesh large-eddy simulation) and for a 3D scramjet combustor (with trusted-source data coming from CARS and SPIV measurements). The results show the potential of the new method as a means of constraining a large-eddy simulation so that its statistics evolve more in accord with trusted-source data. Though applied to problems relevant to high-speed propulsion in this paper, the method is generally applicable to large-eddy simulations of statisticallystationary flows.

A procedure for simulating the injection of supercritical ethylene into nitrogen is used to investigate aspects of the injection of supercritical fuels, considered to be an enabling technology in the design of hydrocarbons-fueled scramjet engines. The method solves the compressible Navier-Stokes equations for an ethylene/nitrogen mixture, with the thermodynamic behavior of ethylene described using the Peng-Robinson equation of state. Homogeneous equilibrium and finite-rate phase-transition models are used to describe the growth of a condensed ethylene phase in several axisymmetric and three-dimensional injector nozzles. Predictions are compared with shadowgraph and direct-lighting imaging data, mass flow rate measurements, mole-fraction and temperature measurements in the jet mixing zone, and wall pressure distributions. Qualitative trends relating to jet structure, the appearance of a condensed phase, and the effects of back pressure and injectant temperature are in good agreement with experimental results but indicate the need for improved characterization of the nozzle flow before injection and the inclusion of a better turbulence model for the jet mixing zone. For conditions where both are applicable, a nucleation/ growth phase transition model provides a similar bulk fluid response as a homogeneous equilibrium model but also yields predictions of number density and average droplet size.

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.

An algorithm based on the combination of time-derivative preconditioning strategies with low-diffusion upwinding methods is developed and applied to multiphase, compressible flows characteristic of underwater projectile motion. Multiphase compressible flows are assumed to be in kinematic and thermodynamic equilibrium and are modeled using a homogeneous mixture formulation. Compressibility effects in liquid-phase water are modeled using a temperature-adjusted Tait equation, and gaseous phases (water vapor and air) are treated as an ideal gas. The algorithm is applied to subsonic and supersonic projectiles in water, general multiphase shock tubes, and a high-speed water entry problem. Low-speed solutions are presented and compared to experimental results for validation. Solutions for high-subsonic and transonic projectile flows are compared to experimental imaging results and theoretical results. Results are also presented for several multiphase shock tube calculations. Finally, calculations are presented for a high-speed axisymmetric supercavitating projectile during the important water entry phase of flight.

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.

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.

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

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

The development of a class of low-diffusion upwinding methods for computing dense gas-solid flows is presented in this work. An artificial compressibility/low-Mach preconditioning strategy is developed for a hyperbolic two-phase flow equation system consisting of separate solids and gas momentum and continuity equations. The eigenvalues of this system are used to devise extensions of the AUSM+ [1] and LDFSS [2] flux-splitting methods that provide high resolution capturing of bubble growth and collapse in gas-solid fluidized beds. Applications to several problems in fluidization are presented.

Computational and experimental results for pitching airfoils are used to study the time lag associated with boundary-layer convection, and to develop a model that can be used to augment inviscid theoretical methods for unsteady flows past airfoils to include the effects of trailing-edge separation and unsteady stall. Computations using an unsteady RANS code were used to obtain results for an airfoil in steady flow and for several pitch-up-return motions. The motions were selected such that stall occurred only due to trailing-edge separation without leading-edge vortex formation. A leading-edge suction parameter, from earlier research, is used as the variable to connect the aerodynamic state in unsteady motion with a steady state condition. The time lag between unsteady stall and steady stall from the CFD studies was seen to be constant for a given non-dimensional pitch rate. When separation is modeled in an inviscid method using a decambering flap and this decambering is applied with a time lag to provide viscous correction to inviscid unsteady calculations, the resulting predictions of stall, hysteresis loops, and reattachment agree fairly well with CFD results both for individual cases and for trends between motions. The method, when applied to experimental results for sinusoidal pitch motions from the literature, show good agreement. While further studies are needed to extend the range of validity of the findings, the results show promise for an approach to augmenting unsteady inviscid theory for the effects of trailing edge separation and stall.

A large-eddy simulation / Reynolds-averaged Navier-Stokes (LES/RANS) model is used to simulate a supersonic nozzle and diffuser with secondary mass injection, operating at low pressures and Reynolds number. Two simulations with varied back pressure are performed with the goal of assessing the ability to capture the location and strength of the shock train in the diffuser section. The model is able to accurately predict the location of the pressure rise in both cases, but the rate of pressure recovery at the wall is slower than indicated by experimental data. Analysis of the flow data shows the creation of persistent corner vortices that provide a pathway for upstream propagation of the back pressure, but otherwise the level of turbulence mixing between the boundary layer and free-stream in the vicinity of the pressure rise is low, and the performance of the hybrid LES/RANS model remains sensitive to the choice of wall model.

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.

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%

Methods for extending the AUSM+ low-diffusion flux-splitting scheme toward the calculation of real fluid flows at all speeds are presented. The single-phase behavior of the fluid is defined by the Sanchez-Lacombe equation of state, a lattice-fluid description. Liquid-vapor phase transitions are modeled through a homogeneous equilibrium approach. Time-derivative preconditioning is utilized to allow effective integration of the equation system at all flow speeds and all states of compressibility. Modifications to the preconditioned variant of AUSM+ necessary to preserve solution accuracy under such conditions are presented in detail. One-dimensional results are presented for the faucet problem, a classic test case for multifluid algorithms, as well as for liquid octane flow through a converging-diverging nozzle. Two-dimensional calculations are presented for water flow over a hemisphere/cylinder geometry and liquid carbon dioxide flow through a capillary nozzle

The development of an effective implicit integration strategy for two-dimensional (axisymmetric) combustion calculations at all speeds is presented. A time-derivative preconditioning technique is first combined with an implicit line relaxation algorithm to yield an approach capable of removing the acoustic time step restriction at low flow speeds while handling stiff chemical kinetics in a fully implicit fashion. Numerical performance is further improved through the addition of a full multigrid/full approximation storage (FMG-FAS) convergence acceleration strategy. Numerical simulations of a subsonic reacting shear layer (finite rate hydrogen-air chemistry), a subsonic bluff-body stabilized flame (mixing-limited methane-air chemistry), and a supersonic jet diffusion flame (finite rate hydrogen-air chemistry) are presented to test the basic attributes of the algorithm. Comparisons with experimental data are presented for all cases, and a detailed examination of the computational efficiency of the new procedure is conducted. The strengths and weaknesses of multigrid ideas for fully coupled combustion calculations are particularly highlighted.

Methods for extending the advective upwind splitting method (AUSM) family of low-diffusion flux-splitting schemes to operate effectively at all flow speeds are developed. The extensions developed are designed for use with time-derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the Mach number becomes small. Using this criterion, alternative definitions for the interface Mach numbers are developed, and methods for ensuring pressure-velocity coupling at low speeds are formulated. Results are presented for inviscid flows through a channel at various Mach numbers, developing viscous flow in a two-dimensional duct, driven-cavity flows at various Mach and Reynolds numbers, flow over a backward-facing step, and hydrogen-nitrogen mixing layers

This research has developed a new hybrid large-eddy /Reynolds-averaged Navier-Stokes turbulence closure strategy specifically designed for strongly interacting, wall-bounded flows. The model differs from its predecessor in that the need to pre-calibrate a model constant is removed through the use of ensemble-averaged turbulence information to estimate an outer-layer turbulence length scale. The model has been applied to a variety of shock / boundary layer interactions and has shown a good level of predictive capability for both mean and second-moment quantities. A specific result of the shock / boundary layer interaction study is a strong correlation between the most probable time of a fluid within the recirculation region formed through shock interaction and the dominant low-frequency signal of the interaction. This provides evidence that the appearance of a low-frequency mode of separation-shock unsteadiness is intimately connected with the structure of the backflow region and the mean entrainment patterns. With this knowledge in place, it may be possible to predict low-frequency dynamics of complicated interactions by examination of the mean structure of the interactions. The LES/RANS model was also tested for turbulent flow over an airfoil near static stall as an initial step toward its use in predicting dynamic stall

Hybrid large-eddy / Reynolds-averaged Navier–Stokes simulations of turbulence / chemistry interactions occurring within a ramp-injected, hydrogen-fueled scramjet combustor are presented in this work. The experimental geometry is one of several studied at the Universty of Virginia as part of the National Center for Hypersonic Combined Cycle Propulsion and consists of an isolator, a combustor, and an extender section. Data collected includes coherent anti-Stokes Raman spectroscopy (CARS) measurements of major species composition and temperature at several streamwise planes, stereoscopic particle image velocimetry (PIV) measurements, hydroxyl planar-induced fluorescence (OH-PLIF) imagery, wall pressure distributions, and line-of-sight profiles of temperature and water concentration obtained using tunable diode laser spectroscopy (TDLAS). This paper focuses on an equivalence ratio of 0.17, which does not produce enough heat release to force a shock train into the isolator. The computational methods utilize a hybrid fourth-order central-difference / upwind strategy to enable accurate resolution of turbulent structures and employ a nine-species hydrogen oxidation mechanism. Generally accurate predictions of temperature, velocity, and nitrogen mole fraction are achieved through a ‘laminar chemistry’ assumption for the filtered species production rates, though results do improve slightly with the use of a simple turbulence / chemistry subgrid closure model. The predictions are most sensitive to the choice of isolator inflow boundary condition, with the use of a recycling / rescaling technique to sustain turbulent fluctuations resulting in an ‘over-mixing’ effect immediately downstream of the fuel injector. Turbulence–chemistry interactions in the flameholding region are examined from the standpoint of laminar flamelet theory. A region of high scalar dissipation rate, coincident with the breakdown of the fuel plume and the interaction of a reflected shock wave with the plume, inhibits flame propagation, forming a ‘hole’ in the flame. Advection of cooler fluid downstream into regions of moderate scalar dissipation enlarges the ‘hole’, but eventually the flame reconnects. These results point to one potential disadvantage of fuel-air mixing technologies that enhance axial vorticity – even if conditions for combustion are favorable, high strain rates generated by the interaction and breakdown of vortex pairs can lead to flame suppression.

The development of a new flux-splitting approach for perfect-gas reacting-gas Navier-Stokes computations is presented in this work. Three distinct variants are proposed, each of which is designed to capture a stationary contact discontinuity without excess numerical diffusion while providing a monotone resolution of strong normal shock waves. The variants differ in their resolution of strong oblique shock waves and in their performance for unsteady flow situations. A straightforward extension of the methods to general flows in thermo-chemical non-equilibrium is also proposed, and the construction of robust approximate linearizations of the schemes is discussed. Comparisons of the new splittings with other upwinding techniques are presented for four steady-state test cases: Mach 8 viscous flow over a 15 ° wedge (perfect gas), Mach 6 viscous flow over a cone-flare configuration (perfect gas), Mach 16 viscous flow over a cylinder (five-species reacting-air), and a subsonic reacting shear layer (seven-species hydrogen-air chemistry). Shock tube simulations are also performed to ascertain the effectiveness of the schemes for unsteady flow situations. It is shown that the new methods combine the desirable traits of more sophisticated Godunov-type schemes in the resolution of discontinuities with the robustness and simplicity of flux-vector splittings.

Unsteady aerodynamic phenomena are encountered in a large number of modern aerospace and non-aerospace applications. Leading edge vortices (LEVs) are of particular interest because of their large impact on the forces and performance. In rotorcraft applications, they cause large vibrations and torsional loads (dynamic stall), affecting the performance adversely. In insect \ud flight however, they contribute positively by enabling high-lift flight. Identifying the conditions that result in LEV formation and modeling their effects on the flow is an important ongoing challenge. Perching (airfoil decelerates to rest) and hovering (zero freestream velocity) maneuvers are of special interest. In earlier work by the authors, a Leading Edge Suction Parameter (LESP) was developed to predict LEV formation for airfoils undergoing arbitrary variation in pitch and plunge at a constant freestream velocity. In this research, the LESP criterion is extended to situations where the freestream velocity is varying or zero. A point-vortex model based on this criterion is developed and results from the model are compared against those from a computational fluid dynamics (CFD) method. Abstractions of perching and hovering maneuvers are used to validate the low-order model's performance in highly unsteady vortex-dominated flows, where the time-varying freestream/translational velocity is small in magnitude compared to the other contributions to the velocity experienced by the leading edge region of the airfoil. Time instants of LEV formation, flow topologies and force coefficient histories for the various motion kinematics from the low-order model and CFD are obtained and compared. The LESP criterion is seen to be successful in predicting the start of LEV formation and the point-vortex method is effective in modeling the flow development and forces on the airfoil. Typical run-times for the low-order method are between 30-40 seconds, making it a potentially convenient tool for control/design applications.

We examine several eddy-viscosity turbulence models for their ability to reproduce the experimental data in a strong three-dimensional external-shock-wave-turbulent-boundary-layer interaction. The four models investigated are the zero-equation Baldwin-Lomax model, the one-equation models of Baldwin and Barth and of Spalart and Allmaras, and the two-equation k-e closure.

An evaluation of four one-equation eddy viscosity-transport turbulence closure models as applied to three-dimensional shock wave/boundary-layer interactions is presented herein. Comparisons of two versions of the Baldwin-Barth model, an approach of Edwards and McRae, and a modified form of the Spalart-Allmaras model are presented for two test cases, one involving Mach 8 flow over a flat plate/sharp fin apparatus and the other involving Mach 3 flow over a cylinder-offset-cone geometry. Strengths and weaknesses of the one-equation approaches are highlighted through direct comparison with experimental data, and the effect of grid refinement is examined.

A hybrid Large-Eddy Simulation/Reynolds-Averaged Navier-Stokes (LES/RANS) method is used to simulate the Mach 6 flow around a scaled model similar to NASA’s Orion Multi-Purpose Crew Vehicle (MPCV). The results for surface pressure and heat transfer are compared to experimental data from previous base flow experiments conducted at CUBRC. Using the highest Reynolds number test case (