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NASA NTRS1982

An experimental investigation and a numerical prediction of a transonic normal shock wave/turbulent boundary layer interaction

Detailed pitot, static and wall pressure measurements have been obtained for a transonic normal shock wave/turbulent boundary layer interaction at free-stream Mach numbers of 1.28, 1.37 and 1.48 and at a constant unit Reynolds number of 4.92 x 10 to the 6th per meter in an axisymmetric, internal flow. Measurements have also been obtained at a unit Reynolds number of 9.84 x 10 to the 6th per meter at a free-stream Mach number of 1.29. The interaction depends very strongly on the Mach number. The effect of Reynolds number under study is small. Flow confinement due to the wind-tunnel wall boundary layer produces a weaker interaction and a much larger supersonic tongue than is observed for planar flows. Comparisons are made with solutions to the time-dependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model (1980). The computations are in agreement with the experimental results.

Om, D.↗

NASA NTRS1983

An integral analysis of transonic normal shock wave/turbulent boundary layer interactions in internal flow

An approximate integral viscous-inviscid interaction method is presented for calculating the development of a turbulent boundary layer subjected to a normal shock wave induced adverse pressure gradient in an internal axisymmetric flow. The inflow conditions and the downstream pressure are provided for the computation. In the supersonic region of shock pressure rise, the Prandtl-Meyer function is used to couple the viscous and inviscid flows. An analytical model for the coupling process is postulated and appropriate equations are defined. Downstream of the sonic point, one-dimensional inviscid flow is assumed for coupling with the viscous flow. The turbulent boundary layer is calculated using Green's integral lag-entrainment method. Comparisons of the solutions with the experimental data are made for interactions which are unseparated, near separation and separated. For comparison purposes, solutions to the time-dependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model are also shown. The computed results from the integral method show good agreement with experimental data for unseparated interactions and reasonable agreement with the trend of the viscous effects when the interaction becomes increasingly separated.

Om, D.↗

NASA NTRS1978

An evaluation of several compressible turbulent boundary-layer models Effects of pressure gradient and Reynolds number

Computations, employing several turbulence models, are compared with a series of attached supersonic turbulent boundary-layer experiments over an extensive range of Reynolds numbers (11.7 x 10 to the 6th to 314 x 10 to the 6th). These experiments included measurements of surface pressure and skin friction for adverse pressure gradients ranging in magnitude from those of previous investigations to an order of magnitude greater. The turbulence models evaluated include algebraic and two-equation eddy-viscosity models and two full Reynolds stress models. In general all the models tested performed well independently of the magnitude of the pressure gradient or Reynolds number and could predict the measured skin friction for most cases with sufficient accuracy for engineering purposes.

Horstman, C. C.↗

NASA NTRS1981

Prediction of swirling reacting flow in ramjet combustors

Numerical computations have been undertaken for a basic two-dimensional axisymmetric flowfield which is similar to that found in conventional gas turbine and ramjet combustors. A swirling flow enters a larger chamber via a sudden or gradual expansion. The calculation method involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation turbulence energy-turbulence dissipation rate turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. The results include recirculation zone characterization and predicted mean streamline patterns. Predictions with and without chemical reaction are obtained. An associated isothermal experimental flow study is providing a useful data base. Successful outcomes of the work can be incorporated into the more combustion- and hardware-oriented activities of industrial concerns.

Lilley, D. G.↗

NASA NTRS1976

Computation of turbulent flows

The essential ingredients and the effectiveness of several levels of turbulent-flow partial differential equation models are considered. Zero-equation models use only the partial differential equation (pde) for the mean velocity field and do not employ turbulence pde's. One-equation models make use of an additional pde relating to the turbulence velocity scale. Attention is also given to two-equation models, stress-equation models, and large eddy simulations. Large-eddy simulations are concerned with a three-dimensional time-dependent numerical computation of the large-scale turbulence.

Reynolds, W. C.↗

NASA NTRS1977

A critical evaluation of invariant second-order closure models for subsonic boundary layers

Computations based on several second-order turbulence models, including full Reynolds stress and two-equation models, are compared with a number of boundary-layer experiments. In general, the models represent the data reasonably well, with skin friction tending to be somewhat overpredicted in the far downstream region of the adverse pressure gradient experiments. A discussion of the behavior of the ARAP full Reynolds stress model in predicting the components of the Reynolds stress tensor is given. It is concluded that compatibility at the wall may necessitate the use of more than one length scale.

Rubesin, M. W.↗

NASA NTRS1980

Progress in turbulence modeling for complex flow fields including effects of compressibility

Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.

Wilcox, D. C.↗

NASA NTRS1977

Turbulence modeling of shock separated boundary-layer flows

Computations of transonic and hypersonic shock-separated boundary-layer flows using zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence eddy viscosity models are described and compared with measurements. The computations make use of a new Navier-Stokes computer algorithm that has reduced computing times by one to two orders of magnitude. The algorithm, and how the turbulence models are incorporated into it, are described. Results for the transonic flow show that the unmodified one-equation model is superior to the zero-equation model in skin-friction predictions. For the hypersonic flow, a highly modified one-equation model that accurately predicts surface pressure and heat transfer is described. Preliminary two-equation model results are also presented.

Coakley, T. J.↗

NASA NTRS1977

Evaluation of turbulence models for three primary types of shock-separated boundary layers

Zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence eddy viscosity models were used in computing three basic types of shock-separated boundary-layer flows. The three basic types of shock boundary-layer interaction discussed are: (1) a normal shock wave at transonic speeds, (2) a compression corner shock at supersonic speeds, and (3) an incident oblique shock at hypersonic speeds. The models tested are simple, unmodified models used extensively for incompressible, unseparated flows. A comparison of computed and measured results for the compressible, separated flows described herein indicates that model performance is dependent on flow configuration with no distinct superiority of one model over the other for all three flow configurations.

Coakley, T. J.↗

NASA NTRS1979

Effects of turbulence model selection on the prediction of complex aerodynamic flows

Numerical simulations of viscous transonic flow over a circular-arc airfoil and in a diffuser are described. The simulations are made with a new computer program designed to serve as a tool in the development of improved turbulence models for complex flows. The program incorporates zero-, one-, and two-equation eddy viscosity models and includes a variety of subsonic and supersonic boundary conditions. The airfoil flow contains a shock-separated boundary-layer interaction that has resisted previous attempts at simulation. The diffuser flow also contains a shock-boundary-layer interaction, which has not been simulated previously. Calculations using standard turbulence models, developed originally for incompressible unseparated flows, are described. Results indicate that although there are interesting differences in predictions between the various models, none of them predict the flows accurately. Suggestions for improved turbulence models are discussed.

Coakley, T. J.↗

NASA NTRS1981

An experimental and computational investigation of the transport of Reynolds stress in an axisymmetric swirling boundary layer

A coordinated experimental and computational investigation of the transport and interaction of the individual Reynolds stresses within a turbulent axisymmetric swirling boundary layer flowing over a stationary cylinder is described. The cylinder is instrumented with new directional surface fence skin-friction gages developed for the experiment. The longitudinal and transverse mean velocity profiles are measured with a miniature directional pressure probe. These data provided a standard on which to compare computed results employing a variety of turbulence models. The turbulence models tested range from a simple mixing length model, through a two-equation model, on to the Reynolds stress equation models. The full Reynolds stress equation models are tested with various sets of modeling coefficients for the pressure rate-of-strain correlation. It is shown that while even the simplest model shows the general features of the data, agreement with the experimental data is enhanced through the use of the more complex models. For a better prediction of the data, however, further model improvement is still required.

Higuchi, H.↗

NASA NTRS1982

Flow aerodynamics modeling of an MHD swirl combustor - Calculations and experimental verification

This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Turbulence simulation is by way of a two-equation Kappa-epsilon model. The code produces as output the flowfield map of the nondimensional stream function, axial, and swirl velocity. Good agreement was obtained between the theoretical predictions and the qualitative experimental results. The best seed injector location for uniform seed distribution at combustor exit is with injector located centrally on the combustor axis at entrance to the second stage combustor.

Gupta, A. K.↗

NASA NTRS1978

Behavior of a turbulent boundary layer subjected to sudden transverse strain

Data from two experiments on the development of the components of the Reynolds stress tensor after a sudden application of transverse strain are compared. Computations were based on four different turbulence models: a first-order mixing length model, a second-order two-equation eddy viscosity model, and two second-order Reynolds stress models. The second-order models do not produce dramatic improvements over the simple mixing length model. The Reynolds stress models still need development to represent the physics of shear-strained turbulence well. Finally, it is demonstrated that the assumption of a scalar eddy viscosity, often used in engineering calculations of three-dimensional boundary layers, is quite reasonable.

Higuchi, H.↗

NASA NTRS1975

Influence of external disturbances and compressibility on free turbulent mixing

It is shown that disturbances in external flow can significantly affect, by as much as an order of magnitude, the turbulent mixing rate in free shear layers and that the length scale of the external flow disturbances is as important as the amplitude. The difference between the effect of wide-band and narrow-band disturbances is stressed. The model for pressure fluctuation term in the kinetic energy equation is included in a two-equation model. The reduced spreading rate in high Mach number, high Reynolds number, adiabatic, free turbulent shear layers is predicted.

Oh, Y. H.↗

NASA NTRSDate not supplied

Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor

Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.

LES↗

NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗

NASA NTRS1982

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

Baker, A. J.↗

NASA NTRS1983

Turbulence modeling methods for the compressible Navier-Stokes equations

Turbulence modeling methods for the compressible Navier-Stokes equations, including several zero- and two-equation eddy-viscosity models, are described and applied. Advantages and disadvantages of the models are discussed with respect to mathematical simplicity, conformity with physical theory, and numerical compatibility with methods. A new two-equation model is introduced which shows advantages over other two-equation models with regard to numerical compatibility and the ability to predict low-Reynolds-number transitional phenomena. Calculations of various transonic airfoil flows are compared with experimental results. A new implicit upwind-differencing method is used which enhances numerical stability and accuracy, and leads to rapidly convergent steady-state solutions.

Coakley, T. J.↗