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NASA NTRS1982

Features of a reattaching turbulent shear layer subject to an adverse pressure gradient

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model

Driver, D. M.↗

NASA NTRS1987

Numerical study of finite-rate supersonic combustion using parabolized equations

A set of partial differential equations, describing the two-dimensional supersonic chemically-reacting flow of the hydrogen-air system, is formulated such that the equations are parabolic in the streamwise direction. A fully-implicit fully-coupled finite-difference algorithm is used to develop a computer code which solves the governing equations by marching in the streamwise direction. The combustion process is modeled by a two-step finite-rate chemistry whereas turbulence is simulated by an algebraic turbulence model. Results of two calculations of internal supersonic reacting flow show fairly good agreement with the results obtained by the more costly full Navier-Stokes procedure.

Chitsomboon, T.↗

NASA NTRS1989

Interaction of an oblique shock wave with turbulent hypersonic blunt body flows

A shock-on-shock interaction near the cowl lip of an engine inlet is studied numerically by solving the compressible full Navier-Stokes equations. The present study focuses on Edney's type III shock interference pattern in which the turbulent free shear layer impinges on the cowl lip (modeled as a cylinder). Van Leer's flux-vector splitting upwind MUSCL scheme is used in the solver with algebraic turbulence models. Turbulent solutions of surface pressures and heat fluxes along the cowl lip are in reasonably good agreement with experiment except in the local shear layer impingement region. The present study showed some indications that higher order turbulent models may be required to improve the solution near the free shear layer impingement region.

Moon, Young J.↗

NASA NTRS1999

Viscous Analysis of Ref. H Based Wing/Bodies

Computations have been performed on the baseline Reference H wing/body configuration, as well as the Wing 704 configuration, an optimized wing and fuselage combination derived from Ref. H through automated optimization. The parabolized Navier-Stokes solver UPS was employed with viscous terms in two directions in an effort to understand the source and level of potential viscous/inviscid interactions. The paper briefly describes the UPS code and the grids used to obtain the solutions before the discussion of results. Results of these computations indicate that viscous/inviscid interaction can contribute increments to both the pressure- and friction-related drag. Computations were performed for wind tunnel conditions-1.675% scale models at a Reynolds number of 4 million per foot. Turbulent flow results were obtained using the Baldwin-Lomax algebraic turbulence model and were compared with laminar flow results. The laminar flow fields were used to obtain upper bounds on potential interaction effects.

Lawrence, Scott L.↗

NASA NTRS1988

K-epsilon turbulence model assessment with reduced numerical diffusion for coaxial jets

A numerical study has been conducted to evaluate the performance of the k-epsilon turbulence model for axisymmetric, unconfined, swirling, and nonswirling coaxial jet flows. Two lower order schemes, hybrid and power-law, and two higher order schemes, flux-spline and bounded skew upwind differencing, were employed in this investigation. The predicted results indicate that the higher order numerical schemes have greater potential for future model improvements and complex flow calculations in terms of storage, accuracy, and execution time. For the nonswirling flow, computations using an algebraic stress model have also been presented.

Nikjooy, M.↗

NASA NTRS1991

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Hicks, Raymond M.↗

NASA NTRS1990

Extensions of algebraic image operators: An approach to model-based vision

Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

Lerner, Bao-Ting↗

NASA NTRS1989

On the modelling of scalar and mass transport in combustor flows

Results are presented of a numerical study of swirling and nonswirling combustor flows with and without density variations. Constant-density arguments are used to justify closure assumptions invoked for the transport equations for turbulent momentum and scalar fluxes, which are written in terms of density-weighted variables. Comparisons are carried out with measurements obtained from three different axisymmetric model combustor experiments covering recirculating flow, swirling flow, and variable-density swirling flow inside the model combustors. Results show that the Reynolds stress/flux models do a credible job of predicting constant-density swirling and nonswirling combustor flows with passive scalar transport. However, their improvements over algebraic stress/flux models are marginal. The extension of the constant-density models to variable-density flow calculations shows that the models are equally valid for such flows.

Nikjooy, M.↗

NASA NTRS1994

Modeling of Wall-Bounded Complex Flows and Free Shear Flows

Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope was the first to introduce this kind of constitutive relation to turbulence modeling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k-E eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown an encouraging success in modeling complex turbulent flows.

Shih, Tsan-Hsing↗

NASA NTRS2001

Turbulence Modeling Workshop

Advances in turbulence modeling are needed in order to calculate high Reynolds number flows near the onset of separation and beyond. To this end, the participants in this workshop made the following recommendations. (1) A national/international database and standards for turbulence modeling assessment should be established. Existing experimental data sets should be reviewed and categorized. Advantage should be taken of other efforts already under-way, such as that of the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) consortium. Carefully selected "unit" experiments will be needed, as well as advances in instrumentation, to fill the gaps in existing datasets. A high priority should be given to document existing turbulence model capabilities in a standard form, including numerical implementation issues such as grid quality and resolution. (2) NASA should support long-term research on Algebraic Stress Models and Reynolds Stress Models. The emphasis should be placed on improving the length-scale equation, since it is the least understood and is a key component of two-equation and higher models. Second priority should be given to the development of improved near-wall models. Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) would provide valuable guidance in developing and validating new Reynolds-averaged Navier-Stokes (RANS) models. Although not the focus of this workshop, DNS, LES, and hybrid methods currently represent viable approaches for analysis on a limited basis. Therefore, although computer limitations require the use of RANS methods for realistic configurations at high Reynolds number in the foreseeable future, a balanced effort in turbulence modeling development, validation, and implementation should include these approaches as well.

Rubinstein, R.↗

NASA NTRS1991

Nonlinear Reynolds stress model for turbulent shear flows

A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

Barton, J. Michael↗

NASA NTRS1980

A computational and experimental study of high Reynolds number viscous/inviscid interaction about a cone at high angle of attack

The flow over a 5 deg semi-angle cone at incidence in supersonic flow is studied as a model problem for the flow over aircraft forebodies. A computational method utilizing the conically symmetric Navier-Stokes equations is used to obtain theoretical flow results which are compared with experimental data from the Ames Research Center 6- by 6-Foot Wind Tunnel and with results from a cone model sting mounted on an F-15 aircraft. The computed results agree well with the wind-tunnel data but less well with the flight data. Modification of the algebraic turbulence model was necessary to reflect an apparent lower turbulence level in flight than was present in the wind tunnel.

Mcrae, D. S.↗

NASA NTRS1992

Comparison of turbulence models for powered-lift flow fields

The development of a practical turbulence model for the complex flows with strong streamline curvature associated with powered-lift aircraft was investigated. The approach was to modify existing models that were compatible with the widely used kappa-epsilon model already available in an existing 3D Navier-Stokes code. The state-of-the-art of current turbulence models was examined. Several models that provide curvature corrections to the kappa-epsilon model were numerically investigated. An algebraic Reynolds stress model, which provides additional physics, was also examined. Test cases including an impinging jet, an impinging jet in a crossflow, and two adjacent impinging jets with the resultant upwash fountain were calculated. The first two test cases could be modeled reasonsbly well with some of the models. The upwash fountain could not be modeled with sufficient accuracy, which is consistent with the findings of other investigators.

Roberts, Donald W.↗

NASA NTRS1993

Research activities at the Center for Modeling of Turbulence and Transition

The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.

Shih, Tsan-Hsing↗

NASA NTRS1996

Comparison of Turbulence Models for Nozzle-Afterbody Flows with Propulsive Jets

A numerical investigation was conducted to assess the accuracy of two turbulence models when computing non-axisymmetric nozzle-afterbody flows with propulsive jets. Navier-Stokes solutions were obtained for a Convergent-divergent non-axisymmetric nozzle-afterbody and its associated jet exhaust plume at free-stream Mach numbers of 0.600 and 0.938 at an angle of attack of 0 deg. The Reynolds number based on model length was approximately 20 x 10(exp 6). Turbulent dissipation was modeled by the algebraic Baldwin-Lomax turbulence model with the Degani-Schiff modification and by the standard Jones-Launder kappa-epsilon turbulence model. At flow conditions without strong shocks and with little or no separation, both turbulence models predicted the pressures on the surfaces of the nozzle very well. When strong shocks and massive separation existed, both turbulence models were unable to predict the flow accurately. Mixing of the jet exhaust plume and the external flow was underpredicted. The differences in drag coefficients for the two turbulence models illustrate that substantial development is still required for computing very complex flows before nozzle performance can be predicted accurately for all external flow conditions.

Compton, William B., III↗

NASA NTRS1998

Compressibility and Turbulence Effects Due to Airfoil Clocking in Axial Compressors

Axial compressors have inherently unsteady flow fields because of relative motion between rotor and stator airfoils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead to progressively more complex wake/wake and wake/airfoil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. In addition, as the Mach number increases the interaction between blade rows is intensified due to potential effects. The current study uses an unsteady, two-dimensional Navier-Stokes approach to investigate the unsteady aerodynamics of stator clocking in a 1-1/2 stage compressor, typical of high-pressure compressors used in advanced commercial jet engines. The effects of turbulence are modeled with both algebraic and two-equation models. Results include surface pressures, efficiencies, boundary layer quantities and turbulence quantities. In addition, the growth of turbulence and the effects of compressibility on airfoil are discussed.

Dorney, Daniel J.↗

NASA NTRS1993

A lag model for turbulent boundary layers developing over rough bleed surfaces

Boundary layer mass removal (bleed) through spanwise bands of holes on a surface is used to prevent or control separation and to stabilize the normal shock in supersonic inlets. The addition of a transport equation lag relationship for eddy viscosity to the rough wall algebraic turbulence model of Cebeci and Chang was found to improve agreement between predicted and measured mean velocity distributions downstream of a bleed band. The model was demonstrated for a range of bleed configurations, bleed rates, and local free stream Mach numbers. In addition, the model was applied to the boundary layer development over acoustic lining materials for the inlets and nozzles of commercial aircraft. The model was found to yield accurate results for integral boundary layer properties unless there was a strong adverse pressure gradient.

Lee, J.↗

NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗