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NASA NTRS2003

Grid-Independent Large-Eddy Simulation in Turbulent Channel Flow using Three-Dimensional Explicit Filtering

In this paper, turbulence-closure models are evaluated using the 'true' LES approach in turbulent channel flow. The study is an extension of the work presented by Gullbrand (2001), where fourth-order commutative filter functions are applied in three dimensions in a fourth-order finite-difference code. The true LES solution is the grid-independent solution to the filtered governing equations. The solution is obtained by keeping the filter width constant while the computational grid is refined. As the grid is refined, the solution converges towards the true LES solution. The true LES solution will depend on the filter width used, but will be independent of the grid resolution. In traditional LES, because the filter is implicit and directly connected to the grid spacing, the solution converges towards a direct numerical simulation (DNS) as the grid is refined, and not towards the solution of the filtered Navier-Stokes equations. The effect of turbulence-closure models is therefore difficult to determine in traditional LES because, as the grid is refined, more turbulence length scales are resolved and less influence from the models is expected. In contrast, in the true LES formulation, the explicit filter eliminates all scales that are smaller than the filter cutoff, regardless of the grid resolution. This ensures that the resolved length-scales do not vary as the grid resolution is changed. In true LES, the cell size must be smaller than or equal to the cutoff length scale of the filter function. The turbulence-closure models investigated are the dynamic Smagorinsky model (DSM), the dynamic mixed model (DMM), and the dynamic reconstruction model (DRM). These turbulence models were previously studied using two-dimensional explicit filtering in turbulent channel flow by Gullbrand & Chow (2002). The DSM by Germano et al. (1991) is used as the USFS model in all the simulations. This enables evaluation of different reconstruction models for the RSFS stresses. The DMM consists of the scale-similarity model (SSM) by Bardina et al. (1983), which is an RSFS model, in linear combination with the DSM. In the DRM, the RSFS stresses are modeled by using an estimate of the unfiltered velocity in the unclosed term, while the USFS stresses are modeled by the DSM. The DSM and the DMM are two commonly used turbulence-closure models, while the DRM is a more recent model.

Gullbrand, Jessica↗
NASA NTRS1991

Near-wall turbine closure for curved flows

At present, turbulence closures for curved flows only account for curvature effects in the fully turbulent region where the Reynolds number is large. The justification is that, near a wall, viscous effects dominate and curvature effects are only of secondary importance. Recent direct simulation data show that this assumption is not valid, even for simple two-dimensional fully developed turbulent curved channel flows. This paper presents an approach to develop a near-wall turbulence closure for wall-bounded curved flows. The curved channel direct simulation data is used as a guide to held develop such a closure. The proposed closure has the unique property of approaching conventional high-Reynolds-number Reynolds-stress closures far away from the wall. Hence, curvature effects in both the near-wall and the fully turbulent parts of the flow are accounted for properly. Validations of the closure are carried out with a set of low-Reynolds-number simulation data and with experimental measurements at high Reynolds number. Good agreement is obtained in both cases; in particular, the anisotropic behavior of the normal stresses and the shear stress behavior near the convex and concave walls.

So, R. M. C.↗
NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the in- fluence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:1 prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morison, J. H.↗
NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the influence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:l prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morrison, J. H.↗
NASA NTRS1990

Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.

Haminh, Hieu↗
NASA NTRS1986

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Amano, R. S.↗
NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗
NASA NTRS1992

A mapping closure for turbulent scalar mixing using a time-evolving reference field

A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.

Girimaji, Sharath S.↗
NASA NTRS1988

Design of a nonsingular Level 2.5 second-order closure model for the prediction of atmospheric turbulence

The suitability of applying the Mellor and Yamada (1974, 1982) Level 2.5 second-order turbulence closure model to general circulation models is investigated by examining not only the scheme's simulation of fully (or nearly fully) developed turbulence, but also its simulation of rapidly growing or strongly decaying turbulence. The behavior of the model is presented over its entire domain of definition, with special consideration given to the pathologies of the model. The model is then modified for the case of growing turbulence to rectify some of its physical shortcomings for that case, and to remove the pathologies that prohibit its use in a general circulation model. The performance of the modified Level 2.5 model is compared to the performance of various other modified versions through the numerical simulation for a growing convective PBL. The results show that the modified Level 2.5 model is a viable candidate for the prediction of turbulence and the simulation of the PBL in general circulation models.

Helfand, H. M.↗
NASA NTRS1980

A Navier-Stokes fast solver for turbulence modeling applications

A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Murphy, J. D.↗
NASA NTRS1979

Numerical analysis of turbulent wakes of axial flow turbomachinery rotor blades

The wakes of rotor blades are turbulent, three-dimensional, and are subjected to curvature and rotation effects. The objective of this study is to predict the development of such wakes and compare the predictions with the existing data. A finite difference procedure is employed in the numerical analysis of the wake utilizing the continuity, momentum, and turbulence closure equations in the rotating curvilinear and non-orthogonal coordinate system. The turbulence closure is affected by the two equations model and the simplified Reynolds stress model. The predictions from both the models agree well with the mean velocity and the turbulence data.

Hah, C.↗
NASA NTRS2002

Cloud-Scale Numerical Modeling of the Arctic Boundary Layer

The research objective of this NASA grant-funded project was to determine in detail how large-scale processes. in combination with cloud-scale radiative, microphysical, and dynamical processes, govern the formation and multi-layered structure of Arctic stratus clouds. This information will be useful for developing and improving 1D (one dimensional) boundary layer models for the Arctic. Also, to quantitatively determine the effects of leads on the large-scale budgets of sensible heat, water vapor, and condensate in a variety of Arctic winter conditions. This information will be used to identify the most important lead-flux processes that require parameterization in climate models. Our approach was to use a high-resolution numerical model, the 2D (two dimensional) University of Utah Cloud Resolving Model (UU CRM), and its 1D version, the University of Utah Turbulence Closure Model (UU TCM), a boundary layer model based on third-moment turbulence closure, as well as a large-eddy simulation (LES) model originally developed by C.H. Moeng.

Kruegen, Steven K.↗
NASA NTRS1990

Analytical methods for the development of Reynolds stress closures in turbulence

Analytical methods for the development of Reynolds stress models in turbulence are reviewed in detail. Zero, one and two equation models are discussed along with second-order closures. A strong case is made for the superior predictive capabilities of second-order closure models in comparison to the simpler models. The central points are illustrated by examples from both homogeneous and inhomogeneous turbulence. A discussion of the author's views concerning the progress made in Reynolds stress modeling is also provided along with a brief history of the subject.

Speziale, Charles G.↗
NASA NTRS1995

Diagnostic Statistics for the Assessment and Characterization of Complex Turbulent Flows

A simple parameterization scheme for a complex turbulent flow using nondimensional parameters coming from the Reynolds stress equations is given. Definitions and brief descriptions of the physical significance of several nondimensional parameters that are used to characterize turbulence from the viewpoint of single-point turbulence closures are given. These nondimensional parameters reflect measures of (1) the spectral band width of the turbulence; (2) deviations from the ideal Kolmogorov behavior; (3) the relative magnitude, orientation, and temporal duration of the deformation to which the turbulence is subjected; (4) one and two-point measures of the large and small scale anisotropy of the turbulence; and (5) inhomogeneity. This is an attempt to create a more systematic methodology for the diagnosis and classification of turbulent flows as well as in the development, validation, and application of turbulence model strategies. The parameters serve also to indicate the adequacy of various assumptions made in single-point turbulence models and in suggesting the appropriate turbulence strategy for a particular complex flow. The compilation will be of interest to experimentalists and to those involved in either computing turbulent flows or whose interests lies in verifying the adequacy of the phenomenological beliefs used in turbulence closures.

Ristorcelli, J. R.↗
NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗
NASA NTRSDate not supplied

Flow Physics at a Large Rotor Tip Gap in a Multi-Stage Axial Compressor

The flow physics in a large rotor tip gap in a 1.5-stage axial compressor is investigated in the current study. The flow structure in the rotor tip region is complex with several dominant vortical structures of opposite rotation, resulting in inhomogeneous and highly anisotropic turbulence. Earlier measurements show that eddy viscosity is negative over large parts of the tip region and eddy viscosity varies among stress/strain components. The present study aims to understand how the complex nature of rotor tip leakage flow affects compressor performance when the tip gap size is greater than 4–5% of the rotor span, which is typical of advanced small core engines. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques are applied to study flow physics in a large rotor tip gap (5.5% of rotor span) in a 1.5-stage axial compressor. Calculated flow fields from the two different approaches are compared with available measurements and examined in detail. LES calculates the pressure rise in the present compressor fairly well, while URANS with a standard two-equation turbulence closure underpredicts the pressure rise by 15-20% of the measured values. The current study shows that URANS with the current turbulence closure produces much higher all-positive eddy viscosity in the tip-gap region compared to measurements and LES. The distribution of eddy viscosity in the URANS simulation is also wrong. Consequently, the flow in the tip region is highly damped with significantly larger blockage generation, which results in the tip leakage vortex (TLV) staying closer to the blade suction side compared to the measurement. When the TLV stays closer to the blade, both flow turning and the pressure rise across the compressor are reduced compared to the measurements. It appears that this effect is amplified by a large rotor tip gap.

tip gap↗
NASA NTRS1998

A Kinematically Consistent Two-Point Correlation Function

A simple kinematically consistent expression for the longitudinal two-point correlation function related to both the integral length scale and the Taylor microscale is obtained. On the inner scale, in a region of width inversely proportional to the turbulent Reynolds number, the function has the appropriate curvature at the origin. The expression for two-point correlation is related to the nonlinear cascade rate, or dissipation epsilon, a quantity that is carried as part of a typical single-point turbulence closure simulation. Constructing an expression for the two-point correlation whose curvature at the origin is the Taylor microscale incorporates one of the fundamental quantities characterizing turbulence, epsilon, into a model for the two-point correlation function. The integral of the function also gives, as is required, an outer integral length scale of the turbulence independent of viscosity. The proposed expression is obtained by kinematic arguments; the intention is to produce a practically applicable expression in terms of simple elementary functions that allow an analytical evaluation, by asymptotic methods, of diverse functionals relevant to single-point turbulence closures. Using the expression devised an example of the asymptotic method by which functionals of the two-point correlation can be evaluated is given.

Ristorcelli, J. R.↗