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DOE OSTI2023

Advanced Turbulence Models for Large-Scale Atmospheric Boundary Layer Flows

We present high-fidelity large-eddy-simulation (LES) modeling approaches for the turbulent atmospheric boundary layer (ABL) flows. Wind energy is a prime example of an application driven by ABL. Generation of electrical energy from farms of wind turbines at night in the stable ABL is a particularly interesting situation. In this report, we consider the well-known GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) stably stratified benchmark LES case. We use a high-order spectral element code Nek5000/RS, which is supported under the DOE's Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms. In our earlier ANL report, we demonstrated our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. In this report, we extend the range of our SGS modeling approaches in the context of the mean-field eddy viscosity (MFEV), to include the solution of an SGS turbulent kinetic energy equation (TKE). We demonstrate the model fidelity of Nek5000/RS in comparison to that of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, with which we studied scaling performance for both codes in comparison on DOE's leadership computing platforms.

17 WIND ENERGY↗

NASA NTRS1976

Development of relaxation turbulence models

Relaxation turbulence models have been intensively studied. The complete time dependent mass averaged Navier-Stokes equations have been solved for flow into a two dimensional compression corner. A new numerical scheme has been incorporated into the developed computed code with an attendant order of magnitude reduction in computation time. Computed solutions are compared with experimental measurements of Law for supersonic flow. Details of the relaxation process have been studied; several different relaxation models, including different relaxation processes and varying relaxation length, are tested and compared. Then a parametric study has been conducted in which both Reynolds number and wedge angle are varied. To assess effects of Reynolds number and wedge angle, the parametric study includes the comparison of computed separation location and upstream extent of pressure rise; numerical results are also compared with the measurements of surface pressure, skin friction and mean velocity field.

Hung, C. M.↗

NASA NTRS1982

Compressibility effects in turbulence modeling

Numerical turbulence modeling is discussed with attention given to fluid property variations caused by compressibility in an adiabatic flow. The models are considered in terms of integral quantities expressed by ordinary differential equations and by those formulated as partial differential equations. Compressibility corrections for both integral and partial differential methods are reviewed. Eddy-viscosity models are explored for their capability to characterize the mass-weighted Reynolds stress, which can be accounted for with primitive and/or mass-weighted variables. Compressible flow simulations are currently constrained to low Re and zero mean dilation. The effects of compressibility are defined in wave number space by resolving the Fourier transforms of the velocity vectors into components which are perpendicular and parallel to the wave number vector. Statistical correlations then permit obtaining a value for each contribution.

Rubesin, M. W.↗

NASA NTRS1984

Swirl flow turbulence modeling

Confined turbulent swirling flow data obtained from a single hot-wire using a six-orientation technique are analyzed numerically. The effects of swirl strength and the presence of a strong contraction nozzle further downstream on deduced parameters is also presented and discussed for the case of chamber-to-inlet diameter ratio D/d = 2. Three swirl strengths are considered with inlet swirl vane angles of 0, 45 and 70 deg. A strong contraction nozzle with an area ratio of 4 is located two chamber-diameters downstream of the inlet to the flowfield. It is found that both the swirl strength and the contraction have strong effects on the turbulence parameters. Generally, the most dramatic effect of increase of swirl strength is the considerable increase in values of all the parameters considered, (rx-viscosity, kinetic energy of turbulence, length scales, and degree of nonisotropy). The presence of a strong contraction nozzle tends to increase the turbulence parameter values in regions of acceleration and to reduce them in deceleration regions. Based on similarity of viscosity and length scale profiles, a C sub mu formulation is deduced which is shown to improve the predictive capability of the standard k-epsilon turbulence model in swirling recirculating flows.

Abujelala, M. T.↗

NASA NTRS1995

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗

NASA NTRS1990

Near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

A near-wall turbulence model and its incorporation into a multiple-timescale turbulence model are presented. The near-wall turbulence model is obtained from a k-equation turbulence model and a near-wall analysis. In the method, the equations for the conservation of mass, momentum, and turbulent kinetic energy are integrated up to the wall, and the energy transfer and the dissipation rates inside the near-wall layer are obtained from algebraic equations. Fully developed turbulent channel and pipe flows are solved using a finite element method. The computational results compare favorably with experimental data. It is also shown that the turbulence model can resolve the overshoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

Kim, S.-W.↗

NASA NTRS1988

A near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

A near wall turbulence model and its incorporation into a multiple-time-scale turbulence model are presented. In the method, the conservation of mass, momentum, and the turbulent kinetic energy equations are integrated up to the wall; and the energy transfer rate and the dissipation rate inside the near wall layer are obtained from algebraic equations. The algebraic equations for the energy transfer rate and the dissipation rate inside the near wall layer were obtained from a k-equation turbulence model and the near wall analysis. A fully developed turbulent channel flow and fully developed turbulent pipe flows were solved using a finite element method to test the predictive capability of the turbulence model. The computational results compared favorably with experimental data. It is also shown that the present turbulence model could resolve the over shoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

Kim, S.-W.↗

NASA NTRS1987

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Kim, S.-W.↗

NASA NTRS1988

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

The paper presents a multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method. Consideration is given to a class of turbulent boundary layer flows and of separated and/or swirling elliptic turbulent flows. For the separated and/or swirling turbulent flows, the present turbulence model yielded significantly improved computational results over those obtained with the standard k-epsilon turbulence model.

Kim, S.-W.↗

NASA NTRS2006

Estimating Resolution Lengths of Hybrid Turbulence Models

A two-stage procedure has been devised for estimating the spatial resolution achievable in the simulation of a given flow on a given computational grid by a computational fluid dynamics (CFD) code that incorporates a hybrid model of turbulence. The hybrid models to which this procedure is especially relevant are those of the Reynolds-averaged Navier-Stokes (RANS) and the partial-averaged Navier-Stokes (PANS) approaches. This procedure represents the first step toward adding variable-resolution turbulence-modeling capabilities to CFD codes as part of a continuing effort to increase the accuracy and robustness of CFD simulations of unsteady flows. Some background information is prerequisite to a meaningful summary of the procedure. Among experts in CFD, it is well known that combination of the Reynolds-averaged Navier-Stokes (RANS) approach and eddy-viscosity turbulence models offers limited capability for simulating unsteady and complex flows. The RANS approach includes an assumption that most of the energy in a given flow is modeled through turbulence-transport equations and is resolved in a computational grid used to simulate the flow. RANS also overpredicts eddy viscosity, thereby yielding excessive damping of unsteady motion. The eddy viscosity attains an unphysically large value because of unresolved scales, and suppresses most temporal and spatial fluctuations in the resolved flow field. One approach used to overcome this deficiency is to provide a mechanism for the RANS equations to resolve motion only on the largest scales and to use a hybrid model to represent effects at smaller scales. The RANS approach involves the use of a standard two-equation turbulence model in which the effect of turbulence is summarized by a viscosity that is a function of (1) the time-averaged kinetic- energy density (k) associated with the local fluctuating (turbulent) component of flow and (2) the time-averaged rate of dissipation of the turbulent-kinetic- energy density ( ). In PANS, which was developed to overcome the grid dependency associated with other hybrid turbulence models (including that of RANS), the standard two-equation turbulence model is replaced by another two-equation model in which one solves for the previously unresolved k and , which are now allowed to vary in space and time.

Abdol-Hamid, Khaled S.↗

NASA NTRS1988

A finite element computation of turbulent boundary layer flows with an algebraic stress turbulence model

An algebraic stress turbulence model and a computational procedure for turbulent boundary layer flows which is based on the semidiscrete Galerkin FEM are discussed. In the algebraic stress turbulence model, the eddy viscosity expression is obtained from the Reynolds stress turbulence model, and the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale. Good agreement with experimental data is found for the examples of a fully developed channel flow, a fully developed pipe flow, a flat plate boundary layer flow, a plane jet exhausting into a moving stream, a circular jet exhausting into a moving stream, and a wall jet flow.

Kim, Sang-Wook↗

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 NTRS1986

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

Kim, Sang-Wook↗

NASA NTRS1989

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

Kim, S.-W.↗

NASA NTRS1993

Assessment and development of second order turbulence models

Second order turbulence models describe the effect of mean flow and external agencies (such as buoyancy) on the evolution of turbulence. Therefore, in principle, these models give a more accurate description of complicated flow fields (e.g. flows with large anisotropy in turbulence, such as near the leading edge of a turbine blade) than the two equation models. The objectives of this document are to assess the performance of the various second order turbulence models in benchmark flows and to seek improvements where necessary in models for the pressure correlation term in the scalar flux equation and for the scalar dissipation equation.

Shabbir, Aamir↗

NASA NTRSDate not supplied

HLPW-4: Turbulence Model Verification Study

Turbulence Model Verification study for the Fourth High Lift Prediction Workshop to be held at Aviation 2021

Turbulence Model Verification↗

NASA NTRS1995

Overview of turbulence model development and applications at Rocketdyne

This viewgraph presentation discusses turbulence modeling requirements, development philosophy, and approach; two major areas of concentration (high speed and low speed turbulence modeling); high speed turbulence modeling; compressibility effects; turbulence models adapted to USA code; M = 9.2 flat plate flow; Mach 7.05 flow over axisymmetric flare; Mach 8.6 flow over cold wall edge; low speed turbulence modeling; turbulence models being assessed; turbulence model deck structure and integration with Navier-Stokes solver; nonlinear algebraic-stress model; rotation modified k-epsilon model; and Reynolds stress model.

Hadid, A. H.↗

NASA NTRS1978

Comparison of multiequation turbulence models for several shock-separated boundary-layer interaction flows

Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.

Viegas, J. R.↗