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Unsteady CFD Simulations of a Compression Corner Geometry Using Wall-Modeled LES Methods in Loci/CHEM

Several wall-modeled large eddy simulation (WMLES) methods are tested by simulating an unsteady Mach 2.0 compression corner geometry in Mississippi State’s Loci/CHEM solver. This study is conducted to evaluate the usage and requirements of these WMLES methods for applications regarding fluctuating pressure environments on launch vehicles with computational fluid dynamics (CFD). Two hybrid Reynolds-averaged Navier-Stokes (RANS)-large eddy simulation (LES) methods, Dynamic Hybrid RANS-LES (DHRL) and Improved Delayed Detached Eddy Simulation (IDDES), and one wall-stress-model, the Algebraic Wall Model for Wall-Modeled LES (AWMLES), are tested on varying grid and timestep refinement levels. These grid and timestep sizes are chosen to test the minimum requirements for successfully running these WMLES methods. The simulations are evaluated based on turbulent boundary layer properties in the developed boundary layer as well as unsteady quantities relating to fluctuating pressure environments in the region of the compression corner. The DHRL method shows good agreement with the comparison wind tunnel data and shows good grid and timestep convergence. The results from the IDDES and WMLES simulations show good agreement for several quantities with some discrepancies regarding others. The results presented in this paper will be used to inform further studies in predicting unsteady environments on higher-complexity geometries.

Bryson Frank↗

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 NTRS1987

Studies of unsteady viscous flows using a two-equation model of turbulence

A two equation model of turbulence, based on the turbulent kinetic energy and energy dissipation, suitable for prediction of unsteady viscous flows, was developed. Also, the performance of the two equation model was compared with simpler algebraic models such as the Baldwin-Lomax two layer eddy viscosity model, and a model by Johnson and King which accounts for upstream history of the turbulent kinetic energy. A brief discussion of this study is given.

Sankar, L. N.↗

NASA NTRS1987

Prediction of hypersonic shock-wave/turbulent-boundary-layer interaction flows

Solutions of the Reynolds-averaged Navier-Stokes equations are presented and compared with experimental surface data for a series of hypersonic shock-wave/turbulent-boundary-layer interaction flows. The turbulence models used include algebraic and two-equation eddy-viscosity models developed for transonic and supersonic flows. Also several additional modifications to the two-equation model to account for compressibility effects are developed and used. Although the modifications improve the agreement with the experimental data, no single model or modification correctly predicts all the test cases.

Horstman, C. C.↗

NASA NTRS1986

Impact of turbulence modeling on numerical accuracy and efficiency of compressible flow simulations

Discussed is the numerical implementation of turbulence models used in viscous compressible flow simulations and their performance described with respect to numerical accuracy, efficiency and stability. The basic approach utilizes the Reynolds-averaged compressible Navier-Stokes equations in which the Reynolds stresses and heat fluxes are mathematically modeled by suitable turbulence models. The turbulence models investigated include zero-, one-, and two-equation eddy viscosity models. The flow fields investigated include theoretical and supersonic flows about two-dimensional and axisymmetric bodies. Discussions concerning the numerical implementation of models include differencing procedures and boundary conditions used to assume numerical stability and accuracy. Numerical performance is also evaluated by comparing computations with experimental results.

Coakley, Thomas J.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗

NASA NTRS1995

A turbulence module for the NPARC code

A turbulence module is developed for the 2D version of the NPARC code which is currently restricted to planar or axisymmetric flows without swirling. Four turbulence models have been built into the module: Baldwin-Lomax, Chien, Shih-Lumley and CMOTT models. The first is a mixing-length eddy-viscosity model which is mainly used for initialization of computational fields and the last three are the low Reynolds number two-equation models. Unlike chien's model, both the Shih-Lumley and CMOTT models do not involve the dimensionless wall distance y(sup +), an advantage for separated flow calculations. Contrary to the NPARC and most other compressible codes, the non-delta form of transport equations is used which leads to a simpler linearization and is more effective than using the delta form in ensuring the positiveness of the turbulent kinetic energy and its dissipation rate. To reduce numerical diffusion while maintaining necessary stability, a second-order accurate and bounded scheme is used for the convective terms of the turbulent transport equations. This scheme is implemented in a deferred correction manner so that the main coefficients of the resulting difference equations are always positive, thus making the numerical solutions process unconditionally stable. The system of equations is solved via a decoupled method and by the alternating direction TDMA of Thomas. The module can be easily linked to the NPARC code for turbulent flow calculations.

Zhu, J.↗

NASA NTRS1983

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Menon, Suresh↗

NASA NTRS2000

Determining the Ocean's Role on the Variable Gravity Field and Earth Rotation

Our three year investigation, carried out over the period 18-19 Nov 2000, focused on the study of the variability in ocean angular momentum and mass signals and their relation to the Earth's variable rotation and gravity field. This final report includes a summary description of our work and a list of related publications and presentations. One thrust of the investigation was to determine and interpret the changes in the ocean mass field, as they impact on the variable gravity field and Earth rotation. In this regard, the seasonal cycle in local vertically-integrated ocean mass was analyzed using two ocean models of different complexity: (1) the simple constant-density, coarse resolution model of Ponte; and (2) the fully stratified, eddy-resolving model of Semtner and Chervin. The dynamics and thermodynamics of the seasonal variability in ocean mass were examined in detail, as well as the methodologies to calculate those changes under different model formulations. Another thrust of the investigation was to examine signals in ocean angular momentum (OAM) in relation to Earth rotation changes. A number of efforts were undertaken in this regard. Sensitivity of the oceanic excitation to different assumptions about how the ocean is forced and how it dissipates its energy was explored.

Ponte, Rui M.↗

NASA NTRS2018

Validation of a CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in a Small-Scale Tank in Normal Gravity

A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.

multiphase flow↗

NASA NTRS2018

Validation of A CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in A Small-Scale Tank in Normal Gravity

A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011 [1]. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. [2]. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.

multiphase flow↗

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.↗

NASA NTRS1995

Large eddy simulations of compressible turbulent flows

An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.

Porter-Locklear, Freda↗