Turbulent mixing /analysis/
Approximate methods for solving differential equations of motion to predict free turbulent mixing processes - single-form eddy viscosity model
EDDY VISCOSITY↗
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Lumley's PODT definition of large eddies and a trio of numerical procedures
Lumley's 1967 Moscow paper provided, for the first time, a completely rational definition of the physically-useful term 'large eddy', popular for a half-century. The numerical procedures based upon his results are: (1) PODT (Proper Orthogonal Decomposition Theorem), which extracts the Large Eddy structure of stochastic processes from physical or computer simulation two-point covariances, and 2) LEIM (Large-Eddy Interaction Model), a predictive scheme for the dynamical large eddies based upon higher order turbulence modeling. Earlier Lumley's work (1964) forms the basis for the final member of the triad of numerical procedures: this predicts the global neutral modes of turbulence which have surprising agreement with both structural eigenmodes and those obtained from the dynamical equations. The ultimate goal of improved engineering design tools for turbulence may be near at hand, partly due to the power and storage of 'supermicrocomputer' workstations finally becoming adequate for the demanding numerics of these procedures.
Payne, Fred R.↗
Numerical Simulations of Two-Phase Reacting Flow in a Single-Element Lean Direct Injection (LDI) Combustor Using NCC
A series of numerical simulations of Jet-A spray reacting flow in a single-element lean direct injection (LDI) combustor have been conducted by using the National Combustion Code (NCC). The simulations have been carried out using the time filtered Navier-Stokes (TFNS) approach ranging from the steady Reynolds-averaged Navier-Stokes (RANS), unsteady RANS (URANS), to the dynamic flow structure simulation (DFS). The sub-grid model employed for turbulent mixing and combustion includes the well-mixed model, the linear eddy mixing (LEM) model, and the filtered mass density function (FDF/PDF) model. The starting condition of the injected liquid spray is specified via empirical droplet size correlation, and a five-species single-step global reduced mechanism is employed for fuel chemistry. All the calculations use the same grid whose resolution is of the RANS type. Comparisons of results from various models are presented.
Liu, Nan-Suey↗
The relationship between eddy-transport and second-order closure models for stratified media and for vortices
The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed.
Donaldson, C. D.↗
Development of a second order closure model for computation of turbulent diffusion flames
A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.
Varma, A. K.↗
A simple model for the interaction between vertical eddy heat fluxes and static stability
A numerical model for studying the interaction of vertical eddy heat fluxes and vertical temperature structure in midlatitude regions is described. The temperature profile for the model was derived from calculations of the equilibrium among heating rates in simplified representations of large-scale vertical eddy heat flux, moist convection and radiation. An eddy flux profile is calculated based on the quasi-geostrophic, liner baroclinic instability of a single wave. Model equilibrium states for summer and winter conditions are compared with observations, and the results are discussed in detail.
Gutowski, W. J., Jr.↗
Nonadiabatic and three-dimensional effects in compressible turbulent boundary layers
A defect stream function formulation for nonadiabatic flow with small crossflow is developed. The first-integral property of this formulation provides for two removal of the streamline curvature term in the governing equation so that the form of the reduced equation for small crossflow is the same as that for two dimensional flow. The combined law of the wall and wake is used in place of the no-slip boundary condition. The tangential velocity equation for law-of-the-wall flow is shown to be the same for three-dimensions as for two when the Boussinesq approximation applies, and a closed form solution for the crossflow angle in the inner region is obtained. Analytic solutions for nonadiabatic, compressible, equilibrium flow with a Clauser outer-region eddy-viscosity model are obtained, and excellent agreement with experimental skin friction and velocity profile data for nonadiabatic, compressible flat-plate flow is achieved. An analytic solution for a linear inner-region eddy-viscosity model is also obtained; the wake function part of this solution is found to be inconsistent with the empirically established law of the wake.
Barnwell, Richard W.↗
Large-Eddy Simulation of Axisymmetric Compression Corner Flow
The Wall-Modeled Large Eddy Simulation (WMLES) approach is used to study the interaction of a shock wave with a high Reynolds number turbulent boundary layer. Since the near wall region is modeled, high Reynolds number turbulent flows can be simulated at a moderate computational cost. The case considered is that of an axisymmetric Mach 2.85 turbulent boundary layer over a 30 compression corner. The Reynolds number of the boundary layer upstream of the interaction based on momentum thickness (Re theta = u sub infinity theta/v sub infinity) is ~12,000. The geometry and flow conditions match the experiments of Dunagan et al. (NASA TM 88227, 1986). The simulations were performed using equilibrium and non-equilibrium wall models. The agreement with experiment is encouraging for the finest grid with respect to the separation bubble length, unsteady shock structure and wall pressure distribution. Sensitivity ofWMLES results to grid, wall model, and blockage effects in the tunnel are reported.
Iyer, Prahladh S.↗
Turbulence modelling in CFD: Present status, future prospects
Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.
Launder, Brian E.↗
A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations
Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.
Winckelmans, G. S.↗
Hybrid Reynolds-Averaged/Large Eddy Simulation of a Cavity Flameholder; Assessment of Modeling Sensitivities
Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit Reynolds stress model. Fortunately, the numerical error assessment at most of the axial stations used to compare with measurements clearly indicated that the scale-resolving simulations were improving (i.e. approaching the measured values) as the grid was refined. Hence, unlike a Reynolds-averaged simulation, the hybrid approach provides a mechanism to the end-user for reducing model-form errors.
Baurle, R. A.↗
Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations
An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.
Harris, J. E.↗
Numerical simulation of compressible, turbulent, two-phase flow
A computer program for numerically simulating compressible, turbulent, two-phase flows is described and applied. Special attention is given to flows in which dust is ingested into the turbulent boundary layer behind shock waves moving over the earth's surface. it is assumed that the two phases are interpenetrating continua which are coupled by drag forces and heat transfer. The particle phase is assumed to be dilute, and turbulent effects are modeled by zero- and two-equation eddy viscosity models. An important feature of the turbulence modeling is the treatment of surface boundary conditions which control the ingestion of particles into the boundary layer by turbulent friction and diffusion. The numerical method uses second-order implicit upwind differencing of the inviscid terms of the equations and second-order central differencing of the viscous terms. A diagonal form of the implicit algorithm is used to improve efficiency, and the transformation to a curvilinear coordinate system is accomplished by the finite volume techniques. Applications to a series of representative flows include a two-phase nozzle flow, the steady flow of air over a sand bed, and the air flow behind a normal shock wave in uniform motion over a sand bed. Results of the latter two applications are compared with experimental results.
Coakley, t. J.↗
Three-dimensional compressible jet-in-crossflow calculations using improved viscosity models and adapted grid
Previous calculations of jet-in-crossflow problems have been sensitive to the turbulence and artificial viscosity models and to the grid. Consequently, the eddy viscosity model in the PARC3D code was modified to consider the turbulent jet by switching from the Baldwin-Lomax (1978) model to an axisymmetric jet model. A modified artificial viscosity model has been utilized and evaluated in this study as well. The new model includes cell size scaling and a directional dependence in the coefficients. Computational results from PARC3D demonstrate the effects of the viscosity models on the pressure distribution fore and aft of the jet and the ability of the adaptive grid scheme to adjust to the three-dimensional gradients around the jet.
Lytle, John K.↗
Modeling and strain gauging of eddy current repulsion deicing systems
Work described in this paper confirms and extends work done by Zumwalt, et al., on a variety of in-flight deicing systems that use eddy current repulsion for repelling ice. Two such systems are known as electro-impulse deicing (EIDI) and the eddy current repulsion deicing strip (EDS). Mathematical models for these systems are discussed for their capabilities and limitations. The author duplicates a particular model of the EDS. Theoretical voltage, current, and force results are compared directly to experimental results. Dynamic strain measurements results are presented for the EDS system. Dynamic strain measurements near EDS or EIDI coils are complicated by the high magnetic fields in the vicinity of the coils. High magnetic fields induce false voltage signals out of the gages.
Smith, Samuel O.↗
A vorticity dynamics based model for the turbulent dissipation: Model development and validation
A new model dissipation rate equation is proposed based on the dynamic equation of the mean-square vorticity fluctuation for large Reynolds number turbulence. The advantage of working with the vorticity fluctuation equation is that the physical meanings of the terms in this equation are more clear than those in the dissipation rate equation. Hence, the model development based on the vorticity fluctuation equation is more straightforward. The resulting form of the model equation is consistent with the spectral energy cascade analysis introduced by Lumley. The proposed model dissipation rate equation is numerically well behaved and can be applied to any level of turbulence modeling. It is applied to a realizable eddy viscosity model. Flows that are examined include: rotating homogeneous shear flows; free shear flows; a channel flow and flat plate boundary layers with and without pressure gradients; and backward facing step separated flows. In most cases, the present model predictions show considerable improvement over the standard kappa-epsilon model.
Shih, Tsan-Hsing↗
Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies
Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.
Jongen, T.↗
3D Radiative Transfer Effects in Multi-Angle/Multi-Spectral Radio-Polarimetric Signals from a Mixture of Clouds and Aerosols Viewed by a Non-Imaging Sensor
When observing a spatially complex mix of aerosols and clouds in a single relatively large field-of-view, nature entangles their signals non-linearly through polarized radiation transport processes that unfold in the 3D position and direction spaces. In contrast, any practical forward model in a retrieval algorithm will use only 1D vector radiative transfer (vRT) in a linear mixing technique. We assess the difference between the observed and predicted signals using synthetic data from a high-fidelity 3D vRT model with clouds generated using a Large Eddy Simulation model and an aerosol climatology. We find that this difference is signal--not noise--for the Aerosol Polarimetry Sensor (APS), an instrument developed by NASA. Moreover, the worst case scenario is also the most interesting case, namely, when the aerosol burden is large, hence hase the most impact on the cloud microphysics and dynamics. Based on our findings, we formulate a mitigation strategy for these unresolved cloud adjacency effects assuming that some spatial information is available about the structure of the clouds at higher resolution from "context" cameras, as was planned for NASA's ill-fated Glory mission that was to carry the APS but failed to reach orbit. Application to POLDER (POLarization and Directionality of Earth Reflectances) data from the period when PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) was in the A-train is briefly discussed.
APS↗