Molecular-level simulations of turbulent Couette flow over rough surfaces
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APS DFD 2024 presentation
The derivation of smoothed or filtered momentum and continuity equations for large-scale, energy-containing eddies is considered. Questions regarding the energy loss of large-scale turbulence are discussed along with aspects of turbulent diffusion of a passive scalar. It is found that the large-scale fluctuations satisfy filtered or averaged momentum and continuity equations. An averaging of the nonlinear advection term yields two terms.
A code developed for simulating high Reynolds number transonic flow fields of arbitrary configuration is described. This code, in conjunction with laboratory experiments, is used to devise and test turbulence transport models which may be suitable in the prediction of such flow fields, with particular emphasis on regions of flow separation. The solutions describe the flow field, including both the shock-induced and trailing-edge separation regions, in sufficient detail to provide the profile and friction drag.
Numerical studies of turbulent flow in an axisymmetric 45-deg-expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-epsilon model were solved in a nonorthogonal curvilinear coordinate system. A zonal-grid method, where the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. Boundary overlap and interpolating techniques were used, and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite-differencing methods (hybrid, quadratic upwind, and skew upwind) were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
Four numerical algorithms and three turbulence models are used to solve the thin layer three-dimensional Reynolds-averaged Navier-Stokes equations for the supersonic flow past a nonaxisymmetric nozzle. The four numerical algorithms evaluated are based on upwind differencing and feature time-dependent, space relaxation, and parabolized schemes. The three different algebraic turbulence models are the Baldwin-Lomax (1978), the nonequilibrium model of Johnson and King (1985), and the Goldberg (1989) modification for the separated flow region. The present investigation was conducted at freestream Mach numbers of 1.2 and 1.3 and at an angle of attack of 0.0 deg. The Reynolds numbers for the investigation ranged from 20.5 million to 21.5 million, based on the model length. The calculations are compared with experimental data.
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A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magnetohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS algorithm. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous complete Navier-Stokes calculations.
Three different simulation approaches, namely unsteady Reynolds-averaged Navier-Stokes (URANS), delayed detached-eddy simulation (DDES), and wall-modeled large-eddy simulation (WMLES) are employed to simulate transonic flow over an NACA-0012 airfoil at different angles of attack covering pre- and post-buffet-onset regimes. The freestream Mach number is 0.75, and the Reynolds number based on the chord length is 10 million. These conditions are the same as the wind-tunnel experimental conditions of McDevitt and Okuno (1985). The NASA FUN3D solver is used for the simulations, which is an unstructured, compressible flow solver. The URANS simulations are performed using the Spalart-Allmaras (SA) model with the compressibility correction, the DDES predictions are based on the SA model, and the WMLES are performed using an equilibrium wall-model. The unsteady RANS simulations, only with the compressibility correction, predict the pre- and post- buffet characteristics, which compare well with the experimental results. DDES results predicted a lower buffet onset angle compared to experiment. The predicted shock locations are upstream of the locations predicted by URANS. Using a fine grid in the spanwise direction, WMLES predictions show buffeting consistent with the experiment.
Three different simulation approaches, namely unsteady Reynolds-averaged Navier-Stokes (URANS), delayed detached-eddy simulation (DDES), and wall-modeled large-eddy simulation (WMLES) are employed to simulate transonic flow over an NACA-0012 airfoil at different angles of attack covering pre-and post-buffet-onset regimes. The freestream Mach number is 0.75,and the Reynolds number based on the chord length is 10million. These conditions are the same as the wind-tunnel experimental conditions of McDevitt and Okuno (1985). The NASA FUN3D solver is used for the simulations, which is an unstructured, compressible flow solver. The URANS simulations are performed using the Spalart-Allmaras (SA) model with the compressibility correction, the DDES predictions are based on the SA model, and the WMLES are performed using an equilibrium wall-model. The unsteady RANS simulations, only with the compressibility correction, predict the pre-and post-buffet characteristics, which compare well with the experimental results. DDES results predicted a lower buffet onset angle compared to experiment. The predicted shock locations are upstream of the locations predicted by URANS. Using a fine grid in the span wise direction, WMLES predictions show buffeting consistent with the experiment.
Three different simulation approaches, namely unsteady Reynolds-averaged Navier-Stokes (URANS), delayed detached-eddy simulation (DDES),and wall-modeled large-eddy simulation (WMLES)are employed to simulate transonic flow over an NACA-0012 airfoil at different angles of attack covering pre- and post-buffet-onset regimes. The freestream Mach number is 0.75,and the Reynolds number based on the chord length is 10million. These conditions are the same as the wind-tunnel experimental conditions of McDevitt and Okuno (1985).1The NASA FUN3D solver is used for the simulations, which is an unstructured, compressible flow solver. The URANS simulations are performed using the Spalart-Allmaras (SA) model with the compressibility correction, the DDES predictions are based on the SA model, and the WMLES are performed using an equilibrium wall-model.The unsteady RANS simulations,only with the compressibility correction,predict the pre- and post-buffet characteristics,which compare well with the experimental results. DDES results predicted a lower buffet onset angle compared to experiment.The predicted shock locations are upstream of the locations predicted by URANS. Using a fine grid in the spanwise direction, WMLES predictions show buffeting consistent with the experiment
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Turbulent plane Couette flow was numerically simulated at a Reynolds number (U(sub w)h/nu) of 6000, where U(sub w) is the relative wall speed and h is half the channel-height. Unlike in Poiseuille flow, where the mean shear rate changes its sign at the centerline, the sign of mean shear rate in plane Couette flow remains the same across the whole channel. This difference is expected to yield several differences between the two flows, especially in the core region. The most significant and dramatic difference observed was the existence of large-scale structures in the core region of the plane Couette flow. The large eddies are extremely long in the flow direction and fill the entire channel (i.e., their vertical extent is 2h). The large-scale structures have the largest contribution from the wavenumber (k(sub x)h,k(sub z)h) = (0, plus or minus 1.5), corresponding to a wavelength lambda(sub z)/h is approximately equal to 4. The secondary motion associated with the k(sub x)h = 0 mode consists of the large-scale vortices. The large eddies contribute about 30 percent of turbulent kinetic energy.
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.
Investigations of one- and two-dimensional (1- or 2-D) simulations of Stirling machines centered around experimental data generated by the U. of Minnesota Mechanical Engineering Test Rig (METR) are covered. This rig was used to investigate oscillating flows about a zero mean with emphasis on laminar/turbulent flow transitions in tubes. The Space Power Demonstrator Engine (SPDE) and in particular, its heater, were the subjects of the simulations. The heater was treated as a 1- or 2-D entity in an otherwise 1-D system. The 2-D flow effects impacted the transient flow predictions in the heater itself but did not have a major impact on overall system performance. Information propagation effects may be a significant issue in the simulation (if not the performance) of high-frequency, high-pressure Stirling machines. This was investigated further by comparing a simulation against an experimentally validated analytic solution for the fluid dynamics of a transmission line. The applicability of the pressure-linking algorithm for compressible flows may be limited by characteristic number (defined as flow path information traverses per cycle); this warrants further study. Lastly the METR was simulated in 1- and 2-D. A two-parameter k-w foldback function turbulence model was developed and tested against a limited set of METR experimental data.
Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.
A direct numerical simulation of a turbulent channel flow with three passive scalars at different molecular Prandtl numbers is performed. Computed statistics including the turbulent Prandtl numbers are compared with existing experimental data. The computed fields are also examined to investigate the spatial structure of the scalar fields. The scalar fields are highly correlated with the streamwise velocity; the correlation coefficient between the temperature and the streamwise velocity is as high as 0.95 in the wall region. The joint probability distributions between the temperature and velocity fluctuations are also examined; they suggest that it might be possible to model the scalar fluxes in the wall region in a manner similar to the Reynolds stresses.