Simulations of turbulence and profile evolution across the edge and scrape-off-layer of diverted tokamaks
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An existing two-dimensional, compressible flow, Navier-Stokes computer code, containing a full Reynolds stress turbulence model, was adapted for use as a test bed for assessing and improving turbulence models based on turbulence simulation experiments. To date, the results of using the code in comparison with simulated channel flow and over an oscillating flat plate have shown that the turbulence model used in the code needs improvement for these flows. It is also shown that direct simulation of turbulent flows over a range of Reynolds numbers are needed to guide subsequent improvement of turbulence models.
Significant research has been underway for several years in NASA Glenn Research Center's nozzle branch to develop advanced computational methods for simulating turbulent flows in exhaust nozzles. The primary efforts of this research have concentrated on improving our ability to calculate the turbulent mixing layers that dominate flows both in the exhaust systems of modern-day aircraft and in those of hypersonic vehicles under development. As part of these efforts, a hybrid numerical method was recently developed to simulate such turbulent mixing layers. The method developed here is intended for configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. Interest in Large Eddy Simulation (LES) methods have increased in recent years, but applying an LES method to calculate the wide range of turbulent scales from small eddies in the wall-bounded regions to large eddies in the mixing region is not yet possible with current computers. As a result, the hybrid method developed here uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall-bounded regions entering a mixing section and uses a LES procedure to calculate the mixing-dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. With this technique, closure for the RANS equations is obtained by using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The LES equations are closed using the Smagorinsky subgrid scale model. Although the function of the Cebeci-Smith model to replace all of the turbulent stresses is quite different from that of the Smagorinsky subgrid model, which only replaces the small subgrid turbulent stresses, both are eddy viscosity models and both are derived at least in part from mixing-length theory. The similar formulation of these two models enables the RANS and LES equations to be solved with a single solution scheme and computational grid. The hybrid RANS-LES method has been applied to a benchmark compressible mixing layer experiment in which two isolated supersonic streams, separated by a splitter plate, provide the flows to a constant-area mixing section. Although the configuration is largely two dimensional in nature, three-dimensional calculations were found to be necessary to enable disturbances to develop in three spatial directions and to transition to turbulence. The flow in the initial part of the mixing section consists of a periodic vortex shedding downstream of the splitter plate trailing edge. This organized vortex shedding then rapidly transitions to a turbulent structure, which is very similar to the flow development observed in the experiments. Although the qualitative nature of the large-scale turbulent development in the entire mixing section is captured well by the LES part of the current hybrid method, further efforts are planned to directly calculate a greater portion of the turbulence spectrum and to limit the subgrid scale modeling to only the very small scales. This will be accomplished by the use of higher accuracy solution schemes and more powerful computers, measured both in speed and memory capabilities.
A concept is presented which can permit turbulence simulation in the vicinity of microbursts. The method involves a large data base, but should be fast enough for use with flight simulators. The model permits any pilot to simulate any flight maneuver in any aircraft. The model simulates a wind field with three-component mean winds and three-component turbulent gusts, and gust variation over the body of an aircraft so that all aerodynamic loads and moments can be calculated. The time and space variation of mean winds and turbulent intensities associated with a particular atmospheric phenomenon such as a microburst is used in the model. In fact, Doppler radar data such as provided by JAWS is uniquely suited for use with the proposed model. The concept is completely general and is not restricted to microburst studies. Reentry and flight in terrestrial or planetary atmospheres could be realistically simulated if supporting data of sufficient resolution were available.
Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.
Three models of simulated atmospheric turbulence were used to determine their respective influence on a computer-simulated, DC-8 type, aircraft landing. Statistical results based on a sample of 20 simulated landings illustrate the influence of turbulence simulated by the different models. For the same spectrum function, a non-Gaussian turbulence model produces the higher degree of touchdown variability. When different spectrum functions are used the von Karman model induces a smaller standard deviation in position error than the Dryden model. The turbulence energy contained by the higher frequency fluctuation has little effect on the landing position.
The structure of a numerically simulated turbulent boundary layer over a flat plate at Re(theta) = 670 was studied using the invariants of the velocity gradient tensor (Q and R) and a related scalar quantity, the cubic discriminant (D = 27R(exp 2)/4 + Q(exp 3)). These invariants have previously been used to study the properties of the small-scale motions responsible for the dissipation of turbulent kinetic energy. In addition, these scalar quantities allow the local flow patterns to be unambiguously classified according to the terminology proposed by Chong et al. The use of the discriminant as a marker of coherent motions reveals complex, large-scale flow structures that are shown to be associated with the generation of Reynolds shear stress -u'v'(bar). These motions are characterized by high spatial gradients of the discriminant and are believed to be an important part of the mechanism that sustains turbulence in the near-wall region.
A method that produces realistic simulations of atmospheric turbulence is developed and analyzed. The procedure makes use of a generalized spectral analysis, often called a proper orthogonal decomposition or the Karhunen-Loeve expansion. A set of criteria, emphasizing a realistic appearance, a correct spectral shape, and non-Gaussian statistics, is selected in order to evaluate the model turbulence. An actual turbulence record is analyzed in detail, providing both a standard for comparison and input statistics for the generalized spectral analysis. The simulation utilizes the eigenfunction-expansion procedure to produce preliminary time histories of the three velocity components simultaneously. It is found that important cross-statistical features are reasonably well-behaved.
Full turbulence simulation has been conducted of homogeneous turbulence subject to irrotational strains and under relaxation from these. Effects of the mode and strength of the imposed mean strain rate on the Reynolds stress, dissipation and vorticity fields are analyzed, yielding new insight. Tensorial models for the relaxation process are proposed for the vorticity dissipation and Reynolds stress anisotropies.
Advanced analytical methods applied to airline digital flight records and ATC radar tracking data are providing new insights into atmospheric disturbances that cause serious operating problems for aircraft. Performance-based methods for estimating unmeasured flow angles and the possible influence of rain on lift and drag, and a state-estimation procedure for determining winds along the flightpath are reviewed. The methods are applied to data records from the Delta Flight 191 wind-shear accident at the Dallas/Ft. Worth Airport (August 2, 1985) which involved an L-1011 airliner on final approach. The results indicate that the aircraft encountered a strong downlow followed by a strong outflow accompanied by large and rapid changes in the vertical wind. This pattern of low-level winds is consistent with the model that treats a downburst as a vortex ring. Although rain was present in the downburst, the analysis showed no evidence of performance loss. The results obtained from analyses of airline turbulence encounters provide a means for simulating turbulence phenomena and for training pilots for future encounters.
Direct simulations of homogeneous turbulence have, in recent years, come into widespread use for the evaluation of models for the pressure-strain correlation of turbulence. While work in this area has been beneficial, the increasingly common practice of testing the slow and rapid parts of these models separately in uniformly strained turbulent flows is shown in this paper to be unsound. For such flows, the decomposition of models for the total pressure-strain correlation into slow and rapid parts is ambiguous. Consequently, when tested in this manner, misleading conclusions can be drawn about the performance of pressure-strain models. This point is amplified by illustrative calculations of homogeneous shear flow where other pitfalls in the evaluation of models are also uncovered. More meaningful measures for testing the performance of pressure-strain models in uniformly strained turbulent flows are proposed and the implications for turbulence modeling are discussed.
This paper describes the simulation of turbulent boundary layers by direct numerical solution of the three-dimensional, time-dependent Navier-Stokes equations, using a spectral method. The flow is incompressible, with Re sub delta = 1000. The equations are written in the self-similar coordinate system and periodic streamwise and spanwise boundary conditions are imposed. A family of nine 'equilibrium' boundary layers, from the strongly accelerated 'sink' flow to Stratford's separating boundary layer is treated. Good general agreement with experiments is observed. The effects of pressure gradients on the structures and statistics, both in the wall and wake regions are discussed.
Incompressible turbulent channel flow is investigated by large eddy simulation using improved numerical methods and boundary conditions. In downstream and spanwise directions, cyclic boundary conditions are imposed for velocity and pressure, and two types of boundary conditions near the wall are used and compared. One type is based on the logarithmic law of the mean velocity near the wall and has a slip boundary condition where the molecular-viscous term is neglected. The other type is based on a no-slip boundary condition, where fine mesh spacing near the wall is used to take account of the molecular viscosity. Although the present study employs a coarse mesh (16 x 16 x 21), its results are in good agreement with those of Moin and Kim (1981).
Direct and large eddy simulations of forced and decaying isotropic turbulence have been performed using a pseudospectral and a finite-difference code. Subgrid models that include a one-equation subgrid kinetic energy model with and without a stochastic backscatter forcing term and a new scale similarity model have been analyzed in both Fourier space and physical space. The Fourier space analysis showed that the energy transfer across the cutoff wavenumber k(sub c) is dominated by local interaction. The correlation between the exact and the modeled (by a spectral eddy viscosity) nonlinear terms and the subgrid energy transfer in physical space was found to be quite low. In physical space, a similar correlation analysis was carried out using top hat filtering. Results show that the subgrid stress and the energy flux predicted by the subgrid models correlates very well with the exact data. The scale similarity model showed very high correlation for reasonable grid resolution. However, with decrease in grid resolution, the scale similarity model became more uncorrelated, when compared to the kinetic energy subgrid model. The subgrid models were then used for large-eddy simulations for a range of Reynolds number. It was determined that the dissipation was modeled poorly and that the correlation with the exact results was quite low for all the models. In general, for coarse grid resolution, the scale similarity model consistently showed very low correlation while the kinetic energy model showed a relatively higher correlation. These results suggest that to use the scale similarity model relatively fine grid resolution may be required, whereas, the kinetic energy model could be used even in coarse grid.
Spectral methods for simulating flows are reviewed, emphasizing their recent applications to reacting flow problems. Various classifications of spectral methods and their convergence properties are described and the 'spectral element' method is presented, highlighting its flexibility in dealing with complex flow geometries. The applications considered include chemical reactions in homogeneous turbulence, temporally evolving mixing layers, variable-density simulations, nonequilibrium chemistry, and spatially evolving mixing layers.
The dataset archives model-simulated turbulence intensity and meteorological profiles and timeseries at the lidar buoys sites off the coast of California (Humboldt and Morro Bay). The simulated data are interpolated in time and/or space according to observed quantities. The simulations were carried out for the north Pacific region using the revised Weather Research and Forecasting (WRF) model version 4.2 that incorporates the implementation of online turbulence intensity (TI) calculations (Tai et al. 2023). The simulated atmospheric profiles near the Shell Exploration and Production Corporation's Tension Leg Platforms Ursa and Mars are archived. Physics parameterizations chosen for the simulations include the Thompson microphysics parameterization, Mellor-Yamada-Nakanishi Niino (MYNN) boundary layer parameterization, Mellor-Yamada-Janjic surface layer parameterization, Unified Noah land-surface parameterization, and the RRTMG longwave and shortwave radiation parameterization. Initial and boundary conditions are taken from NOAA’s High-Resolution Rapid Refresh (HRRR) product. The JPL 0.01-degree Level 4 Multiscale Ultrahigh Resolution (MUR) Global Foundation Sea Surface Temperature (SST) Analysis (V4.1) data are used as the model’s SST forcing.