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In the report we present a summary of the new models and algorithms developed by the PI and the students supported by this grant. These developments are described in detail in ten peer-reviewed journal articles that acknowledge support from this grant.
Curvature-driven turbulence in a helical open-field-line plasma is investigated using electrostatic five-dimensional gyrokinetic continuum simulations in an all-bad-curvature helical-slab geometry. Parameters for a National Spherical Torus Experiment scrape-off-layer plasma are used in the model. Here, the formation and convective radial transport of plasma blobs is observed, and it is shown that the radial particle-transport levels are several times higher than diffusive Bohm-transport estimates. By reducing the strength of the poloidal magnetic field, the profile of the heat flux to the divertor plate is observed to broaden.
In this work, turbulent flow inside a modified differentially heated cavity at high Rayleigh number (Ra ~ 10 9 ) has been studied through fully resolved direct numerical simulation (DNS) using the high-order spectral element method code Nek5000. The flow configuration includes two separate physical phenomena: the natural recirculation itself, and the flow inside a curved channel. Simulations have been carried out using both the Boussinesq approximation and the low-Mach compressible formulation. Significant discrepancies between the two methods inform of the extreme caution that should be exercised when using the Boussinesq approximation in the limits of its applicability. The DNS solutions are analyzed in terms of polynomial-order convergence and Reynolds stress budgets, and the turbulence quantities and velocity profiles are presented as a reference for the validation of turbulence models.
Atmospheric turbulence simulated in wind tunnel by air jets
Direct numerical simulations (DNS) of turbulent flows provide a complete data base to develop and to test turbulence models. In this article, the progress made in developing models for the dissipation rate equation is reviewed. New scaling arguments for the various terms in the dissipation rate equation were tested using data from DNS of homogeneous shear flows. Modifications to the epsilon-equation model that take into account near-wall effects were developed using DNS of turbulent channel flows. Testing of new models for flows under mean compression was carried out using data from DNS of isotropically compressed turbulence. In all of these studies the data from the simulations was essential in guiding the model development. The next generation of DNS will be at higher Reynolds numbers, and will undoubtedly lead to improved models for computations of flows of practical interest.
Numerical simulations of a planar turbulent wall jet and a planar VTOL upwash fountain were performed. These are three dimensional simulations which resolve large scale unsteady motions in the flows. The wall jet simulation shows good agreement with experimental data and is presented to verify the simulation methodology. Simulation of the upwash fountain predicts elevated shear stress and a half velocity width spreading rate of 33% which agrees well with experiment. Turbulence mechanisms which contribute to the enhanced spreading rate are examined.
The three-dimensional time dependent equations of motion were numerically integrated for fully-developed turbulent channel flow. A large scale flow field was obtained directly from the solution of these equations, and small scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC 4 computer. The computed flow patterns show that the wall layer consists of coherent structures of low speed and high speed streaks alternating in the spanwise direction. These structures were absent in the regions away from the wall. Hot spots, small localized regions of very large turbulent shear stress, were frequently observed. The profiles of the pressure velocity-gradient correlations show a significant transfer of energy from the normal to the spanwise component of turbulent kinetic energy in the immediate neighborhood of the wall ('the splatting effect').
Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics within each LES grid cell. Finite-rate kinetics can be included without any closure and this approach actually provides a means to predict the turbulent rates and the turbulent flame speed. The subgrid combustion model requires resolution of the local time scales associated with small-scale mixing, molecular diffusion and chemical kinetics and, therefore, within each grid cell, a significant amount of computations must be carried out before the large-scale (LES resolved) effects are incorporated. Therefore, this approach is uniquely suited for parallel processing and has been implemented on various systems such as: Intel Paragon, IBM SP-2, Cray T3D and SGI Power Challenge (PC) using the system independent Message Passing Interface (MPI) compiler. In this paper, timing data on these machines is reported along with some characteristic results.
A database of heating and pressure measurements on a 7-deg half-angle cone in a highenthalpy expansion tunnel in CO2 has been generated to support development and validation of computational models to be employed in the design of future Mars missions. Laminar, transitional, and turbulent simulations were performed at the test conditions for comparisons with the data. Close agreement was obtained for both fully-laminar and fully turbulent conditions. For the remaining transitional/turbulent conditions, agreement to within, or slightly more than, the estimated experimental uncertainty was demonstrated. The influence of transition intermittency and transition length models on predicted heating levels was demonstrated, as were differences in turbulent heating predictions generated using various algebraic, one-equation, and two-equation turbulence models. These comparisons provide some measure of confidence in turbulent simulation capabilities; however, because the data were not obtained on a relevant entry vehicle geometry, it is not possible to fully quantify computational uncertainties for the definition of Mars mission aerothermodynamic environments at this time
The Reynolds numbers that characterize geophysical and astrophysical turbulence (Re approximately equals 10(exp 8) for the planetary boundary layer and Re approximately equals 10(exp 14) for the Sun's interior) are too large to allow a direct numerical simulation (DNS) of the fundamental Navier-Stokes and temperature equations. In fact, the spatial number of grid points N approximately Re(exp 9/4) exceeds the computational capability of today's supercomputers. Alternative treatments are the ensemble-time average approach, and/or the volume average approach. Since the first method (Reynolds stress approach) is largely analytical, the resulting turbulence equations entail manageable computational requirements and can thus be linked to a stellar evolutionary code or, in the geophysical case, to general circulation models. In the volume average approach, one carries out a large eddy simulation (LES) which resolves numerically the largest scales, while the unresolved scales must be treated theoretically with a subgrid scale model (SGS). Contrary to the ensemble average approach, the LES+SGS approach has considerable computational requirements. Even if this prevents (for the time being) a LES+SGS model to be linked to stellar or geophysical codes, it is still of the greatest relevance as an 'experimental tool' to be used, inter alia, to improve the parameterizations needed in the ensemble average approach. Such a methodology has been successfully adopted in studies of the convective planetary boundary layer. Experienc e with the LES+SGS approach from different fields has shown that its reliability depends on the healthiness of the SGS model for numerical stability as well as for physical completeness. At present, the most widely used SGS model, the Smagorinsky model, accounts for the effect of the shear induced by the large resolved scales on the unresolved scales but does not account for the effects of buoyancy, anisotropy, rotation, and stable stratification. The latter phenomenon, which affects both geophysical and astrophysical turbulence (e.g., oceanic structure and convective overshooting in stars), has been singularly difficult to account for in turbulence modeling. For example, the widely used model of Deardorff has not been confirmed by recent LES results. As of today, there is no SGS model capable of incorporating buoyancy, rotation, shear, anistropy, and stable stratification (gravity waves). In this paper, we construct such a model which we call CM (complete model). We also present a hierarchy of simpler algebraic models (called AM) of varying complexity. Finally, we present a set of models which are simplified even further (called SM), the simplest of which is the Smagorinsky-Lilly model. The incorporation of these models into the presently available LES codes should begin with the SM, to be followed by the AM and finally by the CM.
As a continuation of Year 2 of the Department of Energy's Nuclear Safety Research and Development (NSRD) project, high-fidelity computational tools developed at Sandia National Laboratories (SNL) were used to substantiate airborne release fraction and respirable fraction data in DOE-HDBK-3010. For this research, SNL's incompressible Fuego computational fluid dynamics (CFD) code was coupled onto thousands of Lagrangian aerosol particles that were individually tracked. Although Fuego does not currently have a particle interaction model (e.g., agglomeration), aerosol resuspension was implemented this year as a part of this project. The model improvement from exploratory simulations, as described in the previous year, will be discussed in this paper, along with other simulations for other aerosol experiments that use the resuspension model. In addition, key experiment turbulence parameters will be calculated, and various turbulence models will be examined for applicability towards complex geometries and dispersal conditions. (authors)
The fundamental nature of turbulent density fluctuations in standard Wendelstein 7-X (W7-X) stellarator discharges is investigated experimentally via phase contrast imaging (PCI) in combination with gyrokinetic simulations with the code GENE. We find that density fluctuations are ion-temperature-gradient-driven and radially localised in the outer half of the plasma. It is shown that the line-integrated PCI measurements cover the right range of wavenumbers and a favourable toroidal and poloidal location to capture some of the strongest density fluctuations in W7-X. Due to the radial localisation of fluctuations, measured wavenumber–frequency spectra exhibit a dominant phase velocity, which can be related to the E × B rotation velocity at the radial position of a well in the neoclassical radial electric field. The match is robust against variations of heating power and line-integrated density, which is partly due to the localisation of fluctuations and partly due to effects of the radial gradient in the E × B velocity profile on the wavenumber–frequency spectrum. The latter effect is studied with a newly built synthetic PCI diagnostic and global gyrokinetic simulations with GENE-3D.
A review is given of recent advances in two distinct computational methods for evaluating turbulence fields, namely, statistical Reynolds stress modeling and turbulence simulation, where large eddies are followed in time. It is shown that evaluation of the mean Reynolds stresses, rather than use of a scalar eddy viscosity, permits an explanation of streamline curvature effects found in several experiments. Turbulence simulation, with a new volume averaging technique and third-order accurate finite-difference computing is shown to predict the decay of isotropic turbulence in incompressible flow with rather modest computer storage requirements, even at Reynolds numbers of aerodynamic interest.
Radiation feedback from young star clusters embedded in giant molecular clouds (GMCs) is believed to be important to the control of star formation. For the most massive and dense clouds, including those in which super star clusters (SSCs) are born, pressure from reprocessed radiation exerted on dust grains may disperse a significant portion of the cloud mass back into the interstellar medium. Using our radiation hydrodynamics code, Hyperion, we conduct a series of numerical simulations to test this idea. Our models follow the evolution of self-gravitating, strongly turbulent clouds in which collapsing regions are replaced by radiating sink particles representing stellar clusters. We evaluate the dependence of the star formation efficiency (SFE) on the size and mass of the cloud and κ, the opacity of the gas to infrared (IR) radiation. We find that the single most important parameter determining the evolutionary outcome is κ, with κ≳15 cm{sup 2} g{sup −1} needed to disrupt clouds. For κ=20−40 cm{sup 2} g{sup −1}, the resulting SFE = 50%−70% is similar to empirical estimates for some SSC-forming clouds. The opacities required for GMC disruption likely apply only in dust-enriched environments. We find that the subgrid model approach of boosting the direct radiation force L/c by a “trapping factor” equal to a cloud’s mean IR optical depth can overestimate the true radiation force by factors of ∼4−5. We conclude that feedback from reprocessed IR radiation alone is unlikely to significantly reduce star formation within GMCs unless their dust abundances or cluster light-to-mass ratios are enhanced.
In this paper, turbulence-closure models are evaluated using the 'true' LES approach in turbulent channel flow. The study is an extension of the work presented by Gullbrand (2001), where fourth-order commutative filter functions are applied in three dimensions in a fourth-order finite-difference code. The true LES solution is the grid-independent solution to the filtered governing equations. The solution is obtained by keeping the filter width constant while the computational grid is refined. As the grid is refined, the solution converges towards the true LES solution. The true LES solution will depend on the filter width used, but will be independent of the grid resolution. In traditional LES, because the filter is implicit and directly connected to the grid spacing, the solution converges towards a direct numerical simulation (DNS) as the grid is refined, and not towards the solution of the filtered Navier-Stokes equations. The effect of turbulence-closure models is therefore difficult to determine in traditional LES because, as the grid is refined, more turbulence length scales are resolved and less influence from the models is expected. In contrast, in the true LES formulation, the explicit filter eliminates all scales that are smaller than the filter cutoff, regardless of the grid resolution. This ensures that the resolved length-scales do not vary as the grid resolution is changed. In true LES, the cell size must be smaller than or equal to the cutoff length scale of the filter function. The turbulence-closure models investigated are the dynamic Smagorinsky model (DSM), the dynamic mixed model (DMM), and the dynamic reconstruction model (DRM). These turbulence models were previously studied using two-dimensional explicit filtering in turbulent channel flow by Gullbrand & Chow (2002). The DSM by Germano et al. (1991) is used as the USFS model in all the simulations. This enables evaluation of different reconstruction models for the RSFS stresses. The DMM consists of the scale-similarity model (SSM) by Bardina et al. (1983), which is an RSFS model, in linear combination with the DSM. In the DRM, the RSFS stresses are modeled by using an estimate of the unfiltered velocity in the unclosed term, while the USFS stresses are modeled by the DSM. The DSM and the DMM are two commonly used turbulence-closure models, while the DRM is a more recent model.
In this paper, we present a critical survey of the current airframe noise (AFN) prediction methodologies. Four methodologies are recognized. These are the fully analytic method, CFD combined with the acoustic analogy, the semi-empirical method and fully numerical method. It is argued that for the immediate need of the aircraft industry, the semi-empirical method based on recent high quality acoustic database is the best available method. The method based on CFD and the Ffowcs William- Hawkings (FW-H) equation with penetrable data surface (FW-Hpds ) has advanced considerably and much experience has been gained in its use. However, more research is needed in the near future particularly in the area of turbulence simulation. The fully numerical method will take longer to reach maturity. Based on the current trends, it is predicted that this method will eventually develop into the method of choice. Both the turbulence simulation and propagation methods need to develop more for this method to become useful. Nonetheless, the authors propose that the method based on a combination of numerical and analytical techniques, e.g., CFD combined with FW-H equation, should also be worked on. In this effort, the current symbolic algebra software will allow more analytical approaches to be incorporated into AFN prediction methods.
Thermal convection was proposed as a possible mechanism for generation and maintenance of turbulence in the inner accretion disk regime of the primordial solar nebula. It is of fundamental interest to design experiments with the basic physical features of the solar nebula conditions cannot be produced in the laboratory, numerical simulations of hydrodynamic flows, which have been very successful in describing aerodynamic flows, can be suitable modified to provide experimental data for solar nebula modelling. The goals are to modify an extant, proven hydrodynamics code with the most important features of the solar nebula and other thin accretion disks: bouyancy terms to generate convection, internal heating representing the release of gravitational potential energy, a variable gravity linearly proportional the the distance from the vertical midplane due to centrifugal balance, rapid rotation with axis aligned with gravity, and Keplerian rotational shear; to determine the effect that these features have on the turbulent convection by introducing them individually and to determine the cumulative nature of the turbulent convection for accretion disk conditions; and to model the convection and the turbulence. In this manner, prior solar nebula models can be tested and their deficiencies rectified.
Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance of shock-capturing schemes such as the weighted essentially non-oscillatory (WENO) scheme as an essential ingredient of the numerical solver. However, these schemes are complex and have more computational cost than the simple high-order compact or non-compact schemes. In this paper, we present the implementation of a seventh-order, minimally-dissipative mapped WENO (WENO7M) scheme in a newly developed direct numerical simulation (DNS) code called KAUST Adaptive Reactive Flows Solver (KARFS). In order to make efficient use of the computer resources and reduce the solution time, without compromising the resolution requirement, the WENO routines are accelerated via graphics processing unit (GPU) computation. The performance characteristics and scalability of the code are studied using different grid sizes and block decomposition. Furthermore, the performance portability of KARFS is demonstrated on a variety of architectures including NVIDIA Tesla P100 GPUs and NVIDIA Kepler K20X GPUs. In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.