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Supersaturation Variability from Scalar Mixing: Evaluation of a New Subgrid-Scale Model Using Direct Numerical Simulations of Turbulent Rayleigh–Bénard Convection
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Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates
The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.
Computation of the sound generated by isotropic turbulence
The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.
A numerical study of the turbulent Ekman layer
The three-dimensional time-dependent turbulent flow in a neutrally stratified Ekman layer over a smooth flat surface was numerically simulated by directly solving the Navier-Stokes equations. Issues addressed using the direct numerical simulation (DNS) fields include the presence or absence of large-scale coherent structures ('longitudinal' or 'roll' vortices) in neutrally stratified Ekman-layer turbulence, the effects of the horizontal component of the angular velocity vector (i.e., latitude), and implications for models of the PBL. Experimental and DNS profiles are compared.
Numerical simulations of compressible mixing layers
Direct numerical simulations of two-dimensional temporally growing compressible mixing layers are presented. The Kelvin-Helmholtz instability is initially excited by a white-noise perturbation superimposed onto a hyperbolic tangent meanflow profile. The linear regime is studied at low resolution in the case of two flows of equal temperatures, for convective Mach numbers from 0.1 to 1 and for different values of the Reynolds number. At higher resolution, the complete evolution of a two-eddy mixing layer between two flows of different temperatures is simulated at moderate Reynolds number. Similarities and differences between flows of equal convective Mach numbers are discussed.
Coherent structures in a simulated turbulent mixing layer
A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth.
The Effect of Two-Dimensional Forcing on Self-Similar Turbulent Plane Wakes
Three direct numerical simulations of time-evolving turbulent plane wakes with velocity deficit Reynolds numbers of about 2,000 have been simulated using a spectral numerical method with up to 600 x 260 x 160 modes. The initial conditions for the simulations are generated from direct numerical simulations of a turbulent boundary layer (momentum thickness Reynolds number of 670), and varying amounts of additional two- dimensional, forcing. In order to preserve the self-similar flow evolution, the forcing is implemented by multiplying all the two-dimensional modes in the initial condition by a constant factor. In the "natural" case no additional forcing is used; in the "forced" and "heavily forced" cases this factor is 5 and 20, respectively. The wake spreading rate Is increased by factors of 1.7 and 7.1 for the two forced cases. The Reynolds stresses are also increased by a similar or even larger factor. These results indicate that the plane wake is much more sensitive to initial forcing than the plane mixing layer. As in the plane mixing layer, two-dimensional forcing promotes more organized large-scale vortical flow structures and these structures axe sometimes separated by "braid regions" containing streamwise "rib" vortices, unlike in the unforced wake.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
The objective of this research is to continue our efforts in advancing the state of knowledge in Large Eddy Simulation (LES), Direct Numerical Simulation (DNS), and Reynolds Averaged Navier Stokes (RANS) methods for the analysis of high-speed reacting turbulent flows. In the first phase of this research, conducted within the past six months, focus was in three directions: RANS of turbulent reacting flows by Probability Density Function (PDF) methods, RANS of non-reacting turbulent flows by advanced turbulence closures, and LES of mixing dominated reacting flows by a dynamics subgrid closure. A summary of our efforts within the past six months of this research is provided in this semi-annual progress report.
Modeling and simulation of transitional Rayleigh–Taylor flow with partially averaged Navier–Stokes equations
In this work, the partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters $f_\phi$ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity $\phi$ of the turbulent closure, $f_\phi$. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations’ fidelity.
Some Results Relevant to Statistical Closures for Compressible Turbulence
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
Dynamics of Aerosol Particles in Stationary, Isotropic Turbulence
A detailed study of the dynamics of sub-Kolmogorov-size aerosol particles in stationary isotropic turbulence has been performed. The study combined direct numerical simulations (DNS; directed by Prof. Collins) and high-resolution experimental measurements (directed by Prof. Meng) under conditions of nearly perfect geometric and parametric overlap. The goal was to measure the accumulation of particles in low-vorticity regions of the flow that arises from the effect commonly referred to as preferential concentration. The grant technically was initiated on June 13, 2000; however, funding was not available until July 11, 2000. The grant was originally awarded to Penn State University (numerical simulations) and SUNY-Buffalo (experiments); however, Prof. Collins effort was moved to Cornell University on January 2002 when he joined that university. He completed the study there. A list of the specific tasks that were completed under this study is presented.
Partially averaged Navier-Stokes closure modeling for variable-density turbulent flow
We report this work extends the framework of the partially averaged Navier-Stokes (PANS) equations to variable-density flow, i.e., multimaterial and/or compressible mixing problems with density variations and production of turbulence kinetic energy by both shear and buoyancy mechanisms. The proposed methodology is utilized to derive the PANS BHR-LEVM closure. This includes a priori testing to analyze and develop guidelines toward the efficient selection of the parameters controlling the physical resolution and, consequently, the range of resolved scales of PANS. Two archetypal test-cases involving transient turbulence, hydrodynamic instabilities, and coherent structures are used to illustrate the accuracy and potential of the method: the Taylor-Green vortex at Reynolds number Re = 3000, and the Rayleigh-Taylor flow at Atwood number 0.5 and (Re) max ≈ 500. These representative problems, for which turbulence is generated by shear and buoyancy processes, constitute the initial validation space of the new model, and their results are comprehensively discussed in two subsequent studies. The computations indicate that PANS can accurately predict the selected flow problems, resolving only a fraction of the scales of large-eddy simulation and direct numerical simulation strategies. The results also reiterate that the physical resolution of the PANS model must guarantee that the key instabilities and coherent structures of the flow are resolved. The remaining scales can be modeled through an adequate turbulence scale-dependent closure.
Large Eddy Simulation of Convective Heat Transfer in a Random Pebble Bed Using the Spectral Element Method
The development of fluoride-cooled high-temperature reactors has drastically increased the demand for an in-depth understanding of the heat transfer (HT) in packed beds cooled by liquid salts. The complex flow fields and space-dependent porosity found in a pebble bed require a detailed understanding to ensure the proper cooling of the reactor core during normal and accident conditions. As detailed experimental data are complicated to obtain for these configurations, high-fidelity simulation such as large eddy simulation and direct numerical simulation (DNS) can be employed to create a high-resolution heat transfer numerical database that can assist in addressing industrial-driven issues associated with the heat transfer behavior of fluoride-cooled high-temperature reactors. In this paper, we performed a series of large eddy simulation using computational fluid dynamics (CFD) code NekRS to investigate the heat transfer for a bed of 1741 pebbles. Further, the characteristics of the flow, such as average, rms, and time series of velocity and temperature, have been analyzed. Porous media averages have also been performed. The simulation results show a good agreement between non-conjugate heat transfer and conjugate heat transfer. The generated data will be used to benchmark heat transfer modeling methods and local maxima/minima of heat transfer parameters. It will also be used for supporting convective heat transfer quantification for Kairos Power and benchmarking lower fidelity models.
PeleLMeX [SWR-22-48]
PeleLMeX is a solver for high fidelity reactive flow simulations, namely direct numerical simulation (DNS) and large eddy simulation (LES). The solver combines a low Mach number approach, adaptive mesh refinement (AMR), embedded boundary (EB) geometry treatment and high performance computing (HPC) to provide a flexible tool to address research questions on platforms ranging from small workstations to the world's largest GPU-accelerated supercomputers. PeleLMeX has been used to study complex flame/turbulence interactions in RCCI engines and hydrogen combustion or the effect of sustainable aviation fuel on gas turbine combustion. PeleLMeX is part of the Pele combustion Suite (https://amrex-combustion.github.io/)
An experimental study of the effects of rapid rotation on turbulence
Experiments, large eddy simulations and direct numerical simulations all show that rapid rotation has a striking effect on homogeneous nearly isotropic turbulence. The cascade process is effectively inhibited by rotation, and thus dissipation is greatly reduced. Some attempts have been made to incorporate this effect in turbulence models. Numerical simulation further showed the somewhat surprising result that anisotropic homogeneous turbulence subjected to rotation tended towards an isotropic state; however, the residual anisotropy was not zero. Reynolds (1989) performed a detailed analysis using Rapid Distortion Theory (RDT) and showed that a reduction in the anisotropy is indeed expected and if the anisotropy is produced by irrotational strain then the anisotropy tensor b(sub ij) is asymptotically driven to half its initial value. Our objective is to extend the work of the experiments mentioned above to lower turbulent Rossby numbers and to confirm some of the results obtained by Reynolds (1989) for anisotropic turbulence.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.