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Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

Squires, Kyle D.↗

Emulator of PR‐DNS: Accelerating Dynamical Fields With Neural Operators in Particle‐Resolved Direct Numerical Simulation

Abstract Particle‐resolved direct numerical simulations (PR‐DNS) play an increasing role in investigating aerosol‐cloud‐turbulence interactions at the most fundamental level of processes. However, the high computational cost associated with high resolution simulations poses considerable challenges for large domain or long duration simulation using PR‐DNS. To address these issues, here we present an emulator of the complex physics‐based PR‐DNS developed by use of the data‐driven Fourier Neural Operator (FNO) method. The effectiveness of the method is showcased by presenting turbulence and temperature fields in a two‐dimensional space. The results demonstrate high accuracy at various resolutions and the emulator is two orders of magnitude cheaper in terms of computational demand compared to the physics‐based PR‐DNS model. Furthermore, the FNO emulator exhibits strong generalization capabilities for different initial conditions and ultra‐high‐resolution without the need to retrain models. These findings highlight the potential of the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our understanding of the aerosol‐cloud‐precipitation system.

99 GENERAL AND MISCELLANEOUS↗

Scalar Dissipation Modeling for Passive and Active Scalars: a priori Study Using Direct Numerical Simulation

Transitional databases from Direct Numerical Simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar dissipation Probability Distribution Function (PDF) may be modeled as a Gaussian. The databases encompass a single-component fuel and four multicomponent fuels, two initial Reynolds numbers (Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the (beta)-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the fourteen databases. For each statistical measure, the proposed (beta)-PDF model is shown to be much superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the (beta)-PDF even improves when the comparison is performed for higher initial Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the (beta)-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the (beta)-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.

scalar dissipation modeling↗

The use of direct numerical simulation data in turbulence modeling

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.

Mansour, N. N.↗

On direct numerical simulations of turbulent reacting flows

A description of the emerging field of direct numerical simulations of turbulent, chemically reacting flows is presented. The types of direct numerical simulations, physical issues related to implementing the simulations, as well as the various numerical methods used are described. Examples are presented of recent applications of direct numerical simulations to a variety of problems, displaying both the potential of the method and also some of its limitations. Finally, our view of the potential role of direct numerical simulations in future research on turbulent, chemically reacting flows is presented.

Jou, W.-H.↗

Direct Numerical Simulation of Acoustic Noise Generation from the Nozzle Wall of a Hypersonic Wind Tunnel

The acoustic radiation from the turbulent boundary layer on the nozzle wall of a Mach 6 Ludwieg Tube is simulated using Direct Numerical Simulations (DNS), with the flow conditions falling within the operational range of the Mach 6 Hypersonic Ludwieg Tube, Braunschweig (HLB). The mean and turbulence statistics of the nozzle-wall boundary layer show good agreement with those predicted by Pate's correlation and Reynolds Averaged Navier-Stokes (RANS) computations. The rms pressure fluctuation P'(rms)/T(w) plateaus in the freestream core of the nozzle. The intensity of the freestream noise within the nozzle is approximately 20% higher than that radiated from a single at pate with a similar freestream Mach number, potentially because of the contributions to the acoustic radiation from multiple azimuthal segments of the nozzle wall.

Huang, Junji↗

Direct Numerical Simulation of Involute Channel Turbulence

A direct numerical simulation (DNS) study was performed on turbulent flow in the high flux isotope reactor involute channel geometry to develop a numerical database and determine the differences compared with a flat parallel channel. The varying channel curvature along the walls was studied for differences in mean profiles. Parameters of interest include streamwise velocity, turbulent kinetic energy (TKE), and turbulence dissipation rate, as well as Reynolds stresses and turbulence transport terms. Profile sampling was carried out at 10 locations along the span of the involute. Additional DNS studies were performed on smaller domains of comparable curvature to the involute domain: a high curvature channel (high circular), a low curvature channel (low circular), and a flat channel (flat). Here, each of these four cases was compared against each other and to other DNS studies performed on parallel flows. The results indicate that the bulk involute channel flow does not differ significantly from a flat parallel channel flow and that the curvature of the walls does not significantly alter the mean flow parameters. However, the regions of the involute channel near the side walls exhibit relatively low magnitude twin recirculation structures driven toward the side walls from the centerline of the channel, which warrants further study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Direct numerical simulation of compressible free shear flows

Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified.

Lele, Sanjiva K.↗

Interactions of Tollmien-Schlichting waves and Dean vortices. Comparison of direct numerical simulation and a weakly nonlinear theory

Direct numerical simulation is used to evaluate a weakly nonlinear theory describing the interaction of Tollmien-Schlichting waves with Dean vortices in curved channel flow. The theory and the simulation agree for certain combinations of parameters, but the two approaches give conflicting results for other combinations. Some possibilities for these discrepancies are discussed.

Singer, Bart A.↗

Direct numerical simulation of compressible free shear flows

Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. A simple explanation of the stabilizing effect of compressibility is offered. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified.

Lele, Sanjiva K.↗

Direct numerical simulation of compressible free shear flows

Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. A simple explanation of the stabilizing effect of compressibility is offered. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified.

Lele, Sanjiva K.↗

Parallel spatial direct numerical simulations on the Intel iPSC/860 hypercube

The implementation and performance of a parallel spatial direct numerical simulation (PSDNS) approach on the Intel iPSC/860 hypercube is documented. The direct numerical simulation approach is used to compute spatially evolving disturbances associated with the laminar-to-turbulent transition in boundary-layer flows. The feasibility of using the PSDNS on the hypercube to perform transition studies is examined. The results indicate that the direct numerical simulation approach can effectively be parallelized on a distributed-memory parallel machine. By increasing the number of processors nearly ideal linear speedups are achieved with nonoptimized routines; slower than linear speedups are achieved with optimized (machine dependent library) routines. This slower than linear speedup results because the Fast Fourier Transform (FFT) routine dominates the computational cost and because the routine indicates less than ideal speedups. However with the machine-dependent routines the total computational cost decreases by a factor of 4 to 5 compared with standard FORTRAN routines. The computational cost increases linearly with spanwise wall-normal and streamwise grid refinements. The hypercube with 32 processors was estimated to require approximately twice the amount of Cray supercomputer single processor time to complete a comparable simulation; however it is estimated that a subgrid-scale model which reduces the required number of grid points and becomes a large-eddy simulation (PSLES) would reduce the computational cost and memory requirements by a factor of 10 over the PSDNS. This PSLES implementation would enable transition simulations on the hypercube at a reasonable computational cost.

Joslin, Ronald D.↗

Direct Numerical Simulations of Turbulent Flow over Misaligned Traveling Waves

Direct numerical simulations of turbulent flow over prescribed traveling waves in a half-channel flow setup subject to a combined streamwise and spanwise pressure gradient are performed at a friction Reynolds number of 180. The simulations undertaken in this study consider both flow-aligned (including opposing and following) and misaligned waves as we attempt to quantify the effect of wave misalignment on turbulence statistics, the pressure drag force, and the wave attenuation rate. For the simulations, we consider three characteristic wave age values corresponding to slow-, intermediate-, and fast-moving waves. Wave misalignment is taken into account by applying a spanwise pressure gradient vertical to the traveling waves, which results in a three-dimensional turbulent flow field above the moving waves. Key flow quantities such as the mean velocity, velocity variances, and momentum fluxes are found to vary with the wave parameters, confirming the findings of previous studies.

direct numerical simulation↗

Direct numerical simulations of transition in a compressible wake

Direct numerical simulations of a compressible wake are performed to determine the sensitivity of large-scale motions to initial phase lags between the most unstable two-dimensional wave and a pair of oblique waves, and to determine the effect of Mach number on the development of three-dimensional motions. The vorticity dynamics of the flow are studied, and it is determined that, depending upon the initial phase lag, the interaction of the streamwise vorticity with the spanwise vortices may result in the formation of closed vortex loops, or in the removal of streamwise vorticity from the saddle region between the spanwise vortices. Due to lower growth rates experienced at high Mach numbers, the roll-up process is delayed, and the resultant nonlinear motions are much more diffuse.

Chen, Jacqueline H.↗

Direct Numerical Simulation of a Weakly Stratified Turbulent Wake

Direct numerical simulation (DNS) is used to investigate a time-dependent turbulent wake evolving in a stably stratified background. A large initial Froude number is chosen to allow the wake to become fully turbulent and axisymmetric before stratification affects the spreading rate of the mean defect. The uncertainty introduced by the finite sample size associated with gathering statistics from a simulation of a time-dependent flow is reduced, compared to earlier simulations of this flow. The DNS reveals the buoyancy-induced changes to the turbulence structure, as well as to the mean-defect history and the terms in the mean-momentum and turbulence-kinetic-energy budgets, that characterize the various states of this flow - namely the three-dimensional (essentially unstratified), non-equilibrium (or 'wake-collapse') and quasi-two-dimensional (or 'two-component') regimes observed elsewhere for wakes embedded in both weakly and strongly stratified backgrounds. The wake-collapse regime is not accompanied by transfer (or 'reconversion') of the potential energy of the turbulence to the kinetic energy of the turbulence, implying that this is not an essential feature of stratified-wake dynamics. The dependence upon Reynolds number of the duration of the wake-collapse period is demonstrated, and the effect of the details of the initial/near-field conditions of the wake on its subsequent development is examined.

Redford, J. A.↗

Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2

Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO 2 , it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO 2 . While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO 2 -brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO 2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO 2 obtained from core flow experiments and direct numerical simulation.

Kohanpur, Amir H.↗