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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Challenge Problem 1: Preliminary Results of the Direct Numerical Simulation of Transient Flows

This report presents the first direct numerical simulations (DNS) of transient mixed convection in an idealized downcomer-like channel (Challenge Problem 1, Phase II). Using the GPU-accelerated NekRS solver, we modeled a sudden decay in driving pressure, mimicking loss-of-flow events, and tracked the resulting evolution of Reynolds number, boundary-layer structure, turbulence statistics, and heat-transfer metrics. Key findings include the systematic thickening and eventual asymmetry of velocity and thermal boundary layers under buoyant deceleration; minimal “memory” lag in Reynolds shear stress and TKE profiles when sampled at matching Re, yet clear shifts of peak locations toward the cooled wall; overshoots in transient eddy-viscosity and eddy-diffusivity (and corresponding sub-unity turbulent Prandtl numbers) on the cooled side; and a pronounced transient Nusselt-number enhancement driven by wall-temperature inertia and residual eddy mixing. These effects combined to offer a temporary cooling margin above steady-state predictions during reactor LOF transients. Future work will extend this work to a more complex “Case II” geometry (90° turn + lower plenum) and generate multi-Re/Pr datasets for data-driven turbulence closures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1997

Direct numerical simulations of fluid flow, heat transfer and phase changes

Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

Phase Transformations↗
NASA NTRS1984

Direct numerical simulation of reacting flows

The objectives of this work are: (1) to extend the technique of direct numerical simulations to turbulent, chemically reacting flows, (2) to test the validity of the method by comparing computational results with laboratory data, and (3) to use the simulations to gain a better understanding of the effects of turbulence on chemical reactions. The effects of both the large scale structure and the smaller scale turbulence on the overall reaction rates are addressed. The relationship between infinite reaction rate and finite reaction rate chemistry is compared with some of the results of calculations with existing theories and laboratory data. The direct numerical simulation method involves the numerical solution of the detailed evolution of the complex turbulent velocity and concentration fields. Using very efficient numerical methods (e.g., pseudospectral methods), the fully nonlinear (possibly low pass filtered) equations of motion are solved and no closure assumptions or turbulence models are used. Statistical data are obtained by performing spatial, temporal, and/or ensemble averages over the computed flow fields.

Riley, J. J.↗
NASA NTRS1995

Scalability of Parallel Spatial Direct Numerical Simulations on Intel Hypercube and IBM SP1 and SP2

The implementation and performance of a parallel spatial direct numerical simulation (PSDNS) approach on the Intel iPSC/860 hypercube and IBM SP1 and SP2 parallel computers is documented. Spatially evolving disturbances associated with the laminar-to-turbulent transition in boundary-layer flows are computed with the PSDNS code. The feasibility of using the PSDNS to perform transition studies on these computers is examined. The results indicate that PSDNS approach can effectively be parallelized on a distributed-memory parallel machine by remapping the distributed data structure during the course of the calculation. Scalability information is provided to estimate computational costs to match the actual costs relative to changes in the number of grid points. By increasing the number of processors, slower than linear speedups are achieved with optimized (machine-dependent library) routines. This slower than linear speedup results because the computational cost is dominated by FFT routine, which yields less than ideal speedups. By using appropriate compile options and optimized library routines on the SP1, the serial code achieves 52-56 M ops on a single node of the SP1 (45 percent of theoretical peak performance). The actual performance of the PSDNS code on the SP1 is evaluated with a "real world" simulation that consists of 1.7 million grid points. One time step of this simulation is calculated on eight nodes of the SP1 in the same time as required by a Cray Y/MP supercomputer. For the same simulation, 32-nodes of the SP1 and SP2 are required to reach the performance of a Cray C-90. A 32 node SP1 (SP2) configuration is 2.9 (4.6) times faster than a Cray Y/MP for this simulation, while the hypercube is roughly 2 times slower than the Y/MP for this application. KEY WORDS: Spatial direct numerical simulations; incompressible viscous flows; spectral methods; finite differences; parallel computing.

Joslin, Ronald D.↗
NASA NTRS1978

The direct numerical simulations of the turbulent wakes of axisymmetric bodies

Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.

Riley, J. J.↗
NASA NTRS1986

Direct numerical simulations of chemically reacting turbulent mixing layers

The results of direct numerical simulations of chemically reacting, turbulent mixing layers are presented. The reaction considered is a binary, irreversible reaction with no heat release, so that only the effect of the turbulence on the chemical reaction is investigated. The simulation results are shown to be consistent with similarity theory, and are found to be in approximate agreement with laboratory data, even though there are no adjustable parameters in the method.

Riley, J. J.↗
NASA NTRS1993

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Direct numerical simulations are used to investigate the interaction of isotropic quasi-incompressible turbulence with a weak shock wave. A linear analysis of the interaction is conducted for comparison with the simulations. Both the simulations and the analysis show that turbulence is enhanced during the interaction. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. It is suggested that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behavior not reproduced by the linear analysis. Analysis of the budget of the turbulent kinetic energy transport equation shows that this behavior can be attributed to the pressure transport term. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

Lee, Sangsan↗
NASA NTRS1998

Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow

A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.

Sharma, Chirdeep↗
NASA NTRS2002

Aspects of Supercritical Turbulence: Direct Numerical Simulation of O2/H2 and C7H16/N2 Temporal Mixing Layers

Results from Direct Numerical Simulations of temporal, supercritical mixing layers for two species systems are analyzed to elucidate species-specific turbulence aspects. The two species systems, O2/H2 and C7HG16/N2, have different thermodynamic characteristics; thus, although the simulations are performed at similar reduced pressure (ratio of the pressure to the critical pressure), the former system is dose to mixture ideality and has a relatively high solubility with respect to the latter, which exhibits strong departures from mixture ideality Due to the specified, smaller initial density stratification, the C7H16/N2 layers display higher growth and increased global molecular mixing as well as larger turbulence levels. However, smaller density gradients at the transitional state for the O2/H2 system indicate that on a local basis, the layer exhibits an enhanced mixing, this being attributed to the increased solubility and to mixture ideality. These thermodynamic features are shown to affect the irreversible entropy production (i.e. the dissipation), which is larger for the O2/H2 layer and is primarily concentrated in high density-gradient magnitude regions that are distortions of the initial density stratification boundary. In contrast, the regions of largest dissipation in the C7H16/N2 layer are located in high density-gradient magnitude regions resulting from the mixing of the two fluids.

Bellan, J.↗
NASA NTRS2013

Direct Numerical Simulation of Transition in a Swept-Wing Boundary Layer

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing derived from a two-dimensional, partial-differential-equation based eigenvalue computation; and the mode selected for forcing corresponds to the most amplified secondary instability mode which, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. Both the growth of the secondary instability wave and the resulting onset of laminar-turbulent transition are captured within the DNS computations. The growth of the secondary instability wave in the DNS solution compares well with linear secondary instability theory when the amplitude is small; the linear growth is followed by a region of reduced growth resulting from nonlinear effects before an explosive onset of laminar breakdown to turbulence. The peak fluctuations are concentrated near the boundary layer edge during the initial stage of transition, but rapidly propagates towards the surface during the process of laminar breakdown. Both time-averaged statistics and flow visualization based on the DNS reveal a sawtooth transition pattern that is analogous to previously documented surface flow visualizations of transition due to stationary crossflow instability. The memory of the stationary crossflow vortex is found to persist through the transition zone and well beyond the location of the maximum skin friction.

Duan, Lian↗
NASA NTRS2014

Direct Numerical Simulations of High-Speed Turbulent Boundary Layers over Riblets

Direct numerical simulations (DNS) of spatially developing turbulent boundary layers over riblets with a broad range of riblet spacings are conducted to investigate the effects of riblets on skin friction at high speeds. Zero-pressure gradient boundary layers under two flow conditions (Mach 2:5 with T(sub w)/T(sub r) = 1 and Mach 7:2 with T(sub w)/T(sub r) = 0:5) are considered. The DNS results show that the drag-reduction curve (delta C(sub f)/C(sub f) vs l(sup +)(sub g )) at both supersonic speeds follows the trend of low-speed data and consists of a `viscous' regime for small riblet size, a `breakdown' regime with optimal drag reduction, and a `drag-increasing' regime for larger riblet sizes. At l l(sup +)(sub g) approx. 10 (corresponding to s+ approx 20 for the current triangular riblets), drag reduction of approximately 7% is achieved at both Mach numbers, and con rms the observations of the few existing experiments under supersonic conditions. The Mach- number dependence of the drag-reduction curve occurs for riblet sizes that are larger than the optimal size, with smaller slopes of (delta C(sub f)/C(sub f) for larger freestream Mach numbers. The Reynolds analogy holds with 2(C(sub h)=C(sub f) approximately equal to that of at plates for both drag-reducing and drag-increasing configurations.

Duan, Lian↗
NASA NTRS2020

Direct Numerical Simulations of Acoustic Disturbances in Various Rectangular Nozzle Configurations

We perform Direct Numerical Simulations (DNS) to study the acoustic freestream disturbances radiating from the turbulent boundary layers along the contoured nozzle walls of a hypersonic wind tunnel with a rectangular test section. To begin with, the effects of the spanwise end walls are suppressed by confining the spanwise computational domain to a finite segment of the overall nozzle cross section and by imposing periodic boundary conditions across that spanwise domain. Besides providing a building-block configuration to reveal par- tial effects of the enclosed acoustic environment within the wind tunnel, these computations serve as a stepping stone toward the goal of fully-3D computations including the nozzle end walls. Building upon the earlier simulations of Deegan et al. (2018), we show that the computed acoustic characteristics in the spanwise periodic simulations are insensitive to changes in the grid resolution parameters (e.g., x+ and z+). This is relative to the previous simulations that involved a coarser resolution in the streamwise and wall-normal directions, especially up- stream of the test section. Furthermore, we outline a comparison of the pressure fluctuations induced by the turbulent boundary layers over the contoured nozzle walls and several other calculations involving boundary layers over a single flat plate at nearly the same value of the edge Mach number. We also show the impact of having only one turbulent boundary layer instead of two within the computational setup. Various flow statistics, including the first and second moments of the unsteady flow field, are computed for the different flow configurations. Good comparisons of the statistics of the nozzle-wall boundary-layer turbulence and of the freestream acoustic disturbances between the simulations of coarser and finer grids confirms DNS procedure, but also the insensitivity of noise characteristics t section to the inflow turbulence generation technique.

Hildebrand, Nathaniel↗
NASA NTRS1990

Direct numerical simulations of stably-stratified sheared turbulence: Implications for oceanic mixing

Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent shear flows have been performed for several Richardson numbers Ri and Reynolds numbers R(sub lambda) in earlier works. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ri(sub s), the turbulence intensity grows at all scales, and the growth rate appears to be a function of Ri. The size of the vertical density inversions also increases. On the other hand, when Ri is greater than or equal to Ri(sub s) the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale L(sub E) and the Ozmidov (buoyancy) scale L(sub O) are equal. At this point, the mixing efficiency is maximal and corresponds to a flux Richardson number R(sub f) = 0.20. The vertical mass flux becomes counter-gradient when epsilon = 19(nu)N(exp 2) and vertical density overturns are suppressed in less than half a Brunt-Vaisala period. The results of the simulations were also recast in terms of the Hydrodynamic Phase Diagram introduced in fossil turbulence models. The so-called point of fossilization occurs when epsilon = 4DCN(exp 2); Gibson proposed 13DCN(exp 2). This value is in agreement with indirect laboratory observations and field observations. Finally, the validity of the steady-state models to estimate vertical eddy diffusivities in the oceanic thermocline is discussed.

Itsweire, E. C.↗
NASA NTRS1992

Direct numerical simulation of instabilities in parallel flow with spherical roughness elements

Results from a direct numerical simulation of laminar flow over a flat surface with spherical roughness elements using a spectral-element method are given. The numerical simulation approximates roughness as a cellular pattern of identical spheres protruding from a smooth wall. Periodic boundary conditions on the domain's horizontal faces simulate an infinite array of roughness elements extending in the streamwise and spanwise directions, which implies the parallel-flow assumption, and results in a closed domain. A body force, designed to yield the horizontal Blasius velocity in the absence of roughness, sustains the flow. Instabilities above a critical Reynolds number reveal negligible oscillations in the recirculation regions behind each sphere and in the free stream, high-amplitude oscillations in the layer directly above the spheres, and a mean profile with an inflection point near the sphere's crest. The inflection point yields an unstable layer above the roughness (where U''(y) is less than 0) and a stable region within the roughness (where U''(y) is greater than 0). Evidently, the instability begins when the low-momentum or wake region behind an element, being the region most affected by disturbances (purely numerical in this case), goes unstable and moves. In compressible flow with periodic boundaries, this motion sends disturbances to all regions of the domain. In the unstable layer just above the inflection point, the disturbances grow while being carried downstream with a propagation speed equal to the local mean velocity; they do not grow amid the low energy region near the roughness patch. The most amplified disturbance eventually arrives at the next roughness element downstream, perturbing its wake and inducing a global response at a frequency governed by the streamwise spacing between spheres and the mean velocity of the most amplified layer.

Deanna, R. G.↗
DOE OSTI2020

Simulation scaling studies of reactor core two-phase flow using direct numerical simulation

Tremendous growth in supercomputing power in recent years has resulted in the emergence of high-resolution flow analysis methods as an advanced research tool to evaluate single and two-phase flow behavior. In particular, unstructured mesh-based methods have been applied to analyze flows in complex reactor core geometries, including those of light water reactors (LWR). The finite-element based code, PHASTA, is utilized to perform large-scale simulations of two-phase bubbly flows in LWR geometries. Given the large computational cost of direct numerical simulation (DNS) coupled with interface tracking methods (ITM), typical domains encompass a portion of a single subchannel. In the presented research, the state-of-the-art analysis of turbulent two-phase flows in complex LWR subchannel geometries are demonstrated at both prototypical reactor parameters as well as scaled low pressure conditions. Three different cases are studied, a high-pressure simulation in prototypical reactor subchannel geometry, a low-pressure case in prototypical geometry and a final low-pressure case in a geometry scaled up to conserve the ratio between the bubble size and the domain pitch. Utilizing advanced statistical processing tools, these simulation conditions are compared to shed light on the relevancy of two-phase flow characteristics given the significant differences between LWR and low-pressure conditions. These findings can lead to the generation of useful guiding principles when researchers need to scale the two-phase flow behavior captured at low pressure and temperature conditions to those at reactor operating conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. As a result, both quantities compare favorably with experiments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗