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DOE OSTI2023

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

Engineering↗

NASA NTRSDate not supplied

Large Eddy Simulations of Upper-Ocean Turbulence Across the Equatorial Pacific Cold Tongue

Turbulence in the equatorial Pacific cold tongue plays multiple roles in the sea-surface temperature budget. However, observations of turbulence are limited to a handful of field experiments lasting from a few days to one month at 0 N , 140 W, and the key turbulent fluxes can only be inferred. Although explicit simulations of turbulence resolve these fluxes, the required large eddy simulations (LES) are costly and thus also limited to a few weeks. A two-fold hypothesis motivates this contribution to the PUMP pre-field modelling experiments in support of TPOS: 1) that there exist useful relationships between the surface wind, wave, and buoyancy forcing, oceanic shear and stratification, and turbulent mixing, but 2) these relationships differ between regions of equatorial dynamics (f~0) and higher latitudes, such that the state space is insufficiently sampled to understand these relationships and represent them in ocean general circulation models (OGCM). To address the lack of observations, we simulated 35 continuous days of upper ocean turbulence using LES during October-November 1985 at sites in two regions (70 days in total) of the cold tongue: 0 N, 140 W and 3 N, 140 W. The model reproduces many features of the observed turbulence at 0,140W, including the “deep-cycle” observed by Gregg et al. (1985) Nature and the turbulent pulses every few hours during the night and in the early morning. Furthermore, the results at 3 N support the hypothesis advanced by Cherian et al. (2021) JPO that strong, but intermittent deep-cycle turbulence is observed to the north of the equator in the presence of strong shear associated with Tropical Instability Waves. Comparisons with the K-profile parameterization (KPP) scheme show that additional tuning of the KPP parameters can reduce differences between the turbulent fluxes produced by KPP and LES at both sites. The results will suggest modifications to OGCMs and already emphasize the need for a more extensive measurements of vertical profiles of shear, stratification and turbulent mixing to reveal the spatio-temporal structure of turbulence and how it relates to forcing, shear and stratification across the equatorial Pacific Cold tongue.

Large Eddy Simulations↗

DOE OSTI2019

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(10 5 )) moving bodies, utilizing many computational cores (O(10 5 )), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS

The role of turbulence and magnetic fields is studied for star formation in molecular clouds. We derive and compare six theoretical models for the star formation rate (SFR)-the Krumholz and McKee (KM), Padoan and Nordlund (PN), and Hennebelle and Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC-all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields and show that the SFR depends on four basic parameters: (1) virial parameter {alpha}{sub vir}; (2) sonic Mach number M; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma {beta}=2M{sub A}{sup 2}/M{sup 2} with the Alfven Mach number M{sub A}. We compare all six theories with MHD simulations, covering cloud masses of 300 to 4 Multiplication-Sign 10{sup 6} M{sub Sun} and Mach numbers M=3-50 and M{sub A}=1-{infinity}, with solenoidal (b = 1/3), mixed (b = 0.4), and compressive turbulent (b = 1) forcings. We find that the SFR increases by a factor of four between M=5 and 50 for compressive turbulent forcing and {alpha}{sub vir} {approx} 1. Comparing forcing parameters, we see that the SFR is more than 10 times higher with compressive than solenoidal forcing for M=10 simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All simulations are fit simultaneously by the multi-freefall KM and multi-freefall PN theories within a factor of two over two orders of magnitude in SFR. The simulated SFRs cover the range and correlation of SFR column density with gas column density observed in Galactic clouds, and agree well for star formation efficiencies SFE = 1%-10% and local efficiencies {epsilon} = 0.3-0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Three-dimensional hybrid simulation study of anisotropic turbulence in the proton kinetic regime

Three-dimensional numerical hybrid simulations with particle protons and quasi-neutralizing fluid electrons are conducted for a freely decaying turbulence that is anisotropic with respect to the background magnetic field. The turbulence evolution is determined by both the combined root-mean-square (rms) amplitude for fluctuating proton bulk velocity and magnetic field and by the ratio of perpendicular to parallel wavenumbers. This kind of relationship had been considered in the past with regard to interplanetary turbulence. The fluctuations nonlinearly evolve to a turbulent phase whose net wave vector anisotropy is usually more perpendicular than the initial one, irrespective of the initial ratio of perpendicular to parallel wavenumbers. Self-similar anisotropy evolution is found as a function of the rms amplitude and parallel wavenumber. Proton heating rates in the turbulent phase vary strongly with the rms amplitude but only weakly with the initial wave vector anisotropy. Even in the limit where wave vectors are confined to the plane perpendicular to the background magnetic field, the heating rate remains close to the corresponding case with finite parallel wave vector components. Simulation results obtained as a function of proton plasma to background magnetic pressure ratio β {sub p} in the range 0.1-0.5 show that the wave vector anisotropy also weakly depends on β {sub p}.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2007

Turbulence Modeling for the Simulation of Transition in Wall Shear Flows

Our research involves study of the behavior of k-epsilon turbulence models for simulation of bypass-level transition over flat surfaces and turbine blades. One facet of the research has been to assess the performance of a multitude of k-epsilon models in what we call "natural transition", i.e. no modifications to the k-e models. The study has been to ascertain what features in the dynamics of the model affect the start and end of the transition. Some of the findings are in keeping with those reported by others (e.g. ERCOFTAC). A second facet of the research has been to develop and benchmark a new multi-time scale k-epsilon model (MTS) for use in simulating bypass-level transition. This model has certain features of the published MTS models by Hanjalic, Launder, and Schiestel, and by Kim and his coworkers. The major new feature of our MTS model is that it can be used to compute wall shear flows as a low-turbulence Reynolds number type of model, i.e. there is no required partition with patching a one-equation k model in the near-wall region to a two-equation k-epsilon model in the outer part of the flow. Our MTS model has been studied extensively to understand its dynamics in predicting the onset of transition and the end-stage of the transition. Results to date indicate that it far superior to the standard unmodified k-epsilon models. The effects of protracted pressure gradients on the model behavior are currently being investigated.

Crawford, Michael E.↗

NASA NTRS1982

Numerical simulation of wall-bounded turbulent shear flows

Developments in three dimensional, time dependent numerical simulation of turbulent flows bounded by a wall are reviewed. Both direct and large eddy simulation techniques are considered within the same computational framework. The computational spatial grid requirements as dictated by the known structure of turbulent boundary layers are presented. The numerical methods currently in use are reviewed and some of the features of these algorithms, including spatial differencing and accuracy, time advancement, and data management are discussed. A selection of the results of the recent calculations of turbulent channel flow, including the effects of system rotation and transpiration on the flow are included.

Moin, P.↗

NASA NTRS1982

Numerical simulation of wall-bounded turbulent shear flows

Moin, P.↗

DOE OSTI2024

Large-scale Linear Magnetic Holes with Magnetic Mirror Properties in Hybrid Simulations of Solar Wind Turbulence

Magnetic holes (MHs) are coherent magnetic field dips whose size ranges from fluid to kinetic scale, ubiquitously observed in the heliosphere and in planetary environments. Despite the long-standing effort in interpreting the abundance of observations, the origin and properties of MHs are still debated. In this Letter, we investigate the interplay between plasma turbulence and MHs, using a 2D hybrid simulation initialized with solar wind parameters. We show that fully developed turbulence exhibits localized elongated magnetic depressions, whose properties are consistent with linear MHs frequently encountered in space. The observed MHs develop self-consistently from the initial magnetic field perturbations by trapping hot ions with large pitch angles. Ion trapping produces an enhanced perpendicular temperature anisotropy that makes MHs stable for hundreds of ion gyroperiods, despite the surrounding turbulence. We introduce a new quantity, based on local magnetic field and ion temperature values, to measure the efficiency of ion trapping, with potential applications to the detection of MHs in satellite measurements. We complement this method by analyzing the ion velocity distribution functions inside MHs. Our diagnostics reveal the presence of trapped gyrotropic ion populations, whose velocity distribution is consistent with a loss cone, as expected for the motion of particles inside a magnetic mirror. Our results have potential implications for the theoretical and numerical modeling of MHs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian–Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, “Numerical study of collisional particle dynamics in cluster-induced turbulence,” J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.

42 ENGINEERING↗

NASA NTRS1990

Plane waves and structures in turbulent channel flow

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

Sirovich, L.↗

NASA NTRS2014

Shock Wave Interactions: A CFD Study of CUBRC LENS-II Turbulent Experiments

Results of flow simulations of turbulent shock wave boundary layer interaction experiments performed in the LENS-II tunnel at CUBRC.

Turbulent flow↗

NASA NTRS1997

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗

NASA NTRS1995

Simulation of rotor blade element turbulence

A piloted, motion-based simulation of Sikorsky's Black Hawk helicopter was used as a platform for the investigation of rotorcraft responses to vertical turbulence. By using an innovative temporal and geometrical distribution algorithm that preserved the statistical characteristics of the turbulence over the rotor disc, stochastic velocity components were applied at each of twenty blade-element stations. This model was implemented on NASA Ames' Vertical Motion Simulator (VMS), and ten test pilots were used to establish that the model created realistic cues. The objectives of this research included the establishment of a simulation-technology basis for future investigation into real-time turbulence modeling. This goal was achieved; our extensive additions to the rotor model added less than a 10 percent computational overhead. Using a VAX 9000 computer the entire simulation required a cycle time of less than 12 msec. Pilot opinion during this simulation was generally quite favorable. For low speed flight the consensus was that SORBET (acronym for title) was better than the conventional body-fixed model, which was used for comparison purposes, and was determined to be too violent (like a washboard). For high speed flight the pilots could not identify differences between these models. These opinions were something of a surprise because only the vertical turbulence component on the rotor system was implemented in SORBET. Because of the finite-element distribution of the inputs, induced outputs were observed in all translational and rotational axes. Extensive post-simulation spectral analyses of the SORBET model suggest that proper rotorcraft turbulence modeling requires that vertical atmospheric disturbances not be superimposed at the vehicle center of gravity but, rather, be input into the rotor system, where the rotor-to-body transfer function severely attenuates high frequency rotorcraft responses.

Mcfarland, R. E.↗

DOE OSTI2026

Simulations of a hypersonic turbulent boundary layer over wavy surfaces

Here, we conduct large-eddy simulations of a Mach 5.84 cold wall turbulent boundary layer over one-dimensional wavy walls with varying amplitudes and wavelengths. Across all wall topologies, a series of alternating shock and expansion waves is shown to influence the entire boundary layer, and generate repeating wave patterns in the turbulent stresses, dispersive stresses, and turbulent kinetic energy budget. The series of alternating shocks and expansions imposes repeating adverse and favourable pressure gradients across the wavy wall, and at sufficient wall amplitude, triggers flow separation in the trough of the wave. Flow separation is demonstrated to influence the behaviour of wall pressure fluctuations over the wavy wall. In attached flows, the prominent frequencies are consistent with integral-scale boundary layer turbulence, whereas in separated flows, a two-decade frequency range is present, akin to two-dimensional shock–boundary layer interactions. Counter-rotating streamwise-oriented structures are observed on the windward side of the wave, which diminish over the wave crest. A conditional analysis demonstrates that these structures are present in the upstream boundary layer, and are amplified with increasing wall amplitude. An examination of the Görtler number and probability density function (PDF) of the fluctuating lateral wall shear stress demonstrates the strong correlation between a large Görtler number and growth of the PDF tail density, suggesting that the amplification of the counter-rotating streamwise-oriented structures are linked to centrifugal instabilities in regions of streamline concavity.

boundary layers↗

DOE OSTI2019

Self-consistent simulation of transport and turbulence in tokamak edge plasma by coupling SOLPS-ITER and BOUT++

The status of coupling the fluid plasma/neutral 2D transport code SOLPS-ITER and the fluid 3D turbulence code BOUT++ is reported. Both codes simulated the same region, which is from several cm inside the magnetic separatrix to the far scrape-off layer (SOL). Compared to the profile evolution time scale, the characteristic time scale of the turbulence is quite short. For the turbulence code BOUT++, the time scale is around 10 -6 s. However, for the transport code SOLPS-ITER, the time scale is around 10 -3 –10 -2 s. An iterative scheme is used that each system is evolved on its own characteristic time scale. SOLPS-ITER can provide the background profiles of density, ion, and electron temperature to BOUT++. In turn, BOUT++ can provide the corresponding radial transport coefficients to SOLPS-ITER. The coupling has involved the ion density, ion temperature, and electron temperature. After several steps of iteration, the profiles of density, ion, and electron temperature show fluctuations, and the differences of the changes between two consecutive profiles are getting smaller and smaller. Finally, the self-consistent solutions of turbulence and transport can be obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Viscosity Control Experiment Feasibility Study

Turbulent mix has been invoked to explain many results in Inertial Confinement Fusion (ICF) and High Energy Density (HED) physics, such as reduced yield in capsule implosions. Many ICF capsule implosions exhibit interfacial instabilities seeded by the drive shock, but it is not clear that fully developed turbulence results from this. Many simulations use turbulent mix models to help match simulation results to data, but this is not appropriate if turbulence is not present. It would be useful to have an experiment where turbulent mixing could be turned on or off by design. The use of high-Z dopants to modify viscosity and the resulting influence on turbulence is considered here. A complicating factor is that the plasma in some implosions can become strongly coupled, which makes the Spitzer expression for viscosity invalid. We first consider equations that cover a broad parameter space in temperature and density to address regimes for various experimental applications. Next, a previous shock-tube and other ICF experiments that investigate viscosity or use doping to examine the effects on yield are reviewed. How viscosity and dopants play a role in capsule yield depends on the region and process under consideration. Experiments and simulations have been performed to study the effects of viscosity on both the hot spot and the fuel/ablator mix. Increases in yield have been seen for some designs, but not all. We then discuss the effect of adding krypton dopant to the gas region of a typical OMEGA and a 2-shock NIF implosion to determine approximately the effect of adding dopant on the computed Reynolds number. Recommendations for a path forward for possible experiments using high-Z dopants to affect viscosity and turbulence are made.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

An LES study of secondary motion and wall shear stresses in a pipe bend

In this study, large-eddy simulations (LES) of a single-phase, turbulent flow in a 90 ° pipe bend are performed at three Reynolds numbers (5300, 27 000, and 45 000) to investigate the correlation between secondary flow motion and wall shear stresses, which is suspected to be a potential mechanism responsible for material erosion. The isothermal flows are validated against available experimental and numerical data first. The snapshot proper orthogonal decomposition (POD) is applied for the medium and high Reynolds number flows to identify the secondary flow motions and the oscillation of the Dean vortices that are found to cause swirl-switching. Distinguished frequencies of the POD time coefficients at Strouhal numbers of 0.25 and 0.28 are identified for Reynolds numbers at 27 000 and 45 000, respectively. Moreover, shear stress on the pipe wall and the associated power spectral density are obtained and shown to have the same oscillating frequency as the swirl-switching.

42 ENGINEERING↗