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NASA NTRS1978

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

Sislian, J. P.↗

NASA NTRS1998

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

SanAndres, Luis↗

DOE OSTI2023

As a Matter of Dynamical Range – Scale Dependent Energy Dynamics in MHD Turbulence

Abstract Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, and direct numerical simulation (DNS)). Using an energy transfer analysis framework we calculate the effective numerical viscosities and resistivities, and demonstrate that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that—contrary to hydrodynamic turbulence—the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at 2048 3 cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

Origin and dynamics of emission line clouds in cooling flow environments

The author suggests that since clouds are born co-moving in a turbulent intra-cluster medium (ICM), the allowed parameter space can now be opened up to a more acceptable range. Large-scale motions can be driven in the central parts of cooling flows by a number of mechanisms including the motion of the central and other galaxies, and the dissipation of advected, focussed rotational and magnetic energy. In addition to the velocity width paradox, two other paradoxes (Heckman et al. 1989) can be solved if the ICM is turbulent. Firstly, the heating source for the emission line regions has always been puzzling - line luminosities are extremely high for a given (optical or radio) galaxy luminosity compared to those in non-cooling flow galaxies, therefore a mechanism peculiar to cooling flows must be at work. However most, if not all, previously suggested heating mechanisms either fail to provide enough ionization or give the wrong line ratios, or both. The kinetic energy in the turbulence provides a natural energy source if it can be efficiently converted to cloud heat. Researchers suggest that this can be done via magneto-hydrodynamic waves through plasma slip. Secondly, while the x ray observations indicate extended mass deposition, the optical line emission is more centrally concentrated. Since many of the turbulence-inducing mechanisms are strongest in the central regions of the ICM, so is the method of heating. In other words material is dropping out everywhere but only being lit up in the center.

Loewenstein, Michael↗

NASA NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

DOE OSTI2026

Divertor detachment and heat exhaust mitigation control in KSTAR with tungsten divertor

KSTAR has recently undergone an upgrade to use a new tungsten divertor to run experiments in ITER-relevant scenarios. Even with a high melting point of tungsten, it is important to control the heat flux impinging on tungsten divertor targets to minimize sputtering and contamination of the core plasma. Heat flux on the divertor is often controlled by increasing the degree of detachment of scrape-off layer plasma from the target plates. In this work, we have demonstrated successful divertor detachment and heat exhaust dissipation control experiments using two different methods. The first method uses attachment fraction as a control variable which is estimated using ion saturation current measurements from embedded Langmuir probes in the divertor. The second method uses a novel machine-learning-based surrogate model of 2D UEDGE simulation database, DivControlNN. We demonstrated running inference operation of DivControlNN in realtime to estimate heat flux at the divertor and use it as the control variable in a feedback loop with impurity gas flow. We present interesting insights from these experiments including a systematic approach to tuning controllers and discuss future improvements in the control infrastructure and control variables for future burning plasma experiments.

KSTAR tungsten divertor operations↗

NASA NTRS1975

Experimental and Theoretical Studies of Pulsating Turbulent Flow

The objective of this investigation was to study the effects of small amplitude sinusoidal pulsations on fully developed turbulent flow in a tube from both experimental and theoretical viewpoints. Theoretical models for the macroscopic behavior of pulsating turbulent tube flow were developed for the two cases of very low and very high pulsation frequencies. The models are based on assumptions of quasi-steady and frozen eddy viscosity flow behavior, respectively. The models successfully predict unsteady velocity profiles, thereby supporting the currently proposed definitions of frequency regimes in pulsating turbulent flow. Experimental measurements were made of the time-dependent pressure drop and velocity profiles over the range of frequency-to-Reynolds number ratios from 0.0095 to 0.24. The two macroscopic models developed in this study predict unsteady velocity profiles which are in moderately good agreement with the experiments in their respective frequency regimes, and a previously developed quasi-steady model is found to predict experimental velocity profiles well in both the quasisteady and the frozen eddy viscosity frequency regimes. The effect of flow pulsations on the dissipation of turbulence energy in the vicinity of the wall was measured in the lower transition frequency regime. The long-time averaged dissipation was observed to be unchanged from the steady flow dissipation, within the accuracy of the experiment. A theoretical model of the periodic viscous sublayer was also developed and applied to pulsating flow in a tube, in order to investigate the effects of flow pulsations on the rate of production of turbulence in the region of the wall. The periodic viscous sublayer model predicts sublayer growth periods in steady flow which agree with the published experimental data. When the model is applied to pulsating flow, the response of the sublayer growth period falls into three frequency regimes, the parameters of which are in approximate agreement with the frequency regimes which are defined on the basis of macroscopic flow behavior. The sublayer renewal cycle exhibits quasi-steady flow behavior when the sublayer growth period is much less than the pulsation period, transition behavior when these two periods are approximately equal, and frozen eddy viscosity behavior when the sublayer period is much longer than the pulsation period. The effect of the sublayer growth and renewal cycle on the level of turbulence was investigated by two methods. The velocity fluctuations seen by a point velocity probe located close to the wall were predicted from the model in one method and the rate of turbulence production was estimated from the frequency of sublayer renewal events in the other.

Kingston, G. C.↗

NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗

NASA NTRS2020

Implicit Large-Eddy Simulations of Hot and Cold Supersonic Jets in Loci-CHEM

Turbulence is a critical factor in most aero- and propulsion-related flows. For many years, the industry-standard approach to incorporating the effect of turbulence in computational fluid dynamics (CFD)calculations has been the Reynolds Averaged Navier Stokes (RANS) modeling approach. RANS implicitly time-averages turbulent motion, and models its effect on the mixing of species, momentum, and energy in a flow field. The approach is economical and often allows a CFD calculation to proceed to steady-state. However, it makes several simplifying assumptions, and the results will only be as good as the RANS turbulence model. Meanwhile, the last two decades have witnessed rapid and explosive growth in computational power, the development of CFD codes which scale well over thousands of processors, and the refinement of unstructured grid-generation tools which facilitate rapid surface and volume gridding of complex geometries. CFD engineering calculations of 108– 109 finite-volume cells have become routine. Thus, large eddy simulation (LES), which attempts to directly resolve the unsteady motion of the largest scales of turbulence, is increasingly of interest for many fluids engineering problems. Additionally, hybrid RANS-LES approaches such as Spalart’s Detached Eddy Simulation (DES), which attempt to marry the best strengths of both methods, are in active use and development. Because it seeks to accurately resolve the unsteady motion of the largest scales of turbulence, LES places certain requirements on the numerical method used to discretize and advance the Navier Stokes equations. In particular, LES requires high time accuracy and minimal intrinsic numerical dispersion and dissipation over a wide range of length scales.

C I Morris↗

NASA NTRS1998

Self-Similar Compressible Free Vortices

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

vonEllenrieder, Karl↗

DOE OSTI2023

Large eddy simulation of atmospheric boundary layer flow over complex terrain in comparison with RANS simulation and on-site measurements under neutral stability condition

Large eddy simulation (LES) of the atmospheric boundary layer (ABL) flow over complex terrain is presented with a validation using meteorological tower (met-tower) data through an improved neutral stability sampling approach. The proposed stability sampling procedure includes a condition based on the most-likely occurrence time-periods of the neutral ABL and reduces the variabilities of the conditional wind statistics calculated at the met-towers in comparison to our previous work. The ABL flow simulations are carried out over a potential wind site with a prominent hill based using the OpenFOAM-based simulator for on/off-shore wind farm applications by applying the Lagrangian-averaged scale-invariant dynamic sub-grid scale turbulence model. A low-dissipative scale-selective discretization scheme for the non-linear convection term in the LES governing equation is adopted implicitly to ensure both the second-order accuracy and bounded solution. The LES inflow is generated through a precursor method with a “tiling” approach based on the flow driving parameters obtained from a corresponding Reynolds-averaged Navier–Stokes (RANS) simulation. Overall, the averaged wind velocity profiles predicted by the LES approach at all met-tower locations show a similar tendency as the RANS results, which are also in reasonable agreement with the met-tower data. An obvious difference in wind speed standard deviation profiles is seen between LES and RANS, especially at regions downstream of the hill edge, where the LES shows under-predicted results at the highest measurement levels in comparison to the tower data. The computational costs of the LES are found to be about 20 times higher than the RANS simulations.

Energy & Fuels↗

NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗

NASA NTRS1999

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Yee, H. C.↗

NASA NTRS2010

An Attempt to Derive the epsilon Equation from a Two-Point Closure

The goal of this paper is to derive the equation for the turbulence dissipation rate epsilon for a shear-driven flow. In 1961, Davydov used a one-point closure model to derive the epsilon equation from first principles but the final result contained undetermined terms and thus lacked predictive power. Both in 1987 and in 2001, attempts were made to derive the epsilon equation from first principles using a two-point closure, but their methods relied on a phenomenological assumption. The standard practice has thus been to employ a heuristic form of the equation that contains three empirical ingredients: two constants, c(sub 1 epsilon), and c(sub 2 epsilon), and a diffusion term D(sub epsilon) In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c(sub 1), c(sub 2), which are now functions of Kappa and epsilon; 2) c(sub 1) and c(sub 2) are not independent because a general relation between the two that are valid for any Kappa and epsilon are derived; 3) c(sub 1), c(sub 2) become constant with values close to the empirical values c(sub 1 epsilon), c(sub epsilon 2), (i.e., homogenous flows); and 4) the empirical form of the diffusion term D(sub epsilon) is no longer needed because it gets substituted by the Kappa-epsilon dependence of c(sub 1), c(sub 2), which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy D(sub Kappa), which now enters the new equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c(sub 1 epsilon), c(sub epsilon 2), D (sub epsilon)are replaced by a single function c(sub 1)(Kappa, epsilon ) or c(sub 2)(Kappa, epsilon ), plus a D(sub Kappa)term. Three tests of the new equation for epsilon are presented: one concerning channel flow and two concerning the shear-driven planetary boundary layer (PBL).

Canuto, V. M.↗

DOE OSTI2024

DRDMannTurb: A Python package for scalable, data-driven synthetic turbulence

Synthetic turbulence models (STMs) are used in wind engineering to generate realistic flow fields and are employed as inputs to industrial wind simulations. Examples include prescribing inlet conditions in large eddy simulations that model loads on wind turbines and tall buildings. We are interested in STMs capable of generating fluctuations based on prescribed second-moment statistics since such models can simulate environmental conditions that closely resemble on-site observations. To this end, the widely used Mann model (see Mann, 1994, 1998) is the inspiration for DRDMannTurb. The Mann model is described by three physical parameters: a magnitude parameter influencing the global variance of the wind field and corresponding to the Kolmogorov constant multiplied by the rate of viscous dissipation of the turbulent kinetic energy to the two-thirds, αϵ 2/3 , a turbulence length scale parameter L, and a nondimensional parameter Γ related to the lifetime of the eddies. A number of studies, as well as international standards (e.g., those by the International Electrotechnical Commission (IEC)), include recommended values for these three parameters with the goal of standardizing wind simulations according to observed energy spectra. Yet, having only three parameters, the Mann model faces limitations in accurately representing the diversity of observable spectra. This Python package enables users to extend the Mann model and more accurately fit field measurements through flexible neural network models of the eddy lifetime function. Following Keith et al. (2021), we refer to this class of models as Deep Rapid Distortion (DRD) models. DRDMannTurb also includes a general module implementing an efficient method for synthetic turbulence generation based on a domain decomposition technique. This technique is also described in Keith et al. (2021).

17 WIND ENERGY↗

DOE OSTI2020

Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics

Euler-Lagrange point-particle simulation has emerged as a premier methodology for studying dispersed particle-laden flows. This method's popularity stems from its ability to resolve fine-scale fluid structures while also tracking individual particles at reduced cost using an appropriate particle acceleration model. However, the point-particle model has known convergence issues in that refinement of the fluid grid can lead to changes in the predicted statistics. The reasons for non-convergence are twofold: the point-particle two-way coupling force in the Navier-Stokes equations requires a numerical regularization and, without careful implementation, yields a singular force on the fluid with grid refinement. The second factor that yields grid-dependent statistics is that the point-particle force model in general depends on the undisturbed fluid velocity. When the undisturbed fluid velocity is not robustly modeled in a grid-insensitive way, the calculated force for both particles and fluid will be grid-dependent, contaminating their respective statistics. While the first issue regarding regularizing the point-particle source term has received attention in the literature, the consequences of robustly modeling the undisturbed velocity in the context of grid refinement of turbulence has received little attention. Here, we consider decaying homogeneous isotropic turbulence laden with particles at different Stokes numbers. For a given Stokes number, we systematically refine the grid and demonstrate that explicitly modeling the undisturbed fluid velocity yields relative grid insensitivity for the energy of the particle and fluid phases, as well as acceleration of the particles. We also demonstrate that an appropriately defined dissipation rate is also grid-insensitive when an undisturbed fluid velocity correction is used. In contrast, when the undisturbed fluid velocity is modeled using the conventional approach of interpolating the local fluid velocity to the particle location, we show this procedure yields divergent statistics with grid refinement. In particular, we show that higher-order interpolation of the fluid velocity in two-way coupled problems is worse than lower-order interpolation, in the absence of a correction procedure to estimate the undisturbed fluid velocity. We also examine velocity derivative statistics of the fluid phase and demonstrate that these statistics are not in general convergent even when the undisturbed fluid velocity is explicitly modeled. Collectively, the observations in this paper are used to present a philosophy on the types of questions which are answerable with point-particle methods.

42 ENGINEERING↗

NASA NTRS1998

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.

Hogan, Robert C.↗

DOE OSTI2024

Large-eddy simulations of turbulent wake flows behind helical- and straight-bladed vertical axis wind turbines rotating at low tip speed ratios

Turbulent wake flows behind helical- and straight-bladed vertical axis wind turbines (VAWTs) rotating at low tip speed ratios (TSRs) are studied numerically. The turbulent flows are simulated using the large-eddy simulation (LES) model, and the rotating turbine blades are modeled using the actuator line method. The helical VAWT has identical key parameters as the straight VAWT except for the 135° helical twist of the blades over the 0.3m vertical span. A set of LES runs are performed for two TSRs, 0.6 and 0.4, and the results are reported and analyzed. At these low TSRs, the wake behind the straight-bladed VAWT exhibits two-dimensional dominant flow motions (in the horizontal plane perpendicular to the straight blades) in the near-wake region that cause considerable spanwise expansion of the wake as it extends downstream. In contrast, the helical-bladed VAWT generates highly three-dimensional (3D) wake flow structures and upward/downward mean flow motions within the wake that cause the wake to expand mainly in the vertical direction. Turbulence statistical analyses also show that the 3D wake flow features induced by the helical blades accelerate the wake transition to turbulence and enhance the small-scale turbulent dissipation (as shown by the subgrid-scale turbulent dissipation in the LES), which leads to a more rapid decay of the wake turbulence intensity than that in the straight-bladed VAWT case at the same TSR. Finally, compared with the straight-bladed VAWT, the helical-bladed VAWT also exhibits much smaller temporal variations for the torque and power coefficients during the rotation cycle, which can be beneficial for wind power generation.

17 WIND ENERGY↗