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NASA NTRS1990

Evolution and interaction of two- and three-dimensional instability waves

The present work is concerned with the nonlinear interactions of high-amplitude two- and three-dimensional instability waves in jets. A jet is excited by multifrequency axisymmetric and helical modes. Formulations are presented here for the nonlinear development of both the amplitudes and phases of the instability waves. The development of these waves are also coupled with the development of the mean flow and the background turbulence. In formulating this model it is assumed that each flow component can be characterized by conservations equations supplemented by closure models.

Mankbadi, R. R.↗

DOE OSTI2022

Closures for multicomponent reacting flows based on dispersion analysis

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters [N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000)] and based on work by Corrsin [S. Corrsin, The reactant concentration spectrum in turbulent mixing with a first-order reaction, J. Fluid Mech. 11, 407 (1961)] beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of nonreactive species and linear reactions, respectively.

42 ENGINEERING↗

DOE OSTI2018

Propagation, proppant transport and the evolution of transport properties of hydraulic fractures

Hydraulic fracturing is a widely used method for well stimulation to enhance hydrocarbon recovery. Permeability, or fluid conductivity, of the hydraulic fracture is a key parameter to determine the fluid production rate, and is principally conditioned by fracture geometry and the distribution of the encased proppant. A numerical model is developed to describe proppant transport within a propagating blade-shaped fracture towards defining the fracture conductivity and reservoir production after fracture closure. Fracture propagation is formulated based on the PKN-formalism coupled with advective transport of an equivalent slurry representing a proppant-laden fluid. Empirical constitutive relations are incorporated to define rheology of the slurry, proppant transport with bulk slurry flow, proppant gravitational settling, and finally the transition from Poiseuille (fracture) flow to Darcy (proppant pack) flow. At the maximum extent of the fluid-driven fracture, as driving pressure is released, a fracture closure model is employed to follow the evolution of fracture conductivity with the decreasing fluid pressure. This model is capable of accommodating the mechanical response of the proppant pack, fracture closure of potentially contacting rough surfaces, proppant embedment into fracture walls, and most importantly flexural displacement of the unsupported spans of the fracture. Results show that reduced fluid viscosity increases the length of the resulting fracture, while rapid leak-off decreases it, with both characteristics minimizing fracture width over converse conditions. Proppant density and size do not significantly influence fracture propagation. Proppant settling ensues throughout fracture advance, and is accelerated by a lower viscosity fluid or greater proppant density or size, resulting in accumulation of a proppant bed at the fracture base. ‘Screen-out’ of proppant at the fracture tip can occur where the fracture aperture is only several times the diameter of the individual proppant particles. After fracture closure, proppant packs comprising larger particles exhibit higher conductivity. More importantly, high-conductivity flow channels are necessarily formed around proppant banks due to the flexural displacement of the fracture walls, which offer preferential flow pathways and significantly influence the distribution of fluid transport. Higher compacting stresses are observed around the edge of proppant banks, resulting in greater depths of proppant embedment into the fracture walls and/or an increased potential for proppant crushing.

Mechanics↗

DOE OSTI2022

Internal energy balance and aerodynamic heating predictions for hypersonic turbulent boundary layers

The elemental equation governing heat transfer in aerodynamic flows is the internal energy equation. For a boundary layer flow, a double integration of the Reynolds-averaged form of this equation provides an expression of the wall heat flux in terms of the integrated effects, over the boundary layer, of various physical processes: turbulent dissipation, mean dissipation, turbulent heat flux, etc. Recently available direct numerical simulation data for a Mach 11 cold-wall turbulent boundary layer allows a comparison of the exact contributions of these terms in the energy equation to the wall heat flux with their counterparts modeled in the Reynolds-averaged Navier-Stokes (RANS) framework. Various approximations involved in RANS, both closure models as well as approximations involved in adapting incompressible RANS models to a compressible form, are assessed through examination of the internal energy balance. There are a number of potentially problematic assumptions and terms identified through this analysis. Here, the effect of compressibility corrections of the dilatational dissipation type is explored, as is the role of the modeled turbulent dissipation, in the context of wall heat flux predictions. The results indicate several potential avenues for RANS model improvement for hypersonic cold-wall boundary-layer flows.

42 ENGINEERING↗

NASA NTRS1991

Pressure flux-split viscous solutions for subsonic diffusers

A method for predicting flow in diffusers with inlet swirl has been developed. Solutions of the pressure flux-split Reduced Navier Stokes (RNS) equations are obtained for flows in axisymmetric diffusers. Viscous-Inviscid interactions and flow fields with toroidal recirculation regions are efficiently captured. The computational model is verified by comparision with experimental data and other computations. The extreme sensitivity to grid, turbulent closure model and inlet profiles is discussed.

Pordal, H. S.↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

Peter A Liever↗

DOE OSTI2021

Development of CTF modeling of interfacial drag, wall shear, and interfacial heat transfer for bubbly and annular-mist flow regimes

This milestone report discusses improvements to CTF closure models for modeling of bubbly and annular mist two-phase flow conditions, which are important for accurate modeling and simulation for boiling water reactor (BWR) conditions. Models that were improved include the two-phase wall shear, wall boiling, and phase mass and heat transfer. A new flow regime map was implemented to improve on the prediction of transition to annular flow, which was generally largely over-predicted by the legacy CTF flow regime map. The annular mist interfacial drag models were also reviewed and new models were proposed for implementation into the code. In addition to implementing new models, an activity was performed to calibrate these new models to experimental data using a Markov Chain Monte Carlo technique, thus further improving their accuracy. Finally, new experiments were implemented into the CTF validation matrix which add more two-phase pressure drop and void measurements for the assessment of CTF for modeling of BWRs. The results show that the Chisholm model, which was implemented and then calibrated, results in significantly improved comparison against the Riso two-phase pressure drop data. Furthermore, improvements in the implicit heat transfer and wall boiling models resulted in good agreement with the void measurement data.

42 ENGINEERING↗

DOE OSTI2019

Assessment on DNB performance for high pressure subcooled boiling with modified CASL boiling model

Understanding and predicting the Departure from Nucleation Boiling phenomena in the nuclear power industry has been a grand challenge due to its large impact on the reactor safety and operational economics. Over the past several years, CASL THM team has extensively investigated and demonstrated a state of art Multiphase CFD framework to provide a high-fidelity DNB simulation capability based on the two-fluid Eulerian model in conjunction with a wall heat flux partitioning approach. The overarching goal of this task is to develop and demonstrate a robust CFD-based DNB model which is capable of predicting an entire boiling history up to the DNB condition in which the wall boiling mode is transitioning from the nucleate boiling mode to the film boiling mode. Three different flow channel configurations (pipe flow, 5x5 fuel bundle with and without mixing vane tests) were studied and thorough closure sensitivity studies were performed to evaluate the wall boiling and momentum closure effect on the DNB performance. Predicated DNB values were compared to the measurements from high pressure subcooled flow boiling tests resulting in a consistent under-predictive trend for all three validation campaigns in FY16-18. With extensive closure sensitivity study, a modified CASL boiling closure model (i.e. Gen1-FY19) is introduced with the following key changes: 1) improved wall boiling closure for high pressure application, 2) newly calibrated lift and wall lubrication force models with modified interfacial length scale model, and 3) updated liquid phase condensation model calibrated for the subcooled boiling application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1989

Numerical simulation of nonlinear development of instability waves

The nonlinear interactions of high amplitude instability waves in turbulent jets are described. In plane shear layers Riley and Metcalf (1980) and Monkewitz (1987) have shown that these interactions are dependent, among other parameters, on the phase-difference between the two instability waves. Therefore, here researchers consider the nonlinear development of both the amplitudes and the phase of the instability waves. The development of these waves are also coupled with the development of the mean flow and the background turbulence. In formulating this model it is assumed that each of the flow components can be characterized by conservation equations supplemented by closure models. Results for the interactions between the two instability waves under high-amplitude forcing at fundamental and subharmonic frequencies are presented here. Qualitative agreements are found between the present predictions and available experimental data.

Mankbadi, Reda R.↗

NASA NTRS1991

Modeling turbulent boundary layers in adverse pressure gradients

Many of the turbulent layers encountered in practical flows develop in adverse pressure gradients; hence, the dynamics of the thickening and possible separation of the boundary layer has important implications for design practices. What are the key physical processes that govern how a turbulent boundary layer responds to an adverse pressure gradient, and how should these processes be modeled? Despite the ubiquity of such flows in engineering and nature, these equations remain largely unanswered. The turbulence closure models presently used to describe these flows commonly use 'wall functions' that have ad hoc corrections for the effects of pressure gradients. There is, therefore, a practical and theoretical need to examine the effects of adverse pressure gradients on wall bounded turbulent flows in order to develop models based on sound physical principle. The evolution of a turbulent boundary layer on a flat wall with an externally imposed pressure gradient is studied.

Belcher, Stephen E.↗

DOE OSTI2018

Two-point spectral model for variable-density homogeneous turbulence

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wave number $k$ of the correlation of density and specific volume $b$($k$), the velocity associated with the turbulent mass flux $a$($k$) , and the turbulent kinetic energy $E$($k$) , using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the velocity $a$($k$) has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b$($k$) and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system and their impact on the statistical quantities. We next assess the accuracy of the model, relative to direct numerical simulation of the complete hydrodynamical equations, using $b$, $a$, and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Molecular fluctuations inhibit intermittency in compressible turbulence

In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.

compressible turbulence↗

DOE OSTI2016

THE SOURCE STRUCTURE OF 0642+449 DETECTED FROM THE CONT14 OBSERVATIONS

The CONT14 campaign with state-of-the-art very long baseline interferometry (VLBI) data has observed the source 0642+449 with about 1000 observables each day during a continuous observing period of 15 days, providing tens of thousands of closure delays—the sum of the delays around a closed loop of baselines. The closure delay is independent of the instrumental and propagation delays and provides valuable additional information about the source structure. We demonstrate the use of this new “observable” for the determination of the structure in the radio source 0642+449. This source, as one of the defining sources in the second realization of the International Celestial Reference Frame, is found to have two point-like components with a relative position offset of −426 microarcseconds ( μ as) in R.A. and −66 μ as in decl. The two components are almost equally bright, with a flux-density ratio of 0.92. The standard deviation of closure delays for source 0642+449 was reduced from 139 to 90 ps by using this two-component model. Closure delays larger than 1 ns are found to be related to the source structure, demonstrating that structure effects for a source with this simple structure could be up to tens of nanoseconds. The method described in this paper does not rely on a priori source structure information, such as knowledge of source structure determined from direct (Fourier) imaging of the same observations or observations at other epochs. We anticipate our study to be a starting point for more effective determination of the structure effect in VLBI observations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Progress in modeling hypersonic turbulent boundary layers

A good knowledge of the turbulence structure, wall heat transfer, and friction in turbulent boundary layers (TBL) at high speeds is required for the design of hypersonic air breathing airplanes and reentry space vehicles. This work reports on recent progress in the modeling of high speed TBL flows. The specific research goal described here is the development of a second order closure model for zero pressure gradient TBL's for the range of Mach numbers up to hypersonic speeds with arbitrary wall cooling requirements.

Zeman, Otto↗

NASA NTRS1995

Turbulence modeling for non-equilibrium flow

The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.

Durbin, P. A.↗

NASA NTRS1999

Asymptotic Behavior of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models too account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distort,ion theory (RDT). The relationship between RDT and linear stability theory is exploit,c d in order to obtain a closed set, of modeled equations. The linear disturbance equations are solved directly so that, the numerical simulation yields a database from which the closure coefficient,s in the ensemble-averaged disturbance equations can he determined.

Thacker, W. D.↗

NASA NTRS1999

Disturbance Dynamics in Transitional and Turbulent Flows

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Grosch, Chester E.↗