DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

Abstract

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and showsmore » to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.« less

Authors:
 [1];  [1];  [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1239104
Report Number(s):
LA-UR-14-27431
Journal ID: ISSN 1386-6184; PII: 9643
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Flow, Turbulence and Combustion
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 1386-6184
Publisher:
European Research Community on Flow, Turbulence and Combustion (ERCOFTAC)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 04 OIL SHALES AND TAR SANDS; 24 POWER TRANSMISSION AND DISTRIBUTION; Turbulence; mixing; variable density; Reynolds stress; closure model; shear flow; Rayleigh-Taylor; Richtmyer-Meshkov; direct numerical simulation; shocks; Favre average; compressible flows; density fl

Citation Formats

Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., and Ristorcelli, J. R.. A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing. United States: N. p., 2015. Web. doi:10.1007/s10494-015-9643-z.
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., & Ristorcelli, J. R.. A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing. United States. https://doi.org/10.1007/s10494-015-9643-z
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., and Ristorcelli, J. R.. Tue . "A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing". United States. https://doi.org/10.1007/s10494-015-9643-z. https://www.osti.gov/servlets/purl/1239104.
@article{osti_1239104,
title = {A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing},
author = {Schwarzkopf, J. D. and Livescu, D. and Baltzer, J. R. and Gore, R. A. and Ristorcelli, J. R.},
abstractNote = {A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.},
doi = {10.1007/s10494-015-9643-z},
journal = {Flow, Turbulence and Combustion},
number = 1,
volume = 96,
place = {United States},
year = {Tue Sep 08 00:00:00 EDT 2015},
month = {Tue Sep 08 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 69 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Direct simulation of a self‐similar turbulent mixing layer
journal, February 1994

  • Rogers, Michael M.; Moser, Robert D.
  • Physics of Fluids, Vol. 6, Issue 2
  • DOI: 10.1063/1.868325

Development of a two-stream mixing layer from tripped and untripped boundary layers
journal, December 1990

  • Bell, James H.; Mehta, Rabindra D.
  • AIAA Journal, Vol. 28, Issue 12
  • DOI: 10.2514/3.10519

A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics
journal, January 1991

  • Young, David P.; Melvin, Robin G.; Bieterman, Michael B.
  • Journal of Computational Physics, Vol. 92, Issue 1
  • DOI: 10.1016/0021-9991(91)90291-r

Modeling shock unsteadiness in shock/turbulence interaction
journal, August 2003

  • Sinha, Krishnendu; Mahesh, Krishnan; Candler, Graham V.
  • Physics of Fluids, Vol. 15, Issue 8
  • DOI: 10.1063/1.1588306

An update on the energy dissipation rate in isotropic turbulence
journal, February 1998

  • Sreenivasan, Katepalli R.
  • Physics of Fluids, Vol. 10, Issue 2
  • DOI: 10.1063/1.869575

High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009


Direct numerical simulations of chemically reacting turbulent mixing layers
journal, January 1986

  • Riley, James J.; Metcalfe, Ralph W.; Orszag, Steven A.
  • Physics of Fluids, Vol. 29, Issue 2
  • DOI: 10.1063/1.865724

A Reynolds stress model of turbulence and its application to thin shear flows
journal, April 1972


Turbulence structure behind the shock in canonical shock–vortical turbulence interaction
journal, September 2014


The RAGE radiation-hydrodynamic code
journal, October 2008


Experimental study of a normal shock/homogeneous turbulence interaction
journal, May 1996

  • Barre, S.; Alem, D.; Bonnet, J. P.
  • AIAA Journal, Vol. 34, Issue 5
  • DOI: 10.2514/3.13175

A k –ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows
journal, May 2012

  • King, A. T.; Tinoco, R. O.; Cowen, E. A.
  • Journal of Fluid Mechanics, Vol. 701
  • DOI: 10.1017/jfm.2012.113

Kinetics of Fluorescence Quenching by Electron and H-Atom Transfer
journal, January 1970


A second-order turbulence model for gaseous mixtures induced by Richtmyer—Meshkov instability
journal, January 2005


On the logarithmic region in wall turbulence
journal, January 2013

  • Marusic, Ivan; Monty, Jason P.; Hultmark, Marcus
  • Journal of Fluid Mechanics, Vol. 716
  • DOI: 10.1017/jfm.2012.511

Multiple-time-scale modeling of turbulent flows in one-point closures
journal, January 1987


Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability
journal, November 1998

  • Poggi, Françoise; Thorembey, Marie-Hélène; Rodriguez, Gérard
  • Physics of Fluids, Vol. 10, Issue 11
  • DOI: 10.1063/1.869794

Bayesian estimates of parameter variability in the k–ε turbulence model
journal, February 2014


Modeling turbulent dissipation at low and moderate Reynolds numbers
journal, January 2006


Enthalpy diffusion in multicomponent flows
journal, May 2009


Decay of isotropic turbulence in the initial period
journal, July 1948

  • Batchelor, George Keith; Townsend, Albert Alan
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 193, Issue 1035, p. 539-558
  • DOI: 10.1098/rspa.1948.0061

Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate
journal, January 2009


Second-moment closure: present… and future?
journal, December 1989


Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae
journal, July 2006

  • Cabot, William H.; Cook, Andrew W.
  • Nature Physics, Vol. 2, Issue 8
  • DOI: 10.1038/nphys361

Vorticity dynamics after the shock–turbulence interaction
journal, July 2015


Taylor instability in shock acceleration of compressible fluids
journal, May 1960

  • Richtmyer, Robert D.
  • Communications on Pure and Applied Mathematics, Vol. 13, Issue 2
  • DOI: 10.1002/cpa.3160130207

Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
journal, March 2011

  • Grinstein, F. F.; Gowardhan, A. A.; Wachtor, A. J.
  • Physics of Fluids, Vol. 23, Issue 3
  • DOI: 10.1063/1.3555635

Development and validation of a turbulent-mix model for variable-density and compressible flows
journal, October 2010


Turbulent Flows
book, July 2012


Progress in the development of a Reynolds-stress turbulence closure
journal, April 1975


A new k-ϵ eddy viscosity model for high reynolds number turbulent flows
journal, March 1995


The decay power law in grid-generated turbulence
journal, October 1990


Buoyancy-driven variable-density turbulence
journal, October 2007


Variable-density mixing in buoyancy-driven turbulence
journal, May 2008


Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1
journal, March 1981


The structure of the vorticity field in homogeneous turbulent flows
journal, March 1987


Statistische Theorie nichthomogener Turbulenz
journal, November 1951


New phenomena in variable-density Rayleigh–Taylor turbulence
journal, December 2010


Late-time quadratic growth in single-mode Rayleigh-Taylor instability
journal, October 2012


A study of compressibility effects in the high-speed turbulent shear layer using direct simulation
journal, January 2002


The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup
journal, October 1992


Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields
journal, January 1999

  • Agui, Juan H.; Briassulis, George; Andreopoulos, Yiannis
  • Journal of Fluid Mechanics, Vol. 524
  • DOI: 10.1017/S0022112004002514

Instability of the interface of two gases accelerated by a shock wave
journal, January 1972


Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface
journal, March 1995


Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock
journal, June 2006


Experimental study of a normal shock/homogeneous turbulence interaction
conference, August 1995

  • Barre, S.; Alem, D.; Bonnet, J.
  • 33rd Aerospace Sciences Meeting and Exhibit
  • DOI: 10.2514/6.1995-579

Turbulent Flows
journal, October 2001


Development of a two-stream mixing layer from tripped and untripped boundary layers
conference, August 1990


Experimental Study of a Normal Shock/Homogeneous Turbulence Interaction
conference, February 2009

  • Auvity, Bruno; Barre, Ste´phane; Bonnet, Jean-Paul
  • ASME 2002 Joint U.S.-European Fluids Engineering Division Conference, Volume 1: Fora, Parts A and B
  • DOI: 10.1115/fedsm2002-31090

Works referencing / citing this record:

The modeling of delayed-onset Rayleigh-Taylor and transition to mixing in laser-driven HED experiments
journal, May 2019

  • Di Stefano, C. A.; Doss, F. W.; Rasmus, A. M.
  • Physics of Plasmas, Vol. 26, Issue 5
  • DOI: 10.1063/1.5085332

Large eddy simulation investigation of the canonical shock–turbulence interaction
journal, November 2018

  • Braun, N. O.; Pullin, D. I.; Meiron, D. I.
  • Journal of Fluid Mechanics, Vol. 858
  • DOI: 10.1017/jfm.2018.766

Observation and analysis of emergent coherent structures in a high-energy-density shock-driven planar mixing layer experiment
journal, August 2016


A review of pressure strain correlation modeling for Reynolds stress models
journal, December 2019

  • Panda, Jp
  • Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 234, Issue 8
  • DOI: 10.1177/0954406219893397

A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence
journal, July 2019


Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability
journal, September 2019

  • Thornber, B.; Griffond, J.; Bigdelou, P.
  • Physics of Fluids, Vol. 31, Issue 9
  • DOI: 10.1063/1.5111681

Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities
journal, August 2019

  • Zhou, Ye; Clark, Timothy T.; Clark, Daniel S.
  • Physics of Plasmas, Vol. 26, Issue 8
  • DOI: 10.1063/1.5088745

Numerical study of variable density turbulence interaction with a normal shock wave
journal, September 2017

  • Tian, Yifeng; Jaberi, Farhad A.; Li, Zhaorui
  • Journal of Fluid Mechanics, Vol. 829
  • DOI: 10.1017/jfm.2017.542

Evaluation of turbulent mixing transition in a shock-driven variable-density flow
journal, October 2017

  • Mohaghar, Mohammad; Carter, John; Musci, Benjamin
  • Journal of Fluid Mechanics, Vol. 831
  • DOI: 10.1017/jfm.2017.664

The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions
journal, May 2019

  • Mohaghar, Mohammad; Carter, John; Pathikonda, Gokul
  • Journal of Fluid Mechanics, Vol. 871
  • DOI: 10.1017/jfm.2019.330

Late-time mixing and turbulent behavior in high-energy-density shear experiments at high Atwood numbers
journal, May 2018

  • Flippo, K. A.; Doss, F. W.; Merritt, E. C.
  • Physics of Plasmas, Vol. 25, Issue 5
  • DOI: 10.1063/1.5027194