Kε Turbulence Model Parameter Estimates Using an Approximate Selfsimilar JetinCrossflow Solution
Abstract
The kε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged NavierStokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of wellestablished canonical flows such as homogeneous shear flow, loglaw behavior, etc. While this procedure does yield a set of socalled nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the kε model using jetincrossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a selfsimilar asymptotic solution for axisymmetric jetincrossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The selfsimilar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical farfield scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. Amore »
 Authors:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States); Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1399490
 Report Number(s):
 SAND20171388J
651099
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 AIAA Journal
 Additional Journal Information:
 Conference: 8. AIAA Theoretical Fluid Mechanics Conference, Denver, CO (United States), 59 Jun 2017
 Country of Publication:
 United States
 Language:
 English
Citation Formats
DeChant, Lawrence, Ray, Jaideep, Lefantzi, Sophia, Ling, Julia, and Arunajatesan, Srinivasan. Kε Turbulence Model Parameter Estimates Using an Approximate Selfsimilar JetinCrossflow Solution. United States: N. p., 2017.
Web. doi:10.2514/6.20174167.
DeChant, Lawrence, Ray, Jaideep, Lefantzi, Sophia, Ling, Julia, & Arunajatesan, Srinivasan. Kε Turbulence Model Parameter Estimates Using an Approximate Selfsimilar JetinCrossflow Solution. United States. doi:10.2514/6.20174167.
DeChant, Lawrence, Ray, Jaideep, Lefantzi, Sophia, Ling, Julia, and Arunajatesan, Srinivasan. 2017.
"Kε Turbulence Model Parameter Estimates Using an Approximate Selfsimilar JetinCrossflow Solution". United States.
doi:10.2514/6.20174167.
@article{osti_1399490,
title = {Kε Turbulence Model Parameter Estimates Using an Approximate Selfsimilar JetinCrossflow Solution},
author = {DeChant, Lawrence and Ray, Jaideep and Lefantzi, Sophia and Ling, Julia and Arunajatesan, Srinivasan},
abstractNote = {The kε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged NavierStokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of wellestablished canonical flows such as homogeneous shear flow, loglaw behavior, etc. While this procedure does yield a set of socalled nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the kε model using jetincrossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a selfsimilar asymptotic solution for axisymmetric jetincrossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The selfsimilar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical farfield scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.},
doi = {10.2514/6.20174167},
journal = {AIAA Journal},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 6
}

Estimates of confinement time and energy gain for plasma liner driven magnetoinertial fusion using an analytic selfsimilar converging shock model
Plasma liner driven magnetoinertial fusion (PLMIF) is a fusion energy concept that utilizes an imploding plasma liner to shock heat and compress a magnetized target plasma to fusion conditions. The fusion burn fraction is linearly proportional to the confinement (or ''dwell'') time of the linertarget system at peak compression, and therefore it is important to estimate the dwell time accurately in order to assess the fusion energy yield and gain. In this work, the dwell time has been estimated using the exact solution to a selfsimilar converging shock model. The dwell time was found to be determined by the summore » 
Standing RankineHugoniot shocks in the hybrid model flows. II. Nonaxisymmetric selfsimilar solution. [Stellar mass accretion]
Previous work on axisymmetric shock solutions in hybrid model flows is extended to the case when the shocks are nonaxisymmetric. The properties of the sonic surface as well as the shocks are characterized analytically. The shocks are assumed to be selfsimilar, and the flow everywhere is assumed to be in hydrostatic equilibrium in the vertical direction. The shocks are found to be formed for two different states of the fluid: a high state, when the rotational velocity is much larger compared to the radial velocity, and a low state, when the radial velocity is much larger compared to the rotationalmore » 
Semianalytic theory of selfsimilar optical propagation and mode locking using a shapeadaptive model pulse
A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be continuously tweaked between a pure Gaussian and a pure parabolic profile and can even represent sechlike pulses, the shape of a soliton. This approach allows us to describe the pulse evolution in the selfsimilar and other regimes of optical propagation. Employing the method of moments, the evolution equations for the characteristic pulse parameters are derived from the governing nonlinear Schroedinger or GinzburgLandau equation. Due to its greatly reducedmore »