BEYOND NAVIER–STOKES: BURNETT EQUATIONS FOR FLOW SIMULATIONS IN THE CONTINUUM–TRANSITION REGIME

2001 ◽  
pp. 211-251 ◽  
Author(s):  
RAMESH K. AGARWAL ◽  
KEON-YOUNG YUN ◽  
RAMESH BALAKRISHNAN
Keyword(s):  
Navier Stokes ◽  
Transition Regime ◽  
Burnett Equations ◽  
Flow Simulations ◽  
The Continuum

Burnett equations for simulation of transitional flows

2002 ◽  
Vol 55 (3) ◽  
pp. 219-240 ◽  
Author(s):  
Ramesh K Agarwal ◽  
Keon-Young Yun
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Deviation ◽  
Review Article ◽  
Navier Stokes ◽  
Space Vehicles ◽  
Surface Boundary ◽  
Transition Regime ◽  
Burnett Equations ◽  
The Continuum

Hypersonic flows about space vehicles in low earth orbits and flows in microchannels of microelectromechanical devices produce local Knudsen numbers which lie in the continuum-transition regime. The Navier-Stokes equations cannot model these flows adequately since they are based on the assumption of small deviation from local thermodynamic equilibrium. A number of extended hydrodynamics (E-H) or generalized hydrodynamics (G-H) models as well as the Direct Simulation Monte Carlo (DSMC) approach have been proposed to model the flows in the continuum-transition regime over the past 50 years. One of these models is the Burnett equations which are obtained from the Chapman-Enskog expansion of the Boltzmann equation (with Knudsen number (Kn) as a small parameter) to OKn2. With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations. However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with this model. Several improvements to the conventional Burnett equations have been proposed in recent years to address both the physical and numerical issues; two of the most well known are the Augmented Burnett Equations and the BGK-Burnett Equations. This review article traces the history of the Burnett model and describes some of the recent developments. The relationship between the Burnett equations and Grad’s 13 moment equations as shown by Struchtrup by employing the Maxwell-Truesdell-Green iteration is also presented. Also, the recent work of Jin and Slemrod on regularization of the Burnett equations via viscoelastic relaxation that ensures positive entropy production and eliminates the instability paradox is discussed. Numerical solutions in 1D, 2D, and 3D are provided to assess the accuracy and applicability of Burnett equations for modeling flows in the continuum-transition regime. The important issue of surface boundary conditions is addressed. Computations are compared with the available experimental data, Navier-Stokes calculations, Burnett solutions of other investigators, and DSMC solutions wherever possible. This review article cites 56 references.

Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime

2001 ◽  
Vol 13 (10) ◽  
pp. 3061-3085 ◽  
Author(s):  
Ramesh K. Agarwal ◽  
Keon-Young Yun ◽  
Ramesh Balakrishnan
Keyword(s):  
Navier Stokes ◽  
Transition Regime ◽  
Burnett Equations ◽  
The Continuum

Luminosity calculation of meteor entry based on detailed flow simulations in the continuum regime

2020 ◽  
Vol 635 ◽  
pp. A184 ◽  
Author(s):  
B. Dias ◽  
J. B. Scoggins ◽  
T. E. Magin
Keyword(s):  
Radiation Effects ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Coupled Flow ◽  
Navier Stokes Equations ◽  
Lost City ◽  
Flow Simulations ◽  
Chemical Models ◽  
The Continuum

Context. Composition, mass, and trajectory parameters of meteors can be derived by combining observations with the meteor physics equations. The fidelity of these equations, which rely on heuristic coefficients, significantly affects the accuracy of the properties inferred. Aims. Our objective is to present a methodology that can be used to compute the luminosity of meteor entry based on detailed flow simulations in the continuum regime. Methods. The methodology consists in solving the Navier–Stokes equations using state-of-the-art physico-chemical models for hypersonic flows. It includes accurate boundary conditions to simulate the surface evaporation of the molten material and coupled flow-radiation effects. Such detailed simulations allow for the calculation of heat-transfer coefficients and luminous efficiency, which can be incorporated into the meteor physics equations. Finally, we integrate the radiative transfer equation over a line of sight from the ground to the meteor to derive the luminosity magnitude. Results. We use the developed methodology to simulate the Lost City bolide and to derive the luminosity magnitude, obtaining good agreement between numerical results and observations. The computed color index is more prominent than the observations. This is attributed to a lack of refractory elements such as Ca in the modeled flow that might originate from the vaporization of droplets in the trail, a phenomenon currently not included in the model.

BGK-Burnett Equations for Flows in the Continuum-Transition Regime

1999 ◽  
Vol 13 (4) ◽  
pp. 397-410 ◽  
Author(s):  
Ramesh Balakrishnan ◽  
Ramesh K. Agarwal ◽  
Keon-Young Yun
Keyword(s):  
Transition Regime ◽  
Burnett Equations ◽  
The Continuum

Flow Characteristics of Microfilter in Slip/Transition Regime

2011 ◽  
Vol 694 ◽  
pp. 831-837
Author(s):  
Fu Bing Bao ◽  
Jin Xing Wang ◽  
Jian Zhong Lin
Keyword(s):  
Pressure Drop ◽  
Knudsen Number ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Transition Regime ◽  
Burnett Equations ◽  
Slip Boundary ◽  
The Difference ◽  
Slip Transition

The Burnett equations with slip boundary conditions are used in present paper to investigate the flow characteristics of microfilter in slip/transition regime. Convergent results of the Burnett equations agree very well with the results of DSMC method. The difference between the results of the Burnett and the Navier-Stokes equations increases with the increase of Knudsen number. The variation of non-dimensional pressure drop with Reynolds number and the opening factor are presented. The non-dimensional pressure drop is independent of Knudsen number.

Reducing Undesired Wave Reflection at Domain Boundaries in 3D Finite Volume-Based Flow Simulations via Forcing Zones

2020 ◽  
Vol 64 (01) ◽  
pp. 23-47
Author(s):  
Robinson Peric ◽  
Moustafa Abdel-Maksoud
Keyword(s):  
Finite Volume ◽  
Wave Reflection ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Special Focus ◽  
Computational Domain ◽  
Wave Reflections ◽  
Flow Simulations ◽  
Large Eddy ◽  
Domain Boundaries

This article reviews different types of forcing zones (sponge layers, damping zones, relaxation zones, etc.) as used in finite volume-based flow simulations to reduce undesired wave reflections at domain boundaries, with special focus on the case of strongly reflecting bodies subjected to long-crested incidence waves. Limitations and possible sources of errors are discussed. A novel forcing-zone arrangement is presented and validated via three-dimensional (3D) flow simulations. Furthermore, a recently published theory for predicting the forcing-zone behavior was investigated with regard to its relevance for practical 3D hydrodynamics problems. It was found that the theory can be used to optimally tune the case-dependent parameters of the forcing zones before running the simulations. 1. Introduction Wave reflections at the boundaries of the computational domain can cause significant errors in flow simulations, and must therefore be reduced. In contrast to boundary element codes, where much progress in this respect has been made decades ago (see e.g., Clement 1996; Grilli &Horillo 1997), for finite volume-based flow solvers, there are many unresolved questions, especially:How to reliably reduce reflections and disturbances from the domain boundaries?How to predict the amount of undesired wave reflection before running the simulation? This work aims to provide further insight to these questions for flow simulations based on Navier-Stokes-type equations (Reynolds-averaged Navier-Stokes, Euler equations, Large Eddy Simulations, etc.), when using forcing zones to reduce undesired reflections. The term "forcing zones" is used here to describe approaches that gradually force the solution in the vicinity of the boundary towards some reference solution, as described in Section 2; some examples are absorbing layers, sponge layers, damping zones, relaxation zones, or the Euler overlay method (Mayer et al. 1998; Park et al. 1999; Chen et al. 2006; Choi &Yoon 2009; Jacobsen et al. 2012; Kimet al. 2012; Schmitt & Elsaesser 2015; Perić & Abdel-Maksoud 2016a; Vukčević et al. 2016).

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