On numerical solutions of Burnett equations for hypersonic flow past2-D circular blunt leading edges in continuum transition regime

1993 ◽  
Author(s):  
XIAOLIN ZHONG
Keyword(s):  
Hypersonic Flow ◽  
Numerical Solutions ◽  
Transition Regime ◽  
Burnett Equations ◽  
Leading Edges

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.

scholarly journals Some aspects of hypersonic flow over power law bodies

1969 ◽  
Vol 39 (1) ◽  
pp. 143-162 ◽  
Author(s):  
H. G. Hornung
Keyword(s):  
Mach Number ◽  
Hypersonic Flow ◽  
Blast Wave ◽  
Power Law ◽  
Numerical Solutions ◽  
The Body ◽  
Stagnation Temperature ◽  
Free Layer ◽  
Plane Flow ◽  
Wave Limit

This study concerns the hypersonic flow over blunt bodies in two specific cases. The first is the case when the Mach number is infinite and the ratio of the specific heats approaches one. This is sometimes referred to as the ‘Newtonian limit’. The second is the case of infinite Mach number and very large streamwise distance from the blunt nose with a strong shock wave, or the ‘blast wave limit’. In both cases attention is restricted to power law bodies. Experiments are described of such flows at M∞ = 7·55 in air.The Newtonian flow over bodies of the shape y ∞ xm at zero incidence is shown to be divisible into three regions: the attached layer at small x, the free layer and the blast wave region. As m increases from zero, the free-layer region reduces in extent until it disappears at m = 1/(2+j) (j = 1 and 0 for axisymmetric and plane flow respectively). A difficulty arises in a transition solution of the type given by Freeman (1962b) connecting the free layer with the blast wave result. At m > 2/(3+j) the attached layer merges smoothly into the Lees-Kubota solution which replaces the blast-wave result in this range.In the blast wave limit, solutions were obtained for flow over axisymmetric power law shapes in the range ½γ < m < ½. Second-order results taking account of the body shape are given. These solutions are compared with experimental results obtained in air at a free stream Mach number of 7·55 and stagnation temperature of 630 °K, as well as with numerical solutions at Mach number of 100. The numerical method is tested by comparing solutions corresponding to the experimental conditions with experiment.

Coupling of Heat and Momentum Transfer Between Nanostructured Surfaces

2009 ◽  
Author(s):  
Alexander A. Donkov ◽  
Steffen Hardt ◽  
Sudarshan Tiwari ◽  
Axel Klar
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Numerical Solutions ◽  
Small Scale ◽  
Molecular Flow ◽  
Transition Regime ◽  
Free Molecular Flow ◽  
Direction Parallel ◽  
Nanostructured Surfaces

Heat transfer between nanostructured surfaces separated by a thin gas film is studied in the free-molecular flow and in the transition regime. Besides topographic features the surfaces are characterized by regions with different boundary conditions displaying either diffuse or specular reflection of the molecules. The thermal conductivity of the materials on both sides of the gas film is assumed to be very high such that isothermal conditions may be applied at both surfaces. We analyze the problem using a combination of analytical techniques in the free-molecular flow regime and Monte-Carlo simulations. Under certain conditions, when the surfaces are held at different temperatures heat transfer is accompanied by a transfer of momentum such that a force is created parallel to the surfaces. This force can be significant and vanishes in the classical regime when the continuum transport equations can be applied. It is only observed if the reflection symmetry in a direction parallel to the surfaces is broken. We derive an analytical expression for the thermally-induced force as a function of the geometric parameters characterizing the surface topography and compare the results to Monte-Carlo simulations. The latter provide numerical solutions of the Boltzmann equation both in the free-molecular flow and in the transition regime. The scenario studied points to a novel method for conversion of thermal into kinetic energy and may find applications in small-scale energy converters.

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