522
M. Abhay et al.
1 Introduction
Macroscopic approach uses the set of continuity, momentum and energy equation
for the calculation of properties such as pressure, temperature, velocity, etc. Same
set of equations can also be used for microscopic analysis but requires incorporation
of transport and heat-flux equations too. It is the use of these set of deterministic
equations which accurately models rarefied flow. Use of these additional equations in
an analysis breaks the assumption of macroscopic approach rather than the increase
in mean free-path between two molecules. Basically, Knudsen number gives the
degree of rarefaction and is defined as
K n =
λ
l
(1)
where l is the characteristic length, λ is the mean free-path and ρ is the density of
gas (air). For the flow to be considered as the rarefied flow, Kn should be more than
0.1 and molecular approach needs to be incorporated. Macroscopic approach starts
to yields inaccurate results as rarefaction increases. At Kn equal to 0.2 it becomes
important to use the molecular approach and macroscopic model no longer can be
used.
In this paper, the analysis was carried out for an altitude of 105 km from the
mean sea level with the flow velocity ∼ 8050 m/s. At an altitude of 105 km pressure,
temperature, density and Knudsen number are 0.01182 N/m
2 , 196.0 K, 2.006×10
−7
and 0.31193 respectively. As the Knudsen number at this altitude is more than 0.2,
molecular approach can be used to get accurate results. Direct Simulation Monte
Carlo (DSMC) method [1], based on molecular kinematics, is used in this paper to
study the flow field around and on a blunt nose re-entry vehicle (REV) using DSMC
openFOAM platform.
2 Geometry and Mesh
The configuration used for analysis is the blunt spherical double conic section of 20°
and 25°, respectively and the representative sketch of the same is shown in Fig. 1.
Length to Diameter ratio (Aspect ratio (AR)), is 0.6. A sector of 5° in the Z-direction is
used for the analysis. DSMC uses three-dimensional body to carry out analysis since
2D analysis is not possible owing to the fact that molecular approach is used which
considers random scattering of molecules in all directions. 3D configuration with the
sector of less than or equal to 5° is a good approximation of 2D axisymmetric body.
The base of the configuration is flat.
3D mesh was created by revolving the structured mesh by an angle of 5°. Fine
mesh was created near the body and a gradual growth rate of 1.2 times from the first
cell height was given towards the outer domain. In Fig. 2, isometric views is shown
M. Abhay et al.
1 Introduction
Macroscopic approach uses the set of continuity, momentum and energy equation
for the calculation of properties such as pressure, temperature, velocity, etc. Same
set of equations can also be used for microscopic analysis but requires incorporation
of transport and heat-flux equations too. It is the use of these set of deterministic
equations which accurately models rarefied flow. Use of these additional equations in
an analysis breaks the assumption of macroscopic approach rather than the increase
in mean free-path between two molecules. Basically, Knudsen number gives the
degree of rarefaction and is defined as
K n =
λ
l
(1)
where l is the characteristic length, λ is the mean free-path and ρ is the density of
gas (air). For the flow to be considered as the rarefied flow, Kn should be more than
0.1 and molecular approach needs to be incorporated. Macroscopic approach starts
to yields inaccurate results as rarefaction increases. At Kn equal to 0.2 it becomes
important to use the molecular approach and macroscopic model no longer can be
used.
In this paper, the analysis was carried out for an altitude of 105 km from the
mean sea level with the flow velocity ∼ 8050 m/s. At an altitude of 105 km pressure,
temperature, density and Knudsen number are 0.01182 N/m
2 , 196.0 K, 2.006×10
−7
and 0.31193 respectively. As the Knudsen number at this altitude is more than 0.2,
molecular approach can be used to get accurate results. Direct Simulation Monte
Carlo (DSMC) method [1], based on molecular kinematics, is used in this paper to
study the flow field around and on a blunt nose re-entry vehicle (REV) using DSMC
openFOAM platform.
2 Geometry and Mesh
The configuration used for analysis is the blunt spherical double conic section of 20°
and 25°, respectively and the representative sketch of the same is shown in Fig. 1.
Length to Diameter ratio (Aspect ratio (AR)), is 0.6. A sector of 5° in the Z-direction is
used for the analysis. DSMC uses three-dimensional body to carry out analysis since
2D analysis is not possible owing to the fact that molecular approach is used which
considers random scattering of molecules in all directions. 3D configuration with the
sector of less than or equal to 5° is a good approximation of 2D axisymmetric body.
The base of the configuration is flat.
3D mesh was created by revolving the structured mesh by an angle of 5°. Fine
mesh was created near the body and a gradual growth rate of 1.2 times from the first
cell height was given towards the outer domain. In Fig. 2, isometric views is shown