#
APS April Meeting 2016

## Volume 61, Number 6

##
Saturday–Tuesday, April 16–19, 2016;
Salt Lake City, Utah

### Session C11: Computational Physics

1:30 PM–3:18 PM,
Saturday, April 16, 2016

Room: 250C

Sponsoring
Unit:
DCOMP

Abstract ID: BAPS.2016.APR.C11.1

### Abstract: C11.00001 : Analysis of High-Speed Rotating Flow in 2D Polar \textbf{\textit{(r - }}$\theta $\textbf{\textit{) }}\textbf{ Coordinate}

1:30 PM–1:42 PM

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Abstract

####
Author:

S. Pradhan

(Dept of Chemical Engineering, Indian Institute of Science)

The generalized analytical model for the radial boundary layer in a
high-speed rotating cylinder is formulated for studying the gas flow field
due to insertion of mass, momentum and energy into the rotating cylinder in
the polar $(r - \theta ) $ plane. The analytical solution includes the sixth order
differential equation for the radial boundary layer at the cylindrical
curved surface in terms of master potential ($\chi )$, which is derived from
the equations of motion in a polar $(r - \theta )$ plane. The linearization
approximation (Wood {\&} Morton, \textit{J. Fluid Mech}-1980; Pradhan {\&} Kumaran, \textit{J. Fluid Mech}-2011; Kumaran
{\&} Pradhan, \textit{J. Fluid Mech}-2014) is used, where the equations of motion are truncated at
linear order in the velocity and pressure disturbances to the base flow,
which is a solid-body rotation. Additional assumptions in the analytical
model include constant temperature in the base state (isothermal condition),
and high Reynolds number, but there is no limitation on the stratification
parameter. In this limit, the gas flow is restricted to a boundary layer of
thickness \textit{(Re\textasciicircum \textbraceleft }$-$\textit{1/3\textbraceright R)} at the wall of the cylinder. Here, the stratification
parameter $A = \surd ((m \Omega $\textit{\textasciicircum 2 R\textasciicircum 2)/(2 k\textunderscore B T)).} This parameter $A $is the ratio of the peripheral
speed, $\Omega R$, to the most probable molecular speed, $\surd $\textit{(2 k\textunderscore B T/m),} the
Reynolds number Re $= \quad (\rho $\textit{\textunderscore w }$\Omega $\textit{ R\textasciicircum 2/}$\mu )$, where $m$ is the molecular mass,
$\Omega $ and $R$ are the rotational speed and radius of the cylinder,
\textit{k\textunderscore B} is the Boltzmann constant, $T$ is the gas temperature, $\rho $\textit{\textunderscore w} is the gas
density at wall, and $\mu $ is the gas viscosity. The analytical solutions
are then compared with direct simulation Monte Carlo (DSMC) simulations.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2016.APR.C11.1