(621dw) Transport Effects in Homogeneous-Heterogeneous Combustion

Transport
Effects in Homogeneous-Heterogeneous Combustion

Imran
Alam¹, David H. West² and Vemuri
Balakotaiah¹

¹Chemical and Biomolecular Engineering Department,

University of
Houston, 4800 Calhoun Road, Houston, TX 77004

²SABIC Technology
Center, Sugarland, TX 77478

Author emails: Imran Alam : ialam@uh.edu, David
West:dwest@americas.sabic.com ,Vemuri Balakoataiah :
bala@uh.edu

ABSTRACT

Introduction

Catalytic
partial oxidation is an attractive technology for meeting future energy demands
and production of intermediate chemicals. The models describing this process
typically involve both catalytic and homogeneous reactions. Homogeneous
ignition in catalytic combustion has been investigated in various settings such
as stagnation point flows, external boundary layer flows and two-dimensional
channel flows. However, most of these studies have been numerical, mostly
relying on CFD packages. In this work, we seek to understand the effects of
various transport parameters representing the heat and mass transfer phenomena
on coupled homogeneous-heterogeneous combustion. Our approach uses tools of
Linear Operator theory to provide analytical expressions for concentration and
temperature in two-dimensional domains. We also
obtain expressions for relevant transport parameters such as the Nusselt and Sherwood numbers. These results provide
insights on the qualitative features of the thermally coupled
homogeneous-heterogeneous combustion process.

Mathematical Models & Analysis

We
present mathematical models for the combustion in monolith and parallel plate
reactors. We focus on the limiting case where the catalytic reaction is very fast
and the system is in the mass transfer controlled regime. We consider a
homogeneous reaction and solve the resulting partial differential equations in
two space dimensions. This yields contour plots for temperature and
concentration. We study this system for Dirichlet and
Danckwerts inlet conditions, for varying Lewis and
radial Peclet numbers. We observe that hot spot
formation may be possible both near the wall and near the center, and that the
temperature variation in the direction transverse to flow need not be
monotonic. In either case, temperature at the center never exceeds the
adiabatic value as claimed by Zheng and Mantzaras,
[1].

Results and
Discussion

We
show below typical contour plots for concentration and temperature. Different
values of Lewis number, Peclet number and Thiele
modulus yield different qualitative behavior. Figure 1 shows a typical concentration
contour plot for a 2-D model for parallel plate reactor with a homogeneous
reaction and Danckwerts inlet conditions. The Thiele
modulus is 1.0 and the radial Peclet number is taken
to be 5.0. Next we have shown in figure 2, two temperature contour plots- (i) a system with a radial Peclet
number 5, Lewis number of 0.5 and Thiele modulus of 3, and (ii) a system with a
radial Peclet number of 5, Lewis number of 2.5 and
Thiele modulus of 30. Figure 2 (i) shows the
situation where the wall is always hotter than the center while figure 2 (ii)
shows that the center can be hotter than the wall as well. In figure 3, we show
a plot for the Nusselt number as a function of axial
distance for a radial Peclet number 10, Lewis number
of 5 and Thiele modulus of 1. This plot shows a minimum near the inlet and to
our knowledge, is a novel result.

The
physical insight derived from this analysis can be useful in a bifurcation
study of a combustion system. In our earlier work ([2]), we found that the
thermally coupled hysteresis locus is virtually unchanged from the hysteresis
locus for a system with infinitely fast wall reaction. Hence an analysis for
homogeneous combustion with a very fast catalytic reaction is useful to
understand and compute bifurcation features of thermally coupled combustion
systems. A comprehensive analysis of the system will be presented.

Figure 1: Concentration contour plot for a 2-D model for
parallel plate reactor with a homogeneous reaction. The Thiele modulus is 1.0
and the radial Peclet number is taken to be 5.0.

(i)

(ii)

Figure 2: Temperature contour plots for a 2-D model for
parallel plate reactor with a homogeneous reaction. The parameters are (i) radial Peclet number 5, Lewis
number 0.5 and Thiele modulus 3, and (ii) radial Peclet
number 5, Lewis number 2.5 and Thiele modulus 30.

Figure 3: Nusselt number as a
function of axial distance for a radial Peclet number
10, Lewis number of 5 and Thiele modulus of 1.

References

[1]. X. Zheng, J. Mantzaras, Combustion and Flame 161
(2014) 1911-1922.

[2]. I. Alam, D. H. West, V. Balakotaiah, Chem. Eng. Journal (under review).