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A numerical solution for reacting and non reacting flow

  • Part 2: Contributed Lectures
  • Conference paper
  • First Online:
Numerical Combustion

Part of the book series: Lecture Notes in Physics ((LNP,volume 351))

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Abstract

A Numerical technique for the prediction of laminar flows, with and without chemical reaction, through the solution of the compressible time-dependent NavierStokes equations is presented. The solution consists of an explicit, time marching, control volume technique which is second order accurate in time and space. The technique has been applied to two cases: Laminar flow through a channel with sudden expansion and laminar channel flow with chemical reaction. The obtained steady state numerical results and their good comparison with experimental data show the accuracy and applicability of the technique.

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Abbreviations

a:

half the height of the channel

Cp :

Coefficient of specific heat (at constant pressure)

Dj :

Diffusion coefficient of specie j

h:

Total enthalpy (including enthalpy of formation)

hRj :

Enthalpy of formation of specie j

K:

Thermal conductivity

KR :

Constant appearing in source term for mi for test case 2

mj :

Mass fraction of specie j

M f :

Molecular weight of specie j

n:

Number of species

p:

Pressure Universal gas constant S Source term ( vector, equation (1) )

t:

Time

T:

Temperature

u:

Longitudinal velocity

v:

Transverse velocity or volume

V:

Volume

z,Y:

Cartesian coordinates

δ:

Variation of variable between time level n and n + 1 ΔtTime step

γ:

Ratio of x heats

μ:

Coefficient of laminar viscosity

ϱ:

Mixture density

1:

First order variation

2:

Second order variation

n, n + 1:

Time level n or n + 1

1,2,3,4:

Calculated at point 1,2,3,4

A, B, C, D:

Relative to the cells A, B, C, D

g:

Volume delimited by points 7-9-3-5-7

i:

Computational point i

in:

Conditions at the inlet

j:

Relative to the specie j

n:

Specie n or time level n

References

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  4. Gamm (1984). Workshop on Analysis of Laminar Flow over a Backward Facing Step, eds., K. Morgan, J. Periaux, F. Thomasset, Vieweg, Brannschweig.

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Author information

Authors and Affiliations

  1. Dept. Applied Mathematics Ecole Polytechnique de Montreal, P.O. Box 6079, H3C 3A7, Stn A, Montreal, Canada

    David Elkaim, Mohamed Agouzoul & Ricardo Camarero

Authors
  1. David Elkaim
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  2. Mohamed Agouzoul
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  3. Ricardo Camarero
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Editor information

Alain Dervieux Bernard Larrouturou

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© 1989 Springer-Verlag

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Elkaim, D., Agouzoul, M., Camarero, R. (1989). A numerical solution for reacting and non reacting flow. In: Dervieux, A., Larrouturou, B. (eds) Numerical Combustion. Lecture Notes in Physics, vol 351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51968-8_89

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  • DOI: https://doi.org/10.1007/3-540-51968-8_89

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51968-3

  • Online ISBN: 978-3-540-46866-0

  • eBook Packages: Springer Book Archive

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