TURBULENCE HEATFLUX MODELLING OF NATURAL CONVECTION IN TWODIMENSIONAL THINENCLOSURE

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TURBULENCE HEAT-FLUX MODELLING OF NATURAL
CONVECTION IN TWO-DIMENSIONAL THIN-ENCLOSURE
Zarko M. Stevanovic
VINCA Institute for Nuclear Sciences Laboratory
for Thermal Engineering and Energy 11001
Belgrade, P.O. Box 522, Yugoslavia zare_at_rt270.vin.
bg.ac.yu
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C O N T E N T Objective of Work 3 Turbulence
Modelling 5 Differential - to - Algebraic
Truncation 6 Computational Details 8 Computati
onal Results 9 Conclusions 13
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O b j e c t i v e o f W o r k
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• These prospects have motivated present work,
  aimed at verifying the current practice in
  modeling of the transport equations for the
  turbulent heat-flux and temperature-variance and
  at exploring the limits of simpler turbulence
  models at the algebraic level.
• Results of direct numerical simulation and
  experimental data of turbulent natural convection
  between two differentially heated vertical plates
  for Ra 8.227x105 and for Ra 5.4x105 have been
  used to validate the algebraic heat flux model.

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T u r b u l e n c e M o d e l l i n g
Transport Equations
Modelled Terms
Specification of Coefficients
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D i f f e r e n t i a l - t o - A l g e b r a i c
T r u n c a t i o n
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Reduced Model to the Three-Equation Model k - ?
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- Lam-Bremhorst Low-Re k - ? model
- Additional Transport Equation for
- Reduced Algebraic Expression for
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C o m p u t a t i o n a l D e t a i l s

• Basic References
• Betts, P.L. and Boghari, I.H., (1996),
  Experiments on turbulent natural convection of
  air in tall cavity, Proc. of the 5th ERCOFTAC
  workshop on Refined Flow Modeling, Chatou,
  France.
• Versteegh, T.A.M., (1998), Numerical simulation
  of natural convection in a differentially heated,
  vertical channel, Ph.D. Thesis, Printed by
  Ponsen Looijen, The Netherlands.

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C o m p u t a t i o n a l R e s u l t s
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Finally, we can conclude that one of the minimum
level of modeling which can reproduce the major
flow features in more complex geometry is the
algebraic model which accounts for all major
sources of turbulent heat flux and thus far
expresses the turbulent heat flux vector in terms
of the mean temperature gradient, mean flow
deformation and temperature variance interacting
with the gravitational vector. Also, in the
complex geometry of natural convection fluid flow
problems, one of the most convenience turbulence
model is LVEL model, proposed by professor D.B.
Spalding.