# Instability Regimes for Buoyancy Induced Flows in a Nonuniformly Cooled Duct - PowerPoint PPT Presentation

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## Instability Regimes for Buoyancy Induced Flows in a Nonuniformly Cooled Duct

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Title: Instability Regimes for Buoyancy Induced Flows in a Nonuniformly Cooled Duct

1
__________________________________________________
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__________________________________________________
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Instability Regimes for Buoyancy Induced Flows in
a Nonuniformly Cooled Duct
Doctoral Candidate Professor
Mechanical Engineering Department Southern
Methodist University Dallas, Texas
2
OUTLINE
• Introduction
• Numerical method
• Solution accuracy
• Results and discussions
• Low Rayleigh number
• Intermediate Rayleigh number
• High Rayleigh number
• Analysis
• Conclusions

3
Introduction
• Heating Ventilating and Air Conditioning (HVAC)
Unit in a Contained Room

4
Introduction (contd)
• Buoyancy-induced flow of a hot gas through a
vertical duct
• Cooling of the gas by walls and open top
initiates a buoyancy-induced secondary flow that
opposes the main upward motion

Physics
Mathematics
5
Numerical Method
• The fluid momentum is computed by a direct
solution of the Navier-Stokes equations, coupled
with the continuity equations

NS
C
• Heat transfer is computed by solution of energy
equation coupled with N-S and continuity
equations

E
• Oberbek-Boussinesq approximation is used, i.e.
• Fluid density in non-linear convective terms is
held constant.
• Fluid density that appears in gravitational terms
is considered to vary with temperature according
to following relation

6
Numerical Method (contd)
• A projection method is used to solve momentum
equations coupled with continuity equation.
• Finite Volume equations solved over an Eulerian,
staggered grid.
• Energy equation is solved by a control volume
method (Patankar).

7
Results and discussions
• Many cases (gt100) considered in order to obtain
accurate map of temperature bifurcation.
• 18 cases are presented for following values of
Rayleigh and Reynolds numbers
• Ra5.83 x 104, 5.83 x 105, 1.75 x 106.
• Re0, 12.5, 25, 175, 250, 750.
• Four different regimes are observed, three steady
and one periodic with a dominant frequency.

8
Results and discussions (contd)
• Low Rayleigh Number (Ra5.83 x 104).
• Two distinct flow regimes are observed
• Regime 1 corresponds to high values of Re is
characterized by a thin boundary layer (easily
predictable both numerically and analytically).
• Regime 2 is characterized by a drop in boundary
layer causing significant buoyancy induced flow
recirculation in the cavity.

Isotherms
Isotherms
Streamlines
Re250
Re25
9
Results and discussions (contd)
• Intermediate Rayleigh Number (Ra5.83 x 105).
• Three different regime flows are observed
• Regime 1 and regime 2 corresponding to high and
medium values of Re are similar with the the
previous regimes (for Ra5.83 x 104).
• Regime 3 occurs at lower Re and is one of

Isotherms during one period of oscillation
(Re25)
10
Results and discussions (contd)
• High Rayleigh Number (Ra1.75 x 106).
• Four different regime flows are observed
• Results for this Ra indicate the existence of all
three regimes previously observed in addition to
a different (fourth) flow regime.
• Regime 4 is observed at the low end of the
considered range of Reynolds numbers.

Streamlines
Isotherms
Re25
11
Results and discussions (contd)
• Map of observed thermal boundary layers

12
Results and discussions (contd)
• Temperature at the top centerline of the duct.

13
Results and discussions (contd)
LEGEND Non-dimensional Temperature
• Isotherms during one period of oscillation
• Ra5.83 x 105
• Re12.5.

HOT
COLD
14
__________________________________________________
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__________________________________________________
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Instability Regimes for Buoyancy Induced Flows in
a Nonuniformly Cooled Duct