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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
Mihai G. Burzo Dani Fadda
Peter E. Raad Doctoral Student
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
    quasi-steady oscillation.

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
__________________________________________________
__
__________________________________________________
__
Instability Regimes for Buoyancy Induced Flows in
a Nonuniformly Cooled Duct
Dani Fadda fadda_at_seas.smu.edu,
http//www.seas.smu.edu/fadda
Mihai G. Burzo bmg_at_seas.smu.edu,
http//www.seas.smu.edu/bmg
Peter E. Raad peter_at_seas.smu.edu,
http//www.seas.smu.edu/peter
Mechanical Engineering Department Southern
Methodist University Dallas, Texas 75275-0337
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