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Turbulent Thermal Convection Turbulent Thermal Convection inside Enclosures inside Enclosures by Direct Numerical Simulationby Direct Numerical Simulationand Nonlinear Analysisand Nonlinear Analysis
Alfredo José Rodríguez AlarcónAlfredo José Rodríguez Alarcón
Advisors:Advisors:Dr. Francesc GiraltDr. Francesc GiraltDr. Joan HerreroDr. Joan Herrero
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
22
SchemeScheme
Why study thermal convection inside enclosures?Why study thermal convection inside enclosures?
ObjectivesObjectives
Natural (free) convectionNatural (free) convection
Two dimensional convective heat transfer inside enclosuresTwo dimensional convective heat transfer inside enclosures
RemarksRemarks
Project emphasis and summaryProject emphasis and summary
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
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Thermal convection insideThermal convection insideenclosuresenclosures
T2
T1
T1>T2g Fluid
ProblemProblem configurationconfiguration
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
44
Why study thermal convection Why study thermal convection inside enclosures?inside enclosures?
This configuration is This configuration is often employed for the often employed for the reduction of energy reduction of energy loss, e.g.loss, e.g.
1.1. Thermal insulation Thermal insulation of furnaces and of furnaces and similar systems.similar systems.
2.2. Solar energy Solar energy collectors.collectors.
Sketch of a flat-plate collector
Compact Vacuum Furnace
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
55
Why study thermal convection Why study thermal convection inside enclosures?inside enclosures?
In manufacturing systems, In manufacturing systems,
flow regimes determination is flow regimes determination is
important because product important because product
quality can be affected by the quality can be affected by the
flow patterns, e. g.flow patterns, e. g.
1.1. Crystal growing facilitiesCrystal growing facilities
2.2. Melting furnacesMelting furnaces
3.3. Plastic molding systemsPlastic molding systemsVertical velocity contours in the Vertical velocity contours in the horizontal midplane z=0 for horizontal midplane z=0 for different flow patterns (Puigjaner different flow patterns (Puigjaner et al. 2004)et al. 2004)
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
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Why study free convection insideWhy study free convection insideenclosures heated from below?enclosures heated from below?
Theoretical developments and Theoretical developments and
understanding of the convective understanding of the convective
heat transfer phenomena. heat transfer phenomena.
““Convection is a major feature Convection is a major feature of the dynamics of the oceans, of the dynamics of the oceans, the atmosphere, and the interior the atmosphere, and the interior of stars and planets.” of stars and planets.” (Bodenschatz (Bodenschatz et al.et al. 2000) 2000)
Temperature isosurface for the nondimensional value of T=0.6Pr=100. (Breuer et al. 2004)
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
77
ObjectivesObjectives
OverallOverall
To carry out a primary study on turbulent thermal convection inside To carry out a primary study on turbulent thermal convection inside
cubical enclosures by direct numerical simulation and nonlinear cubical enclosures by direct numerical simulation and nonlinear
analysis.analysis.
SecondarySecondary
To develop an adequate computational code for the study of To develop an adequate computational code for the study of
turbulent thermal convection inside cubical enclosures.turbulent thermal convection inside cubical enclosures.
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
88
Natural (thermal) convectionNatural (thermal) convection
The two basic Heat Transfer processes are The two basic Heat Transfer processes are conductionconduction and and
radiationradiation. .
Conduction is due to the motion of microscopic particles that Conduction is due to the motion of microscopic particles that
comprise a material.comprise a material.
Convection occurs when Convection occurs when conductive heat transfer is coupled with conductive heat transfer is coupled with
the motion of the fluidthe motion of the fluid..
In general, in the natural convection fluid movement is due to In general, in the natural convection fluid movement is due to
density differencesdensity differences in presence of a body field (i.e. gravitational in presence of a body field (i.e. gravitational
acceleration).acceleration).
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
99
Two dimensional convective Two dimensional convective heat transfer inside enclosuresheat transfer inside enclosures
H
T1
T2
T1>T2
g
RaH < 1708
NuH = 1
Quiescent, thermally stratified fluid
H
T1
T2
T1>T2
RaH > 1708
NuH > 1
Cellular flow pattern
g
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
1010
Two dimensional convective Two dimensional convective heat transfer inside enclosuresheat transfer inside enclosures
31 2
H
g H T TRa
Rayleigh number (RaRayleigh number (RaHH), Nusselt number (Nu), Nusselt number (NuHH) as well as Prandlt ) as well as Prandlt
number (Pr) appear in scale analysis and dimensionless number (Pr) appear in scale analysis and dimensionless
equations.equations.
When governing equations are written in dimensionless When governing equations are written in dimensionless
disturbance variables, the Radisturbance variables, the RaHH determines the emerging of flow determines the emerging of flow
instabilities.instabilities.
CPr p
k
H
hHNu
k
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
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RemarksRemarks
The initial flow is laminar and with The initial flow is laminar and with increasing Raincreasing Ra, it , it
undergoes undergoes transition to turbulencetransition to turbulence..
NuNuHH, is function of Ra, is function of RaHH, Pr, geometry, thermal , Pr, geometry, thermal
boundary conditions, flow structures.boundary conditions, flow structures.
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
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RemarksRemarks
Currently, turbulent thermal convection has been Currently, turbulent thermal convection has been
better studied through experiments, hence better studied through experiments, hence there are there are
not enough 3D numerical simulationsnot enough 3D numerical simulations..
TransitionTransition to turbulence to turbulence and turbulenceand turbulence itself need itself need
further understanding due to the difficulty of further understanding due to the difficulty of
characterizing both numerically as well as characterizing both numerically as well as
experimentally chaotic fluid movement.experimentally chaotic fluid movement.
Fenòmens de TranspFenòmens de Transport (FeT), URVort (FeT), URV
Turb. Thermal Convec. In. EnclsrsTurb. Thermal Convec. In. Enclsrs. by DNS & Nonlin. Anal.. by DNS & Nonlin. Anal.
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Project emphasisProject emphasis
1.1. To understand the physics of thermal convection inside To understand the physics of thermal convection inside
enclosures. enclosures.
2.2. To be aware of the advantages and limitations of current To be aware of the advantages and limitations of current
numerical methods available for the problem of study.numerical methods available for the problem of study.
3.3. Select the appropriate numerical scheme to develop Select the appropriate numerical scheme to develop
computational code in FORTRAM.computational code in FORTRAM.
4.4. Test code developed with known problems and previous Test code developed with known problems and previous
analysis.analysis.