Alfredo José Rodríguez Alarcón Advisors: Dr. Francesc Giralt Dr. Joan Herrero

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.

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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



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Thermal convection insideThermal convection insideenclosuresenclosures

T2

T1

T1>T2g Fluid

ProblemProblem configurationconfiguration



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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



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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)



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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)



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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.



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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).



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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



1010

Two dimensional convective Two dimensional convective heat transfer inside enclosuresheat transfer inside enclosures

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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



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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.



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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.



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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.



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Questions, comments?Questions, comments?

Thank youThank you

Documents

Alfredo José Rodríguez Alarcón Advisors: Dr. Francesc Giralt Dr. Joan Herrero