Phase Change Materials - COMSOL Multiphysics...PCM Donato Rubinetti Appendix A - Modeling Functions...

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Final Remarks

Phase Change MaterialsModeling Approach to Facilitate Thermal Energy Management in Buildings

Donato Rubinetti 1 Daniel A. Weiss 1 Arnab Chaudhuri 2 Dimitrios Kraniotis 2

1Institute of Thermal and Fluid EngineeringUniversity of Applied Sciences and Arts Northwestern Switzerland

2Department of Civil Engineering and Energy TechnologyOslo Metropolitan University, Norway

27.09.2018

DonatoRubinetti

Introduction

Application

Modeling

PhysicalModel

NumericalModel

ApplicationExample

Final Remarks

IntroductionWhat are PCMs and what are their application areas?

• Materials with a characteristically large enthalpy of fusion

• Latent heat energy storage systems

• Decouple energy supply and demand → increase efficiency

• Wide range of applications from -40 to 500◦C, i.e. space to photovoltaics

DonatoRubinetti

Introduction

Application

Modeling

PhysicalModel

NumericalModel

ApplicationExample

Final Remarks

IntroductionThe need for modeling PCM

• Obtain fundamental understanding for freezing and melting cycle

• Predict the complex behavior well enough

• Efficiently choose among the vast selection of suitable PCM

• Design improvements

• Reduce development costs

DonatoRubinetti

Introduction

PhysicalModel

Couplings

NumericalModel

ApplicationExample

Final Remarks

Physical ModelMultiphysical couplings

Heat Transfer Fluid Flow

Geometry

Phase Change

Natural Convection

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

Implementation

Melted fraction

ApplicationExample

Final Remarks

Numerical ModelImplementation into COMSOL Multiphysics

Laminar Flow (CFD)

Heat Transfer in Fluids

auxiliary algebraicequations for material

properties

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

Implementation

Melted fraction

ApplicationExample

Final Remarks

Numerical ModelMelted fraction θ(T )

θ(T ) =

0, solidT−(Tm−∆T/2)

∆T, mushy

1, liquid

Temperature T [°C]M

35.4 36.4 37.4

Tm + 1

2 ∆T

Tm − 1

2 ∆T

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Wall coretemperature

Final Remarks

Application ExampleObserved week in Oslo, temperature profile

Operation / Day Time [h]

0 24 48 72 96 120 144 168

4/18−10

Weather Forecast Oslo. 2018. url: https://www.wunderground.com/weather/no/oslo

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Final Remarks

Application ExampleWall crossection of a typical Norwegian building

9 15 15 50 50 120 100

x [mm] 21

1 2 3 4 5 6 7

Thermostat: Keep 19 < T < 26 °C+ internal heat gains

Weather data for T

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Final Remarks

Application ExampleResults - energy savings?

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Final Remarks

Application ExampleA less instulated wall crosssection

9 50 50 100

x [mm] 2

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Final Remarks

Application ExampleResults - substantial energy savings!

Operation Time [h]

0 24 48 72 96 120 144 168

w/o PCM (66%)w/ PCM (13%)

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Temperature

Crossection 1

Results

Crosssection 2

Thermostat

Final Remarks

Application ExampleWall core temperature

0 24 48 72 96 120 144 168

Time−averaged Room Temperature without PCM

Time−averaged Room Temperature with PCM

Melting Temperature (Liquefaction / Heat Absorption)

Freezing Temperature (Liquefaction / Heat Release)

With PCMWithout PCMPhase State

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Final Remarks

Discussion• Release heat to reduce heating demand• For well insulated walls → marginal savings!• But: PCM reduces peak temperatures on both extremes• Cold climates → main benefit in summer

Conclusion• Comprehensive and suitable modeling approach for phase change phenomena

developed• Rapid orientation whether a PCM meets thermal, technical and economic

requirements• Model shows the importance of including indoor dynamics to assess the PCM

potential• Numerically stable model, extendable to enhanced PCM

DonatoRubinetti

Introduction

PhysicalModel

NumericalModel

ApplicationExample

Final Remarks

Thank you for your attention!

DonatoRubinetti

Appendix

A - ModelingFunctions

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

D -ApplicationExample

E - 2DTest-Case

F -DimensionlessEstimation

A - Modeling FunctionsMelt Fraction θ(T )

θ(T ) =

0, solidT−(Tm−∆T/2)

∆T, mushy

1, liquid

35.4 36.4 37.4

Tm + 1

2 ∆T

Tm − 1

2 ∆T

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsGaussian Distribution Function D(T )

D(T ) =e−

(T − Tm)2

(∆T/4)2√π(∆T/4)2

Temperature T [°C]G

35.4 36.4 37.4

34.9 37.9

∆T = 2 K

∆T = 3 K

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsModified Heat Capacity Cp(T )

Cp(T ) = Cp,s+θ(T )(Cp,l−Cp,s)+D(T )L(4)

Temperature T [°C]H

35.4 36.4 37.4

D(T) L

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsModified Material Density ρ(T )

ρ(T ) = ρs+θ(T )(ρl−ρs)(5)

35.4 36.4 37.4

Tm − 1

2 ∆T

Tm + 1

2 ∆T

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsModified Thermal Conductivity k(T )

k(T ) = ks+k(T )(kl−ks)(6)

35.4 36.4 37.4

Tm − 1

2 ∆T

Tm + 1

2 ∆T

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsCarman-Kozeny Porosity Function S(T )

S(T ) = Am(1− θ(T ))2

θ(T )3 + ε(7)

Temperature T [°C]

Solid dominatedmushy−zone

Liquid dominatedmushy−zone

35.4 36.4 37.4

Ali C. Kheirabadi and Dominic Groulx. “Simulating Phase Change Heat Transfer using COMSOL and FLUENT: Effect of the Mushy-ZoneConstant”. In: Computational Thermal Sciences: An International Journal 7.5-6 (2015). doi: 10.1615/ComputThermalScien.2016014279

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsViscosity of n-eicosane µ(T )

µ(T ) = (9×10−4 T 2−0.6529 T+119.94)×10−3

40 50 60 70 80 90

Temperature T [°C]D

n − eicosanewater

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsBasic numerical requirements to govern the physics of PCM

conservation equation solid fraction liquid fraction

continuity Xmomentum Xenergy X X

→ direct approach: two subdomains for liquid and solid fraction with front trackingalgorithm

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsAlternative approach: introduction of a mushy zone

• Idea: material properties are smeared out over an user-defined meltingtemperature range

• Method: use of porosity formulation, liquid and solid co-exist in the mushyzone• Benefits:

• avoid numerical singularities• use one single mesh• easy to implement

• Setback: highly mesh-dependent solution in terms of physical accuracy

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling Functions2D Test-case

Ω 1 x 1 cm2

n-eicosane

𝑇𝑇1 = 55 °C

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsBoundary conditions and setup

Boundary CFD Heat Transfer

No slipwall

𝑻𝑻𝑹𝑹 = 𝟒𝟒𝟒𝟒,𝟓𝟓𝟓𝟓,𝟕𝟕𝟒𝟒 °𝐂𝐂

Thermal insulation❸

𝒈𝒈

Pressure constraint point, 𝒑𝒑 = 𝟒𝟒 𝐏𝐏𝐏𝐏

Transient study, 𝟒𝟒 < 𝒕𝒕 < 𝟏𝟏𝟒𝟒𝟒𝟒𝟒𝟒 𝐬𝐬

DonatoRubinetti

Appendix

Melt Fraction

Gaussian

Heat Capacity

Density

Th. Conductivity

Carman-Kozeny

Viscosity

Requirements

Mushy zone

2D Test-case

Carman-Kozeny

Validation

C - Results

E - 2DTest-Case

A - Modeling FunctionsCarman-Kozeny porosity function S(T )

S(T ) = Am(1− θ(T ))2

θ(T )3 + ε(9)

Temperature T [°C]

Solid dominatedmushy−zone

Liquid dominatedmushy−zone

35.4 36.4 37.4

Ali C. Kheirabadi and Dominic Groulx. “Simulating Phase Change Heat Transfer using COMSOL and FLUENT: Effect of the Mushy-ZoneConstant”. In: Computational Thermal Sciences: An International Journal 7.5-6 (2015). doi: 10.1615/ComputThermalScien.2016014279

DonatoRubinetti

Appendix

Validation

Results

Model Setup

Material properties

C - Results

E - 2DTest-Case

B - Comparison to Experimental DataResults

−30 −20 −10 0 10 20 30

Radial Distance r [mm]

SimulationExperiment

t = 2164 s

−30 −20 −10 0 10 20 30

Radial Distance r [mm]A

t = 6964 s

−30 −20 −10 0 10 20 30

m] Simulation

Experiment

t = 11524 s

DonatoRubinetti

Appendix

Validation

Results

Model Setup

Material properties

C - Results

E - 2DTest-Case

B - Comparison to Experimental DataModel Setup

𝑻𝑻𝑹𝑹 = 45 °C

n-eicosane

𝑯𝑯 = 59.8 mm

𝟐𝟐𝑹𝑹 = 63.8 mm

𝑻𝑻𝑩𝑩 = 32 °C

DonatoRubinetti

Appendix

Validation

Results

Model Setup

Material properties

C - Results

E - 2DTest-Case

B - Comparison to Experimental DataMaterial properties of n-eicosane, comparison with water

n-eicosane watersolid liquid solid liquid

density ρ [kg m−3] 910 769 916 997thermal conductivity k [W m−1 K−1] 0.423 0.146 1.6 0.6heat capacity Cp [kJ kg−1 K−1] 1.9 2.4 2.1 4.2melting temperature Tm [◦C] 36.4 - 0 -latent heat of fusion L [kJ kg−1] 248 - 334 -

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsGrashof Number

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsMelt Fraction

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsMesh sensitivity - melting front prediction

0.000 0.002 0.004 0.006 0.008 0.010

x−Coordinate [m]

Mesh cells25 x 2550 x 50100 x 100150 x 150

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsMelt fraction - curvature of melting front

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsLocal Grashof number - influence of natural convection

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsValidation case - setup

𝑻𝑻𝑹𝑹 = 45 °C

n-eicosane

𝑯𝑯 = 59.8 mm

𝟐𝟐𝑹𝑹 = 63.8 mm

𝑻𝑻𝑩𝑩 = 32 °C

Benjamin J. Jones et al. “Experimental and numerical study of melting in a cylinder”. In: International Journal of Heat and Mass Transfer49.15-16 (2006), pp. 2724–2738

DonatoRubinetti

Appendix

Validation

C - Results

Grashof Number

Melt Fraction

Mesh sensisitvity

Melt fraction

Validation I

Validation II

E - 2DTest-Case

C - ResultsValidation case - comparison to experimental data

−30 −20 −10 0 10 20 30

t = 2164 s

−30 −20 −10 0 10 20 30

60Radial Distance r [mm]

t = 6964 s

−30 −20 −10 0 10 20 30

m] Simulation

Experiment

t = 11524 s

DonatoRubinetti

Appendix

Validation

C - Results

Internal Heat Gains,Hourly

Indoor Temperaturew/o PCM

Indoor Temperaturew/ PCM

Thermostat

Wall CoreTemperature

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleInternal Heat Gains, Hourly

Hour of day [h]

0:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00

PeopleLightingEl. equipmentRadiationSum

Komite-SN/K-034. Bygningers energiytelse, Beregning av energibehov of energiforsyning (engl.: Energy performance of buildings, calculationof energy needs and energy supply). URL:https://www.standard.no/no/Nettbutikk/produktkatalogen/Produktpresentasjon/?ProductID=859500. 2016

DonatoRubinetti

Appendix

Validation

C - Results

Thermostat

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleIndoor Temperature w/o PCM

0 24 48 72 96 120 144 168

2025 Comfort

TemperatureRange

AmbientIndoor

DonatoRubinetti

Appendix

Validation

C - Results

Thermostat

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleIndoor Temperature w/ PCM

0 24 48 72 96 120 144 168

2025 Comfort

TemperatureRange

AmbientIndoor

DonatoRubinetti

Appendix

Validation

C - Results

Thermostat

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleThermostat

Operation Time [h]

0 24 48 72 96 120 144 168

w/o PCM (66%)w/ PCM (13%)

DonatoRubinetti

Appendix

Validation

C - Results

Thermostat

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleWall Core Temperature

0 24 48 72 96 120 144 168

Time−averaged Room Temperature without PCM

Time−averaged Room Temperature with PCM

Melting Temperature (Liquefaction / Heat Absorption)

Freezing Temperature (Liquefaction / Heat Release)

With PCMWithout PCMPhase State

DonatoRubinetti

Appendix

Validation

C - Results

Thermostat

Wall Cross-Section

E - 2DTest-Case

D - Application ExampleWall Cross-Section

9 15 15 50 50 120 100

x [mm] 21

1 2 3 4 5 6 7

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

2D Test-Case

Couplings

2D Test-case

E - 2D Test-Case2D Test-Case

Ω 0.01 x 0.01 m2

𝑻𝑻𝑹𝑹

n-eicosane

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

2D Test-Case

Couplings

2D Test-case

E - 2D Test-CaseMultiphysical couplings

𝑻𝑻𝑹𝑹 ≫ 𝑻𝑻𝒎𝒎

𝑻𝑻𝑹𝑹 > 𝑻𝑻𝒎𝒎

Liquid

𝑻𝑻𝑹𝑹: Boundary Temperature

𝑻𝑻𝒎𝒎: Melting Temperature

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

2D Test-Case

Couplings

2D Test-case

E - 2D Test-Case2D Test-case

Ω 0.01 x 0.01 m2

𝑻𝑻𝑹𝑹= 40, 55, 70 °C

n-eicosane

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

Mushy ZoneInvestigation

Scaling Variables

DimensionlessEquations

DimensionlessNumbers

Values For LiquidFraction

F - Dimensionless EstimationMushy Zone Investigation

Temperature T [°C]

Tm−1/2∆T Tm Tm+1/2∆T

Solid dominated

mushy−zone

Liquid dominated

mushy−zone

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

Scaling Variables

F - Dimensionless EstimationScaling Variables

p − prefρu0

t =u0t

Huuu =

T − Tref

TR − Tref

Φv ∇ = H∇ D

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

Scaling Variables

F - Dimensionless EstimationDimensionless Equations

∇ · uuu = 0 (10)

Dt= −∇p +

]∇2uuu −

[gβ(TR − Tm)H

)(T − Tm) (11)

u0ρHCp

]∇2T +

ρHCp(TR − Tm)

]Φv (12)

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

Scaling Variables

F - Dimensionless EstimationDimensionless Numbers

Brinkman Br =µu0

k∆Theat production visc. dissipation vs heat transport by cond.

Grashof Gr =gβ∆TH3

ν2buoyant forces vs viscous forces

Prandtl Pr =ν

αmomentum diffusivity vs thermal diffusivity

Rayleigh Ra =gβ∆TH3

αν= GrPr heat transport conv. vs cond.

Reynolds Re =ρu0H

µinertial vs viscous forces

DonatoRubinetti

Appendix

Validation

C - Results

E - 2DTest-Case

Scaling Variables

F - Dimensionless EstimationValues For Liquid Fraction

Dimensionless group TR

40 ◦C 55 ◦C 70 ◦C[µ

Re1 1 1

[gβ(TR − Tm)H

PrRe2266 1376 2486

u0ρHCp

RePr0.008 0.008 0.008

ρHCp(TR − Tm)

RePr1.25 × 10−10 2.42 × 10−11 1.34 × 10−11

Phase Change Materials - COMSOL Multiphysics...PCM Donato Rubinetti Appendix A - Modeling Functions...

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