Analysis by CFD models of deterioration heat transfer phenomena for supercritical fluids

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1 D IPARTIMENTO DI I NGEGNERIA DELL ’E NERGIA, DEI S ISTEMI, DEL T ERRITORIO E DELLE C OSTRUZIONI

C ^{ORSO DI} L ^AUREA M AGISTRALE IN I ^NGEGNERIA E ^NERGETICA

T ESI DI L AUREA M AGISTRALE

Analysis by CFD models of deterioration heat transfer phenomena for supercritical fluids

Relatori Candidata

Prof. Walter Ambrosini Irene Borroni

Dott. Ing. Nicola Forgione matr.472301

Dott. Ing. Medhat Sharabi

Anno Accademico 2013/2014

Appello di Laurea 5 maggio 2014

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2

Abstract

This work is focused on the study of the deteriorated heat transfer phenomena for fluids at supercritical pressure and of the ability of different RANS four-equation turbulence models in predicting their characteristics.

Fluids at supercritical pressure are characterized by a strong variation of fluid properties across a particular value of temperature, named “pseudocritical”. At the pseudocritical condition, in fact, specific heat, density, thermal conductivity and dynamic viscosity show significant changes; in particular, across the pseudocritical temperature the fluid transforms its behaviour from “liquid-like” to “gas-like”. This occurrence may cause the impairment or the enhancement of heat transfer depending on operating conditions.

Two-equation low Reynolds number models (both and ) have been thoroughly assessed in past studies for heat transfer prediction with supercritical pressure fluids, but they were frequently found unable to provide good results in such conditions, especially when working close to the pseudocritical temperature. In this work, basing on a previous study, four-equation turbulence models are used and analyses are made considering the effect of different values of the turbulent Prandtl number and evaluating the influence of relevant coefficients appearing in turbulence equations.

Models making use of four-equations are adopted both in their original form and as hybrid models, obtained by combining equations for a turbulent velocity field with those for the turbulent thermal model in a mixed way. This allows assessing multiple combinations, thus showing their potential in improving results that are often quantitatively inaccurate. Most of the analyses are made with an in-house code named THEMAT (Sharabi, 2008) and, in some cases, using STAR CCM+. Experimental data for wall temperature in vertical pipes with supercritical pressure water are compared with the results obtained from the simulations. A comparison between RANS and LES data, made available by the Paul Scherrer Institut (PSI, Switzerland) for a relevant case, is also reported.

Finally, a promising approach for evaluating the effect of wall roughness on the

prediction of heat transfer is presented, proposing a preliminary validation and its first results in

the application to supercritical fluids.

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3

Acknowledgements

The financing by the European Commission, through the EU THINS Project, of the research in whose frame my study was performed is acknowledged.

I want to thank the tutors and especially Prof. Walter Ambrosini, for his guidance, for

encouraging and patiently supporting me during these months. I also wish to thank the persons

who helped me in performing this work, as Ing. Andrea Pucciarelli and Dr. Medhat Sharabi, who

supported me very much in the various phases of this study.

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4

Nomenclature

Roman letters G Mass flux [kg/m

²

s]

a

1

, a

3

, a

5

Model constants G

k

Production term due to the buoyancy [m

²

/s

³

]

A

D1

, A

D2

Model constants Gr Grashof number

B Additive constant for smooth wall h Heat Transfer Coefficient [W(/m

²

K)]

Bo Buoyancy parameter H Specific enthalpy [J/kg]

Specific heat [J/kgK] k Turbulent kinetic energy [m

²

/s

²

] C

ε1

, C

ε2

,

C

ε3

, C

µ

, C

λ

, C

m

, C

P1

, C

P2

C

D1

, C

D2

,

Turbulence model constants for the velocity field

K von Karman’s constant

K

eps

Constant of smoothing function Nu Nusselt number

p Pressure [MPa]

P

k

Production term due to the shear stress

C

t

, C

t1

, C

t2

, C

t3

, C’

t1

Constants of the turbulent heat flux

Pr, Pr

t

Molecular and turbulent Prandtl number

q’’ Heat flux [W/m

²

]

C

rough

Constant of turbulent kinetic

energy source related to roughness q’’’ Volumetric power [W/m

³

]

D Pipe diameter [m] R Timescale ratio

D

h

Hydraulic diameter [m]

R

ε

Turbulent Reynolds number defined by Kolmogorov scale

E Source term

f

ε1

, f

ε

, f

µ

, f

_λ

, f

P1

, f

P2

f

D1

, f

D2

, f

2

Turbulence model functions for the temperature field

R

y

Damping function for calculating eddy viscosity

R

t

Turbulent Reynolds number S

ij

Strain rate tensor

f

Actual

Skin friction coefficient ̂

Local turbulence production

f

Rough

Friction coefficient by Colebrook formulation

S

k,rough

Source of turbulent kinetic energy

F

k,rough

Smoothing function

g Gravitational acceleration [m/s

²

]

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5 ̅̅̅̅ Temperature variance [K

²

] Wall shear stress T Temperature [°C] [K]

φ,Φ,φ’

General flow property, mean value and varying fluctuating

components T

k

Kolmogorov time scale

T

t

Turbulent time scale

u, v, w Velocity [m/s] ω Specific dissipation rate [1/s]

̅̅̅̅, ̅̅̅̅, ̅̅̅̅̅

Variances of velocity fluctuations [m

²

/s

²

]

u

⁺

Dimensionless velocity Subscript

V Volume [m

³

] cr Critical value

w

t

Friction velocity or shear velocity

[m/s] dyn Dynamic

x, y, z spatial coordinates [m/s] in Inlet y

⁺

Dimensionless distance from the

wall

i, j Indices of Einstein’s notation pc Pseudocritical value

w Wall

Greek letters

Molecular and turbulent thermal

diffusivities [m

²

/s] Acronyms

β Thermal expansion coefficient

[1/K] AKN Abe Kondoh Nagano model

(1995)

δ

ij

Kronecker delta CFD Computational Fluid Dynamics

ΔBr Roughness additive constant DNS Direct Numerical Simulation Dissipation rate of k [m

²

/s

³

] JL Jones Launder model (1972) ε

⁺

Dimensionless roughness height HL Hwang Lin model (1999)

ε

rough

Roughness height [m] HTC Heat Transfer Coefficient

ζ Parameters of the roughness

additive constant LES Large Eddy Simulation

λ Thermal conductivity [W/mK] LS Launder Sharma model (1974) ν, ν

t

Molecular and turbulent kinematic

viscosities [m

²

/s] RANS Reynolds Averaged Navier-Stokes equations

Density [kg/m

³

] SCWR Supercritical Water Reactor

σ

k

, σ

_ε

, σ

_Φ

and σ

h

Turbulence model constants for

diffusion of ̅ and YS Yang Shih model (1993)

Timescale of velocity and

temperature

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6 Abstract 2

Acknowledgements 3

Nomenclature 4

Table of contents 6

1. Introduction 8

1.1 General Background 8 1.2 Thesis Outline 10

2.Heat transfer to fluids at supercritical pressure 11

2.1 Physical properties of fluids in critical and pseudocritical regions 11

2.2. Mechanism of the heat transfer deterioration 14

2.3. Experimental data 17

2.4. Previous Results 20

3.Turbulence models 23

3.1. Governing equations 23

3.2. Turbulent flow calculations 25

3.3. Considered two equation models 28

3.4.Four equations models 30

3.5.Turbulent heat flux modelling 37

3.6. Codes Overview: generalized consideration 38

4. Analysis of Supercritical Water Data 41

4.1 Experimental data Pis’menny et al. (2005) 41

4.1.1 Case series 1: D = 6.28 mm, Tin = 300 °C, G = 509 kg/(m

²

s), q’’ = 390 kW/m

²

43

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7 4.1.2 Comparison between LES data and STAR CCM+ 53

4.1.3 Case series 2: D = 6.28 mm, Tin = 17 °C, G = 428 kg/(m

²

s), Upward flow 60

4.1.4 Case series 3: D = 6.28 mm, Tin = 200 °C, G = 249 kg/(m

²

s), Upward flow 71

4.1.5Case series 4: D = 9.5 mm, Tin = 100 °C, G = 248 kg/(m

²

s), Upward flow 78

4.2 Experimental data by Ornatskii et al. (1971) 89

4.2.1 Case series 1: D = 3 mm, Tin = 300 K, G = 1500 kg/(m

²

s), q’’ = 1320 kW/m

²

Upward flow 89

4.2.2 Case series 2: D = 3 mm, Tin = 300 K, G = 1500 kg/(m

²

s), q’’ = 1810 kW/m

²

Upward flow 92

4.3 Experimental data by Watts (1980) 96

4.3.1 Case series 1: D = 25.4 mm, Tin = 150 °C, q’’ = 250 kW/m

²

Analysis by CFD models of deterioration heat transfer phenomena for supercritical fluids

1

D IPARTIMENTO DI I NGEGNERIA DELL ’E NERGIA, DEI S ISTEMI, DEL T ERRITORIO E DELLE C OSTRUZIONI

C ORSO DI L AUREA M AGISTRALE IN I NGEGNERIA E NERGETICA

T ESI DI L AUREA M AGISTRALE

Analysis by CFD models of deterioration heat transfer phenomena for supercritical fluids

Relatori Candidata

Prof. Walter Ambrosini Irene Borroni

Dott. Ing. Nicola Forgione matr.472301

Dott. Ing. Medhat Sharabi

Anno Accademico 2013/2014

Appello di Laurea 5 maggio 2014

2

Abstract

This work is focused on the study of the deteriorated heat transfer phenomena for fluids at supercritical pressure and of the ability of different RANS four-equation turbulence models in predicting their characteristics.

Finally, a promising approach for evaluating the effect of wall roughness on the

prediction of heat transfer is presented, proposing a preliminary validation and its first results in

the application to supercritical fluids.

3

Acknowledgements

The financing by the European Commission, through the EU THINS Project, of the research in whose frame my study was performed is acknowledged.

I want to thank the tutors and especially Prof. Walter Ambrosini, for his guidance, for

encouraging and patiently supporting me during these months. I also wish to thank the persons

who helped me in performing this work, as Ing. Andrea Pucciarelli and Dr. Medhat Sharabi, who

supported me very much in the various phases of this study.

4

Nomenclature

Roman letters G Mass flux [kg/m

s]

a

, a

, a

Model constants G

Production term due to the buoyancy [m

/s

]

A

, A

Model constants Gr Grashof number

B Additive constant for smooth wall h Heat Transfer Coefficient [W(/m

K)]

Bo Buoyancy parameter H Specific enthalpy [J/kg]

Specific heat [J/kgK] k Turbulent kinetic energy [m

/s

] C

, C

,

C

, C

, C

, C

, C

, C

C

, C

,

Turbulence model constants for the velocity field

K von Karman’s constant

K

Constant of smoothing function Nu Nusselt number

p Pressure [MPa]

P

Production term due to the shear stress

C

, C

, C

, C

, C’

Constants of the turbulent heat flux

Pr, Pr

Molecular and turbulent Prandtl number

q’’ Heat flux [W/m

]

C

Constant of turbulent kinetic

energy source related to roughness q’’’ Volumetric power [W/m

]

D Pipe diameter [m] R Timescale ratio

D

Hydraulic diameter [m]

C ^{ORSO DI} L ^AUREA M AGISTRALE IN I ^NGEGNERIA E ^NERGETICA