Computational Fluid-Dynamic Analysis of Experimental Data in Heat Transfer Deterioration with Supercritical Water

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Alla mia famiglia

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I The present work is aimed to investigate the heat transfer problem in heated channels with water at super-critical pressure. The study is conducted with a commercial Computational Fluid-Dynamics code, STAR-CCM+, with the aim to observe the performance of different low-Reynolds number turbulence models in predicting heat transfer features in fluids at supercritical pressure, with a particular attention on the influence of buoyancy and acceleration.

Several simulations have been performed and the predicted results are compared with the data obtained by Watts experimental facility (Watt, 1980), reported in Jackson (2009a), in the Nuclear Engineering Laboratory at the University of Manchester at the end of seventy-years. The relevance of these experimental data is mainly due to the deterioration phenomena shown in several upward flow conditions with wall temperatures below and above the pseudo-critical temperature. The computational domain of the test section is 3 metres long with a diameter of 25.4 mm (1”), in a simple two-dimensional axial-symmetric geometry, created with STAR-Design. Different boundary conditions of heat flux, mass flux and inlet temperature are imposed in both downward and upward flow for water at 25 MPa. The consequent heat transfer deterioration or enhancement phenomena are pointed out considering the ratio between the actually computed Nusselt number and the Nusselt number obtained in case of pure forced convection.

The numerical analysis was mainly conducted using the Standard LIEN k – ε turbulence model, available in the STAR-CCM+ code. Moreover, to better understand the numerical aspects of the model, a comparison of some of the results obtained by the LIEN k –ε turbulence model with those of other two models is performed; in particular, the AKN k – ε turbulence model and the SST k – ω_{turbulence model}_{are considered. The results of these}

models are compared together and with experimental data, using as reference variable the predicted inner wall temperature.

Finally, the work reports on the results of a systematic comparison between different fluids at supercritical pressures, basing on similarity principles conceived to establish a rationale for fluid-to-fluid comparison. Simulations have been performed with NH3, CO2 and R23 and the results are compared with the phenomena predicted in the mentioned experimental data by Watts, in the aim to understand the capabilities of this theory.

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III I would like to express my gratitude to Prof. Walter Ambrosini, for his guidance, encouraging and patiently supporting during this months. I wish to thank Prof. Em. J.D. Jackson, Dr.

Nicola Forgione and Dr. Shuisheng He for their comments and revision of the present thesis. Many thanks also go to all degrees and doctoral students in the Department of Mechanical, Nuclear and Production Engineering for their friendly and nice company during this period. In particular, a special thank for all our laughter goes to Nico Montagnani, Silvestro Di Sarno, Francesco Poli, Guido Galgani, Eugenio Molfese, Marco Mucci, Daniele Martelli, Morena Angelucci, Alessio Rocchi, and Gabriele Guetta.

The International Atomic Energy Agency (IAEA) is acknowledged for including the research per-formed at the University of Pisa in the Co-ordinated Research Project in ‘Heat transfer behaviour and thermo-hydraulics code testing for super-critical water cooled reactors (SCWRs), through the Research Agreement No. 14272.

CD-Adapco, in the person of Dr. Emilio Baglietto, is kindly acknowledged for supporting this research.

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V

Table of Contents ... V

Lists of Figures ... VII

Lists of Tables ... XIII

Nomenclature ... XV

1 - Introduction... 1

1.1 General background ... 1

1.2 Motivation for the present work ... 2

1.3 Thesis outline ... 3

2 - Heat transfer at supercritical pressure... 7

2.1 Relevant thermodynamic and thermo-physical properties ... 7

2.2 Features of heat transfer ... 12

2.2.1 Heat transfer across the pseudo-critical temperature ... 14

3 – Overview of some available experimental data for CFD model

validation ... 19

3.1 Review of experiments with water ... 19

3.2 Experimental data considered in this work ... 34

3.2.1 Design parameters ... 34

3.2.2 Test facility ... 36

4 – Description of the adopted numerical models ... 43

4.1 Governing equations ... 43

4.2 Turbulence models ... 45

4.2.1 The k – ε Models ... 45

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Table of contents

VI

4.2.2 The k – ω Models ... 51

4.2.2.1 The SST k – ω model ... 52

4.3 General considerations on the Star-CCM+ code ... 54

4.3.1 Discretization of the computational domain ... 55

4.3.2 Fluid properties ... 58

5 – Results and discussion ... 59

5.1 Introductory considerations ... 59

5.1.1 Addressed experimental tests ... 59

5.1.2 The Nusselt ratio analysis ... 60

5.2 Buoyancy aided cases (upward flow) ... 63

5.3 Buoyancy opposed cases (downward flow) ... 87

5.4 Model comparisons ... 94

6 - Conclusions ... 103

References ... 107

Appendix A -

Application Of Similarity Principles For Heat Transfer And Fluid-Dynamics To Different Fluids At Supercritical Pressure.

... 113

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VII

Figure 2.1: The supercritical zone in p-T diagram ... 7

Figure 2.2: Water density at different supercritical pressure values (Sharabi, 2008) ... 9

Figure 2.3: Specific heat at different supercritical pressures values(Sharabi, 2008) ... 9

Figure 2.4: Variation of the maxium specific heat with pressure (Sharabi, 2008) ... 10

Figure 2.5: Pseudo-critical line for water as function of pressure (Sharabi, 2008) ... 10

Figure 2.6: Enthalpy trends as function of temperature at different supercritical pressures (Sharabi, 2008) ... 10

Figure 2.7: Thermal conductivity of water as function of temperature (Sharabi, 2008) ... 11

Figure 2.8: Viscosity of water as function of temperature (Sharabi, 2008) ... 11

Figure 2.9: Prandtl number of water as function of temperature (Sharabi, 2008)... 11

Figure 2.10: Thermal expansion coefficient of water as function of temperature (Sharabi, 2008) . 11 Figure 2.11: Water property trends as function of enthalpy for water at 25 MPa (Sharabi, 2008) .. 11

Figure 2.12: Effect of fluid properties on HTC under condition of forced convection with CO2 (He et al., 2007)... 12

Figure 2.13: Radial distribution of flow velocity (left) and turbulence kinetic energy (right) Mass flux: G = 39 kg(m2s); Heat flux [W/m2]: A) 100, B) 450, C) 550, D) 2000, E) 10000 (Koshizuka et al., 1995) ... 13

Figure 2.14: Heat transfer schematization (Licht et al., 2008) ... 14

Figure 2.15: Relation between the Nusselt number and the Grashof number. Flow rate: 39kg/(m2s); Heat fluxes [W/m2]: A=100, B=450, C=550, D=2000, E=10000 (Koshizuka et al., 1995) ... 16

Figure 2.16: The buoyancy influence for upward and downward flows (Jackson, 2009c)... 17

Figure 3.1: Range of investigated parameters for selected experiments with water at supercritical pressures (Pioro and Duffey, 2007) ... 19

Figure 3.2: Effect of pressure and heat flux on HTC (Swenson et al., 1965 ) ... 24

Figure 3.3: Variation in HTC values of water flowing in a tube (Styrikovic et al., 1967 )... 25

Figure 3.4: HTC vs. bulk-fluid enthalpy with upward flow at pressure of: a) 22.6; b) 24.5; c) 29.4 MPa (Yamagata et al., 1971)... 27

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List of Figures

VIII

Figure 3.5: Temperature profiles along heated lenght of vertical tube in upward flow (Alekseev et

al., 1976) ... 28

Figure 3.6: Temperature and HTC variations along a 1 m long circular tube at various heat fluxes and inlet temperatures with the following nominal conditions: pin=24.9, G=200 kg/(m2s), Hpc=2149 kJ/kg. (Kirillov et al., 2005) ... 29

Figure 3.7: Temperature and HTC variations along a 4 m circular tube with the following nominal conditions: p=24 MPa, G=1500 kg/(m2s), Q=880 kW/m2; hpc=2159 kJ/kg. (Kirillov et al., 2005) 30 Figure 3.8: Temperature profiles in vertical tube with upward flow at p=23.5 MPa. ... 30

Figure 3.9: Temperature profiles and heat transfer variation sat mixed convection in vertical tube (D=9.50) in upward flow; p=23.5 MPa, G=249 kg/(m2s) and Tin=200°C. (Pis'menny et al., 2005b) ... 31

Figure 3.10: Effect of mixed convection on deteriorated heat transfer (a) and variations of ratio Gr/Re2 along heated lenght (b) at Q=390 kW/m2: p=23.5 MPa, D=6.28, G=509 kg/(m2s), Tin≈300°C. 1 - upward flow; 2 - downward flow. (Pis'menny et al., 2005a) ... 31

Figure 3.11: Effect of mixed convection on heat transfer in vertical tubes with upward (1) and downward (2) flows of supercritical water: p=23.5 MPa, L/D≈50. (Pis'menny et al., 2005a) ... 32

Figure 3.12: Heat transfer deterioration at different mass fluxes (Licht et al., 2008) ... 32

Figure 3.13: Experimental heat transfer coefficient for high mass flux: G=1120 kg/m2s (Licht et al., 2008) ... 33

Figure 3.14: Supercritical water test facility in Simon Laboratory in Manchester (Jackson, 2009a) ... 35

Figure 3.15: Test section and power (Jackson, 2009a)... 36

Figure 3.16: Air cooler in the roof (Jackson, 2009a)... 37

Figure 3.17: Sample sets of observations (Jackson, 2009a) ... 38

Figure 3.18: Example of plot for upward flow with different mass fluxes at a specific values of inlet temperatures and heat fluxes (Jackson, 2009a) ... 40

Figure 3.19: Example of plot for downward flow with different mass fluxes at specific values of inlet temperatures and heat fluxes (Jackson, 2009a) ... 41

Figure 4.1: Comparison between inner wall temperature profile using Yang-Shih low-Reynolds number k- model and Standard “Wall function” k- model (Mucci, 2010) ... 46

Figure 4.2: Test section schematization ... 55

Figure 4.3: Mesh adopted in STAR-CCM+ code ... 55

Figure 5.1: Inner wall and bulk enthalpy axial trends extracted by the post-processing program. .. 61

Figure 5.2: Axial trends of calculated Nusselt numbers for simulated cases in mixed and forced convection, compared with data trends and the Dittus-Boelter equation. ... 62

Figure 5.3: Axial trends of calculated wall and bulk Prandtl numbers for a simulated ... 62

Figure 5.4: Comparison between experimental (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model, Upward flow, q”=250 W/m2, Tin = 150 °C ... 63

Figure 5.5: Comparison between experimental (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model, Upward flow, q”=250 W/m2, Tin = 150 °C ... 64

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List of Figures

IX Figure 5.6: Comparison between experimental (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model, Upward flow, q”=340 W/m2, Tin = 150 °C ... 64 Figure 5.7: Comparison between experimental (dashed line) and simulated (continuous line) wall temperature. Lien k – ε model, Upward flow, q”=340 W/m2, Tin = 150 °C ... 65 Figure 5.8: Nusselt ratio along the heated length. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 150 ° ... 65 Figure 5.9: Nusselt ratio along the heated length. Lien k – ε model. Upward flow, q”=340 W/m2, Tin = 150 °C ... 66 Figure 5.10: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres] Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 150 °C ... 67 Figure 5.11: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 150 °C ... 68 Figure 5.12: Comparison between experimental data (dashed line) and calculated(continuous line) wall temperature. Lien k – ε model, Upward flow, q”=250 W/m2, Tin = 200 °C ... 69 Figure 5.13: Comparison between experimental data (dashed line) and calculated(continuous line) wall temperature. Lien k – ε model, Upward flow, q”=250 W/m2, Tin = 200 °C ... 69 Figure 5.14: Comparison between experimental data (dashed line) and calculated(continuous line) wall temperature. Lien k – ε model, Upward flow, q”=250 W/m2, Tin = 200 °C ... 70 Figure 5.15: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C ... 70 Figure 5.16: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C ... 71 Figure 5.17: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C ... 71 Figure 5.18: Nusselt ratio along the heated length. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 200 °C ... 72 Figure 5.19: Nusselt ratio along the heated length. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C ... 72 Figure 5.20: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 200 °C ... 73 Figure 5.21: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C ... 74 Figure 5.22: Fluid temperature 3D profile. Lien k – ε model. Upward flow, q”=250 W/m2, Tin =

200 °C, G = 340 kg/(m2s). ... 75 Figure 5.23: x- Velocity 3D profile. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 200 °C, G

= 340 kg/(m2s). ... 75 Figure 5.24: Turbulent kinetic energy 3D profile. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 200 °C, G = 340 kg/(m

2

s). ... 76 Figure 5.25: Turbulent kinetic energy 3D profile. Lien k – ε model. Upward flow, q”=250 W/m2, Tin = 200 °C, G = 340 kg/(m2s) ... 76

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List of Figures

X

Figure 5.26: Temperature 3D profile. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C,

G = 390 kg/(m2s). ... 77 Figure 5.27: x- Velocity 3D profile. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C, G

= 390 kg/(m2s). ... 77 Figure 5.28: Turbulent kinetic energy 3D profile. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 200 °C, G = 390 kg/(m

2

s) ... 78 Figure 5.29: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=340 W/m2, Tin = 250 °C ... 79 Figure 5.30: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=340 W/m2, Tin = 250 °C ... 79 Figure 5.31: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 250 °C ... 80 Figure 5.32: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 250 °C ... 80 Figure 5.33: Nusselt ratio along the heated length. Upward flow, Lien k – ε model, q”=340 W/m2, Tin = 250 °C ... 81 Figure 5.34: Nusselt ratio along the heated length. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 250 °C ... 81 Figure 5.35: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=340 W/m2, Tin = 250 °C ... 82 Figure 5.36: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 250 °C ... 83 Figure 5.37: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 310 °C ... 84 Figure 5.38: Wall temperature profile in forced and mixed convection... 85 Figure 5.39: Nusselt ratio along the heated length. Lien k – ε model. ... 85 Figure 5.40: profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Upward flow, q”=400 W/m2, Tin = 310 °C ... 86 Figure 5.41: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Downward flow, q”=250 W/m2, Tin = 150 °C ... 87 Figure 5.42: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Downward flow, q”=340 W/m2, Tin = 150 °C ... 88 Figure 5.43: Nusselt ratio along the heated length. Lien k – ε model. Downward flow, q”=250

W/m2, Tin = 150 °C ... 88 Figure 5.44: Nusselt ratio along the heated length. Lien k – ε model. Downward flow, q”=340

W/m2, Tin = 150 °C ... 89 Figure 5.45: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Downward flow, q”=250 W/m2, Tin = 150 °C ... 90 Figure 5.46: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Downward flow, q”=340 W/m2, Tin = 150 °C ... 91

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List of Figures

XI Figure 5.47: Comparison between experimental data (dashed line) and calculated (continuous line) wall temperature. Lien k – ε model. Downward flow, q”=250 W/m2, Tin = 200 °C ... 92 Figure 5.48: Nusselt ratio along the heated length. Lien k – ε model. Downward flow, q”=250

W/m2, Tin = 200 °C ... 92 Figure 5.49: Radial profiles of velocity and turbulence kinetic energy at different axial coordinate [in metres]. Lien k – ε model. Downward flow, q”=340 W/m2, Tin = 150 °C ... 93 Figure 5.50: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 150 °C, G = 364 kg/(m2s). ... 95 Figure 5.51: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 150 °C, G = 376 kg/(m2s). ... 95 Figure 5.52: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 150 °C, G = 445 kg/(m2s). ... 96 Figure 5.53: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 150 °C, G = 516 kg/(m2s). ... 96 Figure 5.54: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 250 °C, G = 392 kg/(m2s). ... 97 Figure 5.55: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 250 °C, G = 425 kg/(m2s). ... 97 Figure 5.56: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 250 °C, G = 445 kg/(m2s). ... 98 Figure 5.57: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=340 W/m2, Tin = 250 °C, G = 543 kg/(m2s). ... 98 Figure 5.58: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=400 W/m2, Tin = 250 °C, G = 394 kg/(m2s). ... 99 Figure 5.59: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=400 W/m2, Tin = 250 °C, G = 425 kg/(m2s). ... 99 Figure 5.60: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=400 W/m2, Tin = 250 °C, G = 434 kg/(m2s). ... 100 Figure 5.61: Comparison between experimental and simulated inner wall temperature for different turbulence models. Upward flow, q”=400 W/m2, Tin = 250 °C, G = 495 kg/(m2s). ... 100 Figure 6.1: Nusselt ratio along the pipe for different mass flux values in upward and downward flow. Lien k – ε model. q”=250 W/m2, Tin = 150 °C ... 104

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XIII

Table 2.1: Critical properties for common fluids ( Pioro and Duffey, 2007 ) ... 8

Table 3.1: Some selected experiments with water flowing in different geometries at supercritical pressure. ... 20

Table 3.2: Range of input values for Watt’s experiment in the two different flow directions ... 34

Table 4.1: Constants and term values in the AKN k – ε models ... 47

Table 4.2: Damping functions in the AKN k – ε models ... 47

Table 4.3: Constant and term values in the LIEN k – ε models ... 50

Table 4.4: Damping functions in the LIEN k – ε models ... 50

Table 4.5: Damping functions in the k – ω models ... 51

Table 4.6: Coefficient of the SST k – ω models... 53

Table 4.7: Mesh detail (axial x radial); STAR-CCM+ code ... 56

Table 5.1: Simulated cases of Watts experimental data ( Watts, 1980 and Jackson, 2009a ) ... 60

Table 5.2: Cases selected to compare different turbulence models ... 94

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XV

Roman Letters

Bo* Buoyancy parameter

D Pipe inner diameter [m] or term

value

Cp

Specific heat at constant pressure [J/(kgK)]

Cµ, Cε1,

C ε2

Constant values

fA,R,λ Model functions

fw Wall distance function

fµ, f1,f2 Damping function

E Term value

g Gravitational acceleration

G Mass flux _·

Gk Gravitational production term

Gr Grashof number

h, H Enthalpy

k Turbulent Kinetic Energy

l Length scale L Pipe length Nu Nusselt number Nusselt ratio p pressure

Pk Shear stress production

Pr Prandtl number

Q, q” Heat flux

r Radial coordinate [m]

Re Reynolds number

Sij second-moment closure term

Sk Shear production term

t time

T, T' Temperature [°C] Time scale ratio

ut Friction velocity scale

uε Kolmogorov velocity scale

U, u Velocity component in the

x-direction

V, v Velocity component in the

r-direction

x Axial coordinate [m]

y+, Ry a-dimensional distance

Greek Letters

α Heat transfer coefficient

αt Eddy diffusivity β Thermal expansion δij Kronecker delta ε Dissipation Rate of k λ Thermal conductivity _· µ (Molecular) viscosity _· ρ Density τ Viscous stress

τk Kolmogorov time scale

τt Characteristic time scale

τij Reynolds stress tensor

υ Kinematic viscosity

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Nomenclature XVI Subscript 0 Ideal b Bulk cr Critical e Effective f Forced pc Pseudocritical T Turbulent w Wall Abbreviations

CFD Computational Fluid Dynamics DNS Direct Numerical Simulation HTC Heat Transfer Coefficient

IAEA -CRP International Atomic Energy Agency – Coordinated Research Project LES Large Eddy Simulation

RANS Reynolds-Averaged Navier-Stokes SCWR Supercritical Cooler Water Reactor

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1

1.1 General background

The idea of making use of fluids at supercritical conditions in the energy sector was developed in the period 1950s-1980s in USA and USSR, with the aim of increasing the thermal efficiency of the fossil-fired power plant. The most important Supercritical Steam Generation Units were developed in USSR and USA, and more recently other power-plants were built in China, Denmark, Germany and Japan with an increase of efficiency to values around 45% to 50%, (Pioro and Duffey, 2007).

In the ‘60s some studies began to investigate the possibility to use fluids at supercritical pressure as the coolant in nuclear power plants. The advantages of these proposals are based on the particular properties of fluids under these conditions; in particular, it was pointed out as a result of the considerable increase of temperature of the fluid at supercritical conditions the efficiency of the modern nuclear power plant can rise from the current value of 33-35 % to 40-45% with also some benefits in terms decreasing the operational and capital costs and hence a decreasing electrical energy costs by about 30% or more (Duffey et al., 2010).

The Supercritical Water-cooled Reactor (SCWR) is included as a possible future development in list of so-called Generation IV reactors. In fact, it is one of the six candidate projects selected by U.S. and GIF (2002) for the next generation of nuclear reactors. This developing technology has to compete in terms of cost, safety and reliability with other types of power generation system; to achieve this objective, significant research and development in materials and structures technology is required, essentially due to the demanding operating conditions (high temperatures, corrosion etc.). The important technology gaps for this reactor are essentially centred on the behaviour of materials under irradiation, safety research, stability against flow and power oscillations, heat transfer at supercritical conditions, internal configuration, start-up strategies, containment building. So, this reactor system is not expected to be developed before about 2030.

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1 - Introduction

2

1.2 Motivation for the present work

The strong variation of the thermo-physical properties of the fluids crossing the pseudo-critical temperature (see Chapter 2) affects heat transfer and poses new problems in predicting fluid behaviour. In fact, an accurate prediction of the flow paths and temperature profiles in the core region is of fundamental importance for safety design.

Computational fluid-dynamics (CFD) adopts numerical methods to solve problems which involve fluid flows and is a powerful tool to obtain predictions of temperature and velocity fields in rod bundles. In the last decade, several studies were conducted with the aim of testing CFD models against experimental data. In fact, most of the existing codes were not specifically developed for use with fluids at supercritical pressure and their validity in this area needs to be tested to see whether they can correctly capture the complex phenomena observed in experimental data.

The Coordinated Research Programme (CRP) of the International Atomic Energy Agency (IAEA) on “Heat Transfer Behaviour and Thermo-hydraulics Codes Testing for SCWRs” (IAEA, 2009) is included in the frame work of the ongoing researches on the subject in the international scientific field. This IAEA-CRP promotes international collaboration among IAEA Member States for the development of Supercritical Water-Cooled Reactors in the thermo-hydraulics and heat transfer areas. The objectives of the program are:

to collect accurate data for heat transfer, pressure drop, blowdown, natural convection and stability regarding fluids at supercritical pressure;

to test method to analyse the SCWR thermo-hydraulic behaviour, identifying the necessary code developments.

The University of Pisa is one of the twelve institutions participating in this CRP and it is also involved with the University of Manchester and the University of Aberdeen in a co-operation programme to assess available CFD codes against relevant experimental data. This co-operation is still ongoing with the aim of producing new data to assess the present level of reliably in describing heat transfer to supercritical fluids and establishing the development needs for codes and models. In the frame work of this co-operation, simulations were performed to study the behaviour of computational models implemented available in various codes.

The present work is part of this broader research activity, as a continuation of studies conducted in past years, starting with that of Medhat Sharabi Doctoral (Sharabi, 2008) in which a different set of experimental data (Pis'menny et al., 2005a, Yamagata et al., 1971 and

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3 Kim et al., 2005 were rised with an in-house CFD code, and also commercial codes, with the aim of studying the heat transfer phenomena with fluids at supercritical pressure flowing in circular, square and triangular channels. A subsequent study rising Pis’menny’s experimental data was conducted by Badiali (2009) using STAR-CCM+ code (CD-ADAPCO, 2009). Mucci (2010) addressed Watts’ data (see Watts, 1980 and Jackson, 2009c) to assess some numerical models implemented in the commercial codes, as FLUENT (FLUENT Inc., 2005) STAR-CCM+ (CD-ADAPCO, 2009), and the in-house code, SWIRL (He et al., 2004). The interest in the Watt’s data is related to their relevance for studying deterioration effects exhibited by upward flows with temperatures below the pseudo-critical value, for the purpose of understanding model behaviour. For these reasons, the work with these experimental data is continued in the present study and with the work of Guetta (2010), as a continuation of Mucci’s work.

The results obtained in the present study and in the previous ones mentioned is being summarized in a paper (De Rosa et al., 2011) submitted at the 5th International Symposium on SCWRs that will be held in Vancouver on March 2011, highlighting the lessons learned from the overall activity.

1.3 Thesis outline

The aim of this work is to further extend turbulence model validation on the basis of the prediction of heat transfer behaviour with fluids at supercritical pressure. The commercial CFD code STAR-CCM+ is used. The Watt’s experimental data, already used for this purpose with other CFD codes, are used to perform the analysis. a number of simulations have been performed, investigating different operating conditions and testing different turbulence models implemented in STAR-CCM+.

The thesis is subdivided in to six chapters, the content of which is summarised hereafter. Chapter 2 introduces the subject, describing the properties of fluids in supercritical

conditions and their thermal and fluid-dynamics characteristics. A first description of the heat transfer mechanisms is included, pointing out the anomalies observed and the currently credited explanations.

Chapter 3 presents a literature survey in relation to the experimental data available with water at supercritical pressure, suitable for turbulence model validation. Moreover, a description of the experimental facility on which the data considered in this work were generated (see Watts, 1980 and Jackson, 2009a) is included.

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4

In Chapter 4 the numerical approach adopted to simulate the heat transfer problem is described. After a short general description of the RANS equations for turbulence with low-Reynolds number models, the most important differences between the turbulence models adopted in the work are commented upon. Then, a general description of the STAR-CCM+ code with its main characteristics is introduced.

Chapter 5 presents a detailed analysis of the results obtained in under conditions of upward and downward flow in comparison with the experimental data. All the cases considered are reported showing temperature, velocity and turbulent kinetic energy profiles. A comparison is made of the results obtained with different turbulence models.

In Chapter 6 a summary of the conclusions obtained concerning model capabilities in describing heat transfer behaviour is reported, together with recommendations for future work.

Finally, Appendix A reports a paper submitted at the 5th International Symposium on SCWR that will be held in Vancouver in March 2011. This paper reports on the results of a comparison between different fluids (H2O, CO2, NH3, R23) at supercritical pressure, based on similarity principles conceived to establish a rationale for fluid-to-fluid comparison (Ambrosini, 2010). The contribution given to the work in the framework of this study consisted in performing supporting calculations based on the computational model developed for the analysis of Watts’ data. In particular, with the aim of understanding the capabilities of the proposed theory. Some of Watts’ experimental cases were selected and simulated with scaled inlet conditions for the other fluids.

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7

2.1 Relevant thermodynamic and thermo-physical properties

Heat transfer at supercritical pressure is influenced by large uniformities in the fluid properties. The critical point corresponds to the highest temperature and pressure at which the fluid can be in both saturated liquid and vapour form. The greatest variation of thermo-physical properties occurs at the critical point and, beyond it, at the so-called pseudo-critical points. In general, at the pseudo-critical point we have (Kaye and Laby, 1973):

Above this condition, the fluid cannot be liquefied by simple cooling and the two distinct phases do not exist anymore. The fluid is neither gas or liquid, resulting in a single-phase fluid without the occurrence of interfaces.

Figure 2.1: The supercritical zone in p-T diagram

2 - Heat transfer at supercritical pressure

(2.1)

Supercritical fluid region

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2 – Heat transfer at supercritical pressure

8

The thermo-physical properties of water at different pressures and temperatures, including the supercritical region, can be evaluated using the NIST software (NIST, 2002 ). Carbon dioxide is of particular interest for its relatively low critical temperature (31 °C) and pressure (7.38 MPa); for this reason and also for its characteristics of being a non-toxic, non-flammable and not too expensive fluid, it is one of the most frequently studied fluids. Also water has been used in many studies, due to its importance in applications; the critical point of water is identified by relatively high critical temperature (373.95 °C) and pressure (22.06 MPa). The characteristics of some of the most interesting fluids adopted in the supercritical range are listed in Table 2.1.

Table 2.1: Critical properties for common fluids (Pioro and Duffey, 2007 )

Fluid Tcr [°C] pcr [MPa] ρcr [g/cm3] Air -140.50 3.80 0.333 Ammonia (NH3) 132.25 11.33 0.225 Argon (Ar) -122.46 4.86 0.536 Benzene (C6H6) 288.90 4.89 0.309 Iso-Butane (C10H10) 134.70 3.64 0.224

Carbone dioxide (CO2) 30.98 7.38 0.468

Ethanol (C2H6O) 240.80 6.15 0.276 Freon 23 (CHF3) 25.70 4.82 0.526 Helium (He) -267.95 0.23 0.069 n-Heptane (C7H16) 266.98 2.74 0.232 Hydrogen (H2) -239.96 1.32 0.030 Methanol (CH4O) 239.45 8.10 0.276 Nitrogen (N2) -146.96 3.40 0.313

Nitrous oxide (N2O) 36.50 7.17 0.450

n-Octane (C8H18) 296.17 2.50 0.235 Oxygen (O2) -118.57 5.04 0.436 Iso-Pentane 187.20 3.40 0.236 Propanol (C3H8O) 235.20 4.76 0.270 Toluene (C7H8) 318.60 4.13 0.292 Xenon (Xe) 16.60 5.84 0.120 Water (H2O) 373.95 22.06 0.322

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9 In the following figures, the main thermodynamic and thermo-physical properties of water as function of temperature and pressure are represented. All these plots (from Sharabi, 2008) were obtained making use of the NIST Standard Reference Database 23, version 7 (NIST, 2002).

Figure 2.2: Water density at different supercritical pressure values (Sharabi, 2008)

In Figure 2.2 it should be noted that density decreases sharply in a narrow temperature range, especially at the values of pressure closer to the critical one. Nevertheless, the fluid changes without discontinuity from a high density condition (“liquid-like” fluid) to a low density condition (“gas-like” fluid).

Specific heat has a different trend, as during the “pseudo-phase change” it shows a sharp peak, as reported in Figure 2.3. The temperature at which this peak is experienced is called

pseudo-critical temperature, Tpc, While the values of Tpc increases with increasing

pressure, the peak in specific heat decreases with it.

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10

Moreover, we can also observe in Figure 2.4 and Figure 2.5 that the locus of the curve of the pseudo-critical temperature is an extension of the saturation line in the supercritical region; it is also called pseudo-critical line. Due the sharp peaks in specific heat, the enthalpy has a characteristic trend as a function of temperature, exhibiting a sharp increase while crossing the pseudo-critical value (see Figure 2.6). The additional figures show the trends of the most important thermo-physical properties of water near the pseudo-critical zone: thermal conductivity (Figure 2.7), dynamic viscosity (Figure 2.8), the Prandtl number (Figure 2.9) and thermal expansion coefficient (Figure 2.10). All this figures show that all fluid properties have a steep variation crossing the pseudo-critical zone.

In Figure 2.11 the trends of these properties is shown vs. enthalpy; smoother changes than with respect to temperature across the pseudo-critical condition can be observed. These changes are due to the large internal energy gained by the fluid during heating at these particular conditions.

Figure 2.6: Enthalpy trends as function of temperature at different supercritical pressures (Sharabi, 2008)

Figure 2.5: Pseudo-critical line for water as function of pressure (Sharabi, 2008) Figure 2.4: Variation of the maxium specific

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11

Figure 2.11: Water property trends as function of enthalpy for water at 25 MPa (Sharabi, 2008)

Figure 2.10: Thermal expansion coefficient of water as function of temperature

(Sharabi, 2008)

Figure 2.8: Viscosity of water as function of temperature (Sharabi, 2008) Figure 2.7: Thermal conductivity of water as

function of temperature (Sharabi, 2008)

Figure 2.9: Prandtl number of water as function of temperature (Sharabi, 2008)

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12

2.2 Features of heat transfer

Heat transfer to fluids near the critical condition is more complex than with ordinary fluids. Many experiments were performed (generally heated circular tubes cooled with water or carbon dioxide) and a reasonable amount of information was gained. The most important factors that influence heat transfer to supercritical fluids are summarized below.

Influence of property variation: the strong variation of the thermo-physical properties near the pseudo-critical temperature, already described in the previous paragraph, complicates the heat transfer process. Figure 2.12 reports the trend of the heat transfer coefficient as a function bulk temperature, for CO2 near the pseudo-critical temperature at 7.58 bar (32.2 °C), calculated with the Dittus-Boelter equation:

It’s interesting to note that the HTC values are similar on either side of Tpc, even though the property values are very different. It can be shown that peak of HTC is mainly due to the sharp increase in specific heat near the Tpc .

Influence of buoyancy: another particular effect, also connected with the property changes, is laminarization. The strong change in density, from liquid-like to gas-like values (see Figure 2.2), can affect the turbulence production. There are two basic mechanisms for buoyancy to influence turbulence (He et al., 2007): the direct (structural effect), with an increase of turbulence kinetic energy, and the indirect (external effect), due to a mean flow modification:

o for buoyancy-opposed flow cases (e.g., downward flow with heating) the buoyancy effect reduces the near-wall velocity with a modification of the mean flow and, as a consequence, an enhancement of turbulence production and a improvement of turbulence diffusion occours.

. · .!_{· "#}.$

(2.2) Figure 2.12: Effect of fluid properties on HTC

under condition of forced convection with CO2

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13 o in the buoyancy-aided case (e.g., upward flow with heating), buoyancy causes a flattened velocity gradient of the flow (see Figure 2.13) except in the region very close to the wall. The turbolent production is reduced and heat transfer is decreased. If buoyancy increases (for example by reducing the flow rate and/or increasing heat flux), this deterioration effect is more marked. As already said, in literature this effect is called flow laminarization (or reversed transition), because flows cosidered to be turbulent show typical low heat transfer efficiency as in a laminar flows (Mc Eligot and Jackson, 2004; He et al., 2008). If buoyancy continues to increase, negative values of the shear stress are generated near the core region and turbulence production can be reestablished at that location. This effect can restore heat transfer effectiveness.

Figure 2.13: Radial distribution of flow velocity (left) and turbulence kinetic energy (right)

Mass flux: G = 39 kg(m2s); Heat flux [W/m2]: A) 100, B) 450, C) 550, D) 2000, E) 10000

(Koshizuka et al., 1995)

In the literature, criteria to establish when the laminarization phenomenon can occurs have been proposed. For instance, a simple criterion is provided by the following equation (Jackson and Hall, 1979b; Mc Eligot and Jackson, 2004; Jackson, 2009b):

Influence of flow acceleration: in the case in which mass flow rate is sufficiently high, the buoyancy effect near the wall does not occur but another mechanism of heat transfer impairment may take place, due to the acceleration caused by thermal

%#&'

&.("#.! ) 3 · +

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14

expansion of the fluid because of heating. So, when the channel exit density is much lower than the inlet one, the flow accelerates causing a near wall shear stress distribution modification, with a consequent reduction in heat transfer. This acceleration effect causes a near wall shear stress alteration with a reduction in heat transfer. This effect causes an impairment in heat transfer in both upward and downward flow, whereas the previously mentioned buoyancy effect causes an impairment in upward flow and an enhancement in downward flow.

2.2.1 Heat transfer across the pseudo-critical temperature

Many of the heat transfer experiments (see Chapter 3 for a list of the most important ones) have shown a similar deviation from the normal heat transfer described by Dittus-Boelter equation. In general, these effects have been found to occur when the wall temperature is greater than the pseudo-critical temperature and the bulk temperature is lower than the pseudo-critical temperature (Tw > Tpc > Tb) (Cheng and Schulenberg, 2001). In that case, large property variations occur within the near wall region.

The consequences on heat transfer were described in literature by Jackson and Hall (1979a) and can be explained with the help of Figure 2.14 (Licht et al., 2008). In case a), for reference purposes the typical heat transfer with no property variation is shown, in which the pipe flow has a power law velocity profile.

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15 On the other hand, in case of property variation, three different cases may occur:

Heat transfer enhancement: this case (Figure 2.14b) occurs at low heat fluxes and with bulk temperatures near the pseudo-critical value; in this condition, the energy input is not sufficient to increase the fluid temperature beyond the pseudo-critical threshold and, owing to the high value of specific heat, a low temperature difference between wall and the bulk fluid is observed;

Impairment of the enhancement of heat transfer: if there is an increase of heat flux, the energy input becomes sufficient to overcome the higher value of specific heat (whose effect influences all boundary layer) and, thus the temperature gradient increases. In this way, the higher value of specific heat becomes more localized inside the boundary layer and this effect can produce an impairment of the enhancement of heat transfer (Figure 2.14c).

Deterioration of heat transfer: if the mass flux is low, it is possible that the buoyancy effects become dominant, causing deterioration (Figure 2.14c)in upward flow with the previously described mechanism. Figure 2.14d shows the recovery of heat transfer due, as already explained, to the production of shear stress near the core region with the new turbulence production in this zone.

In literature, different methods were proposed to evaluate the occurrence of deterioration:

o Koshizuka et al. (1995) for example, define a Deterioration ratio . .⁄ where α is the effective heat transfer coefficient and α0 is the ideal heat transfer coefficient; in general heat transfer is considered to be deteriorated if this ratio is smaller than 0.3; Figure 2.15 shows the relation between the Nusselt number and the Grashof number (related to the ratio of buoyancy and viscous forces) defined by the following equations: %# 012₄₅$3 & (2.4) ₈ 677 9, 8& 2 4& (2.5)

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16

In Figure 2.15 it is possible to observe that in the presence of buoyancy, the Nusselt number remains constant when the Grashof number is relatively low (forced convection). If the Grashof number increases, buoyancy effects raise and the Nusselt number shows a minimum value (at about Gr ~ 2·107) and then increases again (natural convection). The minimum point can be considered as a boundary between the two different flow modes.

Figure 2.15: Relation between the Nusselt number and the Grashof number. Flow rate:

39kg/(m2s); Heat fluxes [W/m2]: A=100, B=450, C=550, D=2000, E=10000

(Koshizuka et al., 1995)

o Another method is based on the definition of a Nusselt Ratio ⁄ _: (Mc Eligot and Jackson (2004), He et al. (2008), Jackson (2009b,c)) where Nu is the Nusselt number for mixed convection and Nuf is Nusselt number in forced convection (i.e., evaluated disregarding gravity). This Nusselt ratio allows to establish the buoyancy influence in the flow development. Figure 2.16 shows the trend of the Nusselt ratio as a function of a parameter that takes into account buoyancy. It is possible to note the degradation and the enhancement (or recovery) of heat transfer in upward flow and the enhancement of heat transfer in downward flows as described previously. This approach is also used in the present work to evaluate the heat transfer behaviour.

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2

Figure 2.16: The influence

influence buoyancy for upward and downward flows (

17

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19

3.1 Review of experiments with water

Many heat transfer experiments on water of supercritical pressure have been performed in the past sixty years for various conditions of bulk temperature, heat flux and mass flux. There are also textbooks and review papers analyzing the problems of heat transfer deterioration of fluids near the supercritical zones. The study of heat transfer at supercritical pressure started in the beginning of 60s, mainly thanks to the works of Russian scientists.

The most important results in this area were achieved in the following three decades in which many papers on computational and experimental studies were produced. Some data sets have been lost, especially those data obtained before 1965, when computers were not used in laboratories; moreover, many papers and books cited in this review (see Table 3.1) are proprietary or commercial without public access. In other cases, the data are only available in graphical form without numerical tables; these data can be extracted by using available software for digitalization. In this part of the work, the most important available experiments with water are considered to

provide an overview on state of art. Water is one of the most investigated fluids in near-critical and supercritical regions. Pioro

and Duffey (2007) reviewed the

literature of supercritical heat transfer experiments and presented the data sets currently available. Figure 3. shows the range of the main parameters in which SCHT was studied.

3 – Overview of some available experimental data

for CFD model validation

Figure 3.1: Range of investigated parameters for selected experiments with water at supercritical pressures

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Table 3.1: Some selected experiments with water flowing in different geometries at supercritical pressure.

Reference p [MPa] T [°C] q” [MW/m2] G [kg/m2s] Flow Geometry

H [kJ/kg]

Randall 1956 27.6-55.2 Tb=204-538 Tw=204-760

0.31-9.44 2034 - 5425 Hastelloy C vertical tube (D=1.27; 1.57; 1.9 mm, L=203.2 mm)

Miropol'skiy and Shitsman

1957, 1958a 0.4-27.4

Tb=2.5-420

Tw=2.5-420

0.42-8.4 170 - 3000 SS tube (D=7.8; 8.2 mm, L=160mm) upward flow

Dickinson 1958 25-32.1 ---- 0.88-1.8 2100-3400 Tube (D=7.6 mm, L=1.6 m)

Armand et al. 1959 23-26.3 Tb=300-380 0.17-0.35 450 - 650

SS and nichel tube (D=6; 8 mm, L=250; 350 mm) upward flow

Doroshchuk et al. 1959 24.3 Tb=100-250 3.06-3.9 3535 - 8760 Silver tube (D=3 mm, L=246 mm) upward flow

Schmidt (1959) 17-30 Tb=200-700 0.29-0.82 700-1700 Tube (D=5mm) vertical and horizontal

Goldmann 1961, Chalfant

1954, Randall 1956 34.5

Tb=204 - 538

Tw=204-760

0.31-9.4 2034 - 5424 Tubes (D=1.27; 1.8 mm, L=0.203 m) upward flow

Shitsman 1962 22.8-26.3 Tb=300-425

Tw=260-380

0.291-5.82 100 - 2500

Vertical and horizontal copper and carbon steel tubes (D=8 mm, Dext=46mm, L=170mm) upward and horizontal

flows

Bishop et al. (1962, 1965) 22.6 - 27.5 Tb=294-525 0.31-3.5 680-3600 Tube (D=2.5-5.1 mm; L/D=30-565)

Shitsman 1963 22.6-24.5 Tb=280-580 0.28-1.1 300 - 1500 SS tube (D=8 mm, L=1.5 m)

Domin 1963 22-26 Tb ≤ 450 0.6-5.1 600-5100 Tube (D=2; 4 mm L=1.075; 1.233 m)

Swenson et al. 1965 23-41 Tb=75-576 Tw=93-649

0.2-1.8 542-2150 SS tube (D=9.42 mm, L=1,83 m) flow

Smolin & Polyakov 1965 25.4; 27.4; 30.4 Tb=250-440 0.7 -1.75 1500-3000 SS tube (D=10; 8 mm, L=2.6 m) upward flow

Vikhrev et al. 1967 1971 24.5-26.5 Hb=230-2750 0.23-1.25 485-1900 SS tube (D=7.85; 20.4 mm, L=1.515; 6 m)

Bourke & Denton 1967 23-25.4 Tb=310-380 1.2-2.2 1207;2712 Tube (D=4.06 mm, L=1.2 m)

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H [kJ/kg]

paper)

Herkenrath et al. 1967 14-25 Tbmin=345-370 Tbmin=374-437

0.06-1.4 720-3620 Tube (D=10; 20 mm) vertical

Krasyakova et al. 1967 23 Hin=837-2721 0.23-0.7 300-1500

Vertical and horizontal SS tubes (D=20 mm, L=2.8 m) upward and horizontal flows

Alferov et al. 1968 14.7-29.4 Tb=160-325 0.17-0.6 250-1000 SS tubes (D/L=14/1.4; 20/3.7 mm/m)

Shitsman (1968) 22-25 Tb=100-250 0.27-0.7 400 Tube (D=3; 8; 16) vertical

Kamenetsky and Shitsman

1970 24.5 Hb=80-2300 0.19-1.33 50-1750

Vertical and horizontal SS tubes (D=22 mm, L=3 m) non-uniform circumferential heat flux, upward and horizontal flows

Ackerman 1970 22.8-41.3 Tb=77-482 0.126-1.73 136-2170

Smooth (D=9.4; 11.9 and 24.4 mm with L=1.83 m; D=18.5 mm with L=2.74 m) and ribbed (D=18 mm, L=1.83 m six helical ribs, pitch 21.8) tubes

Ornatsky et al. 1970 22.6; 25.5; 29.4 Hin=420-1400 0.28-1.2 450-3000

Five SS parallels tubes (D=3 mm, L=0.75 m) upward, stable and pulsating flows

Baurlin et al. 1971 22.5-26.5 Tb=50-500

Tw=60-750

0.2-0.65 480-5000 Vertical and horizontal tubes (D=3; 8; 20 mm, L/D<300) upward, downward and horizontal flows

Belyakov et al. 1971 24.5 Hb=80-2300 0.23-1.4 300-3000

Vertical and horizontal SS tubes (D=20 mm, L=4-7.5 m) upward and horizontal flows

Ornatskii et al. 1971 22.6; 25.5; 29.7 Hb=100-3000 0.4-1.8 500-3000 SS tube (D=3 mm, L=0.75 m) upward and downward flow

Yamagata et al. 1972 22.6-29.4 Tb=230-540 0.12-0.93 310-1830

Vertical and horizontal SS tubes (D/L=7.5/1.5; 10/2 mm/m) upward, downward and horizontal flows

Glushchenko et al. 1972 22.6; 25.5; 29.5 Hb=85-2400 1.15-3 500-3000

Tubes (D=3; 4; 6; 8 mm, L=0.75-1 m) upward flow (D=3 mm) downward flow

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H [kJ/kg]

Chakrygin et al. 1974 26.5 Tin=220 q was not provided 445-1270 SS tube (D=10, L=0.6 m) upward and downward flow

Lee & Haller 1974 24.1 Tb=260-383 0.25-1.57 542-2441 SS tubes (D=20 mm, L=3.7 m) tube with ribs

Aflerov et al. 1975 26.5 Tb=80-250 0.48 447 Tube (D=20 mm, L=3.7 m), upward and downward flows

Kamenetsky 1975 23.5; 24.5 Hin=100-2300 1.2 50-1700

Steel tube (D=21; 22 mm, L=3 m) non-uniform circumferential heat flux

Alekseev et al. 1976 24.5 Tin=100-350 0.1-0.9 380; 490; 650; 820 SS tube (D=10.4 mm, L=0.5; 0.7 m) upward flow

Ishigai et al. 1976 24.5; 29.5; 39.2 Hb=220-800 0.14-1.4 500; 1000; 1500

Vertical and horizontal SS polished tubes (D=3.92 mm; L=0.63 m vertical; D=4.44 mm, L=0.87 m horizontal)

Harrison and Watson 1976

a,b 24.5 Tb=50-350 1.3; 2.3 940; 1560

Vertical and horizontal SS tubes (D=1.64; 3.1 mm; L=0.4; 0.12 m)

Treshchev and Sukhov

1977 23; 25 Hin=1331 0.69-1.16 740-770 Tubes (L=0.5-1 m) stable and pulsating upward flows

Krasyakova et al. 1977 24.5 Tb=90-340 0.11-1.4 90-2000 Tube (D=20mm, Dext=28mm, L=3.5 m), downward flow

Sminrnov and Krasnov

1978 - 1980 25; 28; 30 Tw=250-700 0.25-1 500-1200

SS tubes (D=4.08 mm, L=1.09m) downward and upward flow

Kamenetskii 1980 24.5 Hb=100-2200 0.37-1.3 300-1700

Vertical and horizontal SS tubes with and without spoiler (D=22 mm, L=3m)

Watt 1980 25 Tb=150-310 0.175-0.4 232-908

SS Tube ASTM A321 (D = 25.4 mm) upward and downward flow

Watts and Chou 1982 25 Tb=150-310

Tw=260-520

0.175-0.44 106-1060 Tubes (D=25, 32.2 mm, L=2 m) upward and downward flow

Selivanov and Smirnov

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H [kJ/kg]

Kirillov et al. 1986 25 Tin=385 0.4; 0.6 1000 SS Tube (D=10mm, Dext=14mm, L=1 m)

Razumovskiy et al. 1990 23.5 Hin=1400 0.657-3.385; 1.6; 1.8 2190 Tube (D=6.28 mm, L=1.44 m) downward flow

Griem (1999) 22-27 --- 0.2-0.7 300-2500 Tube (D=10,24 mm) vertical and horizontal tubes

Chen 2004 24 Hin=1305; 1600 300 400

SS vertical and inclined tubes (smooth with uniform and non-uniform radial heating and ribbed)

Pis'mennyy et al. 2005 23.5 Tin=100-415 up to 3.21 250-2200

Vertical SS tubes (D=6.28 mm, L=600; 360 mm; D=9.50 mm, L=600; 400 mm) upward and downward.

Kirillov et al. 2005 24-25 Tin=300-380 0.09-1.05 200-1500 SS Tube (D=10mm, L=1;4 m)

Bazarrgan et al. 2005 23-27 Tw=405-670 up to 0.31 330-1200 Tube D=10.4mm vertical

Razumoviskiy (2005) 23.5 Tin=20-380 up to 0.515 250-500 Tube (D=6.28-9.5) vertical

Seo et al (2005) 23-24.5 Hb=1500-2500 0.21-0.933 430-1260 Tube (D=7.5-8 mm) vertical

Licht et al. (2007) 25 Tin=300-400 0.25-1.00 350-1425

Circular (Dext = 42.9 mm) and square annular (B=28.8

mm) tube with internal heater rod (length: 3.3 m)

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3 - Overview of some available experimental data for CFD model validation

24

Table 3.1 lists the most important experiments conducted in the last sixty years. It can be

noted that the experimental studies available in literature cover a wide range of parameters:

Pressure: 14 – 55 MPa

Mass Flux: 0.05 – 10 103 kg/(m2s)

Heat Flux: 0.06 – 9.5 MW/m2

Bulk temperature: ≤ 700 °C

Tube diameter: 1.2 – 32 mm

A short description of some of the main experiments and of their relevant results is reported hereafter.

Swenson et al. (1965) investigated local forced convection HTCs in supercritical water flowing inside smooth tubes (SS tube (D=9.42 mm, L=1,83 m). The results of their studies were obtained with tests performed within the following parameter ranges:

o Pressure: 22.8 – 41.4 MPa

o Mass Flux: 542 – 2150 kg/(m2s)

o Wall Temperature: 93 – 649 °C o Bulk Temperature: 75 – 576 °C

o Heat Flux: 200 – 1800 kW/m2

They found that the heat transfer coefficient (HTC) shows a sharp peak when the film temperature is within the pseudo-critical temperature range (Figure 3.2). This peak in HTC decreases with increasing pressure and; moreover, the HTC in the supercritical region is strongly affected by heat flux; in fact, at low fluxes a sharp peak near the pseudo-critical temperature is observed; at high fluxes, the HTC was found generally lower with no pronounced peak.

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25 Moreover, it was discovered that conventional correlations, as the Dittus-Boelter one, did not produce good results near the pseudo-critical point, due to the sharp changes occurring in the thermo-physical properties of the fluid. So, they proposed another correlation to describe HTC in this condition:

• Styrikovich et al. (1967) investigated heat transfer deterioration through a similar experiment in a circular tube. In their results, it is possible to observe improved and deteriorated heat transfer as well as a peak in HTC near the pseudo-critical condition, as shown in Figure 3.3.

• Ackermann (1970) used water flowing in a vertical tube (with and without ribs) at supercritical pressure within a range of pressures, maximum fluxes, heat fluxes and diameters suitable to investigate the heat transfer deterioration. He found the presence of a pseudo-boiling phenomenon due to the large variation of fluid density crossing the pseudo-critical zone. In fact, below the pseudo-critical point we can observe a high density fluid, as “liquid”; instead, beyond this point we have a low density fluid, as “gas”. The process is similar to film boiling which occurs at subcritical pressures and, in fact, it is called pseudo-film boiling.

9 . $(; 9.;"#<<<<9.=+>?_?9

&@ (3.1)

Figure 3.3: Variation in HTC values of water flowing in a tube (Styrikovic et al., 1967 )

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26

Ackerman noted that this pseudo-film boiling phenomenon may not be the only reason of heat transfer deterioration because, if we have the pseudo critical temperature between the bulk temperature and the wall surface temperature, heat transfer deterioration becomes unpredictable.

• Ornatsky et al. (1970) used five parallel tubes (D=3 mm, L=0.75 m) with stable and pulsating upward flow at supercritical pressure. They found that heat transfer deterioration occurs in different conditions as described below:

o Stable flow: q/G = 0.95 – 1.05 kJ/kg and inlet bulk enthalpy: Hin= 1330 – 1500 kJ/kg.

o Pulsating flow: q/G ≥ 0.68 – 0.9 kJ/kg

They estimated that the start of the heat transfer deterioration was usually noticed within certain zones along the tube, where (Tw + Tb)/2 reach the maximum value. They also established the possibility of the simultaneous existence of several local zones of deteriorated heat transfer along the tubes. The experimental data of their tests with forced convection was correlated with the following correlation:

where Pmin is the minimum value of Prw or Prb.

• Yamagata et al. (1971) investigated forced-convective heat transfer of water flowing in vertical and horizontal tube at supercritical pressure. The test section was an AISI316 stainless steel tube of 7.5 mm inner diameter, with a heated length of 1500 mm. The system pressure was 24.5 MPa and the mass velocity was 1260 kg/(m2s). In the experiment heating was obtained in the test section by directly applying an electrical current at low voltage. The outside test section temperature was measured by some thermocouples positioned at uniform longitudinal intervals (see Figure 3.4 for some example).

The result of their studies was that near the pseudo-critical region the HTC increases very quickly. The maximum value of HTC corresponds to a bulk fluid enthalpy, which is less than the pseudo-critical bulk-fluid enthalpy, and it also decreases with increasing heat flux and pressure.

_& . _&.!_"# ABC .! _>?9 ?&@ . (3.2)

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27

Figure 3.4: HTC vs. bulk-fluid enthalpy with upward flow at pressure of: a) 22.6; b) 24.5; c) 29.4 MPa (Yamagata et al., 1971)

They also suggested the following correlation to describe the convective heat transfer: where: D_E F G H G I + B: J K + . =- LMNEO.(>_PP_N&N@ C+ B: Q J Q + >PN PN&@ C B: J ) R and JST8NEU8&V_T89U8&V C+SO.-->+W_"#NE+ @W+.$;

CSO+.$$>+W_"#NE+ @O.(

• Alekseev et al. (1976) made experiments using water at supercritical pressure flowing in a circular vertical tube. They found that at q/G < 0.8 kJ/kg normal heat transfer occurred. Figure 3.5 shows that in this condition the wall temperature increased & &.!("#&.!DE (3.3)

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28

smoothly along the tubes (see q=0.27 and 0.35 MW/m2). Beyond this value the deterioration in heat transfer occurred (see the other curves in Figure 3.5a and Figure 3.5b); for increasing heat flux, it is observed that the wall temperature increases with a peak (if inlet temperature is 300 °C) or a hump (if inlet temperature is 100 °C).

Figure 3.5: Temperature profiles along heated lenght of vertical tube in upward flow (Alekseev et al., 1976)

• Watts (1980) studied supercritical pressure water using a test facility in different conditions of mass flux, heat flux and flow direction. The basic design parameters adopted for the supercritical pressure water flow loop, used to achieve the experiments, are reported below (Jackson, 2009a):

Pressure: 22.1 to 31 MPa

Fluid bulk temperature: 150 – 310 °C

Heat flux: 0.175 – 0.4 MW

Mass Flux: 232 – 908 kg/(m2s)

Test section size: D=25.4 mm (1”); heated length L=2 m. Flow directions: Upward and downward

A description of this experiment will be reported with greater detail in the next paragraph for the reason that Watt’s results, reported in Jackson (2009a) in graph form, are the data taken as reference in the present work for comparison with numerical results.

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29 • Kirillov et al. (2005) made heat transfer experiments in vertical tubes. Typically, in the entrance region (L/D ≤ 30) the wall temperature rises sharply; this profile depends on the thermal boundary layer development. Experimental data obtained with high mass flux (G = 1500 kg/(m2s)) show good agreement between the calculated and the measured outlet bulk fluid temperature; on the other hand, at low mass flux (G = 200 kg/m2s) there is a greater difference between these values (due to the increased measurement uncertainty at low mass-flow rates). In general, the experimental data shown in Figure 3.6 and in Figure 3.7 are below the deteriorated heat transfer (in fact, in agreement with literature, deterioration can appear at q/G > 0.4 kJ/kg).

Figure 3.6: Temperature and HTC variations along a 1 m long circular tube at various heat

fluxes and inlet temperatures with the following nominal conditions: pin=24.9,

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30

Figure 3.7: Temperature and HTC variations along a 4 m circular tube with the following

nominal conditions: p=24 MPa, G=1500 kg/(m2s), Q=880 kW/m2; hpc=2159 kJ/kg.

(Kirillov et al., 2005)

Pis’menny et al. (2005): the objective of these experiments was to investigate the heat transfer in vertical tubes for water at supercritical pressure in a gas-like state or affected by mixed convection in upward and downward flows. The tube inner diameters were 6.28 and 9.50 mm and the operating pressure was 23.5 MPa. The external part of the tube was heated by an electric coil using direct or alternate electric current and the temperature was measured using thermocouples.

They found that using water with Tin > Tpc in vertical tubes, heating to mass flux ratio below the value of q/G ≤ 0.70 kJ/kg (Tw ≤ 600°C) and mass flux G ≤ 2193 kg/(m2s) the heat transfer was normal with stable

temperature profile along the tube length (see Figure 3.8 and Figure 3.9).

Figure 3.8: Temperature profiles in vertical tube with upward flow at p=23.5 MPa.