Development of supercritical water heat-transfer correlation for vertical bare tubes

International Conference

NNNuuucccllleeeaaarrr EEEnnneeerrrgggyyy fffooorrr NNNeeewww EEEuuurrrooopppeee 222000000999 Bled / Slovenia / September 14-17

210. 1

DEVELOPMENT OF SUPERCRITICAL WATER

HEAT-TRANSFER CORRELATION FOR VERTICAL BARE TUBES

Sarah Mokry, Amjad Farah, Krysten King, Sahil Gupta, Igor Pioro Faculty of Energy Systems and Nuclear Science

University of Ontario Institute of Technology 2000 Simcoe Str. N., Oshawa ON L1K 7K4 Canada

[email protected], [email protected], [email protected], [email protected], [email protected]

Pavel Kirillov State Scientific Centre of the Russian Federation - Institute of Physics and Power Engineering (IPPE)

named after A.I. Leipunsky, Obninsk, Russia [email protected]

ABSTRACT

This paper presents an analysis of heat-transfer to supercritical water in bare vertical tubes. A large set of experimental data obtained in Russia was analyzed, and a new heat-transfer correlation for supercritical water was developed. This experimental dataset was obtained within conditions similar to those in SuperCritical Water-cooled nuclear Reactor (SCWR) concepts.

The experimental dataset was obtained in supercritical water flowing upward in 4-m long vertical bare tube with 10-mm ID. The data were collected at pressures of about 24 MPa, inlet temperatures from 320 to 350°C, values of mass flux ranged from 200–1500 kg/m2s and heat fluxes up to 1250 kW/m2 for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature.

A dimensional analysis was conducted using the Buckingham Π-theorem to derive a general form of empirical supercritical water heat-transfer correlation for the Nusselt number, which was finalized based on the experimental data obtained at the normal heat-transfer regime. Also, experimental HTC values at the normal heat-transfer regime were compared with those calculated according to several correlations from the open literature, CFD code and those of the derived correlation.

The comparison showed that the Dittus-Boelter correlation significantly overestimates experimental HTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also to deviate substantially from the experimental data within the pseudocritical range. The Swenson et al. correlation provided a better fit for the experimental data than the previous three correlations within some flow conditions, but does not follow up closely the experimental data within others. Also, HTC and wall temperature values calculated with the FLUENT CFD code might deviate significantly from the experimental data, for example, the k-ε model (wall function). However, the k-ε model (low Reynolds numbers) shows better fit within some flow conditions.

210. 2

Nevertheless, the derived correlation showed the best fit for the experimental data within a wide range of flow conditions. This correlation has uncertainty of about ±25% for HTC values and about ±15% for calculated wall temperature.

Therefore, the derived correlation can be used for HTC calculations of SCW heat exchangers, for preliminary HTC calculations in SCWR fuel bundles, for future comparison with other datasets, for verification of computer codes and scaling parameters between water and modelling fluids.

1 INTRODUCTION

Heat-transfer at supercritical pressures is influenced by significant changes in thermophysical properties at these conditions [1]. The most significant properties variations occur within critical and pseudocritical points [1].

1.1. Supercritical Fluids

Supercritical fluids have unique properties [1]. Figure 1 shows properties variations in water passing through the pseudocritical point at 25 MPa, the proposed operating pressure for SCWRs. The most significant changes in properties occur within ±25°C from the pseudocritical temperature (384.9°C). The NIST REFPROP software was used to calculate these thermophysical properties [2].

Temperature, oC

250 300 350 400 450 500 550 600

Den

sity

, kg/

m3

0

100

200

300

400

500

600

700

800

900

1000

c p, kJ

/kg-

K

0

20

40

60

80

100

120

140

160

180

200

220

Ther

mal

Con

duct

ivity

, W/m

-K

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Visc

osity

, μPa

-s

20

30

40

50

60

70

80

90

100

110

120

130

140

Fluid Densitycp

Thermal ConductivityViscosity

Water, P=25 MPa~ 50 oC

Tpc= 384.9oC

Fig.1: Selected properties of supercritical water within pseudocritical point.

1.2 SCWR Concepts

As part of the Generation IV International Forum (GIF), SCWR concepts (Table 1), which include pressure-vessel (PV) and pressure-tube (PT) options, are currently under

Proceedings of the International Conference Nuclear Energy for New Europe, Bled, Slovenia, Sept. 14-17, 2009

210. 3

development worldwide. Canada is working on development of a PT-reactor concept – SCW CANDU reactor (Table 1 and Fig. 2) [1], [3]−[5].

One of the main objectives for developing and utilizing SCWRs is that SuperCritical Water (SCW) Nuclear Power Plants (NPPs) offer an increased thermal efficiency, approximately 45–50%, compared to that of current generation NPPs (30–35%).

The current Canadian SCWR concept includes a fuel channel comprised only of a pressure tube insulated internally, which would enable the pressure tube to operate at temperatures close to that of the moderator [1].

T1,P1

T 2,P 2

T3,P3

T1,P1

T 2,P 2

T3,P3

T1,P1

T 2,P 2

T3,P3

H.P. S

C ON DEN SER

H.P. S

C ON DEN SER

Brine

Heat for Co-Generation or IP/LP Turbines

Turbine

Pump GeneratorCore

Sustainable Fuel input Electric powerElectric power

Hydrogen and process heat Hydrogen and process heat

Drinking water Drinking water

Multiple products are key to sustainable future and competitive designs

Industrial isotopes Industrial isotopes

H.P

Turbine

Fig. 2: SCW CANDU reactor schematic (courtesy of Dr. R. Duffey, AECL).

Table 1: Major parameters of SCW CANDU (Canada) and SCW VVER-SCP (Russia)

nuclear-reactor concepts.

Parameters SCW CANDU® VVER-SCP Reactor type PT PV Reactor spectrum Thermal Fast Thermal power, MW 2540 3830 Electric power, MW 1220 1700 Thermal efficiency, % 48 44 Pressure, MPa 25 25 Inlet temperature, °C 350 280 Outlet temperature, °C 625 530 Flowrate, kg/s 1320 1860 Number of fuel channels 300 241 Number of fuel elements in a bundle 43 252 Length of a bundle string, m 6 4

2 BACKGROUND

Currently, there is just one SCW heat-transfer correlation for fuel bundles developed by Dyadyakin and Popov [1]. This correlation was obtained in a 7-element helically-finned


210. 4

bundle. However, heat-transfer correlations for bundles are usually quite sensitive to a particular bundle design. Therefore, this correlation cannot be applied to other bundle geometries.

To overcome this problem, a wide-range heat-transfer correlations based on bare-tube data can be developed as a conservative approach. The conservative approach is based on the fact that HTCs in bare tubes are generally lower than those in bundle geometries where heat transfer is enhanced with appendages (endplates, bearing pads, spacers, button, etc.).

A number of empirical generalized correlations have been proposed to calculate the HTC in forced convection for various fluids including water at supercritical pressures. However, differences in calculated HTC values can be up to several hundred percent [1].

2.1 Experimental Data

The experimental data used in the current paper were obtained at the State Scientific Center of Russian Federation – Institute for Physics and Power Engineering supercritical-test facility (Obninsk, Russia) [1], [6]−[8]. This set of data was obtained within operating conditions close to those of SCWRs including a hydraulic-equivalent diameter.

The data for this study was obtained within the following conditions: Vertical stainless steel (12Cr18Ni10Ti) smooth tube: D=10 mm, δw=2 mm, and Lh=4 m; tube internal-surface roughness Ra=0.63–0.8 μm; and upward flow. Table 2 lists test-matrix parameters, and Table 3 – their uncertainties.

Table 2: Test matrix.

P Tin Tout Tw q G MPa ºC °C °C kW/m2 kg/m2s

24 320–350 380–406 <700 70–1250 200, 500; 1000; 1500

Table 3: Uncertainties of primary parameters.

Parameter Uncertainty Test-section power ±1.0% Inlet pressure ±0.25% Wall temperature ±3.0% Mass-flow rate ±1.5% Heat loss ≤3.0%

2.2 Existing Correlations

The most widely used heat-transfer correlation at subcritical pressures for forced convection is the Dittus-Boelter correlation [9]. McAdams [10] proposed the use of the Dittus-Boelter correlation in the following form for forced-convective heat transfer in turbulent flows at subcritical pressures (this statement was based on the recent study by Winterton [11]):

0.4

b0.8bb PrReNu 02430.= (1)

Later, Eq. (1) was also used at supercritical conditions. According to Schnurr et al. [12], Eq. (1) showed good agreement with experimental data of supercritical water flowing inside


210. 5

circular tubes at a pressure of 31 MPa with low heat fluxes. However, it was noted that Eq. (1) might produce unrealistic results within some flow conditions, especially near the critical and pseudocritical points, because it is very sensitive to properties variations. In general, this classical correlation was used extensively as a basis for various supercritical heat-transfer correlations.

Jackson [13] modified the original correlation of Krasnoshchekov et al. [14] (for details, see [1]) for forced-convective heat transfer in water and carbon dioxide at supercritical pressures to employ the Dittus-Boelter type form for Nu0. Finally, the following correlation was obtained:

n

pb

p

b

w

cc

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

3.0

5.082.00183.0ρρ

bbb PrReNu (2)

Where the exponent n is defined as following:

n=0.4 for Tb<Tw<Tpc and for 1.2 Tpc<Tb<Tw;

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 12.04.0

pc

w

TTn

for Tb<Tpc<Tw; and

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟⎟

⎠

⎞⎜⎜⎝

⎛−+= 15112.04.0

pc

b

pc

w

TT

TTn for Tpc<Tb<1.2 Tpc and Tb<Tw.

An analysis performed by Pioro and Duffey [1] showed that the two following correlations: 1) Bishop et al. [15] and 2) Swenson et al. [16]; were obtained within the same range of operating conditions as those for SCWRs.

Bishop et al. [15] conducted experiments in supercritical water flowing upward inside bare tubes and annuli within the following range of operating parameters: P=22.8–27.6 MPa, Tb=282–527ºC, m=651–3662 kg/m2s and q=0.31–3.46 MW/m2. Their data for heat transfer in tubes were generalized using the following correlation with a fit of ±15%:

⎟⎠⎞

⎜⎝⎛ +⎟⎟

⎠

⎞⎜⎜⎝

⎛=

xD..

.

b

w 42100690430

ρρ0.66

b0.9bb PrReNu

(3)

Equation (3) uses a cross-sectional averaged Prandtl number and the last term in the correlation (1+2.4 D/x) accounts for the entrance-region effect. However, in the present comparison the Bishop et al. correlation was used without the entrance-region term as the other correlations (see Eqs. (1) and (2)).

Swenson et al. [16] found that conventional correlations, which use a bulk-fluid temperature as a basis for calculating the majority of thermophysical properties, did not work well. And they have suggested the following correlation in which thermophysical properties are mainly based on a wall temperature:

231.0

613.0923.000459.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

b

w

ρρ

www PrReNu (4)


210. 6

Equation (4) was obtained within the following range: pressure 22.8−41.4 MPa, bulk-fluid temperature 75−576ºC, wall temperature 93−649ºC and mass flux 542−2150 kg/m2s; and predicts the experimental data within ±15%.

The majority of empirical correlations were proposed in the sixties-seventies, when experimental techniques were not at the same level (i.e., advanced level) as they are today. Also, thermophysical properties of water have been updated since that time (for example, a peak in thermal conductivity in critical and pseudocritical points, within a range of pressures from 22.1 to 25 MPa, was not officially recognized until the nineties [1]).

Therefore, it was necessary to develop a new or an updated correlation based on a new set of heat-transfer data and the latest thermophysical properties of water [2] within the SCWRs operating range.

It should be noted that all heat-transfer correlations presented in the paper are intended only for the normal heat-transfer regime calculations.

The following empirical correlation was proposed for calculating the minimum heat flux at which the deteriorated heat-transfer regime appears [17]:

Gqdht ⋅+−= 745.097.58 , kW/m2 (5)

3 DEVELOPING NEW CORRELATION

3.1 Dimensional Analysis A dimensional analysis was performed in order to obtain a general empirical form of a

correlation for the HTC calculations. It is well known that HTC is not an independent variable, and that HTC values are affected with velocity, inside diameter and thermophysical properties variations. Therefore, a set of the most important variables, which affects the HTC, were identified based on theoretical and experimental HTC studies. Table 4 lists parameters identified as essential for the analysis of heat-transfer processes for forced convection at supercritical conditions.

Table 4: Description of Various Heat-Transfer Parameters.

Variable Description SI units Dimensions ( M, L, T, K) HTC Heat transfer coefficient W/m2K MT-3K-1

D Inside diameter of tube m L kb Thermal conductivity of fluid at Tb W/m·K MLT-3K-1

kw Thermal conductivity of fluid at Tw W/m·K MLT-3K-1

ρb Density of fluid at Tb kg/m3 ML-3

ρw Density of fluid at Tw kg/m3 ML-3

µb Viscosity of fluid at Tb Pa·s ML-1T-1

µw Viscosity of fluid at Tw Pa·s ML-1T-1

cp Specific heat J/kg·K L2T-2K-1

V Velocity m/s LT-1

The Buckingham П-Theorem for dimensional analysis [18] was used to produce the

following expression for HTC as a function of the identified heat-transfer parameters.

HTC = f (D , kb ,, kw , ρw , ρb , µw , µb , cp , V) (6)

Through consideration of the primary dimensions (mass, length, time and temperature), six unique dimensionless Π terms were determined. Table 5 lists these terms.


210. 7

Table 5: Π-Terms of Empirical Correlation.

Π-terms Dimensionless group Name

Π1bk

DHTC ⋅ Nusselt number

Π2b

DVμ

ρ ⋅⋅ Reynolds number

Π3b

bp

kc μ⋅

Prandtl number

Π4b

w

kk Thermal conductivity ratio

Π5b

w

μμ Viscosity ratio

Π6b

w

ρρ Density ratio

The resulting relationship based on this analysis is as follows: Π1 =f (Π2, Π3, Π4, Π5, Π6) or

543

21

n

b

w

n

b

w

n

b

wnb

nbb k

kC ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

ρρ

μμPrReNu (7)

3.3 Finalizing Correlation

As a result of the experimental-data analysis, the following preliminary correlation for heat transfer to supercritical water was obtained:

518.0

654.00053.0 ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

b

w

ρρ

b0.914bb PrReNu (8)

To finalize the development of the correlation, the complete set of primary data and Eq.

(8) were fed into the SigmaPlot Dynamic Fit Wizard to perform final adjustments. The final correlation is as follows:

564.0

684.000610 ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

b

w.ρρ

b0.904bb PrReNu

(9)

Figure 3 shows scatter plots of experimental HTC values versus calculated HTC values

according to Eqs. (8), (9) and calculated and experimental values for wall temperatures. Both plots lie along a 45 degree straight line with an experimental data spread of ±25% for the HTC values and ±15% for the wall temperatures.


210. 8

3.4 Verifying Derived Correlation

Figures (4)−(7) show a comparison between experimentally obtained HTC and wall temperature values and those calculated with the Dittus-Boelter, Jackson, Bishop et al., Swenson et al. and derived (Mokry et al.) correlations. Figures (8) and (9) show a comparison between experimentally obtained HTC and wall temperature values and those calculated with FLUENT CFD code and derived (Mokry et al.) correlation.

An analysis of these plots shows that the Dittus-Boelter correlation significantly overestimates experimental HTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also to deviate substantially from the experimental data within the pseudocritical range. The Swenson et al. correlation provided a better fit for the experimental data than the previous three correlations within some flow conditions, but does not follow up closely the experimental data within others. Also, HTC and wall temperature values calculated with the FLUENT CFD code might deviate significantly from the experimental data (for example, the k-ε model (wall function)). However, the k-ε model (low Reynolds numbers) shows better fit within some flow conditions.

Nevertheless, the derived correlation showed the best fit for the experimental data within a wide range of flow conditions. This correlation has uncertainty of about ±25% for HTC values and about ±15% for calculated wall temperature.

Therefore, the derived correlation can be used for a preliminary HTC calculations in SCWR fuel bundles, for future comparison with other datasets, for verification of computer codes and scaling parameters between water and modelling fluids.

Twexp

300 400 500 600 700

Twca

lc

300

400

500

600

700

G= 500 kg/m2sG=1000 kg/m2sG=1500 kg/m2s

-15%

+15%

(a) (b)

Figure 3: Comparison of data fit with experimental data: (a) for HTC and (b) for Tw.


210. 9

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

375

400

425

HTC

, kW

/m2 K

51015202530354045505560657075

Bulk-Fluid Enthalpy, kJ/kg

1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600

Heated lengthBulk-fluid temperature

Heat transfer coefficient

Pin = 24.1 MPaG = 1495 kg/m2

qave = 884 kW/m2

qdht = 1055 kW/m2

Hpc

Tpc= 382oC Tin

Tout

Bishop et al. corr.

Dittus-Boelter corr.

Swenson et al. corr.

Jackson corr.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

350

400

325

375

425


1600 1800 2000 2200 2400 2600 2800

HTC

, kW

/m2 K

0

4

8

12

16

20

24

28

32

Heated length

Bulk-fluid temperatureTin

Tout


Pin = 24.2 MPa G = 500 kg/m2sqave = 335 kW/m2

qdht = 314 kW/m2

Hpc

Tpc = 382oC

Bishop et al. c

orr.

Dittus-Boelter corr.

Swenson et al. corr.

Jackson corr.

Fig. 4: Comparison of HTC values calculated with derived correlation (Mokry et al.) and other correlations from open literature with experimental data along 4-m circular tube

(D=10 mm): Pin=24.0 MPa and G=1500 and 500 kg/m2s.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

375

400

425

HTC

, kW

/m2 K

02468


1600 1800 2000 2200 2400 2600


Inside-wall temperature


Pin = 24.1 MPaG = 203 kg/m2sqave= 129 kW/m2

qdht = 92 kW/m2

Hpc

Tpc= 381.5oC Tin

Tout

Mokry et al. corr.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

375

400

450

475

425

HTC

, kW

/m2 K

0246


1400 1600 1800 2000 2200 2400 2600





qdht = 91 kW/m2

Hpc

Tpc= 381.6oC

Tin

Tout

Mokry et al. corr.

Fig. 5: Temperature and HTC variations at various heat fluxes along 4-m circular tube (D=10 mm): Pin=24.0 MPa and G=200 kg/m2s.


210. 10

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

350

400

375


1600 1700 1800 1900 2000 2100

HTC

, kW

/m2 K

010203040506070

Heated length

Bulk-fluid temperature

Tin

Tout




qdht = 317 kW/m2

Hpc=2138.1 kL/kg

Mokry et al. corr.

Tpc = 382oC

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

300

350

400

450

325

375

425

475500


1600 1800 2000 2200 2400 2600

HTC

, kW

/m2 K

4812

0

Heated lengthBulk-fluid temperatureTin

Tout




qdht = 313 kW/m2

Hpc

Tpc = 381oC

Mokry et al. corr.

Fig. 6: Temperature and HTC variations at various heat fluxes along 4-m circular tube

(D=10 mm): Pin=24.0 MPa and G=500 kg/m2s.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

400

375

300


1500 1600 1700 1800 1900 2000 2100

HTC

, kW

/m2 K

5101520253035404550

Heated length


Tin

Tout




qdht = 688 kW/m2

Hpc=2138.3 kJ/kg

Tpc= 381oC

Mokry et al. corr.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

400

375

425

450

475


1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600

HTC

, kW

/m2 K

8121620242832

Heated lengthBulk-fluid temperatureTin

Tout




qdht = 683 kW/m2

Hpc

Tpc = 381oC

Mokry et al. corr.



210. 11

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

375

400

HTC

, kW

/m2 K

30

40

50

6055

25

35

45


1600 1700 1800 1900 2000 2100 2200 2300

Heated length





qdht = 1061 kW/m2

Hpc

Tpc= 381.6oC Tin

Tout

Mokry et al. corr.

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

325

350

375

400

HTC

, kW

/m2 K

15

20

25

30

35

40


1400 1600 1800 2000 2200




Pin = 24.1 MPaG = 1496 kg/m2s qave= 729 kW/m2

qdht= 1056 kW/m2

Hpc

Tpc= 381.4oC

Tin

Tout

Mokry et al. corr.


Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

350

400

450


1600 1800 2000 2200 2400 2600 2800

HTC

, kW

/m2 K

610141822

2

263034

Heated length


Tin

Tout


Pin = 23.9 MPaG = 1002 kg/m2sqave = 681 kW/m2

qdht = 688 kW/m2

Hpc

Tpc = 381oC

Mokry et al. corr

k-e model (wall function)

k-e model (low Reynolds)

k-w model (SST)

Tem

pera

ture

, o C

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

, o C

350

400

450

500

Heated length


Tin

Tout

Inside-wall te

mperature

Pin = 23.9 MPaG = 1002 kg/m2sqave = 681 kW/m2

qdht = 688 kW/m2

Hpc

Tpc = 381oC

Mokry et al. corr.

k-w model (SST)

k-e model (low reylonds)

k-e model (wall function)

Fig. 9: Comparison of HTC and wall temperature values calculated with derived

correlation (Mokry et al.) and FLUENT CFD-code [19] with experimental data along 4-m circular tube (D=10 mm): Pin=24.0 MPa and G=1000 kg/m2s.

4 CONCLUSIONS

The following supercritical-water heat-transfer dataset obtained in a vertical bare tube was used for development of a new heat-transfer correlation and its comparison with the experimental data, with other correlations from the open literature and with FLUENT CFD code: P=24 MPa, Tin=320−350ºC, G=200−1500 kg/m2s and q≤1250 kW/m2. This dataset was obtained within the SCWR operating conditions.

The comparison showed that the Dittus-Boelter correlation significantly overestimates experimental HTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also to deviate substantially from the experimental data within the pseudocritical range. The Swenson et al. correlation provided a better fit for the experimental data than the previous three correlations within some flow conditions, but does not follow up


210. 12

closely the experimental data within others. Also, HTC and wall temperature values calculated with the FLUENT CFD code might deviate significantly from the experimental data (for example, the k-ε model (wall function)). However, the k-ε model (low Reynolds numbers) shows better fit within some flow conditions.

Nevertheless, the derived correlation showed the best fit for the experimental data within a wide range of flow conditions. This correlation has uncertainty about ±25% for HTC values and about ±15% for calculated wall temperature.

Therefore, the derived correlation can be used for HTC calculations of SCW heat exchangers, for preliminary HTC calculations in SCWR fuel bundles, for future comparison with other datasets, for verification of computer codes and scaling parameters between water and modelling fluids.

5 NOMENCLATURE

C constant cp specific heat at constant pressure, J/kg·K

pc average specific heat, J/kg·K, ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

bw

b

TTHH w

D inside diameter, m f function G mass flux, kg/m2s H enthalpy, J/kg h heat transfer coefficient, W/m2K k thermal conductivity, W/m·K L length, m P pressure, Pa q heat flux, W/m2

Ra surface roughness, µm T temperature, ºC V velocity, m/s x axial location, m

Greek letters

μ dynamic viscosity, Pa·s ρ density, kg/m3

δ thickness, mm

Dimensionless numbers

Nu Nusselt number ⎟⎠⎞

⎜⎝⎛ ⋅

kDh

Pr Prandtl number ⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅

kc pμ

Pr average Prandtl number ⎟⎠⎞

⎜⎝⎛ ⋅

kc pμ

Re Reynolds number ⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅μ

DG

Subscripts

ave average b bulk calc calculated dht deteriorated heat-transfer exp experimental h heated in inlet out outlet pc pseudocritical w wall Abbreviations: AECL Atomic Energy Canada Limited CANDU CANada Deuterium Uranium

(reactor) HTC Heat Transfer Coefficient ID Inside Diameter NIST National Institute of Standards

and Technology NPP Nuclear Power Plant PT Pressure Tube (reactor) PV Pressure Vessel (reactor) SCW SuperCritical Water SCWR SuperCritical Water Reactor VVER-SCP Water Water Power Reactor of

SuperCritical Pressure (in Russian abbreviations)


International Conference

NNNuuucccllleeeaaarrr EEEnnneeerrrgggyyy fffooorrr NNNeeewww EEEuuurrrooopppeee 222000000999 Bled / Slovenia / September 14-17

210. 13

ACKNOWLEDGMENTS

Financial supports from the NSERC Discovery Grant, NSERC/NRCan/AECL Generation IV Energy Technologies Program and the Ontario Research Excellence Fund are gratefully acknowledged.

REFERENCES

[1] Pioro, I. and Duffey, R., 2007. Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Power Engineering Applications, ASME Press, New York, NY, USA, 334 pages.

[2] National Institute of Standards and Technology, 2007. NIST Reference Fluid Thermodynamic and Transport Properties-REFPROP. NIST Standard Reference Database 23, Ver. 8.0. Boulder, CO, U.S.: Department of Commerce.

[3] Naidin, M., Mokry, S., Baig, F. et al., 2009. Thermal-Design Options for Pressure-Channel SCWRs with Co-Generation of Hydrogen, J. of Engineering for Gas Turbines and Power, Vol. 131, January, 8 pages.

[4] Naidin M., Pioro I., Zirn, U. et al., 2009. Supercritical Water-Cooled NPPs with Co-Generation of Hydrogen: General Layout and Thermodynamic-Cycles Options, Proc. 4th Int. Symp. on Supercritical Water-Cooled Reactors, March 8-11, Heidelberg, Germany, Paper No. 78, 11 pages.

[5] Duffey, R., Pioro, I. Zhou, T. et al., 2008. Supercritical Water-Cooled Nuclear Reactors (SCWRs): Current and Future Concepts – Steam-Cycle Options, Proc. ICONE-16, Orlando, Florida, USA, May 11–15, Paper #48869, 9 pages.

[6] Kirillov, P., Pometko, R., Smirnov, A. et al., 2005. Experimental Study on Heat Transfer to Supercritical Water flowing in 1- and 4-m-Long Vertical Tubes, Proc. GLOBAL’05, Tsukuba, Japan, Oct. 9-13, Paper No. 518.

[7] Pioro, I.L., Kirillov, P.L., Mokry, S.J. and Gospodinov, Y.K., 2008. Supercritical Water Heat Transfer in a Vertical Bare Tube: Normal, Improved and Deteriorated Regimes, Proc. ICAPP’08, Anaheim, CA, USA, June 8-12, Paper #8333, pp. 1843-1852.

[8] Gospodinov, Ye., Mokry, S., Pioro, I. and Kirillov, P.L., 2008. Supercritical Water Heat Transfer in a Vertical Bare Tube, Proc. ICONE-16, Orlando, Florida, USA, May 11–15, Paper #48546, 11 pages.

[9] Dittus, F.W. and Boelter, L.M.K., 1930. University of California, Berkeley, Publications on Engineering, Vol. 2, p. 443.

[10] McAdams, W., 1942. Heat Transmission, 2nd ed., McGraw-Hill, New York, NY, USA, 459 pages.

[11] Winterton, R.H.S., 1998. Where Did the Dittus and Boelter Equation Come From? Int. J. Heat and Mass Transfer, 41 (4–5), pp. 809–810.

[12] Schnurr, N.M., Sastry, V.S., and Shapiro, A.B., 1976. A Numerical Analysis of Heat Transfer to Fluids near the Thermodynamic Critical Point Including the Thermal Entrance Region, Journal of Heat Transfer, Transactions of the ASME, 98 (4), pp. 609-615.

[13] Jackson, J.D., 2002. Consideration of the Heat Transfer Properties of Supercritical Pressure Water in Connection with the Cooling of Advanced Nuclear Reactors, Proc. 13th Pacific Basin Nuclear Conference, Shenzhen City, China, October 21-25.

[14] Krasnoshchekov, E., Protopopov, V., Van, F., and Kuraeva, I., 1967. Experimental Investigation of Heat Transfer for Carbon Dioxide in the Supercritical Region, Proc. 2nd All-

210. 14

Soviet Union Conf. on Heat and Mass Transfer, Minsk, Belarus’, May, 1964, Published as Rand Report R-451-PR, Edited by C. Gazley, Jr., J. Harnett & E. Ecker, Vol. 1, pp.26-35.

[15] Bishop, A.A., Sandberg, R.O., and Tong, L.S., 1964. High Temperature Supercritical Pressure Water Loop: Part IV, Forced Convection Heat Transfer to Water at Near-Critical Temperatures and Super-Critical Pressures, Westinghouse Electric Corporation, Pittsburgh, Pennsylvania.

[16] Swenson, H.S., Carver,J.R., and Kakarala, C.R, 1965. Heat Transfer to Supercritical Water in Smooth-Bore Tubes, J. of Heat Transfer, Trans. ASME Series C, 87 (4), pp. 477-484.

[17] Mokry, S., Gospodinov, Ye., Pioro, I. and Kirillov, P.L., 2009. Supercritical Water Heat-Transfer Correlation for Vertical Bare Tubes, Proc. ICONE-17, July 12-16, Brussels, Belgium, Paper #76010, 8 pages.

[18] Munson, B., Young, D. and Okiishi, Th., 2005. Fundamentals of Fluid Mechanics, 5th ed., New York, NY, J. Wiley & Sons.

[19] Vanyukova, G., Kuznetsov, Yu., Loninov, A. et al., 2009. Application of CFD-Code to Calculations of Heat Transfer in a Fuel Bundle of SCW Pressure-Channel Reactor, Proc. 4th Int. Symp. on Supercritical Water-Cooled Reactors, March 8-11, Heidelberg, Germany, Paper No. 28, 9 pages.


Development of supercritical water heat-transfer correlation for vertical bare tubes

Documents

Transcript of Development of supercritical water heat-transfer correlation for vertical bare tubes