Experimental measurements and CFD simulation of convective boiling

Heat Mass Transfer DOI 10.1007/s00231-014-1449-3

ORIGINAL

Experimental measurements and CFD simulation of convective boiling during subcooled developing flow of R-11 within vertical annulus Y. Bouaichaoui • R. Kibboua • M. Matkovicˇ

Received: 16 December 2013 / Accepted: 12 October 2014 Ó Springer-Verlag Berlin Heidelberg 2014

Abstract In this paper a convective flow boiling of refrigerant R-11 in a vertical annular channel has been investigated. Measurements were performed under various conditions of mass flux, heat flux, and inlet subcooling, which enabled to study the influence of different boundary conditions on the development of local flow parameters. Also, some measurements have been compared to the predictions by the three-dimensional two-fluid model of subcooled boiling flow carried out with the computer code ANSYS-CFX-13. Simulation results successfully predict the main experimental tendencies associated with the heat flux and Reynolds number variation. A sensitivity analysis of several modelling parameters on the radial distribution of flow quantities has highlighted the importance of correct description of the boiling boundary layer. In general a good quantitative and qualitative agreement with experimental data was obtained.

1 Introduction Multiphase flows and the associated heat transfer are some of the most important phenomena which not only affect the reactivity of the nuclear reactors but also determine the

Y. Bouaichaoui (&) Birine Nuclear Research Center/CRNB/COMENA/ALGERIA, Aı¨n Oussera, BO. 180, 17 200 Djelfa, Algeria e-mail: [email protected] Y. Bouaichaoui  R. Kibboua LTPMP/FGMGP/USTHB, El Alia, BO. 32, 16111 Bab Ezzouar, Algeria M. Matkovicˇ Jozˇef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

criticality of the equipment in nuclear power plants. In the special case of nuclear applications where very high heat fluxes are involved, boiling may enhance significantly heat transfer. Nevertheless, under some operating conditions, this can lead to a dangerous phenomenon namely the boiling crisis, a limit never to be reached during reactor operation. In accident conditions a convective flow boiling can occur in narrow flow passages between the heated fuel rods of a pressurized water reactor core. In the case of exceeding the critical heat flux the boiling flow-regime may lead to the departure from nucleate boiling (DNB). The DNB corresponds to the formation of a vapour layer between the surface being cooled and the refrigerant. This is accompanied by an abrupt decreasing of heat transfer and, consequently, a prompt rising of wall temperature up to eventually the melting point. To correctly predict DNB occurrence, we must be first able to understand and simulate the governing mechanisms of convective flow boiling. The phenomena associated with convective flow boiling are usually three-dimensional and many small-scale processes are not well understood yet, therefore, the multidimensional CFD modelling of such flow is necessary. Commonly a two-fluid Eulerian approach is used in CFD codes. Modelling of interfacial transfer determines the degree of thermal and hydrodynamic non-equilibrium between the phases, so the reliability and accuracy of the predicted results usually depend on the implemented constitutive relations for interfacial transfer [1]. Due to the complexity of the subcooled flow boiling it is rather difficult to establish a general model able to cover a wide range of test conditions [2–4]. However, the development of computer and digital technology has led to the emergence of CFD codes capable of analyzing three-dimensional structure of the subcooled boiling flow realistically through the adoption of mechanistic modelling implemented in the

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code [5]. Although many studies of the critical heat flux and the mechanisms underlying this phenomenon have been undertaken in several nuclear laboratories worldwide [6–8], the DNB is as of today a poorly understood phenomenon. In this context, it was considered important to contribute to this particular field by experimental studies and modeling of the convective subcooled flow boiling in an annular channel [9]. It is simulating, to a certain extent, a simple nuclear reactor channel with a single fuel pin [10, 11]. The outer tube of the test section is made of Pyrex so as to perform visualisation tests during diabatic runs. The refrigerant is R11, which offers the advantage to obtain phase change at relatively low heat fluxes if compared to water. Nevertheless, a CFD modelling of steady state flow boiling phenomenon within aforementioned geometry was also adopted herein. The calculation model covers a wide range of two phase flow conditions. It predicts the heat transfer rates and transitions points for each flow regime. The model was implemented in the ANSYS CFX-13. The results of the simulation were compared with experimental data.

2 Experimental facility Figure 1 shows a schematic of the test facility. The test loop [12, 13] is composed of three cooling systems. The primary circuit comprises the test section and uses R11 as a refrigerant; the secondary cooling circuit

Fig. 1 Schematic diagram of the test facility

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uses water as a coolant. The complementary circuit, a classical refrigerating system, enables to control the inlet temperature of R-11 to the test section. R11 from the tank is pumped from the preheater into the test section where it is successively heated by Joule effect. The energy absorbed by the fluid is then transferred, in a heat exchanger, to the secondary cooling water which, in turn, transfers it through the coaxial evaporator of the refrigerating system to R22. The primary circuit comprises, in addition, other components such as the phase separator, which separates the liquid phase from the vapour phase and the condenser, which is used to fully condense R11 before returning to the tank. 2.1 Test section The test section (Fig. 2) consists of a vertical annular channel with a heated inner tube (i.d. = 20 mm) and an adiabatic outer tube (i.d. = 40 mm, o.d. = 45 mm). The inner tube is made of stainless steel while the outer transparent tube is made of Pyrex. The total length of the annular channel is 1,100 mm and the 1,020 mm long upper part of the inner tube is heated by means of electric heater. The fluid temperature was measured by Type J thermocouples at the inlet and outlet of the channel. Ten Type K thermocouples are insulated and embedded in the wall of the heating element. They are uniformly distributed along the length; the distance between two successive locations is 10 cm. The thermocouples are connected to a protection system that prevents the diabatic wall from overheating

Heat Mass Transfer

Fig. 2 Test section

when local heat transfer is for some reason reduced. In fact, the electrical heating stops automatically as soon as one of them reaches a prefixed value of temperature. 2.2 Measurements The uncertainty of the temperature measurement was estimated to be ±0.2 °C. To calculate the wall temperature measured by thermocouples placed at the center of the heating element and according to the relatively large drop in temperature, we assume a relatively large uncertainty of 4 % on the temperature difference TW-Tb. The absolute pressures were measured at the inlet and outlet with the estimated uncertainties of ±0.0025 and ±0.001 MPa, respectively. The mass flux was determined with the inlet volumetric flow rate measured by a variable area flow meter, R11 density and flow area. The uncertainty was estimated to be ±0.25 % of the rated mass flux. The test channel inlet temperature was controlled by a preheater which has a maximum capacity of 24 kW. The inlet subcooling was calculated from the measured temperature and absolute pressure at the inlet and the uncertainty was estimated to be ±0.5 °C. Heat flux was calculated from the measured voltage across the heated tube, the current through it and the heated surface area. It was controlled by an AC thyristors power supply and the uncertainty was estimated to be ±0.8 % of the rated heat flux. Heat balance in the single-phase liquid flow was also checked across the test channel to examine the accuracy of the heat flux calculation. The heat flux, which was obtained from the liquid flow rate and the temperature increase between the test channel inlet and outlet, was calculated to be less than 1.5 % smaller compared to the value calculated from the measured current and voltage drop. The discrepancy was associated to the heat loss around the test section. The uncertainty in the heat transfer coefficient measurement is estimated through an error propagation analysis and, for the range of conditions investigated, it provided errors around 5 % for the experimental heat transfer coefficient.

3 CFD modelling A two-fluid Eulerian approach is used for mathematical description of the subcooled boiling flow. The code ANSYS-CFX 13 was used to solve the set of two-fluid transport equations with additional source terms for modeling of wall boiling. The basis of the code is a conservative finite volume method with all variables defined at the center of control volumes, which fill the physical domain being considered, and space discretization follows a structured mesh. Only some most relevant closures are described here, whereas other models are merely mentioned. 3.1 Wall boiling model After the bubbles are generated in the activated nucleation sites on the heated surface, they move through the subcooled bulk liquid flow, they condense and release the latent heat. In this way the bulk liquid flow is intensively heated up, up to the saturation temperature when bubbles stop condensing. The interfacial heat and mass transfer due to condensation in the subcooled flow was modeled by Ranz-Marshall [14] correlation. The evaporation mass flow on the wall m_ w is applied to the near-wall cells and is modelled in a mechanistic way, taking into account the total mass of bubbles periodically departing from nucleation sites:   p  d3bw m_ w ¼ ð1Þ  qg  f  Na 6 Where dbw is the bubble departure diameter, f is the bubble departure frequency and Na is the nucleation site density. The boundary conditions for the heat transfer at the wall require a model for wall heat flux partitioning. According to the mechanistic model of subcooled boiling flow by Kurul and Podowski [11], the wall heat øw comprises three different modes of heat transfer (Fig. 3): single-phase convection that prevails in the absence of vapour generation øC1, quenching that transfers cold liquid from the bulk

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Heat Mass Transfer Fig. 3 Wall heat flux partitioning mechanisms

flow to the wall periodically øQ and evaporation component needed to generate vapor bubbles øe. Heat flux components are calculated as follows: /w ¼ /C1 þ /Q þ /e ð2Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sQ kl ql cpl ¼ Stql cpl tl Afc ðTW  Tl Þ þ 2f Atc ðTw  Tl Þ p 3 pd ð3Þ þ Na f bw qg hlg 6

the local liquid subcooling. Most of the closure relations (e.g. quenching heat flux, bubble departure diameter) are based on the averaged cross-sectional values of liquid temperature and velocity and are later adopted for CFD calculations. When these correlations are applied straightforwardly, as CFD boundary conditions simply by replacing averaged values by local ones, this would lead to the grid dependent solution.

where St is local Stanton number, Tw is the wall temperature, Tl,tl, bulk are the local liquid temperature and velocity in the near-wall computational cell, respectively. The quenching time interval sQ between the departure of a bubble and the beginning of the growth of the new one is defined as sQ = 0.8/f. Atc is the area fraction influenced by the nucleating bubbles and Afc is the fraction influenced only by the single-phase convection calculated by Eq. (4).

3.2 Turbulence intensities

Afc ¼ 1  Atc ¼ 1 

pNa D2l 4

ð4Þ

Lemmert and Chawla [15] correlation and Van Stralen [16] correlation were adopted to compute active nucleation site density Na and the bubble departure frequency f, respectively. Na ¼ ½210ðTw  Tsat Þ1:8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ql  qg g f ¼ 3 ql Dl

ð5Þ ð6Þ

In the current work the simplest model for the bubble departure diameter proposed by Tolubinski and Kostanchuk [17] is used:    DTsub dbw ¼ min 1:4½mm; 0:6½mm exp  ð7Þ 45½K The model was derived from the high-pressure water boiling experimental data with the upper limit for the bubble departure diameter, dbw = 1.4 mm. The correlation includes three adjustable parameters and depends solely on

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The turbulence stresses are modelled only for the liquid phase using the shear stress turbulence model. The turbulence in the vapour-phase is negligible with respect to the liquid phase term, therefore it was not modelled. The bubbles however bring an important contribution to the overall liquid turbulence intensity through the bubbleinduced turbulence term. In fact, in bubbly two-phase flows, an additional production of the liquid turbulence generated by fluctuating wakes behind the bubbles may occur. The bubble-induced turbulence is taken into account by additional viscosity term in the momentum equation according to the assumption by Sato et al. [18] turb leff þ lbl l ¼ l l þ ll

ð8Þ

turb whereleff and lbl denote effective, molecular, the l ,ll, ll shear-induced and bubble-induced viscosity of the liquid respectively. Bubble-induced viscosity depends on the vapour phase volume fraction a, the local bubble diameter db and the relative velocity between the phases: *  * lbl ¼ Cs  ql  db  a  ug  ul  ð9Þ

For the considered experiments a constant value of bubble diameter, db = 1 mm, was estimated from the experimental observations and Cs = 0.6 was used. Taking into account the eddy viscosity calculation from Eq. 10: lturb ¼ Cl  ql  l

k2 eL

ð10Þ

where Cl = 0.09, one can deduce the bubble induced turbulence from Eqs. 9 and 10:

Heat Mass Transfer Fig. 4 3D equidistant grids structured meshing 20 9 20 9 200 (left) and 2D equidistant grids structured meshing 20 9 20 (right)

Table 1 Distance of the centre of the first computational cells from the heated wall and number of nodes for tested meshes

3.4 Boundary conditions

Grid

Experimental cases presented in Table 2, were simulated. The length of the simulated annular channel was the 1,020 mm long heated part. For the liquid phase a no-slip and for the gaseous phase a free slip boundary condition was used at the wall. The flow through the annular vertical tube is assumed to be axis-symmetric. A constant heat flux boundary condition was applied at the heated part of the inner wall. The unheated inlet section was not included in the domain. The outer wall of the annulus is assumed to be adiabatic. At the inlet, uniform velocity and temperature profiles were set, whereas pressure boundary condition was applied at the annulus outlet. The subcooled boiling model in the code assumes incompressible flow at a constant absolute pressure. The saturation temperature and the latent heat of evaporation are specified at this pressure. The model uses constant physical properties evaluated at the saturation temperature. Results of the numerical simulations have been plotted for axial positions corresponding to the actual locations of the wall thermocouples distributed downstream the experimental test section. The local parameters were calculated over ten different distances from the heating wall across the annular section. In this context, the radial profiles of the local flow parameters were plotted versus the dimensionless width of the annulus defined as: Rp = r-R0/R-R0. Here, r, R and R0 are the radial location measured from the symmetry axis, inner radius of the external tube and external radius of the inner tube respectively (Fig. 5). The CFX-13 calculations were run in the ‘‘steady-state’’ mode.

10 9 10

20 9 20

40 9 40

80 9 80

y (mm)

0.5

0.25

0.125

0.0625

Nodes

35,739

71,839

302,679

2,490,159

sffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *  eL  lbl * ¼ e L  a  db   ug  ul  kB ¼ Cs q

ð11Þ

where eL denotes the turbulent energy dissipation rate. Finally the overall effective turbulence comes out as a sum of the shear induced and bubble induced turbulence: keff ¼ kL þ kB

ð12Þ

The interfacial transfer of momentum is modeled with *

the interfacial forces, which include drag force F D , lift *

*

force F L and turbulent dispersion force F TD . The interfacial drag force is calculated according to the Ishii and Zuber [19]. Default models for the lift force and turbulent dispersion force were used, whereas the wall lubrication force was not implemented in the model setup. 3.3 Geometrical model and mesh design The same geometry domain as the one adopted in the experimental apparatus has been designed and used for all numerical simulations. The 3D annular geometry and meshing (Fig. 4) were both created with ICEM CFD. Given the axial symmetry conditions, only an angular sector h of 60° is taken into account in the calculation. Mesh sensitivity analysis has been carried by analyzing the hexahedral mesh elements quality and its refinement influence on the solution. Simulations with four different 3D equidistant grids were tested (10 9 10 9 100, 20 9 20 9 200, 40 9 40 9 200 and 80 9 80 9 400). Number of nodes and distance of the centre of the first computational cell from the heated wall for all computational grids are presented in Table 1.

Table 2 Experimental conditions Exp no

P (bar)

qwW/ cm2

G (kg/m2 s)

Tsat (°C)

Tinlet (°C)

Exp1 (sp)

1.6

1.81

622

35

25

Exp2

1.6

3.94

996

35

25

Exp3

1.6

3.94

435

35

25

Exp4

1.6

4.60

996

35

25

Exp5

1.6

4.72

435

35

25

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Heat Mass Transfer

Fig. 7 Wall temperature profiles along the test section during flow boiling of R11 with mass velocity 996 kg/m2 s and heat flux 3.94 W/cm2

Fig. 5 2D computational domain in different cross-section over the test section

Fig. 6 Liquid temperature profiles across the annular channel during flow boiling of R11 with mass velocity 996 kg/m2 s and heat flux 3.94 W/cm2

3.5 Mesh sensitivity analysis; validation against temperature measurement The solutions obtained with the four different uniform numerical grids are shown in Figs. 6, 7, 8 and 9. A special criterion was adopted to evaluate the calculation procedure by comparing the experimental wall temperatures with the

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calculated values. In this context, the 60° section of the simulated annulus was ‘‘sliced’’ into ten flow cross-sections distributed downstream the heated section. The distribution of the calculation domains corresponded to the actual location of the local temperature measurements in the test section (Fig. 10). Experimental conditions depicted under Exp2 in the Table 2 were selected for the mesh validation. The radial profile of the liquid temperature has been plotted for two different locations; 650 and 750 mm from the inlet (Fig. 6). The R11 radial temperature distributions calculated for the coarse grid 10 9 10 and the fine grid 80 9 80 deviate the most in the near wall region where difference exceeds 1 °C. This is quite reasonable as the first computing cell in the coarse grid covers the entire boundary layer thickness. For the same experimental conditions (Exp2), the comparative results for three different mesh refinements are shown in Fig. 8. Here, temperature fields are plotted with contours in color shade, which gives a better illustration of the gradients in the radial profile. At 650 mm downstream the test section inlet, there is a good agreement observed between the experimental measurements and the calculated temperatures with ANSYS CFX. On the other hand, considerable discrepancies have been found between the radial distributions of the void fraction calculated with different mesh refinements. Liquid temperature evolution and void fraction distribution along the test section are shown in Fig. 10 for the lowest studied heat flux of 3.94 W/cm2. The wall temperatures calculated from the wall superheat (DTsup = Tw-Tsat) are compared against the experimental data (Fig. 7). Not only has a very good

Heat Mass Transfer

Fig. 8 Calculated contours of liquid temperature during flow boiling of R11 with mass velocity 996 kg/m2 s and heat flux 3.94 W/cm2

Fig. 9 Calculated contours of void fraction during flow boiling of R11 with mass velocity 996 kg/m2 s and heat flux 3.94 W/cm2

Fig. 10 Calculated liquid temperature field (left) and void fraction evolution (right) during flow boiling of R11 with mass velocity 996 kg/m2 s and heat flux 3.94 W/cm2

agreement between the calculations and the experimental measurements been observed; a set of grid independent solutions of the wall temperature have identified an optimum mesh density used. It proves that the numerical grid addressed as ‘‘fine mesh’’fine mesh (20 9 20 9 200) with 19 grid cells in radial and circumferential directions and 200 grid cells along the channel height, (Fig. 4) is sufficient to obtain a grid independent result. This grid refinement has been used in most calculations. For a limited set of boundary conditions the fine grid seems to be good enough to achieve acceptable numerical accuracy within a reasonable CPU time. Note also that the calculations are stopped when the average error of each variable reaches 10-4 and the number of iterations was set to 8,000.

4 Comparisons of experimental results with calculations of a three-dimensional two-fluid model In order to demonstrate the capability of CFD codes to predict the complex phenomena of boiling in subcooled flow, a comparison was carried out between the calculated results performed with the commercial code ANSYS CFX and the measurements from the experimental setup. For this purpose, single-phase heat transfer experimental studies were first carried out. The heat transfer coefficient results were compared against the simulation results. Only after the agreement was found satisfactory, we focused on the flow boiling process and the associated phenomena. In particular, we studied onset of nucleate boiling (ONB)

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while trying to characterize the onset of significant void (OSV). It should be noted that all physical properties appearing in the dimensionless numbers are set at the average temperature of the fluid in the measuring section. Different correlations are later used to account for variation of the properties with temperature. 4.1 Single phase flow It usually refers to the liquid-phase or vapour-phase flow within the pipe. When validating numerical results of a diabatic fluid flow relative to a various flow conditions; single phase experiments are the first set of tests to be compared against the experimental results. In this context, it is essential to determine the local liquid-phase heat transfer coefficients accurately. To conduct this, the experiment has been carried out with low heat flux so as to avoid the appearance of vapor bubbles in the flow. 4.1.1 The experimental heat transfer coefficient The experimental heat transfer coefficient can be obtained by calculating the liquid temperature Tl,bulk from the heat balance (Eq. 15) and by measuring the surface temperature of the heated section. Having measured the temperature of the inner surface of the thin-wall heater, the temperature of the outer wall Tw can be obtained by solving a steady-state heat conduction equation for cylindrical geometries.The heat transfer coefficient is defined by the following relation: hfc ¼

/w ðTw  Tl;bulk Þ

ð13Þ

where h is the local heat transfer coefficient [W/(m2 K)], q is the heat flux (kW/m2), and Tw and Tl,bulk are respectively the wall and fluid temperature (K). The Dittus–Bo¨lter correlation is given by hfc

av

¼ 0:023

kl Re0:8 Prl0:4 Dhyd l

ð14Þ

Heat balance in the single-phase liquid flow was also checked across the test channel to calculate the liquid temperature. _ pl ðTl;bulk ðxÞ  Tinlet Þ QðxÞ ¼ mC

ð15Þ

where m_ is the mass flow of the coolant, TInlet, the inlet temperature, Cpl liquid specific heat and Q(x) is the overall heat flow rate within the heating length x. Hence, by rearranging Eq. 15, the local bulk temperature:

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Tl;bulk ðxÞ ¼ Tinlet þ

QðxÞ _ pl mC

ð16Þ

is used to determine the local heat transfer coefficient below: hðxÞ ¼

/w ðTw ðxÞ  Tl;bulk ðxÞÞ

ð17Þ

The average heat transfer coefficient is obtained by the following integral: Z 1 L hfc av ¼ hx ðxÞdx ð18Þ L 0 This integral is also calculated by trapezoidal rule as follows: 1 Xn hfcav ¼ ½h ðx Þ þ hx ðxiþ1 Þðxiþ1  xi Þ ð19Þ i¼1 x i 2L 4.1.2 Results and discussion The evolution of axial wall temperature profile along the test section is shown in Fig. 7. Very good agreement has been found between measured temperatures are the calculed value by ANSYS CFX code. The wall temperature profile from the Fig. 11 (left) shows a gradual increase in temperature downstream the measuring section followed by a sudden temperature drop at the last measurement point. This can be attributed to the boundary effects of the test section. Nevertheless, the fluid (R11) temperature profile along the test section has also been plotted in the Fig. 11 (right). The coolant temperature increase along the section is linear. Here, the temperatures at the outlet of the test section that are estimated from the heat balance perfectly match the experimental values. Figure 12 shows the axial variation of the heat transfer coefficients along the heating section. The heat transfer coefficients were modelled with the CFD code, measured experimentally and, calculated with the Dittus–Boelter equation. The average experimental value was calculated for the first six measurements only that are unaffected by the outlet effects. The average experimental value of 1,255 W/m2 K is between the modelled HTCs with the ANSYS CFX (1,156 W/m2 K) and the calculated results obtained from the Dittus–Boelter correlation (1,385 W/m2 K). Thus a maximum deviation does not exceed 10 %. It should be noted that the Dittus–Boelter correlation as written in Eq. 14 has been established for the circular tubes while it can be applied in fully developed turbulent flows, i.e. Re  104 , 0:7  Pr  100 and, DL  60

Heat Mass Transfer

Fig. 11 Axial wall temperature (left) and liquid temperature (right) profiles for mass velocity 622 kg/m2 s and heat flux 1.8 W/cm2

Fig. 12 Comparison of the experimental and calculated heat transfer coefficients along the measuring section for mass velocity 622 kg/ m2 s and heat flux 1.8 W/cm2

4.2 Boiling flow In a reactor channel, the creation of vapor bubbles on the outer surface of the fuel pin will have adverse consequences on the integrity of the fuel elements. Initiation of boiling is considered the first safety limit not be achieved in a research reactor. However, when boiling is foreseen in the design of the reactor, surface temperatures have to be maintained sufficiently low not to exceed the critical heat flux conditions. In this context, accurate prediction of different flow boiling heat transfer mechanisms and their transitions is essential for safe and reliable operation of these systems.

Fig. 13 Schematic description of the axial void fraction profile in the subcooled boiling regions for upward vertical flow

When the wall becomes superheated, vapour bubbles can form even when the core liquid is still subcooled. The position where the first bubbles occur at the wall is denoted as the ONB. According to this criterion, a bubble will grow from a vapour embryo occupying a cavity in the wall if the liquid temperature at the tip of the embryo is at least equal to the saturation temperature corresponding to the bubble pressure. As shown in Fig. 13, the subcooled boiling region in vertical upward flow is commonly divided into two major regions, i.e. ‘‘highly subcooled’’ and ‘‘low subcooling’’ region. Just downstream of ONB, the bubbles are still small enough that they remain attached to the heater surface. Farther downstream, as the bulk liquid temperature increases, the bubbles grow larger and begin to depart from their

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sites of origin. These bubbles then slide along the heater surface and eventually lift off from the wall. The location where the bubbles begin to lift off from the heated wall is called the location of Onset of Significant Void (OSV). In the region between ONB and OSV, the void fraction is small but increases rapidly downstream of OSV. Ultimately, if heating continues with the same pace, the DNB will occur. Le Corre et al. [20] analysed the available experimental data on CHF under subcooled flow boiling conditions. They distinguished three dominant DNB flow regimes. Bubbly flow [21] is namely observed under high mass velocities and high subcoolings, which are typical operating conditions for PWR reactors. As subcooling becomes moderate, Vapour clots type is observed [22]. The last type of DNB flow regime, Slug flow is usually observed under low mass velocity and near saturation. As DNB phenomenon and associated problems go beyond the scope of the present article it will not be further discussed herein. Fig. 14 ONB and OSV experiment at 996 kg/m2 s mass velocity and heat flux of 4.6 W/cm2

4.2.1 Onset of nucleate boiling The required wall superheat at the ONB point is defined according to: Bergles and Rohsenow (from Collier 1981); 5  qw 1:156 0:463p0:0234 DT w;ONB ¼ ðTw  Tsat ÞONB ¼ p 9 1100 ð20Þ Frost and Dzakowic; DTw;ONB ¼ Tw;ONB  Tsat ¼

8r/Tsat qg hlg kl

!0;5 Prl

Or Saha and Zuber 8 /w Dhyd > > Pe\70; 000 < Tsat  0; 0022 kl Tl;OSV ¼ /w > > Pe [ 70; 000 : Tsat  153,8 Gcql

ð21Þ

ð22Þ

where p is in kPa, DTw,ONB is in °C, and qw is in W/m2, r in N/m and Pe is Peclet number 4.2.2 Results and discussion To highlight the boiling initiation, the experimental conditions of the Exp 4 (Table 2) were performed by gradually increasing the heating power until the appearance of the vapor bubbles in the fluid flow. The data acquisition system and the test section outer glass allowed not only for quantitative measurements, but also visual inspection of the boiling phenomenon. It is possible to follow in real time the evolution of the wall temperature and the bubble occurrence at two distinct points in the channel. One is

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located 75 cm far from the channel inlet in a single phase flow region, whereas the other is set further 10 cm downstream the test section in a zone where bubbles are generated. The two zones are clearly distinguished in the Fig. 14. To illustrate the wall temperature behaviour during the experiment, the readings from the corresponding thermocouples TC6 and TC7 are also plotted in the figure. In fact, during the increasing power while the flow is single phase over the whole length of the channel, the temperatures are increasing with increasing power. Here, TC7 is always slightly higher than TC6. After 10 s, the two temperatures are stabilized at constant values when the heat flux is maintained at 4.6 W/cm2. In this region, it is noticeable that even though the average bulk fluid temperature is increased downstream the heating section, TC7 indicates lower temperature than TC6. It means that, in this region heat extraction from the heating wall is much better than the heat transfer in the region with a single phase flow. Hence, initiation of the fluid boiling significantly enhances heat transfer. However, vapour generation becomes more pronounced with the onset of significant void (OSV) where bubbles begin to lift off from the heated wall (Fig. 14). The same experimental conditions were applied during the simulation studies with the ANSYS-CFX. The wall temperature profiles obtained from the numerical simulations are compared against the experimental data and selected correlations. The axial evolution of the calculated R11 radial temperature profiles is presented in Fig. 15. The numerical results show that the temperature of R11 increases linearly along the channel up to the initiation of the boiling phenomenon. Since the wall temperature is locally decreased

Heat Mass Transfer Fig. 15 Radial temperature profiles at different cross sections along the heating length. Data refer to R11 mass velocity of 996 kg/m2 s and heat flux of 4.6 W/cm2

Fig. 16 Radial temperature profiles at different cross sections downstream the TC6 location at 75 cm from the test section inlet. Data refer to the mass velocity of 996 kg/m2 s and heat flux of 4.6 W/cm2

in that region while the average bulk temperature increases continuously, the liquid radial temperature profiles become more flattened. This is well illustrated in Fig. 16 where the radial temperature profiles from readings corresponding to the locations downstream the TC6 are presented. The increase in liquid temperatures of R11 can be attributed to different heat transfer mechanisms, of which a substantial share is associated to the latent heat of condensation of the bubbles downstream the ONB. The plot of the contours of the void fraction for both sections clearly shows that the generation of steam is much higher at 85 cm from the test section inlet compared to the location at 75 cm (Figs. 17, 18).

Fig. 17 Void friction distribution at 75 cm from the test section inlet. Simulation results refer to the mass velocity of 996 kg/m2 s and heat flux of 4.6 W/cm2

Although the Kurul and Podowski [11] model is not based on flow pattern, it takes into account a criterion that OSV occurs when wall temperature exceeds the saturation temperature. This is different from the criteria of OSV and ONB based on more physical considerations such as Bergles and Rohsenow (Eq. 20), Frost and Dzakowic (Eq. 21), Saha and Zuber (Eq. 22). However, when sufficient superheating is achieved the evaporation is initiated and maintained downstream the ONB. Followed by the OSV the importance of predicting ONB is significant. Indeed,

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Heat Mass Transfer

Fig. 18 Void friction distribution at 85 cm from the test section inlet. Simulation results refer to the mass velocity of 996 kg/m2 s and heat flux of 4.6 W/cm2

Fig. 19 Experimentally defined location of ONB occurrence and the calculated boundaries corresponding to the measured saturation

one of the main considerations of the OSV criterion during the flow boiling process is related to the axial position of the wall boiling phenomenon occurrence. Figure 19 illustrates the ONB position’s dependence on mass velocity for a heat flux of 4.6 W/cm2 and an inlet temperature of 25 °C. The theoretical position of ONB versus mass velocity has been plotted on the same graph for a given heat flux and inlet subcooling. The data clearly show that the position of the ONB is moving towards the

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Fig. 20 Cross-section averaged void fraction along the measuring section

exit channel when mass flux is being increased. Not only does the ONB depend on liquid subcooling, it is also strongly related to the saturation temperature. The last depends solely on pressure when pure fluids such as R11 are considered. Because periodical pressure oscillations between 0.14 and 0.16 MPa have taken place during the experiment the two theoretical boundaries have been plotted in the figure. The effect of heat flux on the axial void fraction distribution is shown in Fig. 20 for a selected mass flux. The increase of the calculated void fraction gradient (at about Z = 0.4 m) coincides with the ONB in our experiment (Fig. 19). The predicted decrease in slope of the axial void fraction downstream the Z = 0.4 m, is probably caused by sudden variation in heat flux partitioning mechanisms. This led us to plot the distribution of different wall boiling parameters shown in Figs. 21, 22, 23 and 24. Figures 21 and 22 shows the evolution of the heat flux associated to the liquid and to the vapour phase respectively. The calculated components are obtained from the Kurul and Podowski [11] heat flux partitioning model. Although the subcooling is relatively high (*12 °C), the applied heat flux is sufficient to initiate boiling at the beginning of the heated section. Although the single-phase convection heat transfer is dominant over the entire length of the heated section, it is progressively decreasing with different rates in the first 0.4 m of the test section. After this point the single phase convective heat transfer is increasing again at the expense of the quenching and evaporation heat fluxes.

Heat Mass Transfer

Fig. 21 Axial evolution of the quenching and evaporation heat flux

Fig. 22 Axial evolution of the single-phase convection heat flux to the liquid

This turnaround in heat transfer mechanisms could be explained with bubble induced mixing. In fact, bubbles are attached on the wall downstream the ONB. Convection is relatively small, hence the wall temperature is increased and the nucleation sites are multiple, while vapor generation is controlled with smaller bubbles and corresponding frequencies. Once the OSV conditions have been reached, bubble induced turbulence becomes important. Higher turbulence enhances single phase heat transfer and mixing with the bulk fluid; this in turn reduces superheating in the near wall region and subcooling outside the boundary layer. Lower superheating reduces active nucleation site

Fig. 23 Axial evolution of the nucleation site density

Fig. 24 Axial evolution of the bubble departure diameter

density (Fig. 23), while reduced subcooling increases bubble departure diameters (Fig. 24). Since constant heat flux is applied in the system, the heat flux associated to the boiling process (Fig. 22) is penalized with the enhanced single-phase hear transfer (Fig. 21).

5 Conclusion A flow boiling of refrigerant R-11 in a vertical annular channel has been simulated by the CFX code. The simulation results have been validated against Birine Nuclear Research Center (CRNB) experimental data. The experimental wall temperatures are reasonably well predicted, the

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Heat Mass Transfer

Kurul and Podowski heat partitioning wall boiling model is adequate for calculation of the wall temperature. By predicting the temperature at the wall surface, critical regions can be identified. This strengthens our determination, both on the experimental and numerical modelling level, to better predict the parameters that may lead to the departure from the nucleate boiling DNB. Acknowledgments The authors gratefully acknowledge close cooperation with researcher Bosˇtjan Koncˇar from Reactor Engineering Division at Jozˇef Stefan Institute in Slovenia.

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