A study and comparison of nucleate boiling with analytical and Computational formulation

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International Journal on Theoretical and Applied Research in Mechanical Engineering (IJTARME)

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ISSN (Print): 2319-3182, Volume -6, Issue-1-2, 2017 43

A study and comparison of nucleate boiling with analytical and Computational formulation

1Sandeep P. Kunjeer, ²Vishal A. Meshram

1Senior Support Engineer, ESI Software (India) Pvt. Ltd., Pune

2Asst. Prof., Mechanical Dept. ICEM, Pune Email : ¹[email protected], ²[email protected] Abstract — A wide variety of empirical equations are

available for the transition to nucleation boiling. This paper deals with comparison of mass flow rate of water evaporate calculated from analytical equations and with CFD results.

The transient CFD analysis is carried out to calculate amount of water evaporates considering the mixture of water-vapor. The formation of vapor bubbles during nucleate boiling process is captured with CFD approach.

Index Terms — Nucleate boiling, analytical correlation, CFD, VOF approach

I. NOMENCLATURE

CFD Computational Fluid Dynamics Subscript:

Specific heat of liquid, J/kg-⁰C

Experimental constant that depends on surface-fluid combination

Gravitational acceleration, m/s² Enthalpy of vaporization, J/kg The rate of evaporation of water, kg/s Experimental constant that depends on the fluid

Prandtl number of the liquid

The rate of heat transfer during nucleate boiling, Watt

Nucleate boiling heat flux, Watt

Surface temperature of heating surface, ⁰C Saturation temperature of fluid, ⁰C Greek:

Density of liquid, kg/m³ Density of vapor, kg/m³

Surface tension of liquid-vapor interface, N/m

Viscosity of liquid, kg/m- s

II. INTRODUCTION

Boiling is a complicated phenomenon as the large number of variables involved in the process and complex fluid motion patterns caused by the bubbles

At the early stages of boiling, it will not notice anything significant except some bubbles that stick to surface of pan. These bubbles are caused by the release of air

molecules dissolved in liquid water and should not be confused with vapor bubbles. As water temperature rises, it will notice chunks of liquid water rolling up and down as a result of natural convection currents, followed by the first vapor bubbles forming at the bottom surface of the pan. These bubbles get smaller as they detach from the surface and start rising, and eventually collapse in the cooler water above. The intensity of bubble formation increases as the water temperature rises further, and it will notice waves of vapor bubbles coming from the bottom and rising to the top when water temperature reaches the saturation temperature.

The four different boiling regimes are observed; natural convection boiling, nucleate boiling, transition boiling and film boiling. A pure substance at specified pressure starts boiling when it reaches the saturation temperature at that pressure. But in practice we do not see any bubbles forming on the heating surface until the liquid is heated a few degrees above the saturation temperature (about 2 ^oC to 6 ^oC for water). The liquid is slightly superheated in this case and evaporates when it rises to the free surface. The fluid motion in this mode of boiling is governed by natural convection currents, and heat transfer from the heating surface to the fluid by natural convection.

The first bubble starts forming at various preferential sites on the heating surface. The bubbles form at an increasing rate at an increasing number of nucleation sites as move along the boiling curve. The nucleate boiling regime can be separated into two distinct regions. In first region, isolated bubbles are formed at various preferential nucleation sites on the heated surface. But these bubbles are dissipated in the liquid shortly after they separate from the surface. The space vacated by rising bubbles is filled by the liquid in the vicinity of the heater surface, and the process is repeated.

In second region, the heater temperature is further increased, and bubbles form at such great rates at such a large number of nucleation sites that they form numerous continues columns of vapor in the liquid. These bubbles move all the way up to the free surface, where they break up and release their vapor content, the large heat fluxes obtainable in this region are caused by the combined effect of liquid entrainment and evaporation [5].

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The amount of heat taken for the evaporation is proportional to the part of the heating surface covered by the active nucleation sites while the rest of the surface is subjected to the liquid surface natural convection. The intensification of the heat transfer is hence driven by the continuous activation of the nucleation sites upon heating [1].

III. PROBLEM DEFINITION

A two-phase mixture of water is considered within pot.

The two-phase mixture consists of 90% of water liquid and 10% of water vapor within a pot. The two-dimensional pot of 300mm X 200mm is considered for the analytical and CFD calculations. The geometrical representation of two dimensional pot as shown in Fig. 1.

Fig.1 Geometrical representation of pot

These dimensions of the pot needs to be consider for the calculation of mass of water evaporates with analytical and later it compares with CFD

IV. ANALYTICAL FORMULATION

In the nucleate boiling regime, the rate of heat transfer strongly depends on the nature of nucleation. The type and the condition of heated surface also affect the heat transfer. The most widely used correlation for the rate of heat transfer in the nucleate boiling regime was proposed in 1952 by Rohsenow, and expressed as equation (1) below;

(1) The surface tension at liquid-vapor interface is given in [5] for water. The experimental value of constants are given in [5] for water-stainless steel combination. The values of surface tension, constants and Prandtl number are mention in Table 1 below;

Table 1: Values of surface tension, coefficients and Prandtl number

(N/m) 0.0589

Coefficients

= 0.0130 n =1 1

The other unknowns from the equation (1) are determined from the steam table for of 100 ^oC.

The rate of heat transfer during nucleate boiling is calculated by equation (2) as mention below;

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The rate of evaporation of water is determined by equation (3) as mentioned below;

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The rate of evaporation of water is calculated as 0.0241 kg/s

V. CFD METHODOLOGY

The main area of interest in CFD simulation is to observe the formation of bubbles during nucleation boiling process. A 2D simulation is carried out by assuming flow as laminar. The Volume of Fluid (VOF) multiphase approach is considered for the mixture of water-liquid and water-vapor. This two phase mixture is consists of 90% of water liquid and 10% of water vapor. This CFD simulation is carried out with help of Ansys-Fluent CFD code. The simulation is carried out for total time of 0.033 sec. The boundary conditions used for CFD simulation are mention in Table 2.

Table 2: Representation of boundary conditions respect to zones of the domain

Zones Boundary Condition Quantity Unit

Bottom wall Temperature 110 ^oC

Other walls Adiabatic walls - -

Mixture Temperature 17 ^oC

The Fig 2 shows the representation of volume fraction of liquid in water-liquid and water-vapor mixture. Fig. 2 also shows the representation of formation of vapor bubbles at enlarged region of pot shown with square boundary.

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Fig.2 Representation of volume fraction of water liquid in the mixture of water liquid and water vapor Initially, isolated bubbles are formed at the bottom surface of pan. As time progress, the bubbles form at such large number of nucleation sites. The bubbles move towards sides and top surface, where they break up and release their vapor content as shown in Fig 2.

The rate of heat transfer is directly obtained from the Ansys-Fluent code. Dividing this heat transfer rate by , the rate of evaporation of water is calculated as 0.0375 kg/s

VI. RESULTS AND DISCUSSION

The Table 3 shows the mass flow rate of water evaporates obtained from the analytical correlations and CFD approach;

Table 3: Representation of rate of mass flow rate of water evaporates

Approach Rate of water evaporates (kg/sec) (grams/sec) Analytical correlations 0.0241 24.1

CFD 0.0375 37.5

The variation in the mass flow rate of water evaporate is observed due to the assumptions mentioned in analytical and CFD procedure. The analytical correlations which are mentioned in equation (1) to equation (3) are exists for steady operating condition only. Also the motion of water vapor from pot bottom to free surface of liquid may not be taken in to consider more accurately. The top surface of pot is also free to atmosphere. On the other side, CFD approach is carried out for transient operating condition, because of formation of bubbles can’t exist at steady operating condition. Also the motion of bubble can’t predict with CFD approach more accurately, due to the

assumption of laminar flow of the water liquid and water vapor mixture. The top surface of pot is assumed as adiabatic wall.

VII. CONCLUSION

The nucleate boiling regime, first isolated bubbles are formed at various preferential nucleation sites on the heated surface. These bubbles are dissipated in the shortly after they separate from the surface. The space vacated by the rising bubbles is filled by the liquid in the vicinity of the heated surface and process is repeated. On the other hand if heater temperature is further increased, the bubbles form at such great rates at such a large number of nucleation sites. These bubbles are move all the way up to the free surface, where they break up and release their vapor content. Hence motion of this bubbles are needs to be captured more accurately. Currently, CFD analysis is carried out by considering flow as laminar. In future stage CFD analysis is need to be carried out by considering flow as turbulent to capture the motion of the bubbles through water liquid more accurately.

REFERENCES

[1] B. V. Balakin, M. I. Delov, A. Kosinska, K. V.

Kutsenko, and A. A. Lavrukhin, “Heat transfer during transition to nucleate boiling,”

International Journal of Heat and Mass Transfer, pp. 1101-1105, 2015.

[2] J. M. Saiz Jabardo, “Nucleate Boiling Heat Transfer”, ECI International Conference on Boiling and Heat Transfer, 3-7 May 2009.

[3] Mohamed S. El Genk, Arthur Suszko, “Effect of inclination angle and liquid subcooling on nucleate boiling on dimpled copper surfaces,” International Journal of Heat and Mass Transfer, no. 5, pp.

650-661, 2016.

[4] S. Fau, W. Bergez, C. Colin, “Transition between nucleate and Film boiling in rapid transient heating”, Experimental Thermal and Fluid Science, pp.118-128, 2017.

[5] Yunus A. Cengel, “Heat and Mass Transfer,”

TATA McGRAW HILL, vol. ED-03, pp. 562-573, 2007.

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