HEFAT2002 1 ST international Conference on Heat Transfer, Fluid Dynamics and Thermodynamics 8-10 April 2002, Kruger National Park, South Africa KS1
INSIGHT INTO MECHANICSMS AND REVIEW OF AVAILABLE MODELS FOR CRITICAL HEAT FLUX (CHF) IN POOL BOILING
Satish G. KANDLIKAR Department of Mechanical Engineering Rochester Institute of Technology Rochester, NY 14623
[email protected]
ABSTRACT Greek Symbols Critical Heat Flux (CHF) has been a subject of interest for boiling equipment designers from design as well safety as viewpoints. Although considerable data exists in literature, a fundamental knowledge of the mechanisms responsible for the CHF phenomenon is needed to develop better predictive methods and efficient enhancement strategies. A critical assessment of the CHF models available in the literature is presented here, highlighting the needs for future research in this area.
φ - angle of inclination of the tube with horizontal ψm - cavity mouth angle, degrees µL – liquid viscosity, Ns/m2 θ - contact angle, degrees ρ L , ρ G - liquid and vapor density, kg/m3 σ - surface tension, N/m
1. INTRODUCTION NOMENCLATURE Dc – cavity mouth diameter, m g – acceleration due to gravity, m2/s h – heat transfer coefficient, W/m2K h L – single phase heat transfer coefficient with liquid phase, W/m2K iLG – latent heat of vaporization, J/kg k – thermal conductivity, W/mK K – contstant in eq. (4) Na – number of active cavities, number/cm2 Nas – number of available cavities, number/cm2 q – heat flux, W/m2 q C – critical heat flux, W/m2 Tsat – saturation temperature, K ∆Tsat - wall superheat, K
∆Tsat,ONB - wall superheat at ONB, K u- flow velocity, m/s v LG – specific volume difference between vapor and liquid, m3/kg
Critical Heat Flux, or CHF, represents the maximum heat flux that can be dissipated by nucleate boiling. Any further increase in the wall superheat leads into transition boiling mode with deterioration in the accompanying heat transfer rate. In heat flux controlled systems, CHF represents the point of discontinuity where an increase in the heat flux causes a rapid temperature excursion in the wall temperature, terminating nucleate boiling and leading into film boiling mode of heat transfer. As early as in 1888, Lang [1] recognized through his experiments with high pressure water that as the wall temperature increased beyond a certain point, it resulted in a reduction in the heat transfer rate in a nucleate boiling system. However, it was Nukiyama [2] who realized that the “maximum heat transmission rate” might occur at relatively modest temperature differences. Drew and Mueller [3] present an excellent summary of the historical development in this area. A recent survey of the critical heat flux literature is presented by Kandlikar [4].
2. THERMAL AND HYDRODYNAMIC CONDITIONS PRIOR TO CHF
required for the bubble to grow beyond the cavity opening, (same as ∆Tsat ,ONB ), was obtained as
The models proposed in the literature are generally based on the physical phenomena that are supported by experimental evidence. A brief overview of the thermal and hydrodynamic conditions existing on the heater surface prior to reaching CHF is presented in this section. 2.1 Nucleation and Bubble Dynamics Bubble Characteristics over the Nucleate Boiling Range: The bubble characteristics during nucleate boiling was investigated with a high-speed motion camera by Gaertner [5]. He identified different regions based on these characteristics as illustrated in Fig. 1. In the initial phase of nucleate boiling, discrete bubbles are formed over isolated cavities. As the heat flux increases, the bubbles depart in rapid succession forming vapor columns as shown in Fig. 1(b). Subsequently, the neighboring vapor columns merge into a large bubble. This large bubble is referred to as a vapor patch by Zuber [6], and as a hovering bubble by Haramura and Katto [7]. The thin liquid film existing under the large bubble is referred to as the macrolayer. Existence of such macrolayer has been confirmed by Kirby and Westwater [8] and Yu and Mesler [9]. Further increase in the heat flux results in a broader coverage of the heater surface with the large bubbles as shown in Fig. 1(c). Subsequently, the critical heat flux is reached, beyond which point, the degradation caused by the large vapor coverage offsets the increase in the heat transfer due to rapid bubble growth and efficient heat transfer in the macrolayer. The focus of the present discussion is on the exact mechanism that causes the transition from the region depicted in Fig. 1(c) to the CHF condition. Nucleation Site Density: The key elements of pool boiling are bubble nucleation and bubble growth followed by coalescence with neighboring bubbles, and collapse or departure from the heater surface. For a given wall superheat, the range of active cavity sizes is determined by the cavity size distribution on the heater surface. At high heat fluxes, a large number of small diameter cavities are activated. The size and shape of a cavity governs its nucleation characteristics. Griffith and Wallis [10] postulated that as a bubble grows in a cavity, it comes at the mouth of the cavity and assumes a hemispherical shape. This state also represents the point where the radius of curvature of the interface is a minimum. The cavity is assumed to be active when a bubble grows past this condition. Employing the Clasius-Clapeyron equation for the pressure difference between the vapor inside the bubble and the surrounding liquid, the wall superheat
Figure 1. Bubble characteristics in different regions of nucleate boiling, Gaertner, [5].
∆Tsat,ONB =
4σ Tsat ρV i LG Dc
(1)
where Dc is the cavity mouth diameter, m. It is seen that the wall superheat to activate a cavity varies inversely with the cavity diameter. Smaller cavities are activated at higher wall superheats. Subsequently, Hsu [11] and Sato and Matsumura [12] considered the temperature profile in the liquid and suggested that the hemispherical bubble on a cavity will grow if the liquid temperature at the tip of the bubble was above the saturation temperature corresponding to the vapor pressure inside the bubble. Assuming that cavities of all sizes are available, the following expression for the wall superheat at the onset of nucleate boiling, ONB, was obtained.
∆Tsat,ONB
4σ Tsat v LG h L = k L i LG
k L i LG ∆Tsub 1 + 1 + 2σ Tsat v LG h L
(2)
Hsu, and Sato and Matsumura also obtained an expression for the range of active cavity radii. In deriving the above equation, the liquid temperature at the bubble tip was calculated from the single-phase convection heat transfer coefficient in the liquid phase. As boiling progresses, the actual heat transfer coefficient increases progressively. It is therefore expected that nucleation will progress toward smaller cavity sizes more rapidly with an increase in the wall superheat. Indeed, the nucleation site density increases rapidly with an increase in the wall superheat. Nucleation is also facilitated by the availability of vapor from neighboring sites. Following a mechanistic approach, Wang and Dhir [13, 14] derived the following relationship between the nucleation site density and the wall superheat.
N s ( sites / cm2 ) = 5.8 ×10 −5 Dc
−5. 4
(3)
value of wall superheat. The conditions near the wall are therefore very crowded with nucleating bubbles. 3. CHF MODELS CONSIDERATIONS
• • • •
• •
Since the wall superheat is inversely proportional to the cavity diameter, it follows that the nucleation site density varies 5 .4 ∆Tsat . Dhir [15] presented a plot showing this relationship for different values of contact angle (θ ) and cavity mouth opening angle (ψ m ). Figure 2 shows such a plot for a contact
as
angle of 18° and cavity mouth angles below 90°. It can be seen that the number of active cavities increases quite dramatically for smaller cavity diameters (on the order of a few micrometers). Relating the active site density information to the critical heat flux condition, it becomes clear that a large number of cavities, with very small diameters, are activated at the high
ON
HYDRODYNAMIC
As the heat flux is increased to the critical heat flux value, vapor generation rate increases and presents an increasing resistance to the liquid flowing toward the heating surface. The hydrodynamic models of CHF are based on the instability encountered at the liquid-vapor interface. The exact location of the interface where the instability sets in is somewhat different in different models presented in literature:
•
Figure 2 Active nucleation site density variation with cavity mouth diameter, Dc , for a contact angle θ =18° and cavity mouth angle ψ m
