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CHAPTER4 Nucleate Boiling Heat Transfer and Forced Convective Evaporation

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## CHAPTER4 Nucleate Boiling Heat Transfer and Forced Convective Evaporation

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**CHAPTER4 Nucleate Boiling Heat Transfer**and Forced Convective Evaporation • Topics to be presented in this chapter • Onset of Nucleate Boiling • Subcooled Nucleate Boiling • Saturated Nucleate Boiling and Two-Phase Convective Heat Transfer**4.1 Onset of Nucleate Boiling**• Review of single-phase heat transfer • Energy balance dz D Z Wf(kg/s)**Length of subcooled region, zsc**• Let zsc be the entrance length where , zsc can be • determined by the following equation.**Wall temperature distribution in single-phase region**For turbulent flow in a pipe Dittus-Boeiter correlation However, it is commonly used in entrance region.**Boiling incipience (Onset of subcooled nucleate boiling)**• For boiling to occur Tw must be at least ≧Tsat Non-boiling region**Recall that, assuming that a wide range of cavity size**available, • for the onset of nucleate boiling. • For water, the correlation of Bergles and Rohsenow’s correlation • maybe used: • For a tube with a constant heat flux, , a mass flux, G, the location • of boiling incipience may be evaluated in the following way:**Relation between heat flux and wall**superheat at the position incipient boiling (Form Hino & Ueda, 1985 Int. J. Multiphase Flow vol.11, No.3, pp.269-281 )**Boiling hysteresis**Partial subcooled nucleate boiling Fully developed subcooled nucleate boiling Single-phase liquid Non-boiling region**Boiling curve hysteresis**Wall temperature profiles Form: Hino and Ueda, 1985, “Studies on Heat Transfer and Flow Characteristics in Subcooled Flow Boiling – Part1, Boling Characteristics,” Int. J. Multiphase Flow, vol.11, pp.269-281**Experimental data for the onset of boiling compared with eq.**(Forost and Dzakowic34) Form Collier, 1981**4.2 Heat Transfer in Subcooled Nucleate Boiling**I. Partial subcooled boiling i. Few nucleation sites ii. Heat transferred by normal single-phase process between patches of bubble + boiling II.Fully developed subcooled boiling i. Whole surface is covered by bubbles and their influence regions. ii. Velocity and subcooling has little or no effect on the surface temperature.**Partial subcooled boiling**Subcooled boiling heat transfer Single-phase heat transfer**Values of Csf in eq. Obtained in the reduction of the forced**(and natural) convection subcooled boiling data of various investigators (Form Collier, 1981)**Full developed**E ● Partial ● C ● B ● ● Wall temp**Bergles and Rohsenow correlation**• Calculation procedure • Pick Tw • Evaluate and • Determine “C”, ie • form the incipience boiling model • Evaluate from fully-developed • equation but setting**Fully developed subcooled boiling**• -Surface is covered by bubbles and their influence region**-Velocity and subcooling has little or no effect on the**surface temperature Low subcooling High subcooling H Low G L High G H H Fully developed boiling L L**Correlations for fully developed subcooled boiling**• -Jens and Lottes correlation(1951) • -Ranges of data for water only • i.d = 3.63 to 5.74 mm , P = 7 to 172 bar , Tl = 115 to 340℃ • G = 11 to 1.05×10-4 kg/m2s , up to 12.5 MW/m2 • -Thom et al (1965) • for water only**-Jens and Lottes correlation in terms of heat transfer**coefficients**At P=70bar**At P=150bar**It is summarizes the present data of heat transfer of**subcooled flow boiling of water in the swirl tube and hypervapotron under one side heating conditions. The data are obtained by experiments in regions fro non-boiling to highly subcooled partial flow boiling under conditions that surface heat fluxes, flow velocities, and local pressure range form 2 to 3 MW/m2, 4 to 16 m/s and 0.5, 1.9 and 1.5 MPa respectively. In the figure, a new heat transfer correlation for such subcooled partial flow boiling under one sides heating conditions on which no literature exists is proposed. Heat transfer of subcooled water flowing in a swirl tube(Form: S.Toda, ”Advanced Researches of Thermal-Hydraulics under High Heat Load in Fusion Reactor,” Proc. NURETH-8. pp.942-957,1997)**-Shah(1977), ASHRAE Trans. Vol.83, Part1, pp.202-217**-Valid for subcooled nucleated boiling of water, refrigerants and organic fluids, Ref >10000**-Correlation of Bjorge, Hall and Rohsenow, 1982**Int. J. Heat Mass Transfer, vol.25, No.6 pp.753-757 For subcooled and low quality region BM Depends upon boiling surface cavity size distribution and fluids properties For water only, BM=1.89×10-4 in SI units.**Comparison of equation with data of Cheng et al.**From: Bjorge, Hall and Rohsenow, 1982**4.3 Saturated Forced Convective Boiling Evaporation**• -The associated two-phase flow pattern may be bubby, • slug or annular flow • -Assumption of thermodynamic equilibrium is acceptable • -Heat transfer coefficient may be strongly dependent upon • the heat flux and the mass quality. • Quality change in saturated flow boiling**Subcooled**Superheated DNB Saturated Saturated nucleate boiling B Dryout D Two-phase forced-convective heat transfer 0 1 From: Collier & Thome, 1994**-Saturated nucleate boiling**• -Essentially identical to that in the subcooled regions • with zero subcooling. • -Empirical correlation in fully developed subcooled • boiling may be used. • -Suppression of nucleate boiling in two-phase forced convection. • As will be discussed later, in two-phase forced convection • There is a possibility that ΔTsat(=q〞/hTP) • is so low that nucleate boiling will be suppressed.**Heat transfer in vertical annular flow**• Ref.:Ch6 and 9 in Butterworth & Hewitt. • -When boiling is suppressed, heat transfer in two-phase • forced convection can be in a form of annular flow. • -Triangular Relationship • There are three dependent variables in vertical annular two-phase • flow. Any of them can be calculated from a knowledge of the other • two. The knowledge of these three variables are important for the • determination of heat transfer coefficient.**For example, can be calculated from**• by the following procedure: • Evaluate the interfacial shear stress, τi • Force balance on the control volume gives ● ● ● ● ● ● ● ● ● ● P Liquid film Vapor flow**(2) Calculate τ(r)**Force balance on the control volume gives, dz P Vapor flow Liquid film**(3) Calculate the velocity distribution in the film**by integration of the expression (4) Integrate the velocity profile across the film to give**Interfacial waves in annular flow**• -A rough rule of thumb: • “If the liquid film occupies 10% by volume of the channel • then the pressure drop increases by a factor of 10 for the same • total gas flow through the channel compared with the smooth • dry pipe. This gross increase is principally caused by the interfacial • waves.” • -Two distinct types of wave: • (1) Ripples-“Acts as a surface roughness and giving rise to an • increased pressure drop.” • -Do not result in droplet entrainment. • (2) Disturbance waves:(most of cases) • -Highly disturbed interface, several times the mean • film thickness in height. • -Entrainment occurs by the tearing away of film, which • beaks up from the surface of the waves.**Transport of energy in the liquid film**• -Energy equation • Assumption • 1.Steady state • 2.Constant properties • 3.Negligible axial conduction • 4.Negligible viscous dissipation • 5.The flow is one-dimensional • 6.Because of the film is quite thin, the film may be treated as a slab. u z y**Defining the average bulk temperature as:**• Laminar flow solutions • Assume (all the energy is used for evaporation) • and high interfacial shear . • High shear stress with phase change is usually associated with • evaporation in up-ward flowing system.**The flow field is basically driven by the interfacial shear**stress (gravity is negligibly small)**Turbulent flow solutions**-If turbulent eddies are present within the film, the apparent thermal conductivity and hence the heat transfer coefficient significantly will be increased for a given film thickness. -Assumption (1) (2) film surface is flat (3) heat transfer is not affected by the droplets -Model**εH = eddy thermal diffusivity**εM = eddy viscosity εH～εM has usually been assumed in theoretical studies of heat transfer in liquid film. Assume that εM is related to y in the film in the same way as in single-phase full-pipe flow. For example Deissler Model:**Von Karman Model:**Define the nondimensional temperature in the following way:**Recall that**Thus,**To solve T+, u+ needs to be calculated first. u+ depends on**the shear stress and film mass flow rate. Once u+ is determined, T+ can be evaluated and h can be determined accordingly. An approximate approach –following Butterwoth & Hewitt Assume comparing to as in a full-pipe flow and recall that**Assume universal velocity profile, i.e.,**u+=y+, y+ ≦ 5 (viscous sublayer) u+=-0.305+5ln(y+), 5<y+≦30 (buffer zone) u+=5.5+2.5ln(y+), y+ > 30 (turbulent cure) a discontinuity at y+ = 30 -Temperature distribution**Viscous sublayer**5 Applying the B.C. at y+ = δ+**5**30