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
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+