Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

Experimental study of inverted annular film boiling in a vertical tube cooled by R-134a

An experimental investigation of inverted annular film boiling heat transfer has been performed for vertical up-flow in a round tube. The experiments used R-134a coolant and covered a pressure range of 640–2390 kPa (water equivalent range: 4000–14,000 kPa) and a mass flux range of 500–4000 kg m⁻² s⁻¹ (water equivalent range: 700–5700 kg m⁻² s⁻¹). The inlet qualities of the tests ranged from −0.75 to −0.03. The hot-patch technique was used to obtain the subcooled film boiling measurements. It was found that the heat transfer vs. quality curve can be divided into four different regions, each characterized by a different mechanisms and trends. These regions are dependent on pressure, mass flux and local quality. A detailed examination of the parametric trends of the heat transfer coefficient with respect to mass flux, inlet quality, heat flux and pressure was performed; reasonably good agreement between observed trends and those reported in the literature were noted.     

Heat transfer enhancement through liquid film evaporation into countercurrent moist air flow in a vertical plate channel

A numerical analysis has been carried out to study the heat removal process from hot channel plate through liquid film evaporation into a countercurrent air flow. The influences of the wall heat flux, the inlet Reynolds number of liquid film and the inlet Reynolds number of moist air on the transfer characteristics are investigated detailedly. The Results show that the interface latent heat transfer associated with the film vaporization causes a temperature drop of the heated plate in the entry region of air flow, which is more significant for a system with higherq _w , lowerRe _l,in or largerRe _{c, in} . The overall temperature rise of the heated wall is rather small, as compared with the case without interface latent heat transfer. In addition, the difference in results obtained by the one-dimensional and two-dimensional methods is substantial.Die numerische Untersuchung bezieht sich auf den Wärmetransportprozeß von heißen, plattenförmigen Kanalwänden durch Flüssigfilmverdampfung in gegenströmende Luft. Die Einflüsse des Wärmeflusses, der Reynolds-Zahlen, des Flüssigkeitfilms und der Feuchtluft (jeweils am Eintritt) auf das Wärmeübertragungsverhalten werden eingehend untersucht. Die Ergebnisse zeigen, daß die bei der Filmverdampfung eingespeicherte latente Wärme eine Temperaturabnahme der Heizplatte am Eintritt der Luft bewirkt, die mit den Wärmefluß und steigender Reynolds-Zahl für Feuchtluft zunimmt. Die gesamte Temperaturerhöhung der beheizten Wand ist sehr gering im Vergleich mit dem Fall ohne Latentwärmeaustausch. Darüber hinaus resultieren erhebliche Unterschiede in den Ergebnissen, je nachdem, ob eindimensionale oder zweidimensionale Methoden angewandt werden.The financial support of this study by the engineering division of the National Science Council, Taiwan, R.O.C., through the contract NSC 82-0401-E-150-049 is greatly appreciated.     

Dispersion in annular climbing film flow

The dispersion of a tracer injected as a pulse into a climbing liquid film is investigated for a series of water and air flow rates, and for a number of different electrolyte tracers. It is found that at all flow rates the observed concentration distribution depends on the nature of the tracer. This observation is explained in terms of two effects: molecular diffusion in a viscous sub-layer and ion fractionation associated with droplet formation at the gas-liquid interface. The overall dispersive characteristics of the system are described in terms of a mathematical model assuming dispersed plug flow in both the film and entrained droplets with interchange between these phases. This model is fitted to experimental tracer concentration distributions using a non-linear least-squares regression procedure. The parameter values obtained from the fitting procedure are studied to determine trends with flow rates and tracer properties. Values for a film dispersion parameter, $\text{P}{}_{\mathrm{f}}$, are found to correlate significantly with the molecular diffusion coefficients of the tracers. Consistent values for an ion fractionation coefficient, $\text{k}{}_{\mathrm{if}}$, are also obtained.     

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.     

Evaporation heat transfer and friction characteristics of R-134a flowing downward in a vertical corrugated tube

Differently from most previous studies, the heat transfer and friction characteristics of the pure refrigerant HFC-134a during evaporation inside a vertical corrugated tube are experimentally investigated. The double tube test sections are 0.5 m long with refrigerant flowing in the inner tube and heating water flowing in the annulus. The inner tubes are one smooth tube and two corrugated tubes, which are constructed from smooth copper tube of 8.7 mm inner diameter. The test runs are performed at evaporating temperatures of 10, 15, and 20 °C, heat fluxes of 20, 25, and 30 kW/m², and mass fluxes of 200, 300, and 400 kg/m² s. The quality of the refrigerant in the test section is calculated using the temperature and pressure obtained from the experiment. The pressure drop across the test section is measured directly by a differential pressure transducer. The effects of heat flux, mass flux, and evaporation temperature on the heat transfer coefficient and two-phase friction factor are also discussed. It is found that the percentage increases of the heat transfer coefficient and the two-phase friction factor of the corrugated tubes compared with those of the smooth tube are approximately 0-10% and 70-140%, respectively.     

Developed cavitation behind a disk in a vertical tube

The theoretical and experimental investigation of developed cavities in a vertical flow shows [1–3] that the size and shape of the cavities depend in this case to a greater extent on the Froude number than for horizontal flow. Experiments in a longitudinal gravity field are usually made under conditions of a confined flow, which requires analysis of the influence of this circumstance on their results. Such an analysis has been made for horizontal flow confined by walls in both an approximate [4–6] and an exact [7–10] formulation; the problems have been solved for both two- and three-dimensional flows. In the present paper we solve in a nonlinear formulation the axisymmetric cavitation problem of determining the influence of the restriction of flow in a vertical circular tube on a developed cavity. The obtained results describe well the cavities realized under experimental conditions even when there is an appreciable deviation of the shape of the tube section from a circle.     

饱和蒸发和热毛细力作用下低雷诺数液膜在波纹竖壁上的流动

考虑表面蒸发压力和热毛细力作用情况下,对饱和蒸发状态下低雷诺数自由降落液膜在小波幅正弦型波纹壁面上的流动进行理论分析。对控制微分方程及边界条件进行量纲一化并引入流函数,对微分方程及边界条件进行摄动展开,得到了这种情况下液膜流动的简化分析模型,求出了近似解析解。讨论了壁面波纹、表面张力、蒸发压力、热毛细力对液膜流动的影响。研究表明:液膜的波动幅度随蒸发强度和热毛细力的增大而增大;液膜波动与壁面波纹的相位差随蒸发强度增大而增大,随热毛细力增大而减小。     

Heat-transfer characteristics from a bundle of horizontal tubes immersed in aggregative fluidized bed

Experiments were performed to study the effect of air fluidization velocity, particle diameter, tube diameter, and pitch between tubes on heat-transfer coefficient for a bundle of horizontal tubes immersed in an aggregative fluidized bed. Not only horizontal but also vertical distributions of the heat-transfer coefficients within the bundle were also extensively determined. The heat-transfer coefficient and its maximum value were found to be dependent on the particle diameter, the air fluidization velocity, and the gap between the tubes in the bundle. The proposed correlation for the maximum heat-transfer coefficient was in good agreement with the present results.     

Laminar film boiling on a vertical fin

Laminar film boiling on a vertical fin is formulated as a conjugate phenomenon and investigated for no slip and zero shear conditions at the vapor-liquid interface. The results indicate that the combined effects of thermal leakage at the ends of the fin and radiation from its lateral face have profound influence on the average Nusselt number. Further, from the formulation it can be shown that the isothermal condition can be deduced by suitably changing the boundary conditions of the fin at its extremities. The results of the investigation are rendered into dimensionless functional relationships between the average Nusselt numberNu _m, fin parameterM, radiation parameterN _R and temperature ratio term Ψ. The proposed equation can be made use of in design calculations.     

Settling of discs inside a vertical fluid-filled tube

The broadside settling of discs along the centerline of a fluid-filled tube is studied. The Stokes equation is solved by a method of eigenfunction expansions and collocation. Depending on the geometry, the flow field shows different arrangements of recirculating eddies. Due to mutual shielding, the discs settle faster when they are closer together.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Modeling transient churn-annular flows in a long vertical tube

This work investigates the transient behavior of high gas fraction gas-liquid flows in vertical pipes (annular and churn flows). Hyperbolic balance equations for mass, momentum and entropy are written for the gas and liquid, which is split between a continuous film and droplets entrained in the gas core. Closure relationships to calculate the wall and interfacial friction and the rates of droplet entrainment and deposition were obtained from the literature. A finite-difference solution algorithm based on a coefficient matrix splitting method was implemented to deal with sharp variations in the spatial and temporal domains, such as pressure and phase holdup waves. The model results were compared with steady-state experimental data from eight different sources, totaling more than 1500 data points for pressure gradient, liquid film flow rate and void/core fraction. The absolute average deviation between the model and the data was 17% for the pressure gradient and 5.8% for the void fraction. A comparison of the model results with fully transient air-water data generated in a 49-mm ID, 42-m long vertical pipe is also presented. The experimental results consist of two outlet pressure-induced and two inlet mass flow rate-induced transient tests. Two main transient parameters are compared, namely the local void fraction and the pressure difference between selected points along the test section and the outlet (taken as a reference). The comparisons between the experiments and the numerical model indicate that the model was capable of describing the transient annular to churn flow transition with absolute average deviations of 14.5% and 7.9% for the pressure difference and void fraction, respectively.     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.