Two-dimensional flow modelling of a thin slice kettle reboiler

The two-fluid model is applied to a thin sliced kettle reboiler. The tube bundle is treated as a porous medium in which the drag coefficient and tube-wall force are deduced from the empirically-based, one-dimensional model. Methods available in the open literature are used in the two-phase pool surrounding the tube bundle. The predictions are verified by comparing them with experimental data and models available in the open literature.The boundary condition applied at the free surface of the pool is found to be crucial in determining the flow pattern within it. When only liquid re-enters through the boundary an all-liquid pool results. Comparison with the experimental evidence suggests that this boundary condition corresponds to bubbly flow within the tube bundle. Allowing a predominantly vapour re-entry produces a two-phase pool that is consistent with intermittent flow in the tube bundle. When the appropriate boundary condition is applied, the two-fluid model predictions are shown to reproduce the visual records and pressure drop measurements reasonably accurately.     

Recirculation model of kettle reboiler

The present paper deals with the simulation of a kettle reboiler. Considering rectangular tube sheet, concept of internal recirculation developed in a kettle reboiler during boiling, changes in physico-thermal property of liquid and liquid vapour mixture with temperature and pressure and using empirical correlations, a hydrodynamic model has been developed to determine pressure drop, vapour quality, recirculation rate, boiling regime, and heat transfer coefficient at various tube rows of the bundle.Results show, recirculation rate in a reboiler has been found to vary with the heat flux and pressure. Further, at a given value of heat flux and pressure vapour quality, mass flux, and heat transfer coefficient have been found to increase gradually from bottom to top tube row of the bundle.     

A one-fluid,two-dimensional flow simulation model for a kettle reboiler

A one-fluid, or algebraic slip, model has been developed to simulate two-dimensional, two-phase flow in a kettle reboiler. The model uses boundary conditions that allow for a change in flow pattern from bubbly to intermittent flow at a critical superficial gas velocity, as has been observed experimentally. The model is based on established correlations for void fraction and for the force on the fluid by the tubes. It is validated against pressure drop measurements taken over a range of heat fluxes from a kettle reboiler boiling R113 and n-pentane at atmospheric pressure.The model predicts that the flow pattern transition causes a reduction in vertical mass flux, and that the reduction is larger when the transition occurs at a lower level. Before transition, the frequently-used, one-dimensional model and the one-fluid model are shown to predict similar heat-transfer rates because similar magnitudes of mass flux are predicted. After transition, the one-dimensional model significantly over-predicts the mass fluxes. The average heat-transfer coefficient predicted by the one-fluid model is consequently about 10% lower. The one-fluid model shows that tube dryout can be expected at much lower heat fluxes than previously thought and that the fluid kinetic energy available to induce tube vibrations is significantly smaller.     

Investigation of flow phenomena in a kettle reboiler

Two-phase flow phenomena were investigated while boiling R113 and n-pentane in a 241-tube thin slice kettle reboiler. For heat fluxes between 10 and 40 kW/m², row pressure drop measurements were made in three columns and visual observations of the flow patterns were recorded by a video camera. The height of the two-phase mixture above the tube bundle was also varied. The results revealed that the height of the mixture had little effect on the row pressure drop distribution in each column. At heat fluxes below 10 kW/m², the pressure drops were reasonably constant. However, at heat fluxes greater than this, the row pressure drop continuously declined.Two one-point-five-dimensional models were developed, one to aid the investigation of static liquid driven lateral flow in the tube bundle, and another to aid the investigation of the cause of the change from reasonably constant to continually declining row pressure drop. The data and the analysis showed that the flow within the tube bundle was always two-dimensional and that the flow pattern was dominated by the static liquid at the tube bundle edge when the heat flux was less than 10 kW/m². This corresponded to the bubbly flow regime. At larger heat fluxes, the flow pattern changed to intermittent flow. The change occurred when the Kutateladze number was 1.09. Declining row pressure drops occurred in this latter flow regime.     

Experimental and numerical investigation of two-phase pressure drop in vertical cross-flow over a horizontal tube bundle

Experimental pressure drop data for vertical two-phase air–water flow across horizontal tubes is presented for gas mass fractions in the range 0.0005–0.6 and mass fluxes in the range 25–700 kg/m² s. The square in-line tube bundle had one column containing ten tubes and two columns of half tubes attached to the walls. The tubes had a diameter of 38 mm and a pitch to diameter ratio of 1.32. This data and air–water and R113 vapour–liquid data available in the literature are compared with the predictions from two kettle reboiler models, the one-dimensional model and a one-dimensional formulation of the two-fluid model. The one-dimensional model was implemented with three separate void fraction correlations and one two-phase friction multiplier correlation. The results show that the two-fluid model predicts air–water void fraction data well but R113 data poorly with pressure drop predictions for both being unsatisfactory. The one-dimensional model is shown to predict pressure drop and void fraction data reasonably well, provided a careful choice is made for the void fraction correlation.     

Evaluations of Closure Correlations for the Simulation of Two-Phase Flows in Condensers

The effects of different closure correlations on numerical simulations of vapor-liquid two-phase flow and heat transfer in steam surface condensers are critically assessed in this study. A modified k-? turbulence model for two-phase flows is used in the simulation. The closure correlations are those for condensation vapor shear, interphase drag forces, non-condensable air, tube-side fluid flow, inundation, and hydraulic resistance due to the tube bundle. Numerical simulations of a steam surface condenser are carried out using different closure correlations, and the numerical results are compared with the experimental data. Recommendations are given for different closure correlations.     

Interfacial friction factor in vertical upward gas-liquid annular two-phase follow

This paper presents new data on the gas-liquid interfacial friction factor in annular two-phase upward co-current flow in a vertical circular pipe. Different from most previous work, the present studies have been performed at relatively high film thickness, taking into consideration the effect of the entrained droplets which occur from the breakup of the disturbance waves. The test section has an inner diameter of 29 mm and the length of 3 m. The porous wall injector is used to introduce the liquid into the test section. The two phase pressure drop is measured by two static pressure tubes connected with a manometer. The film thickness is measured by calibrated stainless ring electrodes mounted flush in the tube wall. The electrode operates on the principle of the variation of electrical resistance with changes in the liquid film thickness between two parallel eletrode rings. The entrained liquid flow rate is measured by using a sampling probe connected with a cyclone separator. The entrainment flow rate in the gas core is calculated from an assumption that the sampling is carried out in an isokinetic manner. The results from the experiments are compared with those calculated from correlations reported in the literature. A new empirical correlation for predicting the interfacial friction factors for practical applications is proposed.     

Numerical study of heat transfer in a laminar mist flow over a isothermal flat plate

A model for predicting heat and mass transfer in a laminar two-phase gas-vapor-drop mist flow over a flat isothermal flat is developed. Using this model, a numerical study is performed to examine the influence of thermal and flow parameters, i.e., Reynolds number, flow velocity, temperature ratio, concentration of the liquid phase, and drop size, on the profiles of velocity, temperature, composition of the two-phase mixture, and heat-transfer intensification ratio. It is shown that, as the concentration of the liquid phase in the free flow increases, the rate of heat transfer between the plate surface and the vapor-gas mixture increases dramatically, whereas the wall friction increases only insignificantly.     

Correlations of two-phase frictional pressure drop and void fraction in mini-channel

Alternative correlations of two-phase friction pressure drop and void fraction are explored for mini-channels based on the separated flow model and drift-flux model. By applying the artificial neural network, dominant parameters to correlate the two-phase friction multiplier and void fraction are picked out. It is found that in mini-channels the non-dimensional Laplace constant is a main parameter to correlate the Chisholm parameter as well as the distribution parameter. Both previous correlations and the newly developed correlations are extensively evaluated with a variety of data sets collected from the literature.     

The pressure drop in microtubes and the correlation development

This study investigated the pressure drop characteristics in microtubes using R-134a as a test fluid. The test tubes were the circular stainless steel tubes with inner diameters of 0.244, 0.430, and 0.792 mm. Although some of the existing studies reported the early flow transition at the Reynolds number of less than 1000, it was not found in the single-phase flow pressure drop tests. The conventional theory predicted the friction factors well within an absolute average deviation of 8.9%. The two-phase flow pressure drop increased with increasing quality, increasing mass flux, and decreasing tube diameter. The existing correlations failed to predict the two-phase friction multipliers in the microtubes of this study. A new correlation to predict the two-phase flow pressure drop in microtubes was developed in the form of the Lockhart–Martinelli correlation. It includes the effect of the tube diameter, surface tension effect, and the effect of the Reynolds number on the two-phase flow pressure drop in microtubes. The new correlation developed in this study predicted the experimental data within an absolute average deviation of 8.1%.     

Dimensional analysis on the evaporation and condensation of refrigerant R-134a in minichannel plate heat exchangers

Two-phase flow analysis for the evaporation and condensation of refrigerants within the minichannel plate heat exchangers is an area of ongoing research, as reported in the literatures reviewed in this article. The previous studies mostly correlated the two-phase heat transfer and pressure drop in these minichannel heat exchangers using theories and empirical correlations that had previously been established for two-phase flows in conventional macrochannels. However, the two-phase flow characteristics within micro/minichannels may be more sophisticated than conventional macrochannels, and the empirical correlations for one scale may not work for the other one. The objective of this study is to investigate the parameters that affect the two-phase heat transfer within the minichannel plate heat exchangers, and to utilize the dimensional analysis technique to develop appropriate correlations. For this purpose, thermo-hydrodynamic performance of three minichannel brazed-type plate heat exchangers was analyzed experimentally in this study. These heat exchangers were used as the evaporator and condenser of an automotive refrigeration system where the refrigerant R-134a flowed on one side and a 50% glycol–water mixture on the other side in a counter-flow configuration. The heat transfer coefficient for the single-phase flow of the glycol–water mixture was first obtained using a modified Wilson plot technique. The results from the single-phase flow analysis were then used in the two-phase flow analysis, and correlations for the refrigerant evaporation and condensation heat transfer were developed. Correlations for the single-phase and two-phase Fanning friction factors were also obtained based on a homogenous model. The results of this study showed that the two-phase theories and correlations that were established for conventional macrochannel heat exchangers may not hold for the minichannel heat exchangers used in this study.     

Numerical and experimental investigation of pressure drop characteristics during upward boiling two-phase flow of nitrogen

The characteristics of overall pressure drop during upward boiling two-phase flow of nitrogen with constant mass flux and varying heat flux are experimentally investigated using a vertical tube with an inner diameter of 6.0 mm and numerically simulated using the two-fluid model with new closure correlations. Comparison of the numerical results against the experimental data shows that prior to the transition point in the curve of pressure drop evolution, the predicted pressure drop is in a satisfactory agreement with the experimental data. The present study demonstrates that both the wall lubrication force modeling and the bubble diameter modeling have significant effect on the pressure drop prediction. Both the theoretical analysis and the experimental evidence suggest that the transition point in the pressure drop evolution curve reflects the bubbly-to-slug flow regime transition.     

ADVANCED THREE-DIMENSIONAL TWO-FLUID POROUS MEDIA METHOD FOR TRANSIENT TWO-PHASE FLOW THERMAL-HYDRAULICS IN COMPLEX GEOMETRIES

A three-dimensional two-fluid model for two-phase flow within tube or rod bundles is presented. The porous media concept is applied in the model statement. Closure laws for interfacial mass, momentum and energy transfer, bundle flow resistance and heat transfer are presented. Correlations for the interfacial drag force are proposed. Some illustrative examples of application (including also verification) to two-phase flows in complex geometries and across vertical and horizontal tube/rod bundles are presented below. The developed model is suitable for the simulation and analyses of complex multidimensional thermal-hydraulics of nuclear fuel rod bundles or shell-and-tube heat exchangers with vapor generation within a tube bundle on the shell side.     

The Wave Characteristics of Two-Phase Flows Predicted by HLL Scheme Using Interfacial Friction Terms

Wave propagation in the two-phase flows has been numerically investigated. The waves have been generated by various means such as two-phase shock tube, pressure pulse, and void pulse wave. The six compressible two-fluid conservation laws with the interfacial friction terms are solved in the two fractional steps. The first PDE operator step makes use of analytic eigenvalues of an approximate Jacobian matrix in HLL scheme. The second source operator step makes use of the stiff ODE solver in a semi-implicit form. The waves in the two-phase flow field resolved by the present method have shown very small numerical diffusion. An assessment is made on the effect of interfacial friction terms included in the formulation.     

Condensation pressure drop characteristics of various refrigerants in a horizontal smooth tube

The two-phase pressure drop characteristics of the pure refrigerants R410a, R502, and R507a during condensation inside a horizontal tube-in-tube heat exchanger were investigated to determine the two-phase friction factor, the frictional pressure drop, and the total pressure drop. The two-phase friction factor and frictional pressure drop are predicted by means of an equivalent Reynolds number model. Eckels and Pate's experimental data, presented in Choi et al.'s study provided by NIST, were used in the analysis. In their experimental setup, the horizontal test section was a 3.81 m long countercurrent flow double tube heat exchanger with refrigerant flowing in the inner smooth copper tube (8.01 mm i.d.) and cooling water flowing in the annulus (13.7 mm i.d.). Their test runs were performed at saturated condensing temperatures from 38.33 °C to 51.78 °C while the mass fluxes were between 119 and 617 kg m⁻² s⁻¹ for the horizontal test section. The separated flow model was modified by ten different void fraction models and correlations, as well as six different correlations of friction factors, in order to determine the best combination for the validation of the experimental pressure drop values. Carey's friction factor was found to be the most predictive. The refrigerant side total and frictional pressure drops were determined within ± 30% using the above friction factor and the void fraction combinations of Carey, Baroczy, and Armand for R410a; and those of Carey, Spedding and Spence, and Rigot for R502 and R507a. The equivalent Reynolds number model was modified using the void fraction correlation of Rigot in order to determine the frictional condensation pressure drop and the two-phase friction factor. The effects of vapor quality and mass flux on the pressure drop are discussed in this paper. The importance of using the alternative void fraction and friction factor models and correlations for the separated flow model is also addressed.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.     

Convective Heat Transfer and Pressure Drop over Elliptical and Flattened Tube

A numerical study on the effect of the effect of elliptical and flattened tube bundle geometry on the convective heat transfer and pressure drop is presented in this article. The analysis has been carried out to evaluate the performance of these bundle geometries in the design of a compact and effective single phase shell and tube heat exchanger. The temperature, velocity, and pressure drop profiles are obtained from solving the mass, momentum, and energy conservation equations. The comparison is made for inline and staggered bundle with different pitch to diameter ratio and inlet velocity for elliptical and flattened tubes. The pitch to diameter ratio is varied from 1.25 to 2.5 for Reynolds number ranging from 200 to 2000 which is in the laminar flow region. The heat transfer coefficient over the staggered and inline tube bundle decrease with an increase in pitch. The same kind of variation is also observed for the pressure drop in the case of both elliptical and flattened tube bundle. The study shows that the transverse pitch with respect to cross flow affects more than the longitudinal pitch.     

Liquid-solid separation phenomena of two-phase turbulent flow in curved pipes

The present study is to contribute some knowledge of phase separation phenomena of liquid-solid two-phase turbulent flow in curved pipes and provide a basis for the invention and development of a new type of curved pipe separator. Firstly, the solid-liquid two-phase flows in two-dimensional (2D) curved channels were numerically simulated using a two-way coupling Euler-Lagrangian scheme. Phase distribution characteristics of 2D curved channel two-phase flow were examined under conditions of different particle size, liquid flowrate and coil curvature. Based on the numerical results, the dynamic effects and contributions to phase separation of particle-subjected forces, including centrifugal force, drag force, pressure gradient force, gravity force, buoyancy force, virtual mass force and lift force, were exposed by kinematic and dynamic analysis along particle trajectories. Secondly, measurement of particle size and concentration profiles in helically coiled tube two-phase flow was conducted using a nonintrusive Malvern 2600 particle sizer based on laser diffraction. Particle size and concentration distribution characteristics of helically coiled tube two-phase flow and the effect of secondary flow on phase separation were analyzed based on experimental data.     

Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts

An experimental investigation of the heat transfer and pressure drop performance of ten finned tube bundles using serrated fins is presented. All tube bundles had staggered layouts, and the influence on varying tube bundle layout, tube and fin parameters are presented. The heat transfer coefficient experienced a maximum when the flow areas in the transversal and diagonal planes were equal. An increase in the fin pitch increased the heat transfer coefficient; the same was observed with an increase in fin height. The pressure drop coefficient showed no influence of the tube bundle layout for small pitch ratios, but dropped significantly for higher ratios. Increasing fin pitch reduced the pressure drop, whereas varying fin height had insignificant effect. None of the literature correlations were able to reproduce the experiments for the entire range of tested conditions. A set of correlations were developed, reproducing the experimental data to within ±5% at a confidence interval of 95%.     

Influence of oil on R-410A two-phase frictional pressure drop in a small U-type wavy tube

This study presents single-phase and two-phase pressure drop data with oil concentration C = 0, 1, 3 and 5% in a copper wavy tube having an inner diameter of 3.25 mm and a curvature radius of 6.35 mm. The ratio of frictional factor between U-bend in wavy tube and straight tube (f_C/f_S) is about 1.5 to 2.5 for Re = 2500 ∼ 25000. The effect of secondary flow is very crucial in the U-bend that it increases the pressure drop considerably. However, the effect of oil concentration on friction factor is negligible provided the properties are based on mixture. The ratio between two-phase pressure gradients of U-bend and straight tube is about 3. This ratio is increased with oil concentration and vapor quality. The oil effect on two-phase pressure drop is especially pronounced at high vapor quality because the effective oil concentration in liquid mixture is increased with vapor quality. The frictional two-phase multiplier for straight tube can be fairly correlated by using the Chisholm correlation. A modified two-phase friction factor based on the Geary correlation is also utilized to predict the frictional two-phase pressure gradient in U-bend. The predictions give a good agreement to the present oil–refrigerant data with a mean deviation of 12.92%.