Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry

The present paper is part of a research program on two-phase flows and heat transfer studies in tube bundles. An experimental study was carried out to analyse the void fraction for vertical two-phase flows. Boiling across a horizontal tube bundle for three hydrocarbons (n-pentane, propane and iso-butane) under saturated conditions is investigated. The experiments were performed on a tube bundle with 45 plain copper tubes of 19.05 mm outside diameter in a staggered configuration with a pitch to diameter ratio of 1.33. An optical probe has been developed to determine the local void fraction at the minimum cross section between the tubes.     

Vertical, Bubbly, Cross-Flow Characteristics over Tube Bundles

Two-phase flow over tube bundles is commonly observed in shell and tube-type heat exchangers. However, only limited amount of data concerning flow pattern and void fraction exists due to the flow complexity and the difficulties in measurement. The detailed flow structure in tube bundles needs to be understood for reliable and effective design. Therefore, the objective of this study was to clarify the two-phase structure of cross-flow in tube bundles by PIV. Experiments were conducted using two types of models, namely in-line and staggered arrays with a pitch-to-diameter ratio of 1.5. Each test section contains 20 rows of five 15 mm O.D. tubes in each row. The experiment’s data were obtained under very low void fraction (α<0.02). Liquid and gas velocity data in the whole flow field were measured successfully by optical filtering and image processing. The structures of bubbly flow in the two different configurations of tube bundles were described in terms of the velocity vector field, turbulence intensity and void fraction.     

Drift-flux model for upward two-phase cross-flow in horizontal tube bundles

In relation to void fraction prediction of cross-flow in horizontal tube bundle of shell-tube heat exchangers, a drift-flux correlation has been developed to meet the demand on the study of two-phase flow gas and liquid velocities, two-phase pressure drop, heat transfer, flow patterns and flow induced vibrations in the shell side. Two critical parameters such as distribution parameter and drift velocity have been modeled. The distribution parameter is obtained by constant asymptotic values and taking into account the differences in channel geometry. The drift velocity is modelled depending on the density ratio and the non-dimensional viscosity number. The relationship between the channel averaged and gap mass velocity has been discussed in order to obtain the superficial gas and liquid velocities in the drift-flux correlation. The newly developed drift-flux correlation agrees well with cross-flow experimental databases of air-water, R-11 and R-113 in parallel triangular, normal square and normal triangular arrays with the mean absolute error of 1.06% and the standard deviation of 4.47%. In comparison with other existing correlations, the newly developed drift-flux correlation is superior to other studies due to the improved accuracy. In order to extend the applicability of the newly developed drift-flux correlation to void fraction of unity, an interpolation scheme has been developed. The newly developed drift-flux correlation is able to calculate the void fraction of cross-flow over a full range with different sub-channel configurations in shell-tube type heat exchangers.     

AN EXPERIMENTAL STUDY ON THE FLUIDELASTIC FORCES ACTING ON A SQUARE TUBE BUNDLE IN TWO-PHASE CROSS-FLOW

A tube in a square tube bundle of P/D=1·42 was oscillated in the lift direction in air–water two-phase cross-flow, and fluidelastic forces acting on the oscillated tube were measured. First, the tube amplitude was fixed to 3 mm (=0·136 D), and added mass, damping, and stiffness coefficients were obtained as a function of two-phase mixture characteristics such as nondimensional gap velocity and void fraction. When reference mixture density and velocity were estimated, the drift–flux model, in which the relative velocity between the gas and liquid phases was estimated, generated better results than the homogeneous model. The added mass coefficient was obtained from quiescent two-phase flow as a function of void fraction. Using the added mass coefficient, the added stiffness coefficient converged to zero with decreasing nondimensional gap velocity. This overcame the contradiction in the added stiffness estimation without added mass, in which the added stiffness coefficient did not converge to zero with decreasing nondimensional gap velocity. Next, the effects of the vibration amplitude on the fluidelastic force coefficients were considered. When the tube amplitude was 3 mm (=0·136 D) or less, the equivalent added stiffness and damping coefficients were almost constant and nonlinearity was small. This showed the validity of the fluidelastic force coefficients obtained based on the data of amplitude of 3 mm. The linearity did not exist when the tube displacement amplitude was 4·5 mm (=0·205 D) or more; a remarkable nonlinearity appeared in the equivalent added damping coefficient. A method to estimate the limit-cycle amplitude of the fluidelastic vibration was proposed when only one tube in the tube bundle was able to vibrate in the lift direction. The amplitude could be obtained from the amplitude at which the equivalent added damping coefficient changed from negative to positive with increase in the tube amplitude.     

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.     

Heat transfer from a vertical tube bundle under natural circulation conditions

A rectangular loop (thermosyphon) was used to measure the average heat transfer coefficients for water at atmospheric pressure under natural circulation conditions. A twenty-one tube bundle with tubes 1.65 m long and 9.55 mm in diameter, and a pitch-to-diameter ratio of 1.33, was used as a test heat exchanger in one of the vertical legs of the loop. A natural circulation flow in the loop developed due to buoyancy differences of the fluid in its two vertical legs. Flow visualization experiments were performed to determine the flow regimes associated with natural circulation flow longitudinal to a tube bundle. Empirical correlations for the average Nusselt number have been developed and are reported. Grid spacers arranged on tube bundles were shown to enhance heat transfer, especially for laminar flow, without any noticeable increase in pressure drop.     

Heat/mass transfer and pressure drop in a triangular-rib-roughened rectangular channel

In this paper, the heat/mass transfer analogy was used to investigate the heat transfer and pressure drop in a square channel with triangular ribs on its two opposite walls. Reynolds number varied from 1 × 10⁴ to 7 × 10⁴; the dimensionless heights of the triangular ribs H/W were 0.04, 0.07, and 0.1; and their dimensionless pitches S/W were 0.45, 0.63, 1.0, 1.37, 1.55, and 2.1. Experimental results showed that the heat transfer coefficients of the wall with triangular rib were about 1 to 2.3 times larger than those of a smooth-channel wall, and the pressure drops along this roughened channel were about 1 to 10 times larger than those for a smooth channel. Correlations of heat transfer and pressure drop were obtained, which are useful for practical designs.     

Heat transfer and fluid dynamics of air–water two-phase flow in micro-channels

Heat transfer, pressure drop, and void fraction were simultaneously measured for upward heated air–water non-boiling two-phase flow in 0.51 mm ID tube to investigate thermo–hydro dynamic characteristics of two-phase flow in micro-channels. At low liquid superficial velocity j_l frictional pressure drop agreed with Mishima–Hibiki’s correlation, whereas agreed with Chisholm–Laird’s correlation at relatively high j_l. Void fraction was lower than the homogeneous model and conventional empirical correlations. To interpret the decrease of void fraction with decrease of tube diameter, a relation among the void fraction, pressure gradient and tube diameter was derived. Heat transfer coefficient fairly agreed with the data for 1.03 and 2.01 mm ID tubes when j_l was relatively high. But it became lower than that for larger diameter tubes when j_l was low. Analogy between heat transfer and frictional pressure drop was proved to hold roughly for the two-phase flow in micro-channel. But satisfactory relation was not obtained under the condition of low liquid superficial velocity.     

Performance and optimum dimensions of flat fins for tube-and-fin heat exchangers: A generalized analysis

The performance of flat fins for tube-fin heat exchangers has been analyzed for both inline and staggered arrangement of tubes. In earlier published studies, regular square and equilateral triangular array tube layouts were considered. No such restriction is put in the present study. The analysis has been done by a semi-analytical technique where the boundary condition at the fin edge is discretely satisfied at a large number of points by a method of collocation. It has also been demonstrated that the approximate results obtained by the sector method closely agree with the prediction of semi-analytical technique. Finally, a generalized scheme of optimization based on Lagrange multiplier technique has been suggested which shows that irrespective of the volume and thickness of the fins, square and equilateral triangular array of tubes are the optimum layout for inline and staggered arrangements, respectively. This result was known so far only intuitively. The optimum dimensions for flat fins for other layout of tubes have also been obtained specifying the ratio of longitudinal to transverse tube pitch.     

An experimental study on developing air-water two-phase flow along a large vertical pipe: effect of air injection method

The flow structure in a developing air-water two-phase flow was investigated experimentally along a large vertical pipe (inner diameter, D_h: 0.48 m, ratio of length of flow path L to D_h: about 4.2). Two air injection methods (porous sinter injection and nozzle injection) were adopted to realize an extremely different flow structure in the developing region. The flow rate condition in the test section was as follows: superficial air velocity: 0.02–0.87 m/s (at atmospheric pressure) and superficial water velocity: 0.01–0.2 0.01–0.2 m/s, which covers the range of bubbly to slug flow in a small-scale pipe (D_h about 0.05 m).

No air slugs occupying the flow path were recognized in this experiment regardless of the air injection methods even under the condition where slug flow is realized in the small-scale pipe. In the lower half of the test section, the axial distribution of sectional differential pressure and the radial distribution of local void fraction showed peculiar distributions depending on the air injection methods. However, in the upper half of the test section, the effects of the air injection methods are small in respect of the shapes of the differential pressure distribution and the phase distribution. The comparison of sectional void fraction near the top of the test section with Kataoka's correlation indicated that the distribution parameter of the drift-flux model should be modeled including the effect of D_h and the bubble size distribution is affected by the air injection methods. The bubble size distribution is considered to be affected also by L/D_h based on comparison of results with Hills' correlation.     

An experimental investigation of heat transfer characteristics for turbulent flow over staggered ribs in a square duct

An experimental study of developing and fully developed turbulent air flow in a square duct with two opposite rib-roughened walls in which the ribs are attached in a staggered fashion was conducted to determine the heat transfer characteristics. The rib height-to-hydraulic diameter ratio (e/D_H) was 0.19, the rib pitch-to-height ratio (p/e) was 5.31. The streamwise temperature distribution was measured, and a law of the wall for the thermal boundary layer at each free-stream turbulence level was obtained. The effects of free-stream turbulence intensity with variations of 4–11% on heat transfer coefficients were also examined. Finally, the relationship between Nusselt number and Reynolds number was correlated. The results might be used in the design of turbine blade cooling channels.     

Analysis of frictionless two-phase flow in tubes under centrifugal acceleration and minimum heating for choked flow

To determine the void fraction in a tube of a rotating heat exchanger, an analytical investigation was undertaken to model frictionless two-phase flow boiling. Steady, one-dimensional separated two-phase conservation equations in differential form, were first applied to a stationary system. The equations were integrated between the inlet and exit of the flow channel to yield three coupled algebraic equations. The algebraic equations were then modified to represent rotating systems. To obtain closure, the velocity ratio, mass quality and void fraction are defined as a function of pressure.

A numerical technique was used to solve the equations. Sample results are presented in a graph of mass quality versus void fraction. The graph demonstrates that a minimum heat input must be exceeded to change from a single-phase flow to saturated two-phase flow boiling. Also, the void fraction was found to increase for increasing heat input, decreasing mass flow rate, increasing inlet mass quality and decreasing pressure difference between the inlet and exit.     

Void fraction and pressure drop during external upward two-phase cross flow in tube bundles – part II: Predictive methods

The present paper is the Part II of a broad study concerning void fraction and pressure drop for air-water upward external flow across tube bundles. In the Part I, the experimental facility and the data regression procedures were described and the experimental results are presented and discussed. Initially, Part II presents a literature review concerning void fraction and pressure drop predictive methods available in the open literature for two-phase upward flow across tube bundles. Next, the methods from literature are compared among them and with the database presented in paper Part I. Significant discrepancies are observed among the predictive methods, and deviations as high as two orders of magnitude are verified among the predicted values of pressure drop. Then, a new void fraction predictive method is proposed based on the experimental results and on the minimum kinetic energy principle. This method provides satisfactory predictions of the results described in paper Part I and also of independent data from the literature. A new predictive method for frictional pressure drop during two-phase flow based on two-phase multiplier is also proposed. This method predicted 94% of the experimental data obtained in the present study within an error margin of ± 30%, and also provides accurate predictions of independent results for triangular tube bundles gathered in the open literature.     

An experimental study of drag on a single tube and on a tube in an array under two-phase cross flow

In this work, the drag coefficient and the void fraction around a tube subjected to two-phase cross flow were studied for a single tube and for a tube placed in an array. The drag coefficients were determined by measuring the pressure distribution around the perimeter of the tube. Single tube drag data were taken when the tube was held both rigidly and flexibly. The test tube was made of acrylic and was 2.2 cm in diameter and 20 cm in length. In the experiments, liquid Reynolds number ranged from 430 to 21,900 for the single tube and liquid gap Reynolds number ranged from 32,900 and 61,600 for the tube placed in a triangular array. Free stream void fraction was varied from 0 to 0.4. At low Reynolds numbers, the ratio of two-phase to single-phase drag coefficient is found to be a strong function of εGr/Re2. However, at high Reynolds numbers only void fraction is the important parameter. Empirical correlations have been developed for the ratio of two-phase drag on a single tube and on a tube placed in an array.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

MODELLING TWO-PHASE FLOW-EXCITED DAMPING AND FLUIDELASTIC INSTABILITY IN TUBE ARRAYS

This paper reports the results of an experimental study of the flow-induced vibration of a heat exchanger tube array subjected to two-phase cross-flow of refrigerant 11. The primary concern of the research was to develop a methodology for predicting the critical flow velocities for fluidelastic instability which better characterize the physics of two-phase flows. A new method is proposed for calculating the average fluid density and equivalent flow velocity of the two-phase fluid, using a newly developed void fraction model to account for the difference in velocity between the gas and liquid phases. Additionally, damping measurements in two-phase flow were made and compared with the data of other researchers who used a variety of modelling fluids. The results show that the two-phase damping follows a similar trend with respect to homogeneous void fraction, and when normalized, agree well with the data in the literature. The fluidelastic threshold data of several researchers who used a variety of fluids, is re-examined using the proposed void fraction model, and the results show a remarkable change in trend with flow regime. The data corresponding to the bubbly flow regime shows no significant deviation from the trend established by Connors' theory. However, the data corresponding to the intermittent flow regime show a significant decrease in stability which is nearly independent of the mass-damping parameter. It is believed that the velocity fluctuations that are inherent in the intermittent flow regime are responsible for tripping the instability, causing lower than expected stability of the bundle.     

Surface tension effects on adiabatic gas–liquid flow across micro pillars

The effect of surface tension on adiabatic two-phase flow across a bank of 100 μm diameter staggered circular micro pillars, 100 μm long with pitch-to-diameter ratio of 1.5, for Reynolds number between 5 and 50, was investigated. Experiments with ethanol were performed and compared to results with water. Flow maps revealed similar flow patterns, but the transition lines were different for the two liquids. Void fraction measurements of the two fluids were also compared, and no significant deviations were observed. The two-phase pressure drop characteristics were significantly affected by the reduction in surface tension. Interfacial friction was attributed to this deviation, and a two-fluid model was developed to account for surface tension force. In addition, a modified form of Chisholm correlation was developed that accounts for surface tension.     

Experimental study of turbulent round jet flow impinging on a square cylinder laid on a flat plate

A turbulent axisymmetric air jet impinging on a square cylinder mounted on a flat plate has been studied experimentally. Turbulence statistics and flow’s topology were investigated. When the surface was heated through uniform heat flux, local heat transfer coefficient was measured. The jet from a long round pipe, 75 pipe diameters (D) in length, at Reynolds number of 23,000, impinged vertically on the square cylinder (3D × 3D × 43D). Measurements were performed using particle image velocimetry, flow visualization using fluorescent dye and infrared thermography. The flow’s topology demonstrated a three-dimensional recirculation after separating from the square cylinder and a presence of foci between the bottom corner and the recirculation’s detachment line. The distribution of heat transfer coefficient was explained by the influence of these flow’s structures and the advection of kinetic energy. On the impingement wall of the square cylinder, a secondary peak in heat transfer coefficient was observed. Its origin can be attributed to very pronounced shear production coupled with the external turbulence coming from the free jet.