Bubbly-to-cap bubbly flow transition in a long-26 m vertical large diameter pipe at low liquid flow rate

The concurrent upward two-phase flow of air and water in a long vertical large diameter pipe with an inner diameter (D) of 200 mm and a height (z) of 26 m (z/D = 130) was investigated experimentally at low superficial liquid velocities from 0.05009 to 0.3121 m/s and the superficial gas velocities from 0.01779 to 0.5069 m/s. The resultant void fractions range from 0.03579 to 0.4059. According to the observations using a high speed video camera, the flow regimes of bubbly, developing cap bubbly and fully-developed cap bubbly flows prevailed in the flows. The developing cap bubbly flow appeared as a flow regime transition from bubbly to fully-developed cap bubble flow in the vertical large diameter pipe. The developing cap bubbly flow changes gradually and lasts for a long time period and a wide axial region in the flow direction, in contrast to a sudden transition from bubbly to slug flows in a small diameter pipe. The analysis in this study showed that the flow regime transition depends not only on the void fraction but also on the axial distance in the flow and the pipe diameter. The axial flow development brings about the transition to happen in a lower void fraction flow and the increase of pipe diameter causes the transition to happen in a higher void fraction flow. The measured void fraction showed an N-shaped axial changing manner that the void fraction increases monotonously with axial position in the bubbly flow, decreases non-monotonously with axial position in the developing cap bubbly flow, and increases monotonously again with axial position in the fully-developed cap bubbly flow. The temporary void fraction decrease phenomenon in the transition region from bubbly to cap bubbly flow can be attributed to the formation of medium to large cap bubbles and their gradual growth into the maximum size of cap bubble and/or cluster of large cap bubbles in the developing cap bubbly flow. In order to predict the N-shaped axial void fraction changing behaviors in the flow regime transition from bubbly to cap bubbly flow, the existing 12 drift flux correlation sets for large diameter pipes are reviewed and their predictabilities are studied against the present experimental data. Although some drift flux correlation sets, such as those of Clark and Flemmer (1986) and Hibiki and Ishii (2003), can predict the present experimental data with reasonable average relative deviations, no drift flux correlation set for distribution parameter and drift velocity can give a reliable prediction for the observed N-shaped axial void fraction changing behaviors in the region from bubbly to cap bubbly flow in a vertical large diameter pipe.     

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.     

One-group interfacial area transport equation and its sink and source terms in narrow rectangular channel

The characteristics of two-phase flow in a narrow rectangular channel are expected to be different from those in other channel geometries, because of the significant restriction of the bubble shape which, consequently, may affect the heat removal by boiling under various operating conditions. The objective of this study is to develop an interfacial area transport equation with the sink and source terms being properly modeled for the gas–liquid two-phase flow in a narrow rectangular channel. By taking into account the crushed characteristics of the bubbles a new one-group interfacial area transport equation was derived for the two-phase flow in a narrow rectangular channel. The random collisions between bubbles and the impacts of turbulent eddies with bubbles were modeled for the bubble coalescence and breakup respectively in the two-phase flow in a narrow rectangular channel. The newly-developed one-group interfacial area transport equation with the derived sink and source terms was evaluated by using the area-averaged flow parameters of vertical upwardly-moving adiabatic air–water two-phase flows measured in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm. The flow conditions of the data set covered spherical bubbly, crushed pancake bubbly, crushed cap-bubbly and crushed slug flow regimes and their superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. Good agreement with the average relative deviation of 9.98% was obtained between the predicted and measured interfacial area concentrations in this study.     

Developing structure of two-phase flow in a large diameter pipe at low liquid flow rate

In order to develop the interfacial area transport equation for the interfacial transfer terms in the two-fluid model, accurate data sets on axial development of local parameters such as void fraction, interfacial area concentration, interfacial gas velocity and Sauter mean diameter are indispensable to verify the modeled source and sink terms in the interfacial area transport equation. From this point of view, local measurements of both group 1 spherical/distorted bubbles and group 2 cap/slug bubbles in vertical upward air–water two-phase flow in a large diameter pipe with 200 mm in inner diameter and 26 m in height were performed at three axial locations of z/D = 41.5, 82.8 and 113 as well as 11 radial locations from r/R = 0–0.95 by using four-sensor probe method. Here, z, r, D and R are the axial distance from the inlet, radial distance from the pipe center, pipe diameter and pipe radius, respectively. The liquid flow rate and the void fraction ranged from 0.0505 m/s to 0.312 m/s and from 1.98% to 32.6%, respectively in the present experiment. The flow condition covered extensive region of bubbly flow, cap turbulent flow as well as their transition. The extensive analysis on the radial profiles of local flow parameters and their axial developments demonstrate the development of interfacial structures along the flow direction due to the bubble coalescence and breakup and the gas expansion. The significant decrease in void faction and interfacial area concentration and the increase in Sauter mean diameter and interfacial velocity were observed when the gradual flow regime transition occurred. Finally, the net change in the interfacial area concentration due to the bubble coalescence and breakup was quantitatively investigated in the present paper to reflect the true transfer mechanisms in observed two-phase flows.     

Flow regime development analysis in adiabatic upward two-phase flow in a vertical annulus

In this work radial and axial flow regime development in adiabatic upward air-water two-phase flow in a vertical annulus has been investigated. Local flow regimes have been identified using conductivity probes and neural networks techniques. The inner and outer diameters of the annulus are 19.1 mm and 38.1 mm, respectively. The equivalent hydraulic diameter of the flow channel, D_H, is 19.0 mm and the total length is 4.37 m. The flow regime map includes 1080 local flow regimes identifications in 72 flow conditions within a range of 0.01 m/s < 〈j_g〉 < 30 m/s and 0.2 m/s < 〈j_f〉 < 3.5 m/s where 〈j_g〉 and 〈j_f〉 are, respectively, superficial gas and liquid velocities. The local flow regime has been classified into four categories: bubbly, cap-slug, churn-turbulent and annular flows. In order to study the radial and axial development of flow regime the measurements have been performed at five radial locations. The three axial positions correspond to z/D_H = 52, 149 and 230, where z represents the axial position. The flow regime indicator has been chosen as some statistical parameters of local bubble chord length distributions and self-organized neural networks have been used as mapping system. This information has been also used to compare the results given by the existing flow regime transition models. The local flow regime is characterized basically by the void fraction and bubble chord length. The radial development of flow regime shows partial and complete local flow regime combinations. The radial development is controlled by axial location and superficial liquid velocity. The radial flow regime transition is always initiated in the center of the flow channel and it is propagated towards the channel boundaries. The axial development of flow regime is observed in all the flow maps and it is governed by superficial liquid velocity and radial location. The prediction results of the models are compared for each flow regime transition.     

Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor

Two-phase flow measurements were carried out using a resistive void fraction meter coupled to a venturi or orifice plate. The measurement system used to estimate the liquid and gas mass flow rates was evaluated using an air–water experimental facility. Experiments included upward vertical and horizontal flow, annular, bubbly, churn and slug patterns, void fraction ranging from 2% to 85%, water flow rate up to 4000 kg/h, air flow rate up to 50 kg/h, and quality up to almost 10%. The fractional root mean square (RMS) deviation of the two-phase mass flow rate in upward vertical flow through a venturi plate is 6.8% using the correlation of Chisholm (D. Chisholm, Pressure gradients during the flow of incompressible two-phase mixtures through pipes, venturis and orifice plates, British Chemical Engineering 12 (9) (1967) 454–457). For the orifice plate, the RMS deviation of the vertical flow is 5.5% using the correlation of Zhang et al. (H.J. Zhang, W.T. Yue, Z.Y. Huang, Investigation of oil–air two-phase mass flow rate measurement using venturi and void fraction sensor, Journal of Zhejiang University Science 6A (6) (2005) 601–606). The results show that the flow direction has no significant influence on the meters in relation to the pressure drop in the experimental operation range. Quality and slip ratio analyses were also performed. The results show a mean slip ratio lower than 1.1, when bubbly and slug flow patterns are encountered for mean void fractions lower than 70%.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

On the use of area-averaged void fraction and local bubble chord length entropies as two-phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 and 50.8-mm pipes have been calculated. The measured conditions cover ranges from 0.13 to 5 m/s in the superficial liquid velocity j _f and ranges from 0.01 to 25 m/s in the superficial gas velocity j _g. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions.     

Development of a robust image processing technique for bubbly flow measurement in a narrow rectangular channel

This paper presents a robust image processing technique for bubbly flow measurement over a wide range of void fractions. The proposed algorithm combines geometrical, optical and topological information recorded with high speed cameras to separate and reconstruct the overlapping bubbles. The common difficulties such as overlapping, irregular bubble shape, surface deformation and large clustering in digital image processing are solved by combining different information based on a preset decision table and flow chart. Test with synthetic bubble images is performed to evaluate the reliability of the algorithm and quantify the uncertainty of the data. The result shows that the proposed algorithm can accurately measure bubbly flows with void fraction up to 18% for large bubbles. Four runs of bubbly flow images in a 30 mm  ×  10 mm rectangular channel are then recorded by three high speed cameras. The area-averaged void fraction of these test runs range from 2.4% to 9.1%. The axial and lateral distributions of bubble number density are obtained by the present algorithm for studying the characteristics of these flows.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

Void fraction and pressure drop during external upward two-phase crossflow in tube bundles – part I: Experimental investigation

The present paper is the part I of a broad study concerning void fraction and pressure drop for air-water upward external flow across tube bundles. Experimental results were obtained for liquid and gas superficial velocities ranging from 0.02 to 1.50 m/s and 0.20 to 10.00 m/s, respectively. Void fraction measurements were performed for bubbly flow using a capacitive probe. The test section consisted of a triangular tube bundle counting with 19 mm OD tube and transverse pitch of 24 mm. Initially, the paper describes the test facility and the data regression and experimental procedures. Then, the pressure drop and void fraction measurements are validated based on tests for single-phase flow and quiescent liquid conditions, respectively. Finally, the experimental data are presented and analyzed. In the second part of this study (Part II), a literature review on predictive methods for void fraction and pressure drop is presented. Additionally, these methods are compared with the database presented in Part I and new predictive methods for void fraction and frictional pressure drop are proposed.     

Turbulence measurements in the bubbly flow region of hydraulic jumps

A hydraulic jump is characterized by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air–water flow measurements were performed in a large-size facility using two types of phase-detection intrusive probes: i.e. single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent integral time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of Chanson [H. Chanson, Bubbly flow structure in hydraulic jump, Eur. J. Mech. B/Fluids 26 (3) (2007) 367–384], providing the turbulent scales of the eddy structures advecting the air bubbles in the developing shear layer. The length scale L_xz is an integral air–water turbulence length scale which characterized the transverse size of the large vortical structures advecting the air bubbles. The experimental data showed that the dimensionless integral turbulent length scale L_xz/d₁ was closely related to the inflow depth: i.e. L_xz/d₁ = 0.2–0.8, with L_xz increasing towards the free-surface.     

Air–water flow characteristics in high-velocity free-surface flows with 50% void fraction

High-velocity free-surface flows are complex two-phase flows and limited information is available about the interactions between air and water for void fractions of about 50%. Herein a detailed experimental study was conducted in the intermediate flow region (C ∼ 50%) on a stepped spillway and the microscopic air–water flow characteristics were investigated. The results showed differences in water and droplet chord times with comparatively larger number of air chord times (0–2 ms), and larger number of water chord times (2–6 ms). A monotonic decrease of particle chord modes was observed with increasing bubble count rates. Several characteristic time scales were identified based upon inter-particle arrival time analyses of characteristic chord time classes as well as spectral analyses of the instantaneous void fraction signal. Chord times of 3–5 ms appeared to be characteristic time scales of the intermediate flow region having similar time scales compared to the local correlation and integral turbulent time scales and to time scales associated with bubble break-up and turbulent velocity fluctuations. A further characteristic time scale of 100 ms was identified in a frequency analysis of instantaneous void fraction. This time scale was of the same order of magnitude as free-surface auto-correlation time scales suggesting that the air–water flow structure was affected by the free-surface fluctuations.     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Enhancement of channel wall vibration due to acoustic excitation of an internal bubbly flow

The effect of an internal turbulent bubbly flow on vibrations of a channel wall is investigated experimentally and theoretically. Our objective is to determine the spectrum and attenuation rate of sound propagating through a bubbly liquid flow in a channel, and connect these features with the vibrations of the channel wall and associated pressure fluctuations. Vibrations of an isolated channel wall and associated wall pressure fluctuations are measured using several accelerometers and pressure transducers at various gas void fractions and characteristic bubble diameters. A waveguide-theory-based model, consisting of a solution to the three-dimensional Helmholtz equation in an infinitely long channel with the effective physical properties of a bubbly liquid is developed to predict the spectral frequencies of the wall vibrations and pressure fluctuations, the corresponding attenuation coefficients and propagation phase speeds. Results show that the presence of bubbles substantially enhances the power spectral density of the channel wall vibrations and wall pressure fluctuations in the 250–1200 Hz range by up to 27 and 26 dB, respectively, and increases their overall rms values by up to 14.1 and 12.7 times, respectively. In the same frequency range, both vibrations and spectral frequencies increase substantially with increasing void fraction and slightly with increasing bubble diameter. Several weaker spectral peaks above that range are also observed. Trends of the frequency and attenuation coefficients of spectral peaks, as well as the phase velocities are well predicted by the model. This agreement confirms that the origin of enhanced vibrations and pressure fluctuations is the excitation of streamwise propagating pressure waves, which are created by the initial acoustic energy generated during bubble formation.     

Effective property models for homogeneous two-phase flows

Using an analogy between thermal conductivity of porous media and viscosity in two-phase flow, new definitions for two-phase viscosity are proposed. These new definitions satisfy the following two conditions: namely (i) the two-phase viscosity is equal to the liquid viscosity at the mass quality = 0% and (ii) the two-phase viscosity is equal to the gas viscosity at the mass quality = 100%. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. These new models are assessed using published experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels in the form of Fanning friction factor (f_m) versus Reynolds number (Re_m). The published data include different working fluids such as R-12, R-22, argon (R740), R717, R134a, R410A and propane (R290) at different diameters and different saturation temperatures. Models are assessed on the basis minimizing the root mean square error (eRMS). It is shown that these new definitions of two-phase viscosity can be used to analyze the experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels using simple friction models.     

Flow pattern characterization for R-245fa in minichannels: Optical measurement technique and experimental results

An optical measurement method using image processing for two-phase flow pattern characterization in minichannel is developed. The bubble frequency, the percentage of small bubbles as well as their velocity are measured. A high-speed high-definition video camera is used to measure these parameters and to identify the flow regimes and their transitions. The tests are performed in a 3.0 mm glass channel using saturated R-245fa at 60 °C (4.6 bar). The mass velocity is ranging from 100 to 1500 kg/m² s, the heat flux is varying from 10 to 90 kW/m² and the inlet vapor quality from 0 to 1. Four flow patterns (bubbly flow, bubbly–slug flow, slug flow and annular flow) are recognized. The comparison between the present experimental intermittent/annular transition lines and five transition lines from macroscale and microscale flow pattern maps available in the literature is presented. Finally, the influence of the flow pattern on the heat transfer coefficient is highlighted.     

One-dimensional interfacial area transport of vertical upward bubbly flow in narrow rectangular channel

The design and safety analysis for miniature heat exchangers, the cooling system of high performance microelectronics, research nuclear reactors, fusion reactors and the cooling system of the spallation neutron source targets requires the knowledge of the gas–liquid two-phase flow in a narrow rectangular channel. In this study, flow measurements of vertical upward air–water flows in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm were performed at seven axial locations by using the imaging processing technique. The local frictional pressure loss gradients were also measured by a differential pressure cell. In the experiment, the superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. The developing two-phase flow was characterized by the significant axial changes of the local flow parameters due to the bubble coalescence and breakup in the tested flow conditions. The existing two-phase frictional multiplier correlations such as Chisholm, 1967, Mishima et al., 1993 and Lee and Lee (2001) were verified to give a good prediction for the measured two-phase frictional multiplier. The predictions of the drift-flux model with the rectangular channel distribution parameter correlation of Ishii (1977) and several existing drift velocity correlations of Ishii, 1977, Hibiki and Ishii, 2003 and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities. The interfacial area concentration (IAC) model of Hibiki and Ishii (2002) was modified by taking the channel width as the system length scale and the modified IAC model could predict the IAC and Sauter mean diameter acceptably.     

Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination

A circular water jet (Re = 1.6 × 10⁵; We = 8.8 × 10³) plunging at shallow angles (θ ≈ 12.5°) into a quiescent pool is investigated computationally and experimentally. A surprising finding from the work is that cavities, of the order of jet diameter, are formed periodically in the impact location, even though the impinging flow is smooth and completely devoid of such a periodicity. Computational prediction of these frequencies was compared with experimental findings, yielding excellent agreement. The region in the vicinity of the impact is characterized by strong churning due to splashing and formation of air cavities. Measured velocity profiles indicate a concentration of momentum beneath the free surface slightly beyond the impact location (X/D_j ≈ 14), with a subsequent shift towards the free surface further downstream of this point (X/D_j ≈ 30). This shift is due primarily to the action of buoyancy on the cavity/bubble population. Comparisons of the mean velocity profile between simulations and experiments are performed, yielding good agreement, with the exception of the relatively small churning flow region. Further downstream (X/D_j ≳ 40), the flow develops mostly due to diffusion and the location of peak velocity coincides with the free surface. In this region, the free surface acts as an adiabatic boundary and restricts momentum diffusion, causing the peak velocity to occur at the free surface.