Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.     

Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow

This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

On the liquid turbulence energy spectra in two-phase bubbly flow in a large diameter vertical pipe

The liquid turbulence structure of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. A dual optical probe was used to measure the bubble characteristics, while the liquid turbulence was measured using hot-film anemometry. Experiments were performed at two liquid superficial velocities of 0.2 and 0.68 m/s for gas superficial velocities in the range of 0–0.18 m/s, corresponding to an area averaged void fraction up to 13.6%. In general, there is an increase in the liquid turbulence energy when the bubbles are introduced into the liquid flow. The increase in the energy mainly occurs over a range of length scales that are on the order of the bubble diameter. A suppression of the turbulence was observed close to the wall at very low void fraction flows. Initially, the suppression occurs in the low wave number range and then extends to higher wave numbers as the suppression is increased.     

Benchmark PIV database for the validation of CFD simulations in a transitional cavity flow

We present an experimental benchmark database for the transitional cavity flow. The database is obtained by planar Particle Image Velocimetry measurements at the median plane of the cavity model, for Reynolds numbers between 6300 and 19,000 based on the cavity height. A detailed uncertainty analysis of the experimental results is performed via the correlation statistics method for PIV uncertainty quantification and linear error propagation.The experimental results are compared to two-dimensional Reynolds-Averaged Navier Stokes (RANS) numerical simulations with different turbulence models. It is shown that, when the standard k-ω turbulence model is employed, the discrepancy between numerical simulations and experimental results exceeds the uncertainty of the latter. Conversely, RANS simulations with the SST k-ω turbulence model agree well with the experimental data in terms of time-averaged flow properties; however, the turbulent kinetic energy results present significant discrepancies at all considered Reynolds numbers. The data presented in this paper is made available for open-access download via the 4TU.ResearchData repository with DOI: https://doi.org/10.4121/14061233.     

Mass transfer problem for particles,drops and bubbles in a shear flow

A numerical solution of the axisymmetric steady heat and mass transfer problem for spherical particles, drops and bubbles in a linear Stokes shear flow is obtained for the entire range of Péclet numbers. Simple approximate expressions for the average Sherwood number in good agreement with the results of the numerical calculations are proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–141, July–August, 1990.     

Enhancement of heat transfer due to bubbles passing through a narrow vertical rectangular channel (Change in heat transfer along flow)

The objective of this paper is to make clear how heat transfer coefficient changes along the flow with the passing bubbles through a narrow vertical rectangular channel (20 mm wide, 2 mm deep and 450 mm long). The experiments were done using subcooled water of 80, 60, and 40 K at atmospheric pressure in which the air bubbles were injected into the channel at a designated period from 0.125 to 1.0 s and their length was controlled to be equal to 0.03, 0.02, and 0.01 m. The experiment shows that the heat transfer coefficients decrease along the flow and then reach a constant value beyond a certain distance from the leading edge of the heated surface where the flow becomes fully developed in both the velocity and the thermal conditions. Under the fully developed conditions, the heat transfer coefficients are predicted well by the existing theoretical analysis in which both the convective term and evaporation on the interface are ignored.     

Heat and mass transfer analogy for condensation of humid air in a vertical channel

This study examines energy transport associated with liquid film condensation in natural convection flows driven by differences in density due to temperature and concentration gradients. The condensation problem is based on the thin-film assumptions. The most common compositional gradient, which is encountered in humid air at ambient temperature is considered. A steady laminar Boussinesq flow of an ideal gas–vapor mixture is studied for the case of a vertical parallel plate channel. New correlations for the latent and sensible Nusselt numbers are established, and the heat and mass transfer analogy between the sensible Nusselt number and Sherwood number is demonstrated. Received on 15 November 1999     

Theoretical investigation of effects of local cooling of a nozzle divergent section for controlling condensation shock in a supersonic two-phase flow of steam

In supersonic adiabatic two-phase flows of steam, under the influence of supersonic acceleration, the fluid loses its equilibrium conditions and becomes supersaturated. Following this condition and to restore the fluid to equilibrium, micro droplets of water form in the absence of any surface or foreign particles. This phenomenon is called homogeneous nucleation and the formed minute small droplets grow along the fluid flow path. The formation of these droplets and their growth causes the release of the latent heat of evaporation to the gas phase particularly in the nucleation region, and results in an increase in the flow pressure which is called the condensation shock. In this paper, and in continuation of the series of papers by the authors, in addition to analytically solving the adiabatic gas-liquid supersonic flow of steam in a convergent-divergent channel, a novel solution to controlling the undesired effects of this pressure rise (condensation shock) is presented. In the proposed method, with the help of cooling the divergent section of the nozzle, the analytical model for the 1D non-adiabatic two-phase steam flows is further developed which shows considerable decrease in the intensity of the formed condensation shock. Also the growth rate of the formed droplets due to the cooling of the steam flow has higher importance than the nucleation itself.     

Experimental and CFD investigation of flow behavior and sand erosion pattern in a horizontal pipe bend under annular flow

The internal erosion of pipelines in oil and gas storage and transportation engineering is highly risky. High gas velocity of annular flow entrained sand will cause damage to the pipelines, and may further result in thinning of the wall. If this damage lasts for a long time, it may cause pipeline leakage and cause huge economic losses and environmental problems. In this research, an experimental device for studying multiphase flow erosion is designed, including an erosion loop and an experimental elbow that can test the erosion rate. The annular flow state and pipe wall erosion morphology can also be tested by the device. The computational fluid dynamics (CFD) method is combined with the experiment to further study the annular flow erosion mechanism in the pipeline. The relationship between gas-liquid-solid distribution and erosion profile was studied. The results show that the most eroded region occurs between 22.5° and 45° in the axial angle direction and between 90° and 135° in the circumferential angle direction of the elbow. The pits and deep scratches form on the surface of the sample after the sand collision.     

Numerical solutions of pulsating flow and heat transfer characteristics in a pipe

Numerical studies are made of flow and heat transfer characteristics of a pulsating flow in a pipe. Complete time-dependent laminar boundary-layer equations are solved numerically over broad ranges of the parameter spaces, i.e., the frequency parameter β and the amplitude of oscillation A. Recently developed numerical solution procedures for unsteady boundary-layer equations are utilized. The capabilities of the present numerical model are satisfactorily tested by comparing the instantaenous axial velocities with the existing data in various parameters. The time-mean axial velocity profiles are substantially unaffected by the changes in β and A. For high frequencies, the prominent effect of pulsations is felt principally in a thin layer near the solid wall. Skin friction is generally greateer than that of a steady flow. The influence of oscillation on skin friction is appreciable both in terms of magnitude and phase relation. Numerical results for temperature are analyzed to reveal significant heat transfer characteristics. In the downstream fully established region, the Nusselt number either increases or decreases over the steady-flow value, depending on the frequency parameter, although the deviations from the steady values are rather small in magnitude for the parameter ranges computed. The Nusselt number trend is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with previous theoretical predictions.     

The effects of transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder

This paper deals with a theoretical (numerical) analysis of the effects that blowing/injection and suction have on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the cylinder. Both cases of buoyancy forces aid and oppose the development of the boundary layer are considered. Similarity equations are derived and their solutions are dependent upon the mixed convection parameter, the non-dimensional transpiration parameter and the curvature parameter, as well as of the Prandtl number. Dual solutions for the previously studied mixed convection boundary layer flows over an impermeable surface of the cylinder are shown to exist also in the present problem for aiding and opposing flow situations.     

Experimental investigation of three-phase flow in a vertical pipe: Local characteristics of the gas phase for gas-lift conditions

Laboratory experiments have been performed on the flow of oil, water and air through a vertical pipe in order to study the gas-lift technique for oil–water flows. Special attention was paid to the phase inversion phenomenon, by which the continuous phase switches to the dispersed phase and vice versa. By using different types of gas injectors the influence of the bubble size of the injected air on the efficiency of the gas-lift technique (in particular at the point of phase inversion) was studied. Also the gas and liquid mixture velocities were varied. The air bubbles were detected by means of optical fibre probes. Local measurements of the time-averaged gas volume fraction, bubble size and bubble velocity were carried out, as well as pressure measurements.     

Two-phase flow in a vertical pipe and the phenomenon of choking: Homogeneous diffusion model—I. Homogeneous flow models

The paper examines the topological structure of all possible solutions which can exist in flows through adiabatic constant-area ducts for which the homogeneous diffusion model has been assumed. The conservation equations are one-dimensional with the single space variable $\text{z.}$ but gravity effects are included. The conservation equations are coupled with three equations of state: a pure substance, a perfect gas with constant specific heats, and a homogeneous two-phase system in thermodynamic equilibrium. The preferred state variables are pressure $\text{P.}$ enthalpy $\text{h.}$ and mass flux $\text{G}{}^2$.The three conservation equations are first-order but nonlinear. They induce a family of solutions which are interpreted as curves in a four-dimensional phase space conceived as a union of three-dimensional spaces ($\text{P, h, G}{}^2\text{, z}$) with $\text{G}{}^2\text{=}\text{const}$ treated as a parameter. It is shown that all points in these spaces are regular, so that no singular solutions need to be considered. The existence and uniqueness theorem leads to the conclusion that through every point in phase space there passes one and only one solution-curve.The set of differential equations, treated as a system of algebraic equations of each point of the phase space, determines the components of a rate-of-change vector which are obtained explicitly by Cramer's rule. This vector is tangent to the solution curve. Each solution curve turns downward in $\text{z}$ at some specific elevation $\text{z}{}^1$, and this determines the condition for choking. Choking occurs always when the exit flow velocity at $\text{L = z}{}^1$ is equal to the local velocity of propagation of small plane disturbances of sufficiently large wavelength, that is when the flow rate $\text{G}$ becomes equal to a specified, critical flow rate, $\text{G}{}^1$. (The possible dependence of the sonic velocity on frequency in a real flow is ignored, because it has not been allowed for in the equations of the model under study.) A criterion, analogous to the Mach number, which indicates the presence or absence of choking in a cross section is the ratio $\text{K = G/G}{}^7$ of the mass-flow rate $\text{G}$ to the local critical mass flow rate. $\text{G}{}^7$, $\text{K = 1}$ denoting choking. The critical parameters depend only on the thermodynamic properties of the fluid and are independent of the gravitational acceleration and shearing stress at the wall.The topological characteristics of the solutions allow us to study all flow patterns which can, and which cannot, occur in a pipe of given length $\text{L}$ into which fluid is discharged through a rounded entrance from a stagnation reservoir and whose back-pressure is slowly lowered. The set of flow patterns is analogous to that which occurs with a perfect gas, except that the characteristic numerical values are different. They must be obtained by numerical integration and the influence of gravity must be allowed for.The preceding conclusions are valid for all assumptions concerning the shearing stress at the wall which make if dependent on the state parameters only, but not on their derivatives with respect to $\text{z}$. However, the study is limited to upward flows for which the shearing stress at the wall and the gravitational acceleration are codirectional.     

Experimental study on condensation heat transfer in vertical minichannels for new refrigerant R1234ze(E) versus R134a and R236fa

Experimental condensation heat transfer data for the new refrigerant R1234ze(E), trans-1,3,3,3-tetrafluoropropene, are presented and compared with refrigerants R134a and R236fa for a vertically aligned, aluminum multi-port tube. Local condensation heat transfer measurements with such a multi-microchannel test section are very challenging due to the large uncertainties related to the heat flux estimation. Presently, a new experimental test facility was designed with a test section to directly measure the wall temperature along a vertically aligned aluminum multi-port tube with rectangular channels of 1.45 mm hydraulic diameter. Then, a new data reduction process was developed to compute the local condensation heat transfer coefficients accounting for the non-uniform distribution of the local heat flux along the channels. The condensation heat transfer coefficients showed the expected decrease as the vapor quality decreased (1.0-0.0) during the condensation process, as the mass velocity decreased (260-50 kg m⁻² s⁻¹) and as the saturation temperature increased (25-70 °C). However, the heat transfer coefficients were not affected by the condensing heat flux (1-62 kW m⁻²) or by the entrance conditions within the tested range. It was found that the heat transfer performance of R1234ze(E) was about 15-25% lower than for R134a but relatively similar to R236fa. The experimental data were then compared with leading prediction methods from the literature for horizontal channels. In general, the agreement was poor, over-predicting the high Nusselt number data and under-predicting the low Nusselt number data, but capturing the mid-range quite well. A modified correlation was developed and yielded a good agreement with the current database for all three fluids over a wide range of operating conditions.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Experimental study on the direct contact condensation of the steam jet in subcooled water flow in a rectangular channel: Flow patterns and flow field

Direct contact condensation (DCC) of steam jet in subcooled water flow in a channel was experimentally studied. The main inlet parameters, including steam mass flux, water mass flux and water temperature were tested in the ranges of 200–600 kg/(m² s), 7–18 × 10³ kg/(m² s), 288–333 K, respectively. Two unstable flow patterns and two stable flow patterns were observed via visualization window by a high speed camera. The flow patterns were determined by steam mass flux, water mass flux and water temperature, and the relationship between flow patterns and flow field parameters was discussed. The results indicated that whether pressure or temperature distributions on the bottom wall of channel could represent different flow patterns. And the position of pressure peak on the bottom wall could almost represent the condensation length. The upper wall pressure distributions were mainly dependent on steam and water mass flux; and the upper wall temperature distributions were affected by the three main inlet parameters. Moreover, the bottom wall pressure and temperature distributions of different unstable flow patterns had similar characteristics while those of stable flow patterns were affected by shock and expansion waves. The underlying cause of transition between different flow patterns under different inlet parameters was reflected and discussed based on pressure distributions.     

Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate

Heat and mass transfer along a semi-infinite vertical flat plate under the combined buoyancy force effects of thermal and species diffusion is investigated in the presence of a strong non-uniform magnetic field and the Hall currents are taken into account. The induced magnetic field due to the motion of the electrically conducting fluid is negligible. This assumption is valid for a small magnetic Reynolds number. The similarity solutions are obtained using the scale group of transformations. These are the only symmetry transformations admitted by the field equations. The non-linear boundary layer equations with the boundary conditions are transferred to a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the magnetic parameter M in the range of 0-1 with the Hall parameter m taking the values 0.5, 1, 2, and 3.