Numerical and experimental investigation of two phase flow geometrical characteristics

: This paper presents an experimental and numerical analysis of the effect of the geometric parameter on the two-phase flow (white kerosene-water) flow pattern sys-tem. The investigation was carried out using three lengths (1, 2 and 3) m of rectangular horizontal smooth channel and three channel heights of (5, 7.5 and 10) cm respectively. The flow conditions for the input water velocity (0.2 m/s) and the input kerosene velocity (0.1 m/s) for both measurements have been investigated. Two- inlet techniques have been employed. Firstly, at the inlet, the kerosene was on top of the bath. Then, second, from the center, the kerosene inlets (water is above and below the kerosene). A numerical verification analysis was introduced using the ANSYS software using the method of volume of fluid (VOF) and mixture multiphase flow modeling coupled with the nor-mal k- ε turbulence schemes. A collection of seven methods of CFD types is explored by running 224 instances. Com-parisons were made between numerical and experimental works.


Introduction
In industry the multiphase flows extremely widely are used. Two or three phases were transportation as an immiscible fluid or may be in various physical flow conditions. These flows are occurring in much industrial sectors such as (petroleum, agricultural, food, pharmaceutical, etc.) [1]. Crude oil sources have outlying for the time being from most of strainer and processing centers. The high in pressure losses was major issue of dense and ordinary oil transmission in the horizontal of pipes line, which was high viscosity effect on friction, moreover, the acceleration or deceleration will cause increase these effect. The losses reduction was done by mix it with water. However, the multiphase oil-water pipe flow problem is very complex. It is highly dependent on many parameters such as input of the phases' fraction, velocity of each phase, hydraulics diameter, and smoothness and ribbing inside the wall. There are number of experimental and analytical studies on liquid-liquid flow in conduit. Russell et al. [2] carried out study the liquid-liquid flow where find three flow patterns by visual observations; stratified flow, bubble flow and mixed flow which were the first on this field. Charles et al. [3] investigated flow patterns, holdup ratios and pressure gradients, which had been the flow patterns Ao/w, So/w, Bo/w and Bw/o, and Do/w phase were observed. Karabelas [4] carried out a study to measure size spectra water dispersed in hydrocarbons with various flow rates. In parallel, Arirachakaran et al. [5] investigated pressure drop, flow rate, input water fraction, in-situ holdup, mixture temperature, and flow pattern, which were developed maps and two models to prediction pressure-gradient. Soleimani et al. [6] discussed observation of the flow pattern and pressure drop with two mixer elements were used. Trallero et al. [7], and Chakrabarti et al. [8] introduced a two group of liquid-liquid flow patterns were called segregated and dispersed flow, which it were a different classification for flow patterns, and the segregated flow divided at stratified and intermittent flow. Fairuzov et al. [9] investigated by using a multi-point sampling probe a flow pattern transitions in horizontal pipelines carrying oil-water mixtures. Elseth [10] studied the behavior of the simultaneous focus have been on stratified and dispersed flow with pressure drops and local phase fractions of oil/water in horizontal conduits. Lovick and Angeli [11] investigation of the pressure drops, void fraction and flow pattern for two liquids. It was performed test to continuous of dual liquids in a horizontal pipe which was shown at middle mixture velocities. Bannwart et al. [12] studied the flow patterns for vertical and horizontal formed by heavy crude oil and wa-ter, which obtained for horizontal test section (stratified, bubbly-stratified, dispersed bubbles, and annular). Vielma et al. [13] collected several information were obtained on flow patterns, gradient of pressure, volume fraction and droplet size as function of flow patterns, which were used in flow description and validity of an oil-water model. Kumara et al. [14], Ismail et al. [15] and Zhai et al. [16] carried out experimental studies to obtain pressure gradient and flow structure for oil and water. Tan et al. [17] studied the effect of oil viscosity, pipe diameter, pipe material, and oil type on the flow pattern effect.
For the Computational fluid dynamics (CFD) part, Brauner and Maron [18] considered a parametric studied for wide ranges as density and viscosity relations to discuss the stability convergence to various extremes. Brauner [19] predicted the flow transition boundary of stratified to dispersed flow successfully. Gao et al. [20] utilized VOF with RNG k-ε turbulence models combined with a near-wall low-Re to a stratified oil-water for steady-state flow were analyzed, which Pressure loss and hold-up were predictions, such showed acceptable agreement with experimental data. Desmala et al. [21] used VOF method with unsteady flow to predict the flow pattern (plug, slug, stratified wavy, stratified mixed and annular) maps and radial distribution of volume fraction. Shi et al. [22] employed method of the volume of fluid model with the SST k-ω scheme to compare the results with experimental of oil-water flow, which obtained a various flow pattern as core annular, plug of oil in water, oil bubbles in water and dispersed flow. Burlutskii [23] analyzed three dimensional CFD using k-ε turbulence model with standard wall function, which imposed classical Lagrangian method to obtain dispersed flow. Baotong et al. [24] developed a new correlation for immiscible liquid utilized least square technique to compare experimental data with drift-flux correlation.
The objective of this paper is to introduce a new approach to investigate the development ability of oil-water flow in horizontal channel using geometrical parameters to predict the changes in flow pattern experimentally and numerically. A customized rig is built up for the experimental work. The numerical part is done utilizing CFD package FLUENT of ANSYS platform. Four influencing factors: effect of the length channel, the ratio of high to width, type of inlet flow, and the area of inlet ratio are chosen in this study to investigate flow patterns, pressure drops, and hold up.

Mathematical modeling and CFD
Volume of fluid (VOF) and mixture models are employed in this paper utilizing ANSYS FLUENT 19.0 over the other methods [25] due to its ability to predict the factors of each model in one hand. On the other hand, its simplicity and computational low cost. The CFD simulation carried out utilizing VOF and mixture models for different horizontal channels dimensions. Some assumptions are needed before proceeding to the modeling. These assumptions are introduced to simplify the proposed model solution

Assumptions
The fluid flow is considered two dimensional, turbulent, and incompressible, no chemical reaction and the fluid properties are considered as constants.

The standard k-ε model
Based on model transport equations for the turbulence kinetic energy (k) and dissipation rate (ε), the prediction of this model shows good results according to [27]. For incompressible flow, the model has the following form, [21] and [26]: Where σ k and σε are turbulent Prandtl numbers for k and ε respectively; Y M represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate; and S k and Sε are the source terms G k represents the generation of turbulent kinetic energy due to the mean velocity gradient.

VOF model theory
The capture of phase distributions was employed the volume of fluid (VOF) model carry out in the FLUENT. The phases have been engaged conservation equations with single set at the VOF model. Conservation equation was considered without mass transfer and phase change which should be an isothermal system. The equation of mass can be written as: The momentum equation is as follows: The parameters (p, F, and ρg) interaction in dispersed flow will be denoted as Static pressure, external body force and gravitational body force, respectively. The primary phase (water) and the secondary phase (oil) was tracked interface together, which solution the equation of conservation for secondary phase (oil) the void fraction, αo. The equation of the volume fraction is: The volume fraction equation was not solved for the primary phase (water). The volume fraction of the primary phase was determined by the constraint: Oil or water were filled the control volume completely, the volume fraction of the phase has a value of 0 or 1, so that the interface within control volume between 0 and 1. The properties of matter in the transport equations were finding in each control volume by the presence of the component phases. For two phase flow (oil-water), that the density and viscosity in each cell was:

Mixture model theory
The mixture model can be used in different ways, which was a simplified multiphase model can be applied with different phase's flows at different velocities. In addition, it is applicable to model homogeneous multiphase flow and to calculate non-Newtonian viscosity, which can model fluid or particulate for two or more phases when solved both the continuity equation and the momentum equation for the mixture. Furthermore, the mixture model can be a combination of dispersed phase and the continuous phase. The conservation equations used are the mass equation: where ⃗ um: is the mass-averaged velocity and it is given by: ∑︀ n k=1 α k ρ k u k ρm (10) and ρm is the mixture density calculated by: Where α k is the volume fraction of phase. Moreover, the momentum equation: Note that, if the slip velocity is not solved the mixture model is reduced to a homogeneous multiphase model.

Computational geometry
As mentioned previously, four influencing factors are chosen to study the effect on flow pattern, pressure drops, and hold up. These factors are as following: 1. Effect of the channel length chosen to be (1, 2, 3) m.
2. The ratio of high to width is (1/2), selected for the channel heights is (5, 7.5, and 10) cm. 3. Type of inlet flow; halt to half (water in the bottom and upper oil). The other type was the oil inlet from the centre and the water is on the bottom and top of the oil, see Figure 1. 4. The area of inlet ratio is 1-1. i.e. (1 water to 1 oil).

Mesh generation
The geometry and mesh were developed in this study done by Ansys design modeler and imported into FLUENT for

Test of grid independence
The grid generation is a necessary task in any analysis. The condition of Reynolds number is an important to selection the mesh size, which can be divided into three types (fine, medium, and coarse). It was carried out the test to get the acceptable mesh cell size for special geometry. Three mesh faces are considered for 2-D which are listed pervious in the Tables 1 and 2. All three mesh faces are used to plot the (y+) for the channel estimated from Eqs. (13)- (15) and the values depicted in the Table 3. The mesh types were tested with an inlet velocities (Usw=0.2) m/s and (Uso=0.1 m/s) flow conditions of full flow domain of liquid used on the same x-y plot.
The standard wall functions are applied in Fluent program supported at the work of Launder and Spalding [26] since it is well-known and widely used in industry. They Where the dimensionless velocity is: (14) and the dimensionless distance from the wall is: Where: k = 0.4187 (von Karman constant), E = 9.793 (empirical constant) Up = fluid mean velocity near wall cell centroid kp = turbulence kinetic energy near wall cell centroid yp = distance from the centroid near wall cell centroid Cµ = 0.09, µ = fluid dynamic viscosity

Simulation setup
Different setups and geometries were chose in this study for investigation. The types of scheme and high grid of resolution were computationally expensive. In addition, for the objective of discretization, and depend on requirement of solution accuracy were different scheme used as implicit or explicit scheme

Boundary conditions
The kerosene and water were split inlet into the zone, which was the computational domain full of water, then tracking the two liquids in the domain. The fluid properties listed in Table 4. The velocity input were listed in Table 5, where the boundary condition are selected from Lovick and Angeli [11].

Boundary conditions Setup conditions inlet-1 (water) Velocity magnitude 0.2 m/s Setup conditions inlet-2 (kerosene)
Velocity magnitude 0.1 m/s These conditions were summarized in Table 4, which was used in experimental work. Input condition employed for all optimization cases to prepare for a numerical solution that will compare results with experimental measurements. At the inlet, a velocity-inlet boundary type is used in which the water and kerosene velocities and the liquid volume fraction are specified.

Numerical investigation
The discretization of finite volume method was employed in governing transport equations. About continuity equation, and pressure-velocity coupling, which were imposed the algorithms of PRESTO! and PISO originally developed by Patankar [28] and Issa [29] were used. Table 6 shows the numerical relaxation factors and the discretization schemes. Selection volume fraction equation schemes is very important for solving case of multiphase flow problem, employed more than an option (First order, QUICK, Modified HRIC, and Compressive) then the choices are summarized in Table 6 with relaxation factors used for the numerical simulations. Numerical convergence was assumed when the residuals of continuity, momentum, turbulence and volume fraction equations were lowered by (10E−5) of magnitude. Turbulence intensity and hydraulic diameter were selected in the entrance, when turbulence model was active

Experimental setup
An experimental rig is built specifically for the study. The cross-section area was circular for pumping liquid in the pipe line but the channel has been a rectangular cross section area. Furthermore, was specially designed, an adjustment to fit circular cross section to rectangular cross section as seen in Figure 3. Parts of the rig are shown in Figure 4. Rectangular channel was manufactured to observe the flow of liquid-liquids with test section length of (3.6 m). It was provided with two storages tanks (water 2000 L, and oil 250 L), and at the end connected with separated tank has a (500 L). Oil and water were used with physical properties listed in Table 4. It connects with oil and a water pumps which were transport the two fluids from the storage tanks to the rectangular channel.   Characteristics of pumps selected for a water pump of (120 L/min) and for oil pump of (75 L/min). Moreover, the oil and water transmitted from the tank to the test section.

NUMERICAL AND EXPERIMENTAL INVESTIGATION OF TWO PH GEOMETRICAL CHARACTERISTICS
Kerosene was injected from the center, and the water injected from the lower and the upper layers with inclination angle of 8 ∘ with respect to the horizontal axis. The two liquids were mixed at the beginning of the channel entrance.
Moreover, the volumetric flow rates for liquids were controls by using calibrated turbine flow meter (Sorekarain 1") and gear flow meter (Bre 400).

Results and discussion
Two types of experiments were assumed. The first will be called (inlet the kerosene above the water) and the second will be called (inter kerosene from the center). Three heights of channel were assumed (5, 7.5, 10) cm. First of all, (D h = 3.33 cm) with the water velocity is settled at (0.2 m/s) and kerosene velocity at (0.1 m/s) applied at all runs of more than 224 cases (see Table 7).  VOF-implicit-sharp dispersed-compressive VOF-implicit-sharp-compressive VOF-implicit-sharp-modified HRIC [7] used (D h = 5.013 cm) to perform experimental flow pattern map, which appear at (Usw = 0.2 and Uso = 0.1) m/s stratified smooth flow pattern when compared with [8] who used (D h = 2.54 cm) shown stratified wavy at same velocities. Two models are applied, the mixture models contain four schemes and the VOF model used with three schemes listed in Table 8.

One-meter channel
The tests made with one-meter length channel did not show any change in flow pattern with chosen other models or changes in the schemes. The analysis to this group was rapid and no disruption in the progress of the iteration.

Two-meters channel
Compared to the real behaviour in the previous studies, the best settings must be selected in the mathematical analysis. The results show good similarity in showing clearly visible separating layer from the analysis the split layer between the liquids (oil and water).
Reduction the height of channel led to a faster convergence of the solution encouraged the use the residual 10 −4 instead of 10 −3 . An analysis of the cases, shown in Table 7, was simpler and less complicated. The convergence was proceeding at a good pace. It requires some adjustments to volume fraction until reach the final convergence.
For the cases in Table 8 the issue more complicated and requires intervention to adjust the settings of pressure, momentum and volume fraction due to the residual was not progressing regularly.
Changing the accuracy of the solution from (10 −3 to 10 −4 ) is the most recent change in the flow patterns. By increasing the steps of the solution, the breakup of the flow pattern changes. This indicates the instantaneous change of the phase, which is a result that matches the experimental fact corresponding to the computer analysis.
For cases of Table 9, the flow pattern shows a stratified for two liquids in the channel with some changes only in the entrance. Using (L = 2 m, H = 10 cm), the results does not show any change in the flow pattern during progression of the flow inside the channel. Table 10, shows distinct results for the flow pattern of (L = 2 m, H = 7.5 cm). The results show the change in the flow pattern for the low mesh size channel which transfers from straight to random flow patterns which indicates a very important phenomena that, for some cases the separate layer shows mixing the two liquids together. Table 11 shows the inlet of kerosene from the middle for (L = 2 m, H = 10 cm). The flow patterns show some differences through the channel.    The results in the Table 12 show that the flow was identical without any change in the flow pattern and certainly longer time needed to complete the solution.

Three-meters channel
The same inlet velocities were used in this analysis, so the effect of different densities was evident. Apparently, for the three-meter channel, when comparing the current results with previous results, there is a better behavior flow in this range of flow conditions.
The results in Table 13 were shows a little difference. It shows a repeated flow pattern with different models and scheme of analysis. Displays a pattern was similar to stratified flow pattern, and this was helped by increased length of the channel. Knowing that, by increasing the accuracy of mesh, there is no change in the pattern. Table 14 of the channels (L = 3 m, H = 7.5 cm), presents new cases that have been worked to know the effect of reducing the height and increasing the length of the channel on changing the flow pattern. The results were change appeared in flow pattern in the first half of the channel, except the (VOF-implicit-sharp-modified HRIC) no change appeared.
The results in Table 15 show that the flow was identical without any change in the flow pattern even though the height was reduced. Table 16 for the kerosene inters from the middle for two phase flow patterns (L = 3 m, H = 10 cm) represent illogical behavior. The reason is that the difference between the two fluids necessitates the buoyancy of the oil over the water and not the other way around.
In Table 17, this setting (mixture-implicit-no slip-quick), and (mixture-implicit-slip-quick) show a behavior that approximates practical experiments, in other word, the mixture model detects the situation of the expected flow.
In Table 18, the patterns solved by (mixture-implicit-no slip-quick) and (VOF-implicit-sharp-modified HRIC) form are very similar. Same appearance for (mixture-implicitno slip-quick) and (VOF-implicit-sharp-compressive) form. But there is a fundamental difference between the two forms. With deep inspection, the (mixture-implicit-no slipquick) and (mixture-implicit-slip-quick) have mixing of layers whereas the (VOF-implicit-sharp-modified HRIC) and (VOF-implicit-sharp-compressive) form are not. Table 19 shows a comparison between experimental and CFD work for (mixture-implicit-no slip-quick) scheme. The water velocity range from (0.2-1.3) m/s and for kerosene is from (0.02-1.0) m/s. The four flow patterns (ST & MI, Do/w &w/o, Do/w, and Do/w&w) observed from experimental work. The results show a good agreement between the CFD and the experimental work.        The main aim of this study is to investigate the influence of different parameters on the flow pattern of two-phase flow (liquid-liquid) in a rectangular channel. Experimental and numerical investigations were introduced in this work. A specialized rig is built for the experimental part while the numerical part achieved utilizing ANSYS Fluent package. A rectangular horizontal smooth channel of three lengths (1, 2 and 3) m and heights of (5, 7.5 and 10) cm respectively are employed. Kerosene and water are used to represent the fluid-fluid two phase flows. Two-inlet methods were employed. Firstly, the kerosene was interred on the top of water inlet. Then secondly, the kerosene inlets from the center (water is above and below the kerosene). The Flow conditions have been investigated for input water velocity (0.2 m/s) and input kerosene velocity of (0.1 m/s) for all testes. The VOF models and mixture were used in the analysis. More than 226 different cases and scenarios are accomplished in this study. The results indicate a good agreement between the experimental and numerical work. As a future study, different inlet velocities for oil and water will be used for investigation. In addition, ribbed channel will be considered as a new investigation parameter.

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Conflict of interest:
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