Introduction

The separation of fluids mixtures is an attractive study for researches and engineers. Today, using of hydro-cyclones is one of the most important methods for separating liquid–liquid two-phase fluids. Variability in application, simple utilization and low structural and operation costs are the benefits of using hydro-cyclones for this purpose. As shown in Fig. 1, the liquid–liquid hydro-cyclone separator has been made from simple components, such as inlet chamber, the section of cylindrical area, reducing and also tapered section, tail pipe and two overflow sections for offloading the phases [1]. Entering the inlet fluid as a tangential flow to the hydro-cyclone wall provides a circulation inside this hydro-cyclone and makes two vortex flows in this two-phase fluid [2]. The first vortex flow leads the heavier phase toward the cyclone wall, and the second vortex flow leads the lighter phase toward the center-line of this cyclone. This is the mechanism of separation of these phases within this hydro-cyclone. The fluid flow pattern and also extend of these vortex flows are depended to the size and shape of the inlet section [3, 4]. The offloading sections obtain the cyclone capacities attending to the inlet light phase fraction or split ratio. The sizes of these sections are depending on the application type of this cyclone [5]. The size and shape of the cylindrical section affect the vortex flow and the split ratio of this cyclone, subsequently [6]. The reducing section increases the fluid flow velocities, increases the strain stress and pressure drop and may cause the breaking down of droplets and decaying the split ratio of the cyclone [1]. The tapered section has important effects on the split ratio by increasing the residence time of the fluid flow with a suitable vorticity [6]. The tail pipe has been located at the end of tapered section to increase the residence time of the fluids [6, 7]. Various structural and coating materials have been used in these hydro-cyclones, which make their walls hydrophobic or oleophobic.

Fig. 1
figure 1

The configuration of the defined geometry and mesh for the liquid–liquid hydro-cyclone

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Hargreaves and Silvester [8] studied the water–oil flow inside a hydro-cyclone, numerically, using the Euler-Lagrangian method. The obtained experimental results using the laser velocimetry approved their numerical simulation. Young et al. [6] investigated the fluid flow in a liquid–liquid hydro-cyclone. They resulted that the droplets size, densities difference and the dimension of the cylindrical part have important effects on the split ratio of this cyclone. Grady et al. [9] simulated the fluid flow patterns inside an oil separator hydro-cyclone and obtained the velocity profile and also the efficiency of this cyclone. They illustrated that the Reynolds stress model approach is able to simulate the vortex flow within this cyclone, accurately. Petty and Park [10] presented the idea of using very small liquid–liquid hydro-cyclones for oil separation. Their numerical simulation of vortex flow inside these cyclones shows that there is a centrifugal acceleration within these cyclones as more as three times of the gravitational acceleration. Huang [11] presented a three-dimensional simulation for a turbulent flow of water–oil mixture (with a more than 10% of volumetric fraction of desecrated phase) in a hydro-cyclone using the Eulerian–Eulerian and the Reynolds stress modeling viewpoint. He approved the predictions of this numerical model using the experimental data. Kharoua et al. [12] investigated the oil separation and also predicted the velocity profiles which includes axial and tangential velocity components in a hydro-cyclone using the Reynolds stress and k−ε turbulent models. They resulted that these hydro-cyclones have a low performance in the oil separation of high concentrations mixtures. Zhao et al. [13] showed that an air injection to the oil separator hydro-cyclone improves the ability of this cyclone for oil separation. Teja et al. [14] demonstrated the effects of the slope of the tapered area of this hydro-cyclone on its performance, numerically and experimentally. Jiawang et al. [15] presented a numerical design for the water–oil separator hydro-cyclone. They obtained an optimum pressure drop in a high-performance cyclone. Osei et al. [16] used the computational fluids dynamic for investigating the cylindrical section length effect and also the inlet section on the split ratio of the cyclone. Fan [17] used a similar method for investigating the effects of the operating conditions and also the properties of inlet mixture on this ratio. Qian et al. [18] investigated the influence of the slope of the tapered section and also the inlet fluid flow on the droplet concentration within a liquid–liquid hydro-cyclone. Motin and Benard [19] also investigated the effects of the geometry of the circulation section of the hydro-cyclone on its split ratio.

Delgadillo and Rajamani [27] compared three different models of k−ɛ group renormalization, the Reynolds stress and the large eddy simulation (LES), in order to predict air-core dimension, mass split, axial and tangential component of velocity variables in hydro-cyclone. They investigated good agreement of particle tracking by velocity field with experimental size–classification curve. Narasimha et al. [28] simulated the fluid flow through hydro-cyclone by Fluent commercial software package and good agreements have been achieved for the forecasted water splits in the outlet sections for different inlet water amount according to discrete phase modeling technique as first step of process. Additionally, particles classification based on their size has been observed. Delgadillo and Rajamani [29] used Fluent software to investigate desired classification of hydro-cyclone based on hydrodynamics parameters. They used the (LES) approach for simulating turbulence flow and particle-tracking method has been implemented based on the Lagrangian method in order to track particles locations. Six new developed geometries compared with basic geometries in the case of mass balance and classification curve. Chakraborti and Miller [30] presented an acute evaluation of fluid flow models and flow measurement techniques in hydro-cyclones. In their study, empirical, semi-empirical and the equation of Navier–Stokes are discussed.

The transient swirl flow simulation in the hydro-cyclone separators has been done by Chakraborti et al. [31]. They used Fluent package as CFD simulation software. Also, they developed ‘novel multi-objective genetic algorithm’ in their studies. The volume of the locus of zero vertical velocity (LZV) and the overall pressure drop have been optimized simultaneously in their model. Delgadillo and Rajamani [32] compared Reynolds stress model (RSM) and k−ɛ model with velocity profiles. Their investigation has been done in 75 and 250 mm diameter hydro-cyclones. They observed that the RSM and k−ɛ models were not able to estimate velocity profile, and large eddy simulation method has been introduced for velocity profile estimation. Suresh [33] presented the experimental setups for investigating the separation performance characteristics of the dense media hydro-cyclone (DMC). Hsieh and Rajamani [34] developed a new mathematical and theoretical model for hydro-cyclone according to the physical approach of the fluid flow. The velocity profile and separation efficiency curve have been estimated as the output of developed model. They validated their results with laser-doppler velocimeter (LDV) to investigate the velocity values inside a 75-mm hydro-cyclone. In order to illustrate increasing of slurry viscosity, pure water and the mixture of the glycerol-water have been used in the presence of particles. Monredon et al. [35] investigated the stability of developed mathematical model of the hydro-cyclone based on the physics of fluid flow with extreme variation in device geometries. They used five hydro-cyclones, and velocity profiles have been measured by the LDV.

In 2009, Kharoua et al. [36] examined the separation of petroleum from water and predicted axial and tangential velocity components in a hydro-cyclone. In this work, they used the RNG and RSM turbulent models to investigate the effect of mixing on the velocity profiles and the mixed multiphase model for the system in multiphase mode. They investigated the effect of changes in concentration of the oil at the inlet, the size of oil droplets and inlet fluid flow on separation efficiency. Their results showed that, for high oil concentrations, the separation efficiency has been decreased and with increasing the inlet fluid flow, the separation efficiency has been increased. They also resulted that the RSM model has less error with the experimental results, comparing with the RNG model. Cullivan et al. [37] numerically examined the pressure distribution and particle routing. Using the RSM turbulence model, they simulated the air-core inside the hydro-cyclone and found that specifically in this geometry and this flow there is a significant difference between the turbulent RSM model and the turbulent models of the two equations.

  • In the present study, the fluid flow patterns have been simulated using the computational fluids dynamic for investigating the effects of different geometrical and operating effective factors, such as the hydrophobic and oleophobic walls of the hydro-cyclone, on the separation performance of the liquid–liquid hydro-cyclone. Finally, a set of cases, with a full factorial experimental design, of different sizes of three dimensions of this hydro-cyclone has been tested in this simulation for obtaining the optimum geometry with a maximum separation performance in this cyclone. This study presents valuable results for designing a suitable hydro-cyclone for separating oil from water. For designing high-efficiency and low-pressure-drop hydro-cyclone for this propose, the wall hydrophobic properties, inlet zones and also flowrate of the mixture fluid, the sizes of top offloading and also the tail pipes, and different sections of the hydro-cyclone section have been optimized in this study. Therefore, the presented ideas in this study can be developed for designing various hydro-cyclones with different operating purposes.

Methodology

First, a three-dimensional geometry of a predesigned cyclone [20] has been defined as the presented geometry in Fig. 1. Then, a nonstructural tetrahedral hybrid grid has been used for meshing within this geometry, as shown in Fig. 1. Inlet constant fluid flow velocity (6 m s−1), uniform outflows (0.17 and 0.83 kg s−1 mass flows of the top and bottom offloads, respectively) and no-slip are defined boundary conditions for the fluid flow in this cyclone. The properties of inlet mixture have been defined as 95% and 5% volume fractions, 998 and 850 kg m−3 densities and 0.001 and 0.0032 kg m−1 s−1 for the water and oil fluids, respectively.

Attending to the low concentration of oil in the inlet mixture and also low values of the droplet relaxation time (i.e., \(\frac{{\left( {\rho_{m} - \rho_{p} } \right)d_{p}^{2} }}{{18\mu_{f} }}\) = 1.7 × 10–5 that is smaller than 0.001), the mixture model has been considered for this simulation. The continuity equation has been defined as [21]:

$$\frac{\partial }{\partial t}\left( {\rho_{m} } \right) + \nabla .\left( {\rho_{m} \overrightarrow {{v_{m} }} } \right) = 0$$
(1)

where t is time, \(\overrightarrow {{v_{m} }} = \tfrac{{\sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} v_{k} } }}{{\rho_{m} }}\) is the mass averaged velocity of a n-component mixture fluid, \(\rho_{m} = \sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} }\) is the mean density of this mixture and \(\alpha_{k}\) is the volume fraction of kth phase. The momentum balance equation for a mixture is a summation of the balance of the momentum for each phase, which can be presented as below [21]:

$$\frac{\partial }{\partial t}\left( {\rho_{m} \overrightarrow {{v_{m} }} } \right) + \nabla .\left( {\rho_{m} \overrightarrow {{v_{m} }} \overrightarrow {{v_{m} }} } \right) = - \nabla P + \nabla .\left[ {\mu_{m} \left( {\nabla \overrightarrow {{v_{m} }} + \nabla \overrightarrow {{v_{m}^{T} }} } \right)} \right] + \rho_{m} \overrightarrow {g} + \overrightarrow {F} + \nabla .\left( {\sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} \overrightarrow {{v_{dr,k} }} \overrightarrow {{v_{dr,k} }} } } \right)$$
(2)

where P presents the pressure value, \(\overrightarrow {g}\) is the gravitational acceleration vector, \(\overrightarrow {F}\) is the vector of external forces and \(\mu_{m} = \sum\limits_{k = 1}^{n} {\alpha_{k} \mu_{k} }\) is the viscosity of mixture. \(\overrightarrow {{v_{dr,k} }} = \overrightarrow {{v_{k} }} - \overrightarrow {{v_{m} }}\) is the drift velocity vector of the kth phase that can be calculated using the relative velocity of p and q phases (\(\overrightarrow {{v_{pq} }} = \overrightarrow {{v_{p} }} - \overrightarrow {{v_{q} }} = \frac{{\left( {\rho_{p} - \rho_{m} } \right)d_{p}^{2} }}{{18\mu_{q} f_{{{\text{drag}}}} }}\overrightarrow {a}\)) as \(\overrightarrow {{v_{dr,p} }} = \overrightarrow {{v_{pq} }} - \sum\limits_{k = 1}^{n} {\frac{{\alpha_{k} \rho_{k} }}{{\rho_{m} }}\overrightarrow {{v_{qk} }} }\), where \(d_{p}\) is the droplet diameter, \(f_{{{\text{drag}}}} = \left\{ {\begin{array}{*{20}c} {1 + 0.15{\text{Re}}^{0.687} } & {{\text{Re}} \le 1000} \\ {0.0183{\text{Re}} } & {{\text{Re}} > 1000} \\ \end{array} } \right.\) is the drag function and \(\overrightarrow {a} = \overrightarrow {g} - \left( {\overrightarrow {{v_{m} }} .\overrightarrow {\nabla } } \right)\overrightarrow {{v_{m} }} - \frac{{\partial \overrightarrow {{v_{m} }} }}{\partial t}\) is the acceleration vector of droplet. The volume fraction of another phase has been calculated using the following equation [21]:

$$\frac{\partial }{\partial t}\left( {\alpha_{k} \rho_{k} } \right) + \nabla .\left( {\alpha_{k} \rho_{k} \overrightarrow {{v_{m} }} } \right) = - \nabla .\left( {\alpha_{k} \rho_{k} \overrightarrow {{v_{dr,\,k} }} } \right)$$
(3)

The previous studies approved the abilities of the Reynold stress model for an accurate simulation of this turbulent flow inside the hydro-cyclone [7, 22,23,24]. Therefore, this model has been used for simulating this fluid flow as below [25]:

$$\begin{aligned} & \frac{\partial }{\partial t}\left( {\rho \overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }} } \right) + \frac{\partial }{{\partial x_{k} }}\left( {\rho u_{k} \overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }} } \right) = - \frac{\partial }{{\partial x_{k} }}\left[ {\overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} u_{k}^{^{\prime}} }} + P^{^{\prime}} \left( {\delta_{kj} u_{j}^{^{\prime}} + \delta_{ik} u_{j}^{^{\prime}} } \right)} \right] + \frac{\partial }{{\partial x_{k} }}\left[ {\mu_{m} \frac{\partial }{{\partial x_{k} }}\left( {\overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }} } \right)} \right] \\ & \quad - \rho_{m} \left( {\overline{{u_{i}^{^{\prime}} u_{k}^{^{\prime}} }} \frac{{\partial u_{j} }}{{\partial x_{k} }} + \overline{{u_{i}^{^{\prime}} u_{k}^{^{\prime}} }} \frac{{\partial u_{i} }}{{\partial x_{k} }}} \right) + \overline{{P^{^{\prime}} \left( {\frac{{\partial u_{i}^{^{\prime}} }}{{\partial x_{j} }} + \frac{{\partial u_{j}^{^{\prime}} }}{{\partial x_{i} }}} \right) - 2\mu_{m} }} \overline{{\frac{{\partial u_{i}^{^{\prime}} }}{{\partial x_{j} }}\frac{{\partial u_{j}^{^{\prime}} }}{{\partial x_{i} }}}} \\ \end{aligned}$$
(4)

hence P' and u' are the fluctuations of the pressure and velocity values, and δ is the kronecker delta. The presented governing equations have been solved, numerically, using the QUICK method. The SIMPLE algorithm and PRESTO model have been used for relating the pressure to the velocity and discretization of the pressure in this simulation, respectively. The acceptable accuracy for the convergence of these calculations has been considered as 10–5. Finally, a set of numerical simulations with a full factorial design has been investigated for obtaining the optimum sizes for the reduced section length and diameter and also the length of the cylindrical section.

Results and Discussion

All the presented results in this section have been based on \({\text{Efficiency}} = \frac{{{\text{Mass}}\,{\text{flowrate}}\,{\text{of}}\,{\text{outlet}}\,{\text{oil}}\,{\text{from}}\,{\text{top}}\,{\text{offload}}}}{{{\text{Mass}}\,{\text{flowrate}}\,{\text{of}}\,{\text{inlet}}\,{\text{oil}}}}\) and \({\text{Pressure}}\,{\text{drop}}\,{\text{ratio = }}\frac{{{\text{Inlet}}\,{\text{pressure}}\,{\text{of}}\,{\text{top}}\,{\text{offload}}}}{{{\text{Inlet}}\,{\text{pressure}} - {\text{Pressure}}\,{\text{of}}\,{\text{bottom}}\,{\text{offload}}}}\). First, the grid study has been presented to show the mesh independency of this numerical solution. For this purpose, the hydro-cyclone has been meshed with 105,000, 300,000 and 380,000 calculation cells. The results of this study have been presented in Fig. 2. As seen in this figure, 300,000 cells have suitable accuracy and calculation time. Therefore, this mesh was used for this simulation. In the second step, the accuracy of the developed model is validated with the experimental data of Belaidi and Thew [26] study for validating the accuracy of these predictions. Figure 2 shows this comparison, and this comparison approves the ability of this model to simulate this fluid flow.

Fig. 2
figure 2

Mesh study and comparing the model predictions with the experimental data [26]

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The entered pressure on the oil in the radial direction, which has been provided by the vortex flow inside the hydro-cyclone (as seen in Fig. 3), causes the motions of the oil and water phases toward the center and wall of the hydro-cyclone, respectively. Figure 4 shows this phenomenon inside the cyclone. Figure 5 shows the pressure variations within the hydro-cyclone. The formed vortex flow by the tangential fluid inlet provided radial and axial pressure gradients. It is clear that the fluid pressure value close to the cyclone walls is more than its center-line. A vacuum zone is near the top offloading zone, which caused the upward fluid flow inside the cyclone.

Fig. 3
figure 3

The fluid flow contour plot inside the cyclone

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Fig. 4
figure 4

The velocity of fluid flow inside the cyclone

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Fig. 5
figure 5

The pressure variation of the fluid flow in the inner part of the cyclone

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Figure 6a compares the separation efficiency of the hydro-cyclone with different inlet flowrates. It is clear that increasing this flowrate improves the efficiency of this cyclone. The oil separation in the tapered section has been resulted from the entered circulation force on the oil droplets in its residence time. This force has been provided by a suitable entrance flow of the mixture fluid. High flowrates of inlet fluid flow improve the vortex flow inside the cyclone and increase the oil separation rate from the water, consequently. This figure also presents the pressure drop ratios (PDR) for different inlet flowrates. It is clear that increasing this flowrate decreases this ratio.

Fig. 6
figure 6

Comparing the separation efficiencies and pressure drop ratio of the hydro-cyclone with different a inlet flowrates, b diameters of top offloading pipe and c diameters of reducing section

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Figure 6b compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different diameters of top offloading pipe. It is observed that increasing this diameter ameliorates the cyclone separation efficiency and decreases the pressure drop ratio in this cyclone. Figure 6c compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different diameters of reducing section. It is clear that increasing this diameter increases the residence time of mixture inside the hydro-cyclone with a suitable vortex velocity, increases the separation efficiency of the cyclone and increases its pressure drop ratio, consequently. Figure 7a compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different diameters of tapered section. Increasing the size of this section increases the residence time of mixture fluid inside this section of cyclone with a suitable centrifugal force. But, increasing the diameter of this section decays the vortex velocity of the fluid; therefore, this increment decreases the oil separation of this hydro-cyclone. This increment also increases the pressure drop ratio of the cyclone.

Fig. 7
figure 7

Comparing the separation efficiencies and pressure drop ratio of the hydro-cyclone with different a diameters of tapered section, b lengths of cylindrical section and c lengths of tapered section

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Figure 7b compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different lengths of cylindrical section. Increasing the length of this section of hydro-cyclone increments the residence time of the mixture fluid inside the section of cyclone with a low vortex velocity. In addition, increasing the length of this section of cyclone increases the entered force from the wall side to the fluid, decreases the vortex flow velocity and decays the separation efficiency of the cyclone and also increases its pressure drop ratio, consequently. Figure 7c compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different lengths of tapered section. Increasing this length increases the residence time of the mixture fluid inside this section of the cyclone that has a suitable vortex velocity for this separation. However, increasing this length also increases the entered force from the cyclone wall to the fluid flow and prevents its separation efficiency improvement for too long tapered sections. It is the reason of increasing of the pressure drop ratio of the cyclone with increasing the longitudinal dimension of this section. Figure 8a compares the separation efficiencies and also pressure drop ratio of the hydro-cyclone with different lengths of reducing section. It is clear that increasing the length of this section decays the separation efficiency of the hydro-cyclone. Attending to the slope of the cyclone wall and also high velocity of the fluid flow in this section, this increment increases the extent of the flow turbulence and decays the separation efficiency, as a result. This increment also increases the pressure drop ratio of the cyclone. Figure 8(b) compares the separation efficiencies and also pressure drop ratio for length variation of the tail pipe. Increasing the length of this pipe increases the residence time of the mixture fluid inside the cyclone, but also increases the wall effects that decays the vortex velocity of the fluid flow. These factors have positive and negative effects on the separation efficiency of related cyclone. By increasing the length of this section of the cyclone also, the pressure drop ratio decreases.

Fig. 8
figure 8

Comparing the separation efficiencies and pressure drop ratio of the hydro-cyclone with different a lengths of reducing section and b lengths of the tail pipe, and also c effects of hydrophobic and oleophobic walls of the cyclone on its separation efficiency

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Figure 8c shows the effects of hydrophobic and oleophobic walls of the cyclone on its separation efficiency. It is clear that oleophobic wall has no important effect on the cyclone performance, because the oil volume fraction in the mixture fluid is low. Nevertheless, the hydrophobic wall has an important effect on the cyclone separation efficiency improvement. Attending to the slip condition of this type of cyclone wall for the water fluid, this wall has no effects on the vortex flow velocity (see the fluid velocity profiles in Fig. 9). Figure 10 illustrates the effects of the number of inlet pipes of the hydro-cyclone on its performance. It is clear that the symmetry of the flow inside the cyclone with double inlet pipes is more than the cyclone with a single inlet pipe. This symmetry improves the vortex flow inside the cyclone and improves its separation ratio, consequently.

Fig. 9
figure 9

Effects of hydrophobic wall of the cyclone on the fluid velocity profiles

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Fig. 10
figure 10

Effects of the number of inlet pipes of the hydro-cyclone on its performance

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Figure 11 demonstrates the axial direction of the fluid velocities in three various heights of the hydro-cyclone. The results investigated that, near the wall, the fluid velocity is negative, which means that flow is downward, and at the axial location of the hydro-cyclone, the fluid velocity is positive, indicating the reverse flow (upward flow) at this axis. The junction of these two fluid flows with opposite directions is known as the zero vertical velocity (LZV). Drops in this area have an equal chance for entering to the upstream (reverse flow) or downstream flow. The results show that, from the upside to the bottom part of the hydro-cyclone, the reverse flow has been decreased and the downward flow has been increased. Figure 12 illustrates the volume fractions of the dispersed oil phase within the hydro-cyclone at different heights of the hydro-cyclone. It is clear that, from the top to the downward part of the hydro-cyclone, the volume fraction of the dispersed phase has been decreased, which confirms the existence of the reverse flow.

Fig. 11
figure 11

Axial velocities at a 10, b 50 and c 90 mm from the top part of the hydro-cyclone

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Fig. 12
figure 12

Volume fractions of the dispersed oil phase within the hydro-cyclone at a 10, b 50 and c 90 mm from top of the hydro-cyclone

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As previously described, a full fractional factorial design of numerical runs has been developed for obtaining the optimum sizes of the most important dimensions of the hydro-cyclone geometry. Therefore, 27 cases of hydro-cyclone with different length dimension of the cylindrical section and the length and diameter of the reducing segment have been simulated and the predicted values of the separation efficiency and also the pressure drop ratio of the cyclone have been compared. Table 1 presents the obtained values for these target parameters in these cases. Considering the presented values in this table, the optimum values for the cylindrical section length and the length and diameter of the reducing section are 25, 60 and 20 mm, respectively. The obtained optimum design for this cyclone has 84.2% separation efficiency.

Table 1 Obtaining the optimum geometry of the cyclone using a set of numerical simulations
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Conclusions

In this study, a three-dimensional simulation of the oil–water two-phase mixture fluid separation in a hydro-cyclone has been presented. The mixture model and also the Reynold stress model were used for this modeling. After the grid study in order to show independency of grid and validation of the presented model with experimental results, effects of various geometrical and operational parameters on the cyclone performance were investigated. Finally, an optimum design with high separation efficiency was presented. The following conclusions were obtained in the present study:

  • Increasing the inlet flowrate of the mixture fluid enhances the separation efficiency factor and reduced the pressure drop ratio of the cyclone.

  • Increasing the top offloading pipe decreases the separation efficiency and also the pressure drop ratio of the cyclone.

  • Increasing the diameter of the reducing section increments the separation efficiency and additionally the pressure drop ratio of the cyclone.

  • Increasing the diameter of the tapered section increases the separation efficiency and also the pressure drop ratio of the cyclone.

  • By increasing the length of the cylindrical section, the separation efficiency and the pressure drop ratio of the cyclone decreases and increases, respectively.

  • Increasing the axial dimension of the tapered section increases the separation efficiency and additionally the pressure drop ratio of the cyclone.

  • Increasing the length of the reducing section decreases the separation efficiency and increases the pressure drop ratio of the cyclone.

  • Increasing the length of the tail pipe increases the separation efficiency and decreases the pressure drop ratio of the cyclone.

  • A double inlet cyclone has a more separation efficiency than a single inlet cyclone.

  • A hydrophobic wall improves the separation efficiency of the hydro-cyclone.

  • The optimum sizes for the length of the cylindrical section and the length and diameter of the reducing section are 25, 60 and 20 mm, respectively.