Numerical investigation of swirling flow in cylindrical

chemical engineering research and design 8 9 ( 2 0 1 1 ) 2521–2539

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Numerical investigation of swirling flow in cylindrical cyclones Rainier Hreiz, Caroline Gentric ∗ , Noël Midoux LRGP, CNRS-UPR 3349, Nancy-Université, ENSIC, 1 rue Grandville, BP 20451 Nancy Cedex, France

a b s t r a c t This paper constitutes a preliminary study of the two-phase flow in a Gas–Liquid Cylindrical Cyclone (GLCC©1 ) separator. A GLCC consists in a vertical pipe with a downward inclined tangential inlet. The incoming flow forms a swirling motion producing a centrifugal force. The gas and liquid are thus separated due to both centrifugal and gravity forces. Therefore the separation efficiency is higher than for conventional vessel type separators, allowing more compactness. In this study, the aim is to better understand the swirling hydrodynamics of this separator via CFD simulations. Therefore, the single-phase hydrodynamics is calculated for swirling flows generated by means of tangential injection(s) in a straight pipe. Geometry and flow conditions are chosen according to the experimental study of Erdal (2001a), who performed local measurements of the axial and tangential velocities. RANS, URANS and LES simulations are carried out using different turbulence models and different near wall treatments. Among the Reynolds Averaged Navier–Stokes (RANS) models, the high-Reynolds realizable k– model performs the best for predicting the local mean axial and tangential velocities. Its results are as good as the LES ones when the fluid is injected through only one inlet, while LES predicted flow is closer to the experimental one for two inlets. Numerical results also show that, contrary to the common approximation of the literature, the radial velocity magnitude is not negligible. The vortex core precession is well predicted by the simulations, which show that its direction is the opposite of the swirl one. We think that the growth of the turbulence kinetic energy in the core of the flow is directly linked to this phenomenon. Finally computations are conducted to investigate the effect of the inlet geometry on the cyclone hydrodynamics. According to simulations, the rectangular inlet performs better than a circular one, since it reduces the vortex distortion, which is supposed to improve the separation efficiency. © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Cylindrical cyclone separator; Swirling flow; CFD; Precessing vortex core

1.

Introduction

For most gas–liquid separations, the gas and petroleum industry has traditionally used conventional vessel type separators, which are heavy, bulky and expensive. The continuous increase of the number of off-shore installations and the emergence of sub-sea separation has increased the need for more compact separators which can lead to significant cost reducing. Among the possible alternatives, the GLCC (Gas–Liquid Cylindrical Cyclone), a cyclone separator developed by Tulsa University and Chevron, uses the centrifugal force in addition to gravity, and thus enhances the separation efficiency compared to conventional separators. A GLCC consists of a vertical

∗

pipe with a downward inclined tangential inlet located at midheight and two outlets located at the top and the bottom of the cylinder, dedicated respectively to the gas and the liquid collection. Fig. 1 shows a schematic plot of a GLCC. Due to gravity, the lower part of the separator is mainly occupied by liquid, while gas occupies the upper one. The tangential feeding forces the flow to swirl, thus producing centrifugal forces which result in a vortex formation within the GLCC body. So below the inlet, gas bubbles trapped by the liquid are pushed radially toward the cylinder axis, forming a gas filament which rejoins the vortex. In the upper part, liquid droplets are centrifuged to the separator walls, where they form a compact mass which is thus difficult to be dragged by the gas.

Corresponding author at: GEPEA, CNRS-UMR 6144, 37 Bd de l’Université, BP 406, 44602 Saint-Nazaire Cedex, France. E-mail address: [email protected] (C. Gentric). Received 9 January 2011; Received in revised form 24 March 2011; Accepted 4 May 2011 0263-8762/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2011.05.001

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Nomenclature k r R Re Sni u U Uav v V w W x y+

Turbulent kinetic energy (m2 /s2 ) Radial position (cylindrical coordinates) (m) Main pipe radius (m) Reynolds number based on the bulk average axial velocity ith definition of the swirl number x-velocity component (m/s) Average x-velocity (m/s) Bulk average axial velocity (m/s) y-velocity component (m/s) Average y-velocity (m/s) z-velocity component (m/s) Average z-velocity (m/s) Axial position (m) Dimensionless wall distance in wallcoordinates

Greek letters Density of the working fluid (kg/m3 ) Angular position (cylindrical coordinates) ␪ Friction coefficient in fully developed pipe flow Superscripts Fluctuating component

Despite its numerous advantages (compactness, low investment and operating costs, . . .), the GLCC deployment has not reached yet its merited expansion because its sizing remains mostly empirical. In fact, the complex phenomena taking place in GLCCs are still not fully understood. CFD, when used in combination to experiments, can be a useful tool to better understand and predict the complex two-phase

hydrodynamics of this separator. Some studies have begun to deal with the subject, mainly performed by the team of Tulsa University Separation Technology Projects (TUSTP); they show that a lot of physical analysis and simulation validation remains to be done (Motta et al., 1997; Erdal et al., 1997, 1998). A correct two-phase simulation of a GLCC hydrodynamics has to be based on a reliable turbulence model, which must first predict the hydrodynamics of a single phase swirling flow. This is not a simple task because of the high complexity of these flows which still remain a challenge for CFD. In this paper, after a state of the art of the swirling flows and their numerical modeling, single-phase flow in a GLCC geometry will be simulated for several experimental conditions. Results will be compared to the experimental data collected by Erdal (2001a). Several turbulence RANS models will be tested, the Large Eddy Simulation (LES) will also be employed. Different near-wall treatments will be compared. This whole study will allow on the one hand to determine the most suited modeling approach and on the other hand to explore some important details of the flow which were not accessible experimentally via the 2D LDV used by Erdal (2001a).

2.

Swirl flow in straight pipes

Swirl flows are generated by imparting a tangential component to an axial flow, resulting in a helical winding of the streamlines. They can be found in natural flows as in industrial flows, where they find a broad range of engineering applications. They are used in cyclone type separators (GLCCs, swirl tubes, foam-breaking cyclones, demisting cyclones, . . .), for heat transfer enhancement (Chang and Dhir, 1994; Martemaniov and Okulov, 2004), to avoid blockage and minimize localized wear in conveying pipes of hydraulic and pneumatic transport (Fokeer, 2006), to stabilize flames in combustion chambers (Wegner et al., 2004; Truffin, 2005), or flare stacks, . . .

2.1.

Swirl generation

According to Gupta et al. (1984), the methods used to induce swirl can be classified into three main categories: • Tangential injection: propeller type swirl generators (Steenbergen and Voskamp, 1998), single (Erdal, 2001a; Gupta and Kumar, 2007) or multiple tangential slots (Erdal, 2001a; Chang and Dhir, 1994), axial-plus-tangential entry, guided vanes (Kitoh, 1991), . . . • Passage of the flow through profiled objects: twisted ribbon, helical swirl inducing pipe (Fokeer, 2006). • Rotation of a piece through which the fluid is flowing: rotating honeycomb (Baur, 1995; Najafi et al., 2005), direct rotation of the confining walls, . . . Swirl can be induced in a continuous way along the whole pipe or in a localized manner. In this second case, swirl intensity will decay while going downstream.

2.2.

Fig. 1 – Schematic plot of a GLCC.

Swirl characteristics

The swirl characteristics not only depend on the Reynolds number and on the swirl intensity (see Section 2.2.5) but also strongly on the way the swirl has been generated (Kitoh, 1991; Steenbergen and Voskamp, 1998; Martemaniov and Okulov,


Forced Vortex

Transition region

Free vortex

Wall region

5 4.5 4

W / U av

3.5 3 2.5 2 1.5 1 0.5 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r/R

Fig. 2 – Typical average tangential velocity profile in swirl flows.

2004). According to Martemaniov and Okulov (2004), under the same integral parameters of the flow (Reynolds number and swirl intensity), vortices with left-handed and right-handed helical symmetry can exist. Another specificity of swirl flows is that they present long history effects, since they keep their initial specificity for a long distance as noticed by Kitoh (1991). This paper will focus on swirl flows as they are generated in GLCCs but in a geometry adapted to single phase liquid flow, i.e. with a tangential injection in a cylindrical channel and a single outlet located at the bottom. It appears that experimental data on such systems are rare. Even the first studies of the Tulsa group have been firstly based on the data reported by Algifri et al. (1988); Kitoh (1991) and Chang and Dhir (1994), three works where the swirl was not generated by a unique tangential inlet. Algifri et al. (1988) worked with air and induced swirling motion in a pipe by using radial cascade blades. Measurements were done by means of a hot-wire anemometer. Kitoh (1991) used guide vanes to generate swirl. Initially, he used air as a working fluid and measured the axial and tangential velocity profiles and the Reynolds stress components using x-wire anemometers. Then, he worked with water and measured wall shear stress and swirl intensities. Chang and Dhir (1994) used 4 or 6 horizontal tangential injectors located at a same height. They used air as the bulk fluid and measurements were realized with a single rotated straight hot wire anemometer. The swirl movement in these three studies has been approximated as axisymmetric due to the relatively smooth conditions of generation. The first experimental study on a GLCC geometry was carried out by Erdal (2001a). Using a single inclined inlet slot, he noticed that a strongly non-axisymmetric flow was obtained, contrary to the above mentioned studies. In fact, the unique tangential inlet induces a strongly pronounced asymmetry. This particular feature had already been observed: for instance, Kumar and Conover (1993) had found that axial symmetry of the flow does not hold in a cylindrical cyclone. In this section, the main swirl flow characteristics will be detailed. The important history effects of swirl flows must be kept in mind, as well as the strong dependency of the flow structure on the swirl generation method.

2.2.1.

Mean tangential velocity profile

A typical mean tangential velocity profile (Algifri et al., 1988; Kitoh, 1991; Chang and Dhir, 1994) is depicted in Fig. 2. It can be divided in several regions:

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• A core region where the tangential velocity profile corresponds to a forced vortex (solid rotation): according to the Rayleigh criterion for stability to small perturbations, this velocity distribution has a strong stabilizing effect, so the small scale turbulent motion dies rapidly while history effects persist (Kitoh, 1991). When going downstream, as the swirl decays, the position of the maximum tangential velocity shifts toward the pipe centre, which can be seen as a decrease in the extent of this region. • An annular region where the profile corresponds to a free vortex: it is separated from the core region by a transition zone which can be quite large. The centrifugal action is destabilizing in this region and the skewness of the flow is very high. Flow direction, shear direction and velocity gradient direction do not coincide and turbulence is highly anisotropic. Kitoh (1991) and Chang and Dhir (1994) found that the calculated eddy viscosity components can become negative at some locations of the core region. One can expect that the turbulence models based on the Boussinesq approximation will fail to predict the flow behavior in this region. • A wall region: it consists in a small layer near the wall where the tangential velocity decreases with a steep gradient to be equal to zero at the wall. One may wonder if the universal log law of the wall still holds here. Flow skewness being negligible in this region (Kitoh, 1991), turbulence will only be affected by the streamline curvature. According to Bradshaw (1969), there is a strong similarity between the streamline curvature and the buoyancy effect which may result in a modification of the mixing length in analogy with the Monin–Oboukhov formula. Kitoh (1991) adopted the same idea: he proved theoretically and showed experimentally that it resulted in a deviation of the velocity from the universal logarithmic profile. However, the universal loglaw profile can approximate reasonably the velocity despite in a reduced range of y + compared to a purely axial flow. The experimental results of Erdal (2001a) are in accordance with the existence of these three regions, but it may be mentioned that the asymmetry of the flow is more pronounced, and that the tangential velocity profile in the annular zone can differ from the one obtained with a free vortex (see Section 7.1.3).

2.2.2.

Mean axial velocity profile

According to Mantilla (1998), on the base of the previous mentioned studies, the axial velocity profile in the GLCC can be described by one of the three flow regimes presented in Fig. 3. The first profile presents a quasi-uniform forward axial velocity on the entire cross-section and corresponds to a very weak swirl. The second one corresponds to a more important swirl intensity. With a high enough swirl intensity, flow can be reversed near the cyclone axis. In fact, the swirl motion tries to pull the fluid to the outer region of the pipe, resulting in a low pressure near the pipe axis. Going downstream, the pressure near the axis can increase because of the swirl decay or/and the 3D helical aspect of the flow. This adverse pressure gradient, if severe enough, can reverse the flow direction. It is the typical flow structure encountered in GLCCs but with an accentuated asymmetry (Erdal, 2001a). The third profile presents a double flow reversal, with forward flow near the axis and the wall, and backward flow in the intermediate region. However, this third flow structure has never been mentioned in swirl flows generated by a single inlet. It has been observed by Nissan and Bresan (1961) and Guo and Dhir (1990)

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stabilizing/destabilizing effects of the centrifugal force which will determine if the fluctuating components will be absorbed or not by the mean flow. According to Kitoh (1991) data, the turbulent kinetic energy decreases in the annular region while going downstream whereas it can increase in the core region. This was confirmed by Erdal (2001a). But the measurement method did not allow to determine whether the increase of k was due to purely turbulent phenomena or to coherent structures (see Section 2.2.6).

2.2.5.

Swirl decay

If not maintained, the swirl motion will decrease while going downstream of the swirl generating device. The swirl dissipation can be described in two ways: • The first one is based on the streamline angle evaluated at some position in the cross-section. • The other one is based on the swirl quantification using dimensionless numbers. The second evaluation is more interesting since it seems not to depend on the swirl type and therefore should be more universal (Steenbergen and Voskamp, 1998). But there is no standard and the swirl number definition may vary between authors. Chang and Dhir (1994) defined the swirl number as:

2 R Sn1 = Fig. 3 – Typical average axial velocity profiles in swirl flows according to Mantilla (1998). who used multiple tangential inlets and by Erdal (2001a) when using two diametrically opposed inlets. For the same Reynolds number, but with a unique injection, this author obtained the second type of profile. It must be noticed that the injection section for the case involving dual inlets was slightly lower than the one with a single inlet because of manufacturing difficulties, which entailed a higher swirl intensity.

2.2.3.

Mean radial velocity profile

To the authors’ knowledge, no measurements of the radial velocity components for swirling flows in straight pipes have been reported in the literature. Algifri et al. (1988), Kitoh (1991), Chang and Dhir (1994) and Baur (1995) have calculated the mean radial velocity by using the continuity equation, while assuming an axisymmetric flow. According to their results, the mean radial velocity is about two or three orders of magnitude less than the bulk velocity. The TUSTP team of Tulsa, considering that it still holds for the swirl flow in the GLCC, has always neglected the radial velocity components in their mechanistic models. In the present study, it will be verified if the radial velocity remains negligible for swirl flows in GLCCs, which is not obvious since the hydrodynamics is highly 3-dimensional and the swirl flow characteristics strongly depend on the way it was generated.

2.2.4.

0

0

UWrdrd

2 R2 Uav

(1)

They reported that swirl decays with an exponential manner except for axial distances less than two diameters downstream the inlet. Near the inlet, swirl appears to be nearly constant, which may be explained, according to these authors, to the vortex breakdown in this zone. They also developed a correlation based on their experimental data in order to predict the swirl intensity as a function of the axial distance. This correlation has been modified by Mantilla (1998) to take in account the number of inlets and the fluid properties via the Reynolds number. Then, Erdal (2001a) adapted this correlation to take into account the inlet angle and to satisfy his experimental data. Kitoh (1991) and Steenbergen and Voskamp (1998) used another swirl number definition:

2 R Sn2 =

0

0

UWr2 drd

2 R3 Uav

(2)

According to Kitoh (1991), the swirl decay with the axial position can be approximated as piecewise exponential, the decay coefficient depending on the swirl intensity. Yu and Kitoh (1994) developed an analytical method to predict the decay of the swirl motion and indicated that swirl decays faster as the Reynolds number decreases. Steenbergen and Voskamp (1998) indicated that the swirl decrease can be approximated as exponential, and that for low to moderate swirls, the decay coefficient can be estimated as follows:

Turbulent quantities

Still according to Algifri et al. (1988), Kitoh (1991), Chang and Dhir (1994) and Erdal (2001a) results, the swirl presence increases significantly turbulence levels compared to swirlfree axial pipe flows. Turbulent kinetic energy is not only important near the walls but also near the pipe axis. In swirl flows, the turbulent kinetic energy is strongly coupled to the

ˇ = (1.49 ± 0.07)

(3)

where is the friction coefficient for fully developed pipe flow. This formula has been validated on different swirl types but never on a swirl generated by a unique tangential inlet. It must be noticed that these studies are based on the approxima-

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Table 1 – Simulated experimental cases. Case number 1 2 3 4 5 6

Number of inlets 1 1 1 1 2 2

Water–glycerin Water–glycerin Water Water Water Water

tion that the flow is axisymmetric. Steenbergen and Voskamp (1998) verified that the decay is not really sensitive to the flow asymmetry but not for situations with so much asymmetry as in GLCCs. Other definitions of the swirl number, which are more physical, can be found in Gupta et al. (1984). But they contain pressure and Reynolds stress terms which are difficult to measure and therefore their use has been limited.

2.2.6.

Precessing vortex core phenomenon

The precession of vortex core, known as the PVC phenomenon, is a hydrodynamic instability often encountered in swirl flows. It consists in a coherent quasi-periodic precession of the vortex centre. The conditions for its appearance remain a question of debate. The phenomenon has been quite well studied for swirl flows in burners since it can cause dysfunction of the system (Wegner et al., 2004; Truffin, 2005). Kitoh (1991) has mentioned that a very-low frequency motion prevails in the core region. This could be linked to the PVC. In the case of cyclone separators, one can mention the observations of Peng et al. (2005) who used a stroboscopic technique in a reverse type cyclone. They observed that the vortex tail attaches to the walls and undergoes a rotation movement. Gupta and Kumar (2007), investigating with Particle Tracking Velocimetry (PTV) a water flow in a GLCC type geometry, also observed a precession of the vortex centre around an imaginary axis.

3.

Flow rate (m3 /s)

Working fluid

Numerical modeling of swirl flows

Swirl flows as encountered in industrial applications are mostly turbulent and their geometries are diverse, making theoretical analysis difficult. Consequently, CFD numerical studies have occupied a privileged place when dealing with such flows. But concerning GLCC-like geometries, successful studies are rare. In fact, the numerical modeling of those flows still remains a great challenge for CFD because of the complexity of the transport phenomena involved and of the 3-dimensional character of the hydrodynamics. Besides, the turbulence is highly anisotropic and the turbulent viscosity components can be negative since the mean turbulent momentum transport can be opposite to the mean momentum gradient. Therefore turbulence models relying on the Boussinesq approximation are a priori less efficient than the second-moment closure models among which the Reynolds Stress Model (RSM) is the most employed. Concerning GLCC geometries, the CFD studies of Erdal and Shirazi (2001b) and Gupta and Kumar (2007) can be mentioned. Erdal and Shirazi (2001b) ran 3D steady-state simulations for a high Re swirling water flow in a GLCC (see Section 5, case 4 in Table 1). They tested the standard k– model and a RSM model. Surprisingly, the standard k– predictions were better, even if none of the two models was able to correctly capture the details of the flow. Gupta and Kumar (2007) have acquired data about tangential velocities by using PTV. They simulated

0.00068 0.00339 0.00063 0.00454 0.00063 0.00454

Uav (m/s)

Re

0.109 0.545 0.102 0.731 0.102 0.731

1514 7570 9285 66,855 9285 66,855

the hydrodynamics using the RNG k– model allowing a global accordance with the experimental trends. Gas–solid cyclones, presenting a conical body with a tangential inlet and a vortex finder outlet both located at the top of the geometry, have been much more extensively studied via CFD. For instance, Hoekstra et al. (1999) simulated the gas flow in the cyclone assuming axisymmetry: RSM predictions were in reasonable agreement with experiments whereas results obtained with the standard k– model were unrealistic. Gong and Wang (2004) used the RSM model to simulate two configurations of a gas–solid cyclone: with or without Reducing Pressure Drop Stick, and obtained a good agreement with experiments in both cases. Concerning swirl flows in straight pipes which are not generated via a tangential inlet, Najafi et al. (2005) and Escue and Cui (2010) simulated swirl flows generated by honeycomb-like swirlers using an axisymmetric geometry. According to these studies, the RSM and RNG k– models give satisfying predictions and present similar performances. However, according to Najafi et al. (2005), the RSM model coupled to a double-layer approach for the near-wall treatment performs slightly better, whereas according to Escue and Cui (2010), the RNG k– model is better suited to low swirl conditions. Pruvost et al. (2004) simulated swirl flows in curved pipes: in their conditions, the performances of the standard k– model were better than both the RSM and the RNG k– ones. Thus, the current literature shows that no turbulence model performs better for all kinds of swirl flows. Because of the large variety of swirl flows, it is possible that a model which would be well suited for one application, performs only poorly for another type of swirl flow. Besides RANS models, with the development of calculation resources, Large Eddy Simulations (LES) are getting more and more developed and in particular the number of studies of swirl flows using this approach is increasing. Derksen (2005) simulated different flows in vortex tubes, and his simulations were capable to reproduce flow details, including vortex breakdown, core laminarization, Taylor-Görtler vortices. Pisarev et al. (2011) used LES to study the End of Vortex Phenomenon in centrifugal separators. Truffin (2005) and Wegner et al. (2004) successfully captured the PVC phenomenon with LES. Contrary to RANS models, LES gives satisfying results irrespective of the type of swirl and of its generation method. However, because of the important computing times required by LES, RANS simulations are still useful when dealing with large scale or high Reynolds processes.

4.

Objectives of the present study

The present paper aims at numerically studying single-phase swirl flows in a GLCC geometry. Conditions will be chosen according to the data of Erdal (2001a), who measured tangential and axial velocity profiles by mean of a 2D LDV. First, different RANS simulations will be carried out with different

2526


turbulence models and different near-wall treatments. In a second step, Large Eddy Simulations will be carried out. The goals of the study are threefold: • Comparison with experimental results will allow to define which turbulence model is the best suited for this type of hydrodynamics, to determine its limits and to compare its performances with the LES ones. The chosen model will be used in a further study dealing with two-phase flows in GLCCs. • Results which will appear to reproduce satisfyingly experimental data will be used to analyze hydrodynamics characteristics which Erdal (2001a) could not access with 2D LDV: the radial velocity field will be investigated to verify the hypothesis of negligible radial velocities, then the swirl decay and the existence of a PVC phenomenon will be examined. • Finally, the influence of the inlet configuration on the cyclone hydrodynamics will be studied: in particular, the case of rectangular inlets will be analyzed in terms of separation efficiency of the GLCC and compared to the circular inlet used by Erdal (2001a). These results should provide useful information to improve GLCC performances. Fig. 4 – Dimensions of the experimental set-up and position of the LDV measurement plane.

5. Former experimental set-up and measurement techniques Simulation results will be compared to the experimental data of Erdal (2001a) who carried out single-phase flow experiments in order to get a better knowledge of the liquid flow field that takes place in gas–liquid cylindrical cyclones. The cyclone was made of clear acrylic and the main section had an internal diameter of 8.9 cm. During the experiments, a blee valve was used to release air from the system and thus the cyclone was filled with liquid up to the top. Local measurements of the tangential and axial velocity components have been carried out using a two-components Laser Doppler Velocimeter (LDV). They were performed in the main pipe mid-plane, at 24 locations along the diameter going from a distance of 31.7 cm to 89.9 cm below the inlet. Different inlet configurations were studied among which single and dual inclined inlets (diametrically opposed). The inlet presents a 27◦ angle with respect to the horizontal plane: it corresponds to the angle generally adopted for a GLCC inlet in order to promote stratification for the gas–liquid mixture before it enters the separator body (Kouba et al., 1995). Fig. 4 represents the cyclone used by Erdal (2001a), the different dimensions of the geometry, the coordinate system and shows the position of the LDV measurement plane. Two bulk fluids were studied: water, and a mixture of water and glycerin, with a dynamic viscosity of 7 × 10−3 Pa s, and a density of 1093 kg/m3 . Flows with different Reynolds numbers have been investigated. Since no measurements were made for the radial velocity component, Erdal (2001a) approximated the turbulence kinetic energy using the following formula for the radial velocity fluctuations:

v2 =

1 ( 2

u2+

w 2)

(4)

Table 1 sums up the experimental cases that have been simulated in the present study. The Reynolds number has been varied either by varying the flowrate or the fluid properties (cases 1–4) and the influence of the inlet number has been

tested (cases 1–4 on the one hand and cases 5 and 6 on the other hand).

6.

Numerical methods

All numerical simulations were performed on a 3D grid in the present study. The flow was treated as incompressible and isothermal.

6.1.

Geometry, mesh and boundary conditions

The considered geometry was composed of the main cyclone section, and of two or three pipe sections of 5 cm corresponding respectively to the inlet(s) and outlet pipes. The grid was generated using the commercial software GAMBIT. Two main types of meshes were used:

• A first mesh type (mesh type 1) which is mainly composed of unstructured hexahedral elements, except two thin layers of tetrahedral elements near the feed and outlet pipes. Indeed, owing to the sharp-pointed angles at the intersection between the inlet/outlet pipes and the cyclone body, and to avoid the use of non-conformal grid that could induce interpolation errors, the use of those 2 tetrahedral layers was necessary to avoid highly skewed cells. This type of mesh was used for simulations where the near-wall treatment relies on the classical log-law. • A second mesh type (mesh type 2) which is totally composed of hexahedral elements, with a structured boundary layer mesh near the wall of the cyclone, and non-conformal interfaces at the intersection of the main pipe with the inlet and outlet pipes. This mesh has been used for simulations where the low-Reynolds or two-layer approaches were employed to describe the near-wall flow.

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A velocity inlet condition was used for the inlet(s), a condition of fully developed flow for the outlet, and a wall condition with no slip was taken for the remaining boundaries.

−0.5

0

The solver

The Fluent 6.3 commercial software has been used during this study. This code uses the finite-volume method. Several RANS turbulence models have been evaluated for the single-phase simulation of a GLCC hydrodynamics:

U / U av

6.2.

−1

0.5

1

1.5 Experimental data High−Re k−ε Realizable

• The Spalart–Allmaras model with two different options to account for the turbulence production: a first one based on the vorticity of the flow and a second one which also takes into consideration the effect of the mean strain rate. • Three k– models: the standard, RNG, and realizable k– variants. The RNG model in Fluent includes an option which is supposed to better account for swirl effects. • The RSM model, with 3 different modeling approaches for the pressure-strain term: a linear pressure-strain RSM model, a quadratic pressure-strain RSM model, and the lowRe stress-omega RSM model. • The standard and the Shear Stress Transport k-omega models. For near-wall regions different modeling possibilities have been investigated: • Wall functions approaches which are available for all models. • The two-layer zonal model which can be coupled to the k– and RSM models. • Low-Reynolds near wall treatment which is possible for the standard k– and the RNG k– approaches, and for the RSM model which is called low-Re stress-omega. The Spalart–Allmaras and k-omega models are intrinsically lowReynolds. The implicit LES techniques have also been investigated with different sub-grid scale models among which the Smagorinsky model, the dynamic Smagorinsky–Lilly model, the WALE model and the dynamic kinetic-energy sub-grid scale model. Concerning the discretization of the convective terms, the first order and the QUICK schemes have been compared. Diffusion terms are central-differenced, and thus

2

High−Re k−ω SST High−Re Spalart−Allmaras (second version)

2.5

High−Re k−ε RNG (with Fluent’s swirl adaptation)

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

r (m)

Fig. 5 – Axial velocity predictions 90 cm below the inlet – case 3: comparison of different turbulence models. are always second-order accurate. For pressure interpolation, standard, linear, body force weighted, second order and PRESTO! schemes have been investigated. Turbulence models and numerical schemes as implemented in Fluent are well known and have been extensively used in CFD calculations. For details, Fluent User’s guide (Inc., 2006), or classical CFD books (Wilcox, 1994; Versteeg and Malalasekera, 1995) can be consulted.

7.

Simulation results and discussions

7.1.

Simulation of cases involving a single inlet

7.1.1.

Simulations with RANS models

In a first step, experimental cases 3 and 4 (see Table 1) have been simulated using all the turbulence models presented in Section 6.2 in order to determine the best turbulence model suitable for GLCC hydrodynamics simulation. Cases 3 and 4 have been chosen since they allow to discriminate between all turbulence models for a low and a high Reynolds flow. Each turbulence model has been tested with the different possible near-wall treatments: in every case, the mesh has been chosen to allow the y + values near the walls to be in the correct range (y+ 1 for the low Reynolds approach or the two-layer model and y+ slightly greater than 30 for wall functions). Convection terms have been discretized using the QUICK scheme, since low order schemes as the first order UPWIND scheme overestimate the swirl dissipation along the separator

Fig. 6 – Average tangential velocity profiles predictions at respectively 31.7 and 59.4 cm below the inlet - case 1.

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Fig. 7 – Average tangential velocity profiles predictions at respectively 33, 46.7 and 89.9 cm below the inlet – case 2. body. The standard interpolation scheme has been used for pressure interpolation. The SIMPLE algorithm has been used in this whole study for pressure velocity coupling. Simulations with high-Reynolds turbulence models have been realized with two meshes of type 1 (see Section 6.1): the first one with around 650,000 cells and the second one with approximately 990,000 cells. Comparing the results on both grids showed only a small discrepancy. Simulations with low Reynolds turbulence models or with the two-layer approach

were carried out with two meshes of type 2, with respectively around 990,000 and 1,720,000 cells. The 1,720,000 elements grid ensured grid independency since the results with these two meshes were very close. Numerical results were compared to experimental data. RSM steady-state simulation could not converge or led to velocity fields far from experimental results. For both simulated cases, the high-Reynolds version of the realizable k– model presented the best agreement with experiments.

Fig. 8 – Average tangential velocity profiles predictions at respectively 31.7, 46.7, 68.6 and 89.9 cm below the inlet – case 3.


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Fig. 9 – Average tangential velocity profiles predictions at respectively 31.7 and 75.7 cm below the inlet – case 4.

Fig. 10 – Average axial velocity profiles predictions at respectively 31.7 and 59.4 cm below the inlet – case 1. Except the second form of the Spalart–Almaras model, all other models overestimate the swirl dissipation and they are only as good as the realizable model near the inlet. The results of the realizable model when used with the two-layer wall-treatment are very close to the high-Reynolds treatment

near the inlet, but both results become different when going downstream where the high-Reynolds version performs better. Fig. 5 compares the average axial velocity profile using different turbulence models with their high-Reynolds versions to

Fig. 11 – Average axial velocity profiles predictions at respectively 33, 46.7 and 89.9 cm below the inlet – case 2.

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Fig. 12 – Average axial velocity profiles predictions at respectively 31.7, 46.7, 68.6 and 89.9 cm below the inlet - case 3. the experimental data for case 3 at a distance of 90 cm below the inlet. Finally, different pressure interpolation schemes have been compared. Cases 1, 2, 3 and 4 have been simulated using the high-Reynolds k– realizable model for each of the pressure interpolation schemes mentioned in Section 6.2. It appeared that the second order scheme performs slightly better than the other ones. RANS results presented in the rest of the paper have been obtained with the high-Reynolds realizable k– model, the QUICK scheme for the convective terms discretization and a second-order pressure interpolation scheme.

7.1.2.

is not realistic because of the prohibitive calculation means it would require. The second order discretization scheme has been employed for the pressure interpolation. For convective terms, central scheme is recommended for LES simulations to avoid numerical dispersion. Because of the unboundedness of this scheme, unphysical wiggles can appear. Therefore, the Bounded Central Differencing Scheme was adopted. The mesh is composed of about 1,900,000 cells. A second-order implicit scheme has been employed for temporal discretization. The chosen time step was 0.0003 s. Different subgrid models have been investigated with very close results. Thus only the results obtained with the WALE model will be exposed for clarity.

LES simulations

Since LES is very time consuming, it has been decided to investigate only case 3 among the experimental cases involving a single inclined inlet. The wall function approach has been used for the near-wall treatment. Even if such a coarse treatment of this region could alter the results, a finer description

7.1.3.

Comparison with experimental data

Average tangential velocity profiles. Average tangential velocity predictions for the experimental cases 1, 2, 3 and 4 are presented in Figs. 6–9. Agreement between experimental and simulation results is very good. However the forced vortex

Fig. 13 – Average axial velocity profiles predictions at respectively 31.7 and 75.7 cm below the inlet - case 4.


Fig. 14 – Experimental contours of the average axial velocity for case 1 (left), case 3 (center) and case 4 (right) (Erdal, 2001a).

size is slightly overpredicted when the distance to the inlet increases. Average axial velocity profiles. Average axial velocity predictions are compared to experimental profiles in Figs. 10–13, corresponding respectively to cases 1–4. A satisfying agreement is obtained between experimental and numerical data. The effect of the Reynolds number

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Fig. 15 – Simulated contours (realizable k– model) of the average axial velocity for case 1 (left), case 3 (center) and case 4 (right). is correctly reproduced. Concerning the results obtained with the realizable model, simulation predicts the backflow zone closer to the pipe axis than in experiments. Also, the magnitude and width of this backflow zone, often called capture diameter when flows in cyclones are investigated, are overpredicted, this discrepancy is more important close to the

Fig. 16 – Turbulent kinetic energy profiles predictions at respectively 31.7, 46.7 and 89.9 cm below the inlet – case 3.

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Fig. 17 – Average tangential velocity profiles predictions at respectively 31.7, 46.7 and 89.9 cm below the inlet – case 5. inlet. These problems were not encountered with the LES simulations, even if their results are not really better than those obtained with the realizable model, since the LES results still present a slight discrepancy with the experimental ones. Vortex helical pitch. The term helical pitch is extended to the present case while not completely appropriate: the flow is viscous and thus the vortex wavelength is modified while going downstream. Numerical results provide a very good estimation of the vortex helical pitch as shown in Figs. 14 and 15, presenting respectively the experimental and numerical contours (obtained with the realizable model) of the average axial velocities for cases 1, 3 and 4. In these figures, the experimental profiles have a width of only 8.2 cm since the flow close to the wall is not accessible to LDV measurements. Turbulence kinetic energy. Turbulence kinetic energy predictions are quite important since, in studies where the gas

presence in the cyclone will be taken into account, it will affect bubble trajectories calculations, bubble turbulent dispersion, bubble coalescence and break-up, as well as the gas filament integrity. For LES results, the turbulence kinetic energy has been calculated from the resolved scales and for a better comparison with experimental results, a comparison with the k value given by the approximation of Erdal (2001a) (Eq. 4) is also given. Results are presented in Fig. 16. The realizable k– model strongly underestimates the turbulence kinetic energy and fails in reproducing the experimental variations. The same problem has been encountered with the other RANS turbulence models investigated. The same tendency has already been observed by other authors (Wegner et al., 2004; Escue and Cui, 2010). Increasing the inlet boundary turbulent intensity does not reduce this important discrepancy.

Fig. 18 – Average axial velocity profiles predictions at respectively 31.7, 46.7 and 89.9 cm below the inlet – case 5.


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Fig. 19 – Contours of the average axial velocity for case 5: experimental (left) (Erdal, 2001a) and simulated with the realizable model (center) or with LES (right). LES also underestimates the turbulence kinetic energy but follows better its variations. One explanation for the underestimation is that k is calculated using the solved scales: therefore the smaller scales are not accounted for. If k is estimated using Eq. 4, simulated results become slightly closer to experiments. Whereas the LES does not perform better than the realizable approach for the axial and tangential velocities, the k estimation is clearly better. In fact, the turbulent kinetic energy measured by LDV is not only composed of turbulent agitation but also results from the motion of coherent structures (see Section 2.2.6). It is recognized that LES performs much better than RANS approaches to capture these kinds of movements. Finally, we must also keep in mind that the LDV tends to overestimate the turbulence kinetic energy, especially in the regions where strong mean velocity gradients exist, and this because of the finite size of the measurement volume.

7.2.

be able to predict such a flow, in order to avoid it, especially since we have little knowledge about its origin. Thus, experimental cases 5 and 6 have been investigated using different RANS models and LES techniques with different sub-grid scale models. Numerical schemes and simulation approaches are the same as in Section 7.1.

Simulation of cases involving a dual inlet

The configuration with two inlets, diametrically opposed, was tested in Erdal (2001a) with the objective of obtaining a more symmetrical flow structure, thus reducing vortex warping. Indeed, this 3-dimensionality is expected to promote mixture and maybe limit the stability of the air filament. But it appeared that, if the flow structure was quite axisymmetric, an unexpected phenomenon appeared in experimental case 6 (at the most important Reynolds number): a downward flow at the center surrounded by an upward flow region was observed. It corresponds to the double flow reversal situation presented in Section 2.2.2, a situation which is not desirable in practice when the objective is to separate the gas and liquid phases since the bubbles entrained to the center will experience a downward flow with the liquid phase, which may cause gas carry under in the liquid leg. However, it is also important to

Fig. 20 – Experimental (left) (Erdal, 2001a) and simulated (right) axial velocity contours with a LES approach – case 6.

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Fig. 21 – Simulated contours (realizable k– model) of the average y-velocity for case 1 (left), case 3 (center) and case 4 (right).

7.2.1.

Case with single flow reversal

Once again, among the RANS models, the high-Reynolds version of the realizable k– model gives the best agreement with experiments. LES results with different subgrid models are also very close, therefore only those obtained with the WALE model will be presented. Average tangential velocity profiles. Fig. 17 compares the experimental and numerical mean tangential velocity profiles. The results from the realizable approach gets poorer when going downstream. On the contrary, LES provides good results at any altitude In this case, it performs clearly better than the RANS approach. Average axial velocity profiles. In Fig. 18 are shown the mean axial velocity profiles. CFD predictions are in good agreement with experiments. Nevertheless the numerical field is more axisymmetric than the experimental one. The difference is more pronounced with the realizable model than with LES. Experimental and numerical axial velocity contours are compared in Fig. 19 showing a global good accordance for LES simulations. Comparing these contours to the ones of case 3 (see Fig. 14 – case 3) which presents the same Reynolds number, one can notice that the backflow is more important and that the capture radius is wider. Downward velocities do not reach the same magnitudes.

7.2.2.

Case with double flow reversal

The realizable k– model and all the other RANS models failed to predict the occurrence of the double flow reversal phenomenon. LES simulations were performed with a 2,560,000 cells mesh and a time step of 0.0001 s. LES simulations with different subgrid models managed to predict qualitatively the axial velocity field, i.e. the presence of three axial velocity

Fig. 22 – Contours of the simulated (LES approach, WALE sub-grid model) average y-velocity for case 5.


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Fig. 23 – Precessing Vortex Core phenomenon (case 3, section located at x = 90 cm) as observed with LES approach (WALE as sub-grid scale model). The time step between consecutive frames is 0.3 s. Numbers indicate the successive positions of the vortex centre. optima in the cylinder central region. However, no LES simulation was able to predict another flow inversion (downward flow) at the centre. The results closest to the experimental ones were obtained with the WALE subgrid model, with a central velocity quasi equal to zero. Fig. 20 compares the experimental axial velocity contour to the simulated one with a LES approach (WALE subgrid model). Simulation over-predicts the velocity magnitude near the walls and under-predicts it around the axis.

8.

Results beyond experimental data

Since comparison with available experimental data shows that CFD is able to predict satisfyingly the GLCC hydro-

dynamics, CFD results have been used to investigate phenomena that have not been studied experimentally by Erdal (2001a).

8.1.

Mean radial velocity

As already mentioned (see Section 2.2.3), radial velocities in GLCCs have always been considered as negligible, a result which has been extrapolated from the ones obtained for axisymmetric swirl flows. Our simulations predict quite accurately the axial and tangential velocity components, thus the radial velocities should also be correctly predicted since the three values are linked through the continuity equation.

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Cases with single inlet

8.1.2.

Cases with dual inlet

Fig. 22 presents the y-velocity contours in the LDV measurement plane for experimental case 5. These contours have been obtained via LES simulations, using the WALE sub-grid model. Near the inlets, the radial velocity contours have a structure which is different from the single inlet case since they are directed toward the cyclone axis in one zone and toward the walls in the adjacent zones. This behavior cannot be easily explained but may be due to the interference between the two inlet jets. When going downstream, the radial flow evolves toward a structure which is similar to the one observed for the single inlet case. It can be noticed that the radial velocity magnitude is lower for the two-inlet case, showing that the flow becomes more axisymmetric.

8.2.

Precessing vortex core

LES simulations of cases 3, 5 and 6 reveal a precession of the vortex core (see Fig. 23). This rotation seems to take place in the direction opposite to the swirl one. The ability of URANS simulations to predict such a structure is still a subject of debate. Unsteady simulations of cases 1–5 were performed with a 0.01 s time step using the realizable k– model. Results show a coherent oscillation of the vortex core but with a much smaller magnitude than the one obtained with LES simulations. This could explain the poor prediction of the turbulent kinetic energy given by the RANS models (see Section 7.1.3). The same observation was made by Wegner et al. (2004) who simulated the PVC phenomenon in an unconfined swirl flow using unsteady Reynolds Stress Model (RSM) and LES simulations: the unsteady RSM approach allowed a better prediction of the precession frequency but under-estimated strongly the energy contained in the coherent movement.

8.3.

4 3.5 3

2

RANS and LES simulations both reveal that the radial velocity magnitude is not negligible contrary the hypothesis encountered in the literature. Fig. 21 shows the contours of the mean y-velocity (corresponding to the radial direction in the measurement plane) simulated with the realizable k– turbulence model obtained for cases 1, 3 and 4 respectively. These contours show that the y-velocity field describes a series of cells of alternate signs. In fact, the radial velocity is mainly due to the eccentricity of the vortex center, so the same wavelength is observed as for the axial velocity (see Fig. 15). The radial velocity magnitude is minimal when the vortex center is located in the measurement plane, and increases when the distance of the vortex center to the measurement plane increases.

4.5

2.5

Sn

8.1.1.


2 Case 1: CFD data 1.5 1

Case 1: Equation 3 Case 2: CFD data Case 2: Equation 3 Case 3: CFD data Case 3: Equation 3

0.5

Case 4: CFD data Case 4: Equation 3

0 10

10

10

10

10

10

x (m)

Fig. 24 – Evolution along the axis of the swirl number defined by Eq. (2) for cases 1–4 – in each case, the simulated swirl number evolution is compared to the one given by Eq. (3). • Apart from the inlet zone, the swirl decay can be approximated as exponential. The swirl decay rate decreases with respect to the Reynolds number, as noticed by Yu and Kitoh (1994) and Steenbergen and Voskamp (1998). • Comparison of the simulated swirl number with Eq. (3) shows that this equation cannot be used to estimate the swirl intensity in a GLCC since it under-estimates the decay rate. In fact, this equation has been established from experimental data obtained for axisymmetric swirls. Erdal (2001a) had noticed that swirl decay is more rapid for a single inlet than for two inlets which make the flow more symmetric. The fact that Eq. (3) does only account for the Re number, and not for the number of inlets, could explain that it cannot distinguish the decay of swirls generated by a single or by multiple tangential inlets. Since it is supposed to predict correctly the axisymmetric swirl decay, this equation will underestimate the decay of swirls generated by a single tangential inlet.

9. Investigation of other inlet configurations As CFD allows to reproduce reasonably well the hydrodynamics of the GLCC, it has been used as a predictive tool to investigate the effect of other inlet configurations. This is supposed to allow to better understand the GLCC hydrodynamics but also constitutes a useful tool to optimize the inlet geometry. Four inlet configurations have been investigated, Inlets 1–3 present the same section as the one used by Erdal (2001a):

Swirl decay

The swirl intensity axial variation was calculated from the results of the simulations carried out with the high-Re realizable model for the experimental cases 1–4 and using the swirl number as defined by Eqs. (1) or (2). The Sn2 variations are presented in Fig. 24 (averaged values on the GLCC section were calculated). The figure also shows a comparison between the simulated swirl number evolution and the one calculated using Eq. 3 (Steenbergen and Voskamp, 1998). It can be seen that: • Near the inlet, the swirl decay is very low, as mentioned by Chang and Dhir (1994).

• Inlet 1: circular inlet similar to the one used by Erdal (2001a) but placed horizontally. The objective is to understand the impact of the inlet angle on the flow. • Inlet 2 presents a square section. • Inlet 3 is rectangular; its width is 3.2 cm. • Inlet 4 is also rectangular, its width is 3.2 cm, but its section is half the preceding ones. Simulations have been performed with the high-Reynolds realizable k– model for the conditions of experimental case 3 (Table 1). Simulation procedure and numerical parameters are the same as in Section 7.1. Simulated results show that the hydrodynamics obtained with a square inlet (inlet 2) is similar


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Fig. 25 – Comparison of the tangential velocity profiles obtained for different inlet configurations (realizable k– model). to the one obtained with a circular inlet. For clarity, only the results for inlet 2 will be presented.

9.1.

Mean tangential velocity

Fig. 25 compares the mean tangential velocity profiles for the considered inlets. Compared to the experimental situation, the use of inlet 1 or 3 induces more important tangential velocities near the walls. For the horizontal inlet it is explained by the fact that most of the inlet momentum is used to gener-

ate angular flow and not a vertical one. For the rectangular inlet, it can be explained by the fact that it concentrates better the angular momentum near the walls. The Inlet 4 configuration obviously leads to more important tangential velocities.

9.2.

Mean axial velocity

Fig. 26 compares the mean axial velocity profiles obtained for different inlet configurations.

Fig. 26 – Comparison of the axial velocity profiles obtained for different inlet configurations (realizable k– model).

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Results indicate that the Inlet 4 configuration leads to a more important backflow and to a larger capture radius. Thus, it should allow a better separation efficiency since bubbles should be removed more easily. The counterpart would be a larger pressure drop, and thus more energy required. The inlet configurations 1 and 3 lead to a more axisymmetrical flow which is confirmed by lower radial velocities (not shown here). This should allow a better separation efficiency. It is also noticed that a more axisymmetric flow reduces the magnitude of the downward velocities near the walls (while for the circular inlet the maximum mean axial velocity is about 3.6 Uav in the measurement plane, its value is 2.7 Uav when using a rectangular inlet) which also favors separation. In fact, high downward velocities lead to a reduced residence time, i.e. a kind of short-cut for certain fluid particles, and thus to a worse separation. These results show that a rectangular inlet is preferable to a circular one since it concentrates the angular momentum near the walls and simultaneously reduces the vortex asymmetry and the downward velocities which could alter the separator efficiency. The inlet angle seems to increase the flow asymmetry, but this 27◦ angle is imposed to promote the gas–liquid stratification in the inlet pipe.

10.

Conclusion

In this paper, the single-phase swirl flow in a GLCC-like geometry has been simulated using a CFD commercial code. The objectives were to find the most suitable turbulence model for simulating such flows and its limitations, and also to give complementary information to experimental characterization. The most important conclusions that emerged are the following ones:

• From the RANS models investigated, it is the high-Re realizable k– model that gives the best results. Its performances are as good as LES for predicting the velocity profiles when the swirl is generated by a single tangential inlet. To predict the flow characteristics when the swirl is generated by dual inlets, LES results were better by far. • RANS and LES both underestimate the turbulence kinetic energy level. However, LES captures the shape of the profile. • Simulations show that the magnitude of the radial velocity, contrary to the commonly used assumption, is not negligible. It is mainly due to the 3D nature of the swirl flow in the GLCC (the vortex centre eccentricity). • Simulations have shown that the vortex core is subject to the PVC instability. The phenomenon is well reproduced by LES, while URANS seems to severely underestimate the precession movement amplitude. • For the same section, using a rectangular inlet instead of a circular one reduces the vortex warping, and increases the angular momentum. Thus separation should be improved.

These parameters will thus be taken into account in the conception of a GLCC experimental set-up.

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