Turbulence Modelling of a Single-Phase Flow Cyclone Gasifier

The current work aims to make a foundation for an engineering design of a cyclone gasifier to be able not only to predict its flow field with a suitable accuracy but also to investigate a large number of design alternatives with limited computer resources. A good single-phase flow model that can form the basis in an Euler-Lagrange model for multi-phase flow is also necessary for modelling the reacting flow inside a cyclone gasifier. The present paper provides an objective comparison between several popular turbulence modelling options including standard k-ε and SST with curvature corrections, SSG-RSM and LES Smagorinsky models, for the single-phase flow inside cyclone separators/gasifiers that can serve as a guide for further work on the reacting multi-phase flow inside cyclone gasifiers and similar devices. A detailed comparison between the models and experimental data for the mean velocity and fluctuating parts of the velocity profiles are presented. Furthermore, the capabilities of the turbulence models to capture the physical phenomena present in a cyclone gasifier that affects the design process are investigated.


Introduction
Cyclone is a stationary mechanical apparatus to separate solid or liquid particles from a carrier gas by utilizing the centrifugal force. One of the recent advanced applications of this device is to use it for biomass gasification, i.e. cyclone gasifier.
In a cyclone gasifier, pulverized biomass fuel is fed together with air tangentially Engineering along the inside surface of a cyclone geometry [1] [2] [3]. Partial combustion inside the cyclone gasifier generates a high temperature that results in conversion of the powder to a medium heating value gas and possibly also a small char residue. So far, several laboratory-scale studies have been carried out to understand the key concepts of this device [4] [5] [6]. Some attempts have also been done to simulate the flow, heat transfer and chemical reactions [7] [8]. The main problem with the CFD approach in combination with turbulent heat transfer and chemical reactions is that the complexity of the global model makes it difficult to assess the accuracy of individual sub-models. For instance, in the recently published papers [7] [8], the models are based on relatively simple eddy-viscosity turbulence models. Although the agreement between these gasifier models and experiments has been encouraging, one cannot rule out the possibility whether this is an effect of cancellation of errors in the different sub models or not. Therefore, it is the purpose of the present paper to focus on the fluid dynamics modeling of the cold single-phase flow in a cyclone gasifier separately in order to develop a better foundation for continued modeling of the reactant multi-phase flow with particle tracking and phase change, but also to have a better understanding of peculiarities in the gas flow of a cyclone geometry.
The flow pattern inside abiomass cyclone gasifier is quite similar to a cyclone separator. However, since the temperature of walls is quite high (around 900˚C), the solid wood particles are converted into char and ash. Cyclone separator modeling was pioneered by Barth [9] and was later improved significantly by Muschelknautz [10]. These semi-empirical models can predict the core swirling velocity, pressure drop and separation efficiency in cyclone separators based on geometrical parameters and frictional factors. However, some of the assumptions in these models about the flow pattern are contradicted by experiments [11].
Boysan et al. [12] were among the first to present numerical simulations of the flow field in a cyclone separator. Since then, computational fluid dynamics (CFD) has been frequently used as a tool to predict more geometrical details and performance estimations of cyclone separators. The earliest works showed that eddy viscosity turbulence models such as standard k-ε were incapable of accurate prediction of the swirling flow in cyclones [13] [14]. Others later reported an appropriate agreement with experimental data using a more complex Reynolds Stress turbulence model [15] [16]. Moreover, more demanding modeling with large eddy simulations (LES) was found to give an improved agreement with LDA measurements [17] [18] [19] [20] [21].
Viscous flow in a typical reverse-flow cyclone can be divided into two types: primary flows, which include the flow through the inlet, the swirling flow in the cyclone, the boundary layers on the vertical walls, and the exit flow in the vortex finder tube; furthermore, secondary flows, which include a boundary layer at the lid of the cyclone with radial inflow, lip leakage at the entrance to the vortex finder, Görtler vortices superimposed on the primary flow and a precessing vortex core (PVC) [ The main swirling flow in the cyclone is highly turbulent and three-dimensional.
Velocity distributions in the near-wall regions and in the shear region between the downward flow near the wall and the upward flow near the centerline are the most challenging features for the modeler. Typically, the tangential velocity is the largest velocity component, and its profile does not change much with axial position in the cyclone. The tangential velocity profiles are similar to a Rankin vortex: a near loss-free vortex surrounding a core of forced solid body rotation, with its maximum value almost at the radius of the vortex finder tube. The maximum tangential velocity is typically thrice the inlet velocity [11] [23] [24].
The axial velocity is of the same order of magnitude as the superficial inlet velocity. The axial flow is directed downward towards the dust bin in the near wall region, and upwards to the vortex finder tube in the core of the cyclone.
The radial velocity is generally the smallest component, and is more difficult to measure accurately. This component is uniform over the height of the cyclone, except for the greatest inward velocity on the edge of the vortex finder tube opening, generally referred to as "lip leakage". This peak in radial velocity is due to the effect of the secondary flows in the boundary layer of the cyclone lid which can cause slip at the lid leading to non-ideal separation of particles [11]. Apart from the primary flows, secondary flows in the cyclone are produced due to imbalances between the radial pressure gradient from the rapidly rotating flow and inertial forces. There are two phenomena that are of particular importance; the first is the thin boundary layer on the lid of the cyclone that is caused by the no-slip condition at the surface, which means that the centrifugal force diminishes close to the wall while the radial pressure gradient is the same as in the free stream. This in its turn means that there is a net force on the fluid elements that will accelerate the flow inwards in a thin boundary layer [22]. When the boundary layer flow reaches the vortex finder tube it will be forced to flow in the axial direction until it comes to the lip of the vortex finder where it will be entrained by the fast flow going into the vortex finder. The second phenomenon is the possibility for "Taylor-Görtler" flow instabilities caused by the swirling flow in the cylindrical part of the cyclone [22]. Both of these phenomena are unwanted since they will lead to reduced separation efficiency due to carry-over of particles.
Another significant secondary flow phenomenon is the PVC that has been observed in experimental studies [15] [25] [26] [27]. The PVC is a quasi-periodic motion of the main vortex core around the geometrical centerline of the cyclone. Based on numerous experiments, it has been found that cyclones exhibit a distinctly non-axisymmetric and low frequency unstable behavior. Moreover, the vortex core precession about the centerline which is caused by the hydrodynamic instabilities of the flow, enhances velocity fluctuations, and hence, turbulence fluctuations. Therefore, close to the center where the gas goes out through the vortex finder, velocity fluctuation levels are very high. This means that simulations should not only be calculated in terms of average velocities, but also fluctuating velocities are very important. Thus, a high spatial and temporal Engineering resolution is necessary to adequately resolve the single-phase flow field of the cyclone [28].
Accordingly, turbulence is an inherent characteristic of a cyclone gasifier which has a significant effect on the heat and mass transfer in an Eulerian-Lagrangian frame work. However, in the present work, the aim is to choose a model being able to investigate a large number of design alternatives in as short time as possible with limited computer resources. Hence, the cost-performance is a crucial parameter especially since the turbulence model will be applied to predict the multi-phase reacting flow inside of a cyclone gasifier. Tracking particle paths and solving additional equations for the heterogeneous and homogeneous chemical reactions will considerably lengthen the computational time. An essential pre-requisite of an appropriate turbulence model for the reacting flow inside the cyclone geometry is first to have capability to simulate the single-phase flow. The current work aims to model single-phase turbulent gas flow inside isothermal cyclone separator/gasifier using a number of popular turbulence models and to compare the obtained results with each other and with detailed Laser Doppler Anemometry (LDA) velocity measurements, in the literature [29], which can be considered as a benchmark for future modeling of the reactant multi-phase flow.
The turbulence models that have been selected are: 1) standard k-ε with curvature correction; 2) Shear stress transport (SST) with curvature correction; 3) SSG Reynolds stress model (SSG-RSM); and 4) large eddy simulation (LES). The comparison between the mean and root-mean-squared simulated velocity profiles and the experimental data is presented here. However, computational cost and the ability of the models to capture the significant phenomenon in a cyclone will be the main focus.

Governing Equations
The gas flow in a cold flow cyclone gasifier can be treated as incompressible and isothermal. Therefore, the Reynolds-averaged Navier-Stokes (RANS) equations can be written in the following form [30]: where u and u′ are defined as the mean (time-averaged) and fluctuating components of the fluid velocity, respectively, i.e. u u u′ = + . Over barred term, , is known as the Reynolds stress tensor that accounts for turbulent fluctuation in fluid momentum 1 . The objective of RANS-based turbulence models is to calculate the Reynolds stresses. In eddy viscosity based models, the Reynolds stresses are linearly associated to the mean velocity gradients and eddy (turbulent) viscosity as follows [31]: 1 List of symbols at the end of the paper.
where ij δ is the Kronecker delta and t µ is the eddy viscosity that has to be modeled. For the widely used k-ε models, it is linked to the turbulent kinetic energy (k) and rate of dissipation (ε) through the relation [31]: where C µ is an empirical constant (=0.09). The SST turbulence model is another two-equation eddy viscosity model used here, which utilizes the k-ω formulation in the boundary layers of the wall, while it switches to a k-ε behavior to model the free stream [32]. In the k-ω models, the turbulent viscosity is defined based on the turbulent kinetic energy (k) and turbulent frequency (ω): The drawback of the eddy-viscosity models, when considering cyclone flows, is that they are insensitive to swirling flows. Hence, to account for swirling effects, Spalart and Shur [33] derived an empirical modification of eddy-viscosity turbulence models. The empirical function is used as a multiplier of the turbulent production term as follows [33]: where k P is the turbulent production term due to the viscous forces, and r f is the empirical function applied to stabilize the rotating flow [33] [34]. The RSM models are based on directly solving the transport equations to obtain all individual stress components [35]. Since the SSG-RSM developed by Speziale et al. [36] has been shown to be more accurate than the other versions of RSM models for most flows, and particularly for swirling flows, it was selected for this study (based on recommendation of [34]). A detailed explanation of both eddy viscosity and RSM models can be found in [37].
An alternative approach to RANS modeling is the LES technique that directly solves for large-scale fluctuating motions with characteristic size greater than the grid size; and implicitly models sub-grid scales (SGS) for eddies that are smaller than the grid size [38]. For this technique, the time-dependent Navier-Stokes equations are filtered and used as the governing equations. For an incompressible flow, the filtered Navier-Stokes equations can be written in the following way: where u is the filtered fluid velocity; p is the filtered static pressure; and the sgs ij τ term is the SGS stress tensor that is defined by: By using the Boussinesq hypothesis [39], the SGS stress is calculated: where sgs ν is the SGS turbulent viscosity; and sgs ij s is the rate of strain tensor for the large scale defined by:

Numerical Setup
A cylinder-on-cone reverse-flow gas cyclone with tangential inlet, drop tube and dust bin (see Figure 1, Table 1), used in the experimental study by Obermair et al. [29], is considered as the case study.
The 3D-geometry of the considered cyclone was created using ANSYS Design Five grids were produced (Table 2) and used for a grid sensitivity study, using a Richardson extrapolation (RE) method [44] to estimate the errors, using the pressure drop over the cyclone as the evaluation parameter. The mesh convergence study was first performed using the k-ε turbulence model for all five meshes in Table 2. The mean tangential and axial velocities for the five cases compared to experimental results are illustrated in Figure 2. As it can be seen from the figure, the differences between the meshes are small, but the agreement with experiments is poor due to the exaggerated diffusivity of the k-ε model The pressure recovery coefficient, C P , was chosen as the goal function for a formal mesh sensitivity study. C P is defined as follows:   where g ρ is the gas density; and the subscripts in and out denotes values at the inlet and outlet, respectively. The change of C P with mesh size is shown in Figure 3. It can be seen from Figure 3 that the convergence is monotonic but that the solutions for the two coarsest grids (meshes (1) and (2)) seem to be outside the so called "asymptotic region" where a simple power law will give a good fit to the data. In order to quantify the error, the grid convergence index (GCI) method [44], which is based on Richardson extrapolation, was used. The local apparent order of accuracy p in the fine-grid solution is 4.18, and the numerical uncertainty is 0.47%. Assuming that the relative error in C P is representative of the errors in the rest of the variables, this implies that the medium mesh gives an acceptable error for further investigations of other turbulence models.
For the SSG-RSM model also, the three last fine grids were checked, and the results showed the same trend of convergence. However, note that for other    For the unsteady RANS models, i.e. k-ε, SST and SSG-RSM, the high resolution, and for LES simulation, the unbounded central difference advection scheme was applied; however, first-order upwind was used for solving the turbulence equations in all simulations (as suggested by [45]). The second-order backward Euler transient scheme was selected for all simulations, since it was difficult to get a good converged solution using a direct stationary solution approach. It is most likely that the root cause of it comes from the PVC phenomenon that generates continuously fluctuating forces on the flow field near the center [19].
For the convergence criteria, the residual target was set to 1 × 10 −6 root-  Table 3). At the same time, as shown in Table 3 Furthermore, another important criterion is the dimensionless distance from the first mesh node to the wall (the y + value of the first node). The wall function approach and the required y + value depend on the flow behavior and the turbulence model being used. Since k-ε and SSG models use a wall function approach for the near wall region, a maximum distance of the first grid point for all meshes off the wall was adjusted to the range of y + = 40 − 80, and a scalable wall function [45] was applied. However, for the SST and LES models, which solve the transport equations also for the inner parts of the boundary layer, the first grid point should be at a position of 2 y + < [37] and wall function is automatically determined by the software.
At the inlet, a plug flow profile with a normal-direction speed equal to 12.68 (m•s −1 ) was used as the boundary condition. Also, for all RANS models, a At the gas outlet, the boundary condition for all RANS simulations was set to "opening" type boundary condition. This boundary condition is a Neumann type boundary condition that specifies the normal derivative at the outlet for all variables except the pressure, and therefore, the gas can both exit and enter through the outlet. However, for the LES simulation, the "outlet" boundary condition, in which the code makes artificial walls at the outlet as a barrier for the flow to prevent inflow, was used. In fact, since the flow at the outlet tries to return to the computational domain and some recirculation will occur that causes destabilization of the solution for LES simulation, using an outlet boundary condition therefore increases the robustness of the calculation [45].

General Impressions of the Flow Field
A snapshot of the flow-fields from the LES simulation in the x-z cut plane through the center and the x-y plane at a location very close to the cyclone lid is presented in Figure 4. In Figure 4(a), an instantaneous view of the internal flow-field in the cyclone body, conical part and entrance region of the vortex finder is shown. A close inspection of the results shows that there is a thin boundary layer with radial flow towards the vortex finder at the top of the cyclone (see Figure 4(b)), as is to be expected from a local boundary layer analysis [22]. The boundary layer is deflected in the axial direction when it meets the vortex finder wall and the resulting flow is eventually entrained in the main flow leaving the cyclone at the lip of the vortex finder. Another flow detail that can be observed in Figure 4(a) and Figure 4 (b) is the presence of Taylor-Görtler vortices [23] close to the cyclone body wall. These secondary vortices are generated by a centrifugal instability near the concave wall of the cyclone [22].
Notice that the Taylor-Görtler vortices are superimposed on the much faster tangential flow in the cyclone but at the same time they will have a significant effect on the separation efficiency of the cyclone. From Figure 4(c), it can be seen that vortex core is slightly off-axis within the vortex finder which means that the point of zero circumferential velocity at the top of the cyclone is not exactly on the centerline of the cyclone geometry. This is a sign of the existence of a PVC in the simulations. In Figure 5, contour plots of instantaneous velocity values are shown in six cross sections of the body cyclone and conical portion. The results confirm that with increasing the distance from the centerline, the velocity is rising to a maximum value and then decreases towards the wall. Furthermore, signs of the off-axis movement of the core through the centerline can be noticed, which is another proof of the existence of a quasi-periodic motion of the vortex core that is well captured by the LES.

Comparison of Turbulence Models
In order to assess the capability of the turbulence models to represent the peculiarities of the flow field in the cyclone, the mean and RMS values of tangential and axial velocity profiles of single phase CFD simulations and LDA measurement data of [29] have been compared along two diameters in the conical part of the cyclone (shown in Figure 1).  (m•s −1 )). Based on the mesh convergence study, the medium mesh was first used for the SST and SSG-RSM models. However, since the position of the first node for the SST model should be set at a location of 2 y + < , the simulations with the medium grid led to divergence due to the large aspect factor in the mesh. Hence, the fine grid (or mesh (4)) was instead applied for the SST model to obtain a converged solution. Furthermore, as adequately high resolution is a necessity for LES, the finest mesh (mesh (5)) was used in this case to exclude uncertainties connected to the mesh.
The experimental and simulated velocity profiles with different turbulence models are illustrated in Figure 6. The experimental mean tangential velocity profiles are generally captured well by all of the turbulence models. The peak of average tangential velocity and the width of the vortex core region agree properly.
However, as expected, the k-ε model predicts a too wide vortex core, and so it has trouble to predict the location of peak tangential velocity (esp. more clear in the section II-II). In addition, this model fails to reproduce the mean axial velocity in all positions. In particular, it predicts mean axial velocities to be uniform in the inner region of the flow where the other models and LDA shows that the mean axial velocity profile has a significant dip creating a central part of  In conclusion, as expected, the LES approach is the best to represent the effects of turbulent dispersion from the velocity fluctuations. The motions of large eddies in the vicinity of the centerline, which are mainly responsible for anisotropic behavior of the flow, can be simulated directly in LES, while the effect of the smaller eddies are captured by SGS models. Thus, since the flow is predominantly governed by the large eddies rather than small eddies, especially in the central region, a large eddy approach can reveal more of the flow physics in the cyclone geometry. Nevertheless, the negative feature of the LES simulations is the requirement of a much finer computational grid, leading to a higher computational effort. Therefore, based on the results in the conical section, the time-averaged results of SST and RSM-SSG models agree well with the experimental results and are very similar to those in the LES, while they are unable to predict the fluctuations due to the PVC. However, the SSG-RSM model showed that it could work even with coarse grids, so it took less time to accomplish a simulation relative to the SST model. A larger number of mesh elements had to be used for the SST model, so it was more time consuming than the SSG-RSM model. Hence, the SSG-RSM model seems to be the model with the best cost-performance ratio.
For modeling a cyclone gasifier including reactant particles, although the SST and the SSG-RSM models are incapable of capturing the PVC phenomenon in the core region, they both can be used for an engineering modeling. In a cyclone gasifier, there is a hypothesis that the gasification process occurs at the wall and smaller unconverted solid particles in addition to soot and tar moves toward the outlet at the top [8]. Thus, it is likely that the PVC phenomenon doesn't influence the gasification process substantially. The SSG-RSM can be used as a first priority due to its ability to work with the coarser grids which results in less computational time. The SST model due to its sensitivity to the near wall grid point needs a finer grid compared to the SSG-RSM leading to a higher computational time. However, adding heat and mass transfer will definitely change the situation, and probably creates new problems. However, based on the recent studies, the SST model is more popular for combustive and thermal flows than the SSG-RSM [46] [47]. On the other hand, the SSG-RSM is the most used industrial model for simulating a cyclone separator [19] [48]. Accordingly, determination of the suitable turbulence model for the final design depends on the adaptability of the reactant and heat transfer equations to the turbulence models.

Conclusions
The single phase flow of a gas cyclone separator with tangential inlet was simulated with four different turbulence models and all but the k-ε model could be validated against LDA measurement from literature [29]. The four turbulence models are 1) standard k-ε model with curvature correction; 2) SST model with curvature correction; 3) SSG Reynolds stress model and 4) LES with Smagorinsky sub-grid model. For the mean tangential velocities, all RANS models and the LES captured the shape of the tangential velocity profiles with good accuracy; nevertheless, the k-ε model predicted a much wider central region than the experiments and the other simulated results. For the mean axial velocity the situation is more complicated.
The SST model with its integration through the boundary layer all the way to 2 y + < agrees much better with the results than the k-ε model, which was Moreover, the simulations demonstrated a peak in radial velocity just beneath the vortex finder entrance, caused by the lip leakage flow. There are no LDA measurements from this region but lip leakage is a well-known phenomenon in industrial cyclones and it is important that the models can predict it.
Overall, the LES approach was the most accurate one, but also the most time-consuming. However, the SST model required a grid with a larger number of elements to resolve the boundary layers close to the walls while the SSG-RSM model uses a wall function that requires less grid points close to the wall. For this reason, the SST model became more time-consuming and the SSG-RSM model seems to be the best alternative for engineering design where computational cost/performance is of primary importance. However, making a decision for choosing the most appropriate turbulence model for the final design of a gasification process in a cyclone depends on the behavior of the reactant and heat transfer equations against the turbulence models.