Analysis of Dynamic Behavior of Fluidized Bed Gasifier Using CFD

Abstract

Biomass gasification is a thermo-chemical energy conversion process whereby the solid biomass is converted to the useful gaseous product—syngas. With increasing attention to biomass as a clean and sustainable energy source, biomass gasification process is also being studied extensively. Fluidized bed technology is widely used in gasification due to its various advantages like better mass and heat transfer rate, good mixing properties and temperature control. Modeling based on computational fluid dynamics has become popular in describing the dynamic behavior of gas–solid flow and chemical reactions in fluidized bed gasifiers and is used to optimize the gasifier designs. In the present work, an Euler–Euler two-fluid model is employed to simulate the complex transient behavior of gas–solid flow in a bubbling fluidized bed with sand particles. The model is validated by comparing the hydrodynamic parameters with the results obtained from the experiments conducted at different bed heights. In the model, the solid-phase properties are calculated by applying the kinetic theory of granular flow. The effect of different viscosity models, used to determine the solid-phase viscosity terms, on the dynamic behavior of bed is studied. Simulations are carried out with two different models for kinetic and collisional parts of shear viscosity, two different models for frictional part, without considering frictional part, a single model for solid bulk viscosity and without considering bulk viscosity. The results obtained using different viscosity models are compared with respect to pressure drop, axial velocity of particle and volume fraction.

1 Introduction

Increasing global energy demand, climate change and environmental pollution have forced the world community to emphasize on clean, green and renewable energy for sustainable development. Biomass is a prominent clean and sustainable energy source. Different conversion routes of biomass into energy are being studied extensively. Biomass gasification is a thermo-chemical energy conversion process whereby the solid biomass is converted to the useful gaseous product, syngas, which can be used to obtain the end products like electricity, heat, transportation fuels etc. (Sansaniwal et al. 2017). Fluidized bed technology is widely used in gasification due to its various advantages like better mass and heat transfer rate, good mixing properties, and temperature control. Modeling based on computational fluid dynamics has become popular in describing the dynamic behavior of gas–solid flow and chemical reactions in fluidized bed gasifiers and is used to optimize the gasifier designs (Baruah and Baruah 2014; Singh et al. 2013).

Studying the hydrodynamics of fluidized bed is important in developing an accurate model of a gasifier. Further development in hydrodynamic modeling is crucial for better understanding the phase interactions and thereby better control of the process (Philippsen et al. 2015). Two main approaches namely Euler-Euler and Euler-Lagrange are used for numerical modeling of multiphase flow in fluidized bed. Euler–Euler approach is computationally lesser intensive and is appropriate for applications like bubbling fluidized beds where volume fraction of the second phase cannot be neglected. The effect of different modeling parameters like gas–solid drag models (Loha et al. 2012; Sahoo and Sahoo 2015; Estejab and Battaglia 2015), turbulence (Anil et al. 2015), coefficient of restitution (Taghipour et al. 2005; Loha et al. 2014), specularity coefficient (Loha et al. 2013), etc., have been studied by many researchers. Different models are used by researchers for the solid-phase viscosity terms, but studies focused on the effect of different viscosity models on bed hydrodynamics are very few. The present work deals with developing an Euler–Euler 2D multiphase model of fluidized bed with sand particles using ANSYS Fluent 14.0 and studying the effect of different viscosity models on the hydrodynamic behavior of the bed.

2 Numerical Modeling

2.1 Governing Equations

In the Euler–Euler two-fluid model used here, both the gas and solid phases are treated mathematically as interacting and interpenetrating continua. The governing equations for the model are as follows:

Continuity equations for gas phase and solid phase

$$\frac{\partial }{\partial t}\left( {\alpha_{g} \rho_{g} } \right) + \nabla .\left( {\alpha_{g} \rho_{g} \vec{v}_{g} } \right) = 0$$

(7.1)

$$\frac{\partial }{\partial t}\left( {\alpha_{s} \rho_{s} } \right) + \nabla .\left( {\alpha_{s} \rho_{s} \vec{v}_{s} } \right) = 0$$

(7.2)

Momentum equations for gas phase and solid phase

$$\frac{\partial }{\partial t}\left( {\alpha_{g} \rho_{g} \vec{v}_{g} } \right) + \nabla .\left( {\alpha_{g} \rho_{g} \vec{v}_{g} \vec{v}_{g} } \right) = - \alpha_{g} \nabla p + \nabla .\tau_{g} + \alpha_{g} \rho_{g} g + K_{\text{gs}} \left( {\vec{v}_{s } - \vec{v}_{g} } \right)$$

(7.3)

$$\frac{\partial }{\partial t}\left( {\alpha_{s} \rho_{s} \vec{v}_{s} } \right) + \nabla .\left( {\alpha_{s} \rho_{s} \vec{v}_{s} \vec{v}_{s} } \right) = - \alpha_{s} \nabla p + \nabla .\tau_{s} + \alpha_{s} \rho_{s} g + K_{\text{gs}} \left( {\vec{v}_{g } - \vec{v}_{s} } \right)$$

(7.4)

The momentum exchange coefficient is accounted using Gidaspow drag model (Gidaspow et al. 1992) and turbulence is accounted using standard per phase k-ε model. The solid properties are determined as a function of radial distribution function and granular temperature. The solid pressure is given by,

$$p_{s} = \alpha_{s} \rho_{s} \varTheta_{s} + 2\rho_{s} \left( {1 + e_{\text{ss}} } \right)\alpha_{s}^{2} g_{{ 0 , {\text{ss}}}} \varTheta_{s}$$

(7.5)

The gas phase and solid-phase shear tensors are given by,

$$\tau_{g} = \alpha_{g} \mu_{g} \left( {\nabla \vec{v}_{g} + \nabla \vec{v}_{g}^{T} } \right) - \frac{2}{3}\alpha_{g} \mu_{g} .\left( {\nabla .\vec{v}_{g} } \right)I$$

(7.6)

$$\tau_{s} = \alpha_{s} \mu_{s} \left( {\nabla \vec{v}_{s} + \nabla \vec{v}_{s}^{T} } \right) - \alpha_{s} \left( {\lambda_{s} - \frac{2}{3}\mu_{s} } \right)\left( {\nabla .\vec{v}_{s} } \right)I$$

(7.7)

The solid shear viscosity term $(\mu_{s} )$ in the equation for solid-phase tensor consists of three parts namely kinetic, collisional, and frictional part.

$$\mu_{s} = \mu_{{s,{\text{kin}}}} + \mu_{{s,{\text{col}}}} + \mu_{{s,{\text{fr}}}}$$

(7.8)

Two models popularly used by researchers for the kinetic part are Gidaspow model (Gidaspow et al. 1992) and Syamlal-Obrien model (Syamlal and Rogers 1993). The correlations are given below:

Gidaspow model

$$\mu_{{s,{\text{kin}}}} = \frac{{10\rho_{s} d_{s} \sqrt {\varTheta_{s} \pi } }}{{96\alpha_{s} \left( {1 + e_{\text{ss}} } \right)g_{{ 0 , {\text{ss}}}} }}\left[ {1 + \frac{4}{5}g_{{ 0 , {\text{ss}}}} \alpha_{s} \left( {1 + e_{\text{ss}} } \right)} \right]^{2}$$

(7.9)

Syamlal-Obrien model

$$\mu_{{s , {\text{kin}}}} = \frac{{\alpha_{s} d_{s} \rho_{s} \sqrt {\varTheta_{s} \pi } }}{{6(3 - e_{\text{ss}} )}}\left[ {1 + \frac{2}{5}\left( {1 + e_{\text{ss}} } \right)\left( {3e_{\text{ss}} - 1} \right)\alpha_{s} g_{{ 0 , {\text{ss}}}} } \right]$$

(7.10)

For the collisional part of solid shear viscosity, both of these models provide the same correlation.

$$\mu_{{s , {\text{col}}}} = \frac{4}{5}\alpha_{s} \rho_{s} d_{s} g_{{ 0 , {\text{ss}}}} \left( {1 + e_{\text{ss}} } \right)\sqrt {\frac{{\varTheta_{s} }}{\pi }}$$

(7.11)

For the frictional part of shear viscosity, mainly two models are available which are given by Schaeffer (1987) and Johnson and Jackson (1987).

Schaeffer’s model

$$\mu_{{s , {\text{fr}}}} = \frac{{p_{s} \sin (\phi ) }}{{2\sqrt {I_{2D} } }}$$

(7.12)

Model by Johnson and Jackson

$$\mu_{{s , {\text{fr}}}} = p_{\text{fr}} \sin \phi$$

(7.13)

$$p_{\text{fr}} = F_{r} \frac{{\left( {\alpha_{s} - \alpha_{s,\hbox{min} } } \right)^{n} }}{{\left( {\alpha_{s,\hbox{max} } - \alpha_{s} } \right)^{p} }}$$

(7.14)

For solid bulk viscosity model prescribed by Lun et al. (1984) is commonly used.

$$\lambda_{s} = \frac{4}{3}\alpha_{s} \rho_{s} d_{s} g_{{0,{\text{ss}}}} \left( {1 + e_{\text{ss}} } \right)\left( {\frac{{\varTheta_{s} }}{\pi }} \right)^{{\frac{1}{2}}}$$

(7.15)

2.2 Computational Domain and Solution Procedure

The computational domain used for the analysis is shown in Fig. 7.1. The parameters, properties, and the initial and boundary conditions used are listed in Table 7.1. The equations are solved and the simulations are carried out using the CFD package ANSYS Fluent 14.0. Finite volume method is used for domain discretization. A time step size of 0.001 s and convergence criteria of 10⁻³ for the maximum residuals are chosen for the simulation. The simulations are carried out for 15 s with time-averaging of parameters done from 5 to 15 s. Phase Coupled SIMPLE algorithm is used for pressure-velocity coupling. Second order implicit scheme and first order upwind scheme are used for the discretization of unsteady and convective terms, respectively. A grid independence study is conducted to select the appropriate grid size.

Fig. 7.1

Computational domain

Table 7.1 Hydrodynamic parameters and other properties

3 Experimental Setup

Figure 7.2 shows the schematic diagram of the experimental setup used for cold flow analysis of fluidized bed and determination of bed pressure drop. A riser made of acrylic glass with dimensions of 0.15 m inner diameter and 1.2 m height is used for the experiments. Sand particle is used as the bed material. Air is supplied using a centrifugal blower. Flow is regulated using a gate valve and the flow rate is measured by an orifice meter. They are connected using pipes of 50.8 mm inner diameter. Pressure tapings are provided along the riser which are connected to a U-tube manometer to determine the pressure drop. Superficial velocity is calculated using the manometer readings corresponding to the orifice meter.

Fig. 7.2

Schematic diagram of the experimental set up for cold flow analysis

4 Results and Discussion

The grid size for the model is chosen after conducting a grid independence study. The developed 2D numerical model of fluidized bed is validated by comparing the simulation results with the experimental results. The model is used to analyze the effect of using different viscosity models on different hydrodynamic parameters such as pressure drop across the bed, particle volume fraction and axial velocity.

4.1 Grid Independence Study

The grid is generated using uniform quad method available in the ANSYS Fluent’s grid generation package. Simulations are carried out by varying the grid size (2448, 5000, 11400, 14749 and 20000 cells) and are checked for grid independence. Figure 7.3 shows the variation in time-averaged axial particle volume fraction and Table 7.2 shows the variation in time-average pressure drop value across the bed, on changing the grid size. It is observed that there is no significant change in volume fraction or pressure drop when the grid is made finer beyond a grid size of 14749 cells. Hence the grid of 14749 cells (element size = 0.0035 m) is chosen for the analysis.

Fig. 7.3

Time averaged particle volume fraction along the central axis for different grid sizes

Table 7.2 Time-averaged pressure drop for different grid sizes

4.2 Experimental Validation

The bed pressure drop obtained from simulation for different bed heights and velocities is compared with that from experiment (Fig. 7.4). The average percentage error in pressure drop prediction is 11.10%.

Fig. 7.4

Comparison of pressure drop obtained from simulation and experiment (bh = bed height, v = velocity)

4.3 Effect of Solid Viscosity Models

For kinetic and collisional parts of solid shear viscosity (together termed as granular viscosity in Fluent), two different models namely Gidaspow model and Syamlal-Obrien model are used. Simulations are carried out for cases with and without considering frictional part of shear viscosity and solid bulk viscosity terms. Two models namely Schaeffer and Johnson models are used for the frictional part. Lun model is used for the bulk viscosity. All other parameters are kept the same.

Figure 7.5 shows the percentage error in predicting bed pressure drop numerically using different viscosity model combinations with the experimentally found pressure drop of 1075.18 Pa for bed height of 80 mm and superficial gas velocity of 0.4 m/s. A minimum deviation of 10.85% is obtained for a combination of Syamlal-Obrien and Lun model without considering frictional viscosity (Sy-No-L). There is almost negligible change in pressure drop prediction when granular viscosity and bulk viscosity models are changed. Comparatively more change is observed when frictional viscosity models are changed. Johnson model predicts a larger pressure drop than Schaeffer. The predicted pressure drop is lowest when frictional viscosity is not accounted. The frictional viscosity is the contribution of friction between the particles to solid shear viscosity and accounts for the viscous-plastic transition which occurs when solid-phase particles reach the maximum solid volume fraction (Lun et al. 1984). It does not contribute in the dilute or viscous regimes, but only in dense regimes. The change in predicted pressure drop when frictional viscosity is added indicates the presence of dense region in the bed and hence frictional viscosity cannot be neglected.

Fig. 7.5

Comparison of different combination of viscosity models with respect to time-averaged pressure drop and percentage error/deviation with experimental value

It is observed from Fig. 7.6a that there is considerable variation in the axial velocity profile for simulations carried out with Johnson model for frictional viscosity from that of other simulations. All other simulations show similar profiles indicating that the sensitivity to different granular viscosity models are rather low. Figure 7.6b indicates that adding solid bulk viscosity model (Lun model) also has very less effect on predicting axial velocity of the particle. Figure 7.7a, b show that the predicted volume fraction has negligible change when the viscosity models are changed.

Fig. 7.6

Time-averaged axial particle velocity profile along lateral direction, a different granular and frictional viscosity models, b with and without Lun model for solid bulk viscosity

Fig. 7.7

Time-averaged particle volume fraction along the central axis, a different granular and frictional viscosity models, b with and without Lun model for solid bulk viscosity

The granular viscosity (kinetic and collisional part of shear viscosity) accounts for the particle momentum exchange due to translation and collision (FLUENT, ANSYS 2011). Syamlal-Obrien model neglects the kinetic viscosity in the dilute region. But it did not have much effect on predicting the hydrodynamic parameters as the bed is in the dense and viscous regimes. The solid bulk viscosity accounts for the resistance of granular particles to expansion and compression. But adding the bulk viscosity model of Lun did not show much effect on the prediction of hydrodynamic parameters.

5 Conclusion

A 2D Euler-–Euler model of a bubbling fluidized bed with sand particles is developed. The pressure drop predicted by the model is compared with experimental results for different bed heights and velocities and an average deviation of 11.10% is found. Comparing the different combinations of solid viscosity models, the combination of Syamlal-Obrien and Lun without considering frictional viscosity has the least deviation (10.85%) from experimentally obtained pressure drop. Changing the granular viscosity and bulk viscosity models shows negligible effect on prediction of hydrodynamic parameters of the fluidized bed while changing the frictional viscosity models exhibits more effect on the prediction of hydrodynamic parameters of the fluidized bed. Hence, incorporating the accurate viscosity model will improve the prediction accuracy of the overall gasifier model. Further, experimental determination of other hydrodynamic parameters and their comparison with numerically predicted values will help in better understanding and selection of viscosity models.