Heat Transfer Mathematical Modelling Numerical Methods and Information Technology Part 10 potx

Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors 349 classification. Spherical particles with different diameter and a density of 1830 kg/m 3 were fluidized with air at ambient conditions. Typically, the static bed height was 30 and 40cm with a solid volume fraction of 0.6. A roots-type blower supplied the fluidizing gas. A pressure-reducing valve was installed to avoid pressure oscillations and achieve a steady gas flow. The airflow rate was measured using a gas flow meter (rotameter) placed between the blower and the inlet pipe to an electrical heater. Initial solid particle temperature was 300K. An electrical heater was used to increase the inlet gas temperature from ambient temperature to 473K. A cooling system was used to decrease the gas temperature that exited from the reactor in order to form a closed cycle. Fig. 4 (A) shows a schematic of experimental set-up and its equipments. Pressure fluctuations in the bed were measured by three pressure transducers. The pressure transducers were installed in the fluidized bed column at different heights. Seven thermocouples (Type J) were installed in the center of the reactor to measure the variation of gas temperature at different locations. Also, three thermocouples were used in different positions in the set-up to control the gas temperature in the heat exchanger and cooling system. Fig. 4. (B) shows the locations of the pressure transducers and thermocouples. The pressure probes were used to convert fluctuation pressure signals to out-put voltage values proportional to the pressure. The output signal was amplified, digitized, and further processed on-line using a Dynamic Signal Analyzer. Analog signals from the pressure transducers were band pass filtered (0–25 Hz) to remove dc bias, prevent aliasing, and to remove 50 Hz noise associated with nearby ac equipment. The ratio of the distributor pressure drop to the bed pressure drop exceeded 11% for all operating conditions investigated. The overall pressure drop and bed expansion were monitored at different superficial gas velocities from 0 to 1 m/s. For controlling and monitoring the fluidized bed operation process, A/D, DVR cards and other electronic controllers were applied. A video camera (25 frames per s) and a digital camera (Canon 5000) were used to photograph the flow regimes and bubble formation through the transparent wall (external photographs) during the experiments. The captured images were analyzed using image processing software. The viewing area was adjusted for each operating condition to observe the flow pattern in vertical cross sections (notably the bed height oscillations). Image processing was carried out on a power PC computer equipped with a CA image board and modular system software. Using this system, each image had a resolution of 340×270 pixels and 256 levels of gray scales. After a series of preprocessing procedures (e.g., filtering, smoothing, and digitization), the shape of the bed, voidage, and gas volume fraction were identified. Also, the binary system adjusted the pixels under the bed surface to 1 and those above the bed surface to 0. The area below the bed surface was thus calculated, and then divided by the side width of the column to determine the height of the bed and the mean gas and solid volume fraction. Some of experiments were conducted in a Plexiyglas cylinder with 40cm height and 12 cm diameter (Fig. 5). At the lower end of this is a distribution chamber and air distributor which supports the bed when defluidized. This distributor has been designed to ensure uniform air flow into the bed without causing excessive pressure drop and is suitable for the granular material supplied. A Roots-type blower supplied the fluidizing gas. A pressure- reducing valve was installed to avoid pressure oscillations and to achieve a steady gas flow. Upon leaving the bed, the air passes through the chamber and escapes to the atmosphere through a filter. Installed in the bracket are probes for temperature and pressure Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 350 measurement, and a horizontal cylindrical heating element, all of which may move vertically to any level in the bed chamber. Fig. 5. A view of experimental set-up with its equipments. Air is delivered through a filter, pressure regulator and an air flow meter fitted with a control valve and an orifice plate (to measure higher flow rates), to the distribution chamber. The heat transfer rate from the heating element is controlled by a variable transformer, and the voltage and current taken are displayed on the panel. Two thermocouples are embedded in the surface of the element. One of these indicates the surface temperature and the other, in conjunction with a controller, prevents the element temperature exceeding a set value. A digital temperature indicator with a selector displays the temperatures of the element, the air supply to the distributor, and the moveable probe in the bed chamber. Two liquid filled manometers are fitted. One displays the pressure of the air at any level in the bed chamber, and the other displays the orifice differential pressure, from which the higher air flow rates can be determined. Pressure fluctuations in the bed are obtained by two pressure transducers that are installed at the lower and upper level of the column. The electrical heater increases the solid particle temperature, so, initial solid particles temperature was 340K and for inlet air was 300K (atmospheric condition). The ratio of the distributor pressure drop to the bed pressure drop exceeded 14% for all operating conditions investigated. Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors 351 5. Results and discussion Simulation results were compared with the experimental data in order to validate the model. Pressure drop, p Δ , bed expansion ratio, H/H 0 , and voidage were measured experimentally for different superficial gas velocities; and the results were compared with those predicted by the CFD simulations. Fig. 6 compares the predicted bed pressure drop using different drag laws with the experimentally measured values. Fig. 6. Comparison of simulated bed pressure drop using different drag models with the experimental data for a superficial velocity of V g = 50 cm/s. Fig. 7. Comparison of simulated pressure variation versus bed height using Cao-Ahmadi, Syamlal–O’Brien and Gidaspow drag models with the experimental data for a superficial velocity of V g = 50 cm/s and position of pressure transducers (P1, P2 and P3). 1500 2500 3500 4500 5500 6500 7500 8500 012345 Time (Second) Pressure difference (Pa) P1-P3 (Cao-Ahmadi drag) P1-P3 ( Syamlal-O'Brien drag) P1-P3 (Gidaspow drag) Experimental Data Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 352 Fig. 7 compares the simulated pressure variations versus the bed height for different drag laws with the experimentally measured values. The positions of pressure transducers (P1, P2 and P3) that were shown in Fig. 4(B) are identified in this Fig. To increase the number of experimental data for the pressure in the bed, five additional pressure transducers were installed at the thermocouple locations, and the corresponding pressures for a superficial velocity of V g = 50 cm/s were measured. The air enters into the bed at atmospheric pressure and decreases roughly linearly from bottom up to a height of about 60 cm due to the presence of a high concentration of particles. At the bottom of the bed, the solid volume fraction (bed density) is large; therefore, the rate of pressure drop is larger. Beyond the height of 60cm (up to 100cm), there are essentially no solid particles, and the pressure is roughly constant. All three drag models considered show comparable decreasing pressure trends in the column. The predictions of these models are also in good agreement with the experimental measurements. Fig.s 6 and 7 indicate that there is no significant difference between the predicted pressure drops for different drag models for a superficial gas velocity of V g = 50 cm/s. Figs. 6 and 7 show that there is no significant difference between the predicted pressure drops and bed expansion ratio for the different drag models used. That is the fluidization behavior of relatively large Geldart B particles for the bed under study is reasonably well predicted, and all three drag models are suitable for predicting the hydrodynamics of gas– solid flows. Fig. 8. Comparison of experimental and simulated bed pressure drop versus superficial gas velocity. Fig. 8 compares the simulated time-averaged bed pressure drops, (P1-P2) and (P1-P3), against the superficial gas velocity with the experimental data. The Syamlal–O’Brien drag expression was used in these simulations. The locations of pressure transducers (P1, P2, P3) were shown in Fig. 4 (B). The simulation and experimental results show good agreement at velocities above V mf. . For V <V mf, the solid is not fluidized, and the bed dynamic is dominated by inter-particle frictional forces, which is not considered by the multi-fluid models used. Fig. 8 shows that with increasing gas velocity, initially the pressure drops Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors 353 (P1-P2 and P1-P3) increase, but the rate of increase for (P1-P3) is larger than that for (P1-P2). For V >V mf this Fig. shows that (P1-P3) increases with gas velocity, while (P1-P2) decreases slightly, stays roughly constant, and increases slightly. This trend is perhaps due to the expansion of the bed and the decrease in the amount of solids between ports 1 and 2. As the gas velocity increases further, the wall shear stress increases and the pressure drop begins to increase. Ports 1 and 3 cover the entire height of the dense bed in the column, and thus (P1- P3) increases with gas velocity. As indicated in Fig. 9, the bed overall pressure drop decreased significantly at the beginning of fluidization and then fluctuated around a near steady-state value after about 3.5 s. Pressure drop fluctuations are expected as bubbles continuously split and coalesce in a transient manner in the fluidized bed. The results show with increasing the particles size, pressure drop increase. Comparison of the model predictions, using the Syamlal–O’Brien drag functions, and experimental measurements on pressure drop show good agreement for most operating conditions. These results (for d s =0.275 mm) are the same with Tagipour et al. [8] and Behjat et al. [11] results. Fig. 9. Comparison of experimental and simulation bed pressure drop (P1-P2) at different solid particle sizes. Comparison of experimental and simulated bed pressure drop (Pressure difference between two positions, P1-P2 and P1-P3) for two different particle sizes, d s =0.175 mm and d s =0.375 mm, at different superficial gas velocity are shown in Fig. 10. and Fig. 11. Pressure transducers positions (P1, P2, P3) also were shown in Fig. 4(B). The simulation and experimental results show better agreement at velocities above U mf . The discrepancy for U < U mf may be attributed to the solids not being fluidized, thus being dominated by inter particle frictional forces, which are not predicted by the multi fluid model for simulating gas-solid phases. 2500 3500 4500 5500 6500 7500 8500 9500 10500 012345 Time (Second) Pressure difference (Pa) ds=0.175 mm (Simulation) ds=0.275 mm (Simulation) ds=0.375 mm (Simulation) ds=0.175 mm (Experimental) ds=0.275 mm (Experimental) ds=0.375 mm (Experimental) Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 354 Fig. 10. Comparison of experimental and simulated bed pressure drop at different time Fig. 11. Comparison of experimental and simulated bed pressure drop at different gas velocity and particle sizes. Comparison of experimental and simulated bed pressure drop for two different initial bed height, H s =30, H s =40 cm, at different superficial gas velocity are shown in Fig. 11. The results show with increasing the initial static bed height and gas velocity, pressure drop (P1- P2 and P1-P3) increase but the rate of increasing for (P1-P3) is larger than (P1-P2). Comparison of the model predictions and experimental measurements on pressure drop (for both cases) show good agreement at different gas velocity. 2500 3500 4500 5500 6500 7500 8500 9500 10500 012345 Time (Second) Pressure difference (Pa) Hs =20 cm (Simulation) Hs =30 cm (Simulation) Hs =40 cm (Simulation) Hs=20 cm (Experimental) Hs=30 cm (Experimental) Hs=40 cm (Experimental) Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors 355 Fig. 12. Comparison of experimental and simulated bed pressure drop at different superficial gas velocity and static bed height. These Figs. show that with increasing gas velocity, initially the pressure drops (P1-P2 and P1-P3) increase, but the rate of increase for (P1-P3) is larger than for (P1-P2). As indicated in Fig. 12. the bed overall pressure drop decreased significantly at the beginning of fluidization and then fluctuated around a near steady-state value after about 4 s. Pressure drop fluctuations are expected as bubbles continuously split and coalesce in a transient manner in the fluidized bed. The results show with increasing the initial static bed height, pressure drop increase because of increasing the amount of particle, interaction between particle-particle and gas-particle. The results show with increasing the particle size, gas velocity and initial static bed height pressure drop (P1-P2 and P1-P3) increases. Comparison of the model predictions and experimental measurements on pressure drop (for both cases) show good agreement at different gas velocity. The experimental data for time-averaged bed expansions as a function of superficial velocities are compared in Fig. 13 with the corresponding values predicted by the models using the Syamlal–O'Brien, Gidaspow and Cao-Ahmadi drag expressions. This Fig. shows that the models predict the correct increasing trend of the bed height with the increase of superficial gas velocity. There are, however, some deviations and the models slightly underpredict the experimental values. The amount of error for the bed expansion ratio for the Syamlal-O'Brien, the Gidaspow and Cao-Ahmadi models are, respectively, 6.7%, 8.7% and 8.8%. This Fig. suggests that the Syamlal–O'Brien drag function gives a somewhat better prediction when compared with the Gidaspow and Cao-Ahmadi models. In addition, the Syamlal–O’Brien drag law is able to more accurately predict the minimum fluidization velocity. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 1020304050607080 Gas velocity (Vg) cm/s Pressure difference (Pa) P1-P3(Simulation, Hs=40 cm) P1-P2 (Simulation, Hs=40 cm) P1-P2 (Simulation, Hs= 30 cm) P1-P3 (Simulation, Hs=30 cm) P1-P2 (Experimental, Hs=30 cm) P1-P3 (Experimental, Hs=30 cm) P1-P3 (Experimental, Hs=40 cm) P1-P2(Experimental, Hs=40 cm) Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 356 Fig. 13. Comparison of experimental and simulated bed expansion ratio. Fig. 14. Experimental and simulated time-averaged local voidage profiles at z=30 cm, Vg=50 cm/s. The experimental data for the time-averaged voidage profile at a height of 30 cm is compared with the simulation results for the three different drag models in Fig. 14 for V g =50 cm/s. This Fig. shows the profiles of time-averaged voidages for a time interval of 5 to 10 s. In this time duration, the majority of the bubbles move roughly in the bed mid-section toward the bed surface. This Fig. shows that the void fraction profile is roughly uniform in the core of the bed with a slight decrease near the walls. The fluctuation pattern in the void fraction profile is perhaps due to the development of the gas bubble flow pattern in the bed. Similar trends have been observed in the earlier CFD models of fluidized beds [8, 11]. The gas volume fraction average error between CFD simulations and the experimental data for the drag models of Gidaspow, Syamlal–O'Brien and Cao-Ahmadi are, respectively, about 0.6 0.9 1.2 1.5 1.8 2.1 2.4 0 0.2 0.4 0.6 0.8 1 Gas Velocity (Vg) m/s H/H0 Experi mental Syml al O'Brien drag Gi daspow drag Cao-Ahmadi drag Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors 357 12.7%, 7.6% and 7.2%. This observation is comparable to those of the earlier works [8, 11]. It can be seen that Cao- Ahmadi drag expression leads to a better prediction compared with those of Syamlal–O'Brien and Gidaspow drag models for the time averaged voidage. Fig. 15. Comparison of experimental and simulated bed expansion ratio for different solid particle sizes. Time-averaged bed expansions as a function of superficial velocities are compared in Fig. 15. This Fig. shows that the model predicts the correct increasing trend of the bed height with the increase of superficial gas velocity. All cases demonstrate a consistent increase in bed expansion with gas velocity and predict the bed expansion reasonably well. There are, however, some deviations under predict the experimental values. This Fig. shows that with increasing the particles sizes, bed expansion ratio decreases. On the other hand, for the same gas velocity, bed expansion ratio is lager for smaller particles. The experimental data of time-average bed expansion ratio were compared with corresponding values predicted for various velocities as depicted in Fig. 16. The time- average bed expansion ratio error between CFD simulation results and the experimental data for two different initial bed height, H s =30, H s =40 cm, are 6.7% and 8.7% respectively. Both cases demonstrate a consistent increase in bed expansion with gas velocity and predict the bed expansion reasonably well. It can be seen that Syamlal–O'Brien drag function gives a good prediction in terms of bed expansion and also, Syamlal–O'Brien drag law able to predict the minimum fluidization conditions correctly. Simulation results for void fraction profile are show in Fig. 17. In this Fig. symmetry of the void fraction is observed at three different particle sizes. The slight asymmetry in the void fraction profile may result form the development of a certain flow pattern in the bed. Similar asymmetry has been observed in other CFD modeling of fluidized beds. Void fraction profile for large particle is flatter near the center of the bed. The simulation results of time- average cross-sectional void fraction at different solid particles diameter is shown in Fig. 18 0.4 0.7 1 1.3 1.6 1.9 2.2 2.5 0 0.2 0.4 0.6 0.8 1 Gas Velocity (Ug) m/s H/H0 ds=0.175 mm (Simulation) ds=0.175 mm (Experimental) ds=0.275 mm (Simulation) ds=0.275 mm (Experimental) ds=0.375 mm (Simulation) ds=0.375 mm (Experimental) 35 fo r be d Fi g st a Fi g c m Heat T 8 r U g =38 cm/s. T h d hei g ht increas e g . 16. Compariso n a tic bed hei g ht. g . 17. Simulated v m /s, t=5.0s) 1 1.2 1.4 1.6 1.8 2 H/H0 T ransfer - Mathem a h is Fig. shows w i e and stead y stat e n of experimenta l v oid fraction at d i 01020 Hs=40 c Hs=40 c Hs=30 c Hs= 30 a tical Modelling, N u i th increasin g so l e condition arrive l and simulated b i fferent solid par t 30 40 Gas velocity ( V c m (Simulation) c m (Experimental) c m (Simulation) cm (Experimental ) u merical Methods a l id particles dia m rapidl y . b ed expansion ra t t icles diameter ( a 50 60 V g) cm/s ) a nd Information Te c m eter, void fracti o t io for different i n a t z=20 cm, U g =3 8 70 80 c hnology o n and n itial 8 [...]... a Fluidized Bed Chamber Experimentally and Computationally, Proceeding of 3rd Technology and Innovation for Sustainable conference (TISD2 010) in Nong Khai, Thailand, March 4-6, (Best Paper and best presentation on the Topic E: Energy Technology, Thermal Systems and Applied Mechanics) 382 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology [55] Hamzehei, M., Rahimzadeh.,... The information derived for a single particle may not be reliable because of the difficulty in quantifying such local structures in a particle bed 384 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology Alternatively, mathematical modeling has been increasingly accepted as an effective method to study the heat transfer phenomena in a particle-fluid system Generally speaking,... Fluidized Bed Reactor Experimentally and Numerically, Proceeding of Seventh South African Conference on Computational and Applied Mechanics (SACAM10), Pretoria, January 10 13, 2 010 15 Particle Scale Simulation of Heat Transfer in Fluid Bed Reactors Zongyan Zhou, Qinfu Hou and Aibing Yu Laboratory for Simulation and Modelling of Particulate Systems School of Materials Science and Engineering, The University... in Department of Mechanical Engineering of Amirkabir University, National Petrochemical company (NPC) and the Petrochemistry Research and Technology Company for providing financial support for this study 8 Appendix In this section drive an algebraic (discretized) equation from a partial differential equation [39, 40] 372 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology. .. current value of Pg and is added to the source term of the linear equation set The interface transfer term couples all the equations for the same component The definitions for the rest of the terms in Equation (A13) are as follows: (A14) 374 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology (A15) ∑ (A16) (A17) and , which The center coefficient ap and the source term... superficial velocity, the turbulent motion of solid clusters and gas bubbles of various size and shape are observed This bed is then considered to be in a turbulent fluidization regime, which corresponds to Vg=70 -100 cm/s in Fig 25 364 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology Fig 25 Comparison of bubble formation and bed expansion for different superficial gas velocities... fraction also increase and bed arrive to steady state condition rapidly Also in some position the plot is flat, it is means that particle distribution is uniform When void fraction increase suddenly in the bed, it is means that the large bubble product in this position and when decrease, the bubble was collapsed 360 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology Fig 20... of internal friction Granular temperature, m2s-2 Diffusion coefficient Transfer of kinetic energy, J/(m3.s) Collision dissipation of energy, J/(m3.K.s) 377 378 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 0 γ gs μt , g ∏k , g , ∏ε , g κ ηsg ϕ τ F ,sg τ t ,sg μs , fr μs , kin μs ,col Heat transfer coefficient, J/(m3.K.s) Turbulent (or eddy) viscosity, Pa.s Influence... Study of Bed Height and Gas Velocity Effect on Hydrodynamics and Heat Transfer in a Gas-Solid Fluidized Bed Reactor Experimentally and Numerically, Heat Transfer Engineering, 2 010, (Accepted) [52] M., Hamzehei , H., Rahimzadeh, Study of Parameters Effect on Hydrodynamics of a Gas-Solid Chamber Experimentally and Numerically, Proceeding of Experimental Fluid Mechanics Conference, (EFM 2 010) , Liberec, Czech... G., A rate dependent model for turbulent flows of dilute and dense two phase solid-liquid mixtures, powder Technology, 89, 45-56, 1996 [26] Ding, J., Gidaspow, D., A bubbling fluidization model using kinetic theory of granular flow, A.I.Ch.E Journal, 36, 523–538, 1990 380 Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology [27] Gelderbloom, S.J., Gidaspow, D., Lyczkowski, . chamber and escapes to the atmosphere through a filter. Installed in the bracket are probes for temperature and pressure Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology. (Experimental) ds=0.375 mm (Experimental) Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 354 Fig. 10. Comparison of experimental and simulated bed pressure drop. cm) P1-P2(Experimental, Hs=40 cm) Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology 356 Fig. 13. Comparison of experimental and simulated bed expansion ratio.