Pressure drop for the slow flow of dilatant fluids through a fixed bed of spherical particles

The equations of motion in conjunction with the free surface cell model have been solved numerically for the creeping flow of dilatant fluids through a fixed bed of spheres. The effect of the flow behaviour index (1 ≤ n ≤ 2) on the individual as well as the total drag coefficients is elucidated. Finally, the theoretical predictions have been validated using the scant experimental results available in the literature.     

Pressure drop and liquid holdup for two phase concurrent flow in packed beds

Pressure drop and liquid holdup for two-phase concurrent downward flow in packed beds were correlated for various types of packings by taking into account two hydrodynamic regimes: a poor and a high gas-liquid interaction regime.Foaming and non-foaming systems have been considered.In the poor interaction regime, the pressure drop was calculated as due to the gas flowing in a bed restricted by the presence of the liquid. A correlation valid for a free liquid trickling, modified in order to take into account the effect of the pressure drop, is proposed and used to correlate liquid holdup in the presence of a concurrent gas flow.In the high interaction regime, empirical correlations were proposed for both foaming and non-foaming systems.All the employed correlations fit experimental results from several authors better than those proposed in the literature.     

Overall map and correlation of dispersion data for flow through granular packed beds

Measured values of the coefficients of transverse and longitudinal dispersion (D_T and D_L, respectively) are reported for liquid flow through granular packed beds. Measurements of D_T were made for 50<Sc<1950 and 300<Pe_m<10⁵, working with water at temperatures between 278 and 373 K, and values of D_L were measured for Sc≅750 and 1<Pe_m<45, working with water at 293 K; nearly two hundred new data points are reported.The data obtained, together with data from other sources, both for gas and liquid flow, are reported in plots of Pe_T vs Pe_m and Pe_L vs. Pe_m, in order to stress the influence of Sc on dispersion and elucidate the difference between liquid and gas behaviour.Empirical correlations are presented for the prediction of the dispersion coefficients (D_T and D_L) over the entire range of practical values of Sc and Pe_m, and they are shown to give the dispersion coefficients with very good accuracy.     

Pressure drop through a tapered die with optimized flow characteristics

The flow of power-law liquids through tapered dies has been analyzed in an earlier paper.¹ We now consider a taper which is additionally streamlined so as to make the transition from a broad and sluggish flow to a flow which is narrow and fast and as smooth as possible. This involves (1) the rational selection of an appropriate taper function within the relevant flow geometry and (2) the integration, between limits, of that function.     

Pressure drop of pseudo-plastic fluids in static mixers

1 INTRODUCTIONUse of static mixers to process non-Newtonian fluids is quite commn.Data on thepressure drop of non-Newtonian fluids in Kenics static mixers are very useful in thedesign and engineering application of such mixers.However,only a few studies con-cerned with the pressure drop of non-Newtonian fluid flow in static ndxers can befound in literature.Wilkinson and Cliff presented pressure drop data for aqueousglycerine solutions(Newtonian fluids)and aqueous 1% polyacrylamide solution showingviscoelastic behavior.They found no difference between the friction factors of Newtonian     

Pressure drop estimation for polyamide 6 flow through spinnerets and filters

The pressure drop resulting from polyamide 6 flow through industrial spinnerets and wire‐mesh filters was examined as a possible parameter for improving spinning process constancy with experimental techniques and a numerical approach. The rheological characterization of the polymer melt was performed with a capillary rheometer and a controlled‐stress rotational rheometer equipped with a high‐temperature oven cell. Measurements in a nitrogen atmosphere were carried out at different temperatures and at various moisture contents to determine the effect of the postcondensation process on the rheological properties of the polymer melt. These experiments were used to collect all basic material information necessary to fit the data with the purely viscous Cross model and the viscoelastic Kaye, Bernstein, Kearsley, Zappas (K‐BKZ) model. A spinning pilot plant (consisting of an extruder, a gear pump, a pressure sensor, and a spin beam with several spin packs installed) was used to measure pressure drop values through industrial spinnerets and through two types of filters: (1) Dutch twilled weave filters and (2) sintered filters. Pilot plant tests on filters showed that in the examined range of melt throughputs, the pressure drop increased linearly with an increase in the melt flow rate for all the filters considered. The results with respect to the spinneret geometry led to the conclusion that the numerical simulations gave satisfactory predictions even for experimental data coming from complex systems such as spinning plants, as long as extensional properties were accounted for by the model. On the contrary, pressure drop predictions obtained from the Cross model underestimated the pilot plant values by approximately 20% because of the inability of the model to consider the extensional component of the flow. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1577–1587, 2006     

Pressure drop and gas bypassing in recirculating fluidized beds

The effect of different operating and design parameters on the pressure drop profile for a recirculating fluidized bed has been studied. A mathematical model was developed for the pressure drop in the recirculating fluidized bed. The different parameters considered were flow rate, inventory of solids and spacing between the draft-tube bottom and the distribution plate. Geldart D and B particles were used for the study. The gas bypassing from the jet towards the downcomer was calculated on the basis of the mathematical model and the effect of various parameters on gas bypassing were analyzed.     

Pressure drop through tapered dies

A simple method is presented for calculating the pressure drop for the flow of power law liquids in dies with a wide slit profile and with vertical and/or lateral tapers, as well as in dies with the shape of a circular truncated right cone. Tapered dies are known to give improved extrudate quality and/or higher output rates without encountering extrudate defects which occur in dies with parallel channels at similar extrusion pressures. A possible ultimate optimization of the extrusion process—as far as die design is concerned—is discussed. It is suggested that this be based upon an extension of the method from dies with a rectilinear convergent taper to dies with a curvilinearly converging channel aspect the generation of which latter is indicated.     

Pressure drop across packed beds in the low Knudsen number regime

The solutions of Happel and Kuwabara describing flow through systems of multiple spheres have been compared with available pressure drop data to determine the applicability of cell models for analyzing flow in packed beds. The comparisons indicate that these solutions describe the flow with reasonable accuracy. Of the two solutions, the Kuwabara flow field has been found to give better agreement between predictions and experimental results. In order to describe flow in beds operating at low Knudsen numbers the Kuwabara solution has been extended by allowing for gas slippage at the collecting surfaces. The resulting solution is presented as a correction to the Basset-Millikan expression and accounts for the presence of neighboring spheres in low Knudsen number flows. Using this extended solution, the pressure drop across packed beds is predicted as a function of Knudsen number and packing density.     

Pressure drop through in-bulk flax seeds

The airflow resistance of in-bulk flax seeds (Linum usitatissimum) and the effect of airflow rate, bed depth, type of packing, and presence of foreign material (“fines” and “chaff”) were studied. A good fit of the experimental data (R > 0.993) was obtained through the model DPL = cQ + dQ ² (where DPL is pressure drop per unit of bed depth, Pa/m; Q is airflow rate, m³/s-m²; c and d are constants; and airflow range is 0.011–0.141 m³/s-m²). The airflow resistance increases when bulk density and bed depth increase. In dense packing the pressure drop is 1.3 to 1.5 times the pressure drop in loose packing. The resistance increases with the increase of fines and decreases with the increase of chaff.     

Pressure drop in two phase cocurrent upward flow in packed beds: Air/non-newtonian liquid systems

New data on the two phase pressure drop for the concurrent upflow of air-liquid (Newtonian and non-Newtonian) mixtures through packed beds of spherical and non-spherical particles are presented. The results for single phase flows and for the air-Newtonian liquid mixtures have been used both to gauge the overall accuracy of the present experimental methods and to evaluate the validity of the predictive expressions available in the literature. The two phase pressure drop has been measured as a function of the liquid and gas flow rates, column diameter and the power law model constants. Depending upon a suitable combination of the gas and liquid fluxes and the power law index, the two phase pressure drop may be less than its value for the flow of liquid alone. A simple expression is proposed which correlates the present set of experiments (nearly 500 data points) with satisfactory levels of accuracy over the following ranges of conditions: 0.54 ≤ n ≤ 1; 0.001 ≤ Re_L^* ≤ 50; 3.7 ≤ Re_G ≤ 177 and 0.9 ≤χ (Lockhart-Martinelli parameter) ≤ 104.     

Liquid flow through aligned fiber beds

The influence of surface properties on the flow of fluids, including epoxy resin, through aligned glass and other fiber beds has been examined. The observed flow rates were higher than those predicted from the Kozeny-Carman equation, and were influenced by the surface properties of the fluid used. This is attributed to variations in the distribution of porosities and to the presence of air bubbles trapped during the initial wetting of the bed. The implications of these findings to the preparation of composites are discussed.     

喷动床内气固二相流体动力行为颗粒动理学

应用气固二相双流体模型数值模拟了喷动床内流体动力行为,模型中采用稠密固相动力-摩擦应力模型。模型中同时考虑了动理学理论和摩擦应力理论。应用贴体坐标系使得网格与喷动床的倒锥体边界符合良好。模拟得到的喷动床内颗粒速度和浓度实验数据吻合较好。     

Pressure drops for purely viscous non-newtonian fluid flow through beds packed with mixed-size spheres

Extensive new measurements on pressure drop for the flow of purely viscous non-Newtonian fluids through packed beds made up of binary-and-quaternary size spheres are reported herein. These results have been interpreted using the previously available Sabiri and Comiti capillary model (1995), which has been quite successful in correlating the pressure drop data for the beds of uniform size spherical and nonspherical particles. The resulting predictions are also very good for mixed beds if some results are available for a Newtonian fluid, thereby enabling the evaluation of the tortuosity factor. However, since such data is always not available, an empirical scheme for estimating the tortuosity that allows the prediction of pressure drop with a mean relative error of about 10% is also presented. This sort of accuracy is quite acceptable for process engineering design calculations.     

Silo music: Sound emission during the flow of granular materials through tubes

The present work deals with experiments and a model related to the emission of sound during the flow of granular materials through tubes. Experiments have been conducted using tubes fitted either with pistons or orifice plates at the ends. Earlier workers have observed that the height H of the granular material above the piston or orifice must exceed a critical value H_c for the music to occur. The critical height H_c was determined using the recorded sound signal for flow velocities in the range 0.4-1.8 mm/s (piston experiments) and 3-36.2 mm/s (orifice experiments).A simple model is constructed by treating the powder column as a spring and slider in series. The slider interacts with the tube wall via a rate and state variable friction law. The model predicts that the material either moves with a constant velocity (steady sliding) or in a jerky manner (stick-slip), depending on the parameter values used. As suggested by earlier workers, we postulate that the silo music is generated by the stick-slip motion of granular material. For H < H_c, it is postulated that steady sliding occurs, and this is shown to be consistent with the model predictions. For H > H_c, the model predicts that steady sliding is unstable with respect to small perturbations. The velocity of the slider exhibits sustained oscillations, which is the expected behavior of a system undergoing stick-slip motion. The model parameters have been estimated by fitting data on the variation of H_c with the flow velocity. The predicted acceleration of the slider is similar in some respects to the data of Muite et al. (Powder Technol. 145 (2004) 190-202) for the flow of glass beads in a tube fitted with an orifice. Muite et al. found that the dominant frequency of the sound was given by c_s / (4L_a), where c_s is speed of sound in air and L_a is the length of the air column above the granular material. This expression also fits the present data for the piston experiments.