Artin Afacan

Steady incompressible laminar flow in porous media

Steady incompressible laminar flow in porous media is studied. The volume averaging technique is revisited resulting in a new averaging approach to the pressure gradient term. The difference between the traditionally obtained volume averaged equation for very small flow rate and Brinkmans equation is resolved. The Kozeny—Carman theory is modified. By including a two-dimensionally modelled tortuosity and curvature ratio as well as pore cross-sectional area variation, a new semi-empirical equation for the pressure drop for flow through porous media is obtained. The pressure drop dependence on the porosity e for Darcys flow region is established as e−113(1 − e)2 as opposed to e−3(1 − e)2 in the original Kozeny—Carmans theory. A modified Reynolds number is also defined. The regions of Darcys flow and Forchheimers flow are unified. The wall effects are incorporated into the unified pressure drop equation. The final form of the normalized pressure drop equation for a one-dimensional medium is given by for ds = d′s/D < 0.75. Here fv is the normalized pressure drop factor, — Δp′ is the pressure across a fixed thickness L of the porous bed, e is the porosity, d′s is the equivalent spherical particle diameter, D is the bed diameter, U is the superficial velocity or fluid discharge rate, μ is the dynamic viscosity of the fluid and Rem is the modified Reynolds number. The one-dimensional pressure drop equation is also modified to give a shear factor for use with the volume averaged Navier—Stokes equation and it is given as where F is the shear factor and Rev is the local modified Reynolds number. The semi-theoretical model was tested with a available and new experimental pressure drop data for packed beds. Further comparison was made with experimental pressure drop data for flow in a fibrous mat. The model was found to correlate well for the whole range of Reynolds number, wall effects and porosity studied.

The Effect of Impeller and Tank Geometry on Power Number for a Pitched Blade Turbine

Previous studies of the Rushton turbine have shown that the power number is sensitive to the details of impeller geometry, and in particular to the blade thickness, but is independent of the impeller diameter to tank diameter ratio. In this paper, a similar study is reported for the pitched blade impeller. The results show that the power number is independent of blade thickness, but dependent on the impeller to tank diameter ratio. This is exactly the opposite result to that observed for the Rushton turbine. Physical explanations are given for the differences in behaviour between the two impellers. For the Rushton turbine, power consumption is dominated by form drag, so details of the blade geometry and flow separation have a significant impact (30%) on the power number. For the pitched blade impeller, form drag is not as important, but the flow at the impeller interacts strongly with the proximity of the tank walls, so changes in the position of the impeller in the tank can have a significant impact on the power number.

Liquid holdup distribution in packed columns: gamma ray tomography and CFD simulation

In the present study, the liquid (water) holdup distribution was measured in a large scale packed column (0.6 m diameter) filled with 25.4 mm metal Pall rings using noninvasive gamma ray tomography technique. Horizontal scans, at two vertical positions (400 mm apart), were made for two liquid flow rates. Three different designs of liquid distributor were used to examine the effect of inlet liquid distribution on holdup distribution inside the column. A tomographic reconstruction algorithm was used to calculate the spatial variation of liquid holdup over the column cross section. It was found that the liquid holdup distribution was not uniform and that the liquid distributor design had a significant effect on the holdup distribution. To simulate the liquid holdup distribution in a packed column, a set of volume averaged equations for the hydrodynamics has been solved with the commercial computational fluid dynamics (CFD) software, CFX4.2. Simulation results were found to agree with the experimental data.

Bubble size in coalescence dominant regime of turbulent air–water flow through horizontal pipes

An experimental study was performed in a 25.4 mm ID pipeline to evaluate the development of the bubble size distribution in the horizontal flow of an air–water system. As the air stream enters into the flowing water stream through a T-injector, it breaks into bubbles with a log-normal size distribution. Because of the small water velocity (1–3 m/s) and small initial bubble size, coalescence, not breakage, plays the dominant role in the present study. The effects of average water velocity, air volume fraction and air injector diameter on the initial bubble size distribution and its evolution along the length of the pipe in the coalescence dominant regime are investigated. At larger water velocities, the log-normal bubble size distributions are also maintained downstream of the injector. At smaller velocities, the distributions deviate slightly from the log-normal pattern. For all distributions, the value of the ratio d99.8/d32 is about 2.2 and is fairly independent of average water velocity, pipe length, air volume fraction and air injector diameter. It is found that at large velocities of water, the prediction of dmax through Levich’s breakup theory agrees well with the experimental d99.8 values for air volume fraction up to 0.003.

Porosity distribution in random packed columns by gamma ray tomography

Gamma ray tomography experiments have been carried out to detect any spatial patterns in the porosity in a 0.6 m diameter packed column. Three different sizes of stainless steel Pall rings (16, 25 and 38 mm) have been examined. The primary objective is to detect spatial patterns and statistical information on porosity variation in packed distillation columns. Such data are needed in the computational fluid dynamics simulators based on volume averaged equations. Horizontal scans, at different vertical positions of the packed bed, were made for each size of Pall rings. A tomographic reconstruction algorithm has been used to calculate the spatial variation over the column cross section. Radial porosity variation within the packed bed has been determined. The variation of the circumferentially averaged porosity in the radial direction indicates that the porosity in the column wall region is a somewhat higher than that in the bulk region, due to the effect of the column wall. The probability density function for porosity variation has been constructed from the experimental data and it can be represented by a normal distribution.

Modelling and Simulation of Flow Maldistribution in Random Packed Columns with Gas-Liquid Countercurrent Flow

A macroscopic model, based on the volume-averaged equations of momentum and continuity, is presented to predict hydrodynamic characteristics of gas and liquid countercurrent flow in random packed columns. The main advantage of this approach is that the model equations derived from the mass and momentum conversation laws will remain valid on a wider range of length scale, from laboratory to industrial size packed columns. Therefore they can be used as basic tool for more rigorous design and scale up of packed columns. In this study, the large-scale liquid maldistribution was simulated using the proposed model for a 0.6-m diameter column packed with 25mm stainless steel Pall rings. The development of liquid flow patterns along the packed height was obtained for several different initial distributions of liquid phase. Furthermore, the effect of liquid and gas loads on the liquid distribution was examined. The simulation results are in good agreementwith the experimental data obtained in our laboratory for both water/air and isopar/air systems.

Predicting Mass Transfer in Packed Columns Containing Structured Packings

A model has been developed for predicting mass transfer in packed columns containing structured packings. The model was verified by experimental results from a 300 mm diameter distillation column installed with three types of structured packings (Gempak 2.5A, AW7 and AW12). Three systems (methanol/isopropanol, water/acetic acid and methanol/water) and two operating pressures (710 and 260 mmHg) were used in the tests. Hence, a large range of physical properties were covered for the modeling. A total of 62 data points was obtained from the distillation tests. The average deviation between the measured values of HOG and the predicted values is ±10.2%. The deviations are within ±20% for 90% of the data points.

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.

An equation of motion for an incompressible Newtonian fluid in a packed bed

The application of a volume average Navier-Stokes equation for the prediction of pressure drop in packed beds consisting of uniform spherical particles is presented. The development of the bed permeability from an assumed porous microstructure model is given. The final model is quasi-empirical in nature, and is able to correlate a wide variety of literature data over a large Reynolds number range. In beds with wall effects present the model correlates experimental data with an error of less than 10%. Numerical solutions of the volume averaged equation are obtained using a penalty finite element method.

An Experimental Study of Pressure Drop in Helical Pipes

Pressure drops of fully-developed incompressible laminar newtonian flows in helical pipes of constant circular cross-section having a finite pitch are experimentally investigated. For the case of loosely coiled pipes of 0 < η/λ < 41.22, f Re (f is the Fanning friction factor and Re is the Reynolds number) is found to be proportional to the square root of the flow Dean number, Dn = Re λ½. Here λ and η are the normalized curvature ratio and torsion which incorporate both the coil radius and its pitch. In all cases studied, the experimental results for f Re are in excellent agreement with the theoretical prediction of Liu & Masliyah.