Computer-Assisted Numerical Analysis for Oxygen and Carbon Dioxide Mass Transfer in Blood Oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that V(CO2) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO2), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (Q(G)/Q(B)) shows that V(CO2) variation with the gas flow is almost linear up to Q(G)/Q(B) = 2.0. V(O2) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the V(O2) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G)/Q(B) > 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO2) comprise the whole fiber bundle.

Experimental investigation of Vortex-Induced Vibration on rigid, smooth and inclined cylinders

This paper presents new experimental results of Vortex-Induced Vibration (VIV) on inclined cylinders. Models are mounted on a low damping air-bearing elastic base with one degree-of-freedom, constrained to oscillate only in the transverse direction to a free stream. The Reynolds number varied in the range 2000 less than or similar to Re less than or similar to 8000. New measurements on the dynamic response oscillations of inclined cylinders, due to VIV, are compared with previous experiments of a vertical cylinder. Models with circular and elliptical cross sections have been tested. The purpose of this work is to check the validity of the normal velocity correction of VIV studies of inclined structures. The results show that the reduced velocity range, in which the upper and lower branches of VIV occurs, is similar to the vertical cylinder case if the proper projected velocity is considered. Tests have been conducted to support this observation with inclinations up to 45 degrees. We have also observed that the amplitudes of oscillation of the inclined circular cylinder are comparable, but slightly lower than, to the amplitudes observed in the vertical cylinder experiments. Measured forces and added mass also show similar behaviour. However, for cases with an elliptical cylinder, the amplitudes of oscillation are considerably lower than those observed for a circular cylinder. This difference is explained by the higher added mass of the elliptical cylinder. (C) 2009 Elsevier Ltd. All rights reserved.

NON-NEWTONIAN FLOW AND PRESSURE DROP OF PINEAPPLE JUICE IN A PLATE HEAT EXCHANGER

The study of non-Newtonian flow in plate heat exchangers (PHEs) is of great importance for the food industry. The objective of this work was to study the pressure drop of pineapple juice in a PHE with 50 degrees chevron plates. Density and flow properties of pineapple juice were determined and correlated with temperature (17.4 <= T <= 85.8 degrees C) and soluble solids content (11.0 <= X(s) <= 52.4 degrees Brix). The Ostwald-de Waele (power law) model described well the rheological behavior. The friction factor for non-isothermal flow of pineapple juice in the PHE was obtained for diagonal and parallel/side flow. Experimental results were well correlated with the generalized Reynolds number (20 <= Re(g) <= 1230) and were compared with predictions from equations from the literature. The mean absolute error for pressure drop prediction was 4% for the diagonal plate and 10% for the parallel plate.

Friction factor for small diameter polyethylene pipes

On this paper, the results of an experimental study oil the hydraulic friction loss for small-diameter polyethylene pipes are reported. The experiment was carried out using a range of Reynolds number between 6000 to 72000, obtained by varying discharge at 20 degrees C water temperature, with internal pipe diameters of 10.0 mm, 12.9 mm, 16.1 mm, 17.4 mm and 19.7 mm. According to the analysis results and experimental conditions, the friction factor 0 of the Darcy-Weisbach equation call be estimated with c = 0.300 and m = 0.25. The Blasius equation (c = 0.316 and m = 0.25) gives an overestimate of friction loss, although this fact is non-restrictive for micro-irrigation system designs. The analysis shows that both the Blasius and the adjusted equation parameters allow for accurate friction factor estimates, characterized by low mean error (5.1%).

Characterization of turbulent jets from high-aspect-ratio rectangular nozzles

Turbulent free jets issuing from rectangular slots with various high aspect ratios (15-120) are characterized. The centerline mean and rms velocities are measured using hot-wire anemometry over a downstream distance of up to 160 slot heights at a slot-height-based Reynolds number of 10000. Experimental results suggest that a rectangular jet with sufficiently high aspect ratio (> 15) may be distinguished between three flow zones: an initial quasi-plane-jet zone, a transition zone, and a final quasi-axisymmetric-jet zone. In the quasi-plane-jet zone, the turbulent velocity field is statistically similar, but not identical, to those of a plane jet. (c) 2005 American Institute of Physics.

On the mechanism of microbial cell disruption in high-pressure homogenisation

The tensions produced in the wall of a rigid, thin-walled, liquid-filled sphere as it moves with an axisymmetric straining flow are examined. This problem has not been previously addressed. A generalised correlation for the maximum wall tension, expressed in dimensionless form as a Weber number (We), is developed in terms of the acceleration number (Ac) and Reynolds number (Re) of the straining flow. At low Reynolds number We is dominated by viscous forces, while inertial forces due to internal pressure gradients caused by sphere acceleration dominate at higher Re. The generalised correlation has been used to examine the case of a typical yeast cell (a thin-walled, liquid-filled sphere) passing through a typical high-pressure homogeniser (a straining-flow device). At 56 MPa homogenising pressure, a 6 mu m yeast cell experiences tensions in the inertially dominated regime (Re = 100). The correlation gives We = 0.206, corresponding to a maximum wall tension of 8 Nm(-1). This is equivalent to an applied compressive force of 150 mu N and compares favourably with the force required to break yeast cells under compressive micromanipulation (40-90 mu N). Inertial forces may therefore be an important and previously unrecognised. mechanism of microbial cell disruption during high-pressure homogenisation. Further work is required to examine the likelihood of cell deformation in the high-strain-rate short-residence-time environment of the homogeniser, and the effect that such deformation may have on the contribution of inertial forces to disruption. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

Effect of material anisotropy on the onset of convective flow in three-dimensional fluid-saturated faults

In order to investigate the effect of material anisotropy on convective instability of three-dimensional fluid-saturated faults, an exact analytical solution for the critical Rayleigh number of three-dimensional convective flow has been obtained. Using this critical Rayleigh number, effects of different permeability ratios and thermal conductivity ratios on convective instability of a vertically oriented three-dimensional fault have been examined in detail. It has been recognized that (1) if the fault material is isotropic in the horizontal direction, the horizontal to vertical permeability ratio has a significant effect on the critical Rayleigh number of the three-dimensional fault system, but the horizontal to vertical thermal conductivity ratio has little influence on the convective instability of the system, and (2) if the fault material is isotropic in the fault plane, the thermal conductivity ratio of the fault normal to plane has a considerable effect on the critical Rayleigh number of the three-dimensional fault system, but the effect of the permeability ratio of the fault normal to plane on the critical Rayleigh number of three-dimensional convective flow is negligible.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Boundary-layer transition measurements in hypervelocity flows in a shock tunnel

Experiments to investigate the transition process in hypervelocity boundary layers were performed in the T4 free-piston shock tunnel. An array of thin-film heat-transfer gauges was used to detect the location and extent of the transitional region on a 1500 mm long x 120 turn wide flat plate, which formed one of the walls of a duct. The experiments were performed in a Mach 6 flow of air with 6- and 12-MJ/kg nozzle-supply enthalpies at unit Reynolds numbers ranging from 1.6 x 10(6) to 4.9 x 10(6) m(-1). The results show that the characteristics typical of transition taking place through the initiation, growth, and merger of turbulent spots are evident in the heat-transfer signals. A 2-mm-high excrescence located 440 turn from the leading edge was found to be capable of generating a turbulent wedge within an otherwise laminar boundary layer at a unit Reynolds number of 2.6 x 10(6) m(-1) at the 6-MJ/kg condition. A tripping strip, located 100 mm from the leading edge and consisting of a line 37 teeth of 2 rum height equally spaced and spanning the test surface, was also found to be capable of advancing the transition location at the same condition and at the higher enthalpy condition.

Unsaturated liquid percolation flow through nonwetted packed beds

The unsaturated flow of liquid through packed beds of large particles was studied using six different liquids, all with contact angles greater than 90degrees on the bed packing (wax spheres of 9, 15 and 19.4 mm diameter). The liquid flow was discrete in nature, as drops for low flow rates and rivulets for high flow rates. For unsaturated liquid flows, the actual percolation velocity, not superficial velocity, should be used to characterize the flow. The percolation velocity did not vary with packed-bed depth, but was a strong function of liquid flow rate, liquid and particle properties. Effects of liquid and particle properties (but not flow rate) are well captured by a simple correlation between the liquid-particle friction factor and Reynolds number based on actual percolation velocities. Liquid dispersion, characterized by the maximum dispersion angle, varies significantly with liquid and particle properties. The tentative correlation suggested here needs further validation for a wider range of conditions.

Instabilities and drop formation in cylindrical liquid jets in reduced gravity

The effects of convective and absolute instabilities on the formation of drops formed from cylindrical liquid jets of glycerol/water issuing into still air were investigated. Medium-duration reduced gravity tests were conducted aboard NASA's KC-135 and compared to similar tests performed under normal gravity conditions to aid in understanding the drop formation process. In reduced gravity, the Rayleigh-Chandrasekhar Equation was found to accurately predict the transition between a region of absolute and convective instability as defined by a critical Weber number. Observations of the physics of the jet, its breakup, and subsequent drop dynamics under both gravity conditions and the effects of the two instabilities on these processes are presented. All the normal gravity liquid jets investigated, in regions of convective or absolute instability, were subject to significant stretching effects, which affected the subsequent drop and associated geometry and dynamics. These effects were not displayed in reduced gravity and, therefore, the liquid jets would form drops which took longer to form (reduction in drop frequency), larger in size, and more spherical (surface tension effects). Most observed changes, in regions of either absolute or convective instabilities, were due to a reduction in the buoyancy force and an increased importance of the surface tension force acting on the liquid contained in the jet or formed drop. Reduced gravity environments allow better investigations to be performed into the physics of liquid jets, subsequently formed drops, and the effects of instabilities on these systems. In reduced gravity, drops form up to three times more slowly and as a consequence are up to three times larger in volume in the theoretical absolute instability region than in the theoretical convective instability region. This difference was not seen in the corresponding normal gravity tests due to the masking effects of gravity. A drop is shown to be able to form and detach in a region of absolute instability, and spanning the critical Weber number (from a region of convective to absolute instability) resulted in a marked change in dynamics and geometry of the liquid jet and detaching drops. (C) 2002 American Institute of Physics.