Flowing Polymers Through Porous Media: An Experimental Study of Flow Distribution, Polymer Degradation, and Molecular Weight Effects

1993 ◽  
Vol 46 (11S) ◽  
pp. S63-S70 ◽  
Author(s):  
A. J. Mu¨ller ◽  
L. I. Medina ◽  
O. Pe´rez-Martin ◽  
S. Rodriguez ◽  
C. Romero ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Porous Media ◽  
Flow Resistance ◽  
Polymer Concentration ◽  
Flow Distribution ◽  
Rate Of Change ◽  
Mechanical Degradation ◽  
Nonuniform Flow ◽  
Flow Conditions

The flow of aqueous poly(ethylene oxide) solutions through nonconsolidated porous media has been experimentally investigated. Three aspects of practical relevance have been addressed: the effect of polymer on flow distribution under nonuniform flow conditions, the mechanical degradation of the polymer in the porous media, and the effect of molecular weight on flow resistance. The nonuniform flow results indicate that, although the presence of polymer changes the distribution of the flow by affecting the region of the medium that is swept by the fluid, a significant increase in flow resistance is still observed above a critical Reynolds number, as it happens under uniform flow conditions. The degradation experiments show that the polymer is significantly degraded only in the region where a sizable increase in flow resistance is obtained with respect to the Newtonian behavior. The most significant effect of the molecular weight of the polymer is the fact that an increase in that parameter results in a substantial reduction of the Reynolds number at which the increased flow resistance is observed. Furthermore, the rate of change of this onset Reynolds number with polymer concentration appears to be independent of molecular weight. The results presented here indicate that the increase in flow resistance is not exclusively determined by the shear viscosity of the polymer solution.

Effect of viscoelasticity on the soft-wall transition and turbulence in a microchannel

2017 ◽  
Vol 812 ◽  
pp. 1076-1118 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Mass Fraction ◽  
Rectangular Cross Section ◽  
Pure Water ◽  
Polymer Concentration ◽  
Wall Turbulence ◽  
Solution Viscosity ◽  
Soft Wall

The modification of soft-wall turbulence in a microchannel due to small amounts of polymer dissolved in water is experimentally studied. The microchannels are of rectangular cross-section with height ${\sim}$160 $\unicode[STIX]{x03BC}\text{m}$, width ${\sim}$1.5 mm and length ${\sim}$3 cm, with three walls made of hard polydimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of ${\sim}$18 kPa. Solutions of polyacrylamide of molecular weight $5\times 10^{6}$ and mass fraction up to 50 ppm, and of molecular weight $4\times 10^{4}$ and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit below the critical overlap concentration, and the solution viscosity does not exceed that of water by more than 10 %. Two distinct types of flow modifications are observed below and above a threshold mass fraction for the polymer, $w_{t}$, which is ${\sim}$1 ppm and 500 ppm for the solutions of polyacrylamide with molecular weights $5\times 10^{6}$ and $4\times 10^{4}$, respectively. At or below $w_{t}$, there is no change in the transition Reynolds number, but there is significant turbulence attenuation, by up to a factor of 2 in the root-mean-square velocities and a factor of 4 in the Reynolds stress. When the polymer concentration increases beyond $w_{t}$, there is a decrease in the transition Reynolds number and in the intensity of the turbulent fluctuations. The lowest transition Reynolds number is ${\sim}$35 for the solution of polyacrylamide with molecular weight $5\times 10^{6}$ and mass fraction 50 ppm (in contrast to 260–290 for pure water). The fluctuating velocities in the streamwise and cross-stream directions are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water.

The Effect of Compressor Exit Flow Distribution on Air Placement in Annular Combustors

1978 ◽  
Vol 100 (3) ◽  
pp. 444-451 ◽  
Author(s):  
R. C. Adkins
Keyword(s):  
Mathematical Model ◽  
Flow Distribution ◽  
Simple Mathematical Model ◽  
Nonuniform Flow ◽  
Flow Conditions ◽  
Design And Development

A simple mathematical model has been devised which is intended to make a powerful aid to combustor design and development. The model has confirmed that nonuniform flow conditions at inlet to the precombustor diffuser can seriously deter combustor performance.

scholarly journals Investigation on the Drag Coefficient of the Steady and Unsteady Flow Conditions in Coarse Porous Media

2021 ◽  
Author(s):  
Hadi Norouzi ◽  
Jalal Bazargan ◽  
Faezah Azhang ◽  
Rana Nasiri
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Friction Coefficient ◽  
Unsteady Flow ◽  
Drag Coefficient ◽  
Flow Velocity ◽  
Hydraulic Gradient ◽  
Flow Conditions ◽  
Porous Media Equations ◽  
Unsteady Flow Condition

Abstract The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.

Transition of Mixtures of Polymers in a Dilute Aqueous Solution

1970 ◽  
Vol 92 (3) ◽  
pp. 411-418 ◽  
Author(s):  
W. D. White ◽  
D. M. McEligot
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Pressure Ratio ◽  
Polymer Concentration ◽  
Transition Process ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Calibration Data ◽  
Molecular Weight Polymer ◽  
Dilute Aqueous Solution

Data are presented for the flow of deionized water solutions of linear, unbranched polymers—Separan AP-30, Polyox WSR-35 and Polyox WSR-301, and mixtures of the latter two in a 0.0235 in. tube. The Reynolds numbers vary from about 1200 to about 12,000. Measurements were made at 4 deg C and near room temperature. Occurrence of transition is confirmed by oscillograph traces and pressure ratio calculations in addition to the usual “break” on a friction factor-Reynolds number graph. From the calibration data, it appears that for small tubes there is a critical parameter, such as molecular weight or polymer length, below which transition occurs as for water, but above which the transition Reynolds number depends on polymer concentration. The low and high polymers were mixed to vary molecular weight distribution of samples. It was found that the higher molecular weight polymer dominates the transition process, but in the turbulent regime the effects are roughly additive.

scholarly journals Investigation on the Drag Coefficient of the Steady and Unsteady Flow Conditions in Coarse Porous Media

2021 ◽  
Author(s):  
Hadi Norouzi ◽  
Jalal Bazargan ◽  
Faezah Azhang ◽  
Rana Nasiri
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Friction Coefficient ◽  
Unsteady Flow ◽  
Drag Coefficient ◽  
Flow Velocity ◽  
Hydraulic Gradient ◽  
Flow Conditions ◽  
Porous Media Equations ◽  
Unsteady Flow Condition

Abstract The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.

scholarly journals Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Tobias Blanke ◽  
Markus Hagenkamp ◽  
Bernd Döring ◽  
Joachim Göttsche ◽  
Vitali Reger ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Exchangers ◽  
Circular Ring ◽  
Flow Conditions ◽  
Flow Rates ◽  
Mass Flow Rates ◽  
Pipe Radius

AbstractPrevious studies optimized the dimensions of coaxial heat exchangers using constant mass flow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.

Dune-scale cross-strata across the fluvial-deltaic backwater regime: Preservation potential of an autogenic stratigraphic signature

Geology ◽  
2020 ◽  
Vol 48 (12) ◽  
pp. 1144-1148
Author(s):  
Chenliang Wu ◽  
Jeffrey A. Nittrouer ◽  
Travis Swanson ◽  
Hongbo Ma ◽  
Eric Barefoot ◽  
...  
Keyword(s):  
Spatial Variability ◽  
Mississippi River ◽  
Nonuniform Flow ◽  
Hydrodynamic Conditions ◽  
Flow Conditions ◽  
Bed Topography ◽  
Fundamental Building Block ◽  
Bed Form ◽  
Spatially Varying ◽  
Topography Data

Abstract Dune-scale cross-beds are a fundamental building block of fluvial-deltaic stratigraphy and have been recognized on Earth and other terrestrial planets. The architecture of these stratal elements reflects bed-form dynamics that are dependent on river hydrodynamic conditions, and previous work has documented a multitude of scaling relationships to describe the morphodynamic interactions between dunes and fluid flow. However, these relationships are predicated on normal flow conditions for river systems and thus may be unsuitable for application in fluvial-deltaic settings that are impacted by nonuniform flow. The ways in which dune dimensions vary systematically due to the influence of reach-averaged, nonuniform flow, and how such changes may be encoded in dune cross-strata, have not been investigated. Herein, we explored the influence of backwater flow on dune geometry in a large modern fluvial channel and its implications for interpretation of systematic variability in dune cross-strata in outcrop-scale stratigraphy. This was accomplished by analyzing high-resolution channel-bed topography data for the lowermost 410 km of the Mississippi River, which revealed that dune size increases to a maximum before decreasing toward the river outlet. This spatial variability coincides with enhanced channel-bed aggradation and decreasing dune celerity, which arise due to backwater hydrodynamics. An analytical model of bed-form stratification, identifying spatial variability of cross-set thickness, indicates a prominent downstream decrease over the backwater region. These findings can be used to inform studies of ancient fluvial-deltaic settings, by bolstering assessments of proximity to the marine terminus and associated spatially varying paleohydraulics.

Haemorheological Effects on Thrombocyte Adhesion and Aggregation Found Under Controlled Flow Conditions

1979 ◽  
Author(s):  
P.D. Richardson
Keyword(s):  
Rate Of Change ◽  
Continuous Observation ◽  
Flow Conditions ◽  
Wide Range ◽  
Stream Migration ◽  
Local Shear ◽  
Videotape Recording ◽  
Controlled Flow ◽  
A Site

Thrombocyte adhesion and aggregation in a vessel or on a chamber wall can be measured most readily if the flow is controlled and steady, and continuous observation is used. Videotape recording is very helpful for subsequent quantification of the dynamics. The adhesion of each thrombocyte can occur for a finite time interval:this interval has been observed to have a wide range. Platelets which escape often leave open a site which attracts other platelets preferentially. The rate of change of adhesion density (platelets/mm2) is affected by the local shear rate and the shear history upstream. Aggregation is affected similarly, and also proceeds with some platelet turnover. The role of erythrocytes in facilitating cross-stream migration of thrombocytes (which can enhance the growth rate of large thrombi) appears due in part to convective flow fields induced by the motion of erythrocytes in a shear flow, which can be demonstrated theoretically and experimentally. Observations of the phenomenlogy of adhesion and aggregation under controlled flow conditions and comparison with fLu id-dynamically based theory allows representation in terras of a small number of parameters with prospects of prediction of behaviour over a wide range of haemodynamic conditions; biochemical changes lead to changes in values of the parameters, so that activating agents and inhibiting agents modify values in different directions.

scholarly journals Inverse Problem for Looped River Networks – Lower oder River Case Study

2013 ◽  
Vol 39 (1) ◽  
pp. 105-118
Author(s):  
Jacek Kurnatowski
Keyword(s):  
Mathematical Modeling ◽  
Flow Resistance ◽  
Flow Distribution ◽  
River Networks ◽  
Sensitivity Equation ◽  
Flow Measurements ◽  
Sensitivity Equation Method ◽  
Coefficients Identification ◽  
Oder River

Abstract Identification of coefficients determining flow resistance, in particular Manning’s roughness coefficients, is one of the possible inverse problems of mathematical modeling of flow distribution in looped river networks. The paper presents the solution of this problem for the lower Oder River network consisting of 78 branches connected by 62 nodes. Using results of six sets of flow measurements at particular network branches it was demonstrated that the application of iterative algorithm for roughness coefficients identification on the basis of the sensitivity-equation method leads to the explicit solution for all network branches, independent from initial values of identified coefficients.

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