Approximating Wetted Perimeter in Power-Law Cross Section

2000 ◽  
Vol 126 (2) ◽  
pp. 98-109 ◽  
Author(s):  
T. S. Strelkoff ◽  
A. J. Clemmens
Keyword(s):  
Cross Section ◽  
Power Law ◽  
Wetted Perimeter

A Numerical Study of Dean Instability in Non-Newtonian Fluids

2005 ◽  
Vol 128 (1) ◽  
pp. 34-41 ◽  
Author(s):  
H. Fellouah ◽  
C. Castelain ◽  
A. Ould El Moctar ◽  
H. Peerhossaini
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Power Law ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Newtonian Fluids ◽  
Dean Number ◽  
Bingham Number ◽  
Curved Channels ◽  
Power Law Index

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

Numerical Simulation of Laminar Flow of Yield-Power-Law Fluids in Conduits of Arbitrary Cross-Section

1993 ◽  
Vol 115 (4) ◽  
pp. 710-716 ◽  
Author(s):  
Idir Azouz ◽  
Siamack A. Shirazi ◽  
Ali Pilehvari ◽  
J. J. Azar
Keyword(s):  
Laminar Flow ◽  
Cross Section ◽  
Power Law ◽  
Annular Flow ◽  
Flow Behavior ◽  
Arbitrary Cross Section ◽  
Curvilinear Coordinates ◽  
Eccentric Annulus ◽  
Power Law Fluids ◽  
Eccentric Annuli

A numerical model has been developed to simulate laminar flow of Power-law and Yield-Power law fluids in conduits of arbitrary cross-section. The model is based on general, nonorthogonal, boundary-fitted, curvilinear coordinates, and represents a new approach to the solution of annular flow problems. The use of an effective viscosity in the governing equation of the flow allows the study of the flow behavior of any fluid for which the shear stress is a function of shear rate only. The model has been developed primarily to simulate annular flow of fluids used in drilling and completion operations of oil or gas wells. Predicted flow rates versus pressure gradient for laminar flow of Newtonian fluids in concentric and eccentric annuli, and Power-law fluids in concentric annuli compare very well with results derived from analytical expressions. Moreover, the predictions for laminar flow of Power-law and Yield-Power-law fluids in eccentric annuli are in excellent agreement with numerical and experimental data published in the literature. The model was also successfully applied to the case of laminar flow of Power-law fluids in an eccentric annulus containing a stationary bed of drilled cuttings and the results are presented herein.

scholarly journals Peristaltic Transport of Power-Law Fluid in an Elastic Tapered Tube with Variable Cross-Section Induced by Dilating Peristaltic Wave

2021 ◽  
pp. 1293-1306
Author(s):  
Mohammed Ali Murad ◽  
Ahmed M. Abdulhadi
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Peristaltic Transport ◽  
Peristaltic Wave ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Opposite Behavior ◽  
Local Shear

The peristaltic transport of power-law fluid in an elastic tapered tube with variable cross-section induced by dilating peristaltic wave is studied. The exact solution of the expression for axial velocity, radial velocity, stream function, local shear stress, volume of flow rate and pressure gradient are obtained under the assumption of long wavelength and low Reynolds number. The effects of all parameters that appear in the problem are analyzed through graphs. The results showed that the flux is sinusoidal in nature and it is an increasing function with the increase of  whereas it is a decreasing function with the increase of . An opposite behavior for shear strain is noticed compared to pressure gradient.  Finally, trapping phenomenon is presented to explain the physical behavior of various parameters. It is noted that the size of the trapping bolus increases with increasing  whereas it decreases as  increases. MATHEMATICA software is used to plot all figures.

scholarly journals Analysis of the velocity distribution in different types of ventilation system ducts

2018 ◽  
Vol 180 ◽  
pp. 02081 ◽  
Author(s):  
Kazimierz Peszyński ◽  
Lukasz Olszewski ◽  
Emil Smyk ◽  
Daniel Perczyński
Keyword(s):  
Velocity Profile ◽  
Velocity Distribution ◽  
Cross Section ◽  
Power Law ◽  
Flow Rate ◽  
Fundamental Problem ◽  
Ventilation System ◽  
Different Types ◽  
Actual Profile ◽  
Ventilation Duct

The paper presents the results obtained during the preliminary studies of circular and rectangular ducts before testing the properties elements (elbows, tees, etc.)of rectangular with rounded corners ducts. The fundamental problem of the studies was to determine the flow rate in the ventilation duct. Due to the size of the channel it was decided to determine the flow rate based on the integration of flow velocity over the considered cross-section. This method requires knowledge of the velocity distribution in the cross section. Approximation of the measured actual profile by the classic and modified Prandtl power-law velocity profile was analysed.

scholarly journals Computing Neutron Capture Rates in Neutron-Degenerate Matter

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Bryn Knight ◽  
Liliana Caballero
Keyword(s):  
Cross Section ◽  
Power Law ◽  
Cross Sections ◽  
Neutron Capture ◽  
Chemical Potential ◽  
Distribution Functions ◽  
Analytical Integration ◽  
Thermodynamic Conditions ◽  
The Cross ◽  
Capture Rates

Neutron captures are likely to occur in the crust of accreting neutron stars (NSs). Their rate depends on the thermodynamic state of neutrons in the crust. At high densities, neutrons are degenerate. We find degeneracy corrections to neutron capture rates off nuclei, using cross sections evaluated with the reaction code TALYS. We numerically integrate the relevant cross sections over the statistical distribution functions of neutrons at thermodynamic conditions present in the NS crust. We compare our results to analytical calculations of these corrections based on a power-law behavior of the cross section. We find that although an analytical integration can simplify the calculation and incorporation of the results for nucleosynthesis networks, there are uncertainties caused by departures of the cross section from the power-law approach at energies close to the neutron chemical potential. These deviations produce non-negligible corrections that can be important in the NS crust.

scholarly journals The Orbital Eccentricities of Binary Millisecond Pulsars in Globular Clusters

1996 ◽  
Vol 174 ◽  
pp. 383-383
Author(s):  
Frederic A. Rasio ◽  
Douglas C. Heggie
Keyword(s):  
Cross Section ◽  
Power Law ◽  
Globular Clusters ◽  
Major Axis ◽  
Semi Major Axis ◽  
Millisecond Pulsars ◽  
Numerical Integrations ◽  
Order Of Magnitude ◽  
Low Mass ◽  
Analytical Perturbation

Low-mass binary millisecond pulsars are born with very small orbital eccentricities, typically of order ei ∼ 10−6−10−3. In globular clusters, however, higher eccentricities ef ≫ ei can be induced by dynamical interactions with passing stars. Using both analytical perturbation calculations and numerical integrations, we have shown (Heggie & Rasio 1996) that the cross section for this process is much larger than previously estimated. This is because, even for initially circular binaries, the induced eccentricity ef for an encounter with pericentre separation rp beyond a few times the binary semi-major axis a declines only as a power-law, ef ∝ (rp/a)−5/2, and not as an exponential. We find that all currently known low-mass binary millisecond pulsars in globular clusters must have been affected by interactions, with their current eccentricities being at least an order of magnitude larger than at birth (Rasio & Heggie 1995).

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