scholarly journals Flows of Dehaven Fluid in Symmetrically Curved Capillary Fissures and Tubes

2018 ◽  
Vol 23 (2) ◽  
pp. 521-550
Author(s):  
A. Walicka ◽  
J. Falicki ◽  
P. Jurczak
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Cross Section ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Velocity Flow ◽  
Hyperbolic Cosine ◽  
Analytical Expressions

Abstract In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of DeHaven type fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. variable cross-section, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. Each example is concluded with a presentation of the formulae for the velocity flow on the outer surface of a thin porous layer. Upon introduction of hindrance factors, these formulae may be presented in the most general forms.

scholarly journals Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

2018 ◽  
Vol 23 (1) ◽  
pp. 187-211 ◽  
Author(s):  
A. Walicka
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Power Law ◽  
Flow Rate ◽  
Analytical Method ◽  
Volumetric Flow Rate ◽  
Power Law Fluid ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Analytical Expressions

AbstractIn this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

Flow in a Curved Rectangular Channel With Variable Cross-Section Area

2008 ◽  
Author(s):  
Avijit Bhunia ◽  
C. L. Chen
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
Rectangular Channel ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Entry And Exit ◽  
Curved Channel ◽  
Cross Section Area ◽  
Secondary Motion ◽  
Curved Section

Laminar air flow through a curved rectangular channel with a variable cross-section (c/s) area (diverging-converging) is numerically investigated. Such a flow passage is formed between the two fin walls of a 90° bend curved fin heat sink, used in avionics cooling. Simulations are carried out for two different configurations — (a) a curved channel with long, straight, constant c/s area inlet and outlet sections (entry and exit lengths), and (b) a short, curved channel with no entry and exit lengths. Formation of a complex, 3-D flow pattern and its evolution in space is studied through numerical flow visualization. Results show that a secondary motion sets in the radial direction in the curved section, which in combination with the axial (bulk) flow leads to the formation of a base vortex. In addition, under certain circumstances the axial and secondary flow separate from multiple locations on the channel walls, and create Dean vortices and separation bubbles. The role of variable c/s geometry is elucidated by comparing the results with those of a constant c/s area, curved channel. Investigation of the dimensionless friction factor reveals that the overall channel pressure drop is governed by both the curvature effect as well as the area expansion effect. Due to the combined effect pressure drop for developing flow in a short, curved channel can be even less than that of a straight channel.

Choking of liquid flows

1989 ◽  
Vol 199 ◽  
pp. 563-568 ◽  
Author(s):  
S. M. Richardson
Keyword(s):  
Temperature Field ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Liquid Flows ◽  
Increasing Temperature

It is well-known that laminar flow of a liquid in a duct is predicted to choke if the viscosity of the liquid increases exponentially with increasing pressure. In other words, the pressure drop in the duct is predicted to become unbounded when the volumetric flow rate reaches a critical finite value. Choking is not observed in practice, however: the reason why is investigated here. It is shown that choking is always predicted to occur if the viscosity is independent of temperature or heat generation by viscous dissipation is neglected. If the viscosity decreases exponentially with increasing temperature and heat generation is not neglected, however, and if the temperature field is fully developed or if the flow is adiabatic, it is shown that choking is predicted not to occur.

Numerical Investigation of the Pressure-Time Method Considering Pipe With Variable Cross Section

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Simindokht Saemi ◽  
Mehrdad Raisee ◽  
Michel J. Cervantes ◽  
Ahmad Nourbakhsh
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Flow Rate ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Navier Stokes ◽  
Variable Cross ◽  
Pressure Time ◽  
Viscous Losses ◽  
Contraction Angle

A common method to calculate the flow rate and consequently hydraulic efficiency in hydropower plants is the pressure-time method. In the present work, the pressure-time method is studied numerically by three-dimensional (3D) simulations and considering the change in the pipe cross section (a contraction). Four different contraction angles are selected for the investigations. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations and the low-Reynolds k–ω shear stress transport (SST) turbulence model are used to simulate the turbulent flow. The flow physics in the presence of the contraction, and during the deceleration period, is studied. The flow rate is calculated considering all the losses: wall shear stress, normal stresses, and also flux of momentum in the flow. The importance of each term is evaluated showing that the flux of momentum plays a most important role in the flow rate estimation while the viscous losses term is the second important factor. To extend the viscous losses calculations applicability to real systems, the quasi-steady friction approach is employed. The results showed that considering all the losses, the increase in the contraction angle does not influence the calculated errors significantly. However, the use of the quasi-steady friction factor introduces a larger error, and the results are reliable approximately up to a contraction angle of ϴ = 10 deg. The reason imparts to the formation of a local recirculation zone upstream and inside the contraction, which appears earlier as the contraction angle increases. This feature cannot be captured by the quasi-steady friction models, which are derived based on the fully developed flow assumption.

An Analysis of Laminar Flow and Pressure Drop in Complex Shaped Ducts

1976 ◽  
Vol 98 (4) ◽  
pp. 702-706 ◽  
Author(s):  
John P. Zarling
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Cross Section ◽  
Flow Rate ◽  
Series Solution ◽  
Complex Geometry ◽  
Constant Cross Section ◽  
Point Matching ◽  
Friction Factors ◽  
Flow Through

An analytical method is presented for solving the governing equation for fully developed, steady, incompressible laminar flow through ducts of constant cross-section having a complex geometry. The technique uses the Schwarz-Neumann alternating method along with least squares point matching. The method is applied to a complex shaped duct and the resulting velocity series solution is used to calculate the flow rate and pressure drop (f•Re) for a range of duct sizes. Numerical results are presented and compared with experimentally determined friction factors for a duct of similar geometry.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

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