Secondary Flows in Eccentric-Annular Tubes

2019 ◽  
Author(s):  
Mario Letelier ◽  
Dennis A. Siginer ◽  
Diego L. Almendra ◽  
Juan Stockle
Keyword(s):  
Cross Section ◽  
Shape Factor ◽  
Vortical Structure ◽  
Circular Cross Section ◽  
Weissenberg Number ◽  
Secondary Flows ◽  
Material Parameters ◽  
Annular Cross Section ◽  
Nonlinear Viscoelastic ◽  
Transversal Flow

Abstract In this paper, transversal flow field of nonlinear viscoelastic fluids abiding by the modified-Phan-Thien-Tanner (MPTT) constitutive model in straight tubes of eccentric-annular cross-section is investigated. An analytical solution is developed based on an asymptotic expansion in terms of the Weissenberg number coupled with the shape factor method a one-to-one mapping taking the circular cross-section into the eccentric annular cross section. The analysis reveals the formation of transversal flows due to elasticity and to the eccentricity parameter. The number of vortices in the cross-section depends on the ratio of the diameters in addition to the eccentricity parameter. The effect of these parameters on the vortical structure is explored for different values of the material parameters.

Turbulence Generated Secondary Flows in Ducts of Non-Circular Cross-Section

1982 ◽  
Vol 24 (3) ◽  
pp. 119-127
Author(s):  
W. J. Seale
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Secondary Flows ◽  
Algebraic Expression ◽  
Rod Bundle ◽  
Stress Models

The use of algebraic stress models in the prediction of secondary flows in straight ducts of non-circular cross-section is found to be unsatisfactory and to give inconsistent results in the sub-channels within a rod bundle. An algebraic expression is presented which allows the source of axial vorticity to be calculated directly and without iteration. The expression is shown to reproduce secondary velocities in square and triangular ducts, and in a duct consisting of two inter-connected subchannels.

scholarly journals Two-phase flow in channels with non-circular cross-section of pneumatic transport of powder material

2018 ◽  
Vol 22 (Suppl. 5) ◽  
pp. 1407-1424
Author(s):  
Sasa Milanovic ◽  
Milos Jovanovic ◽  
Zivan Spasic ◽  
Boban Nikolic
Keyword(s):  
Cross Section ◽  
Numerical Experiments ◽  
Circular Cross Section ◽  
Pneumatic Transport ◽  
Secondary Flows ◽  
Solid Particles ◽  
Stress Model ◽  
Two Phase ◽  
Initial Flow ◽  
Numerical Grid

The paper presents a numerical simulation of two-phase turbulent flow in straight horizontal channels of pneumatic transport with non-circular cross-section. For the granular flow simulation, we have chosen the flow of solid particles of quartz, flour, and ash in the flow of air, which is transporting fluid. During the modeling of the flow, the transported solid particles are reduced to spherical shapes. A correction of the stress model of turbulence is performed by taking into account the influences of the induction of secondary flows of the second order in the gas phase. The full Reynolds stress model was used for modeling the turbulence, and the complete model is used for the turbulent stresses and turbulent temperature fluxes. All numerical experiments were conducted for the same initial flow conditions and a single uniform grid was adopted for all numerical experiments. The flow is observed in a straight channel of a square cross-section and dimensions of sides of 200 mm and the length of 80 Dh. During the simulation, the fineness of the numerical grid was also tested, and the paper shows results of the numerical grid of the highest resolution beyond which the fineness does not influence the obtained results. The paper offers graphics of velocities of the solid particles transported by the transporting fluid (air) along the channel.

Axial Loading of Bonded Rubber Blocks

2002 ◽  
Vol 69 (6) ◽  
pp. 836-843 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Shape Factor ◽  
Circular Cross Section ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Lateral Profile

Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young’s modulus, Ea, the modified modulus, Ea′, and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating Ea and Ea′ are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S.

scholarly journals Flow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections

2019 ◽  
Vol 377 (2144) ◽  
pp. 20180069 ◽  
Author(s):  
Juan P. Gomez-Constante ◽  
Kumbakonam R. Rajagopal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Cross Section ◽  
Cross Sections ◽  
Applied Mathematics ◽  
Constitutive Relations ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Secondary Flows ◽  
Shear Stresses

Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Heat Transfer Asymptote in Laminar Tube Flows of Non-Linear Viscoelastic Fluids

2010 ◽  
Author(s):  
Dennis A. Siginer
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Heat Transfer Enhancement ◽  
Cross Section ◽  
Viscoelastic Fluids ◽  
Weissenberg Number ◽  
Secondary Flows ◽  
Asymptotic Independence ◽  
Transfer Enhancement ◽  
Elasticity Number

The fully developed thermal field in constant pressure gradient driven laminar flow of a class of nonlinear viscoelastic fluids with instantaneous elasticity in straight pipes of arbitrary contour ∂D with constant wall flux is investigated. The nonlinear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large. Asymptotic series in terms of the Weissenberg number Wi are employed to expand the field variables. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity and temperature fields in tubes with arbitrary cross-section. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is to a very large extent the result of secondary flows in the cross-section but there is a component due to first normal stress differences as well. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Order of magnitude larger enhancements are possible even with slightly viscoelastic fluids. The coupling between inertial and viscoelastic nonlinearities is crucial to enhancement. Isotherms for the temperature field are discussed for non-circular contours such as the ellipse and the equilateral triangle together with the behavior of the average Nusselt number Nu, a function of the Reynolds Re, the Prandtl Pr and the Weissenberg Wi numbers. Analytical evidence for the existence of a heat transfer asymptote in laminar flow of viscoelastic fluids in non-circular contours is given for the first time. Nu becomes asymptotically independent from elasticity with increasing Wi, Nu = f (Pe,Wi) → Nu = f(Pe). This asymptote is the counterpart in laminar flows in non-circular tubes of the heat transfer asymptote in turbulent flows of viscoelastic fluids in round pipes. A different asymptote corresponds to different cross-sectional shapes in straight tubes. The change of type of the vorticity equation governs the trends in the behavior of Nu with increasing Wi and Pe. The implications on the heat transfer enhancement is discussed in particular for slight deviations from Newtonian behavior where a rapid rise in enhancement seems to occur as opposed to the behavior for larger values of the Weissenberg number where the rate of increase is much slower. The asymptotic independence of Nu from elasticity with increasing Wi is related to the extent of the supercritical region controlled by the interaction of the viscoelastic Mach number M and the Elasticity number E, which mitigates and ultimately cancels the effect of the increasingly strong secondary flows with increasing Wi to level off the enhancement. The physics of the interaction of the effects of the Elasticity E, Viscoelastic Mach M, Reynolds Re and Weissenberg Wi numbers on generating the heat transfer enhancement is discussed.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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