Numerical Flow Analysis in a Rotating Square Duct and a Rotating Curved-Duct

A numerical study is conducted on the fully-developed laminar flow of an incompressible viscous fluid in a square duct rotating about a perpendicular axis to the axial direction of the duct. At the straight duct, the rotation produces vortices due to the Coriolis force. Generally two vortex cells are formed and the axial velocity distribution is distorted by the effect of this Coriolis force. When a convective force is weak, two counter-rotating vortices are shown with a quasi-parabolic axial velocity profile for weak rotation rates. As the rotation rate increases, the axial velocity on the vertical centreline of the duct begins to flatten and the location of vorticity center is moved near to wall by the effect of the Coriolis force. When the convective inertia force is strong, a double-vortex secondary flow appears in the transverse planes of the duct for weak rotation rates but as the speed of rotation increases the secondary flow is shown to split into an asymmetric configuration of four counter-rotating vortices. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration. Also, a numerical study is conducted on the laminar flow of an incompressible viscous fluid in a90°-bend square duct that rotates about axis parallel to the axial direction of the inlet. At a90°-bend square duct, the feature of flow by the effect of a Coriolis force and a centrifugal force, namely a secondary flow by the centrifugal force in the curved region and the Coriolis force in the downstream region, is shown since the centrifugal force in curved region and the Coriolis force in downstream region are dominant respectively.

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The effect of spanwise system rotation on Dean vortices

Journal of Fluid Mechanics ◽

10.1017/s0022112094002119 ◽

1994 ◽

Vol 274 ◽

pp. 243-265 ◽

Cited By ~ 20

Author(s):

O. John E. Matsson ◽

P. Henrik Alfredsson

Keyword(s):

Centrifugal Force ◽

Coriolis Force ◽

Travelling Waves ◽

Streamwise Vortices ◽

Longitudinal Vortices ◽

Smoke Visualization ◽

Rotation Rates ◽

Dean Vortices ◽

System Rotation ◽

Secondary Instabilities

An experimental study is reported of the flow in a high-aspect-ratio curved air channel with spanwise system rotation, utilizing hot-wire measurements and smoke visualization. The experiments were made at two different Dean numbers (De), approximately 2 and 4.5 times the critical De for which the flow becomes unstable and develops streamwise vortices. For the lower De without system rotation the primary Dean instability appeared as steady longitudinal vortices. It was shown that negative spanwise system rotation, i.e. the Coriolis force counteracts the centrifugal force, could cancel the primary Dean instability and that for high rotation rates it could give rise to vortices on the inner convex channel wall. For positive spanwise system rotation, i.e. when the Coriolis force enhanced the centrifugal force, splitting and merging of vortex pairs were observed. At the higher De secondary instabilities occurred in the form of travelling waves. The effect of spanwise system rotation on the secondary instability was studied and was found to reduce the amplitude of the twisting and undulating motions for low negative rotation. For low positive rotation the amplitude of the secondary instabilities was unaffected for most regions in parameter space.

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The Torsion Effect on Fully Developed Laminar Flow in Helical Square Ducts

Journal of Fluids Engineering ◽

10.1115/1.2910138 ◽

1993 ◽

Vol 115 (2) ◽

pp. 292-301 ◽

Cited By ~ 8

Author(s):

Wen-Hwa Chen ◽

Ray Jan

Keyword(s):

Laminar Flow ◽

Secondary Flow ◽

Friction Factor ◽

Stokes Equations ◽

Axial Flow ◽

Outer Wall ◽

Square Duct ◽

Torsion Effect ◽

Inclined Angle ◽

Curvature And Torsion

The continuity equation and Navier-Stokes equations derived from a non-orthogonal helical coordinate system are solved by the Galerkin finite-element method in an attempt to study the torsion effect on the fully developed laminar flow in the helical square duct. Since high-order terms of curvature and torsion are considered, the approach is also applicable to the problems with finite curvature and torsion. The interaction effects of curvature, torsion, and the inclined angle of the cross section on the secondary flow, axial velocity, and friction factor in the helical square duct are presented. The results show that the torsion has more pronounced effect on the secondary flow rather than the axial flow. In addition, unlike the flow in the toroidal square duct, Dean’s instability of the secondary flow, which occurs near the outer wall in the helical square duct, can be avoided due to the effects of torsion and/or inclined angle. In such cases, a decrease of the friction factor is observed. However, as the pressure gradient decreases to a small value, the friction factor for the toroidal square duct is also applicable to the helical square duct.

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Numerical study on aerothermal performance of shroud movement in the vivinity of turbine tips

Thermal Science ◽

10.2298/tsci200628321z ◽

2020 ◽

pp. 321-321

Author(s):

Yunsong Zhang ◽

Yongbao Liu ◽

Yujie Li ◽

Qijie Li

Keyword(s):

Heat Transfer ◽

Secondary Flow ◽

Flow Structure ◽

Numerical Study ◽

Three Dimensional ◽

Breakdown Point ◽

Axial Direction ◽

Suction Surface ◽

Initial Location ◽

Dimensional Simulation

In this paper, the effects of shroud movement on transonic flow and heat transfer in the vicinity of turbine tip was studied by using three-dimensional simulation of GE-E3 first-stage HPT. Aerothermal performance and flow structure were analyzed with and without turbine shroud moving, respectively. Based on the distribution of limiting streamlines and the vortex structures, the influential characteristics between the leakage flow and the secondary flow generated by shroud movement were studied. Moreover, the coefficient of heat transfer at the wall were investigated. Results show that the flow structure is changing with the movement of turbine shroud, and the location of the separation line changes significantly by the influence of the secondary flow. The leakage vortex initial location delayed in axial direction and its breakdown point located at 65% cross section. This accelerates the mixing loss and increase the perturbation. In addition, it is observed that the coefficient of average heat transfer is increased obviously by 54.8% in the region of shroud surface. However, this coefficient in the region of suction surface decreased by 11.9%.

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Analysis of Steady Laminar Flow of an Incompressible Newtonian Fluid Through Curved Pipes of Small Curvature

Journal of Fluids Engineering ◽

10.1115/1.3446961 ◽

1973 ◽

Vol 95 (1) ◽

pp. 75-80 ◽

Cited By ~ 10

Author(s):

M. Sankaraiah ◽

Y. V. N. Rao

Keyword(s):

Pressure Drop ◽

Laminar Flow ◽

Secondary Flow ◽

Newtonian Fluid ◽

Axial Velocity ◽

Axial Pressure ◽

Small Curvature ◽

Curved Pipes ◽

Incompressible Newtonian Fluid ◽

Steady Laminar

Steady laminar flow of an incompressible Newtonian fluid through a curved pipe of small curvature is considered. The governing equations of flow are obtained in terms of secondary flow stream function and axial velocity component as suggested by Dean. A method of successive approximations is developed to solve these equations. The first five approximations are computed. The solution obtained is used to determine the axial velocity distribution, secondary flow pattern, axial pressure drop, and pressure distribution along the pipe wall. A semiempirical equation is obtained for axial pressure drop. The theoretical results obtained are compared with the available experimental data on axial pressure drop.

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A Numerical Study on the Generation Mechanism of Turbulence-Driven Secondary Flow in a Square Duct

Journal of Fluids Engineering ◽

10.1115/1.2910103 ◽

1993 ◽

Vol 115 (1) ◽

pp. 172-175 ◽

Cited By ~ 1

Author(s):

Hyon Kook Myong

Keyword(s):

Secondary Flow ◽

Numerical Study ◽

Reynolds Shear Stress ◽

Secondary Flows ◽

Generation Mechanism ◽

Streamwise Vorticity ◽

Reynolds Stresses ◽

Cross Sectional ◽

Square Duct ◽

Vorticity Transport

The generation mechanism of turbulence-driven secondary flows in a square duct is numerically investigated in the present study by using an anisotropic low-Reynolds-number k–ε turbulence model. Special attention is directed to the distributions of turbulence quantities, which are responsible for the secondary flow generation, such as the anisotropy of normal Reynolds stresses and the secondary Reynolds shear stress acting on the cross-sectional plane. The vorticity transport process is also discussed in detail, based on the numerical evaluation of the individual terms which appear in the streamwise vorticity transport equation.

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NUMERICAL STUDY OF FLOW AND HEAT TRANSFER FOR PULSATING FLOW IN A SQUARE DUCT WITH RIBS

10.1615/ihtc16.hte.022757 ◽

2018 ◽

Author(s):

Wei Wang ◽

Bowen Du ◽

Yuemei Jia

Keyword(s):

Heat Transfer ◽

Numerical Study ◽

Pulsating Flow ◽

Square Duct ◽

Flow And Heat Transfer

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Numerical study of the effects of some geometric characteristics of a centrifugal pump impeller that pumps a viscous fluid

Computers & Fluids ◽

10.1016/j.compfluid.2012.02.028 ◽

2012 ◽

Vol 60 ◽

pp. 61-70 ◽

Cited By ~ 74

Author(s):

M.H. Shojaeefard ◽

M. Tahani ◽

M.B. Ehghaghi ◽

M.A. Fallahian ◽

M. Beglari

Keyword(s):

Viscous Fluid ◽

Centrifugal Pump ◽

Numerical Study ◽

Pump Impeller ◽

Geometric Characteristics ◽

Centrifugal Pump Impeller

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On a sphere performing linear and torsional oscillations in a viscous fluid

Canadian Journal of Physics ◽

10.1139/p88-097 ◽

1988 ◽

Vol 66 (7) ◽

pp. 576-579

Author(s):

G. T. Karahalios ◽

C. Sfetsos

Keyword(s):

Boundary Layer ◽

Viscous Fluid ◽

Secondary Flow ◽

Small Amplitude ◽

Equations Of Motion ◽

Successive Approximations ◽

Method Of Successive Approximations ◽

Time Varying ◽

Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

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