scholarly journals On a problem of nonstationary two-dimensional motion of micropolar fluid when normal stress and tangential velocity are given on the boundary

2012 ◽  
Vol 36 (3) ◽  
pp. 1034-1045 ◽  
Author(s):  
Ibrahim H. El-Sirafy ◽  
S.M. Abo-Dahab
Keyword(s):  
Normal Stress ◽  
Micropolar Fluid ◽  
Tangential Velocity ◽  
Two Dimensional

An Analysis of Peristaltic Flow of Finitely Extendable Nonlinear Elastic- Peterlin Fluid in Two-Dimensional Planar Channel and Axisymmetric Tube

2014 ◽  
Vol 69 (8-9) ◽  
pp. 462-472 ◽  
Author(s):  
Nasir Ali ◽  
Zaheer Asghar
Keyword(s):  
Normal Stress ◽  
Fluid Model ◽  
Flow Analysis ◽  
Pressure Rise ◽  
Deborah Number ◽  
Planar Channel ◽  
Two Dimensional ◽  
Frictional Forces ◽  
Nonlinear Elastic ◽  
Axisymmetric Tube

We have investigated the peristaltic motion of a non-Newtonian fluid characterized by the finitely extendable nonlinear elastic-Peterlin (FENE-P) fluid model. A background for the development of the differential constitutive equation of this model has been provided. The flow analysis is carried out both for two-dimensional planar channel and axisymmetric tube. The governing equations have been simplified under the widely used assumptions of long wavelength and low Reynolds number in a frame of reference that moves with constant wave speed. An exact solution is obtained for the stream function and longitudinal pressure gradient with no slip condition. We have portrayed the effects of Deborah number and extensibility parameter on velocity profile, trapping phenomenon, and normal stress. It is observed that normal stress is an increasing function of Deborah number and extensibility parameter. As far as the velocity at the channel (tube) center is concerned, it decreases (increases) by increasing Deborah number (extensibility parameter). The non-Newtonian rheology also affect the size of trapped bolus in a sense that it decreases (increases) by increasing Deborah number (extensibility parameter). Further, it is observed through numerical integration that both Deborah number and extensibility parameter have opposite effects on pressure rise per wavelength and frictional forces at the wall. Moreover, it is shown that the results for the Newtonian model can be deduced as a special case of the FENE-P model

The effective film viscosity coefficients of a thin floating fluid layer

1997 ◽  
Vol 344 ◽  
pp. 335-337 ◽  
Author(s):  
ALASTAIR D. JENKINS ◽  
KRISTIAN B. DYSTHE
Keyword(s):  
Shear Stress ◽  
Thin Layer ◽  
Tangential Stress ◽  
Constitutive Relation ◽  
Shear Viscosity ◽  
Fluid Layer ◽  
Tangential Velocity ◽  
Two Dimensional ◽  
Viscosity Coefficients ◽  
Lower Fluid

We derive a constitutive relation, relating the tangential stress, tangential velocity, thickness h, and viscosity μ, for a thin layer of Newtonian fluid on top of a fluid substrate. We find that the upper layer exerts a viscous tangential shear stress on the lower fluid, behaving as if it were a film with a two-dimensional shear viscosity equal to μh, and a dilatational viscosity 3μh.

The Limit Load of Transonic Turbine Blading

1974 ◽  
Author(s):  
I. Fruchtman
Keyword(s):  
Satisfactory Agreement ◽  
Power Output ◽  
Thermal Efficiency ◽  
Tangential Velocity ◽  
Limit Load ◽  
Two Dimensional ◽  
Low Pressure Turbine ◽  
Transonic Turbine ◽  
Maximum Tangential Velocity ◽  
Turbine Blading

Limit load represents the maximum tangential velocity or blade force that can be generated within a transonic turbine blade. Its accurate prediction is therefore extremely important if the expected thermal efficiency and power output from the turbine is to be obtained. This report presents methods of calculating limit load for typical transonic turbine blading. Comparisons are made between predictions and test data from: (a) two-dimensional stationary cascade and (b) model low pressure turbine with dry steam. Satisfactory agreement is shown between the predictive techniques and the test values of maximum tangential velocity.

Friction Reduction in the Sliding of an Elastic Half-Space Against a Rigid Surface Due to Incident Rectangular Dilatational Waves

1999 ◽  
Vol 122 (1) ◽  
pp. 10-15 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Normal Stress ◽  
Half Space ◽  
Coefficient Of Friction ◽  
Tangential Velocity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Friction Reduction ◽  
Rigid Surface ◽  
Rectangular Wave ◽  
The Coefficient Of Friction

The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. [S0742-4787(00)00201-0]

Minimum power consumption for drag reduction on a circular cylinder by tangential surface motion

2013 ◽  
Vol 715 ◽  
pp. 597-641 ◽  
Author(s):  
Ratnesh K. Shukla ◽  
Jaywant H. Arakeri
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Power Consumption ◽  
Drag Reduction ◽  
Drag Force ◽  
Potential Flow ◽  
Power Loss ◽  
Tangential Velocity ◽  
Two Dimensional ◽  
Tangential Surface

AbstractWe investigate the effect of a prescribed tangential velocity on the drag force on a circular cylinder in a spanwise uniform cross flow. Using a combination of theoretical and numerical techniques we make an attempt at determining the optimal tangential velocity profiles which will reduce the drag force acting on the cylindrical body while minimizing the net power consumption characterized through a non-dimensional power loss coefficient (${C}_{\mathit{PL}} $). A striking conclusion of our analysis is that the tangential velocity associated with the potential flow, which completely suppresses the drag force, is not optimal for both small and large, but finite Reynolds number. When inertial effects are negligible ($\mathit{Re}\ll 1$), theoretical analysis based on two-dimensional Oseen equations gives us the optimal tangential velocity profile which leads to energetically efficient drag reduction. Furthermore, in the limit of zero Reynolds number ($\mathit{Re}\ensuremath{\rightarrow} 0$), minimum power loss is achieved for a tangential velocity profile corresponding to a shear-free perfect slip boundary. At finite $\mathit{Re}$, results from numerical simulations indicate that perfect slip is not optimum and a further reduction in drag can be achieved for reduced power consumption. A gradual increase in the strength of a tangential velocity which involves only the first reflectionally symmetric mode leads to a monotonic reduction in drag and eventual thrust production. Simulations reveal the existence of an optimal strength for which the power consumption attains a minima. At a Reynolds number of 100, minimum value of the power loss coefficient (${C}_{\mathit{PL}} = 0. 37$) is obtained when the maximum in tangential surface velocity is about one and a half times the free stream uniform velocity corresponding to a percentage drag reduction of approximately 77 %; ${C}_{\mathit{PL}} = 0. 42$ and $0. 50$ for perfect slip and potential flow cases, respectively. Our results suggest that potential flow tangential velocity enables energetically efficient propulsion at all Reynolds numbers but optimal drag reduction only for $\mathit{Re}\ensuremath{\rightarrow} \infty $. The two-dimensional strategy of reducing drag while minimizing net power consumption is shown to be effective in three dimensions via numerical simulation of flow past an infinite circular cylinder at a Reynolds number of 300. Finally a strategy of reducing drag, suitable for practical implementation and amenable to experimental testing, through piecewise constant tangential velocities distributed along the cylinder periphery is proposed and analysed.

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