Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Small Parameter ◽  
Pipe Flow ◽  
Quantitative Estimation ◽  
Reynolds Numbers ◽  
Power Law Model ◽  
Viscosity Function ◽  
Small Reynolds Numbers ◽  
Title Problem ◽  
Flow Enhancement ◽  
Method Of Small Parameter

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

scholarly journals Force distribution on a slender body close to an interface

1981 ◽  
Vol 24 (1) ◽  
pp. 27-36 ◽  
Author(s):  
J.R. Blake ◽  
G.R. Fulford
Keyword(s):  
Reynolds Numbers ◽  
Plane Wall ◽  
Slender Body ◽  
Force Distribution ◽  
Immiscible Liquids ◽  
Flat Interface ◽  
Small Reynolds Numbers ◽  
Rigid Plane ◽  
Limiting Case ◽  
Analytical Expressions

The motion of a slender body parallel and very close to a flat interface which separates two immiscible liquids of differing density and viscosity is considered for very small Reynolds numbers. Approximate analytical expressions are obtained for the distribution of forces acting on the slender body. The limiting case of a rigid plane wall yields results obtained previously.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

scholarly journals Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit

2019 ◽  
Vol 874 ◽  
pp. 699-719 ◽  
Author(s):  
Jose M. Lopez ◽  
George H. Choueiri ◽  
Björn Hof
Keyword(s):  
Drag Reduction ◽  
Turbulent Flows ◽  
Pipe Flow ◽  
Domain Size ◽  
Reynolds Numbers ◽  
Weissenberg Number ◽  
Pipe Length ◽  
Low Reynolds Numbers ◽  
Maximum Drag Reduction ◽  
Low Reynolds

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers ($Re$) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $Re$ near transition we find that, indeed, with increasing Weissenberg number ($Wi$), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in $Wi$, the flow fully relaminarizes, in agreement with recent experiments. At even larger $Wi$, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low$Re$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
Author(s):  
Alain Merlen ◽  
Christophe Frankiewicz
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Around A Cylinder ◽  
Low Reynolds Numbers ◽  
Initial Location ◽  
Upstream Pressure ◽  
Small Reynolds Numbers ◽  
Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

scholarly journals MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

2020 ◽  
Vol 46 (4) ◽  
pp. 91-101
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Prandtl Number ◽  
Energy Equation ◽  
Transport Model ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Shear Stress Transport Model ◽  
Small Reynolds Numbers ◽  
Prandtl Numbers

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist. 

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