scholarly journals Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids

1998 ◽  
Vol 377 ◽  
pp. 267-312 ◽  
Author(s):  
A. A. DRAAD ◽  
G. D. C. KUIKEN ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Polymer Solutions ◽  
Reynolds Numbers ◽  
Cylindrical Pipe ◽  
Turbulent Transition ◽  
Wide Range ◽  
Flow Changes ◽  
Transition Points ◽  
The Stability

A cylindrical pipe facility with a length of 32 m and a diameter of 40 mm has been designed. The natural transition Reynolds number, i.e. the Reynolds number at which transition occurs as a result of non-forced, natural disturbances, is approximately 60 000. In this facility we have studied the stability of cylindrical pipe flow to imposed disturbances. The disturbance consists of periodic suction and injection of fluid from a slit over the whole circumference in the pipe wall. The injection and suction are equal in magnitude and each distributed over half the circumference so that the disturbance is divergence free. The amplitude and frequency can be varied over a wide range.First, we consider a Newtonian fluid, water in our case. From the observations we compute the critical disturbance velocity, which is the smallest disturbance at a given Reynolds number for which transition occurs. For large wavenumbers, i.e. large frequencies, the dimensionless critical disturbance velocity scales according to Re−1, while for small wavenumbers, i.e. small frequencies, it scales as Re−2/3. The latter is in agreement with weak nonlinear stability theory. For Reynolds numbers above 30 000 multiple transition points are found which means that increasing the disturbance velocity at constant dimensionless wavenumber leads to the following course of events. First, the flow changes from laminar to turbulent at the critical disturbance velocity; subsequently at a higher value of the disturbance it returns back to laminar and at still larger disturbance velocities the flow again becomes turbulent.Secondly, we have carried out stability measurements for (non-Newtonian) dilute polymer solutions. The results show that the polymers reduce in general the natural transition Reynolds number. The cause of this reduction remains unclear, but a possible explanation may be related to a destabilizing effect of the elasticity on the developing boundary layers in the entry region of the flow. At the same time the polymers have a stabilizing effect with respect to the forced disturbances, namely the critical disturbance velocity for the polymer solutions is larger than for water. The stabilization is stronger for fresh polymer solutions and it is also larger when the polymers adopt a more extended conformation. A delay in transition has been only found for extended fresh polymers where delay means an increase of the critical Reynolds number, i.e. the number below which the flow remains laminar at any imposed disturbance.

scholarly journals Laminar-to-turbulent transition of pipe flows through puffs and slugs

2008 ◽  
Vol 614 ◽  
pp. 425-446 ◽  
Author(s):  
MINA NISHI ◽  
BÜLENT ÜNSAL ◽  
FRANZ DURST ◽  
GAUTAM BISWAS
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Turbulent Pipe Flow ◽  
Test Facility ◽  
Pipe Flows ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Slug Flows

Laminar-to-turbulent transition of pipe flows occurs, for sufficiently high Reynolds numbers, in the form of slugs. These are initiated by disturbances in the entrance region of a pipe flow, and grow in length in the axial direction as they move downstream. Sequences of slugs merge at some distance from the pipe inlet to finally form the state of fully developed turbulent pipe flow. This formation process is generally known, but the randomness in time of naturally occurring slug formation does not permit detailed study of slug flows. For this reason, a special test facility was developed and built for detailed investigation of deterministically generated slugs in pipe flows. It is also employed to generate the puff flows at lower Reynolds numbers. The results reveal a high degree of reproducibility with which the triggering device is able to produce puffs. With increasing Reynolds number, ‘puff splitting’ is observed and the split puffs develop into slugs. Thereafter, the laminar-to-turbulent transition occurs in the same way as found for slug flows. The ring-type obstacle height, h, required to trigger fully developed laminar flows to form first slugs or puffs is determined to show its dependence on the Reynolds number, Re = DU/ν (where D is the pipe diameter, U is the mean velocity in the axial direction and ν is the kinematic viscosity of the fluid). When correctly normalized, h+ turns out to be independent of Reτ (where h+ = hUτ/ν, Reτ = DUτ/ν and $U_{\tau}\,{=}\,\sqrt{\tau_{w}/ \rho}$; τw is the wall shear stress and ρ is the density of the fluid).

The Effect of Pulsed Blowing on the Boundary Layer of a Highly Loaded Low Pressure Turbine Blade

2013 ◽  
Author(s):  
Marion Mack ◽  
Roland Brachmanski ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Highly Loaded

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Lid-Driven Square Cavity Flow: A Benchmark Solution with an 8192x8192 Grid

2021 ◽  
Author(s):  
Carlos Marchi ◽  
Cosmo D. Santiago ◽  
Carlos Alberto Rezende de Carvalho Junior
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Accurate Determination ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Discretization Error ◽  
Square Cavity ◽  
Solution Vector ◽  
Wide Range

Abstract The incompressible steady-state fluid flow inside a lid-driven square cavity was simulated using the mass conservation and Navier-Stokes equations. This system of equations is solved for Reynolds numbers of up to 10,000 to the accuracy of the computational machine round-off error. The computational model used was the second-order accurate finite volume method. A stable solution is obtained using the iterative multigrid methodology with 8192 × 8192 volumes, while degree-10 interpolation and Richardson extrapolation were used to reduce the discretization error. The solution vector comprised five entries of velocities, pressure, and location. For comparison purposes, 65 different variables of interest were chosen, such as velocity profile, its extremum values and location, extremum values and location of the stream function. The discretization error for each variable of interest was estimated using two types of estimators and their apparent order of accuracy. The variations of the 11 selected variables are shown across 38 Reynolds number values between 0.0001 and 10,000. In this study, we provide a more accurate determination of the Reynolds number value at which the upper secondary vortex appears. The results of this study were compared with those of several other studies in the literature. The current solution methodology was observed to produce the most accurate solution till date for a wide range of Reynolds numbers.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

On the Effects of Turbulence Modeling on the Fluid-Structure Interaction of a Rigid Cylinder

2016 ◽  
Author(s):  
Guilherme Feitosa Rosetti ◽  
Guilherme Vaz ◽  
André Luís Condino Fujarra
Keyword(s):  
Turbulence Modeling ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Turbulent Transition ◽  
Moving Cylinder ◽  
Wide Range ◽  
Cylinder Flow ◽  
Laminar Turbulent Transition

The cylinder flow is a canonical problem for Computational Fluid Dynamics (CFD), as it can display several of the most relevant issues for a wide class of flows, such as boundary layer separation, vortex shedding, flow instabilities, laminar-turbulent transition and others. Several applications also display these features justifying the amount of energy invested in studying this problem in a wide range of Reynolds numbers. The Unsteady Reynolds Averaged Navier Stokes (URANS) equations combined with simplifying assumptions for turbulence have been shown inappropriate for the captive cylinder flow in an important range of Reynolds numbers. For that reason, recent improvements in turbulence modeling has been one of the most important lines of research within that issue, aiming at better prediction of flow and loads, mainly targeting the three-dimensional effects and laminar-turbulent transition, which are so important for blunt bodies. In contrast, a much smaller amount of work is observed concerning the investigation of turbulent effects when the cylinder moves with driven or free motions. Evidently, larger understanding of the contribution of turbulence in those situations can lead to more precise mathematical and numerical modeling of the flow around a moving cylinder. In this paper, we present CFD calculations in a range of moderate Reynolds numbers with different turbulence models and considering a cylinder in captive condition, in driven and in free motions. The results corroborate an intuitive notion that the inertial effects indeed play very important role in determining loads and motions. The flow also seems to adapt to the motions in such a way that vortices are more correlated and less influenced by turbulence effects. Due to good comparison of the numerical and experimental results for the moving-cylinder cases, it is observed that the choice of turbulence model for driven and free motions calculations is markedly less decisive than for the captive cylinder case.

Supercritical Reynolds number simulation for two-dimensional flow over circular cylinders

1975 ◽  
Vol 70 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Edmond Szechenyi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Practical Significance ◽  
Circular Cylinders ◽  
Wind Tunnels ◽  
Bluff Bodies ◽  
Wide Range ◽  
Two Dimensional Flow ◽  
Different Diameters

In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number.This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn.

The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 2. Experimental investigation and comparison with computation

1971 ◽  
Vol 50 (4) ◽  
pp. 645-655 ◽  
Author(s):  
M. D. Hughes ◽  
J. H. Gerrard
Keyword(s):  
Free Surface ◽  
Pipe Flow ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Radial Component ◽  
Tube Diameter ◽  
Ring Vortex ◽  
Tracer Particles ◽  
The Stability ◽  
Cylindrical Reservoir

Flow visualization has been used quantitatively to determine the flow relative to a piston and a free surface started from rest. The discharge of water from a cylindrical reservoir was investigated. Flow with a free surface started from rest was found to have a critical Reynolds number (based on tube diameter and surface speed) of about 450 above which a ring vortex was produced just below the surface.Measurements at Reynolds numbers of 525 and 1200 were compared with computations made by the methods described in Part 1. The computed drift of tracer particles agreed well with observed values. The largest discrepancies occurred in the radial component of the drift in the early stages of the motion and amounted to 2½% of the tube diameter.

Recent Research on Cascade-Flow Problems

1966 ◽  
Vol 88 (1) ◽  
pp. 221-228 ◽  
Author(s):  
H. Schlichting ◽  
A. Das
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
High Speed ◽  
Research Work ◽  
Reynolds Numbers ◽  
Tip Clearance ◽  
Flow Problems ◽  
Flow Losses ◽  
Cascade Flow ◽  
Wide Range

A survey is given of extensive research work on cascade-flow problems carried out in recent years in Germany. A considerable part of this work was done in the Variable Density High Speed Cascade Wind Tunnel of the Deutsche Forschungsanstalt fu¨r Luftfahrt at Braunschweig, in which the Reynolds number and the Mach number of the cascade can be varied independently. For compressor cascades with blades of different thickness ratio extensive measurements of the aerodynamic coefficients have been carried out in a wide range of Mach numbers and Reynolds numbers. For very low Reynolds numbers, as they occur for jet engines in high-altitude flight, the influence of turbulence level on loss coefficients has been investigated. Furthermore, comprehensive investigations on secondary-flow losses are reported. The most important parameters in this connection are the ratio of blade length to blade chord, the tip clearance, the Reynolds number, and the deflection of the flow in the cascade. The influence of all these parameters on the secondary-flow losses has been clarified to a certain extent.

The Reynolds number and flaperon deflection influence taken into account when optimizing the wing airfoil of an unmanned aerial vehicle

2020 ◽  
Author(s):  
N.I. Kochurova ◽  
Ye.S. Parkhaev ◽  
N.V. Semenchikov
Keyword(s):  
Reynolds Number ◽  
Unmanned Aerial Vehicle ◽  
Multicriteria Optimization ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Horizontal Flight ◽  
Wide Range ◽  
Aerial Vehicle ◽  
Zero Values ◽  
Wing Airfoil

The paper considers the solutions to the multicriteria problem of optimizing the wing airfoil of a miniature unmanned aerial vehicle (MUAV) under various constraints. The study introduces the statement of the problem of multicriteria optimization of the airfoil shape, following the condition of MUAV horizontal flight, with an additional condition associated with a change in the flight Reynolds number of the MUAV wing. This statement of the problem allows us to optimize the airfoil, taking into account the load on the wing of the designed vehicle. The wing airfoil was optimized in a wide range of lift coefficients of Cya and Reynolds numbers. The study shows that taking into account the Reynolds number makes it possible to improve the quality of the result obtained during optimization, and introduces a technique for multicriteria optimization of the wing airfoil with sealed mechanization, i.e. with flaperon. Findings of research show that for equal values of the relative thickness, the mechanized airfoil obtained as a result of optimization has a lower center line camber (by 1.5%) than the optimized airfoil without mechanization, due to which a gain in the drag coefficient is achieved at close to zero values of the lift coefficient. The study shows how profitable the use of a wing airfoil with a flaperon on MUAV wings can be, in contrast to an airfoil without mechanization.

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