On the impulsively started rotating sphere

1967 ◽  
Vol 27 (4) ◽  
pp. 779-788 ◽  
Author(s):  
K. E. Barrett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Series Solutions ◽  
Rotating Sphere ◽  
Boundary Layer Equations ◽  
Small Times ◽  
3 Omega

The velocity field generated in a fluid of viscosity, v, by impulsively starting at time t = 0, a sphere of radius a spinning with angular velocity Ω about a diameter is described using a new expansion variable 2 √vt/r. It is first shown how the standard time-dependent boundary-layer equations can be modified to give series solutions satisfying all the boundary conditions. Next, that these new solutions are relevant when the Reynolds number R = a2Ω/v goes to infinity in such a way that $R^{\frac{1}{3}} \Omega t$ is large. Lastly, solutions are given, applicable at small times for non-zero Reynolds numbers. These last expansions show that the velocity components decay algebraically rather than exponentially at large distances.

Separation and Stall of an Impulsively Started Elliptic Cylinder

1967 ◽  
Vol 34 (4) ◽  
pp. 823-828 ◽  
Author(s):  
Chang-Yi Wang
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Angle Of Attack ◽  
Elliptic Cylinder ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Thickness Ratio ◽  
Two Dimensional ◽  
Small Times ◽  
Weakly Dependent

Separation and stall of an impulsively started elliptic cylinder at an angle of attack are investigated through the method of inner and outer expansions. The assumptions are large Reynolds numbers and small times. The interactions between the boundary layer and the outer inviscid flow are taken into consideration. Uniformly valid solutions are obtained for general two-dimensional cylinders. The movements of the separation points on an elliptic cylinder are calculated. Stall is found to be strongly dependent on the thickness ratio and the angle of attack of the cylinder but to be weakly dependent on the Reynolds number.

scholarly journals Synchronization of low Reynolds number plane Couette turbulence

2021 ◽  
Vol 933 ◽  
Author(s):  
Marios-Andreas Nikolaidis ◽  
Petros J. Ioannou
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Fourier Decomposition ◽  
Critical Wavelength ◽  
Small Scales ◽  
Flow Components ◽  
Negative Characteristic ◽  
Active Subspace

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$ , that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

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).

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Velocity and Pressure Measurements Along a Row of Confined Cylinders

2006 ◽  
Author(s):  
Barton L. Smith ◽  
Jack J. Stepan ◽  
Donald M. McEligot
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Symmetry Plane ◽  
Field Measurements ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Recirculation Region ◽  
Pressure Measurements ◽  
Layer Transition ◽  
Flow Experiments

The results of flow experiments performed in a cylinder array designed to mimic a VHTR Nuclear Plant lower plenum design are presented. Pressure drop and velocity field measurements were made. Based on these measurements, five regimes of behavior are identified that are found to depend on Reynolds number. It is found that the recirculation region behind the cylinders is shorter than that of half cylinders placed on the wall representing the symmetry plane. Unlike a single cylinder, the separation point is found to always be on the rear of the cylinders, even at very low Reynolds number. Boundary layer transition is found to occur at much lower Reynolds numbers than previously reported.

The Critical Height of Distributed Roughness to Cause Boundary Layer Transition

1959 ◽  
Vol 63 (588) ◽  
pp. 722-722
Author(s):  
R. L. Dommett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Boundary Layer Transition ◽  
Critical Height ◽  
Layer Transition ◽  
Local Conditions ◽  
Additional Advantage ◽  
Boundary Layer Equations ◽  
General Method

It has been found that there is a critical height for “sandpaper” type roughness below which no measurable disturbances are introduced into a laminar boundary layer and above which transition is initiated at the roughness. Braslow and Knox have proposed a method of predicting this height, for flow over a flat plate or a cone, using exact solutions of the laminar boundary layer equations combined with a correlation of experimental results in terms of a Reynolds number based on roughness height, k, and local conditions at the top of the elements. A simpler, yet more general, method can be constructed by taking additional advantage of the linearity of the velocity profile near the wall in a laminar boundary layer.

Non-uniqueness in wakes and boundary layers

1984 ◽  
Vol 391 (1800) ◽  
pp. 1-26 ◽  
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Algebraic Decay ◽  
Scale Separation ◽  
Boundary Layer Equations ◽  
Classical Boundary ◽  
Streamlined Flow ◽  
High Reynolds

In streamlined flow past a flat plate aligned with a uniform stream, it is shown that ( a ) the Goldstein near-wake and ( b ) the Blasius boundary layer are non-unique solutions locally for the classical boundary layer equations, whereas ( c ) the Rott-Hakkinen very-near-wake appears to be unique. In each of ( a ) and ( b ) an alternative solution exists, which has reversed flow and which apparently cannot be discounted on immediate grounds. So, depending mainly on how the alternatives for ( a ), ( b ) develop downstream, the symmetric flow at high Reynolds numbers could have two, four or more steady forms. Concerning non-streamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressure-free viscous symmetric closure of a predominantly slender long wake beyond a large-scale separation. Features arising include non-uniqueness, singularities and algebraic behaviour, consistent with non-entraining shear layers with algebraic decay. Non-uniqueness also seems possible in reattachment onto a solid surface and for non-symmetric or pressure-controlled flows including the wake of a symmetric cascade.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

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