Small Reynolds Number Convection in Rotating Spherical Annuli

1979 ◽  
Vol 101 (3) ◽  
pp. 427-433 ◽  
Author(s):  
R. W. Douglass ◽  
E. J. Shaughnessy ◽  
B. R. Munson
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Velocity Ratio ◽  
Perturbation Expansion ◽  
Reynolds Numbers ◽  
Regular Perturbation ◽  
Optimum Configuration ◽  
Wide Range ◽  
Boussinesq Fluid ◽  
Steady Convection

A fourth order regular perturbation expansion in powers of the Reynolds number is used to investigate the steady convection of a stratified Boussinesq fluid in rotating spherical annuli. The results include the primary and secondary flow patterns, temperature distributions, total heat flux, and torque characteristics emphasizing their dependence on a wide range of radius and angular velocity ratios. Maximum usable Reynolds numbers were found and usually were larger than 10. The optimum configuration for convective heat transfer is a radius ratio of 0.35 and an angular velocity ratio of +1/3. This same configuration gives the largest torque as well.

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.

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.

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.

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.

Hot-wire spatial resolution issues in wall-bounded turbulence

2009 ◽  
Vol 635 ◽  
pp. 103-136 ◽  
Author(s):  
N. HUTCHINS ◽  
T. B. NICKELS ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Spatial Resolution ◽  
Reynolds Numbers ◽  
Energy Spectra ◽  
Small Scale ◽  
Wire Length ◽  
Hot Wire ◽  
Wide Range ◽  
Near Wall

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

Transverse Oscillations of a Jet in a Jet-Splitter System

1972 ◽  
Vol 94 (3) ◽  
pp. 675-681 ◽  
Author(s):  
D. O. Rockwell
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Nozzle Exit ◽  
Reynolds Numbers ◽  
Dimensionless Frequency ◽  
Two Dimensional ◽  
Vena Contracta ◽  
Wide Range ◽  
Jet Behavior ◽  
Transverse Oscillations

The fundamental transverse oscillations of a liquid jet which impinged upon a flow splitter were examined for a wide range of dimensionless splitter distance, nozzle exit Reynolds number, and dimensionless frequency. The results are presented in the form of a design map. The data, taken at low nozzle aspect ratio, reveal that fundamental (stage 1) oscillations can exist for Reynolds numbers up to at least 7000. Up to Reynolds numbers of about 3000, the jet behavior is Reynolds number dependent for all values of splitter distance. Beyond Reynolds number of 3000 the jet behavior is independent of Reynolds number. In general, the Strouhal number, based on nozzle exit-splitter distance, decreases with increasing values of splitter distance. Jets issuing from nozzles with no parallel development sections were considered. Jet nozzle shape influences the dimensionless frequency of oscillation in that the effect of a vena contracta formation outside the nozzle exit is to yield a higher value of dimensionless frequency relative to nozzles which produce parallel flow with small boundary layer thickness at the exit. Similar decreases have been found for two-dimensional jets. Of the above findings, the only comparable results for two-dimensional jets are variations in Strouhal number with nozzle exit-splitter distance.

Modeling Reynolds-Number Effects in Wall-Bounded Turbulent Flows

1996 ◽  
Vol 118 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. M. C. So ◽  
H. Aksoy ◽  
S. P. Yuan ◽  
T. P. Sommer
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Strain Tensor ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Wide Range ◽  
Peak Shear Stress ◽  
Reynolds Number Effects ◽  
Near Wall

Recent experimental and direct numerical simulation data of two-dimensional, isothermal wall-bounded incompressible turbulent flows indicate that Reynolds-number effects are not only present in the outer layer but are also quite noticeable in the inner layer. The effects are most apparent when the turbulence statistics are plotted in terms of inner variables. With recent advances made in Reynolds-stress and near-wall modeling, a near-wall Reynolds-stress closure based on a recently proposed quasi-linear model for the pressure strain tensor is used to analyse wall-bounded flows over a wide range of Reynolds numbers. The Reynolds number varies from a low of 180, based on the friction velocity and pipe radius/channel half-width, to 15406, based on momentum thickness and free stream velocity. In all the flow cases examined, the model replicates the turbulence statistics, including the Reynolds-number effects observed in the inner and outer layers, quite well. Furthermore, the model reproduces the correlation proposed for the location of the peak shear stress and an appropriately defined Reynolds number, and the variations of the near-wall asymptotes with Reynolds numbers. It is conjectured that the ability of the model to replicate the asymptotic behavior of the near-wall flow is most responsible for the correct prediction of the Reynolds-number effects.

Numerical Prediction of Turbulent Flow in Rotating Cavities

1988 ◽  
Vol 110 (2) ◽  
pp. 202-211 ◽  
Author(s):  
A. P. Morse
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Predictive Accuracy ◽  
Turbulent Transport ◽  
Reynolds Numbers ◽  
Spreading Rate ◽  
Flow Conditions ◽  
Wide Range ◽  
Ekman Layers ◽  
Radial Outflow

Predictions of the isothermal, incompressible flow in the cavity formed between two corotating plane disks and a peripheral shroud have been obtained using an elliptic calculation procedure and a low turbulence Reynolds number k–ε model for the estimation of turbulent transport. Both radial inflow and outflow are investigated for a wide range of flow conditions involving rotational Reynolds numbers up to ∼106. Although predictive accuracy is generally good, the computed flow in the Ekman layers for radial outflow often displays a retarded spreading rate and a tendency to laminarize under conditions that are known from experiment to produce turbulent flow.

Experiments With Three-Dimensional Passive Flow Control Devices on Low-Pressure Turbine Airfoils

2004 ◽  
Vol 128 (2) ◽  
pp. 251-260 ◽  
Author(s):  
Douglas G. Bohl ◽  
Ralph J. Volino
Keyword(s):  
Reynolds Number ◽  
Flow Control ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Turbine Airfoils

The effectiveness of three-dimensional passive devices for flow control on low pressure turbine airfoils was investigated experimentally. A row of small cylinders was placed at the pressure minimum on the suction side of a typical airfoil. Cases with Reynolds numbers ranging from 25,000 to 300,000 (based on suction surface length and exit velocity) were considered under low freestream turbulence conditions. Streamwise pressure profiles and velocity profiles near the trailing edge were documented. Without flow control a separation bubble was present, and at the lower Reynolds numbers the bubble did not close. Cylinders with two different heights and a wide range of spanwise spacings were considered. Reattachment moved upstream as the cylinder height was increased or the spacing was decreased. If the spanwise spacing was sufficiently small, the flow at the trailing edge was essentially uniform across the span. The cylinder size and spacing could be optimized to minimize losses at a given Reynolds number, but cylinders optimized for low Reynolds number conditions caused increased losses at high Reynolds numbers. The effectiveness of two-dimensional bars had been studied previously under the same flow conditions. The cylinders were not as effective for maintaining low losses over a range of Reynolds numbers as the bars.

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