Uncoupling the effects of aspect ratio, Reynolds number and Rossby number on a rotating insect-wing planform

2018 ◽  
Vol 859 ◽  
pp. 921-948 ◽  
Author(s):  
Shantanu S. Bhat ◽  
Jisheng Zhao ◽  
John Sheridan ◽  
Kerry Hourigan ◽  
Mark C. Thompson
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Stokes Equations ◽  
Rotation Axis ◽  
Leading Edge ◽  
Rossby Number ◽  
Insect Wing ◽  
Wide Range ◽  
The Individual

The individual and combined influences of aspect ratio ($A$), Reynolds number ($Re$) and Rossby number ($Ro$) on the leading-edge vortex (LEV) of a rotating wing of insect-like planform are investigated numerically. A previous study from our group has determined the wingspan to be an appropriate length scale governing the large-scale LEV structure. In this study, the $A$ range considered is further extended, to show that this scaling works well as $A$ is varied by a factor of 4 ($1.8\leqslant A\leqslant 7.28$) and over a $Re$ range of two orders of magnitude. The present study also extends this scaling for wings with an offset from the rotation axis, which is typically the case for actual insects and often for experiments. Remarkably, the optimum range of $A$ based on the lift coefficients at different $Re$ coincides with that observed in nature. The scaling based on the wingspan is extended to the acceleration terms of the Navier–Stokes equations, suggesting a modified scaling of $Ro$, which decouples the effects of $A$. A detailed investigation of the flow structures, by increasing $Ro$ in a wide range, reveals the weakening of the LEV due to the reduced spanwise flow, resulting in a reduced lift. Overall, the use of span-based scaling of $Re$ and $Ro$, together with $A$, may help reconcile apparent conflicting trends between observed variations in aerodynamic performance in different sets of experiments and simulations.

Flow Structure Above Stationary and Oscillating Low-Aspect-Ratio Wing

2012 ◽  
Author(s):  
Miguel R. Visbal ◽  
Daniel J. Garmann
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Structure ◽  
Large Scale ◽  
Lift Coefficient ◽  
Pressure Fluctuations ◽  
Leading Edge ◽  
Tip Vortex ◽  
Eddy Simulation ◽  
Moderate Reynolds Number

Computations have been carried out in order to describe the complex unsteady flow structure over a stationary and plunging aspect-ratio-two wing under low Reynolds number conditions (Rec = 104). The flow fields are computed employing a high-fidelity implicit large-eddy simulation (ILES) approach found to be effective for moderate Reynolds number flows exhibiting mixed laminar, transitional and turbulent regions. The evolution of the flow structure and aerodynamic loading as a function of increasing angle of attack is presented. Lift and pressure fluctuations are found to be primarily dominated by the large scale circulatory pattern established above the wing due to separation from the leading edge, and by the inherent three dimensionality of the flow induced by the finite aspect ratio. The spanwise distribution of the sectional lift coefficient revealed only a minor direct contribution to the loading exherted by the tip vortex. High-frequency, small-amplitude oscillations are shown to have a significant effect on the separation process and accompanying loads suggesting potential flow control through either suitable actuation or aero-elastic tailoring.

Local Heat Transfer in Internally Cooled Turbine Airfoil Leading Edge Regions: Part II—Impingement Cooling With Film Coolant Extraction

1990 ◽  
Vol 112 (3) ◽  
pp. 459-466 ◽  
Author(s):  
D. E. Metzger ◽  
R. S. Bunker
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Film Cooling ◽  
Large Scale ◽  
Internal Heat ◽  
Leading Edge ◽  
Stagnation Line ◽  
Nusselt Numbers ◽  
Wide Range

An experimental study has been designed and performed to measure very localized internal heat transfer characteristics in large-scale models of turbine blade impingement-cooled leading edge regions that allow extraction, or bleed-off, of a portion of the internal cooling flow to provide leading edge film cooling along the blade external surface. The internal impingement air is provided by a single line of equally spaced multiple jets, aimed at the leading edge apex and generally exiting, minus the bleed-off flow, in the opposite or chordwise direction. The film coolant flow extraction takes place through two lines of holes, one each on the blade suction side and the blade pressure side, both fairly close to the airfoil leading edge. Detailed two-dimensional local surface Nusselt number distributions have been obtained through the use of aerodynamically steady but thermally transient tests employing temperature-indicating coatings. The thin coatings are sprayed directly on the test surfaces, and are observed during a test transient with automated computer vision and data acquisition systems. A wide range of parameter combinations of interest in cooled airfoil practice is covered in the test matrix, including combinations of variations in jet Reynolds number, airfoil leading edge sharpness, jet pitch-to-diameter ratio, and jet nozzle-to-apex travel distance. Measured local Nusselt numbers at each chordwise location back from the stagnation line have been used to calculate both the spanwise-average Nusselt numbers and spanwise Nusselt number gradients as functions of chordwise position. The results without film coolant extraction, presented in the Part I companion paper, are used as a basis of comparison to determine the additional effects of the film cooling bleed. Results indicate that heat transfer is primarily dependent on jet Reynolds number with smaller influences from the flow extraction rate. The results also suggest that changes in the spanwise alignment of the impingement nozzles relative to the position of the film cooling holes can cause significant variations in leading edge metal temperatures.

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.

Performance Estimation of Axial Flow Turbines

1970 ◽  
Vol 185 (1) ◽  
pp. 407-424 ◽  
Author(s):  
H. R. M. Craig ◽  
H. J. A. Cox
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Axial Flow ◽  
Performance Estimation ◽  
Speed Ratio ◽  
Test Results ◽  
Wide Range ◽  
Relevant Variables

A comprehensive method of estimating the performance of axial flow steam and gas turbines is presented, based on analysis of linear cascade tests on blading, on a number of turbine test results, and on air tests of model casings. The validity of the use of such data is briefly considered. Data are presented to allow performance estimation of actual machines over a wide range of Reynolds number, Mach number, aspect ratio and other relevant variables. The use of the method in connection with three-dimensional methods of flow estimation is considered, and data presented showing encouraging agreement between estimates and available test results. Finally ‘carpets’ are presented showing the trends in efficiencies that are attainable in turbines designed over a wide range of loading, axial velocity/blade speed ratio, Reynolds number and aspect ratio.

scholarly journals Solsticial Hadley Cell ascending edge theory from supercriticality

2021 ◽  
Author(s):  
Spencer A. Hill ◽  
Simona Bordoni ◽  
Jonathan L. Mitchell
Keyword(s):  
Large Scale ◽  
Analytical Approximation ◽  
Hadley Cell ◽  
Rossby Number ◽  
Absolute Vorticity ◽  
Rotation Rates ◽  
Planetary Rotation ◽  
Wide Range ◽  
Summer Hemisphere ◽  
Earth’S Climate

AbstractHow far the Hadley circulation’s ascending branch extends into the summer hemisphere is a fundamental but incompletely understood characteristic of Earth’s climate. Here, we present a predictive, analytical theory for this ascending edge latitude based on the extent of supercritical forcing. Supercriticality sets the minimum extent of a large-scale circulation based on the angular momentum and absolute vorticity distributions of the hypothetical state were the circulation absent. We explicitly simulate this latitude-by-latitude radiative-convective equilibrium (RCE) state. Its depth-averaged temperature profile is suitably captured by a simple analytical approximation that increases linearly with sinφ, where φ is latitude, from the winter to the summer pole. This, in turn, yields a one-third power-law scaling of the supercritical forcing extent with the thermal Rossby number. In moist and dry idealized GCM simulations under solsticial forcing performed with a wide range of planetary rotation rates, the ascending edge latitudes largely behave according to this scaling.

scholarly journals Dependence of Model Energy Spectra on Vertical Resolution

2016 ◽  
Vol 144 (4) ◽  
pp. 1407-1421 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Vertical Mixing ◽  
Energy Spectra ◽  
Small Scale ◽  
Rossby Number ◽  
Vertical Resolution ◽  
Wide Range ◽  
Qualitative Shape ◽  
Vertical Grid

Abstract Many high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of −3 at large horizontal scales that shallows to approximately −5/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Δz. Energy spectra are converged for Δz 200 m but are very sensitive to resolution with 500 m ≤ Δz ≤ 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.

scholarly journals On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

2018 ◽  
Vol 15 (143) ◽  
pp. 20170933 ◽  
Author(s):  
T. Jardin ◽  
T. Colonius
Keyword(s):  
Aspect Ratio ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Rossby Number ◽  
Subsequent Work ◽  
High Lift ◽  
Low Aspect Ratio ◽  
Axis Of Rotation ◽  
Edge Vortex ◽  
Convergent Solution

Lentink & Dickinson (2009 J. Exp. Biol. 212 , 2705–2719. ( doi:10.1242/jeb.022269 )) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Experimental analysis of fluid-structure interaction in flexible wings at low Reynolds number flows

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Serdar Genç ◽  
Hacımurat Demir ◽  
Mustafa Özden ◽  
Tuna Murat Bodur
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Fluid Structure Interaction ◽  
Leading Edge ◽  
Flexible Wings ◽  
Flexible Membrane ◽  
Fluid Structure ◽  
Content Type ◽  
Structure Interaction ◽  
Membrane Deformations

Purpose The purpose of this exhaustive experimental study is to investigate the fluid-structure interaction in the flexible membrane wings over a range of angles of attack for various Reynolds numbers. Design/methodology/approach In this paper, an experimental study on fluid-structure interaction of flexible membrane wings was presented at Reynolds numbers of 2.5 × 104, 5 × 104 and 7.5 × 104. In the experimental studies, flow visualization, velocity and deformation measurements for flexible membrane wings were performed by the smoke-wire technique, multichannel constant temperature anemometer and digital image correlation system, respectively. All experimental results were combined and fluid-structure interaction was discussed. Findings In the flexible wings with the higher aspect ratio, higher vibration modes were noticed because the leading-edge separation was dominant at lower angles of attack. As both Reynolds number and the aspect ratio increased, the maximum membrane deformations increased and the vibrations became visible, secondary vibration modes were observed with growing the leading-edge vortices at moderate angles of attack. Moreover, in the graphs of the spectral analysis of the membrane displacement and the velocity; the dominant frequencies coincided because of the interaction of the flow over the wings and the membrane deformations. Originality/value Unlike available literature, obtained results were presented comparatively using the sketches of the smoke-wire photographs with deformation measurement or turbulence statistics from the velocity measurements. In this study, fluid-structure interaction and leading-edge vortices of membrane wings were investigated in detail with increasing both Reynolds number and the aspect ratio.

On the Response of a Strongly Diffusing Flow to Propagating Wakes

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
J. P. Gostelow ◽  
R. L. Thomas ◽  
D. S. Adebayo
Keyword(s):  
Flat Plate ◽  
Large Scale ◽  
Separation Bubble ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Turbulent Spots ◽  
Stall Margin ◽  
Transverse Jet ◽  
Wide Range ◽  
Calming Effect

Further evidence on the similarities between transition and separation phenomena occurring in turbomachinery and wind tunnel flows is provided by measurements on a large scale flat plate under a strong adverse pressure gradient. The flat plate has a long laminar separation bubble and is subjected to a range of disturbances with triggering caused by injection of a transverse jet and subsequently by wakes generated by rods moving transversely upstream of the leading edge. Wakes were originally presented individually. Each individual wake provoked a vigorous turbulent patch, resulting in the instantaneous collapse of the separation bubble. This was followed by a very strong, and stable, calmed region. Following the lead given by the experiments of Gutmark and Blackwelder (1987, “On the Structure of Turbulent Spot in a Heated Laminar Boundary Layer,” Exp. Fluids, 5, pp. 207–229.) on triggered turbulent spots, wakes were then presented in pairs at different wake spacing intervals. In this way wake interaction effects could be investigated in more detail. As in the work on triggered turbulent spots the spacing between impinging wakes was systematically varied; it was found that for close wake spacings the calmed region acted to suppress the turbulence in the following turbulent patch. To investigate whether this phenomenon was a recurring one or whether the flow then reverted back to its unperturbed state, the experiments were repeated with three and four rods instead of two. This has the potential for making available a wide range of variables including direction and speed of rod rotation. It was found that the subsequent wakes were also suppressed by the calming effect. It may be anticipated that this repeating situation is present in a turbomachine, resulting in hidden benefits for blade count and efficiency. There may also conceivably be blade loading advantages while retaining favorable heat transfer conditions in high pressure turbines or stall margin in axial compressors. The inherent and prospective benefits of the calming effect therefore need to be understood thoroughly and new opportunities exploited where this is feasible.a

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