scholarly journals Fully-printed metamaterial-type flexible wings with controllable flight characteristics

2021 ◽  
Author(s):  
Igor' Zhilyaev ◽  
Nitesh Anerao ◽  
Ajay Giri Prakash Kottapalli ◽  
Cihat Yilmaz ◽  
Mustafa Murat ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Low Frequency ◽  
Optimization Procedure ◽  
Structural Equations ◽  
Flapping Flight ◽  
Resonance Excitation ◽  
Periodic Pattern ◽  
Insect Wings

Abstract Insect wings are an outstanding example of how a proper interplay of rigid and flexible materials enables an intricate flapping flight accompanied by sound. The understanding of the aerodynamics and acoustics of insect wings have enabled the development of man-made flying robotic vehicles and explained basic mechanisms of sound generation by natural flyers. This work proposes the concept of artificial wings with a periodic pattern, inspired by metamaterials, and explores how the pattern geometry can be used to control the aerodynamic and acoustic characteristics of the wing. For this, we analyzed bio-inspired wings with anisotropic honeycomb patterns flapping at a low frequency and developed a multi-parameter optimization procedure to tune the pattern design in order to increase lift and, simultaneously, manipulate the produced sound. Our analysis is based on the finite-element solution to a transient three-dimensional fluid-structure interactions problem. The two-way coupling is described by incompressible Navier-Stokes equations for viscous air and structural equations of motion for a wing undergoing large deformations. We manufactured three wing samples by means of 3D printing and validated their robustness and dynamics experimentally. Importantly, we showed that the proposed wings can sustain long-term resonance excitation that opens a possibility to implement resonance-type flights inherent to certain natural flyers. Our results confirm the feasibility of the metamaterial patterns to control the flapping flight dynamics and can open new perspectives for applications of 3D-printed patterned wings, e.g., in the design of drones with the target sound.

scholarly journals Three-dimensional instabilities in compressible flow over open cavities

2008 ◽  
Vol 599 ◽  
pp. 309-339 ◽  
Author(s):  
GUILLAUME A. BRÈS ◽  
TIM COLONIUS
Keyword(s):  
Compressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Vortical Flow ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Mean Flow ◽  
Aspect Ratios ◽  
Open Cavities

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

scholarly journals How Euglena gracilis swims: flow field reconstruction and analysis

2020 ◽  
Author(s):  
Nicola Giuliani ◽  
Massimiliano Rossi ◽  
Giovanni Noselli ◽  
Antonio DeSimone
Keyword(s):  
Flow Field ◽  
Euglena Gracilis ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Body ◽  
Coarse Grained ◽  
Optimal Interpolation ◽  
Flow Field Reconstruction ◽  
Surrounding Fluid

AbstractEuglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke, and the three-dimensional flows that they generate in the surrounding fluid.Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke.We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching.Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.

Analysis of Conjugate Heat Transfer in a Three-Dimensional Microchannel Heat Sink for Cooling of Electronic Components

1999 ◽  
Author(s):  
Andrei G. Fedorov ◽  
Raymond Viskanta
Keyword(s):  
Heat Transfer ◽  
Heat Sink ◽  
Conjugate Heat Transfer ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Solid Substrate ◽  
Microchannel Heat Sink ◽  
Three Dimensional Model ◽  
Wide Range

Abstract A three-dimensional model is developed to investigate flow and conjugate heat transfer in the microchannel-based heat sink for electronic packaging applications. The incompressible laminar flow Navier-Stokes equations of motion as well as the energy conservation equations for the fluid and solid are employed as the governing model equations which are numerically solved using the generalized single-equation framework for solving conjugate problems. First, the theoretical model developed is validated by comparing the model predictions of the thermal resistance and the friction coefficient with available experimental data for a wide range of Reynolds numbers. Then, the parametric calculations are performed to investigate the effects of different working fluids, solid substrate materials and channel geometry on conjugate heat transfer in the microchannel heat sink. The bulk and wall temperature and heat flux distributions as well as the average heat transfer characteristics are reported and discussed. Important practical design recommendations are also provided regarding the cooling efficiency of the microchannel heat sink.

scholarly journals Deterioration of Thermal Barrier Coated Turbine Blades by Erosion

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rohan Swar ◽  
Awatef Hamed ◽  
Dongyun Shin ◽  
Nathanial Woggon ◽  
Robert Miller
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Computational Study ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Particle Surface ◽  
Three Dimensional ◽  
Thermal Barrier ◽  
Erosion Rates ◽  
Particle Ingestion

A combined experimental and computational study was conducted to investigate the erosion of thermal barrier coated (TBC) blade surfaces by alumina particles ingestion in a single-stage turbine. In the experimental investigation, tests were performed to determine the erosion rates and particle restitution characteristics under different impact conditions. The experimental results show that the erosion rates increase with increased impingement angle, impact velocity, and temperature. In the computational simulations, an Euler-Lagrangian two-stage approach is used in obtaining numerical solutions to the three-dimensional compressible Reynolds-Averaged Navier-Stokes equations and the particles equations of motion in each blade passage reference frame. User defined functions (UDFs) were developed to represent experimentally based correlations for particle surface interaction models and TBC erosion rates models. UDFs were employed in the three-dimensional particle trajectory simulations to determine the particle rebound characteristics and TBC erosion rates on the blade surfaces. Computational results are presented in a commercial turbine and a NASA-designed automotive turbine. The similarities between the erosion patterns in the two turbines are discussed for uniform particle ingestion and for particle ingestion concentrated in the inner and outer 5% of the stator blade span to represent the flow cooling of the combustor liner.

A series-expansion study of the Navier–Stokes equations with applications to three-dimensional separation patterns

1986 ◽  
Vol 173 ◽  
pp. 207-223 ◽  
Author(s):  
A. E. Perry ◽  
M. S. Chong
Keyword(s):  
Series Expansion ◽  
Arbitrary Order ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Continuity Equations

An algorithm has been developed which enables local Taylor-series-expansion solutions of the Navier-Stokes and continuity equations to be generated to arbitrary order. Much of the necessary algebra for generating these solutions can be done on a computer. Various properties of the algorithm are investigated and checked by making comparisons with known solutions of the equations of motion. A method of synthesizing nonlinear viscous-flow patterns with certain required properties is developed and applied to the construction of a number of two- and three-dimensional flow-separation patterns. These patterns are asymptotically exact solutions of the equations of motion close to the origin of the expansion. The region where the truncated series solution satisfies the full equations of motion to within a specified accuracy can be found.

Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave

2002 ◽  
Vol 450 ◽  
pp. 1-33 ◽  
Author(s):  
HERMANN F. FASEL
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Free Stream Turbulence ◽  
Turbulent Transition ◽  
Tollmien Schlichting

Direct numerical simulations (DNS) of the Navier–Stokes equations are used to investigate the role of the Klebanoff-mode in laminar–turbulent transition in a flatplate boundary layer. To model the effects of free-stream turbulence, volume forces are used to generate low-frequency streamwise vortices outside the boundary layer. A suction/blowing slot at the wall is used to generate a two-dimensional Tollmien–Schlichting (TS) wave inside the boundary layer. The characteristics of the fluctuations inside the boundary layer agree very well with those measured in experiments. It is shown how the interaction of the Klebanoff-mode with the two-dimensional TS-wave leads to the formation of three-dimensional TS-wavepackets. When the disturbance amplitudes reach a critical level, a fundamental resonance-type secondary instability causes the breakdown of the TS-wavepackets into turbulent spots.

Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins

1995 ◽  
Vol 293 ◽  
pp. 147-180 ◽  
Author(s):  
Travis L. Dodd ◽  
Daniel A. Hammer ◽  
Ashok S. Sangani ◽  
Donald L. Koch
Keyword(s):  
Stokes Equations ◽  
Biological Membrane ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Multipole Expansion ◽  
Hydrodynamic Interactions ◽  
Viscous Drag ◽  
Low Viscosity ◽  
Fixed Beds ◽  
Short Time

Proteins in a biological membrane can be idealized as disks suspended in a thin viscous sheet surrounded by a fluid of lower viscosity (Saffman 1976). To determine the effect of hydrodynamic interactions on protein diffusivities in non-dilute suspensions, we numerically solve the Stokes equations of motion for a system of disks in a bounded periodic two-dimensional fluid using a multipole expansion technique. We consider both free suspensions, in which all the proteins are mobile, and fixed beds, in which a fraction of the proteins are fixed. For free suspensions, we determine both translational and rotational short-time self-diffusivities and the gradient diffusivity as a function of the area fraction of the disks. The translational self- and gradient diffusivities computed in this way grow logarithmically with the number of disks owing to Stokes paradox; to obtain finite values, we renormalize our simulation results by treating long-range interactions in terms of a membrane with an enhanced viscosity in contact with a low-viscosity three-dimensional fluid. The diffusivities in fixed beds require no such adjustment because, at non-dilute area fractions of disks, the Brinkman screening of hydrodynamic interactions is more important that the viscous drag due to the surrounding three-dimensional fluid in limiting the range of hydrodynamic interactions. The diffusivities are determined as functions of the area fractions of both mobile and fixed proteins. We compare our results for diffusivities with experimental measurements of long-time protein self-diffusivity after adjusting our short-time diffusivities calculations in an approximate way to account for effects of hindered diffusion due to volume exclusion, and find very good agreement between the two.

scholarly journals Wave interactions in a three-dimensional attachment-line boundary layer

1990 ◽  
Vol 217 ◽  
pp. 367-390 ◽  
Author(s):  
Philip Hall ◽  
Sharon O. Seddougui
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Hydrodynamic Instability ◽  
Three Dimensional ◽  
Low Frequency ◽  
Leading Edge ◽  
Two Dimensional ◽  
Oblique Wave ◽  
Attachment Line

The three-dimensional boundary layer on a swept wing can support different types of hydrodynamic instability. Here attention is focused on the so-called ‘spanwise instability’ problem which occurs when the attachment-line boundary layer on the leading edge becomes unstable to Tollmien–Schlichting waves. In order to gain insight into the interactions that are important in that problem a simplified basic state is considered. This simplified flow corresponds to the swept attachment-line boundary layer on an infinite flat plate. The basic flow here is an exact solution of the Navier–Stokes equations and its stability to two-dimensional waves propagating along the attachment line can be considered exactly at finite Reynolds number. This has been done in the linear and weakly nonlinear regimes by Hall, Malik & Poll (1984) and Hall & Malik (1986). Here the corresponding problem is studied for oblique waves and their interaction with two-dimensional waves is investigated. In fact oblique modes cannot be described exactly at finite Reynolds number so it is necessary to make a high-Reynolds-number approximation and use triple-deck theory. It is shown that there are two types of oblique wave which, if excited, cause the destabilization of the two-dimensional mode and the breakdown of the disturbed flow at a finite distance from the leading edge. First a low-frequency mode closely related to the viscous stationary crossflow mode discussed by Hall (1986) and MacKerrell (1987) is a possible cause of breakdown. Secondly a class of oblique wave with frequency comparable with that of the two-dimensional mode is another cause of breakdown. It is shown that the relative importance of the modes depends on the distance from the attachment line.

Mixed Lagrangian–Eulerian description of vortical flows for ideal and viscous fluids

2008 ◽  
Vol 600 ◽  
pp. 167-180 ◽  
Author(s):  
E. A. KUZNETSOV
Keyword(s):  
Stokes Equations ◽  
Diffusion Tensor ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Lagrangian Description ◽  
Navier Stokes Equations ◽  
Vortical Flows ◽  
Eulerian Description ◽  
Vortex Lines

It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid is equivalent to the equations of motion of a charged compressible fluid moving due to a self-consistent electromagnetic field. The velocity of new auxiliary fluid coincides with the velocity component normal to the vorticity line for the primitive equations. Therefore this new hydrodynamics represents hydrodynamics of vortex lines. Their compressibility reveals a new mechanism for three-dimensional incompressible vortical flows connected with breaking (or overturning) of vortex lines which can be considered as one of the variants of collapses. Transition to the Lagrangian description in the new hydrodynamics corresponds, for the original Euler equations, to a mixed Lagrangian–Eulerian description – the vortex line representation (VLR). The Jacobian of this mapping defines the density of vortex lines. It is shown also that application of VLR to the Navier–Stokes equations results in an equation of diffusive type for the Cauchy invariant. The diffusion tensor for this equation is defined by the VLR metric.

Parameter Studies on the Effect of Boundary Conditions in Three-Dimensional Calculations of Bubble Column

2002 ◽  
Author(s):  
E. Bourloutski ◽  
M. Sommerfeld
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Bubble Column ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Fluid Phase ◽  
Time Dependent ◽  
Navier Stokes ◽  
Mass Force ◽  
Source Terms

This paper describes an extension and validation of the Euler/Lagrange approach for three-dimensional time-dependent calculations of the flow in a bubble column. The fluid phase was calculated based on the Euler approach solving the unsteady Reynolds-averaged Navier-Stokes equations in a time-dependent way. The conservation equations were closed using the standard k-ε turbulence model. The coupling between the phases is considered through the momentum source terms and source terms in the k- and ε-equations. The usage of the Consistent term for the k-equation and taking into account an additional dissipation due to the presence of small bubbles yielded a reasonable agreement of the predicted turbulent kinetic energy level with measurements. Bubble motion was calculated by solving the equations of motion taking into account drag force, pressure, added mass force, transverse lift force, buoyancy and gravity. Numerical calculations are presented providing information on the sensitivity of the results on several boundary conditions, such as disturbed aeration. The computational results are validated based on available measurements in a laboratory-scale bubble column.

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