Entropy and fractal perspectives of a flapping wing subjected to gust

2021 ◽  
pp. 095441002199329
Author(s):  
Manabendra M De ◽  
Jaideep S Mathur ◽  
Sankaranarayanan Vengadesan
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Operating Regime ◽  
Flapping Wing ◽  
Navier Stokes ◽  
Fluctuation Analysis ◽  
Navier Stokes Equations ◽  
Order Of Magnitude ◽  
Aerial Vehicle ◽  
Dynamic Meshing

Studies on entomopter’s performance under the influence of gust have received impetus in the past decade. There exists a dire need to ascertain the threshold of the frontal gusty conditions which would destabilize these anthropogenic flyers. This would help to devise methods to mitigate the detrimental effects of gust. In light of this aspect, the present study aims at analyzing the onsets of instability in a flapping wing system subjected to temporal gust by employing recurrence period density entropy (RPDE) and detrended fluctuation analysis (DFA). Simulation of the flapping wing along inclined stroke is carried out for a Reynolds number of 150. This Reynolds number lies in the typical operating regime of fruit flies and entomopters like the Pico aerial vehicle. Numerical simulations are carried out to solve the laminar, unsteady, and incompressible Navier–Stokes equations. The dynamic meshing technique is employed to model flapping kinematics. Nine gusts with a combination of frequency and velocity ratios of 0.1, 0.5, and 1.0 are considered. Instantaneous horizontal and vertical forces are estimated. Time series of these forces are analyzed using RPDE and DFA paradigms. These analyses indicate that gust frequency of an order of magnitude higher than flapping frequency and gust amplitude of the order of magnitude as the wing’s root mean square velocity induces a possible onset of instability.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

A Conceptual Model of Flapping-Wing Mechanism Inspired from the Results of Numerical Study

2013 ◽  
Vol 397-400 ◽  
pp. 783-788
Author(s):  
Xing Wei Zhang ◽  
Chao Wang ◽  
Hang Liu
Keyword(s):  
Conceptual Model ◽  
Power Efficiency ◽  
Stokes Equations ◽  
Numerical Study ◽  
Flapping Wing ◽  
Numerical Results ◽  
Navier Stokes ◽  
Active Deformation ◽  
Navier Stokes Equations ◽  
Wing Model

This paper investigates the aerodynamic forces of several plunging wing models by means of computational fluid dynamics. A finite volume method was used to solve the two-dimensional unsteady incompressible Navier-Stokes equations. The forces and power efficiency have been calculated and compared between sets of different models. Current work found that the nonsymmetrical moving can enhance the lift and thrust forces. The numerical results also prove that the flexible wing model can be use to improve the efficiency and reduce the input. Additionally, a new conceptual model for flapping wing mechanism with active deformation and adaptive nonsymmetrical driving motion is proposed base on the numerical results.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

scholarly journals Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

2021 ◽  
Vol 8 (3) ◽  
pp. 418-424
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G. Sankara Sekhar Raju
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Partial Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Slip Conditions ◽  
Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

Flow induced by jets and plumes

1981 ◽  
Vol 108 ◽  
pp. 55-65 ◽  
Author(s):  
W. Schneider
Keyword(s):  
Stokes Equations ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Jet ◽  
Order Of Magnitude ◽  
Valid Solution ◽  
Solid Walls

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

An Implicit Multigrid Scheme for the Compressible Navier-Stokes Equations With Low-Reynolds-Number Turbulence Closure

1998 ◽  
Vol 120 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Peter Gerlinger ◽  
Dieter Bru¨ggemann
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Convergence Acceleration ◽  
Iterative Solvers ◽  
Turbulence Closure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds ◽  
Turbulence Transport

A multigrid method for convergence acceleration is used for solving coupled fluid and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed, which requires very fine grids in the near wall regions. Due to the use of fine grids, convergence of most iterative solvers slows down, making the use of multigrid techniques especially attractive. However, special care has to be taken on the strong nonlinear turbulent source terms during restriction from fine to coarse grids. Due to the hyperbolic character of the governing equations in supersonic flows and the occurrence of shock waves, modifications to standard multigrid techniques are necessary. A simple and effective method is presented that enables the multigrid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mack 2 flow over a backward facing step.

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