Theoretical study on two-dimensional aerodynamic characteristics of unsteady wings

A simple computing method based on a potential theory is developed for two-dimensional steady and unsteady deflected wings. This method of theoretical analysis is essentially related to thin and angular airfoils. Thus, the method is very simple but is effective to forecast aerodynamic forces for deflected or angular airfoils with a small camber operating in high Reynolds number flow, specifically in unsteady motion. The suction force acting on the leading edge of steady airfoils is theoretically obtained by using the Blasius formula. By Polhamus's leading edge suction analogy, the suction force is considered to be directed upward in partially separated flow for real thin airfoil with sharp leading edge. The theory can also be applied to obtain the aerodynamic characteristics of thin airfoils operating on low Reynolds number flow under some degree of approximation. This is very useful for the unsteady aerodynamic analysis because the Navier-Stokes equation can be solved by neither analytical nor numerical method for the thin and angular airfoils, which are common in the insect wing.     

Wake Signature and Strouhal Number Dependence of Finite-Span Flapping Wings

A numerical study was conducted in order to investigate the unsteady aerodynamics of finite-span flapping rigid wings. The unsteady laminar incompressible Navier-Stokes equations were solved on moving overlapping structured grids using a second-order accurate in space and time finite-difference scheme. Specifically, finite-span rigid wings undergoing pure heaving and root-flapping motions were studied. From the results presented, it is found that root-flapping wings produce wake structures similar to those of heaving wings, but with the difference that the latter wing kinematics generates larger vortices and forces than root-flapping wings; aside from this, similar wake regimes occur at comparable values of the Strouhal number. The numerical simulations were performed at a Reynolds number of Re = 250 and at different values of Strouhal number and reduced frequency.     

Parameter study of simplified dragonfly airfoil geometry at Reynolds number of 6000

Aerodynamic study of a simplified Dragonfly airfoil in gliding flight at Reynolds numbers below 10,000 is motivated by both pure scientific interest and technological applications. At these Reynolds numbers, the natural insect flight could provide inspiration for technology development of Micro UAV’s and more. Insect wings are typically characterized by corrugated airfoils. The present study follows a fundamental flow physics study (Levy and Seifert, 2009), that revealed the importance of flow separation from the first corrugation, the roll-up of the separated shear layer to discrete vortices and their role in promoting flow reattachment to the aft arc, as the leading mechanism enabling high-lift, low drag performance of the Dragonfly gliding flight. This paper describes the effect of systematic airfoil geometry variations on the aerodynamic properties of a simplified Dragonfly airfoil at Reynolds number of 6000.The parameter study includes a detailed analysis of small variations of the nominal geometry, such as corrugation placement or height, rear arc and trailing edge shape.Numerical simulations using the 2D laminar Navier-Stokes equations revealed that the flow accelerating over the first corrugation slope is followed by an unsteady pressure recovery, combined with vortex shedding. The latter allows the reattachment of the flow over the rear arc. Also, the drag values are directly linked to the vortices’ magnitude. This parametric study shows that geometric variations which reduce the vortices’ amplitude, as reduction of the rear cavity depth or the reduction of the rear arc and trailing edge curvature, will reduce the drag values. Other changes will extend the flow reattachment over the rear arc for a larger mean lift coefficients range; such as the negative deflection of the forward flat plate. These changes consequently reduce the drag values at higher mean lift coefficients.The detailed geometry study enabled the definition of a corrugated airfoil geometry with enhanced aerodynamic properties, such as range and endurance factors, as compared to the nominal airfoil studied in the literature.     

Convective Flow of Sisko Fluid over a Bidirectional Stretching Surface

The present investigation focuses the flow and heat transfer characteristics of the steady three-dimensional Sisko fluid driven by a bidirectional stretching sheet. The modeled partial differential equations are reduced to coupled ordinary differential equations by a suitable transformation. The resulting equations are solved numerically by the shooting method using adaptive Runge Kutta algorithm in combination with Newton''s method in the domain [0,∞). The numerical results for the velocity and temperature fields are graphically presented and effects of the relevant parameters are discussed in detail. Moreover, the skin-friction coefficient and local Nusselt number for different values of the power-law index and stretching ratio parameter are presented through tabulated data. The numerical results are also verified with the results obtained analytically by the homotopy analysis method (HAM). Additionally, the results are validated with previously published pertinent literature as a limiting case of the problem.     

Turbulence Model Selection for Low Reynolds Number Flows

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Re_θ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.     

Numerical Simulation of Supersonic Gap Flow

Various gaps in the surface of the supersonic aircraft have a significant effect on airflows. In order to predict the effects of attack angle, Mach number and width-to-depth ratio of gap on the local aerodynamic heating environment of supersonic flow, two-dimensional compressible Navier-Stokes equations are solved by the finite volume method, where convective flux of space term adopts the Roe format, and discretization of time term is achieved by 5-step Runge-Kutta algorithm. The numerical results reveal that the heat flux ratio is U-shaped distribution on the gap wall and maximum at the windward corner of the gap. The heat flux ratio decreases as the gap depth and Mach number increase, however, it increases as the attack angle increases. In addition, it is important to find that chamfer in the windward corner can effectively reduce gap effect coefficient. The study will be helpful for the design of the thermal protection system in reentry vehicles.     

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.     

The growth of pure and simple microbial competitors in a moving distributed medium.

The dynamics of pure and simple competition between two microbial species are examined for the case of interaction arising in a distributed and nonstagnant environment. The environment is modeled as a tubular reactor. It is shown that for relatively small values of the dispersion coefficient (i.e., for small, but nonzero, backmixing of the medium), the two competing populations can coexist in a stable steady state. It has been assumed that the species grow uninhibited and that if there are maintenance requirements they are satisfied from endogenous sources. From numerical studies it has been found that a necessary condition for coexistence is that the net specific growth rate curves of the two competitors cross each other at a positive value of the concentration of the rate-limiting substrate. The model equations have been numerically solved by using the methods of orthogonal and spline collocation.     

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.     

Computation of steady flow in a two-dimensional arterial model

The Navier-Stokes equations are solved numerically for steady flow through a double-branched two-dimensional section of a three-dimensional model of a canine aorta for which experimental data is available. The numerical scheme involves transforming the physical coordinates to a curvilinear boundary-fitted coordinate system and performing finite-difference computations in the transformed system. Shear stress at the wall is calculated for a Reynolds number of a 1,000 with branch-to-main aortic flow rate ratios as a parameter. The results are compared with the aforementioned experimental data and show reasonable qualitative agreement.     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.     

A computational study of the aerodynamic performance of a dragonfly wing section in gliding flight

A comprehensive computational fluid-dynamics-based study of a pleated wing section based on the wing of Aeshna cyanea has been performed at ultra-low Reynolds numbers corresponding to the gliding flight of these dragonflies. In addition to the pleated wing, simulations have also been carried out for its smoothed counterpart (called the 'profiled' airfoil) and a flat plate in order to better understand the aerodynamic performance of the pleated wing. The simulations employ a sharp interface Cartesian-grid-based immersed boundary method, and a detailed critical assessment of the computed results was performed giving a high measure of confidence in the fidelity of the current simulations. The simulations demonstrate that the pleated airfoil produces comparable and at times higher lift than the profiled airfoil, with a drag comparable to that of its profiled counterpart. The higher lift and moderate drag associated with the pleated airfoil lead to an aerodynamic performance that is at least equivalent to and sometimes better than the profiled airfoil. The primary cause for the reduction in the overall drag of the pleated airfoil is the negative shear drag produced by the recirculation zones which form within the pleats. The current numerical simulations therefore clearly demonstrate that the pleated wing is an ingenious design of nature, which at times surpasses the aerodynamic performance of a more conventional smooth airfoil as well as that of a flat plate. For this reason, the pleated airfoil is an excellent candidate for a fixed wing micro-aerial vehicle design.     

Transient effects on the initial rate of oxygenation of red blood cells

The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O₂ in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.     

Effect of unstirred layers on binding and reaction kinetics at a membrane surface

The effects of solution unstirred layers on the time course of chemical reactions and transport processes at a membrane surface are determined. A set of equations which describes non-steady-state diffusion through an unstirred layer coupled with chemical reaction at a membrane surface or transport through a membrane is developed. A numerical solution to the equations is obtained by uncoupling diffusive and chemical processes in an iterative manner. The diffusive process is solved by the Crank-Nicolson method; the chemical process is solved by integrating the differential equations describing the kinetics. Diffusive processes in one dimension, in three dimensions, and in the presence of an arbitrary potential near the membrane surface are solved. General characteristics of the calculated reaction time course are discussed using surface binding and membrane transport examples. Small, neglected, unstirred layers are shown to sometimes yield erroneous values of rate parameters for a surface reaction and to simulate competitive reaction kinetics. Experimental approaches for measuring unstirred layer thickness are reviewed.     

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.     

From Markovian to pairwise epidemic models and the performance of moment closure approximations

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness.     

Statistical theory of persuasion in tripartite negotiations

The interaction of three neutral subjects discussing a question is analyzed. The course of the debate is described by three first-order differential equations with coefficients depending on the characteristics of the subjects. Under plausible assumptions the equations are linear and can be solved explicitly. In general, the opinions of the participants approach a common limiting value which is a weighted average of their initial opinions. Special cases are considered in which one or two subjects keep their opinions constant during the discussion. The case of a coalition of two subjects against the third is shown to reduce to a two-party situation. A method of fitting the model to experimental data is suggested. Preliminary trials indicate that it is possible to obtain numerical observations to test this model of a three-party debate.     

High-Lift Effect of Bionic Slat Based on Owl Wing

A slat without a cove is built on the basis of a bionic airfoil （i.e. stowed multi-element airfoil）, which is extracted from a long-eared owl wing. The three-dimensional models with a deployed slat and a stowed slat are measured in a low-turbulence wind tunnel. The results are used to characterize high-lift effect： compared with the stowed slat, the deployed slat works more like a spoiler at low angles of attack, but like a conventional slat or slot at high angles of attack. In addition, it can also increase stall angle and maximum lift coefficient, and postpone the decrease in the gradient of the lift coefficient. At the same time, the flow field visualized around both three-dimensional models suggests the leading-edge separation associated with the decrease in the gradient of the lift coefficient, Furthermore, the related two-dimensional simulation well agrees with the analysis of the lift coefficient, as the complement to the experiment. The bionic slat may be used as reference in the design of leading-edge slats without a cove.     

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.     

Fundamental equation of thermodynamics for protein-ligand binding

For the internal energy and every thermodynamic potential that can be defined by a Legendre transform, there is a fundamental equation that contains all the thermodynamic information about a system. For a system involving the binding of molecular oxygen and hydrogen ions by a protein, fundamental equations are given for the Gibbs energy G, the transformed Gibbs energy G' at specified pH, and the further transformed Gibbs energy G" at specified pH and specified concentration of molecular oxygen. The Maxwell equations for these various Gibbs energies are important because they provide the connection with experimentally determined properties and increase our understanding of these properties. Measurements of the average number of oxygen molecules bound as a function of T, pH and concentration of molecular oxygen make it possible to calculate Delta(f)G"(o) of the reactant. Maxwell equations make it possible to calculate the average number of hydrogen ions bound, Delta(f)S"(o), Delta(f)H"(o) and their partial derivatives. These relations are illustrated with numerical calculations on a simple reaction system.