Influence of wall proximity on vortex shedding from a square cylinder

Mean and fluctuating surface pressure data are presented for a square cylinder of side length D placed near a solid wall at Re _D=18,900. One oncoming boundary layer thickness, d=0.5 D was used. Measurements were made for cylinder to wall gap heights, S, from S/ D=0.07 to 1.6. Four gap-dependent flow regimes were found. For S/ D>0.9, the flow and the vortex shedding strength are similar to the no-wall case. Below the critical gap height of 0.3 D, periodic activity is fully suppressed in the near wake region. In between, for 0.3< S/ D<0.9, the wall exerts a greater influence on the flow. For 0.6< S/ D<0.9, the mean drag and the strength of the shed vortices decrease as the gap is reduced, while the mean lift towards the wall increases. Evidence is presented that for S/ D>0.6 the influence of the viscous wall flow in the gap is not dominant and that, consequently, inviscid flow theory can describe changes in the mean lift as S/ D decreases. For 0.3< S/ D<0.6, the flow reattaches intermittently on the bottom face of the cylinder and viscous effects become important. Below the gap height of 0.4 D, periodic activity cannot be observed on the cylinder.     

Random Fiber Networks and Special Elastic Orthotropy of Paper

We consider a particular in-plane elastic orthotropy observed experimentally for various types of paper, namely: S ₁₁₁₁+S ₂₂₂₂−2S ₁₁₂₂=S ₁₂₁₂, where S _ijkm are components of the in-plane compliance tensor. This is a statement of the invariance of in-plane shear compliance S ₁₂₁₂, which has been observed in some studies but questioned in others. We present a possible explanation of this “special orthotropy” of paper, using an analysis in which paper is modeled as a quasi-planar random microstructure of interacting fiber-beams – a model especially well suited for low basis weight papers. First, it is shown analytically that without disorder a periodic fiber network fails the special orthotropy. Next, using a computational mechanics model, we demonstrate that two-scale geometric disorder in a fiber network is necessary to explain this orthotropy. Indeed, disordered networks with weak flocculation best satisfy this relationship. It is shown that no special angular distribution function of fibers is required, and that the uniform strain assumption should not be used. Finally, it follows from an analogy to the thermal conductivity problem that the kinematic boundary conditions, rather than the traction ones, lead quite rapidly to relatively scale-independent effective constitutive responses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crack initiation and direction for circumferential periodic cracks in pipe under tension and torsion

The S-theory is applied to determine crack initiation angle and critical load of circumferential periodic cracks in pipe. A technique for determining mode II stress intensity factor is proposed by using G^* path independent integral. The method applies also to single-edge crack, double-edge crack and center crack cylindrical panel configurations.     

Global Tchebychev nets on complete two-dimensional Riemannian surfaces

Let S be a given surface. A local Tchebychev net on S is a coordinate chart of S such that the coordinate vector fields have unit magnitudes. It models physical surfaces which are reinforced with two sets of inextensible fibers. The angle between fibers of each set at any point is allowed to change. In this paper S is taken to be a two-dimensional, simply-connected, noncompact, complete Riemannian manifold on which the Gaussian curvature is assumed to have compact support. The existence of a global Tchebychev net on S is investigated.     

The Hopf bifurcation with symmetry for the Navier-Stokes equations in (Lp(Ω)) n,with application to plane poiseuille flow

The existence of periodic solutions of the Navier-Stokes equations in function spaces based upon (L _p())ⁿis proved. The paper has three parts, (a) A proof of the existence of strong solutions of the evolution equation with initial data in a solenoidal subspace of (L _p())ⁿ. (b) The evolution equation is restricted to a space of time periodic functions and a Fredholm integral equation on this space is formed. The Lyapunov-Schmidt method is applied to prove the existence of bifurcating time periodic solutions in the presence of symmetry. (c) The theory is applied to the bifurcation of periodic solutions from planar Poiseuille flow in the presence of symmetry (SO(2) x O(2) x S ¹) yielding new results for this classic problem. The O(2) invariance is in the spanwise direction. With the periodicity in time and in the streamwise direction we find that generically there is a bifurcation to both oblique travelling waves and to travelling waves that are stationary in the spanwise direction. There are however points of degeneracy on the neutral surface. A numerical method is used to identify these points and an analysis in the neighborhood of the degenerate points yields more complex periodic solutions as well as branches of quasi-periodic solutions.     

An analysis of unsteady highly turbulent swirling flow in a model vortex combustor

This paper reports an experimental investigation of a non-reacting turbulent swirling flow in a practical vortex combustor. The flow was examined for the conditions characteristic of the presence of a breakdown zone and a strong flow instability appearing at swirl numbers S>0.5. Flow visualization techniques, LDA measurements and acoustic probes were employed to study the unsteady flow characteristics. Based on the experimental results a positive first helical mode of instability was identified with a wavelength and frequency depending on swirl. The wavelength was confirmed to grow monotonically with S, while the dominant frequency of the flow pulsations was found to have an unusual parabolic evolution with swirl, with a minimum at S _min=0.88. This finding was interpreted using a proposed kinematic model based on the contribution of two mechanisms: rotation and axial motion of the helical vortex. It was concluded that for S<S _min the instability frequency is essentially dominated by the axial translation of the spiral vortex being inversely proportional to S and therefore giving a decreasing trend. For S>S _min the frequency of the flow precession is more dependent on the angular transportation of the vortex core, which resulted in the expected growing dependence on S.     

NMS Flows on S 3 with no Heteroclinic Trajectories Connecting Saddle Orbits

In this paper we find topological conditions for the non existence of heteroclinic trajectories connecting saddle orbits in non singular Morse-Smale flows on S ³. We obtain the non singular Morse-Smale flows that can be decomposed as connected sum of flows and we show that these flows are those who have no heteroclinic trajectories connecting saddle orbits. Moreover, we characterize these flows in terms of links of periodic orbits.     

Variation of crack-opening stresses in three-dimensions: finite thickness plate

Crack growth and closure behavior of a center cracked finite thickness plate subjected to constant amplitude cyclic load is investigated by means of a three-dimensional elastic-plastic finite-element analysis. Results are obtained for initial half crack length c_i to half plate thickness t ratios of c_i/t = 3.891 and 1.465 which shall be referred to, respectively, as thin and thick plate. A constant amplitude load with R = S_min/S_max = 0.1 and S_max/σ₀ = 0.25 is applied, where S stands for the stress amplitude and σ₀ the effective yield stress. Crack closure for the thinner plate is found to be largest at and near the free plate surface and to decrease toward the interior during the unloading portion of cyclic loading. The closure pattern stabilizes at the interior and exterior regions, respectively, for c_i/t = 3.981 at 0.34S_max and 0.56S_max and for c_i/t = 1.465 at 0.26S_max and 0.46S_max.A load-reduced displacement technique was used to determine crack-opening stresses at specified locations in the plate from the displacements calculated after 7th cycle (using unloading and reloading portions of cyclic loading). All locations were on the plate exterior surface and were located behind the crack tip and at the centerline of the crack. The opening stresses at the specified points as certain percentage of the maximum stress amplitude were obtained.     

Interactions of coherent structures in a film flow: Simulations of a highly nonlinear evolution equation

Numerical simulations of the evolution equation [14] for thickness of a film flowing down a vertical fiber are presented. Solutions with periodic boundary conditions on extended axial intervals develop trains of pulse-like structures. Typically, a group of several interacting pulses (or a solitary pulse) is bracketed by spans of nearly uniform thinned film and is virtually isolated: The evolution of such a section is modeled as a solution with periodic boundary conditions on the corresponding, comparatively short, interval. Single-pulse sections are steady-shape traveling waveforms (cells of shorter-period solutions). The collision of two pulses can be either a particle-like elastic rebound, or—and only if a control parameter S (proportional to the average thickness) exceeds a certain critical value, S _c 1—a deeply inelastic coalescence. A pulse which grows by a cascade of coalescences is associated with large drops observed in experiments by Quéré [39] and our S _c is in excellent agreement with its laboratory value.This research was supported in part by U.S. DOE under Grant DE-FG05-90ER14100.     

Measurement of the local wavenumber and frequency spectrum in a plane wake

A digital technique is presented for experimentally measuring the local wavenumber-frequency spectrum S _L(k, f) of a fluctuating velocity field using two probes. From S _L(k, f), the local wavenumber spectrum S _L(k), the averaged dispersion relation, and the broadening of the wavenumber spectrum for a given frequency can be determined. The technique is demonstrated by applying it to the velocity field of a plane wake which is undergoing transition from laminar to turbulent flow. A specially designed two sensor hotwire probe is used to obtain simultaneous records of streamwise velocity fluctuations at two locations having a fixed streamwise separation. New information is obtained concerning: the spatial characteristics of instability waves in the wake; the importance of local wavenumber matching in nonlinear coupling among waves; and broadening of the dispersion relation associated with the transition to turbulence. The usefulness of the S _L(k, f) approach when Taylor's hypothesis is not valid is also discussed.     

Design and application of an S-box using complete Latin square

Since a substitution box (S-box) is the nonlinearity part of a symmetric key encryption scheme, it directly determines the performance and security level of the encryption scheme. Thus, generating S-box with high performance and efficiency is attracting. This paper proposes a novel method to construct S-box using the complete Latin square and chaotic system. First, a complete Latin square is generated using the chaotic sequences produced by a chaotic system. Then an S-box is constructed using the complete Latin square. Performance analyses show that the S-box generated by our proposed method has a high performance and can achieve strong ability to resist many security attacks such as the linear attack, differential attack and so on. To show the efficiency of the constructed S-box, this paper further applies the S-box to image encryption application. Security analyses show that the developed image encryption algorithm is able to encrypt different kinds of images into cipher images with uniformly distributed histograms. Performance evaluations demonstrate that it has a high security level and can outperform several state-of-the-art encryption algorithms.

     

On weak critical posets with respect to the positive definiteness of a quadratic tits form

Let S be a finite P-critical poset, i.e., a poset that is critical with respect to the positive definiteness of a quadratic Tits form. A set S is called weakly P-critical if any infinite poset X ⊃ S contains a P-critical subset that is not isomorphic to S. We prove the existence of weakly P-critical sets. Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 396–407, July–September, 2008.     

Dual-Family Viscous Shock Waves in n Conservation Laws with Application to Multi-Phase Flow in Porous Media

We consider shock waves satisfying the viscous profile criterion in general systems of n conservation laws. We study S _{i, j} dual-family shock waves, which are associated with a pair of characteristic families i and j. We explicitly introduce defining equations relating states and speeds of S _{i, j} shocks, which include the Rankine–Hugoniot conditions and additional equations resulting from the viscous profile requirement. We then develop a constructive method for finding the general local solution of the defining equations for such shocks and derive formulae for the sensitivity analysis of S _{i, j} shocks under change of problem parameters. All possible structures of solutions to the Riemann problems containing S _{i, j} shocks and classical waves are described. As a physical application, all types of S _{i, j} shocks with i>j are detected and studied in a family of models for multi-phase flow in porous media.     

Comparison of the vortex shedding behavior of a single plate and a plate array

This study compares the shedding behavior around and downstream of a single plate positioned in a flow field alone with the shedding behavior around and downstream of the same plate positioned in an array of identical plates. The shedding frequencies and corresponding Strouhal numbers based on chord [S _r (c)] and based on thickness [S _r (t)] are obtained using a hot-wire anemometer. In comparison with the plate positioned as a single plate, the same plate placed in a plate array shows increases in S _r (c) of up to 55.5% and produces a dominant peak in the power spectra that is wider by a factor of 3.5. In contrast to the single-plate results, which exhibit step changes in S _r (c) of about 0.6 at c/t ≈ 6, 8 and 11, the plate positioned in an array shows only one abrupt transition at c/t ≈ 4. Received: 26 January 1999/Accepted: 7 February 2000     

Lower Bound for the Energy of Bloch Walls in Micromagnetics

We study a two-dimensional nonconvex and nonlocal energy in micromagnetics defined over S ²-valued vector fields. This energy depends on two small parameters, β and e{\varepsilon} , penalizing the divergence of the vector field and its vertical component, respectively. Our objective is to analyze the asymptotic regime b << e << 1{\beta \ll \varepsilon \ll 1} through the method of Γ-convergence. Finite energy configurations tend to become divergence-free and in-plane in the magnetic sample except in some small regions of typical width e{\varepsilon} (called Bloch walls) where the magnetization connects two directions on S ². We are interested in quantifying the limit energy of the transition layers in terms of the jump size between these directions. For one-dimensional transition layers, we show by Γ-convergence analysis that the exact line density of the energy is quadratic in the jump size. We expect the same behaviour for the two-dimensional model. In order to prove that, we investigate the concept of entropies. In the prototype case of a periodic strip, we establish a quadratic lower bound for the energy with a non-optimal constant. Then we introduce and study a special class of Lipschitz entropies and obtain lower bounds coinciding with the one-dimensional Γ-limit in some particular cases. Finally, we show that entropies are not appropriate in general for proving the expected sharp lower bound.     

Effect of the Source Term on Steady Free Convection Boundary Layer Flows over an Vertical Plate in a Porous Medium. Part I

The Darcy free convection boundary layer flow over a vertical flat plate is considered in the presence of volumetric heat generation/absorption. In the present first part of the paper it is assumed that the heat generation/absorption takes place in a self-consistent way, the source term q ^′′′≡ S of the energy equation being an analytical function of the local temperature difference T − T _∞. In a forthcoming second part, the case of the externally controlled source terms S = S(x,y ) will be considered. It is shown that due to the presence of S, the physical equivalence of the up- and downflows gets in general broken, in the sense that the free convection flow over the upward projecting hot plate (“upflow”) and over its downward projecting cold counterpart (“downflow”) in general become physically distinct. The consequences of this circumstance are examined for different forms of S. Several analytical solutions are given. Some of them describe algebraically decaying boundary layers which can also be recovered as limiting cases of exponentially decayingones. This asymptotic phenomenon is discussed in some detail.     

On Finite Shear

If a pair of material line elements, passing through a typical particle P in a body, subtend an angle Θ before deformation, and Θ+γ after deformation, the pair of material elements is said to be sheared by the amount γ. Here all pairs of material elements at P are considered for arbitrary deformations. Two main problems are addressed and solved. The first is the determination of all pairs of material line elements at P which are unsheared. The second is the determination of that pair of material line elements at P which suffers the maximum shear. All unsheared pairs of material elements in a given plane π(S) with normal S passing through P are considered. Provided π(S) is not a plane of central circular section of the C-ellipsoid at P (where C is the right Cauchy-Green strain tensor), it is seen that corresponding to any material element in π(S) there is, in general, one companion material element in π(S) such that the element and its companion are unsheared. There are, however, two elements in π(S) which have no companions. We call their corresponding directions \textit{limiting directions.} Equally inclined to the direction of least stretch in the plane π(S), the limiting directions play a central role. It is seen that, in a given plane π(S), the pair of material line elements which suffer the maximum shear lie along the limiting directions in π(S). If Θ _L is the acute angle subtended by the limitig directions in π(S) before deformation, then this angle is sheared into its supplement π−Θ _L so that the maximum shear γ^*;(S) is γ^*=π− 2 Θ _L . If S is given and C is known, then Θ _L may be determined immediately. Its calculation does not involve knowing the eigenvectors or eigenvalues of C. When all possible planes through P are considered, it is seen that the global maximum shear γ^* _G occurs for material elements lying along the limiting directions in the plane spanned by the eigenvectors of C corresponding to the greatest principal stretch λ₃ and the least λ₁. The limiting directions in this principal plane of C subtend the angle and . Generally the maximum shear does not occur for a pair of material elements which are originally orthogonal. For a given material element along the unit vector N, there is, in general, in each plane π(S passing through N at P, a companion vector M such that material elements along N and M are unsheared. A formula, originally due to Joly (1905), is presented for M in terms of N and S. Given an unsheared pair π(S), the limiting directions in π(S) are seen to be easily determined, either analytically or geometrically. Planar shear, the change in the angle between the normals of a pair of material planar elements at X, is also considered. The theory of planar shear runs parallel to the theory of shear of material line elements. Corresponding results are presented. Finally, another concept of shear used in the geology literature, and apparently due to Jaeger, is considered. The connection is shown between Cauchy shear, the change in the angle of a pair of material elements, and the Jaeger shear, the change in the angle between the normal N to a planar element and a material element along the normal N. Although Jaeger's shear is described in terms of one direction N, it is seen to implicitly include a second material line element orthogonal to N. Accepted: May 25, 1999     

Homoclinic Shadowing

A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in Rⁿ is presented. It is a computer-assisted technique with two main components. First, a global Newton’s method is devised to compute a suitable pseudo (approximate) homoclinic orbit to a pseudo periodic orbit. Then, a homoclinic shadowing theorem, which is proved herein, is invoked to establish the existence of a true transversal homoclinic orbit to a true periodic orbit near these pseudo orbits.     

Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement

When swimming in water by flapping its tail, a fish can overcome the drag from uniform flow and propel its body. The involved flow mechanism concerns 3-D and unsteady effects. This paper presents the investigation of the flow mechanism on the basis of a 3-D robotic fish model which has the typical geometry of body and tail with periodic flapping 2-freedom kinematical motion testing in the case of St = 0.78, Re = 6,600 and phase delay mode (φ = −75°), in which may have a greater or maximum propulsion (without consideration of the optimal efficiency). Using a special technique of dye visualization which can clearly show vortex sheet and vortices in detail and using the inner 3-component force balance and cable supporting system with the phase-lock technique, the 3-D flow structure visualized in the wake of fish and the hydrodynamic force measurement were synchronized and obtained. Under the mentioned flapping parameters, we found the key flow structure and its evolution, a pair of complex 3-D chain-shape vortex (S–H vortex-rings, S₁–H₁ and S₂–H₂, and their legs L₁ and L₂) flow structures, which attach the leading edge and the trailing edge, then shed, move downstream and outwards and distribute two anti-symmetric staggering arrays along with the wake of the fish model in different phase stages during the flapping period. It is different with in the case of St = 0.25–0.35. Its typical flow structure and evolution are described and the results prove that they are different from the viewpoints based on the investigation of 2-D cases. For precision of the dynamic force measurement, in this paper it was provided with the method and techniques by subtracting the inertial forces and the forces induced by buoyancy and gravity effect in water, etc. from original data measured. The evolution of the synchronized measuring forces directly matching with the flow structure was also described in this paper.     

Twist Character of the Fourth Order Resonant Periodic Solution

In this paper, we will give, for the periodic solution of the scalar Newtonian equation, some twist criteria which can deal with the fourth order resonant case. These are established by developing some new estimates for the periodic solution of the Ermakov–Pinney equation, for which the associated Hill equation may across the fourth order resonances. As a concrete example, the least amplitude periodic solution of the forced pendulum is proved to be twist even when the frequency acroses the fourth order resonances. This improves the results in Lei et al. (2003). Twist character of the least amplitude periodic solution of the forced pendulm. SIAM J. Math. Anal. 35, 844–867.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.