Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number 40≤ Re ≤200 and various rotation rate θ_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method(FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow.The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases,the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution forθ_iθ_(crit), It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.     

On Symmetries in Time Optimal Control,Sub-Riemannian Geometries,and the <Emphasis Type="Italic">K</Emphasis>−<Emphasis Type="Italic">P</Emphasis> Problem

The goal of this paper is to describe a method to solve a class of time optimal control problems which are equivalent to finding the sub-Riemannian minimizing geodesics on a manifold M. In particular, we assume that the manifold M is acted upon by a group G which is a symmetry group for the dynamics. The action of G on M is proper but not necessarily free. As a consequence, the orbit space M/G is not necessarily a manifold but it presents the more general structure of a stratified space. The main ingredients of the method are a reduction of the problem to the orbit space M/G and an analysis of the reachable sets on this space. We give general results relating the stratified structure of the orbit space, and its decomposition into orbit types, with the optimal synthesis. We consider in more detail the case of the so-called K?P problem where the manifold M is itself a Lie group and the group G is determined by a Cartan decomposition of M. In this case, the geodesics can be explicitly calculated and are analytic. As an illustration, we apply our method and results to the complete optimal synthesis on S O(3).     

General Expansiveness for Diffeomorphisms from the Robust and Generic Properties

Let f:M → M be a diffeomorphism on a closed smooth d(d ≥ 2)-dimensional manifold. For each \(n\in \mathbb N\), if f belongs to C ¹-interior of the set of the n-expansive diffeomorphisms, then f satisfies quasi-Anosov. For C ¹-generic f, if f is n-expansive then f satisfies both Axiom A and the no-cycle condition.     

Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

Cascade Linearization of Invariant Control Systems

Let Pfaffian system ω define an intrinsically nonlinear control system on manifold M that is invariant under the free, regular action of a Lie group G. The problem of identifying and constructing static feedback linearizable G-quotients of ω was solved in De Doná et al. (2016). Building on these results, the present paper proves that the trajectories of ω can often be expressed as the composition of the trajectories of a static feedback linearizable quotient control system, ω/G, on quotient manifold M/G, and those of a separate control system, γ ^G , evolving on a principal G-bundle over a jet space. Furthermore, we point out that ω may not only have a static feedback linearizable quotient, ω/G but additionally, γ ^G itself may possess a static feedback linearizable reduction as well. This enables one to express the trajectories of an intrinsically nonlinear control system as the composition of the trajectories of static feedback linearizable control systems, thereby providing a geometric criterion for the explicit integrability of intrinsically nonlinear systems. Moreover, special integrability properties arise when G is solvable. Examples are presented in which the above phenomena are explicitly demonstrated. An important aspect of the examples is that they gather evidence for the conjecture that our sufficient conditions for explicit integrability are also necessary.     

Multifractal Spectrum for Barycentric Averages

Let \(\left (X,\nu \right ) \) and Y be a measured space and a C A T(0) space, respectively. If \(\mathcal {M}_{2}(Y)\) is the set of measures on Y with finite second moment then a map \(bar:\mathcal {M}_{2}(Y)\rightarrow Y\) can be defined. Also, for any x∈X and for a map \(\varphi :X\rightarrow Y\), a sequence \(\left \{\mathcal {E}_{N,\varphi }(x)\right \} \) of empirical measures on Y can be introduced. The sequence \(\left \{ bar\left (\mathcal {E}_{N,\varphi }(x)\right ) \right \} \) replaces in C A T(0) spaces the usual ergodic averages for real valuated maps. It converges in Y (to a map \(\overline {\varphi }\left (x\right )\)) almost surely for any x∈X (Austin J Topol Anal. 2011;3: 145–152). In this work, we shall consider the following multifractal decomposition in X:

$$K_{y,\varphi}=\left\{ x:\lim\limits_{N\rightarrow\infty}bar\left(\mathcal{E}_{N,\varphi}(x)\right) =y\right\} , $$

and we will obtain a variational formula for this multifractal spectrum.

     

Coupled thermocapillary convection on Marangoni convection in liquid layers with curved free surface

This paper numerically studied the coupled Marangoni convection and thermocapillary convection in a finite liquid layer (Pr = 11.6) in the microgravity conditions. The multi-cellular flow structure and the marginal instability boundary of the coupled convection are predicted. Oscillatory coupled convection is also reported in concave liquid layers of volume ratio between 0.80 and 0.85.     

Influence of gamma radiation on spectral photosensitivity of (Si<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript> (ZnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution

Increase of the photosensitivity of the pSi-n(Si₂)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.01) structure exposed to gamma radiation with photon energy E _ph ≥ 2.3 eV has been demonstrated. It is shown that irradiation with dose up to 10⁴ rad raises and radiation with dose up to 10⁵ rad reduces the forward current of the pSi-n(Si₂)_{1 ? x} (ZnSe) _x structure.     

Analysis of turbulence and surface growth models on the estimation of soot level in ethylene non-premixed flames

Soot prediction in a combustion system has become a subject of attention, as many factors influence its accuracy. An accurate temperature prediction will likely yield better soot predictions, since the inception, growth and destruction of the soot are affected by the temperature. This paper reported the study on the influences of turbulence closure and surface growth models on the prediction of soot levels in turbulent flames. The results demonstrated that a substantial distinction was observed in terms of temperature predictions derived using the k-ε and the Reynolds stress models, for the two ethylene flames studied here amongst the four types of surface growth rate model investigated, the assumption of the soot surface growth rate proportional to the particle number density, but independent on the surface area of soot particles, f(A_s) = ρN_s, yields in closest agreement with the radial data. Without any adjustment to the constants in the surface growth term, other approaches where the surface growth directly proportional to the surface area and square root of surface area, f(A_s) = A_s and f(A_s) = √A_s, result in an under-prediction of soot volume fraction. These results suggest that predictions of soot volume fraction are sensitive to the modelling of surface growth.     

Second-Order Viability Problems with Perturbation in Hilbert Spaces

In this paper, we study the existence of viable solutions to the differential inclusion

$ \ddot{x}(t) \in f\left( {t,x(t),\dot{x}(t)} \right) + F\left( {x(t),\dot{x}(t)} \right), $

where f is a Carathéodory single-valued map and F is an upper semi-continuous multifunction with compact values contained in the Clarke subdifferential ? _c V of an uniformly regular function V.

     

Free Time Optimization of Second-Order Differential Inclusions with Endpoint Constraints

The present paper deals with the optimal control theory given by second-order differential inclusions (P _C ) with a non-fixed time interval and endpoint constraints. Our aim is to establish well-verifiable sufficient conditions of optimality for second-order differential inclusions. Thus, the sufficient conditions, including distinctive t ₁-attainability condition ones, are formulated by using the Euler-Lagrange and Hamiltonian type of inclusions. Here, the basic apparatus of locally adjoint mappings (L A M s) is suggested. Application of these results is illustrated by solving some linear control problem with second-order differential inclusions.     

Multiple-scale analysis of oscillatory thermocapillary convection of high Prandtl number fluids in a rectangular cavity

A lot of research work has been directed toward the study of oscillatory thermocapillary convection for the past about 20 years. However, the real mechanism for the onset of oscillatory thermocapillary convection is still not fully understood. The reasons are as follows. If, to most people, the Marangoni number, Ma, is the only parameter to describe the onset of oscillatory thermocapillary convection, why it cannot correlate the ground-based and microgravity experimental data properly? If the “surface-deformation number” or the so-called “S-parameter” is the parameter which can correlate the experimental data properly, why it cannot be derived without conjectures?To resolve this deficiency, multiple-scale analysis is applied to determine, among others, the characteristic length, time, and velocity scales for an unsteady, two-dimensional thermocapillary convection with a deformable free surface in a rectangular cavity. For flow situations with A²M_a,0?O(1), A²R_σ,0?O(1), and Pr>O(1), the ratio of the free surface-variation time scale to the convective time scale of the main surface flow turns out to be the so-called “S-parameter”. The S-parameter thus implies physically a delayed cooling effect of the return flow on the surface flow. Therefore, the most important contribution of the present study is to provide a theoretical basis for the derivation of the S-parameter and, hopefully, guidance for the study of oscillatory thermocapillary convection.     

Axisymmetric thermocapillary convection in open cylindrical annuli with deforming interfaces

Two-dimensional thermocapillary convection in an open cylindrical annulus heated from the inside wall is computed. The deformable free surface is obtained as a solution of the coupled transport equations, assuming pinned contact points, at Prandtl number of 30 and prescribed geometry. Only steady convection is possible at any Reynolds number (Re) in the axisymmetric computations with either nondeformable or deformable surfaces. Dynamic free-surface deformations do not induce transitions to oscillatory convection even at large Re and capillary numbers (Ca). Free surfaces are convex near the cold wall stagnation point and concave near the hot wall. Two peaks appear at the free surface at low Re while four peaks are possible at larger Re. Free surface shapes and convection in the interior are insensitive to variations in Ca while the magnitudes of surface ripples increase with Ca. At Ca = 0 convection is calculated assuming nondeformable concave surfaces as function of the liquid volume (V) and the contact angle (θ) at the inner boundary. At constant V, peaks of surface velocity increase while central surface temperatures decrease with increasing θ. Curvature significantly influences convection which is more vigorous with increasing V/θ at constant θ/V.     

Thin Semiconductor Films of Fullerene C<Subscript>70</Subscript> Nanoaggregates on the Surface of a Plane Glass Substrate

It was shown for the first time that, in the volume of an evaporating drop of a fullerene C₇₀ solution in toluene located on the surface of a glass substrate, the self-organization of C₇₀ molecules occurs and crystalline nC₇₀ nanoaggregates of a spherical shape are synthesized. Films of nC₇₀ nanoaggregates are deposited on a plane surface of a glass substrate. The physical mechanism of the self-organization of C₇₀ molecules and the formation of large nC₇₀ nanoaggregates are proposed, namely, Ostwald ripening, according to which relatively large nC₇₀ nanoaggregates grow through smaller ones. The possibility of using thin films as solar transducers is discussed.     

Hierarchical Control for the One-dimensional Plate Equation with a Moving Boundary

In this paper, we investigate the controllability for the one-dimensional plate equation in intervals with a moving boundary. This equation models the vertical displacement of a point x at time t in a bar with uniform cross section. We assume the ends of the bar with small and uniform variations. More precisely, we have introduced functions α(t) and β(t) modeling the motion of these ends. We present the following results: the existence and uniqueness of Nash equilibrium, the approximate controllability with respect to the leader control, and the optimality system for the leader control.     

Horizontal Holonomy for Affine Manifolds

In this paper, we consider a smooth connected finite-dimensional manifold M, an affine connection ? with holonomy group H ^? and Δ a smooth completely non integrable distribution. We define the Δ-horizontal holonomy group \({H^{\;\nabla }_{\Delta }}\) as the subgroup of H ^? obtained by ?-parallel transporting frames only along loops tangent to Δ. We first set elementary properties of \({H^{\;\nabla }_{\Delta }}\) and show how to study it using the rolling formalism Chitour and Kokkonen (2011). In particular, it is shown that \({H^{\;\nabla }_{\Delta }}\) is a Lie group. Moreover, we study an explicit example where M is a free step-two homogeneous Carnot group with m ≥ 2 generators, and ? is the Levi-Civita connection associated to a Riemannian metric on M, and show in this particular case that \({H^{\;\nabla }_{\Delta }}\) is compact and strictly included in H ^? as soon as m ≥ 3.     

Existence of Weak Solutions for Generalized Quasilinear Schrödinger Equations

This paper shows the existence of nontrivial weak solutions for the generalized quasilinear Schrödinger equations

$$ -div(g^{p}(u)|\nabla u|^{p-2}\nabla u)+g^{p-1}(u)g^{\prime}(u)|\nabla u|^{p}+ V(x)|u|^{p-2}u=h(u),\,\, x\in \mathbb{R}^{N}, $$

where N ≥ 3, \(g(s): \mathbb {R}\rightarrow \mathbb {R}^{+}\) is C ¹ nondecreasing function with respect to |s|, V is a positive potential bounded away from zero and h(u) is a nonlinear term of subcritical type. By introducing a variable replacement and using minimax methods, we show the existence of a nontrivial solution in \(C^{\alpha }_{loc}(\mathbb {R}^{N})\).

     

Thermovoltaic properties of technical silicon melted by solar radiation

The thermovoltaic characteristics of the p-n junction fabricated on the basis of technical silicon melted by means of solar radiation have been measured. The thermovoltaic effect that becomes apparent at temperatures T ≥ 60°C has been detected. This effect is evidently associated with the thermal generation of electron-hole pairs with the participation of impurities and surface states of intergrain boundaries.     

Natural heat accumulation in large enclosures of premises with an insulation passive solar heating system

This article provides the results of design studies intended to determine the specific amount of heat accumulated in the inner layers of vast enclosures used in premises with an insulation passive solar heating system (Q _acc) by the temperature-wave method. As shown by the calculation data, the value of Q _acc depends significantly on the ratio of the F _te surface area of the translucent enclosure of the considered premise to the F _fl surface area of its floor slabs and the amplitude of air motion in the heated premise. According to the calculated data, Q _acc, at the end of the second decade of March, is 169.0 kJ/m² at F _te/F _fl = 0.30–0.40 whereas the coefficient of natural heat accumulation in the inner layers of the given vast enclosure is ≈0.12.     

Attractor for the nonlinear Schr?dinger equation with a nonlocal nonlinear term

In this paper, we consider the long-time behavior of solutions of the dissipative 1D nonlinear Schrödinger (NLS) equation with nonlocal integral term and with periodic boundary conditions. We prove the existence of the global attractor \( \mathcal{A} \) for the nonlocal equation in the strong topology of H ¹(Ω). We also prove that the global attractor is regular, i.e., \( \mathcal{A} \subset {H^2}\left( \Omega \right) \), assuming that f(x) is of class C ². Furthermore, we estimate the number of the determining modes for this equation.