Vortex ring propagation and interactions studies

This paper experimentally investigates the vortex ring propagation and interactions with thin cylindrical and flat surfaces. Dye-based visualization technique is adopted for the interaction studies. Vortex rings are generated from a circular nozzle of 19 mm diameter with the stroke length ratios (length of the fluid slug to nozzle diameter, L_N/D_N) of 1 to 5, and ejection velocities in the range of 0.05 to 0.2 m/s. Vortex interaction studies are carried out with two different bodies; firstly, with the circular cylinders having the diameters of 0.2, 0.6, 1.5 and 2.5 mm, and secondly with a flat solid surface. Results indicate that the trails in the vortex ring start following at L_N/D_N = 4. The influence of the initial velocity is found to be insignificant on the vortex ring diameter, however, found to depend on stroke length ratio. Vortex-cylinder interaction studies indicated that vortex velocity decreases with increase in cylinder diameter after the interaction. Reconnections of vortex rings are observed in lower cylinder diameter cases. In case of vortex ring interaction with the flat surface, stretching of the vortex core is observed leading to a considerable increase in the vortex ring diameter.     

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements has been studied using numerical simulations for wide ranges of parameters, Reynolds numbers (1?≤?Re?≤?50), Richardson numbers (0?≤?Ri?≤?2), Prandtl numbers (0.7?≤?Pr?≤?50) and confinement ratios (0.2?≤?β?≤?0.8). A hot semi-circular cylinder is symmetrically kept in a 2D rectangular confinement. The circular side of the cylinder faces the upstream flow and the fluid flows against gravity in the channel. The governing equations are numerically solved using FLUENT and the results obtained are presented in the form of isotherms, streamlines, pressure coefficients, drag coefficients, Nusselt numbers, etc. The highest value of pressure coefficient increases with blockage ratio for all cases. The drag coefficient decreases with Re and shows complex phenomena with change in Ri and blockage ratio of the channel. Pressure drag has contributed more as compared with viscous drag in all cases. The curved surface showed more heat transfer than the flat surface of the semi-circular cylinder. The value of β also has great influence at large value of Peclect numbers (=?2500). Overall average heat transfer in terms of average Nusselt number is a function of Ri, Re, Pr and β.     

Solution of the Landau–Ginzburg Equations Using Lattice–Boltzmann

In this paper, we solve the time dependent Ginzburg–Landau (TDGL) equations in two dimensions, using Lattice–Boltzmann (LB) technique and the velocity discretization scheme D2Q9, for a square region with periodic boundary conditions. In order to obtain the solution, we use three distribution functions, each of them obeying the LB equation, and making a proper redefinition of the tensor Π ⁰, we find the (TDGL) equations. Further, we obtain the equilibrium distribution functions for the three LB equations, and then the solution for the components of the magnetic potential vector and the order parameter.     

Oscillating cylinder in viscous fluid: calculation of flow patterns and forces

Laminar and large-eddy-simulation (LES) calculations with the dynamic Smagorinsky model evaluate the flow and force on an oscillating cylinder of diameter D = 2R in otherwise calm fluid, for β = D ²/νT in the range 197–61400 and Keulegan–Carpenter number K = U _m T/D in the range 0.5–8 (ν kinematic viscosity, T oscillation period, U _m maximal velocity). Calculations resolving the streakline patterns of the Honji instability exemplify the local flow structures in the cylinder boundary layer (β ~ 197–300, K ~ 2) but show that the drag and inertia force are not affected by the instability. The present force calculations conform with the classical Stokes–Wang solution for all cases below flow separation corresponding to K < 2 (with β < 61400). The LES calculations of flow separation and vortical flow resolve the flow physics containing a large range of motion scales; it is shown that the energy in the temporal turbulent fluctuations (in fixed points) are resolved. Accurate calculation of the flow separation occurring for K > 2 has strong implication for the force on the cylinder. Present calculations of the force coefficients for K up to 4 and β = 11240 are in agreement with experiments by Otter (Appl Ocean Res 12:153–155, 1990). Drag coeffients when flow separation occurs are smaller than found in U-tube experiments. Inertia coefficients show strong decline for large K (up to 8) and moderate β = 1035 but is close to unity for K = 4 and β = 11240. The finest grid has 2.2 × 10⁶ cells, finest radial Δr/R = 0.0002, number of points along the cylinder circumference of 180, Δz/R = 0.044 and a time step of 0.0005T.     

Surface Effects on the Dynamic Behavior of Vortices in Type II Superconducting Strips with Periodic and Conformal Pinning Arrays

Using molecular dynamics techniques, we simulate the vortex behavior in a type II superconducting strip in the presence of triangular and two types of conformal pinning arrays, one with a pinning gradient perpendicular to the driving force (C1) and the other parallel (C2), at zero temperature. A transport force is applied in the infinite direction of the strip, and the magnetic field is increased until the rate between the density of vortices (n _v ) and pinning (n _p ) reaches n _v /n _p =?1.5. Our results show a monotonic increase, by steps, of the vortex density with the applied magnetic field. Besides, each pinning lattice presents a different vortex penetration delay. For the triangular pinning array, different than the case of infinite films, here the system exhibits only one pronounced depinning force peak at n _v /n _p =?1. However, the depinning force peak is present for only one value of field, in the range of fields where n _v /n _p =?1 is stable. For the case of conformal pinning arrays, in analogy to what is observed in infinite films, no commensurability depinning force peaks were found. In the present case, the C1 array is more efficient at low fields, all arrays are equivalent in the intermediate fields, and the C2 array is more efficient for high fields. We also show that for the C1 array at high fields, vortices depin following the conformal arches, from the edge to the center. For the C2 array, the depinning force is higher when compared to that of C1, because this particular conformal structure prevents the formation of easy vortex flow channels.     

Shape accuracy analysis of multi-point forming process for sheet metal under normal full constrained conditions

In order to study the shape accuracy of multi-point forming (MPF) process for sheet metal under normal full constrained conditions, the in-depth analysis of shape accuracy of workpieces in multi-point forming with individually controlled force-displacement (MPF-ICFD) process is conducted in this paper by combining experiment, theoretical analysis and numerical simulation. The influences of normal force, material thickness and material properties on the shape accuracy of the feature surface are studied, and the shape accuracy characteristics of the sheet under different parameters are obtained. Afterwards, the stress and strain characteristics of sheets are obtained by numerical simulation. Finally, the effect of normal force on shape accuracy was revealed by establishing a mechanical model of the sheet metal under normal full constrained conditions. Moreover, the amount of springback reduction in MPF-ICFD is defined quantitatively. Compared with the normal unconstrained conditions, the shape accuracy of sheet metal is improved significantly under normal full constrained conditions. The stress and plastic deformation are more uniform and the amount of springback is smaller. For Q 295 steel plate with thickness of 2.0 mm, the difference between the maximum value and the minimum value of the reaction force of punch decreases from 4515.9 N to 1475 N when the forming force is 2500 N. Besides, the bending moment of the sheet on the unit width decreases from 357.9 N???mm to 328.1 N???mm. The average shape error E _rr and the amount of springback Δk decreases by 60.05% and 16.03%, respectively.     

Effect of a protruding rod-supported disk on the drag of a nose-controlled cylinder

The drag C _x of a cylinder of diameter D with a front protruding disk supported on a rod of length l has been studied as a function of the relative distance l/D under the conditions of high (supersonic) flight velocities. It is established that the optimum (minimum) drug C _x exists, the value of which agrees with the results of numerical simulations.     

Investigation of breakage behavior of different mineralogical and morphological characteristic pumices

The objective of this study is to analyze dry grinding behavior of four different pumices in terms of Bond grindability value, selection and breakage parameters values. For this purpose, firstly, Bond grindability test were made for four pumices. Then, eight different mono-size fractions for each of pumices were carried out between 1.7 and 0.106 mm formed by a \({\surd 2}\) sieve series, and ground batch wise in a laboratory ball mill for determination of breakage parameters. Finally, S _i and B _i,j equations were determined from the size distributions at different grinding times, and the model parameters (S _i , a _T , α, γ, β and \({\phi_{j}}\)) were compared for four different pumice samples.     

Diagram of the Critical Temperature—Nernst Temperature for the Superconductivity Induced by Modified Electron-Phonon Interaction

We have taken into consideration the Eliashberg equations based on the electron-phonon and the electron-electron-phonon interaction. It has been shown that the Eliashberg equations set generalizes the model based on the canonical transformation, which for the cuprates quantitatively associates with each other the critical temperature (T _C ), the Nernst temperature (T ^??), and the energy gap at 0 K. Next, we have derived the analytical formulas for the basic thermodynamic parameters. The conducted analysis allowed to designate the T _C - T ^?? diagram. Finally, we found the limitation from below for the value of T ^??, occurring for the critical temperature higher than 150 K.     

The sound velocity in liquid binary mixtures of <Emphasis Type="Italic">n</Emphasis>-alkanes

The method of direct measurement of the time of pulse transmission is used for investigating the sound velocity in liquid binary mixtures of n-alkanes, namely, n-hexane + n-hexadecane, n-octane + n-hexadecane, and n-decane + n-hexadecane in the range of temperatures from 298 to 433 K and pressures from 0.1 to 100.1 MPa. The maximal error of measurements is 0.1%. It is for the first time that experimental data for mixtures of n-octane + n-hexadecane and n-decane + n-hexadecane are obtained.     

Simulation of evolution of the two cylinders plasma wake under the electric discharge influence

We consider a close wake behind a pair of cylinders at a Reynolds number of Re ~ 1000 defined by the cylinder diameter in the case of small aspect ratio of cylinders, H/D ≈ 3.5. The large-scale structure of such a wake represents a f low like two interacting Karman streets and it is modeled by two coupled Van der Pol oscillators. The mutual inf luence of closely located Karman streets is accounted for by nonlinear (of a general parabolic type) terms in the equations for oscillators. Moreover, the equations are generalized with allowance for explicit dependence of the oscillation frequency on its amplitude. Within the framework of this three-parametric model, five collective modes of the wake behind cylinders were found. In addition, there are the domains of model parameters where qualitatively different modes of intermittent wake exist.     

Effect of bimodularity on frequency response of cylindrical panels using Galerkin time domain approach

The forced vibration analysis of bimodulus material laminated structures is a challenging problem due to non-smooth nonlinear nature of governing equations. The most commonly used direct time integration schemes show numerical instability and do not predict steady state response except for limited number of cases without considering in-plane inertia. This is due to the sudden change of restoring force from positive/negative half cycle to negative/positive half cycle exciting higher modes/harmonics at every instant of a cycle change leading to numerical instability in the time marching scheme. In the present work, Galerkin time domain approach is successfully used for the forced vibration analysis of bimodular cylindrical panels. The effect of bimodularity ratio on the frequency response of cylindrical panels for few typical geometrical and lamination parameters is studied for the first time. It is found that the positive half cycle amplitude is greater than the negative half cycle amplitude for E _2t /E _2c < 1 and is smaller for E _2t /E _2c > 1. Further, the percentage difference of positive and negative half cycle amplitudes decreases with the increase in E _2t /E _2c . The stresses under dynamic loading are different for positive and negative half of a vibration cycle.     

The Normal Flame Velocity and Analysis of the Effect of the System Parameters on This Velocity

A process chart of flame combustion of gases is suggested, and the region of existence of the normal (or standard) burning velocity U _n is given. The results of analysis of numerous experimental data are used to determine the impact made on U _n by parameters such as pressure, flame temperature, chemical composition of the mixture, and preheating of the mixture. Generalizing dependences of the normal burning velocity U _n on the adiabatic combustion temperature T _a and on the preheating temperature T₀ are obtained for a wide range of combustible hydrocarbon gases.     

Three-Dimensional Numerical Simulation of Pure Solutocapillary Flow in a Shallow Annular Pool for Mixture Fluid with High Schmidt Number

In order to understand the characteristics of pure solutocapillary flow in a shallow annular pool subjected to a constant radial solutal gradient, a series of three-dimensional numerical simulations were performed. The annular pool was filled with the toluene/n-hexane mixture fluid with the Schmidt number of 142.8. The inner and outer cylinders were respectively maintained at low and high solutal concentrations. Aspect ratio of the annular pool is fixed at ε = 0.15 or 0.05. Results indicate that the solutocapillary flow is steady and axisymmetric at a small solutal capillary Reynolds number. The surface fluid flows radially from the inner cylinder toward the outer cylinder and a return flow exists near the bottom. With the increase of the solutal capillary Reynolds number, an axisymmetric oscillatory flow firstly appears and then becomes a three-dimensional oscillatory flow at ε = 0.15. Whereas at ε = 0.05 a direct transition from the steady and axisymmetric flow to the three-dimensional oscillatory flow is observed. Three types of the flow instabilities are the standing wave, hydrosolutal wave and source/sink type wave instabilities. Furthermore, the physical mechanism of the flow destabilization is analyzed.     

The surface energy of cryocrystals

An expression for the surface energy σ₀₀ of a crystal at T = 0 and P = 0 is obtained with allowance for the zero-point vibrations of atoms in the crystal. Particular calculations are performed for the cryocrystals of inert gases and hydrogen isotopes, in which the energy of zero-point vibrations is comparable with the energy of interatomic interactions. It is established that σ₀₀ exhibits highly correlated dependences of the same kind on the atomic (molecular) mass m, the melting temperature T_m, and the interatomic interaction potential D/k_B (k_B is the Boltzmann constant), whereby the function σ₀₀(m, T_m, D/k_B) exhibits nonlinear growth with each argument. The ratio σ₀₀/σ_liquid, where σ_liquid is the surface tension of the liquid phase at T = T_m, also exhibits highly correlated dependences on m, T_m, and D/k_B, which can be divided into two parts of linear growth corresponding to the quantum and classical domains. The σ₀₀/σ_liquid ratio, being smaller in the quantum case than in the classical one, grows with m, T_m, and D/k_B much faster in the quantum than in the classical domain.     

On the Role of Fermi Energy in Determining Properties of Superconductors: a Detailed Comparative Study of Two Elemental Superconductors (Sn and Pb), a Non-cuprate (MgB<Subscript><Emphasis Type="Bold">2</Emphasis></Subscript>) and Three Cuprates (YBCO,Bi-2212 and Tl-2212)

Fermi energies (E _Fs) of high- T _c superconductors (SCs) have of late been evincing considerable interest because they are believed to be the cause of their high T _cs and gap structures. Since Bardeen-Cooper-Schrieffer (BCS) equations for elemental and generalized-BCS equations for non-elemental SCs are derived under the blanket of the assumption E _F/ k θ > > 1 (k = Boltzmann constant, θ = Debye temperature), they cannot shed light on the E _Fs of these SCs. This fact leads us to address the gaps (Δ₀s) and T _cs of both types of SCs via recently derived equations which incorporate E _F as a variable. For the specification of the E _F of any SC, we now need another of its properties. Choosing j ₀, the critical current density of the SC at T = 0, and following an idea due to Pines, we present for both types of SCs new equations for j ₀ that depend solely on the following properties of the SC: E _F, θ, gram-atomic volume, electronic specific heat constant and a dimensionless construct \(y=k\theta \sqrt {2m\ast } \text {/}P_{\text {0}} \sqrt {E_{\mathrm {F}} } \text {,}\) where m* is the effective mass of superconducting electrons and P ₀ their critical momentum. Appeal to the experimental values of Δ₀, T _c and j ₀ of any SC then not only leads to values of E _F, m* and P ₀ but also provides plausible clues about how its j ₀—and therefore T _c—may be increased.     

Variation of Quench Propagation Velocities in YBCO Cables

We show by modelling that the quench propagation velocity is not constant in HTS coils but it changes during the quench. Due to the large temperature margin between the operation and the current sharing temperatures, the normal zone does not propagate with the temperature front. This means that the temperature will rise in a considerably larger volume when compared to the quenched volume. Thus, the evolution of the temperature distribution below current sharing temperature T _{c s} after the quench onset affects the normal zone propagation velocity in HTS more than in LTS coils. This can be seen as an acceleration of the quench propagation velocities while the quench evolves when margin to T _{c s} is high. In this paper, we scrutinize quench propagation in a stack of YBCO cables with an in-house finite element method software which solves the heat diffusion equation. We compute the longitudinal and transverse normal zone propagation velocities at various distances from the hot spot to demonstrate the distance-variation of these velocities. According to the results in our particular simulation case, the longitudinal normal zone propagation velocity is 30 % higher far away from the quench origin compared to its immediate vicinity when T _op=4.2 K and T _{c s} =15 K.     

Experimental modelling of free-surface dry granular flows under a centrifugal acceleration field

We investigate the dynamics of granular flows under the action of a centrifugal acceleration field. The granular flows consist of a monodisperse set of glass beads flowing down an inclined plane. The experiments are performed at variable slope angles \(\zeta \) and equivalent centrifugal accelerations \(a_\text {cf}\equiv Ng\). We study the effect of this parameters on the superficial flow velocity u and flow height h. Two trends are observed, by increasing \(\zeta \) and \(a_\text {cf}\), u increases proportionally, and h decreases asymptotically until a constant height. This relation is analysed in terms of the system potential and kinetic energy, leading to the estimation of equivalent impact forces one order of magnitude larger than those observed in small scale 1g laboratory experiments, with the possibility to reach higher forces by increasing N. Finally, considering the trend of u and h, our results suggest a scaling principle of inertial velocity proportional to \(\sqrt{N}\).     

The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid

The flow induced above an impermeable membrane undergoing orthogonal linear stretching and orthogonal linear shearing is investigated. For an exact solution of the Navier–Stokes equations, the orthogonal shearing motions must be related through the constant σ = γ δ, where γ and δ are the dimensionless streamwise and transverse shear rates, respectively. The resulting similarity reduction leads to three nonlinearly coupled ordinary differential equations governed by σ and the ratio of membrane stretch rates β. All possible solutions of these equations are found either numerically or, in special cases, analytically. Features of the σ = 0 solutions at β = 0 and asymptotically as β → ∞ are found to be in excellent agreement with numerical calculations. An aside calculation shows that orthogonal shearing in the absence of any plate stretching cannot exist. However, shearing in one coordinate direction is possible as long as the membrane stretches in at least one direction with the caveat that there exists uniform suction through a porous membrane.