Nonlinear Weakly Curved Rod by Γ-Convergence

We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use an approach analogous to the one for rods and curved rods and start from the strain energy functional of three dimensional nonlinear elasticity. We do not impose any constitutional behavior of the material and work in a general framework. To derive the model, by means of ??-convergence, we need to set the order of strain energy (i.e., its relation to the thickness of the body h). We analyze the situation when the strain energy (divided by the order of volume) is of the order h ⁴. This is the same approach as the one used in F?ppl-von Kármán model for plates and the analogous model for rods. The obtained model is analogous to Marguerre-von Kármán for shallow shells and its linearization is the linear shallow arch model which can be found in the literature.     

The torsional buckling of a cruciform column under compressive load with a vertex plasticity model

The torsional buckling of a plastically deforming cruciform column under compressive load is investigated. The problem is solved analytically based on the von Kármán shallow shell theory and the virtual work principle. Solutions found in the literature are extended for path-dependent incremental behaviour as typically found in the presence of the vertex effect that is present in metallic polycrystals.At the critical load for buckling the direction of straining changes by an additional shear component. It is shown that the incremental elastic–plastic moduli are spatially nonuniform for such situations, contrary to the classical J₂ flow and deformation theories. The critical shear modulus that governs the buckling equation is obtained as a weighted average of the incremental elastic–plastic moduli over the cross-section of the cruciform.Using a plasticity model proposed by the authors, that includes the vertex effect, the buckling-critical load is computed for a aluminium column both with the analytical model and a FEM-based eigenvalue buckling analysis. The stable post-buckling path is determined by the energy criterion of path-stability. A comparison with the experimentally obtained classical results by Gerard and Becker (1957) shows good agreement without relying on artificial imperfections as necessary in the classical J₂ flow theory.     

Approximation of the third two-point moments of the velocity field in isotropic turbulence

Different methods for approximating the third two-point moments of the velocity fields entering in the von Kármán-Howarth equation are compared using the known experimental results of A. Townsend and R. Stewart, together with the model form of the energy spectrum of turbulence, which makes it possible to approximate the experimentally determined second moments of the velocity field. The latter moments are used for calculating the third two-point moments following the methods proposed by various authors. The calculated results are compared with the experimental data which makes it possible to quantitatively estimate the approximation accuracy. For several models the second-order structure function is calculated from the Kolmogorov equation for the inertial interval. In this case, for the models of K. Hasselmann and Yu.M. Lytkin the power-law dependence D _LL (r) ～ r ^2/3 expected for the inertial interval is obtained for the structure function D _LL (r).     

Improvements to the RADIOM non-LTE model

In 1993, we proposed the RADIOM model [M. Busquet, Phys. Fluids 85 (1993) 4191] where an ionization temperature T_z is used to derive non-LTE properties from LTE data. T_z is obtained from an “extended Saha equation” where unbalanced transitions, like radiative decay, give the non-LTE behavior. Since then, major improvements have been made. T_z has been shown to be more than a heuristic value, but describes the actual distribution of excited and ionized states and can be understood as an “effective temperature”. Therefore we complement the extended Saha equation by introducing explicitly the auto-ionization/dielectronic capture. Also we use the SCROLL model to benchmark the computed values of T_z.     

Exploring k and ? with R–Equation Model Using Elliptic Relaxation Function

An extended version of the isotropic R?Cequation model accompanied by an elliptic relaxation approach to account for the distinct effects of low-Reynolds number (LRN) and wall proximity is proposed. The turbulent kinetic energy k and the dissipation rate ? are evaluated using the R ( $=k^2/\tilde{\epsilon}$ ) transport equation together with some empirical relations. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz?? inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence in the sense that they are sensitized to rotational and nonequilibrium flows. The model is validated against a few well-documented flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model offers some improvement over the Spalart?CAllmaras one?Cequation model and competitiveness with the SST k?C?? model.     

Dynamic behaviour of a thin laminated plate embedded with auxetic layers subject to in-plane excitation

The dynamic modelling of a simply-supported thin laminated plate subject to in-plane excitation is established based on the classic shear theory and von Kármán nonlinear theory. The method of multiple scales is used to determine an approximate solution for the system. According to solvability conditions, the nonlinear modulation equations arising from the principal parametric resonances are obtained and two possible nontrivial solutions are performed. To analyze the nonlinear dynamic response of the plate embedded with auxetic layers, 5-layered sandwich plate, in which two auxetic elastic layers are alternatively sandwiched between three positive Poisson’s ratio (PPR) elastic ones, is presented. The natural frequency of model (m, n) shows an increase with respect to the absolute value of Poisson’s ratio. Particularly, the amplitude-frequency responses of the laminated plate subject to principal parametric resonance are analyzed for different values of Poisson’s ratio. Moreover, it can be found that for model (m, n), there must be some certain value or interval of negative Poisson’s ratio (NPR), which, results in zero response effect, in other words, the in-plane excitation will be ineffective for this model when the Poisson’s ratio just lies at such a value or interval. Furthermore, it can also be observed that the certain interval of Poisson’s ratio becomes wider with the increase of damping.     

Thickness effect of NACA foils on hydrodynamic global parameters,boundary layer states and stall establishment

The present study experimentally investigates the hydrodynamic behaviour of 2-D NACA (15%, 25% and 35%) symmetric hydrofoils at Reynolds number 0.5×10⁶. Particular attention was paid to the hysteretic behaviour at the static stall angle, and a detailed cartography of the boundary layer structures (integral quantities and velocity profiles) is given to support the detachment mechanism and the onset of von Kármán instability for thick hydrofoils.     

Existence Result for a Dynamical Equations of Generalized Marguerre-von Kármán Shallow Shells

In a recent work in the static case, Gratie (Appl. Anal. 81:1107–1126, 2002) has generalized the classical Marguerre-von Kármán equations studied by Ciarlet and Paumier in (Comput. Mech. 1:177–202, 1986), where only a portion of the lateral face of the shallow shell is subjected to boundary conditions of von Kármán type, while the remaining portion is subjected to boundary conditions of free edge. Then Ciarlet and Gratie (Math. Mech. Solids 11:83–100, 2006) have established an existence theorem for these equations. In Chacha et al. (Rev. ARIMA 13:63–76, 2010), we extended formally these studies to the dynamical case. More precisely, we considered a three-dimensional dynamical model for a nonlinearly elastic shallow shell with a specific class of boundary conditions of generalized Marguerre-von Kármán type. Using technics from formal asymptotic analysis, we showed that the scaled three-dimensional solution still leads to two-dimensional dynamical boundary value problem called the dynamical equations of generalized Marguerre-von Kármán shallow shells. In this paper, we establish the existence of solutions to these equations using a compactness method of Lions (Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969).     

Temperature correlations with vorticity and velocity in a turbulent cylinder wake

This work aims to understand the difference in the correlations between the fluctuating temperature and the vorticity from that between the fluctuating temperature and the velocity in a turbulent cylinder near wake. Measurements are made at x/d = 10, 20 and 40, where x is the streamwise distance from the cylinder axis and d is the cylinder diameter, with a Reynolds number of 2.5×10³ based on d and the free-stream velocity. The three components of the fluctuating velocity vector u_i(i = 1, 2 and 3), vorticity vector ω_i (i = 1, 2 and 3), and temperature θ in the plane of the mean shear are measured simultaneously with a multi-wire probe consisting of four X-hotwires and four cold wires. It is found that at x/d = 10, both correlations between u_iand θ and between ω_i and θ predominantly take place at St = 0.21, due to the concentric distribution of the Kármán vortices and the heat. With increasing x/d, the correlation between ω_i (i = 1, 2 and 3) and θ drops rapidly, as a result of the weakened Kármán vortices; in contrast, the correlation between u₁ and θ increases appreciably, largely due to an enhanced correlation between u₁ and θ at low frequencies or scales of motions larger than the Kármán vortex. The slowly decreasing (along x) two-point autocorrelations of u₁ and θ suggest that the very-large-scale motions (VLSMs) found in wall flows occur also in the turbulent wake and are responsible for the high correlation between u₁ and θ at low frequencies.     

On the behavior of viscoelastic free jets with elliptical cross section

In [1,2] we develop a comprehensive theory of one space dimensional closure models (closed systems of 1-D equations for the unknown, or modal, variables) for free viscoelastic jets. These closure models are derived via asymptotics from the full 3-D boundary value problem under the conditions of a Von Kármán-like flow geometry, a Maxwell-Jeffreys constitutive model, elliptical free surface cross section, and a slender jet scaling. The focus of the present paper is to determine the consequences and predictions of the lowest order system of equations in this asymptotic analysis. For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and draw-down of the cross section, in agreement with observed behavior. In the absence of surface tension the transformation from a cross section with major axis in one direction to a cross section with major axis in the perpendicular direction occurs only once, in agreement with the observation of Taylor [4]. In viscoelastic regimes, our model predicts swell of the elliptical extrudate and distortion of the elliptical extrudate cross section from the dimensions of the die aperture.     

Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls

In this work, we present an experimental study of the wall confinement effect on the wake formation behind a circular cylinder of diameter d_c=10 mm and of length L_c=30d_c. The experiments were performed in a water tunnel with the dimensions (length=300d_c, height=3d_c, span L_c=30d_c). The confinement rate was r=1/3 and the Reynolds number was in the range of 30–277. The experiments were done using 2-D PIV measurements. The first instability was delayed by the confinement and the von Kármán vortices characteristics are different from the unconfined case. Proper orthogonal decomposition (POD) of the flow was used for a filtering purpose and to extract the energetic contribution of the different modes. A low-order representation of the flow, constructed from the first pair of modes in the well-defined region of the flow, shows that von Kármán vortices are equivalent to vanishing progressive waves. Measurements done above the cylinder show the presence of 3-D span instabilities showing great similarities with “Mode A” and “Mode B” found in the unconfined case.     

On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions

One of the major drawbacks of the Gurson-type of porous plasticity models is the inability of these models to predict material failure under low stress triaxiality, shear dominated conditions. This study addresses this issue by combining the damage mechanics concept with the porous plasticity model that accounts for void nucleation, growth and coalescence. In particular, the widely adopted Gurson–Tvergaard–Needleman (GTN) model is extended by coupling two damage parameters, representing the volumetric damage (void volume fraction) and the shear damage, respectively, into the yield function and flow potential. The effectiveness of the new model is illustrated through a series of numerical tests comparing its performance with existing models. The current model not only is capable of predicting damage and fracture under low (even negative) triaxiality conditions but also suppresses spurious damage that has been shown to develop in earlier modifications of the GTN model for moderate to high triaxiality regimes. Finally the modified GTN model is applied to predict the ductile fracture behavior of a beta-treated Zircaloy-4 by coupling the proposed damage modeling framework with a recently developed J₂–J₃ plasticity model for the matrix material. Model parameters are calibrated using experimental data, and the calibrated model predicts failure initiation and propagation in various specimens experiencing a wide range of triaxiality and Lode parameter combinations.     

Investigating direction characteristics of the heat transfer coefficient in forced convection reflow oven

In this paper, we investigate the heating capability of forced convection reflow ovens and the effect of the ovens’ construction on it. This parameter depends on the heat transfer coefficient (α) which is mainly determined by the gas flow parameters. First of all we studied the gas flow circumstances in the reflow oven using a stationary and isothermal gas flow model. The conclusions of the model are then proved by experimental results as well. Our experiments were based on measuring the temperature changes on different points which are located around the centre of the ovens’ processing area. From these data, direction characteristics of α were calculated using the heat equation of the investigated reflow oven. Our results are important for effective thermal modelling of the reflow soldering process [B. Illés, G. Harsányi, 3D thermal model to investigate component displacement phenomenon during reflow soldering, Microelectronics Reliability 48 (2008) 1062–1068] and are useful to calibrate reflow ovens. In this project we examined the latest reflow ovens constructed with nozzle-matrix blower system.     

An intermittency model for predicting roughness induced transition

An intermittency transport equation for RANS modeling, formulated in local variables, is extended for roughness-induced transition. To predict roughness effects in the fully turbulent boundary layer, published boundary conditions for k and ω are used. They depend on the equivalent sand-grain roughness height, and account for the effective displacement of wall distance origin. Similarly in our approach, wall distance in the transition model for smooth surfaces is modified by an effective origin, which depends on equivalent sand-grain roughness. Flat plate test cases are computed to show that the proposed model is able to predict transition onset in agreement with a data correlation of transition location versus roughness height, Reynolds number, and inlet turbulence intensity. Experimental data for turbine cascades are compared to the predicted results to validate the proposed model.     

Modeling lattice strain evolution at finite strains and experimental verification for copper and stainless steel using in situ neutron diffraction

An elasto-plastic self-consistent (EPSC) polycrystal model is extended to account, in an approximate fashion, for the kinematics of large strains, rigid body rotations, texture evolution and grain shape evolution. In situ neutron diffraction measurements of the flow stress, internal strain, texture and diffraction peak intensity evolutions were performed on polycrystalline copper and stainless steel, up to true tensile strains of ε = 0.3. Suitably adjusted slip system hardening model parameters enable the model to quantitatively describe the flow stress of the polycrystalline aggregate. Quantitative predictions of the texture evolution and the internal strain evolution along the stress axis are good, while predictions of transverse internal strains (perpendicular to the tensile loading direction) are less satisfactory. The latter exhibit a large dispersion from grain to grain around a macroscopic average, and the implications of this finding for the interpretation of in situ neutron diffraction method are explored. Finally, as a demonstration of the applicability of the model to problems involving finite rotation, as well as deformation, simulations of simple shear were conducted which predict a texture evolution in agreement with published experimental data, and other modeling approaches as well.     

A 3D model of the cyclic thermomechanical behavior of shape memory alloys

The model in the first part of this paper is extended to account for SMA behavior under cyclic loading. To this end, three new state variables are introduced: internal stress B, residual strain ?_r and cumulated martensite volume fraction z_e. Several parameters of the extended model depend on z_e, making them evolve with cyclic phase change. Cyclic SMA effects including training and two-way shape memory are accounted for and several numerical simulations are provided and validated in the case of cyclic superelasticity.     

Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties

Thermal postbuckling analysis is presented for graphene-reinforced composite (GRC) laminated cylindrical shells under a uniform temperature field. The GRC layers are arranged in a functionally graded (FG) graphene reinforcement pattern by varying the graphene volume fraction in each GRC layer. The GRCs possess temperature dependent and anisotropic material properties and the extended Halpin–Tsai model is employed to evaluate the GRC material properties. The governing equations are based on a higher order shear deformation shell theory and include the von Kármán-type kinematic nonlinearity and the thermal effects. A singular perturbation method in conjunction with a two-step perturbation approach is applied to determine the thermal postbuckling equilibrium path for a GRC shell with or without geometric imperfection. An iterative scheme is developed to obtain numerical thermal buckling temperatures and thermal postbuckling load–deflection curves for the shells. The results reveal that the FG-X piece-wise FG graphene distribution can enhance the thermal postbuckling capacity of the shells when the shells are subjected to a uniform temperature loading.

     

Thrust enhancement due to flexible trailing-edge of plunging foils

Drag reduction for hydrofoils is studied through thrust generation on foils plunging at low Strouhal numbers in order to simulate the action of the ocean waves. Force, deformation and flow field measurements are presented for a partially flexible plunging foil in water tunnel experiments. The foil is predominantly rigid with a short flexible trailing-edge plate of length: L=0.1c, 0.2c, or 0.3c. Using flexible plates, whose natural structural frequency is much higher than the frequency of the plunge oscillations, increases thrust compared to the rigid case. Flexibility is generally more effective for larger lengths of the flexible plate and smaller plunge amplitudes. The maximum observed is therefore for the largest length and smallest amplitude studied: L=0.3c and a=0.1c and equates to 28% more thrust than the rigid case. Optima are observed in the non-dimensional rigidity (λ) versus flap angle amplitude (δ, which is a measure of the relative deformation) parameter space. These occur at λ≈2 and δ≈7–13° for a wide range of flexible plate length and plunge amplitude. Whilst a satisfactory explanation of why there is an optimal flap amplitude remains unavailable, the case of optimal flap angle amplitude results in increased trailing-edge vortex circulation, giving a stronger reverse Kármán vortex street and thus a stronger time-averaged jet.     

Linear Eddy Mixing Model Studies of High Karlovitz Number Turbulent Premixed Flames

Turbulent premixed flames exhibit different structural and propagation characteristics with increasing upstream turbulence intensity starting from thin wrinkled flames in the Corrugated Flamelet regimes to a flame with a thicker preheat zone in the Thin Reaction Zone Regime (TRZ) and finally, becoming more disorganized or broken in the Distributed or Broken Reaction Zone (D/BRZ) regimes under intense turbulence. A single comprehensive predictive model that can span all regimes does not currently exist, and in this study we explore the ability of the stand-alone one-dimensional linear-eddy mixing (LEM) model to simulate the flames in all these regimes. Past applications of this 1DLEM model have demonstrated reasonable predictions in the flamelet and TRZ regimes and here, new experiments in the TRZ regime are specifically addressed to evaluate the predictive capability of this model. Additional simulations in the D/BRZ regimes (where no data is currently available) are performed to determine if the model can be extended to the high turbulence regime. Comparison with the data in the TRZ regime shows satisfactory agreement. Analysis suggests varying levels of preheat zone broadening in all the TRZ and D/BRZ cases. While the average heat release distribution for the TRZ cases is nearly identical to the laminar unstrained baseline, changes to the species and heat release distribution are observed only at a high Karlovitz Number K a > 10³. In the D/BRZ regime it is shown that the transition is related to enhanced turbulent diffusion that dominates molecular diffusion effects causing deviations from the laminar baseline.     

Near-wake flow characteristics of a circular cylinder close to a wall

Flow characteristics in the near wake of a circular cylinder located close to a fully developed turbulent boundary layer are investigated experimentally using particle image velocimetry (PIV). The Reynolds number based on the cylinder diameter (D) is 1.2×10⁴ and the incident boundary layer thickness (δ) is 0.4D. Detailed velocity and vorticity fields in the wake region (0<x/D<6) are given for various gap heights (S) between the cylinder and the wall, with S/D ranging from 0.1 to 1.0. Both the ensemble-averaged (including the mean velocity vectors and Reynolds stress) and the instantaneous flow fields are strongly dependent on S/D. Results reveal that for S/D⩾0.3, the flow is characterized by the periodic, Kármán-like vortex shedding from the upper and lower sides of the cylinder. The shed vortices and their evolution are revealed by analyzing the instantaneous flow fields using various vortex identification methods, including Galilean decomposition of velocity vectors, calculation of vorticity and swirling strength. For small and intermediate gap ratios (S/D⩽0.6), the wake flow develops a distinct asymmetry about the cylinder centreline; however, some flow quantities, such as the Strouhal number and the convection velocity of the shed vortex, keep roughly constant and virtually independent of S/D.