Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique

Theoretical and experimental large deflection and stress analysis of a master leaf spring considering stress concentration effect of clamping is reported. The non-uniformly curved master leaf spring under three point bending subjected to moving boundaries is modeled. Geometrically nonlinear strain-displacement relations, as necessary for the theoretical analysis, are derived through visualization of physics behind the large deformation problem. An embedded curvilinear coordinate system is considered, to study the combined effects of non-uniform curvature, bending, stretching and shear deformation including cross-sectional warping. Governing equation of the non-uniformly curved beam system is derived in variational form using energy method, based on linear material constitutive relations and the derived nonlinear kinematic relations. An iterative solution scheme through successive geometry updation is developed and executed in MATLAB® software to solve the governing equation involving strong geometric nonlinearity together with complicating moving boundary effect. Experimental deflection profiles under static loading are obtained through manual image processing technique using AutoCAD® software. Whereas, strain measurements are performed using strain gauges with data acquisition system (HBM-MX840B). Comparison between the theoretical and experimental results lead towards observation on stress concentration effect due to presence of geometric discontinuity in form of a small hole in the physical system. A modified formulation is proposed using domain decomposition method incorporating effect of geometric discontinuity through an equivalent curved beam geometry of variable cross-section. The modified theoretical model is validated successfully with the experimental results, and observations on stress characteristics and effect of hole diameter to beam width ratio are made.

Testing of logarithmic-law for the slip with friction boundary condition

Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ $\bar{u}$ of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.

Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions

In this current study, the transient numerical calculations using CFD code are carried out under different outlet impeller diameters for the flow field within a centrifugal pump under single-phase and cavitation conditions. Both qualitative and quantitative analyses are carried out on all of these results in order to better understand the flow structure within a centrifugal pump. Also, the investigations using different outlet impeller diameters configurations relating to the static pressure, velocity magnitude, vapour volume fraction variations, as well as pressure fluctuations in both time and frequency domain at the impeller and volute of the pump are analysed. Velocity and static pressure variations of the pump under different outlet impeller diameters range (200, 210 and 220 mm) are investigated. Reliable model is developed and validated, at various pump operating conditions, to analyse the characteristics of pressure fluctuations in both time and frequency domain. Cavitation occurrence, under different outlet impeller diameters and flow rates, are detected and correlated, using a CFD model (volume fraction distributions). Based on the developed model’s findings, at the set operating conditions ranges, the distribution and impact (cavitation and head-wises) of both the pressure and velocity are analysed. The average pressure fluctuation in the volute for do = 210 mm is higher than for do = 200 mm by about 6.74%, also the maximum pressure fluctuation for do = 220 mm is higher than for do = 210 mm by around 7.4%. Furthermore, the maximum pressure fluctuation in the impeller for do = 210 mm is higher than for do = 200 mm by 12.48%, also for do = 220 mm is higher than for do = 210 mm by 10.8%. The developed CFD models are proved valuable tools in identifying and optimizing the pump performance and characterization. The head for when do = 220 mm is higher than for when do = 200 mm under both single-phase and cavitation conditions by around 14.13% and 14.69%. The maximum pressure fluctuation for do = 200 mm is lower than for do = 210 mm by 41.58%. Furthermore, the maximum pressure fluctuation at the impeller for do = 220 mm is higher than the two models. There is a small clearance between the impeller and the volute for this model, leading to the pressure fluctuation amplitudes being higher than the other above models.

Numerical study of the energy efficiency of the building envelope containing multi-alveolar structures under Tunisian weather conditions

The study of the thermal inertia of buildings is a subject of major interest. The thermal insulation and the nature of the wall sensitively modify the inertia of the building and are the solutions to improve the energy efficiency of the envelope. The roof is well exposed to solar radiation in summer and contributes to significant losses in winter due to convective exchanges. To lead to a thermal comfort, a thermal insulation is necessary. In this context, we carry out a numerical study of the thermal behavior of a building with two zones in variable meteorological conditions for a Tunisian climate (region of Sousse) based on the thermoelectric analogy and using the nodal method as a numerical method. The object of this work is to study the effect of the thermal inertia of the roof equipped with a multi-alveolar structure on the thermal behavior of the air inside the room and on its energy consumption. Taking into account the energy input of occupant, a complete model was established to increase the accuracy of the calculations. The results show that the multi-alveolar structure placed on the outside of the roof reduces energy consumption during the winter period when the alveolar structure is placed in the conductive direction and during the summer period when the alveolar structure is placed in the insulate direction.

Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition

The present article explores the effect of viscous dissipation on steady natural convection Couette flow subject to convective boundary condition. Due to the nonlinearity and coupling of the governing equations in the present situation, the homotopy perturbation method was employed to obtain the solutions of the energy and momentum equations. The impacts of the controlling parameters were investigated and discussed graphically. In the course of investigation, it was found that fluid temperature increases with an increase in viscous dissipation while the reverse trend was observed in fluid velocity. However, it was also discovered that heat generation leads to a decrease in the rate of heat transfer on the heated plate and it increases on the cold plate. Finally, it was concluded that the velocity boundary layer thickness increases with an increase in Biot number.

Effect of moving stretching sheets on natural convection in partially heated square cavity filled with nanofluid

This article deals with the heat transfer enhancement due to buoyancy force in a partially heated square enclosure filled with nanofluids. The model is developed to analyse the behaviour of nanofluids taking into account of volume fraction and stretching parameter, when square horizontal walls are moving in opposite directions to each other. Implicit alternate direct finite difference method has been used to solve the governing equations of vorticity, energy, and kinematics. Graphically investigated the effect of physical pertinent controlling parameters on the dimensionless velocity, streamlines, isothermal, and Nusselt number. The obtained numerical solution achieves the best configuration for Rayleigh number 103 ≤ Ra ≤ 105, stretching parameter 0 ≤ τ ≤ 2.5, and volume fraction 0 ≤ ϕ ≤ 0.2. It is found that the stretching parameter and direction of moving walls affect the fluid flow, flow strength, and heat transfer in the cavity.

A new clique polynomial approach for fractional partial differential equations

This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.

Solutions and stability for p-Laplacian differential problems with mixed type fractional derivatives

In this note, the main emphasis is to study two kinds of high-order fractional p-Laplacian differential equations with mixed derivatives, which include Caputo type and Riemann–Liouville type fractional derivative. Based on fixed point theorems on the cone, the existence-uniqueness of positive solutions for equations and two iterative schemes to uniformly approximate the unique solutions are discussed theoretically. What’s more, the sufficient conditions for stability of the equations are given. Some exact examples are further provided to verify the analytical results at the end of the article.

On exact solutions of fractional differential-difference equations with Ψ-Riemann–Liouville derivative

The aim of this work is to modify the invariant subspace method (ISM) in order to obtain closed form solutions of fractional differential-difference equations with Ψ-Riemann–Liouville (Ψ-RL) fractional derivative for first time. We have investigated the cases of two-dimensional and the three-dimensional invariant subspaces (ISs) in the suggested scheme. Using the modified ISM, new exact generalized solutions for the general fractional mKdV Lattice equation and the fractional Volterra lattice system are obtained. Compared with similar solution techniques in literature, the presented solution scheme is highly efficient and is capable to find new general exact solutions which cannot be attained by other methods.

Stability analysis of nonlinear impulsive switched positive systems

In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.