Cooling methods are needed for turbine blade tips to ensure a long durability and safe operation. A common way to cool a tip is to use serpentine passages with 180-deg turn under the blade tip-cap taking advantage of the three-dimensional turning effect and impingement like flow. Improved internal convective cooling is therefore required to increase the blade tip lifetime. In the present study, augmented heat transfer of an internal blade tip with pin-fin arrays has been investigated numerically using a conjugate heat transfer method. The computational domain includes the fluid region and the solid pins as well as the tip regions. Turbulent convective heat transfer between the fluid and pins, and heat conduction within pins and tip are simultaneously computed. The main objective of the present study is to observe the effect of the pin material on heat transfer enhancement of the pin-finned tips. It is found that due to the combination of turning, impingement and pin-fin crossflow, the heat transfer coefficient of a pin-finned tip is a factor of 2.9 higher than that of a smooth tip at the cost of an increased pressure drop by less than 10%. The usage of metal pins can reduce the tip temperature effectively and thereby remove the heat load from the tip. Also, it is found that the tip heat transfer is enhanced even by using insulating pins having low thermal conductivity at low Reynolds numbers. The comparisons of overall performances are also included.

In this paper, we study the numerical solution of the Stokes system in deformed axisymmetric geometries. In the azimuthal direction the discretization is carried out by using truncated Fourier series, thus reducing the dimension of the problem. The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables. The meridian domain is subdivided into elements, in each of which the solution is approximated by truncated polynomial series. The results of numerical experiments for several geometries are presented.

In this paper, we investigate the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional delay differential equations (FDDEs) with the Caputo fractional derivative. Some results including an estimate of the solutions of FDDEs are given respectively. Theoretical results are verified by some numerical examples.

In this paper, we analyze the Wilson element method of the eigenvalue problem in arbitrary dimensions by combining a new technique recently developed in [10] and the a posteriori error result. We prove that the discrete eigenvalues are smaller than the exact ones.

In the present paper a combined procedure for the quasi-dimensional modelling of heat transfer, combustion and knock phenomena in a “downsized” Spark Ignition two-cylinder turbocharged engine is presented. The procedure is extended to also include the effects consequent the Cyclic Variability. Heat transfer is modelled by means of a Finite Elements model. Combustion simulation is based on a fractal description of the flame front area. Cyclic Variability (CV) is characterized through the introduction of a random variation on a number of parameters controlling the rate of heat release (air/fuel ratio, initial flame kernel duration and radius, laminar flame speed, turbulence intensity). The intensity of the random variation is specified in order to realize a Coefficient Of Variation (COV) of the Indicated Mean Effective Pressure (IMEP) similar to the one measured during an experimental campaign. Moreover, the relative importance of the various concurring effects is established on the overall COV. A kinetic scheme is then solved within the unburned gas zone, characterized by different thermodynamic conditions occurring cycle-by-cycle. In this way, an optimal choice of the “knock-limited” spark advance is effected and compared with experimental data. Finally, the CV effects on the occurrence of individual knocking cycles are assessed and discussed.

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe’s scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

Let S: [0, 1]→[0, 1] be a chaotic map and let f* be a stationary density of the Frobenius-Perron operator PS: L1→L1 associated with S. We develop a numerical algorithm for approximating f*, using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability consideration. Numerical experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.

In this work, we present and discuss some modifications, in the form of two-sided estimation (and also for arbitrary source functions instead of usual sign-conditions), of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.

Ramp load/unload (L/UL) mechanisms are widely used to rest sliders in hard disk drives (HDDs). Loading/unloading a slider swiftly and smoothly is crucial in a HDD design. A novel, efficient simulation scheme is proposed to investigate the behaviors of a head disk interface (HDI) in ramp unloading processes. A dual scale model is enabled by decoupling the nano-meter scale change of an air bearing and the micro- or milli-meter scale deformation of a suspension. A modified Reynolds equation governing the air bearing was solved numerically. The slider design was characterized with performance functions. Three stages in an unloading process were analyzed with a lumped parameter suspension model. Key parameters for the model were estimated with a comprehensive finite element suspension model. Finally, simulation results are presented for a commercial HDI design.

In this work, the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system. In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling, the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates. Furthermore, to take into account the influence of material deformation and nonlinear wave interaction at the interface, an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states. Numerical tests are presented to verify the resultant method.

Modelling based on Computational Fluid Dynamics (CFD) is by now effectively used in fire research and hazard analysis. Depending on the scenario, radiative heat transfer can play a very important role in enclosure combustion events such as tunnel fires. In this work, the importance of radiation and the effect of the use of different approaches to account for it were assessed. Firstly, small-scale tunnel fire simulations were performed and the results compared with experimental data, then realistic full-scale scenarios were simulated. The results show up the capability of CFD modelling to reproduce with good approximation tunnel fires. Radiation proved to be noteworthy mainly when the scale of the fire is relatively large. Among the various approaches employed to simulate radiation, the use of the Discrete Transfer model gave the most accurate results, mainly when the absorption-emission characteristics of the combustion products were taken into account. Finally, the suitability of the use of CFD in quantitative Fire Hazard Analysis is discussed.

In this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.

In this article, natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method. Results show that the heat transfer decreases when the ball numbers increase. When the magnetic field is increased, the heat transfer is enhanced; however the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles.

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

In this paper, a numerical method employing a finite difference technique is used for an investigation of viscous, incompressible fluid flow in a tube with absorbing wall and slowly varying cross-section. The effect of fluid absorption through permeable wall is accounted by prescribing flux as a function of axial distance. The method is not restricted by the parameters in the problem such as wave number, permeability parameter, amplitude ratio and Reynolds number. The effects of these parameters on the radial velocity and mean pressure drop is studied and the results are presented graphically. Comparison is also made between the results obtained by perturbation method of solution and present approach.

This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conduction-convection equations by using the lowest equal-order pairs of finite elements. This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. The stability of the discrete scheme is derived under some regularity assumptions. Optimal error estimates are obtained by applying the standard Galerkin techniques. Finally, the numerical illustrations agree completely with the theoretical expectations.

The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magneto-thermoelastic solid. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave cases. The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries. The reflection coefficients are depending on the angle of incidence, magnetic field, phase lags and other material constants. Results show that the sum of energy ratios is unity at the interface. The results are discussed and depicted graphically.

Phase change in ice-water systems in the geometry of horizontal cylindrical annulus with constant inner wall temperature and adiabatic outer wall is modeled with an enthalpy-based mixture model. Solidification and melting phenomena under different temperature conditions are analyzed through a sequence of numerical calculations. In the case of freezing of water, the importance of convection and conduction as well as the influence of cold pipe temperature on time for the complete solidification are examined. As for the case of melting of ice, the influence of the inner pipe wall temperature on the shape of the ice-water interface, the flow and temperature fields in the liquid, the heat transfer coefficients and the rate of melting are analyzed. The results of numerical calculations point to good qualitative agreement with the available experimental and other numerical results.

In this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.