During the year, due to weather conditions, the temperature fluctuations at surface level cause problems in underground pipes as a result of freezing water. One of the best prevention strategies is the use of polyurethane floor insulation for keeping the temperature of clay above zero degrees Celsius. In this study to calculate the minimum thickness of polyurethane insulation layer, the differential equation of energy is solved based on principle of separation of variables using imaginary eigenvalues for consistency with the temperature distribution in multi-layer consist of asphalt, gravel and polyurethane with finite thickness and clay as a semi-infinite medium with periodic thermal boundary conditions at surface level. Numerical approach is performed in Matlab and the results show that by using a thin layer of polyurethane it’s possible to greatly reduce the insertion depth of water pipes.

The aim of this work is to compare the effectiveness of two induction heating methods of injection molds by means of thermovision measurement. The problem of selecting external or internal induction heating for thin-walled moldings used in electrical and electronic industry is taken into consideration. At first, the boundary conditions were defined. Then a group of three moldings with different defects were selected. The defects that have been taken to remove by means of induction heating are: weld lines, breaking hinges, air traps and diesel effect. In order to compare the methods of heating two models were created. The first one was made as a block of steel with milled grooves with a width of 2mm and a depth varying from 1 to 12mm. The second model consisted of two parts, one being placed in the second. The research stand consisted of prepared models, induction generator with power of 10kW, specially shaped inductor, thermovision camera and temperature sensor of PT100 type as a reference. First, the surface with milled grooves was heated in four different sectors (because of the shape of inductor) in time of 2s. The area of low-depth grooves heated up to 154°C while the surface with 12 mm grooves heated up to 120°C. It comes from eddy currents flowing. This phenomenon shows that effectiveness of external heating of grooved surface decreases with increasing of grooves depth. In the second case the cavity insert was heated as a coil inside the inductor which was located inside the mold. The measured value was the time of heat transfer from heated area to the forming surface in three configurations.

In this study, three-dimensional computational fluid dynamics (CFD) analyses are performed to assess the thermal-hydraulic characteristics of a commercial Gasketed Plate Heat Exchangers (GPHEx) with 30 degrees of chevron angle (Plate1). The results of CFD analyses are compared with a computer program (ETU HEX) previously developed based on experimental results. Heat transfer plate is scanned using photogrammetric scan method to model GPHEx. CFD model is created as two separate flow zones, one for each of hot and cold domains with a virtual plate. Mass flow inlet and pressure outlet boundary conditions are applied. The working fluid is water. Temperature and pressure distributions are obtained for a Reynolds number range of 700–3400 and total temperature difference and pressure drop values are compared with ETU HEX. A new plate (Plate2) with corrugation pattern using smaller amplitude is designed and analyzed. The thermal properties are in good agreement with experimental data for the commercial plate. For the new plate, the decrease of the amplitude leads to a smaller enlargement factor which causes a low heat transfer rate while the pressure drop remains almost constant.

In this study non-linear thermal buckling of circular shallow arches made of functionally graded materials subjected to a linear temperature gradient is investigated. For this purpose, a functionally graded circular shallow arch is considered that its strain-displacement relation follows the Donnells nonlinear shallow shell theory. The material properties are varied smoothly through the arch thickness according to the power law distribution of the volume fraction of constituent materials. Also, material properties are considered temperature-dependent. The classical single layer theory assumptions that are reasonable for slender arches are implemented. To investigate the large deformations of such arch, the von-Karman type geometrical nonlinearity is utilized that is suitable for moderately large class of rotations. The virtual displacement principle and calculus of variation are employed to derive the governing equilibrium equations and complete set of boundary conditions of the FGM arch. The adjacent equilibrium criterion is employed for the stability analysis of the FGM arch. An analytical approach is accomplished and a closed-forms solution for thermal bifurcation points of the FGM shallow arches is presented. Also critical bifurcation loads corresponding to the critical temperatures with the presence of non-linear pre-buckling deformations is obtained. Illustrative results examine the effect of various involved parameters such as power law index, opening angle, geometric parameter (or otherwise length to thickness ratio). Obtained numerical results represent that, in most cases, thermal bifurcation for the FGM arches occurs in the high temperatures and the critical buckling temperatures are approximately high even for slender FGM arches. Also effective of ceramic or metal rich area at the bottom surface of the FGM arch is investigated and results are presented for both cases and are compared together. Varieties between this two cases due to contrast between material and structural stretching-bending coupling effect. Results presented illustrative the ceramic rich area at the bottom surface cause the higher critical buckling temperatures for the FGM arches.

This paper summarizes a research project in the field of design and manufacturing of a water brake dynamometer for power testing facilities. In the current study, the design process of a water brake with drilled rotor disks is presented. This process is examined against the development of a water brake for a 4MW gas turbine power measurement at 15,000 RPM speed. The proposed algorithm is based on vital assumptions such as; applying product designing issues and limited modular analysis that urges the disciplinary attitude and leads to the possibility of rapid development, easy maintenance and ease of access. The final scheme is divided into six disciplines with functional classification. These disciplines are rotor, housing, cabs, pedestals, skid and accessories. Accessories, itself, consist of cooling system, lubricating system and control unit. Every discipline has its special function and could be optimized separately. It is possible to change any discipline specification without affecting other disciplines modularity. Using FEM software makes it easy to analyze the mechanical component for static and dynamic load condition regarding complex initial and boundary condition. But it is not wise to analyze whole system for designing a product due to numerical calculation errors. Besides, it is not necessary to use calculation to select machine elements. Rotor dynamics is investigated with modal analysis and related Campbell diagram. Also, transient analysis on housing, rotor and load cell arm is presented. The modal analysis on pedestals and skid is performed to predict the structural behavior under periodic loads caused by rotating unbalance. The process presented in this paper is a method for design of water brake dynamometer. Modularity presented by a product tree and a trend for design cycles associated with computer simulation are the basis of this method. The final product that is designed with this algorithm is successfully manufactured and tested.

In this study a numerical study of a suction muffler in a hermetic reciprocating compressor of a domestic refrigerator is performed using a finite volume based flow solver (Fluent). In order to reveal the behavior of the flow realistically, unsteady experimental pressure data has been used in the outlet boundary condition for the simulations. Detailed investigations are carried out to reveal the instantaneous flow behavior in different muffler sections such as channel and chambers based on the mass flow rate variation with respect to crankshaft angle. Power spectrum of pressure fluctuations at selected points help to reveal the noise characteristics of the muffler. This study gives a comprehensive insight into the interaction of muffler chambers with flow through the channel. In a previous study, the ratio of the chamber volumes were shown to be an important design parameter. To verify this assumption, three prototype muffler geometries were simulated. In these prototypes, the plate that divides the muffler into two chambers was moved by 7 mm and 10 mm in the direction to enlarge the second chamber. The flow through the prototype geometries were investigated numerically. The results showed that the aerodynamic performance increased while the aero-acoustic performance slightly decreased. Furthermore, this study aims to be an initial step to a more complicated optimization process which involves the inlet valve dynamics.

Counter current flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. This paper describes experimental and numerical results obtained in a circular column of 240 mm inner diameter with two inner pipes. The counter current flow studied concerns an upward flow of air and a downward flow of water at ambient temperature and pressure. The following range of operating conditions is analyzed: superficial air velocities up to 0.25 m/s and superficial water velocities up to 0.04 m/s, corresponding to global void fractions up to 27.7%. The experimental investigations concerns (i) flow visualization, (ii) local data from a double optical probe and (iii) global void fraction data. Images obtained from an optical camera are used to observe the general flow pattern and to support the boundary conditions of the numerical simulations, in terms of average bubble diameter. Data obtained from the double optical probe are used to study local flow characteristics. The gas disengagement technique is used to obtain the global void fraction over a range of superficial air velocities for the validation of the numerical method. Numerical calculations are performed with an Eulerian two-fluid model using the commercial code ANSYS Fluent Release 14.5.7 and results are compared with experimental data. The effects of bubble diameter and various interfacial drag coefficients are studied. The formulation of the drag coefficient is found to have significant effects on the global void fraction predictions. However, using merely the drag law, numerical results are inaccurate.

Even after many years of the application of numerical CFD techniques to flow through porous fences, still there is disagreement between researchers regarding the best turbulence model to be implemented in this field. Moreover, different sources claim to have achieved good agreement between numerical results and experimental data; however, it is not always possible to compare numerical and experimental results due to the lack of information or variations in test conditions. In this paper, five different turbulence models namely; K-ε models (standard, RNG and Realizable) and K-ω models (Standard and SST), have been applied through a 3D CFD model to investigate air flow behind a porous panel, under the same conditions (boundary conditions and numerical schemes). Results are compared with wind tunnel experiments. Comparison is based on the vertical velocity profile at a location 925 mm downstream of the fence along its center line. All models were capable of reproducing the velocity profile, however, some turbulence models over-predicted the reduction of velocity while it was under-predicted by other models, however, discrepancy between CFD modelling and experimental results was kept around 20%. Comprehensive description of the turbulence structure and the streamlines highlight the fact that the criterion for selecting the best turbulence model cannot rely only on the velocity comparison at one location, it must also include other variables.

The simulation of multiphase compressible flows through high pressure nozzles is presented. The study uses the developed numerical approach. There are many important engineering applications which are concerned with multiphase flows and convergent-divergent nozzles. This work presents the developed extension of the model and numerical algorithm based on the so called parent model earlier introduced by Saurel and Abgrall [Saurel, R. and Abgrall, R., A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys. 150 (1999), 425–467]. This model which consists of conservation laws for each phase complemented with the volume fraction evolution equation is modified by adding a source term to simulate area variation. The model is strictly hyperbolic and non-conservative due to the existence of non-conservative terms. The model is able to deal with compressible and incompressible flows. Moreover, it can deal with mixtures and pure fluids, where each fluid has its own pressure and velocity. The presence of velocity and pressure relaxation terms in the governing equations has made the velocity and pressure relaxation processes essential to tackle the boundary conditions at the interface. The interface separating phases is considered as a numerical diffusion zone in this method. The model is solved using an efficient Eulerian numerical method. A second order Godunov-type scheme with approximate Riemann solver is used to enable capturing of a physical interface by the resolution of the Riemann problem. The solution is obtained by splitting the hyperbolic part and source terms parts in the numerical algorithm. The source terms, including relaxation parts of the model, are tackled in succession using Strang splitting technique. The governing equations are solved at each computational cell using the same numerical algorithm for the whole domain including the interface. The main aim of this work has been to study different flow regimes with respect to pressure boundary conditions through the numerical solutions of single and multiphase flows. The performance of the programme has been verified via well established benchmark test problems for multiphase flows.

An oscillatory, zero-net-mass flux actuator system, Jet and Vortex Actuator (JaVA), is implemented on the step wall of a backward facing step. JaVA is shown previously both experimentally and numerically that it can energize the boundary layer by creating jets or vortices thus it may delay flow separation when used properly. The main part of JaVA is a rectangular cavity with a moving actuator plate. The actuator plate is mounted asymmetrically inside the cavity of the JaVA box, such that there are one narrow and one wide gap between the plate and the box. The main governing parameters are the actuator plate’s width ( b ), the amplitude ( a ) and the operating frequency ( f ). The main target of the control with active jets on the step wall is to influence directly the main recirculation zone, thus as the actuator plate or the step’s vertical wall moves periodically in horizontal direction, a jet emerges into the recirculation zone. Non-dimensional numbers such as the scaled amplitude ( S a = 2π a / b ) and the jet Reynolds number ( Re J = 4 abf /ν) as well as the maximum cross flow velocity characterize the JaVA-induced flow types and effects on the recirculation zone. One period consists of one blowing and one suction phase into the recirculation zone. The actuator plate has a sinusoidal motion determined by the amplitude and the operating frequency. Time-averaged flow fields and boundary layer profiles for actuated and not actuated cases at various operating frequencies indicate the effect of active flow control. The control effectiveness is given by the ratio of the jet Reynolds number to the Reynolds number of the incoming flow ( r = Re J / Re ). A transient finite-volume-based laminar, incompressible Navier-Stokes solver (Fluent) has been used to study the flow fields generated by JaVA. The computational domain consists of a moving zone along the channel and the motion of the actuator plate is generated by a moving grid imposing appropriate boundary conditions with User-Defined-Functions (UDF). Numerical simulations reveal the JaVA-boundary layer interaction in the narrow channel for various governing parameters such as frequencies (jet Reynolds numbers) and channel flow velocities (Reynolds numbers, Re = 200, 400 and 800). The proposed control method based on suction and blowing with an oscillating backward facing step (OsBFS) seems to be effective in shortening the recirculation zone length and delaying the flow separation downstream of the backward facing step.

A new variational formulation of coupled thermo-mechanical boundary-value problems has been recently proposed [1, 2], allowing to write mechanical and thermal balance equation under the form of an optimisation problem of a scalar energy-like functional. This functional is analysed in the framework of a thermo-visco-elastic problem, considering a strong coupling by taking into account the temperature dependency of mechanical properties. Different algorithmic schemes were tested, aiming to find the one that exhibits best computational performance. A simplified case shows that the optimum of the scalar energy-like functional is a saddle point.

Hip replacement failure is mainly attributable to the implant wear. Consequently preclinical wear evaluations are extremely important. As experimental tests are attractive but highly cost/time demanding, several predictive models have been proposed mainly based on finite element simulations and for metal on plastic (MoP) implants. The aim of this study is to develop a mathematical wear model of metal on metal prostheses, revision of the previous one for MoP implants, developed by the same authors. The model, based on the Archard wear law and on the Hertzian theory, was applied to compare a total (THR) and a resurfacing (RHR) hip replacement under both in vivo and in vitro gait conditions. The results were in agreement with the literature predicting wear rates significantly higher for the RHR than for the THR. The effect of the boundary conditions on wear rates/maps was also investigated and the model limitations discussed.

It is well known that the use of inelastic constitutive equations accounting for induced softening leads to pathological space (mesh) and time discretization dependency of the numerical solution of the Initial and Boundary value Problem (IBVP). To solve this drawback a thermodynamically-consistent formulation incorporating first gradient of micromorphic damage in the framework of micromorphic continuum is proposed. In this formulation the damage field is strongly coupled with mixed isotropic and kinematic nonlinear hardening together with micromorphic damage variables. A new finite element with one additional degree of freedom for the micromorphic damage field is developed and implemented into ABAQUS/EXPLICIT using the user’s subroutines VUEL and VUMAT. For the validation purpose, 3D uniaxial tension example of metallic sheet is performed using the proposed micromorphic fully coupled elastoplastic constitutive equations.

Relatively large, alternating in time, operational deformations of distributed piezoelectric actuators used in active vibration control may create a hazard of material degradation and damage of the actuator/host structure coupling. In the presented study a beam-like system with a surface mounted piezoelectric sensor/actuator pair operating in a closed loop with velocity feedback is analysed. The applied actuator is a piezoelectric fiber composite (PFC) with PZT (lead-zirconate-titanate) fibers aligned and polarized longitudinally. The uniform field method based on the rule of mixtures is used to determine the effective properties of the piezocomposite. Two types of the actuator failure are taken into account. The first relates to the edge delamination modelled as a significant reduction of the adhesive interlayer shear stiffness. The second relates to the PFC material degradation, which is regarded as a softening of the matrix material surrounding PZT fibers. It is assumed that the damaged adhesive region of the constant shear stiffness extends uniformly across the actuator from its ends to the centre. In analysis the beam is divided into sections due to its geometry, external loading and the damaged regions supposed. The governing equations of the activated beam sections are coupled equations related to the electrically induced tension/compression of the actuator and bending of the beam, respectively. The obtained steady-state solution satisfies boundary conditions and continuity conditions at the borders of the beam and the actuator sections. Results of calculations show the effects of stiffness degradation of both the bonding interlayer and the piezocomposite matrix material on the beam deflection and transmitted shear stresses. Besides, dynamic responses of the active system regarding changes of the control effectiveness are numerically investigated and discussed.

In this study, dynamic behaviour of trapezoidal and sinusoidal corrugated plates which are widely used in the fields of space, aviation, automotive, construction and shipbuilding have been analyzed. 330 different surface models varying according to corrugation height and number have been created for these plates which have various manufacturing parameters. At this stage, the number of analyses is 660. These models have been analyzed for different boundary conditions and modal analyses to obtain natural frequencies and mode shapes have been conducted using finite element method. In addition, changes in the trapezoidal cross-section profile have also been investigated by analyzing 38 different plates with varying cross-section profiles. Examining these results, the effects of corrugation height and number on natural frequencies and mode shapes have been determined. As a result of the study a total of 368 drawings were prepared and 736 analyses were performed. Besides, the theoretical results have been verified using the experimental modal analysis technique for some selected models which are being manufactured in the market.

Biharmonic problem has been raised in many research fields, such as elasticity problem in plate geometries or the Stokes flow problem formulated by using the stream function. The fourth order partial differential equation can be solved by applying many techniques. When using finite elements C 1 continuity must be assured. For this purpose Hermite interpolations constitute an appealing choice, but it imply the consideration of many degrees of freedom at each node with the consequent impact on the resulting discrete linear problem. Spectral approaches allow exponential convergence whilst a single degree of freedom is needed. However, the enforcement of boundary conditions remains a tricky task. In this paper we propose a separated representation of the stream function which transform the 2D solution in a sequence of 1D problems, each one be solved by using a spectral approximation.

Separated representations allow substituting the resolution of 3D models by a sequence of three one-dimensional problems [1]. This route is especially suitable when models are defined in hexahedral domains. When it is not the case, different possibilities exist. In a former work [2], we explored the route of immersing the domain into a hexahedral domain, and then use a kind of penalty method to solve the model whilst enforcing the boundary conditions. In the present work, we are analyzing two alternative routes. The first one consists of using an inverse technique in order to compute the boundary conditions on the border of the hexahedra in which the complex domain is immersed. The second one consists in solving the model in a regular domain for a number of geometrical parameters considered as extra-coordinates from which we could have access to the solution in any geometry resulting from a choice of those parameters.

In redundant manipulation systems the end-effector path does not completely determine the trajectories of all the individual degrees of freedom (dof). The redundancy is used in this paper to minimize energy consumption. A full electromechanical model is used, and the invested energy is calculated explicitly. The optimization includes also displacement limits via penalty functions that are included in the cost function. The solution is based on separating the system and the input into two parts. One that is completely determined by the end-effector path and the other that is driven by it, yet free for optimization. The boundary conditions are resolved in a similar manner, where the physical values are translated to the scaled down system by using a specific projection. Simulation results show that even with limited joint motion, the redundancy can lead to a considerable saving in energy.

Proper Generalized Decomposition (PGD) is a recent model reduction technique, successfully employed to solve many multidimensional problems. This method is able to circumvent, or at least alleviate, the curse of dimensionality. This method is based on the use of separated representations. By avoiding the exponential complexity of standard grid based discretization techniques, the PGD circumvents the curse of dimensionality in a variety of problems. With the PGD, the problem’s usual coordinates (e.g. space, time), but also model parameters, boundary conditions, and other sources of variability can be viewed globally as coordinates of a high-dimensional space wherein an approximate solution can efficiently be computed at once. Non-matching grids are very common in advanced scientific computing (e.g. contact problems, sub-domains coupling,).In this framework, approximate solutions from one grid to a non-matching second grid needs to be projected. This approach poses substantial numerical complexity which increases when going from one to higher dimensional interfaces. In this paper, we try to simulate a domain, which has a coarse mesh on one side and a fine mesh on other side by PGD. We show that PGD can handle these non -matching grids by using a smooth transition of the separated representation description.

In this paper, the buckling analysis of conical shell under transverse pressure or axial compression is studied using the Differential Quadrature Method (DQM) for various boundary conditions. Based on the Donnell theory of shell, the equilibrium equations are obtained using Hamilton’s principle. The adjacent equilibrium criterion is employed to defining the stability equations of conical shell subjected to lateral pressure and axial compression. Then the stability equations are solved numerically using DQM and employing the concept of extra degrees of freedom. The acquired results in special cases are compared with the results in literature for the accuracy evaluation of the method and a good agreement can be seen. The non-dimensional critical buckling loads are tabulated for different vertex angles, some thickness-radius ratios and various combinations of boundary conditions. Also, the effects of the vertex angle, boundary conditions, length-radius ratio and thickness-length ratio on the buckling behavior of the conical shell are investigated in details.