The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.
The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.
In this work, the hemodynamics in the sinuses of Valsalva after Transcatheter Aortic Valve Implantation is numerically examined. We focus on the physical results in the two-dimensional case. We use a finite element methodology based on a Lagrange multiplier technique that enables to couple the dynamics of blood flow and the leaflets’ movement. A massively parallel implementation of a monolithic and fully implicit solver allows more accuracy and significant computational savings. The elastic properties of the aortic valve are disregarded, and the numerical computations are performed under physiologically correct pressure loads. Computational results depict that blood flow may be subject to stagnation in the lower domain of the sinuses of Valsalva after Transcatheter Aortic Valve Implantation.
In recent decades, flapping wing aerodynamics has attracted great interest. Understanding the physics of biological flyers such as birds and insects can help improve the performance of micro air vehicles. The present research focuses on the aerodynamics of insect-like flapping wing flight with the approach of numerical computation. Insect model of hawkmoth is adopted in the numerical study with rigid wing assumption currently. The numerical model integrates the computational fluid dynamics of the flow and active control of wing kinematics to achieve stable flight. The computation grid is a hybrid consisting of background Cartesian nodes and clouds of mesh-free grids around immersed boundaries. The generalized finite difference method is used in conjunction with single value decomposition (SVD-GFD) in computational fluid dynamics solver to study the dynamics of a free hovering hummingbird hawkmoth. The longitudinal dynamics of the hovering flight is governed by three control parameters, i.e., wing plane angle, mean positional angle and wing beating frequency. In present work, a PID controller works out the appropriate control parameters with the insect motion as input. The controller is adjusted to acquire desired maneuvering of the insect flight. The numerical scheme in present study is proven to be accurate and stable to simulate the flight of the hummingbird hawkmoth, which has relatively high Reynolds number. The PID controller is responsive to provide feedback to the wing kinematics during the hovering flight. The simulated hovering flight agrees well with the real insect flight. The present numerical study offers a promising route to investigate the free flight aerodynamics of insects, which could overcome some of the limitations of experiments.
In this paper, the effect of the intake temperature (IT) and intake pressure (IP) on ignition timing and pollutants emission of Homogeneous Charge Compression Ignition (HCCI) engine is investigated. Numerical computations are performed using the CHEMKIN computer code. The numerical temperature obtained using different boundary conditions is compared to published data and a good agreement is assigned. Results show that the HCCI combustion engine is significantly improved by increasing the IT. With a value of IT lower than 390 K, combustion cannot occur. However, with an IT greater than 420 K, the cylinder pressure decreases. An optimum crank rotation angle is achieved by using IT of 420 K. So, we can conclude that the variation of the IT and IP influence notably the emission concentration.
Three-dimensional incompressible turbulent fluid flow and heat transfer of pin fin heat sinks using air as a cooling fluid are numerically studied in this study. Two different kinds of pin fins are compared in the thermal performance, including circular and square cross sections, both are in-line and staggered arrangements. The turbulent governing equations are solved using a control-volume- based finite-difference method. Subsequently, numerical computations are performed with the realizable k - ԑ turbulence for the parameters studied, the fin height H, fin diameter D, and Reynolds number (Re) in the range of 7 ≤ H ≤ 10, 0.75 ≤ D ≤ 2, 2000 ≤ Re ≤ 126000 respectively. The numerical results are validated with available experimental data in the literature and good agreement has been found. It indicates that circular pin fins are streamlined in comparing with the square pin fins, the pressure drop is small than that of square pin fins, and heat transfer is not as good as the square pin fins. The thermal performance of the staggered pin fins is better than that of in-line pin fins because the staggered arrangements produce large disturbance. Both in-line and staggered arrangements show the same behavior for thermal resistance, pressure drop, and the entropy generation.
To ensure the gas transmittal GCU's efficient operation, leakages through the labyrinth packings (LP) should be minimized. Leakages can be minimized by decreasing the LP gap, which in turn depends on thermal processes and possible rotor vibrations and is designed to ensure absence of mechanical contact. Vibration mitigation allows to minimize the LP gap. It is advantageous to research influence of processes in the dynamic gas-structure system on LP vibrations. This paper considers influence of rotor vibrations on LP gas dynamics and influence of the latter on the rotor structure within the FSI unidirectional dynamical coupled problem. Dependences of nonstationary parameters of gas-dynamic process in LP on rotor vibrations under various gas speeds and pressures, shaft rotation speeds and vibration amplitudes, and working medium features were studied. The programmed multi-processor ANSYS CFX was chosen as a numerical computation tool. The problem was solved using PNRPU high-capacity computer complex. Deformed shaft vibrations are replaced with an unyielding profile that moves in the fixed annulus "up-and-down" according to set harmonic rule. This solves a nonstationary gas-dynamic problem and determines time dependence of total gas-dynamic force value influencing the shaft. Pressure increase from 0.1 to 10 MPa causes growth of gas-dynamic force oscillation amplitude and frequency. The phase shift angle between gas-dynamic force oscillations and those of shaft displacement decreases from 3π/4 to π/2. Damping constant has maximum value under 1 MPa pressure in the gap. Increase of shaft oscillation frequency from 50 to 150 Hz under P=10 MPa causes growth of gas-dynamic force oscillation amplitude. Damping constant has maximum value at 50 Hz equaling 1.012. Increase of shaft vibration amplitude from 20 to 80 µm under P=10 MPa causes the rise of gas-dynamic force amplitude up to 20 times. Damping constant increases from 0.092 to 0.251. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the minimum gas-dynamic force persistent oscillating amplitude under P=0.1 MPa being observed in methane, and maximum in the air. Frequency remains almost unchanged and the phase shift in the air changes from 3π/4 to π/2. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the maximum gas-dynamic force oscillating amplitude under P=10 MPa being observed in methane, and minimum in the air. Air demonstrates surging. Increase of leakage speed from 0 to 20 m/s through LP under P=0.1 MPa causes the gas-dynamic force oscillating amplitude to decrease by 3 orders and oscillation frequency and the phase shift to increase 2 times and stabilize. Increase of leakage speed from 0 to 20 m/s in LP under P=1 MPa causes gas-dynamic force oscillating amplitude to decrease by almost 4 orders. The phase shift angle increases from π/72 to π/2. Oscillations become persistent. Flow rate proved to influence greatly on pressure oscillations amplitude and a phase shift angle. Work medium influence depends on operation conditions. At pressure growth, vibrations are mostly affected in methane (of working substances list considered), and at pressure decrease, in the air at 25 ˚С.
In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.
In this work we use the Discrete Proper Orthogonal Decomposition transform to characterize the properties of coupled dynamics in thin-walled beams by exploiting numerical simulations obtained from finite element simulations. The outcomes of the will improve our understanding of the linear and nonlinear coupled behavior of thin-walled beams structures. Thin-walled beams have widespread usage in modern engineering application in both large scale structures (aeronautical structures), as well as in nano-structures (nano-tubes). Therefore, detailed knowledge in regard to the properties of coupled vibrations and buckling in these structures are of great interest in the research community. Due to the geometric complexity in the overall structure and in particular in the cross-sections it is necessary to involve computational mechanics to numerically simulate the dynamics. In using numerical computational techniques, it is not necessary to over simplify a model in order to solve the equations of motions. Computational dynamics methods produce databases of controlled resolution in time and space. These numerical databases contain information on the properties of the coupled dynamics. In order to extract the system dynamic properties and strength of coupling among the various fields of the motion, processing techniques are required. Time- Proper Orthogonal Decomposition transform is a powerful tool for processing databases for the dynamics. It will be used to study the coupled dynamics of thin-walled basic structures. These structures are ideal to form a basis for a systematic study of coupled dynamics in structures of complex geometry.
In this report we have discussed the theoretical aspects of the flow transformation, occurring through a series of bifurcations. The parameters and their continuous diversion, the intermittent bursts in the transition zone, variation of velocity and pressure with time, effect of roughness in turbulent zone, and changes in friction factor and head loss coefficient as a function of Reynolds number for a transverse flow across a cylinder have been discussed. An analysis of the variation in the wake length with Reynolds number was done in FORTRAN.
Regardless of the manufacturing process used, subtractive or additive, material, purpose and application, produced components are conventionally solid mass with more or less complex shape depending on the production technology selected. Aspects such as reducing the weight of components, associated with the low volume of material required and the almost non-existent material waste, speed and flexibility of production and, primarily, a high mechanical strength combined with high structural performance, are competitive advantages in any industrial sector, from automotive, molds, aviation, aerospace, construction, pharmaceuticals, medicine and more recently in human tissue engineering. Such features, properties and functionalities are attained in metal components produced using the additive technique of Rapid Prototyping from metal powders commonly known as Selective Laser Melting (SLM), with optimized internal topologies and varying densities. In order to produce components with high strength and high structural and functional performance, regardless of the type of application, three different internal topologies were developed and analyzed using numerical computational tools. The developed topologies were numerically submitted to mechanical compression and four point bending testing. Finite Element Analysis results demonstrate how different internal topologies can contribute to improve mechanical properties, even with a high degree of porosity relatively to fully dense components. Results are very promising not only from the point of view of mechanical resistance, but especially through the achievement of considerable variation in density without loss of structural and functional high performance.
The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.
This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm2 ≦q"≦ 40W/cm2. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.
A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.
This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers’ diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.
Computations with higher than the IEEE 754 standard double-precision (about 16 significant digits) are required recently. Although there are available software routines in Fortran and C for high-precision computation, users are required to implement such routines in their own computers with detailed knowledges about them. We have constructed an user-friendly online system for octupleprecision computation. In our Web system users with no knowledges about high-precision computation can easily perform octupleprecision computations, by choosing mathematical functions with argument(s) inputted, by writing simple mathematical expression(s) or by uploading C program(s). In this paper we enhance the Web system above by adding the facility of uploading Fortran programs, which have been widely used in scientific computing. To this end we construct converter routines in two stages.
Eight difference schemes and five limiters are applied to numerical computation of Riemann problem. The resolution of discontinuities of each scheme produced is compared. Numerical dissipation and its estimation are discussed. The result shows that the numerical dissipation of each scheme is vital to improve scheme-s accuracy and stability. MUSCL methodology is an effective approach to increase computational efficiency and resolution. Limiter should be selected appropriately by balancing compressive and diffusive performance.
The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.