Search results for: numerical solver

Authors: M. H. Kazemi, D. Salac

Abstract:

A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

Procedia PDF Downloads 484

Authors: M. Abuziarov

Abstract:

The designed complex is intended for the numerical simulation of fast dynamic processes of interaction of heterogeneous environments susceptible to the significant formability. The main challenges in solving such problems are associated with the construction of the numerical meshes. Currently, there are two basic approaches to solve this problem. One is using of Lagrangian or Lagrangian Eulerian grid associated with the boundaries of media and the second is associated with the fixed Eulerian mesh, boundary cells of which cut boundaries of the environment medium and requires the calculation of these cut volumes. Both approaches require the complex grid generators and significant time for preparing the code’s data for simulation. In this codes these problems are solved using two grids, regular fixed and mobile local Euler Lagrange - Eulerian (ALE approach) accompanying the contact and free boundaries, the surfaces of shock waves and phase transitions, and other possible features of solutions, with mutual interpolation of integrated parameters. For modeling of both liquids and gases, and deformable solids the Godunov scheme of increased accuracy is used in Lagrangian - Eulerian variables, the same for the Euler equations and for the Euler- Cauchy, describing the deformation of the solid. The increased accuracy of the scheme is achieved by using 3D spatial time dependent solution of the discontinuity problem (3D space time dependent Riemann's Problem solver). The same solution is used to calculate the interaction at the liquid-solid surface (Fluid Structure Interaction problem). The codes does not require complex 3D mesh generators, only the surfaces of the calculating objects as the STL files created by means of engineering graphics are given by the user, which greatly simplifies the preparing the task and makes it convenient to use directly by the designer at the design stage. The results of the test solutions and applications related to the generation and extension of the detonation and shock waves, loading the constructions are presented.

Keywords: fluid structure interaction, Riemann's solver, Euler variables, 3D codes

Procedia PDF Downloads 439

Authors: Imen Amari, Kaouther Gasmi, Asma Rebaya, Salem Hasnaoui

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The problem of scheduling and mapping data flow applications on multi-core architectures is notoriously difficult. This difficulty is related to the rapid evaluation of Telecommunication and multimedia systems accompanied by a rapid increase of user requirements in terms of latency, execution time, consumption, energy, etc. Having an optimal scheduling on multi-cores DSP (Digital signal Processors) platforms is a challenging task. In this context, we present a novel technic and algorithm in order to find a valid schedule that optimizes the key performance metrics particularly the Latency. Our contribution is based on Satisfiability Modulo Theories (SMT) solving technologies which is strongly driven by the industrial applications and needs. This paper, describe a scheduling module integrated in our proposed Workflow which is advised to be a successful approach for programming the applications based on NoC-DSP platforms. This workflow transform automatically a Simulink model to a synchronous dataflow (SDF) model. The automatic transformation followed by SMT solver scheduling aim to minimize the final latency and other software/hardware metrics in terms of an optimal schedule. Also, finding the optimal numbers of cores to be used. In fact, our proposed workflow taking as entry point a Simulink file (.mdl or .slx) derived from embedded Matlab functions. We use an approach which is based on the synchronous and hierarchical behavior of both Simulink and SDF. Whence, results of running the scheduler which exist in the Workflow mentioned above using our proposed SMT solver algorithm refinements produce the best possible scheduling in terms of latency and numbers of cores.

Keywords: multi-cores DSP, scheduling, SMT solver, workflow

Procedia PDF Downloads 288

Authors: Chandra Shekhar Prasad, Ludek Pesek Prasad

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In the present day fan blade of aero engine, turboprop propellers, gas turbine or steam turbine low-pressure blades are getting bigger, lighter and thus, become more flexible. Therefore, flutter, forced blade response and vibration related failure of the high aspect ratio blade are of main concern for the designers, thus need to be address properly in order to achieve successful component design. At the preliminary design stage large number of design iteration is need to achieve the utter free safe design. Most of the numerical method used for aeroelastic analysis is based on field-based methods such as finite difference method, finite element method, finite volume method or coupled. These numerical schemes are used to solve the coupled fluid Flow-Structural equation based on full Naiver-Stokes (NS) along with structural mechanics’ equations. These type of schemes provides very accurate results if modeled properly, however, they are computationally very expensive and need large computing recourse along with good personal expertise. Therefore, it is not the first choice for aeroelastic analysis during preliminary design phase. A reduced order aeroelastic model (ROAM) with acceptable accuracy and fast execution is more demanded at this stage. Similar ROAM are being used by other researchers for aeroelastic and force response analysis of turbomachinery. In the present paper new medium fidelity ROAM is successfully developed and implemented in numerical tool to simulated the aeroelastic stability phenomena in turbomachinery and well as flexible wings. In the present, a hybrid flow solver based on 3D viscous-inviscid coupled 3D panel method (PM) and 3d discrete vortex particle method (DVM) is developed, viscous parameters are estimated using boundary layer(BL) approach. This method can simulate flow separation and is a good compromise between accuracy and speed compared to CFD. In the second phase of the research work, the flow solver (PM) will be coupled with ROM non-linear beam element method (BEM) based FEM structural solver (with multibody capabilities) to perform the complete aeroelastic simulation of a steam turbine bladed disk, propellers, fan blades, aircraft wing etc. The partitioned based coupling approach is used for fluid-structure interaction (FSI). The numerical results are compared with experimental data for different test cases and for the blade cascade test case, experimental data is obtained from in-house lab experiments at IT CAS. Furthermore, the results from the new aeroelastic model will be compared with classical CFD-CSD based aeroelastic models. The proposed methodology for the aeroelastic stability analysis of gas turbine or steam turbine blades, or propellers or fan blades will provide researchers and engineers a fast, cost-effective and efficient tool for aeroelastic (classical flutter) analysis for different design at preliminary design stage where large numbers of design iteration are required in short time frame.

Keywords: aeroelasticity, beam element method (BEM), discrete vortex particle method (DVM), classical flutter, fluid-structure interaction (FSI), panel method, reduce order aeroelastic model (ROAM), turbomachinery, viscous-inviscid coupling

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Authors: Bao Liu, Maarten Vanierschot, Frank Buysschaert

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The present work examines the wake dynamics of a rim-driven thruster (RDT) with Computational Fluid Dynamics (CFD). Unsteady Reynolds-averaged Navier-Stokes (URANS) equations were solved in the commercial solver ANSYS Fluent in combination with the SST k-ω turbulence model. The application of the moving reference frame (MRF) and sliding mesh (SM) approach to handling the rotational movement of the propeller were compared in the transient simulations. Validation and verification of the numerical model was performed to ensure numerical accuracy. Two representative scenarios were considered, i.e., the bollard condition (J=0) and a very light loading condition(J=0.7), respectively. From the results, it’s confirmed that compared to the SM method, the MRF method is not suitable for resolving the unsteady flow features as it only gives the general mean flow but smooths out lots of characteristic details in the flow field. By evaluating the simulation results with the SM technique, the instantaneous wake flow field under both conditions is presented and analyzed, most notably the helical vortex structure. It’s observed from the results that the tip vortices, blade shed vortices, and hub vortices are present in the wake flow field and convect downstream in a highly non-linear way. The shear layer vortices shedding from the duct displayed a strong interaction with the distorted tip vortices in an irregularmanner.

Keywords: computational fluid dynamics, rim-driven thruster, sliding mesh, wake dynamics

Procedia PDF Downloads 263

Authors: Aymen Laadhari

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During the last decade, an increasing number of contributions have been made in the fields of scientific computing and numerical methodologies applied to the study of the hemodynamics in the heart. In contrast, the numerical aspects concerning the interaction of pulsatile blood flow with highly deformable thin leaflets have been much less explored. This coupled problem remains extremely challenging and numerical difficulties include e.g. the resolution of full Fluid-Structure Interaction problem with large deformations of extremely thin leaflets, substantial mesh deformations, high transvalvular pressure discontinuities, contact between leaflets. Although the Lagrangian description of the structural motion and strain measures is naturally used, many numerical complexities can arise when studying large deformations of thin structures. Eulerian approaches represent a promising alternative to readily model large deformations and handle contact issues. We present a fully Eulerian finite element methodology tailored for the simulation of pulsatile blood flow in the aorta and sinus of Valsalva interacting with highly deformable thin leaflets. Our method enables to use a fluid solver on a fixed mesh, whilst being able to easily model the mechanical properties of the valve. We introduce a semi-implicit time integration scheme based on a consistent NewtonRaphson linearization. A variant of the classical Newton method is introduced and guarantees a third-order convergence. High-fidelity computational geometries are built and simulations are performed under physiological conditions. We address in detail the main features of the proposed method, and we report several experiments with the aim of illustrating its accuracy and efficiency.

Keywords: eulerian, level set, newton, valve

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Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Mohsen Zahraei

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‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Juhee Lee, Yongjun Lee

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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.

Keywords: finite volume method, fluid flow, laminar flow, unstructured grid

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Authors: Luciano Garelli, Marco Schauer, Jorge D’Elia, Mario A. Storti, Sabine C. Langer

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This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM, a software developed at Centro de Investigación de Métodos Computacionales (CIMEC). The structural part of the coupled process is computed by the research code elementary Parallel Solver (elPaSo) of the Technische Universität Braunschweig, Institut für Konstruktionstechnik (IK).

Keywords: computational fluid dynamics (CFD), fluid structure interaction (FSI), finite element method (FEM), software

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Authors: Chin-Yun Chen

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Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

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Authors: Abhishek Agarwal, Manoj Sarda, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

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Propagation of fire through a non-air conditioned railway compartment is studied by virtue of numerical simulations. Simultaneous computational fire dynamics equations, such as Navier-Stokes, lumped species continuity, overall mass and energy conservation, and heat transfer are solved using finite volume based (for radiation) and finite difference based (for all other equations) solver, Fire Dynamics Simulator (FDS). A single coupe with an eight berth occupancy is used to establish the numerical model, followed by the selection of a three coupe system as the fundamental unit of the locomotive compartment. Heat Release Rate Per Unit Area (HRRPUA) of the initial fire is varied to consider a wide range of compartmental fires. Parameters, such as air inlet velocity relative to the locomotive at the windows, the level of interaction with the ambiance and closure of middle berth are studied through a wide range of numerical simulations. Almost all the loss of lives and properties due to fire breakout can be attributed to the direct or indirect exposure to flames or to the inhalation of toxic gases and resultant suffocation due to smoke and soot. Therefore, the temporal stature of fire and smoke are reported for each of the considered cases which can be used in the present or extended form to develop guidelines to be followed in case of a fire breakout.

Keywords: fire dynamics, flame propagation, locomotive fire, soot flow pattern, non-air-conditioned coaches

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Authors: Elmongi Elbellili, Ben Lauwens, Daan Huybrechs

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The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14.

Keywords: numerical integration, quantized state systems, ordinary differential equations, stiffness, cycle detection, simulation

Procedia PDF Downloads 61

Authors: Mohamed Elghorab, Vendra C. Madhav Rao, Jennifer X. Wen

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Turbulence modelling is still evolving, and efforts are on to improve and develop numerical methods to simulate the real turbulence structures by using the empirical and experimental information. The monotonically integrated large eddy simulation (MILES) is an attractive approach for modelling turbulence in high Re flows, which is based on the solving of the unfiltered flow equations with no explicit sub-grid scale (SGS) model. In the current work, this approach has been used, and the action of the SGS model has been included implicitly by intrinsic nonlinear high-frequency filters built into the convection discretization schemes. The MILES solver is developed using the opensource CFD OpenFOAM libraries. The role of flux limiters schemes namely, Gamma, superBee, van-Albada and van-Leer, is studied in predicting turbulent statistical quantities for a fully developed channel flow with a friction Reynolds number, Re_T = 180, and compared the numerical predictions with the well-established Direct Numerical Simulation (DNS) results for studying the wall generated turbulence. It is inferred from the numerical predictions that Gamma, van-Leer and van-Albada limiters produced more diffusion and overpredicted the velocity profiles, while superBee scheme reproduced velocity profiles and turbulence statistical quantities in good agreement with the reference DNS data in the streamwise direction although it deviated slightly in the spanwise and normal to the wall directions. The simulation results are further discussed in terms of the turbulence intensities and Reynolds stresses averaged in time and space to draw conclusion on the flux limiter schemes performance in OpenFOAM context.

Keywords: flux limiters, implicit SGS, MILES, OpenFOAM, turbulence statistics

Procedia PDF Downloads 191

Authors: Matthias Banholzer, Hagen Müller, Michael Pfitzner

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Gas internal combustion engines are widely used as propulsion systems or in power plants to generate heat and electricity. While there are different types of injection methods including the manifold port fuel injection and the direct injection, the latter has more potential to increase the specific power by avoiding air displacement in the intake and to reduce combustion anomalies such as backfire or pre-ignition. During the opening process of the injector, multiple flow regimes occur: subsonic, transonic and supersonic. To cover the wide range of Mach numbers a compressible pressure-based solver is used. While the standard Pressure Implicit with Splitting of Operators (PISO) method is used for the coupling between velocity and pressure, a high-resolution non-oscillatory central scheme established by Kurganov and Tadmor calculates the convective fluxes. A blending function based on the local Mach- and CFL-number switches between the compressible and incompressible regimes of the developed model. As the considered operating points are well above the critical state of the used fluids, the ideal gas assumption is not valid anymore. For the real gas thermodynamics, the models based on the Soave-Redlich-Kwong equation of state were implemented. The caloric properties are corrected using a departure formalism, for the viscosity and the thermal conductivity the empirical correlation of Chung is used. For the injector geometry, the dimensions of a diesel injector were adapted. Simulations were performed using different nozzle and needle geometries and opening curves. It can be clearly seen that there is a significant influence of all three parameters.

Keywords: high pressure gas injection, hybrid solver, hydrogen injection, needle opening process, real-gas thermodynamics

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Authors: Anastasios Georgoulas, Manolia Andredaki, Marco Marengo

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The present paper investigates the hydrodynamics and heat transfer characteristics of slug-plug flows under saturated flow boiling conditions within circular micro-channels. Numerical simulations are carried out, using an enhanced version of the open-source CFD-based solver ‘interFoam’ of OpenFOAM CFD Toolbox. The proposed user-defined solver is based in the Volume Of Fluid (VOF) method for interface advection, and the mentioned enhancements include the implementation of a smoothing process for spurious current reduction, the coupling with heat transfer and phase change as well as the incorporation of conjugate heat transfer to account for transient solid conduction. In all of the considered cases in the present paper, a single phase simulation is initially conducted until a quasi-steady state is reached with respect to the hydrodynamic and thermal boundary layer development. Then, a predefined and constant frequency of successive vapour bubbles is patched upstream at a certain distance from the channel inlet. The proposed numerical simulation set-up can capture the main hydrodynamic and heat transfer characteristics of slug-plug flow regimes within circular micro-channels. In more detail, the present investigation is focused on exploring the interaction between subsequent vapour slugs with respect to their generation frequency, the hydrodynamic characteristics of the liquid film between the generated vapour slugs and the channel wall as well as of the liquid plug between two subsequent vapour slugs. The proposed investigation is carried out for the 3 different working fluids and three different values of applied heat flux in the heated part of the considered microchannel. The post-processing and analysis of the results indicate that the dynamics of the evolving bubbles in each case are influenced by both the upstream and downstream bubbles in the generated sequence. In each case a slip velocity between the vapour bubbles and the liquid slugs is evident. In most cases interfacial waves appear close to the bubble tail that significantly reduce the liquid film thickness. Finally, in accordance with previous investigations vortices that are identified in the liquid slugs between two subsequent vapour bubbles can significantly enhance the convection heat transfer between the liquid regions and the heated channel walls. The overall results of the present investigation can be used to enhance the present understanding by providing better insight of the complex, underpinned heat transfer mechanisms in saturated boiling within micro-channels in the slug-plug flow regime.

Keywords: slug-plug flow regime, micro-channels, VOF method, OpenFOAM

Procedia PDF Downloads 267

Authors: Dirk Briskorn, Michael Dienstknecht

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Cranes are a key element in construction projects as they are the primary lifting equipment and among the most expensive construction equipment. Thus, selecting cranes and locating them on-site is an important factor for a project's profitability. We focus on a site with supply and demand areas that have to be connected by tower cranes. There are several types of tower cranes differing in certain specifications such as costs or operating radius. The objective is to select cranes and determine their locations such that each demand area is connected to its supply area at minimum cost. We detail the problem setting and show how to obtain a discrete set of candidate locations for each crane type without losing optimality. This discretization allows us to reduce our problem to the classic set cover problem. Despite its NP-hardness, we achieve good results employing a standard solver and a greedy heuristic, respectively.

Keywords: positioning, selection, standard solver, tower cranes

Procedia PDF Downloads 374

Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Ahlem Mougaida, Hedi Bel Hadj Salah

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Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

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Authors: Viet-Hung Truong, Seung-Eock Kim

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This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame

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Authors: Marine Segui, Ruxandra Mihaela Botez

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OpenVSP is an aerodynamic solver developed by National Aeronautics and Space Administration (NASA) that allows building a reliable model of an aircraft. This software performs an aerodynamic simulation according to the angle of attack of the aircraft makes between the incoming airstream, and its speed. A reliable aerodynamic model of the Cessna Citation X was designed but it required a lot of computation time. As a consequence, a prediction method was established that allowed predicting lift and drag coefficients for all Mach numbers and for all angles of attack, exclusively for stall conditions, from a computation of three angles of attack and only one Mach number. Aerodynamic coefficients given by the prediction method for a Cessna Citation X model were finally compared with aerodynamics coefficients obtained using a complete OpenVSP study.

Keywords: aerodynamic, coefficient, cruise, improving, longitudinal, openVSP, solver, time

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Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

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The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: entropy generation, hybrid nano fluid, heat transfer, porous disks

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Zbigniew Czyż, Adam Majczak, Lukasz Grabowski

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The paper presents a description of geometric models, computational algorithms, and results of numerical analyses of charge exchange in a two-stroke opposed-piston engine. The research engine was a newly designed internal Diesel engine. The unit is characterized by three cylinders in which three pairs of opposed-pistons operate. The engine will generate a power output equal to 100 kW at a crankshaft rotation speed of 3800-4000 rpm. The numerical investigations were carried out using ANSYS FLUENT solver. Numerical research, in contrast to experimental research, allows us to validate project assumptions and avoid costly prototype preparation for experimental tests. This makes it possible to optimize the geometrical model in countless variants with no production costs. The geometrical model includes an intake manifold, a cylinder, and an outlet manifold. The study was conducted for a series of modifications of manifolds and intake and exhaust ports to optimize the charge exchange process in the engine. The calculations specified a swirl coefficient obtained under stationary conditions for a full opening of intake and exhaust ports as well as a CA value of 280° for all cylinders. In addition, mass flow rates were identified separately in all of the intake and exhaust ports to achieve the best possible uniformity of flow in the individual cylinders. For the models under consideration, velocity, pressure and streamline contours were generated in important cross sections. The developed models are designed primarily to minimize the flow drag through the intake and exhaust ports while the mass flow rate increases. Firstly, in order to calculate the swirl ratio [-], tangential velocity v [m/s] and then angular velocity ω [rad / s] with respect to the charge as the mean of each element were calculated. The paper contains comparative analyses of all the intake and exhaust manifolds of the designed engine. Acknowledgement: This work has been realized in the cooperation with The Construction Office of WSK "PZL-KALISZ" S.A." and is part of Grant Agreement No. POIR.01.02.00-00-0002/15 financed by the Polish National Centre for Research and Development.

Keywords: computational fluid dynamics, engine swirl, fluid mechanics, mass flow rates, numerical analysis, opposed-piston engine

Procedia PDF Downloads 199

Authors: Mostafa Zandi, Ramin Mansouri

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Spillways are one of the most important hydraulic structures of dams that provide the stability of the dam and downstream areas at the time of flood. Morning-Glory spillway is one of the common spillways for discharging the overflow water behind dams, these kinds of spillways are constructed in dams with small reservoirs. In this research, the hydraulic flow characteristics of a morning-glory spillways are investigated with CFD model. Two dimensional unsteady RANS equations were solved numerically using Finite Volume Method. The PISO scheme was applied for the velocity-pressure coupling. The mostly used two-equation turbulence models, k- and k-, were chosen to model Reynolds shear stress term. The power law scheme was used for discretization of momentum, k , and  equations. The VOF method (geometrically reconstruction algorithm) was adopted for interface simulation. The results show that the fine computational grid, the input speed condition for the flow input boundary, and the output pressure for the boundaries that are in contact with the air provide the best possible results. Also, the standard wall function is chosen for the effect of the wall function, and the turbulent model k -ε (Standard) has the most consistent results with experimental results. When the jet is getting closer to end of basin, the computational results increase with the numerical results of their differences. The lower profile of the water jet has less sensitivity to the hydraulic jet profile than the hydraulic jet profile. In the pressure test, it was also found that the results show that the numerical values of the pressure in the lower landing number differ greatly in experimental results. The characteristics of the complex flows over a Morning-Glory spillway were studied numerically using a RANS solver. Grid study showed that numerical results of a 57512-node grid had the best agreement with the experimental values. The desired downstream channel length was preferred to be 1.5 meter, and the standard k-ε turbulence model produced the best results in Morning-Glory spillway. The numerical free-surface profiles followed the theoretical equations very well.

Keywords: morning-glory spillway, CFD model, hydraulic characteristics, wall function

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

Abstract:

Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Aymen Laadhari, Gábor Székely

Abstract:

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.

Keywords: hemodynamics, simulations, stagnation, valve

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Authors: Christina Peristeri, Tobias Berg, Domenico Caridi, Paul Hutcheson, Robert Winstanley

Abstract:

In recent years the demand for rapid innovations in the automotive industry has led to the need for accelerated simulation procedures while retaining a detailed representation of the simulated phenomena. The project’s aim is to create a fast transient workflow for external aerodynamic CFD simulations of road vehicles. The geometry used was the SAE Notchback Closed Cooling DrivAer model, and the simulation results were compared with data from wind tunnel tests. The meshes generated for this study were of two types. One was a mix of polyhedral cells near the surface and hexahedral cells away from the surface. The other was an octree hex mesh with a rapid method of fitting to the surface. Three different grid refinement levels were used for each mesh type, with the biggest total cell count for the octree mesh being close to 1 billion. A series of steady-state solutions were obtained on three different grid levels using a pseudo-transient coupled solver and a k-omega-based RANS turbulence model. A mesh-independent solution was found in all cases with a medium level of refinement with 200 million cells. Stress-Blended Eddy Simulation (SBES) was chosen for the transient simulations, which uses a shielding function to explicitly switch between RANS and LES mode. A converged pseudo-transient steady-state solution was used to initialize the transient SBES run that was set up with the SIMPLEC pressure-velocity coupling scheme to reach the fastest solution (on both CPU & GPU solvers). An important part of this project was the use of FLUENT’s Multi-GPU solver. Tesla A100 GPU has been shown to be 8x faster than an Intel 48-core Sky Lake CPU system, leading to significant simulation speed-up compared to the traditional CPU solver. The current study used 4 Tesla A100 GPUs and 192 CPU cores. The combination of rapid octree meshing and GPU computing shows significant promise in reducing time and hardware costs for industrial strength aerodynamic simulations.

Keywords: CFD, DrivAer, LES, Multi-GPU solver, octree mesh, RANS

Procedia PDF Downloads 116