Search results for: incompressible%20fluid%20flow

Authors: Ramprasad Srinivasan

Abstract:

Engineers create inventions and put their ideas in concrete terms to design new products. Design drivers must be established, which requires, among other things, a complete understanding of the product design, load paths, etc. For Aerospace Vehicles, weight/strength ratio, strength, stiffness and stability are the important design drivers. A complex built-up structure is made up of an assemblage of primitive structural forms of arbitrary shape, which include 1D structures like beams and frames, 2D structures like membranes, plate and shell structures, and 3D solid structures. Justification through simulation involves a check for all the quantities of interest, namely stresses, deformation, frequencies, and buckling loads and is normally achieved through the finite element (FE) method. Over the past few decades, Fiber-reinforced composites are fast replacing the traditional metallic structures in the weight-sensitive aerospace and aircraft industries due to their high specific strength, high specific stiffness, anisotropic properties, design freedom for tailoring etc. Composite panel constructions are used in aircraft to design primary structure components like wings, empennage, ailerons, etc., while thin-walled composite beams (TWCB) are used to model slender structures like stiffened panels, helicopter, and wind turbine rotor blades, etc. The TWCB demonstrates many non-classical effects like torsional and constrained warping, transverse shear, coupling effects, heterogeneity, etc., which makes the analysis of composite structures far more complex. Conventional FE formulations to model 1D structures suffer from many limitations like shear locking, particularly in slender beams, lower convergence rates due to material coupling in composites, inability to satisfy, equilibrium in the domain and natural boundary conditions (NBC) etc. For 2D structures, the limitations of conventional displacement-based FE formulations include the inability to satisfy NBC explicitly and many pathological problems such as shear and membrane locking, spurious modes, stress oscillations, lower convergence due to mesh distortion etc. This mandates frequent re-meshing to even achieve an acceptable mesh (satisfy stringent quality metrics) for analysis leading to significant cycle time. Besides, currently, there is a need for separate formulations (u/p) to model incompressible materials, and a single unified formulation is missing in the literature. Hence coupled field formulation (CFF) is a unified formulation proposed by the author for the solution of complex 1D and 2D structures addressing the gaps in the literature mentioned above. The salient features of CFF and its many advantages over other conventional methods shall be presented in this paper.

Keywords: coupled field formulation, kinematic and material coupling, natural boundary condition, locking free formulation

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Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

Abstract:

General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

Procedia PDF Downloads 362

Authors: Sireetorn Kuharat, Anwar Beg

Abstract:

Motivation- Solar energy constitutes the most promising renewable energy source on earth. Nanofluids are a very successful family of engineered fluids, which contain well-dispersed nanoparticles suspended in a stable base fluid. The presence of metallic nanoparticles (e.g. gold, silver, copper, aluminum etc) significantly improves the thermo-physical properties of the host fluid and generally results in a considerable boost in thermal conductivity, density, and viscosity of nanofluid compared with the original base (host) fluid. This modification in fundamental thermal properties has profound implications in influencing the convective heat transfer process in solar collectors. The potential for improving solar collector direct absorber efficiency is immense and to gain a deeper insight into the impact of different metallic nanoparticles on efficiency and temperature enhancement, in the present work, we describe recent computational fluid dynamics simulations of an annular solar collector system. The present work studies several different metallic nano-particles and compares their performance. Methodologies- A numerical study of convective heat transfer in an annular pipe solar collector system is conducted. The inner tube contains pure water and the annular region contains nanofluid. Three-dimensional steady-state incompressible laminar flow comprising water- (and other) based nanofluid containing a variety of metallic nanoparticles (copper oxide, aluminum oxide, and titanium oxide nanoparticles) is examined. The Tiwari-Das model is deployed for which thermal conductivity, specific heat capacity and viscosity of the nanofluid suspensions is evaluated as a function of solid nano-particle volume fraction. Radiative heat transfer is also incorporated using the ANSYS solar flux and Rosseland radiative models. The ANSYS FLUENT finite volume code (version 18.1) is employed to simulate the thermo-fluid characteristics via the SIMPLE algorithm. Mesh-independence tests are conducted. Validation of the simulations is also performed with a computational Harlow-Welch MAC (Marker and Cell) finite difference method and excellent correlation achieved. The influence of volume fraction on temperature, velocity, pressure contours is computed and visualized. Main findings- The best overall performance is achieved with copper oxide nanoparticles. Thermal enhancement is generally maximized when water is utilized as the base fluid, although in certain cases ethylene glycol also performs very efficiently. Increasing nanoparticle solid volume fraction elevates temperatures although the effects are less prominent in aluminum and titanium oxide nanofluids. Significant improvement in temperature distributions is achieved with copper oxide nanofluid and this is attributed to the superior thermal conductivity of copper compared to other metallic nano-particles studied. Important fluid dynamic characteristics are also visualized including circulation and temperature shoots near the upper region of the annulus. Radiative flux is observed to enhance temperatures significantly via energization of the nanofluid although again the best elevation in performance is attained consistently with copper oxide. Conclusions-The current study generalizes previous investigations by considering multiple metallic nano-particles and furthermore provides a good benchmark against which to calibrate experimental tests on a new solar collector configuration currently being designed at Salford University. Important insights into the thermal conductivity and viscosity with metallic nano-particles is also provided in detail. The analysis is also extendable to other metallic nano-particles including gold and zinc.

Keywords: heat transfer, annular nanofluid solar collector, ANSYS FLUENT, metallic nanoparticles

Procedia PDF Downloads 115