Mathematical Model and ANSYS CFX Language of Expression - Essay Example

Introduction Pressure vessels are common engineering devices and found literally everywhere. Until lately the basic analysis technique relied on hand calculations or empirical curves. Nonetheless, computer technology advancement has made finite element analysis (FEA) a realistic tool in study and analysis of pressure vessels and related safety valves, more especially in determination of stresses in localized areas including penetrations, O-ring grooves as well as other regions whose analysis by hand are difficult. This project involved running of finite element analysis on a pressure vessel and its corresponding safety release valve. The spring-loaded pressure safety valve (PSV) is a major gadget used in securing the pressure vessel. This paper uses a three-dimensional model for computational fluid dynamics (CFD) alongside dynamic equations. This help in evaluating characteristics as well as dynamic behavior of the spring-loaded PSV. The applied CFD model, including unsteady analysis and the moving mesh methodology are used in prediction of the flow field via the valve and also calculate flow force which acts on the disk against time. To address the limitation associated with the moving mesh technique in software program ANSYS CFX (Version 12.1, ANSYS, Inc. USA) not being able to handle sophisticated configurations in many applications, a number of mesh generation novel techniques and modeling will be employed to make certain valve disk are able to move upwards and downwards successfully without retuning a negative mesh error. As a result, a number of consistent inlet pressure loads will be applied to the resultant model. Response parameters, such as disk displacement, valve mass flow, and applied fluid force on disk, are obtained and matched against behavioral study of PSV when subjected to different loading conditions. Additionally, the modeling technique is useful in valve designers bent on optimizing spring-loaded PSVs. A spring-attached pressure relief valve has a design which makes it open on attainment of a pre-defined pressure and secure the vessel from surplus pressure through removal or relief of fluid from the vessel. See figure below: The primary components of the spring-loaded PSV are a movable disk, and nozzle for inlet and of course, a spring. The nozzle is linked to the vessel to secure it, while the movable disk regulates flow via the nozzle, and the spring regulates disk position. In normal circumstances, the disk is positioned on the nozzle to bar flow of fluid. When system internal pressure surpasses a pre-defined value, the disk is raised and apertures the fluid to secure the vessel. Given that PSVs are fundamental safety devices, a number of researchers have delved into their traits. In recent years, CFD has been used in analysis of PSV flow traits. DDDDD studied complex 3-dimensional flow field for a safety pressure relief vessel. In another case, DDDDDD projected axisymmetric flow patterns within a pressure safety valve model using commercial software package, FIDAP. DDDDD on the other hand conducted finite element analysis study of oil laminar flow via hydraulic pressure relief valve. Dresser Industries Inc. in 1997 made use of commercial CFD code to calculate discharge coefficient of relief valve configuration having varied nozzle sizes. Consequently, as has been reported in various literatures, CFD application in evaluation of pressure safety valve has produced immense benefits including enhanced reliability in flow rate prediction, and loss of pressure at design phase. Sadly, as a result of commercial CFD software limitations and computational resource constraints, various studies have utilized simplified approaches to analysis including usage of axisymmetric models rather than full 3D models to salvage computational duration, and flow investigation via the valve at various fixed locations between wholly closed and wholly opened locations. Nonetheless, such simplifications bring along some disadvantages, for instance, given various conventional safety valve are non-axisymmetric, 2-D axisymmetric simplified model is inaccurate and insufficient in prediction of internal flow field as well as mass flow via the valve in question, particularly the field of flow about the valve disk. Additionally, an evaluation of the valve at a number of fixed positions is insufficient to predict the valve’s dynamic behavior due to the fact that there is a need to ignore various vital transient issues, transient flow traits via the valve, as well as the valve’s dynamic behavior is useful and of critical importance. This study uses ANSYS 12.1 to evaluate transient flow traits as well as dynamic behavior of the pressure safety valve in 3-dimensions. As a result of the sophistication of the valve’s configuration, a number of modeling approaches and simulation methods availed in the software package were used. These include domain de-composition, moving mesh analysis, as well as unsteady flow. The results revealed unsteady fluid moving across the valve and the valve’s dynamic behavior, hence improving understanding of relationship between fluid flow and the valve disk motion. Mathematical Model and ANSYS CFX Language of Expression The disk behaves as a one degree-of-freedom system given it is restricted by the valve body cylinder and hence the disk can only take a perpendicular direction to seat surface. This implies valve disk motion is wholly defined by coupled forces in perpendicular direction acting on the valve. Based on Newton’s second law, the motion equation for 1 degree of freedom system is written as shown below: Whereby, m refers to disk mass, is disk acceleration in perpendicular direction, shows spring force which acts on the disk, and refers to the disk’s flow force. The model presumes that the dissipation force ( resulting from friction between stem and body of the valve is zero and additionally neglects disk gravity due to them being small in comparison to spring force as well as flow force. In its differential form, the left hand side equation’s term is discretized to incorporate the disk displacement equation. Whereby velocity is discretized to the following, The disk’s displacement, also features in spring force expression, Whereby is spring stiffness and refers to the pre-defined force required to overcome the settings effect. Through re-assembly of discrete form of disk motion equation, disk displacement is given as, Given ANSYS CFX is not able to directly read and execute the equations, ANSYS CFX expression language expressions are made use of in transferring them to a form readable and executable to ANSYS CFX, which is a language developed in order to facilitate simulations without alternative to writing and linking of different external FORTRAN procedures. Numerical Analysis Computational Mesh Moving mesh method is used to account for disk motion. Consequently, CFD method takes into account mesh with moving nodes and warping control volumes. Compared to commercial software FLUENT, ANSYS CFX 12.1 is not able to regenerate the mesh also known as re-mesh for relevant region and interpolate flow variables, rather, moves the nodes to proper positions and continues solution. ANSYS CFX 12.1 dynamically finds where and when nodes need to be moved through solving an equation for displacement diffusion. In accordance to ANSYS CFX reference guide, mesh motion’s displacement diffusion model is designed in such a manner to preserve relative initial mesh distribution, for instance, if initial mesh is substantially fine in various domain regions, it will stay relatively fine after solving equation for displacement diffusion equation. Read More