This document presents the results of computational fluid dynamics simulations of lid-driven cavity flow. It compares results from ANSYS Fluent to published results from Ghia et al. for Reynolds number 1. It also compares results from a user-developed fractional step method on a staggered grid to Ghia et al., showing good agreement. Additional simulations at Reynolds number 1000 show agreement with Ghia et al. for the lower Reynolds number simulations but poorer agreement for the higher Reynolds number case, likely due to differences in grid resolution between the studies.
This project aims at simulating lid driven cavity flow problem using package MATLAB. Steady Incompressible Navier-Stokes equation with continuity equation will be studied at various Reynolds number. The main aim is to obtain the velocity field in steady state using the finite difference formulation on momentum equations and continuity equation. Reynold number is the pertinent parameter of the present study. Taylor’s series expansion has been used to convert the governing equations in the algebraic form using finite difference schemes.
Lid driven cavity flow simulation using CFD & MATLABIJSRD
Steady Incompressible Navier-Stokes equation on a uniform grid has been studied at various Reynolds number using CFD (Computational Fluid Dynamics). Present paper aim is to obtain the stream-function and velocity field in steady state using the finite difference formulation on momentum equations and continuity equation. Reynold number dominates the flow problem. Taylor’s series expansion has been used to convert the governing equations in the algebraic form using finite difference schemes. MATLAB has been used to draw to flow simulations inside the driven-cavity.
This document discusses using computational fluid dynamics (CFD) to analyze the flow through a gear pump. It provides background on CFD methodology and applications. It then describes the specific problem of simulating flow through an external gear pump using ANSYS Fluent. It details the geometry, mesh, boundary conditions, solver settings and dynamic mesh setup used. The goal is to determine the mass flow rate of oil through the pump.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
This document provides an overview of setting up co-simulation between ANSYS Mechanical and ANSYS Fluent using System Coupling. It discusses the necessary setup steps in Mechanical including analysis settings, fluid-solid interfaces, and output controls. It also covers the Fluent setup, including defining dynamic mesh zones, solution stabilization options, and notes on fluid compressibility. Finally, it addresses the System Coupling setup for defining data transfers and solution controls between the two solvers.
This document defines and describes different types of fluid flows. It discusses ideal and real fluids, Newtonian and non-Newtonian fluids, laminar and turbulent flow, steady and unsteady flow, uniform and non-uniform flow, compressible and incompressible flow, rotational and irrotational flow, and viscous and non-viscous flow. Key fluid properties like viscosity, density, and compressibility are covered. Examples are provided to illustrate different fluid types and flows.
Computational fluid dynamics (CFD) uses numerical methods to solve equations governing fluid flow. CFD analysis complements testing by reducing experimental effort. CFD modeling involves preprocessing like meshing the domain, setting up physical models and boundary conditions, solving the governing equations, and postprocessing results like visualizing flow patterns. FLUENT is a commercial CFD software that uses the finite volume method to discretize and solve transport equations for various flow properties.
This project aims at simulating lid driven cavity flow problem using package MATLAB. Steady Incompressible Navier-Stokes equation with continuity equation will be studied at various Reynolds number. The main aim is to obtain the velocity field in steady state using the finite difference formulation on momentum equations and continuity equation. Reynold number is the pertinent parameter of the present study. Taylor’s series expansion has been used to convert the governing equations in the algebraic form using finite difference schemes.
Lid driven cavity flow simulation using CFD & MATLABIJSRD
Steady Incompressible Navier-Stokes equation on a uniform grid has been studied at various Reynolds number using CFD (Computational Fluid Dynamics). Present paper aim is to obtain the stream-function and velocity field in steady state using the finite difference formulation on momentum equations and continuity equation. Reynold number dominates the flow problem. Taylor’s series expansion has been used to convert the governing equations in the algebraic form using finite difference schemes. MATLAB has been used to draw to flow simulations inside the driven-cavity.
This document discusses using computational fluid dynamics (CFD) to analyze the flow through a gear pump. It provides background on CFD methodology and applications. It then describes the specific problem of simulating flow through an external gear pump using ANSYS Fluent. It details the geometry, mesh, boundary conditions, solver settings and dynamic mesh setup used. The goal is to determine the mass flow rate of oil through the pump.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
This document provides an overview of setting up co-simulation between ANSYS Mechanical and ANSYS Fluent using System Coupling. It discusses the necessary setup steps in Mechanical including analysis settings, fluid-solid interfaces, and output controls. It also covers the Fluent setup, including defining dynamic mesh zones, solution stabilization options, and notes on fluid compressibility. Finally, it addresses the System Coupling setup for defining data transfers and solution controls between the two solvers.
This document defines and describes different types of fluid flows. It discusses ideal and real fluids, Newtonian and non-Newtonian fluids, laminar and turbulent flow, steady and unsteady flow, uniform and non-uniform flow, compressible and incompressible flow, rotational and irrotational flow, and viscous and non-viscous flow. Key fluid properties like viscosity, density, and compressibility are covered. Examples are provided to illustrate different fluid types and flows.
Computational fluid dynamics (CFD) uses numerical methods to solve equations governing fluid flow. CFD analysis complements testing by reducing experimental effort. CFD modeling involves preprocessing like meshing the domain, setting up physical models and boundary conditions, solving the governing equations, and postprocessing results like visualizing flow patterns. FLUENT is a commercial CFD software that uses the finite volume method to discretize and solve transport equations for various flow properties.
The document summarizes three turbulence models: the standard k-ε model, RNG k-ε model, and realizable k-ε model. The major differences between the models are their methods of calculating turbulent viscosity, turbulent Prandtl numbers, and generation/destruction terms. Some features are similar between the models, including turbulent production, buoyancy effects, and modeling heat/mass transfer. The realizable k-ε model addresses deficiencies of previous models like predicting round jet spreading rates. Buoyancy effects are included in all three models through modifications to the turbulent kinetic energy generation term.
This document discusses several methods for approximating solutions to the Navier-Stokes equations (NSE), including nondimensionalization, creeping flow, inviscid flow, irrotational flow, and potential flow. It explains how these approximations simplify the NSE by removing terms to create linear, analytically solvable forms. Elementary flows like source/sink, vortex, and doublet are introduced that can be combined using superposition to model more complex flows.
The document discusses various modeling approaches for simulating flows in moving domains, including rotating reference frames, mesh deformation, and multiple frame of reference models. Rotating reference frames allow steady-state solutions by solving equations in a rotating frame. Mesh deformation involves moving mesh nodes to accommodate moving boundaries. Multiple frame models are needed when domains rotate at different rates, using approaches like frozen rotor, stage, or transient rotor-stator models.
This document provides an overview of finite difference methods for solving partial differential equations. It introduces partial differential equations and various discretization methods including finite difference methods. It covers the basics of finite difference methods including Taylor series expansions, finite difference quotients, truncation error, explicit and implicit methods like the Crank-Nicolson method. It also discusses consistency, stability, and convergence of finite difference schemes. Finally, it applies these concepts to fluid flow equations and discusses conservative and transportive properties of finite difference formulations.
A shell and tube heat exchanger was designed to raise the temperature of fresh water from 40°C to 50°C using waste water at 80°C. Analytical calculations determined a heat transfer area of 0.7 m2 was required. CFD simulation validated the design, showing the fresh water temperature increased as required while the waste water temperature dropped by the calculated amount. The CFD determined heat transfer coefficient was within 3% of the theoretical value, validating the design calculations.
Erosion Analysis of Subsea Equipment: A Case Study with High Solid LoadingAnsys
Prospect Flow presents a case study that utilizes ANSYS Fluent to analyze flows of a fluid with a high solid content (such as during a well kill operation). Engineers account for the high solid loading and its potential effect on erosion along with wear-induced geometry changes by combining various erosion mechanisms within a multiphase CFD solution.
1) The document discusses fluid kinematics, which deals with the motion of fluids without considering the forces that create motion. It covers topics like velocity fields, acceleration fields, control volumes, and flow visualization techniques.
2) There are two main descriptions of fluid motion - Lagrangian, which follows individual particles, and Eulerian, which observes the flow at fixed points in space. Most practical analysis uses the Eulerian description.
3) The Reynolds Transport Theorem allows equations written for a fluid system to be applied to a fixed control volume, which is useful for analyzing forces on objects in a flow. It relates the time rate of change of an extensive property within the control volume to surface fluxes and the property accumulation.
Computational fluid dynamics (CFD) is the use of computing to simulate fluid flow, heat transfer, and other related phenomena. CFD works by numerically solving the governing equations of fluid dynamics. It allows for analyzing flows that are difficult to study experimentally. CFD has various applications in fields like aerospace, automotive, biomedical, and power generation. The CFD process involves discretizing the domain, applying initial and boundary conditions, numerically solving the governing equations, and post-processing the results. Common discretization methods are finite volume, finite element, and finite difference methods. CFD provides insight into flows and heat transfer while being faster and cheaper than physical experiments.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
Simulation of segregated flow over the 2 d cylinder using star ccm+Burak Turhan
In this thesis numerical simulation for classical case of flow over a cylinder is accomplished for 2D models using commercial CFD code Star CCM+ with k-ϵ model approach. The results are validated by comparing the Drag coefficients to the previously published data. The simulation is carried out to for Reynolds number 3900 to investigate the turbulence modeling on separation from curved surfaces of two different sizes of a circular cylinder, a cylinder with triangular cross section and a rectangular cross section. Investigation of different turbulence models and Mesh convergence is carried out.
The investigation of the turbulence model of the circular cylinder is carried out by the drag coefficient obtained by four different turbulence models such as K-Epsilon Turbulence, K-Omega Turbulence, Reynolds Stress Turbulence and Spalart-Allmaras Turbulence. Drag coefficient found out by different turbulence model is compared with the experimental value of a previously published data. The Mesh Convergence have been carried out by implementing different base mesh size in a decreasing order and the convergence is obtained when the drag coefficient becomes constant
Fluid MechanicsLosses in pipes dynamics of viscous flowsMohsin Siddique
This document discusses fluid flow in pipes. It defines the Reynolds number and explains laminar and turbulent flow regimes. It also covers the Darcy-Weisbach equation for calculating head losses due to pipe friction. The friction factor is determined using Moody diagrams based on Reynolds number and relative pipe roughness. Examples are provided to calculate friction factor, head loss, and flow rate for different pipe flow conditions.
Numerical solution, couette flow using crank nicolson implicit methodManoj maurya
Couette flow is the flow of a fluid between two parallel plates, where the lower plate is stationary and the upper plate is moving, creating shear stresses that drive the fluid flow. The document describes numerically solving the governing equations for Couette flow using the Crank-Nicolson technique, which involves discretizing the equations on a grid and solving the resulting tridiagonal matrix using methods like Thomas algorithm.
This document provides an introduction to boundary layer theory in fluid mechanics. It defines key terms like boundary layer thickness, displacement thickness, and momentum thickness. The boundary layer is a thin region near a solid surface where velocity gradients exist due to no-slip conditions. As fluid flows over a plate, the boundary layer transitions from laminar to turbulent flow. Boundary layer theory divides fluid flow into the boundary layer region with velocity gradients and an external region with nearly uniform free stream velocity.
The document summarizes the development and characteristics of several airfoil series developed by the National Advisory Committee for Aeronautics (NACA). It describes the early 4-digit and 5-digit series which used analytical equations to define airfoil shape based on camber and thickness. Later series like the 6-series used more advanced theoretical methods. The document provides details on naming conventions and equations used to define the geometry of airfoils within each series.
This document defines common pressure measurement terms and describes various pressure sensing and measurement devices. It discusses different types of pressures including absolute, gauge, differential and vacuum pressures. Several pressure measurement instruments are described including mercury and aneroid barometers, manometers, bourdon tube pressure gauges, strain gauge pressure transducers, and pressure transmitters. Applications of pressure switches and the use of orifice plates, venturi tubes and pitot tubes for differential pressure measurement are also covered.
1. Dimensional analysis and the concept of similitude allow experiments using scale models to be used to study full-scale systems. Dimensional analysis uses Buckingham pi theorem to determine the minimum number of dimensionless groups needed to describe a phenomenon in terms of the variables involved.
2. For a model to accurately simulate a prototype system, the dimensionless pi groups that describe the phenomenon must be equal between the model and prototype. This establishes the modeling laws or similarity requirements that a model must satisfy.
3. Common dimensionless groups in fluid mechanics include the Reynolds number, Froude number, Strouhal number, and Weber number. These groups arise frequently in analyzing experimental data from fluid mechanics problems.
This document discusses kinematic elements and pairs that are components of machines. It defines a kinematic link as any part that moves relative to another, and types of links include rigid, flexible, and fluid. Kinematic pairs constrain the relative motion between two links, and types of pairs are classified by the motion (sliding, turning, rolling, etc.) and contact (lower or higher). A kinematic chain combines multiple pairs so each link belongs to two pairs. When one link is fixed, it forms a mechanism that can transmit or transform motion. Common mechanisms are discussed like four-bar linkages and inversions obtained by fixing different links.
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the 13th chapter of book on Chemical Engineering Kinetics, by J. M. Smith. I plan to share most of the stuff I prepared for the GATE exam.
My best wishes to those preparing !
The document provides an introduction to turbomachinery. It discusses the working principle of turbomachines, which involves the transfer of energy between a rotating element and fluid flow using Newton's second law of motion. Turbomachines are classified based on the direction of work (done by or on the fluid) and the fluid flow direction (axial, radial, or mixed). Common applications of turbomachines include centrifugal pumps, compressors, and fans in industries; axial compressors and gas turbines in aircraft; steam and hydraulic turbines; wind turbines; and turbochargers in automobiles.
Integration of the natural cross ventilation in the CFD software UrbaWindStephane Meteodyn
Nowadays, a lot of energy is spent for air-conditioning in the cities for offices and private-housing. A good knowledge of the urban micro climate around the buildings could allow using the wind for natural air ventilation. UrbaWind is an automatic computational fluid dynamics (CFD) code developed in 2008 by Meteodyn to model the wind in urban environment. A module was recently added to assess the buildings air ventilation. First UrbaWind integrates climatology according to the geographic location of the site. Giving the influence of the shape and urban planning on the wind behaviors, UrbaWind solves the equations of fluid mechanics with a specific model which allows taking into account the urban environment effects such as vortexes, venturi or wise effects. Finally, the software is able to compute the wind flow inside each internal volume according to the openings of the buildings.This paper presents this software that has been designed for energy engineers to optimize the energy consumption inside a building. This is also an important tool for architects and project managers to make a building. The shape of the building as well as the orientation and the location of the openings can be designed with the awareness of the wind-induced natural air ventilation.
UrbaWind, a Computational Fluid Dynamics tool to predict wind resource in urb...Stephane Meteodyn
Computational Fluid Dynamics (CFD) is already a necessary tool for modeling the wind over complex country side terrains. Indeed to maximize energetic yield and optimize the costs, before installing the wind systems, a good knowledge of wind characteristics at the site is required. Meteodyn has developed UrbaWind, which is an automatic CFD software for computing the wind between buildings for small wind turbines. Compared to rural open spaces, the geometry in urban areas is more complex and unforeseeable. The effects created by the buildings, such as vortexes at the feet of the towers, Venturi effect or Wise effect, make the modeling of urban flows more difficult. The model used in UrbaWind allows to take these effects into account by solving the equations of Fluid Mechanics with a specific model which can represent the turbulence and the wakes around buildings as well as the porosity of the trees. In order to validate UrbaWind’s results, different study cases proposed by the Architectural Institute of Japan have been set up. The three selected cases have an ascending complexity, from the simple block to the complete rebuilding of a quarter of the Japanese city of Niigata. The results validate UrbaWind as well for theoretical cases as for real cases by offering a minor error margin on the wind speed prediction.
http://meteodyn.com/en
The document summarizes three turbulence models: the standard k-ε model, RNG k-ε model, and realizable k-ε model. The major differences between the models are their methods of calculating turbulent viscosity, turbulent Prandtl numbers, and generation/destruction terms. Some features are similar between the models, including turbulent production, buoyancy effects, and modeling heat/mass transfer. The realizable k-ε model addresses deficiencies of previous models like predicting round jet spreading rates. Buoyancy effects are included in all three models through modifications to the turbulent kinetic energy generation term.
This document discusses several methods for approximating solutions to the Navier-Stokes equations (NSE), including nondimensionalization, creeping flow, inviscid flow, irrotational flow, and potential flow. It explains how these approximations simplify the NSE by removing terms to create linear, analytically solvable forms. Elementary flows like source/sink, vortex, and doublet are introduced that can be combined using superposition to model more complex flows.
The document discusses various modeling approaches for simulating flows in moving domains, including rotating reference frames, mesh deformation, and multiple frame of reference models. Rotating reference frames allow steady-state solutions by solving equations in a rotating frame. Mesh deformation involves moving mesh nodes to accommodate moving boundaries. Multiple frame models are needed when domains rotate at different rates, using approaches like frozen rotor, stage, or transient rotor-stator models.
This document provides an overview of finite difference methods for solving partial differential equations. It introduces partial differential equations and various discretization methods including finite difference methods. It covers the basics of finite difference methods including Taylor series expansions, finite difference quotients, truncation error, explicit and implicit methods like the Crank-Nicolson method. It also discusses consistency, stability, and convergence of finite difference schemes. Finally, it applies these concepts to fluid flow equations and discusses conservative and transportive properties of finite difference formulations.
A shell and tube heat exchanger was designed to raise the temperature of fresh water from 40°C to 50°C using waste water at 80°C. Analytical calculations determined a heat transfer area of 0.7 m2 was required. CFD simulation validated the design, showing the fresh water temperature increased as required while the waste water temperature dropped by the calculated amount. The CFD determined heat transfer coefficient was within 3% of the theoretical value, validating the design calculations.
Erosion Analysis of Subsea Equipment: A Case Study with High Solid LoadingAnsys
Prospect Flow presents a case study that utilizes ANSYS Fluent to analyze flows of a fluid with a high solid content (such as during a well kill operation). Engineers account for the high solid loading and its potential effect on erosion along with wear-induced geometry changes by combining various erosion mechanisms within a multiphase CFD solution.
1) The document discusses fluid kinematics, which deals with the motion of fluids without considering the forces that create motion. It covers topics like velocity fields, acceleration fields, control volumes, and flow visualization techniques.
2) There are two main descriptions of fluid motion - Lagrangian, which follows individual particles, and Eulerian, which observes the flow at fixed points in space. Most practical analysis uses the Eulerian description.
3) The Reynolds Transport Theorem allows equations written for a fluid system to be applied to a fixed control volume, which is useful for analyzing forces on objects in a flow. It relates the time rate of change of an extensive property within the control volume to surface fluxes and the property accumulation.
Computational fluid dynamics (CFD) is the use of computing to simulate fluid flow, heat transfer, and other related phenomena. CFD works by numerically solving the governing equations of fluid dynamics. It allows for analyzing flows that are difficult to study experimentally. CFD has various applications in fields like aerospace, automotive, biomedical, and power generation. The CFD process involves discretizing the domain, applying initial and boundary conditions, numerically solving the governing equations, and post-processing the results. Common discretization methods are finite volume, finite element, and finite difference methods. CFD provides insight into flows and heat transfer while being faster and cheaper than physical experiments.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
Simulation of segregated flow over the 2 d cylinder using star ccm+Burak Turhan
In this thesis numerical simulation for classical case of flow over a cylinder is accomplished for 2D models using commercial CFD code Star CCM+ with k-ϵ model approach. The results are validated by comparing the Drag coefficients to the previously published data. The simulation is carried out to for Reynolds number 3900 to investigate the turbulence modeling on separation from curved surfaces of two different sizes of a circular cylinder, a cylinder with triangular cross section and a rectangular cross section. Investigation of different turbulence models and Mesh convergence is carried out.
The investigation of the turbulence model of the circular cylinder is carried out by the drag coefficient obtained by four different turbulence models such as K-Epsilon Turbulence, K-Omega Turbulence, Reynolds Stress Turbulence and Spalart-Allmaras Turbulence. Drag coefficient found out by different turbulence model is compared with the experimental value of a previously published data. The Mesh Convergence have been carried out by implementing different base mesh size in a decreasing order and the convergence is obtained when the drag coefficient becomes constant
Fluid MechanicsLosses in pipes dynamics of viscous flowsMohsin Siddique
This document discusses fluid flow in pipes. It defines the Reynolds number and explains laminar and turbulent flow regimes. It also covers the Darcy-Weisbach equation for calculating head losses due to pipe friction. The friction factor is determined using Moody diagrams based on Reynolds number and relative pipe roughness. Examples are provided to calculate friction factor, head loss, and flow rate for different pipe flow conditions.
Numerical solution, couette flow using crank nicolson implicit methodManoj maurya
Couette flow is the flow of a fluid between two parallel plates, where the lower plate is stationary and the upper plate is moving, creating shear stresses that drive the fluid flow. The document describes numerically solving the governing equations for Couette flow using the Crank-Nicolson technique, which involves discretizing the equations on a grid and solving the resulting tridiagonal matrix using methods like Thomas algorithm.
This document provides an introduction to boundary layer theory in fluid mechanics. It defines key terms like boundary layer thickness, displacement thickness, and momentum thickness. The boundary layer is a thin region near a solid surface where velocity gradients exist due to no-slip conditions. As fluid flows over a plate, the boundary layer transitions from laminar to turbulent flow. Boundary layer theory divides fluid flow into the boundary layer region with velocity gradients and an external region with nearly uniform free stream velocity.
The document summarizes the development and characteristics of several airfoil series developed by the National Advisory Committee for Aeronautics (NACA). It describes the early 4-digit and 5-digit series which used analytical equations to define airfoil shape based on camber and thickness. Later series like the 6-series used more advanced theoretical methods. The document provides details on naming conventions and equations used to define the geometry of airfoils within each series.
This document defines common pressure measurement terms and describes various pressure sensing and measurement devices. It discusses different types of pressures including absolute, gauge, differential and vacuum pressures. Several pressure measurement instruments are described including mercury and aneroid barometers, manometers, bourdon tube pressure gauges, strain gauge pressure transducers, and pressure transmitters. Applications of pressure switches and the use of orifice plates, venturi tubes and pitot tubes for differential pressure measurement are also covered.
1. Dimensional analysis and the concept of similitude allow experiments using scale models to be used to study full-scale systems. Dimensional analysis uses Buckingham pi theorem to determine the minimum number of dimensionless groups needed to describe a phenomenon in terms of the variables involved.
2. For a model to accurately simulate a prototype system, the dimensionless pi groups that describe the phenomenon must be equal between the model and prototype. This establishes the modeling laws or similarity requirements that a model must satisfy.
3. Common dimensionless groups in fluid mechanics include the Reynolds number, Froude number, Strouhal number, and Weber number. These groups arise frequently in analyzing experimental data from fluid mechanics problems.
This document discusses kinematic elements and pairs that are components of machines. It defines a kinematic link as any part that moves relative to another, and types of links include rigid, flexible, and fluid. Kinematic pairs constrain the relative motion between two links, and types of pairs are classified by the motion (sliding, turning, rolling, etc.) and contact (lower or higher). A kinematic chain combines multiple pairs so each link belongs to two pairs. When one link is fixed, it forms a mechanism that can transmit or transform motion. Common mechanisms are discussed like four-bar linkages and inversions obtained by fixing different links.
Hi All,
These are my CRE (Chemical Reaction Engineering) hand written notes when I was preparing for GATE (Graduate Aptitude Test in Engineering) in 2002 for Chemical Engineering. The current document forms the 13th chapter of book on Chemical Engineering Kinetics, by J. M. Smith. I plan to share most of the stuff I prepared for the GATE exam.
My best wishes to those preparing !
The document provides an introduction to turbomachinery. It discusses the working principle of turbomachines, which involves the transfer of energy between a rotating element and fluid flow using Newton's second law of motion. Turbomachines are classified based on the direction of work (done by or on the fluid) and the fluid flow direction (axial, radial, or mixed). Common applications of turbomachines include centrifugal pumps, compressors, and fans in industries; axial compressors and gas turbines in aircraft; steam and hydraulic turbines; wind turbines; and turbochargers in automobiles.
Integration of the natural cross ventilation in the CFD software UrbaWindStephane Meteodyn
Nowadays, a lot of energy is spent for air-conditioning in the cities for offices and private-housing. A good knowledge of the urban micro climate around the buildings could allow using the wind for natural air ventilation. UrbaWind is an automatic computational fluid dynamics (CFD) code developed in 2008 by Meteodyn to model the wind in urban environment. A module was recently added to assess the buildings air ventilation. First UrbaWind integrates climatology according to the geographic location of the site. Giving the influence of the shape and urban planning on the wind behaviors, UrbaWind solves the equations of fluid mechanics with a specific model which allows taking into account the urban environment effects such as vortexes, venturi or wise effects. Finally, the software is able to compute the wind flow inside each internal volume according to the openings of the buildings.This paper presents this software that has been designed for energy engineers to optimize the energy consumption inside a building. This is also an important tool for architects and project managers to make a building. The shape of the building as well as the orientation and the location of the openings can be designed with the awareness of the wind-induced natural air ventilation.
UrbaWind, a Computational Fluid Dynamics tool to predict wind resource in urb...Stephane Meteodyn
Computational Fluid Dynamics (CFD) is already a necessary tool for modeling the wind over complex country side terrains. Indeed to maximize energetic yield and optimize the costs, before installing the wind systems, a good knowledge of wind characteristics at the site is required. Meteodyn has developed UrbaWind, which is an automatic CFD software for computing the wind between buildings for small wind turbines. Compared to rural open spaces, the geometry in urban areas is more complex and unforeseeable. The effects created by the buildings, such as vortexes at the feet of the towers, Venturi effect or Wise effect, make the modeling of urban flows more difficult. The model used in UrbaWind allows to take these effects into account by solving the equations of Fluid Mechanics with a specific model which can represent the turbulence and the wakes around buildings as well as the porosity of the trees. In order to validate UrbaWind’s results, different study cases proposed by the Architectural Institute of Japan have been set up. The three selected cases have an ascending complexity, from the simple block to the complete rebuilding of a quarter of the Japanese city of Niigata. The results validate UrbaWind as well for theoretical cases as for real cases by offering a minor error margin on the wind speed prediction.
http://meteodyn.com/en
Towards Self healing networks in distribution networks operationVatsalMaheshwari12
The document proposes a self-healing approach for power distribution networks using bipartite graph modeling and reconfiguration algorithms. It describes modeling the network as a bipartite graph to represent switching possibilities abstractly. Two algorithms are presented: one for fault restoration that finds the best reconfiguration to restore power while maintaining topological feasibility, and one for overload mitigation that reconfigures the network to alleviate overloads. An example application to a real distribution network demonstrates initializing the bipartite graph and applying the algorithms to restore faults and reduce overloads through reconfiguration.
A PROJECT REPORT ON REMOVAL OF UNNECESSARY OBJECTS FROM PHOTOS USING MASKINGIRJET Journal
This document presents a project report on removing unnecessary objects from photos using masking techniques. It discusses using algorithms like Fast Marching and Navier-Stokes to fill in missing image data and maintain continuity across boundaries. The Fast Marching method begins at region boundaries and works inward, prioritizing completion of boundary pixels first. Navier-Stokes uses fluid dynamics equations to continue intensity value functions and ensure they remain continuous at boundaries. Color filtering can also be used to segment specific colored objects or regions. The project aims to implement these techniques to remove unwanted objects from images and fill the resulting gaps seamlessly.
This paper proposes an incremental and adaptive method for 3D reconstruction from a single RGB camera. The key features are:
1) An incremental method for updating the cost volume as new frames are added, without needing to store hundreds of comparison images. This reduces processing time and memory usage.
2) A method for dynamically adapting the minimum and maximum depth limits of the cost volume based on estimated scene depth from a semi-dense reconstruction system. This achieves optimal depth resolution.
The algorithm provides dense 3D reconstruction of indoor environments with low computational and memory costs, making it suitable for robotic applications. It is tested on both simulated and real data and shown to outperform previous volumetric reconstruction methods.
This document describes a computer based modelling project to simulate temperature distribution across a plate. The author developed a MATLAB script and graphical user interface (GUI) to allow users to input parameters and visualize the iterative temperature corrections. Key aspects included designing the GUI, implementing a method to correct temperatures using matrix operations based on Laplace's equation, and addressing challenges in modelling a central conducting hole. The completed project allows flexible adjustment of simulation variables and outputs clear graphs of the temperature distribution.
The part is axisymmetrically modeled in solidworks(2D) before importing to ansys workbench where the boundary zones are identified and appropriate mesh settings is applied. The model is then imported in Fluent for analysis . Significant setting changes are Density based solver , Enhanced Eddy viscosity model with near wall treatment , solution steering , FMG initialization etc.
Development of stereo matching algorithm based on sum of absolute RGB color d...IJECEIAES
This article presents local-based stereo matching algorithm which comprises a devel- opment of an algorithm using block matching and two edge preserving filters in the framework. Fundamentally, the matching process consists of several stages which will produce the disparity or depth map. The problem and most challenging work for matching process is to get an accurate corresponding point between two images. Hence, this article proposes an algorithm for stereo matching using improved Sum of Absolute RGB Differences (SAD), gradient matching and edge preserving filters. It is Bilateral Filter (BF) to surge up the accuracy. The SAD and gradient matching will be implemented at the first stage to get the preliminary corresponding result, then the BF works as an edge-preserving filter to remove the noise from the first stage. The second BF is used at the last stage to improve final disparity map and increase the object boundaries. The experimental analysis and validation are using the Middlebury standard benchmarking evaluation system. Based on the results, the proposed work is capable to increase the accuracy and to preserve the object edges. To make the proposed work more reliable with current available methods, the quantitative measurement has been made to compare with other existing methods and it shows the proposed work in this article perform much better.
This document summarizes a survey on graph partitioning algorithms. It begins by defining the graph partitioning problem and describing its applications in areas like VLSI design and parallel finite element methods. It then provides an overview of several categories of sequential graph partitioning algorithms, including local improvement methods like Kernighan-Lin and Fiduccia-Mattheyses, as well as discussing parallel partitioning algorithms and conclusions from experimental comparisons of different approaches.
A detailed analysis of three major dynamics and Non Linear analysis was done, which included:
1. Normal Modes and Frequency Response Analysis (FRA).
2. Large Deformation, Geometric Non-Linearity.
3. Elastoplastic Material Analysis, Material Non-Linearity.
This document presents OpenBowShock2D, an open-source MATLAB code for simulating 2D supersonic and hypersonic flows. The code uses a Steger-Warming/Van Leer scheme to solve the Euler equations on structured grids. It allows users to define arbitrary body shapes and includes options for perfect gas and equilibrium chemistry models. Validation cases show the code accurately captures shock locations and surface pressures compared to experimental data and commercial solvers. The goal is to provide an easy to use tool for educational flow simulations at high speeds.
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PHYS 221Lab 1 - Acceleration Due to GravityPlease work in g.docxmattjtoni51554
PHYS 221 Lab 1 - Acceleration Due to Gravity
Please work in groups of three. Please submit one lab report per person via Canvas.
In this laboratory we will measure the acceleration due to gravity by studying the motion of a cart accelerating down an inclined plane.
Background
Suppose we start with a level track and then tip it, as shown in Figure 1 below. Let L be the distance between two fixed points on a ramp, selected to be as far apart as possible, on the track. Let h be the difference in the vertical height above the table of these two points.
Figure 1 - Schematic of a cart on an inclined plane. The magnitude of the acceleration of the cart down the ramp can be considered a component of the gravitational acceleration: a = g sinθ
Then we have an incline of angle given by Equation 1:
. (1)
The acceleration of gravity, g, acts vertically downward, so the component of parallel to the incline – which is the acceleration of our cart – is given by Equation 2:
(2)
We see in Equation 2 that a graph of acceleration a as a function of sinθ should be linear with slope g. We will take data to plot such a graph and from its slope determine the value of g.
Setup
Gather the following materials:
· 2 m ramp
· Meter stick
· Lab Stand
· Ramp clamp
· Plastic Box with ULI, AC Adapter, and USB Cable
· Motion Sensor
· Magnetic Bumper
1. Connect the ULI to the computer via the USB cable and connect the AC adapter. Open Logger Pro 3.8.7.
2. Attach the ramp clamp to the lab stand and attach one end of the ramp.
3. Elevate one end of the track slightly using the vertical rod. Choose a value of h so that the angle of inclination stays less than about 8 degrees. (Use Equation 1 to verify).
· You can choose any two points along the track to serve as your L, but they must be the same two points for all your runs!
· Measure h by measuring the difference in the two heights of your two points.
4. Connect a motion sensor to the ULI and mount it on the elevated end of the track. The low end of the track should have a magnetic bumper installed on it (magnets face upward along the track).
Procedure
1. Choose at least five values of height h, to vary over the range 1-8 degrees.
2. Record each value of h chosen, and then obtain a graph of velocity versus time for that value.
3. You have two options for collecting velocity data from the cart:
· Release from the elevated end of the track and let it accelerate to the lower end.
· Push the cart from the lower end of the track up the incline. Record data during its entire motion back to its starting point. This will take slightly more finesse, but the data will be better.
The motion sensor will not record accurate data for a cart closer than 40 cm (the limit of its near range). Do not let the cart collide with the end of the track!
4. Determine the acceleration for the cart by using the Linear Fit tool and highlighting the appropriate region of the velocity graph. Record the .
Poster based on research on investigating the non-linear response of a synchronous machine to variations in system parameters (torque and damping), demonstrating the existence of a bifurcation curve within the parameter space. Response was visualized using state space diagrams. This poster was presented at the Power and Energy Conference at the University of Illinois (PECI) in Spring 2017.
Script for Comparison vertical flow models BHR Cannes June 14 2013 presentationPablo Adames
This document summarizes the presentation of a paper comparing mechanistic models of gas-liquid flow in vertical and deviated wells. It introduces the objectives of comparing published models and evaluating if more recent models perform better. The methodology section describes the models selected for comparison, well data used, and a relative performance index developed. The results section shows the original models performed poorly while the Gregory and OLGAS models performed the best overall based on the index calculations.
This document discusses improving two algorithms in the Spot model checking library that create automata with more transitions than necessary. It proposes using a feedback arc set (FAS) to minimize the number of transitions.
It describes an existing heuristic called GR that approximates a minimal FAS in linear time by ordering states. It adapts this heuristic to work on automata rather than graphs by generalizing concepts like in/out degree.
The document evaluates applying the improved FAS computation to the complementation of deterministic Büchi automata and conversion of Rabin automata to Büchi automata. It finds this reduces the size of resulting automata by up to 31% in experiments.
This paper discusses a GPU implementation of the Louvain community detection algorithm. Louvain algorithm obtains hierachical communities as a dendrogram through modularity optimization. Given an undirected weighted graph, all vertices are first considered to be their own communities. In the first phase, each vertex greedily decides to move to the community of one of its neighbours which gives greatest increase in modularity. If moving to no neighbour's community leads to an increase in modularity, the vertex chooses to stay with its own community. This is done sequentially for all the vertices. If the total change in modularity is more than a certain threshold, this phase is repeated. Once this local moving phase is complete, all vertices have formed their first hierarchy of communities. The next phase is called the aggregation phase, where all the vertices belonging to a community are collapsed into a single super-vertex, such that edges between communities are represented as edges between respective super-vertices (edge weights are combined), and edges within each community are represented as self-loops in respective super-vertices (again, edge weights are combined). Together, the local moving and the aggregation phases constitute a stage. This super-vertex graph is then used as input fof the next stage. This process continues until the increase in modularity is below a certain threshold. As a result from each stage, we have a hierarchy of community memberships for each vertex as a dendrogram.
Approaches to perform the Louvain algorithm can be divided into coarse-grained and fine-grained. Coarse-grained approaches process a set of vertices in parallel, while fine-grained approaches process all vertices in parallel. A coarse-grained hybrid-GPU algorithm using multi GPUs has be implemented by Cheong et al. which grabbed my attention. In addition, their algorithm does not use hashing for the local moving phase, but instead sorts each neighbour list based on the community id of each vertex.
https://gist.github.com/wolfram77/7e72c9b8c18c18ab908ae76262099329
A simple finite element solver for thermo-mechanical problems - margonari eng...Scilab
In this paper we would like to show how it is possible to develop a simple but effective finite element solver to deal with thermo-mechanical problems. In many engineering situations it is necessary to solve heat conduction problems, both steady and unsteady state, to estimate the temperature field inside a medium and, at the same time, compute the induced strain and stress states.
To solve such problems many commercial software tools are available. They provide user-friendly interfaces and flexible solvers, which can also take into account very complicated boundary conditions, such as radiation, and nonlinearities of any kind, to allow the user to model the reality in a very accurate and reliable way.
However, there are some situations in which the problem to be solved requires a simple and standard modeling: in these cases it could be sufficient to have a light and dedicated software able to give reliable solutions. Moreover, other two desirable features of such a software could be the possibility to access the source to easily program new tools and, last but not least, to have a cost-and-license free product. This turns out to be very useful when dealing with the solution of optimization problems.
Keeping in mind these considerations, we used the Scilab platform and the gmsh (which are both open source codes) to show that it is possible to build tailored software tools, able to solve standard but complex problems quite efficiently.
MULTIPLE REGION OF INTEREST TRACKING OF NON-RIGID OBJECTS USING DEMON'S ALGOR...cscpconf
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Multiple region of interest tracking of non rigid objects using demon's algor...
Final Report
1. MAE 561 : COMPUTATIONAL FLUID DYNAMICS
Final Project
Lid Driven Cavity
Neel Patel
1206392079
2. 2
Index
Sr.No Title Pg.No.
1. Abstract 3
2. Introduction to the Scheme 4
3. Task 1 ANSYS- FLUENT compared to
Ghia et al
6
4. Task 2 User compared to Ghia et al 10
5. Bonus 15
6. References 18
7. Appendix - Code
Note: The code i.e. one with variable time step has been attached in the end after the report.
3. 3
1. Abstract
To solve the 2-D incompressible Navier-Stokes equation we need a method/
algorithm that will include a pressure correction along with the fractional step
method on a staggered grid. The aim of the first phase of the project is to compare
the results obtained from ANSYS Fluent against the results reported by Ghia.
In the second phase we compare Ghia’s results against the results obtained from
the user’s algorithm. The aim of this phase is to compare the results of Ghia with
the user’s results.
4. 4
2. Introduction to the Scheme
The FTCS method was used for solving the problem is as follows:
The equations given are non-linear in nature and hence these
Equation 4a and 4b cannot be used in this case. We will use the following set of
equations for this case (fractional method on a staggered Grid)
c
a
b
5. 5
In our case the i+1/2,j serves as i,j and i-1/2,j servers as i-1,j. Similarly, for i,j+1/2
and i,j-1/2. The attached sheet of formulas for Task 3 contains the rest of the
formulations.
Now there are a few checks that should be kept in mind while solving these
equations. But first we need to derive the above equations.
d
6. 6
Task 1 ANSYS- FLUENT compared to Ghia et al
The following steps were followed for calculating the solution in ANSYS –
FLUENT:
1.1. A surface was created in the Design Modeler using a sketch of a square (1x1).
The units were kept as meters. This can be in any other unit system but care should
be taken while performing any conversions.
1.2. A quadrilateral mesh was generated of size 128 x128, because the Ghia et al
have used a mesh similar to this mesh. Please provide appropriate names to the
boundaries.
1.3. This mesh was transferred into FLUENT.
1.3.1 Checked the mesh for quality and the boundary names.
1.3.2 All the models were kept as default; make sure that the flow is laminar.
1.3.3 In the materials tab add a new fluid with density=1 kg/m3
and
viscosity = 0.01Kg/m-s.
1.3.4 The cell zone conditions were set to the fluid (the fluid that we have
introduced in the materials tab).
1.3.5 Now set the boundary conditions such that the top wall is a moving
wall with a velocity of 1m/s.
1.3.6 The solution methods to be given are Simple with spatial discretization
options set as follows:
1.3.6.1 Gradient – Least Squares cell Based
1.3.6.2 Pressure – Standard
1.3.6.3 Momentum – Second Order Upwind
1.3.7 In the monitors edit the values for the convergence of the x-velocity, y-
velocity and continuity to 10-10.
This value of residual was set to a lower
value as a lower value indicates that values at the new time step have
increased by a very small value as compared to the previous time step.
7. 7
1.3.8 Initialize the hybrid solution.
1.3.9 Run calculations for 5000 iterations.
1.4. Results
1.4.1 The velocity Comparison
Now create a new iso-surface at the centre of the mesh for both X and Y
direction. This surface was created to plot the velocities at the center of the
grid. Concurrently the values of Ghia for U and V separately with the results
obtained from the FLUENT Analysis were plotted.
Fig. 1. Comparison of the Ghia values to the FLUENT values for the u-velocity
along a vertical line through the geometric center of the cavity
8. 8
Fig. 2 : Comparison of the Ghia values to the FLUENT values for the v-velocity
along a horizontal line through the geometric center of the cavity
Note: The red dots are the Ghia velocities and the black dots are the
velocities obtained from the FLUENT solution.
1.4.2 The vorticity plot
Now introduce vorticity levels at the different values according to the Ghia
values. Since some of the values plotted by Ghia are negative, these values
will not be plotted by FLUENT. Also, the 0 value will not be plotted by
Fluent because the minimum value of vorticity is of 0.0003. The following
plot was obtained for vorticity.
9. 9
Fig 3. Vorticity at the Ghia values.
Note: This plot is missing the plot for 0 on the bottom corners and at the
middle as all the values of FLUENT are greater than 0.
1.4.3. Streamline Plot
The streamline plot was plotted for the specific contour levels of Ghia by
creating iso-stream surfaces for the values provided in table 3 of the paper.
In order to obtain the contours at the two lower corners we offset the values
of Ghia by a specific value.
Fig 4. The Stream function Values for the FLUENT results.
10. 10
Task 2 User compared to Ghia et al
In this section we have used fractional step defined on a staggered grid to get our
solution. The mesh used for this scheme was a 128 x 128 grid. This grid was
chosen as it closely resembles the Ghia grid. The Numerical Scheme used was
FTCS (Forward in Time Central in Space) for calculation of the Predictor step on
the staggered grid (Equations for this grid have been written in Task 2). Then we
have considered a Poisson pressure equation to calculate the pressure and in the
corrector step we have used the pressure equation and velocities calculated in the
predictor step to calculate the final velocities after every time step.
The residuals were calculated for the pressure Poisson and the velocities after the
iterative solution had been performed on these solutions. Also, residual was
calculated on the stream function.
The Convergence criteria used was 10-6
for the residuals. The reason was that for a
low value of residual was that the change in the quantities with time step after a
certain point of time does not change significantly. This provides a stable solution
for the given boundary conditions. However the best method to check for stability
is to determine that the solution has reached the asymptotic region of convergence.
We can use GCI (Grid Convergence Index) to determine e the steady state solution
but in our case since the time step is varying and we don’t have a stable time step
value we cannot use GCI to determine the steady state of the solution. MMS
(Method of Manufactured Solutions) can be used to determine the stable solution.
Fig 5. Staggered Grid for our considerations
11. 11
2.1 The Vorticity Plot
The plot for vorticity was obtained by solving the eq.11 in task 3. The levels that
were used in the plot were obtained from Ghia paper.
Fig 6. Comparison of Ghia Vorticity to results obtained by the code.
The figure above shows a good match between the plots shown obtained by Ghia
and by the code. The circles in the users figure represent the Ghia values.
12. 12
2.2. The U-Velocity along the vertical line.
Fig 7. Comparison of the Ghia values to the user values for the u-velocity along a
vertical line through the geometric center of the cavity
The plot of the U-Velocity shows a good match between the Ghia and the user’s
values. Some Values however seem to be off by a small value is due the fact that
the Ghia values are not completely accurate. This may be due to the computing
limitation about 30 years ago. Also, compiler errors were also a big issue back then
so it is difficult to determine the specific reason or to pin point the reason.
13. 13
2.3. The V-Velocity Plot along the horizontal line
Fig 8. Comparison of the Ghia values to the user values for the the v-velocity along
a horizontal line through the geometric center of the cavity
The plot of the V-Velocity shows a good match between the Ghia and the user’s
values. Some Values however seem to be off by a small value is due the fact that
the Ghia values are not completely accurate. The user’s values are accurate as we
have used a fractional step along with pressure correction to calculate the solution.
This may be due to the computing limitation about 30 years ago. Also, compiler
errors were also a big issue back then so it is difficult to determine the specific
reason or to pin point the reason.
14. 14
2.4 The Stream Function Plot
The stream function was plotted by adding an extra equation for the calculation of
the psi values on the grid.
Fig. 9 : Comparison of the Ghia values to the user values for the stream function
along a horizontal line through the geometric center of the cavity
This Figure and comparison indicates that there is a good comparison between the
user results and the Ghia Results.
15. 15
Bonus
Re =1000
5.1 The Vorticity Plot
The plot for vorticity was obtained by solving the eq.11 in task 3. The levels
that were used in the plot were obtained from Ghia paper.
Fig 10. Comparison of Ghia Vorticity to results obtained by the code.
The figure above shows a good match between the plots shown obtained by
Ghia and by the code. The circles in the users figure represent the Ghia
values.
16. 16
5.2. The U-Velocity along the vertical line.
Fig 11. Comparison of the Ghia values to the user values for the u-velocity along a
vertical line through the geometric center of the cavity
The plot of the U-Velocity shows a good match between the Ghia and the user’s
values. Some Values however seem to be off by a small value is due the fact that
the Ghia values are not completely accurate. This may be due to the computing
limitation about 30 years ago. Also, compiler errors were also a big issue back then
so it is difficult to determine the specific reason or to pin point the reason.
17. 17
5.3. The V-Velocity Plot along the horizontal line
Fig 12. Comparison of the Ghia values to the user values for the v-velocity along a
horizontal line through the geometric center of the cavity
The plot of the V-Velocity shows a good match between the Ghia and the user’s
values. Some Values however seem to be off by a small value is due the fact that
the Ghia values are not completely accurate. The user’s values are accurate as we
have used a fractional step along with pressure correction to calculate the solution.
18. 18
This may be due to the computing limitation about 30 years ago. Also, compiler
errors were also a big issue back then so it is difficult to determine the specific
reason or to pin point the reason.
5.4 The Stream Function Plot
The stream function was plotted by adding an extra equation for the calculation of
the psi values on the grid.
Fig. 13: Comparison of the Ghia values to the user values for the stream function
along a horizontal line through the geometric center of the cavity
This Figure and comparison indicates that there is not a good comparison between
the user results and the Ghia Results. The primary reason is that the grid is half the
size of the grid used in Ghia.
References
1. Ghia, Urmila, Kirti N. Ghia, and C. T. Shin. "High-Re solutions for
incompressible flow using the Navier-Stokes equations and a multigrid method."
Journal of computational physics 48, no. 3 (1982): 387-411.
2. Bruneau, Charles-Henri, and Mazen Saad. "The 2D lid-driven cavity problem
revisited." Computers & Fluids 35, no. 3 (2006): 326-348.
3. Dr. Marcus Hermann MAE 561: Computational Fluid Dynamics Notes.