This document summarizes an unsteady flow simulation around a square cylinder using an upstream rod. It includes an introduction on drag forces on bluff bodies, an overview of how streamlined shapes produce less drag than bluff bodies, and the importance of drag reduction. It then reviews relevant literature on similar studies, identifies gaps in the literature, and outlines the objectives of this study. The study will simulate flow using a square cylinder with an upstream rod, varying parameters like staggered angle, rod diameter and spacing. It will aim to find optimized conditions that produce the least drag. The computational setup and governing equations used in the simulation are also summarized.
Large eddy simulation of the flow over a circular cylinder at high reynolds n...Jesús Martínez
The issue of numerical study of turbulent flow over a circular cylinder for different Reynolds numbers has been studied over almost 20 years. During those two decades, there have been successes and failures in the numerical models. This paper presents the implementation of the method of large eddy simulation (LES) to solve the problem of the external flow over a cylinder under a subcritical Reynolds number (Re = 1.4E +5). The purpose is to evaluate the performance of a computational method and complement experimental and numerical data presented in the literature, this as part of a research work which attempts to explain a method of passive drag reduction.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
This document summarizes a computational fluid dynamics (CFD) study that analyzed the performance of vented cylinders as vortex generators. The study found that using vented cylinders, which have slits, as vortex generators mounted on a flat plate can increase lift forces with only small variations in drag forces when the angle of attack is varied. Specifically:
1) CFD simulations showed that vented cylinders intensify vortex shedding compared to baseline cylinders, increasing lift force.
2) Mounting vented cylinders on a flat plate and varying the angle of attack, lift coefficients increased with small drag coefficient variations.
3) Moving the vented cylinder further from the leading edge of the flat plate allowed more boundary layer development
This document provides an introduction to fluid mechanics. It begins with definitions of mechanics, statics, dynamics, and fluid mechanics. It then discusses different categories of fluid mechanics including fluid statics, fluid kinematics, fluid dynamics, hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document also defines what a fluid is, discusses the properties of fluids including density, specific weight, specific volume, and specific gravity. It concludes by explaining viscosity, kinematic viscosity, and Newton's law of viscosity.
The document discusses various topics related to fluid mechanics and fluid flow. It defines mechanics, fluid mechanics, and related subcategories like hydrodynamics and aerodynamics. It describes the different states of matter and properties of fluids like density, viscosity, and surface tension. The document also discusses concepts like pressure, buoyancy, and fluid flow characteristics such as laminar vs turbulent flow, compressible vs incompressible flow, and one-dimensional, two-dimensional, and three-dimensional flows.
Large eddy simulation of the flow over a circular cylinder at high reynolds n...Jesús Martínez
The issue of numerical study of turbulent flow over a circular cylinder for different Reynolds numbers has been studied over almost 20 years. During those two decades, there have been successes and failures in the numerical models. This paper presents the implementation of the method of large eddy simulation (LES) to solve the problem of the external flow over a cylinder under a subcritical Reynolds number (Re = 1.4E +5). The purpose is to evaluate the performance of a computational method and complement experimental and numerical data presented in the literature, this as part of a research work which attempts to explain a method of passive drag reduction.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
This document summarizes a computational fluid dynamics (CFD) study that analyzed the performance of vented cylinders as vortex generators. The study found that using vented cylinders, which have slits, as vortex generators mounted on a flat plate can increase lift forces with only small variations in drag forces when the angle of attack is varied. Specifically:
1) CFD simulations showed that vented cylinders intensify vortex shedding compared to baseline cylinders, increasing lift force.
2) Mounting vented cylinders on a flat plate and varying the angle of attack, lift coefficients increased with small drag coefficient variations.
3) Moving the vented cylinder further from the leading edge of the flat plate allowed more boundary layer development
This document provides an introduction to fluid mechanics. It begins with definitions of mechanics, statics, dynamics, and fluid mechanics. It then discusses different categories of fluid mechanics including fluid statics, fluid kinematics, fluid dynamics, hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document also defines what a fluid is, discusses the properties of fluids including density, specific weight, specific volume, and specific gravity. It concludes by explaining viscosity, kinematic viscosity, and Newton's law of viscosity.
The document discusses various topics related to fluid mechanics and fluid flow. It defines mechanics, fluid mechanics, and related subcategories like hydrodynamics and aerodynamics. It describes the different states of matter and properties of fluids like density, viscosity, and surface tension. The document also discusses concepts like pressure, buoyancy, and fluid flow characteristics such as laminar vs turbulent flow, compressible vs incompressible flow, and one-dimensional, two-dimensional, and three-dimensional flows.
A STUDY ON VISCOUS FLOW (With A Special Focus On Boundary Layer And Its Effects)Rajibul Alam
This document summarizes a study on viscous flow with a focus on boundary layers and their effects. It defines viscosity and describes the boundary layer that forms along a solid surface moving through a fluid. Laminar and turbulent boundary layers are differentiated. The boundary layer equations are presented and used to derive the Navier-Stokes equations that govern viscous fluid flow. Key properties of boundary layers like thickness and velocity profiles are discussed. The interaction of boundary layers and shockwaves is also summarized.
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.
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry and motion of fluids without considering forces. It defines key concepts like acceleration fields, Lagrangian and Eulerian methods of describing motion, types of flow such as laminar vs turbulent and steady vs unsteady, streamlines vs pathlines vs streaklines, circulation and vorticity, and analytical tools like the stream function and velocity potential function. Flow nets are introduced as a way to graphically study two-dimensional irrotational flows using a grid of intersecting streamlines and equipotential lines.
Fluid Mechanics-Shear stress ,Shear stress distribution,Velocity profile,Flow Of Viscous Fluid Through The circular pipe ,Velocity profile for turbulent flow Boundary layer buildup in pipe,Velocity Distributions
Fluid mechanics - Motion of Fluid Particles and StreamViraj Patel
- Fluid mechanics is the study of fluid motion and the forces acting on fluids. This includes fluid kinematics, which is the study of fluid motion without considering forces.
- There are different frames of reference to describe fluid motion - Lagrangian refers to individual fluid particles, Eulerian refers to fixed points in space.
- Fluid flow can be classified as steady or unsteady, uniform or non-uniform, laminar or turbulent. The continuity equation expresses conservation of mass and relates flow properties between different flow sections.
1. Darcy's law defines permeability as a property of porous media that controls the flow rate and direction of reservoir fluids. It relates flow rate to pressure drop via permeability, fluid properties, and length.
2. Permeability is measured through core flow tests under laminar, single phase flow conditions and is called absolute permeability. It is quantified in units of darcys or millidarcys.
3. Reservoir fluids can be incompressible, slightly compressible, or compressible. Flow regimes include steady-state, unsteady-state, and pseudosteady-state. Reservoir geometry models include radial, linear, spherical and hemispherical flow. Reservoirs can involve single-, two-,
This document discusses open channel flow and its various types. It defines open channel flow as flow with a free surface driven by gravity. It describes four main types of open channel flows:
1. Steady and unsteady flow
2. Uniform and non-uniform flow
3. Laminar and turbulent flow
4. Sub-critical, critical, and super-critical flow
It also discusses discharge equations for open channels including Chezy's formula, Manning's formula, and Bazin's formula. Finally, it covers specific energy, critical depth, and the hydraulic jump in open channel flow.
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
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.
This document provides an overview of fluid kinematics concepts. It describes fluid flow using Lagrangian and Eulerian descriptions, and defines steady and unsteady, uniform and non-uniform flow. Streamlines, pathlines and streaklines are differentiated. Streamlines indicate instantaneous velocity direction, and streamtubes are bundles of streamlines. One, two and three dimensional flows are described. The material derivative, which follows a fluid particle as it moves, is introduced along with its relationship to particle acceleration. Key concepts are illustrated with diagrams.
Flow of viscous fluid through circular pipevaibhav tailor
The document summarizes flow of viscous fluid through a circular pipe. It describes that flow can be laminar, transitional, or turbulent depending on the Reynolds number. It presents the Hagen-Poiseuille law which describes laminar flow in a circular pipe. The law states that velocity distribution varies with the square of the radial distance from the center, and that maximum velocity is twice the average velocity. It also provides the equation for pressure drop along the length of the pipe based on flow properties and pipe dimensions.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
This document defines and describes different types of fluid flows including steady and unsteady flow, uniform and non-uniform flow, laminar and turbulent flow, compressible and incompressible flow, one-dimensional, two-dimensional, and three-dimensional flow. It also discusses boundary layers, boundary layer thickness, displacement thickness, and momentum thickness. Finally, it introduces the Moody diagram which can be used to determine friction factors based on relative roughness and Reynolds number.
This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.
This presentation contains the Fluid flow chapter of Pharmaceutical engineering. This chapter include the definition of flow of fluid, Reynolds number, Bernollis therom, Manometers, Fluid flow measuring equipment's and applications.
This document discusses the objectives and content of a fluid mechanics and machinery course. It includes:
- The objectives of understanding fluid properties, dimensional analysis, and various types of pumps and turbines.
- An introduction to fluid mechanics, including the basic concepts and importance in engineering applications.
- Details about the first unit which will cover fluid properties, flow characteristics using concepts like the continuity, energy, and momentum equations.
This document discusses fluid mechanics and its various branches and concepts. It begins by defining mechanics, statics, dynamics, and fluid mechanics. It then discusses specific types of fluid mechanics like hydrodynamics, hydraulics, gas dynamics, and aerodynamics. It also discusses classifications of fluid flow such as viscous vs inviscid flow, internal vs external flow, and compressible vs incompressible flow. Finally, it covers key concepts like laminar vs turbulent flow, steady vs unsteady flow, and dimensional flows.
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
IRJET- Investigation of Fluid Flow Characteristics for the Forced Convect...IRJET Journal
This document summarizes a study that used computational fluid dynamics (CFD) to investigate fluid flow characteristics over heated elliptical and circular shaped tubes. The study varied the Reynolds number from 438 to 1227 and found that elliptical tubes had lower pressure drop and friction factor values than circular tubes. Velocity distributions showed smaller wakes behind elliptical tubes. Pressure drop and friction factor both increased with Reynolds number but elliptical tubes performed better in both areas. The study concluded elliptical tubes provided better heat transfer characteristics than circular tubes of the same hydraulic diameter.
CFD Simulation of Swirling Effect in S-Shaped Diffusing Duct by Swirl Angle o...IOSR Journals
This document describes a computational fluid dynamics (CFD) simulation of swirling flow through an S-shaped diffusing duct with a 10 degree swirl angle. The study models airflow through a duct with an area ratio of 1.9, length of 300mm, and turning angle of 22.5 degrees. Simulations were conducted for uniform inlet flow and swirling inlet flow clockwise and counter-clockwise. Results show that swirling flow improves static pressure recovery over uniform flow. Clockwise swirling flow provided the highest pressure recovery and most uniform exit flow. Turbulence intensity and secondary flows increased through the duct but did not exceed 15% of inlet velocity.
A STUDY ON VISCOUS FLOW (With A Special Focus On Boundary Layer And Its Effects)Rajibul Alam
This document summarizes a study on viscous flow with a focus on boundary layers and their effects. It defines viscosity and describes the boundary layer that forms along a solid surface moving through a fluid. Laminar and turbulent boundary layers are differentiated. The boundary layer equations are presented and used to derive the Navier-Stokes equations that govern viscous fluid flow. Key properties of boundary layers like thickness and velocity profiles are discussed. The interaction of boundary layers and shockwaves is also summarized.
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.
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry and motion of fluids without considering forces. It defines key concepts like acceleration fields, Lagrangian and Eulerian methods of describing motion, types of flow such as laminar vs turbulent and steady vs unsteady, streamlines vs pathlines vs streaklines, circulation and vorticity, and analytical tools like the stream function and velocity potential function. Flow nets are introduced as a way to graphically study two-dimensional irrotational flows using a grid of intersecting streamlines and equipotential lines.
Fluid Mechanics-Shear stress ,Shear stress distribution,Velocity profile,Flow Of Viscous Fluid Through The circular pipe ,Velocity profile for turbulent flow Boundary layer buildup in pipe,Velocity Distributions
Fluid mechanics - Motion of Fluid Particles and StreamViraj Patel
- Fluid mechanics is the study of fluid motion and the forces acting on fluids. This includes fluid kinematics, which is the study of fluid motion without considering forces.
- There are different frames of reference to describe fluid motion - Lagrangian refers to individual fluid particles, Eulerian refers to fixed points in space.
- Fluid flow can be classified as steady or unsteady, uniform or non-uniform, laminar or turbulent. The continuity equation expresses conservation of mass and relates flow properties between different flow sections.
1. Darcy's law defines permeability as a property of porous media that controls the flow rate and direction of reservoir fluids. It relates flow rate to pressure drop via permeability, fluid properties, and length.
2. Permeability is measured through core flow tests under laminar, single phase flow conditions and is called absolute permeability. It is quantified in units of darcys or millidarcys.
3. Reservoir fluids can be incompressible, slightly compressible, or compressible. Flow regimes include steady-state, unsteady-state, and pseudosteady-state. Reservoir geometry models include radial, linear, spherical and hemispherical flow. Reservoirs can involve single-, two-,
This document discusses open channel flow and its various types. It defines open channel flow as flow with a free surface driven by gravity. It describes four main types of open channel flows:
1. Steady and unsteady flow
2. Uniform and non-uniform flow
3. Laminar and turbulent flow
4. Sub-critical, critical, and super-critical flow
It also discusses discharge equations for open channels including Chezy's formula, Manning's formula, and Bazin's formula. Finally, it covers specific energy, critical depth, and the hydraulic jump in open channel flow.
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
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.
This document provides an overview of fluid kinematics concepts. It describes fluid flow using Lagrangian and Eulerian descriptions, and defines steady and unsteady, uniform and non-uniform flow. Streamlines, pathlines and streaklines are differentiated. Streamlines indicate instantaneous velocity direction, and streamtubes are bundles of streamlines. One, two and three dimensional flows are described. The material derivative, which follows a fluid particle as it moves, is introduced along with its relationship to particle acceleration. Key concepts are illustrated with diagrams.
Flow of viscous fluid through circular pipevaibhav tailor
The document summarizes flow of viscous fluid through a circular pipe. It describes that flow can be laminar, transitional, or turbulent depending on the Reynolds number. It presents the Hagen-Poiseuille law which describes laminar flow in a circular pipe. The law states that velocity distribution varies with the square of the radial distance from the center, and that maximum velocity is twice the average velocity. It also provides the equation for pressure drop along the length of the pipe based on flow properties and pipe dimensions.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
This document defines and describes different types of fluid flows including steady and unsteady flow, uniform and non-uniform flow, laminar and turbulent flow, compressible and incompressible flow, one-dimensional, two-dimensional, and three-dimensional flow. It also discusses boundary layers, boundary layer thickness, displacement thickness, and momentum thickness. Finally, it introduces the Moody diagram which can be used to determine friction factors based on relative roughness and Reynolds number.
This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.
This presentation contains the Fluid flow chapter of Pharmaceutical engineering. This chapter include the definition of flow of fluid, Reynolds number, Bernollis therom, Manometers, Fluid flow measuring equipment's and applications.
This document discusses the objectives and content of a fluid mechanics and machinery course. It includes:
- The objectives of understanding fluid properties, dimensional analysis, and various types of pumps and turbines.
- An introduction to fluid mechanics, including the basic concepts and importance in engineering applications.
- Details about the first unit which will cover fluid properties, flow characteristics using concepts like the continuity, energy, and momentum equations.
This document discusses fluid mechanics and its various branches and concepts. It begins by defining mechanics, statics, dynamics, and fluid mechanics. It then discusses specific types of fluid mechanics like hydrodynamics, hydraulics, gas dynamics, and aerodynamics. It also discusses classifications of fluid flow such as viscous vs inviscid flow, internal vs external flow, and compressible vs incompressible flow. Finally, it covers key concepts like laminar vs turbulent flow, steady vs unsteady flow, and dimensional flows.
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
IRJET- Investigation of Fluid Flow Characteristics for the Forced Convect...IRJET Journal
This document summarizes a study that used computational fluid dynamics (CFD) to investigate fluid flow characteristics over heated elliptical and circular shaped tubes. The study varied the Reynolds number from 438 to 1227 and found that elliptical tubes had lower pressure drop and friction factor values than circular tubes. Velocity distributions showed smaller wakes behind elliptical tubes. Pressure drop and friction factor both increased with Reynolds number but elliptical tubes performed better in both areas. The study concluded elliptical tubes provided better heat transfer characteristics than circular tubes of the same hydraulic diameter.
CFD Simulation of Swirling Effect in S-Shaped Diffusing Duct by Swirl Angle o...IOSR Journals
This document describes a computational fluid dynamics (CFD) simulation of swirling flow through an S-shaped diffusing duct with a 10 degree swirl angle. The study models airflow through a duct with an area ratio of 1.9, length of 300mm, and turning angle of 22.5 degrees. Simulations were conducted for uniform inlet flow and swirling inlet flow clockwise and counter-clockwise. Results show that swirling flow improves static pressure recovery over uniform flow. Clockwise swirling flow provided the highest pressure recovery and most uniform exit flow. Turbulence intensity and secondary flows increased through the duct but did not exceed 15% of inlet velocity.
This document describes a numerical study that simulates two-phase flows in C-shaped and U-shaped pipes using a 1D centerline-based mesh generation technique. The study investigates the effects of four different gravitational directions on pressure changes, bubble dynamics, and flow physics. Governing equations for a two-fluid model are presented and solved using the open-source software OpenFOAM. A 1D centerline mesh generation algorithm is used to divide the pipe geometry into cross-sectional zones for control volume analysis. Simulation results show the influence of buoyancy forces on dynamic pressure and turbulent kinetic energy in the two-phase flows.
Analysis of cross flow induced vibration in an inline and staggered configura...eSAT Journals
Abstract
In many engineering applications like heat exchanger, radiator, evaporator, nuclear power plant and thermal power plant, arrangement of tubes is very crucial. Fluid elastic instability forms the basis for deciding the type of arrangement and tube spacing but the phenomenon of vortex induced vibration is random in nature. Tube spacing also plays a critical role in different types of arrangement. Different type of application requires different tube spacing and the range of tube spacing vary from 1 to 6. Vortex Induced Vibration in cross flow around the inline and staggered arrangement of the tube arrays is experimentally studied for varying P/d (tube spacing) ratio. It is observed that with the increase in the velocity, the amplitude displacement increases. As the amplitude displacement of the tube reduces, the pitch over diameter ratio is increased from 2 to 4. It is also observed that between inline and staggered arrangement, the amplitude displacement of staggered arrangement is more compared to inline arrangement for same tube spacing.
Keywords: Vortex Induced Vibration, Inline Arrangement, Staggered Arrangement, Regression Analysis
The document summarizes research on using fractal patterns as flow conditioners upstream of orifice plate flow meters. It describes two fractal designs tested - a Koch curve and space-filling circles. Experiments with air and water flows showed fractals reduced errors from disturbances. CFD simulations visualized how fractals restored uniform velocity profiles. While fractals alone caused small errors, they significantly reduced errors from blockages and swirl. The research demonstrates fractal conditioners can increase measurement accuracy over conventional straight pipes by requiring less upstream distance and producing fully developed flow. Future work is proposed to further optimize fractal conditioner designs.
CFD and EXPERIMENTAL ANALYSIS of VORTEX SHEDDING BEHIND D-SHAPED CYLINDERAM Publications
The flow around bluff bodies is an area of great research of scientists for several years. Vortex shedding is
one of the most challenging phenomenon in turbulent flows. This phenomenon was first studied by Strouhal. Many
researchers have modeled the various objects as cylinders with different cross-sections among which square and
circular cylinders were the most interested sections to study the vortex shedding phenomenon. The Vortex Shedding
frequency depends on different aspects of the flow field such as the end conditions, blockage ratio of the flow passage,
and width to height ratio. This case studies the wave development behind a D-Shaped cylinder, at different Reynolds
numbers, for which we expect a vortex street in the wake of the D-Shaped cylinder, the well known as von Kármán
Street. This body typically serves some vital operational function in aerodynamic. In circular cylinder flow separation
point changes with Reynolds number but in D-Shaped cylinder there is fix flow separation point. So there is more
wake steadiness in D-Shaped cylinder as compared to Circular cylinder and drag reduction because of wake
steadiness.In the present work CFD simulation is carried out for flow past a D-Shaped cylinder to see the wake
behavior. The Reynolds number regime currently studied corresponds to low Reynolds number, laminar and
nominally two-dimensional wake. The fluid domain is a two-dimensional plane with a D-Shaped cylinder of
dimensions B=90mm, H=80mm and L=200mm. CFD calculations of the 2-D flow past the D-Shaped cylinder are
presented and results are validated by comparing with Experimental results of pressure distribution on cylinder
surface. The experimentation is carried out using small open type wind tunnel. The flow visualization is done by
smoke visualization technique. Results are presented for various B/H ratios and Reynolds numbers. The variation of
Strouhal number with Reynolds number is found from the analysis. The focus of the present research is on reducing
the wake unsteadiness.
CFD BASED ANALYSIS OF VORTEX SHEDDING IN NEAR WAKE OF HEXAGONAL CYLINDERIRJET Journal
This document presents a computational fluid dynamics (CFD) analysis of vortex shedding in the near wake of a hexagonal cylinder. The study examines the effects of Reynolds number on lift, drag, vortex shedding frequency, and Strouhal number. CFD simulations were performed for Reynolds numbers of 100, 500, and 1000. Results showed increases in drag and lift coefficients with increasing Reynolds number. Velocity contours and pressure contours indicated transition to turbulence in the wake with higher Reynolds numbers. Strouhal number and vortex shedding frequency both increased significantly with Reynolds number. The study provides insight into vortex behavior behind hexagonal cylinders under varying flow conditions.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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Vortex Shedding Study using Flow visualisation Lavish Ordia
This document summarizes a study that used flow visualization experiments to examine vortex formation behind various blunt bluff body shapes placed inside a circular pipe. Dye injection was used to visualize complex vortex patterns. Parameters like Strouhal number, vortex formation length, and wake width were measured for different orientations and shapes, including modifications to a trapezoidal cylinder. Both interacting and non-interacting vortex formation with shear layers was observed. The document provides background on the experimental setup and image processing methods used to analyze vortex shedding frequencies and lengths.
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EXPERIMENTAL and ANALYTICAL ANALYSIS of FLOW PAST D-SHAPED CYLINDERAM Publications
The study of flow past the bluff body is very important in aerodynamics. The D-Shaped cylinder is one of the
bluff bodies which serve some vital operational function in aerodynamic. So it is necessary to study the flow past the DShaped
cylinder. In this paper the flow past D-Shaped cylinder of dimensions B=90mm, H=80mm, and L=200mm is
studied experimentally and analytically. The analytical results are validated with experimental results. The flow
parameter drag co-efficient is calculated for different Reynolds number using Drag co-efficient relation and results of
drag co-efficient are validated with experimental results. Based on the experimental and analytical results, the drag coefficient
of circular cylinder and D-Shaped cylinder are compared. The Strouhal number is calculated using Strouhal
number co-relation for different Reynolds number and results of Strouhal number are validated with previous results
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Manufacturing Process of molasses based distillery ppt.pptx
unsteady flow simulation along staggered cylinder arrangement
1. Unsteady Flow Simulation around a Square Cylinder
using Upstream Rod
By
Ramakant pandey
(2010FE13)
under the guidance
of
Er. Akshoy Ranjan Paul
Asst. Professor, Applied Mechanics Department
DEPARTMENT OF APPLIED MECHANICSDEPARTMENT OF APPLIED MECHANICS
MOTI LAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY, ALLAHABADMOTI LAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY, ALLAHABAD
2. INDEX
• Introduction
• Overview
• Importance of Drag reduction
• Literature Review
• Gaps in Literature
• Objectives
• Solution Methodology
• Result and Discussion
• Conclusion (with proposed equation)
• Future Scope
• References
• 3D Animations
3. INTRODUCTION
• As we know that when a body move in air (any fluid) or air move on
still body, body experience a force, That force is called drag force.
In engineering and practical applications, like automobile, aircrafts
and architectural structures, such as bridge decks and monuments,
etc., have either square or rectangular or circular Cross - sections are
subjected to drag force.
• The cross flow around such bodies is characterized by a large region
of flow separation with suction pressure, resulting in a large value of
the resistance force, In many engineering applications, for certain
purposes, it is desirable to diminish this large value of drag
coefficient, CD.
4. Overview
• Experience shows that there is resistance to motion of solid bodies
through real fluid. It depends on the shape of the bodies and velocity
of that body. It act in the direction opposite to incoming flow
velocity.
• Bodies have streamlined shape induce small region of wake
formation compare to blunt body due to this streamlined body have
lower value of pressure drag in comparison to bluff body.
• Total drag consists of pressure drag or form drag and friction drag or
skin drag.
5. Importance of drag reduction
• The ability to manipulate a flow field is of immense technological
importance. For example, if drags of vehicles and buildings can be
reduced, much fuel cost and materials for the buildings would be
saved. Flow control around bluff bodies is of importance and of
interest for wind engineering.
• When one structure is immersed in the wake of another, the
characteristics of the flow and the aerodynamic forces depend
strongly on the shape, spacing between the structures, arrangement
of the structures, and wind direction. It is therefore useful to
investigate these characteristics from a practical point of view.
6. Literature Review
Sr.
No.
Authors
Name
Title of paper Year of
Publish
Nature of
Work(Exp./Comp.)
List of
variables
Major
findings
Further
Scope of
work
1 Moon Kyoung
Kim, Dong
Keon Kim,
Soon Hyun
Yoon and Dae
Hee Lee
Measurements of
the flow fields
around two square
cylinders in a
tandem
arrangement
2008 Experimental
(using PIV)
Spacing
between two
cylinders
Drastic change in
flow pattern at
critical length
Size variation,
shape variation,
staggered
arrangement.
2 P.F. Zhanga,
J.J. Wanga,
L.X. Huangb
Numerical
simulation of flow
around cylinder
with an upstream
rod in
tandem at low
Reynolds numbers
2006 Computational variation of the
center-to-center
spacing ratio
It is found
that the mean drag
and the lift
fluctuation of the
cylinder can be
reduced by the
upstream rod,
Shape variation,
staggered angle
variation.
3 Baris
Gumusel and
Cengiz camci
Aerodynamic drag
characteristics and
shape design
of a radar antenna
used for airport
ground traffic
control.(ASDE-
airport surface
detection
equipment)
2010 computational shape of antena increase in fineness
ratio results in drag
reduction or gives
better relative
improvement.
RI--it is defined as
ratio of drag
cofficient reduction
divided by the drag
cofficient of ASDE-
X cross section.
may be variable
cross section
can be used, or
an aerofile
shape can be
used.
7. Literature Review
4 Yoichi
Yamagishi,
Shigeo Kimura,
Makoto Oki and
Chisa Hatayama
Effect of corner
cutoffs on flow
characteristics
around a square
cylinder
international
conf., 2009,
moscow,
russia.
Experimental,
numerical
analysis and
visualizatin
changing
chamfer shape,
dimensions and
angles of
attack.
variations in the drag
coefficients CD with
the angle of attack α
for cylinders.
5 A. Prasad,
C.H.K.
Wi|liamson
A method for the
reduction of bluff
body drag
1997 Experimental upstream plate
width and
distance
between plate
and cylinder
it is possible to
reduce bluff body
drag dramatically
with the use of small
flat plates placed
upstream
Shape and size
variation,
staggered
arrangement with
angle variation
6 KWANGMIN SON,
JIN CHO,
WOO-PYUNG
JEON AND
HAECHEON CHOI
Mechanism of drag
reduction by a
surface trip wire on
a sphere
2011 Experimental Location of
wire and
diameter of
wire.
three different flow
characteristics are
observed above the
sphere surface,
7 Tamotsu
Igarashi,
Nobuaki Terachi
Drag reduction of
flat plate normal to
airstream by flow
control using a rod.
2002 Experimental Rod diameter
And distance
between axes
of rod and
plate.
The maximum
reduction of the total
drag coefficient is
about 20–30%
compared to the drag
without the rod in the
same range of the
Reynolds
number
Staggered
arrangement,
multi- ple rods can
be use, shape
change of
upstream rod.
8. Literature Review
8 T. Tsutsui, T.
Igarashi
Drag reduction
of a circular
cylinder in an
air-stream
2002 Experimental Upstream rod diameter
and distance between
cylinder and upstream
rod
The optimum
conditions of the drag reduction
are d/D=0.25, L/D=1.75 -2.0.
The reduction of the total drag
including the drag of the rod is
63% compared with that of a
single cylinder
`
9 Ming Zhao,
Liang Cheng,
Bin Teng,
Dongfang
Liang
Numerical
simulation of
viscous flow
past two
circular
cylinders of
different
diameters
2005 Computational The gap between the
small cylinder and the
large cylinder and The
position angle of the
small cylinder relative to
the flow direction
the shedding flow behind the
two cylinders can
be classified into three types, For
the very small gap ratio, there is
only one wake behind the two
cylinders, At medium gap ratios,
there exist strong interactions
between the vortex
shedding from the large cylinder
and the shedding from the small
cylinder, For very
large gap ratios, the interaction
between the shedding from
the two cylinders becomes very
weak
upstream
cylinder
diameter and
shape variation,
staggered angle.
9. Literature Review
Literature review
10 D. Sumner,
O. O.
Akosile
Behaviour of a
closely spaced pair
of circular cylinders
in cross-flow
CSME
2004
Forum 1
Experimental At two Pitch
Ratio,
staggered
angle.
The general behavior of the
force coefficients
and the Strouhal number was
similar for
both pitch ratios, since the
flow pattern for
closely spaced staggered
cylinders is similar to a
single bluff body, with a
single vortex shedding
process.
Two different shapes
can be used,
Reynolds no.
variation.
11 Shun C.
Yen , Jung
H. Liu
Wake flow behind
two side-by-side
square cylinders
2011 Experimental Reynolds No.,
Gap ratio.
Results classified into three
modes single mode, gap-flow
mode, couple vortex-
shedding.
10. Research Gap Identified from Literature
• Lots of studies have been done on drag reduction of circular cylinder but
paid little attention to square cylinder.
• Variation in center distance and size is done for drag reduction but no
findings on the drag reduction analysis by using the rod of different cross
sections.
• Effects of upstream rod shapes are not found in literature review.
• Use of multiple upstream rods not found in literature, which can be used in
staggered arrangement.
• Use of multiple upstream rods of different cross-section simultaneously.
11. Objectives
• To calculate drag, when staggered angle α is varying at
constant L/D and d/D.
• To calculate drag, when staggered angle α is varying at
constant d/D and variable L/D.
• To calculate drag, when staggered angle α, d/D and L/D are
varying.
• To calculate drag, when two upstream rods are used in
staggered arrangement.
• To obtain the least drag condition (optimized condition).
Note:- Multiple upstream rods can be arranged in tandem or staggered
arrangement, In tandem arrangement rods are placed one after another on
an axis while in staggered arrangement rods are placed with some stagger
angle along one side of axis or may be along both the sides of an axis.
14. Computational geometry
• Test section: 2500 mm × 1500 mm × 1500 mm
• Square cylinder: 60 mm × 60 mm × 1000 mm
• Upstream rod:
Length: 1000 mm
Diameter: 16.02 mm
15. Computational specification
Solver: 3D,pressure based, Unsteady.
Viscous model: Realizable K-ε, Standard wall function.
Boundary conditions:
Velocity inlet has taken as inlet boundary condition and zero gauge pressure used as
exit condition. upstream rod and downstream cylinder are given wall as two different
entities.
-velocity inlet: 15 m/s ,Re. No.61,500
. To indicate the turbulence quantities at the inlet, like turbulent kinetic energy (k) and
turbulence dissipation rate (ε), the following relation is used-
Where L – turbulent length scale
I – turbulent intensity = 0.16 (Re)-1/8
No slip boundary condition is specified at the wall.
17. • Conservation of momentum for compressible turbulent flow with no body forces and
source terms can be written as
.( ) 0V
t
ρ
ρ
∂
+∇ =
∂
ur
.
V
V V p
t
ρ τ
∂
+ ∇ =−∇ −∇ ÷
∂
ur
uur ur
. . . 0
e
V e p V V
t
ρ τ
∂
+ ∇ + ∇ − ∇ = ÷
∂
uur ur r uur
• The equation for conservation of mass for an compressible flow in vector
notation can be written as
•Equation for the conservation of Energy for the compressible flow can be
written as
Governing Equations of Fluid Flow
18. ( ) ( ) t
j k b M k
j j k j
k
k ku G G Y S
t x x x
µ
ρ ρ µ ρε
σ
∂ ∂ ∂ ∂
+ = + + + + − + ÷
∂ ∂ ∂ ∂
Model specification
The modelled transport equations for k and in the realizable k- model areԑ ԑ
( ) ( )
2
1 2 1 3
t
j b
j j j
u C S C C C G S
t x x x kk v
ε ε ε
ε
µ ε ε ε
ρε ρε µ ρ ε ρ
σ ε
∂ ∂ ∂ ∂
+ = + + − + + ÷
∂ ∂ ∂ ∂ +
j
k i j
i
u
G u u
x
ρ
∂
′ ′= −
∂
The model constants taken for analysis are 1 21.45, 1.8, 1.0, 1.2kC Cε εσ σ= = = =
In above equation represents the generation of turbulence kinetic energy due to mean
velocity gradient
is the generation of turbulence kinetic energy due to buoyancy
kG
Pr
t
b i
t i
T
G g
x
µ
β
∂
=
∂
bG
YM represents the contribution of the fluctuating dilatation in compressible
turbulence to the overall dissipation rate. and are constants. and are the
turbulent Prandtl numbers for k and respectively.ԑ
1C2C kσ εσ
20. Grid Independency Checking
Any CFD solution heavily depends on the size and fitness of meshing. Therefore, care
must be taken in selecting the grid types (coarse, medium or fine) so not to affect the
solution. In the present case, the solutions of bare cylinder are carried out for different
sizes of grids and coefficient of drag was monitored for each grid types.
Case Elements
% Error in successive cases
1 109643 2.137
-
2 194426 2.063
3.46
3 426552 2.021
2.03
4 594600 1.996
1.237
5 867785 1.979
0.85
6 1184524 1.976
0.15
DC
21. Validation
Two models K-ε RNG and K-ε
Realizable were tested in present
computational work, out of which K-
ε realizable shows better agreement
With reference Experimental paper of
Zhang and wang(2005).
% Error for K-ε RNG and Exp.
(P.F.Zhang -2005)= 16.75%
% Error for K-ε Realizable and Exp.
(P.F.Zhang -2005)= 4.31%
0 5 10 15 20
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Cp
Length along cylinder(mm)
0deg,L/D=1.9,d/D=0.267
Exp.(P.F.Zhang-2005)
Computational(Reliaziable)
Computational(RNG)
22. Validation for the bare cylinder
• For the case of Bare
cylinder Drag given in
reference paper is 2.21
and from present
computational work it
found 1.98.
• Percentage Error in
Drag is 10.40%.
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder (mm)
Exp.(P.F.Zhang-2005)
Present (computational)
Uncertainity=0.26
25. pattern of static pressure contour around square cylinder
Boundary layer
pattern
visualization in
presence of
upstream rod
and in bare
cylinder case.
In bare cylinder flow is coming
directly on front face but when
upstream rod is introduced, due to
wake of rod pressure at front face
of cylinder decreases and reduces
half of the drag acting on square
cylinder.
27. At L/D=1.9,d/D=0.267
Bare cylinder, α=1°,
α=4°, α=6°, α=7°, α=19°
In this figure
as the staggered angle α is
increasing the “shielding
effect” is decreasing which
results in the reduction of
drag, due to decrease in the
shielding effect, the back
suction pressure decreases
which is the main cause of
drag reduction.
At α ≥ 20, the
rod cylinder arrangement
starts acting like a bare
cylinder arrangement.
In wake
independent region rod and
cylinder gives the drag
similar to that in bare
cylinder case, which is 1.98
in the present
computational work.
Flow visualization Velocity pattern
29. Results and discussion
Coefficient of pressure
• The case of the single cylinder is
also presented for comparison. For
a<2, the pressure distribution on the
upper and lower sides of the square
cylinder is roughly symmetrical
about the center line. The upward
side has a low pressure like that at
a=0, which implies that the shield
effect of the rod on the square
cylinder also exists, and that the flow
is in cavity flow mode.
•In wake merging mode (2 ≤ α ≤9),
the enhanced asymmetrical flow
results in the asymmetrical pressure
distribution on the square cylinder.
• Variation in staggered angle α at constant L/D and
d/D
α=0°-9°
L/D=1.9
d/D=0.267
30. Variation in staggered angle α at constant L/D and d/D
α=9°-45°, L/D=1.9, d/D=0.267
• In the weak boundary layer
interaction mode, the effect
of the rod’s wake on the
cylinder is reduced, and the
pressure on the upper and
lower sides tend to that of the
square cylinder alone in a
cross flow. This implies that
the separation bubble on the
lower side of the square
cylinder begins to disappear.
At last in the negligible
interaction mode, the
pressure distribution of the
square cylinder is the same as
that of a single cylinder.
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder (mm)
Bare
9°
19°
31°
45°
31. Drag Calculation For α=0°-45°
L/D=1.9
d/D=0.267
bare 0° 1° 2° 3° 5° 9° 19° 31° 45°
Cd 1.98 0.95 0.99 1.05 1.18 1.32 1.36 1.43 1.50 1.74
% reduction w.r.t bare
cylinder 51.83 49.63 46.67 40.27 33.36 31.33 27.63 24.03 12.29 12.29
Cd
Staggered angle (α)
35. Variation in d/D
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder(mm)
d/D=0.1
angle L/D
2° 1.7
2° 2.3
2° 3.5
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder(mm)
d/D=0.267
angle L/D
4° 2.3
5° 2.7
9° 3.5
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder(mm)
d/D=0.5
angle L/D
11° 2.5
23° 3.5
23° 4.0
Graphs shows the
variation of staggered
angle, L/D distance and
d/D ratio simultaneously.
36. Variation in staggered angle α at variable d/D and L/D
α=2°,11°,23°,L/D=1.7-3.5, d/D=0.1, 0.5
d/D
0.1
0.267
0.5
case 1 2 3 4 5 6 7 8 9
L/D 1.7 2.3 3.5 2.3 2.7 3.5 2.5 3.5 4.0
α 2° 2° 2° 4° 5° 9° 11° 23° 23°
CD 1.69 1.65 1.75 1.12 1.11 1.33 1.45 1.69 1.74
CD
Case
37. Use of two upstream rods
0 5 10 15 20 25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Cp
Length along the cylinder(mm)
angle L/D d/D
5° 1.9 0.1
5° 1.9 0.267
9° 1.9 0.5
Results obtained from above
three conditions are used to
choose the best three conditions
to visualize the effect of multiple
upstream rods to reduce the drag
of square cylinder, taking into
consideration total drag of the
system.
Pressure distribution along
square cylinder in case of 5°
staggered angle at d/D=0.5
gives better results as compared
to single upstream rod as in this
analysis total drag of system is
taken into consideration.
39. Conclusion
• In tandem arrangement, the reduction of drag was mainly caused by the increase of
the rear suction pressure. When the staggered angle was introduced, the shield and
the disturbance effect of the rod on the square cylinder diminished which results in
the increase of the cylinder drag. The side force induced by the staggered angle is
small.
• Drag coefficients have been calculated for staggered angle α,various combinations
of L/D and d/D ratios. The results obtained from the simulations are similar with
the reference paper(P.F.Zhang-2005).
• Cd keeps a low value for α<3–5 at different L/D. Afterwards, it increases quickly
to the value 1.98 (Bare cylinder drag coefficient in the present study). For α>20, Cd
has little variation and remains around the constant value of 1.98.
• The flow modes take place in the following regular order: the cavity mode or the
wake impinge mode (depends on L) occurs first and the wake splitting mode
follows. Then, the wake merging mode appears, and the next one is the weak
boundary layer interaction and the negligible interaction mode terminates the whole
process.
• For two upstream rods case 3 gives the maximum 67.27% reduction in drag with
respect to bare cylinder.
40. Future scope
• Experiments and simulations can be performed for more than one thin rod placed
upstream. Thus various combinations can be tested for different combinations of
diameters of rods and different combination of the distances between them.
• Various geometries of the upstream rod can be tested like triangular cross section
or an aero foil shaped rod.
• Upstream rods can be used with the change in cross-section of downstream cylinder
also.
• In the case of upstream rods, two rods of different cross-sections can be used.
• Slots of various shapes can be used in downstream cylinder to reduce pressure
separation.
41. References
• BLUFF-BODY AERODYNAMICS,Lecture Notes By Guido Buresti,Department of
Aerospace Engineering,University of Pisa, Italy
• Roshko,1960, “Experiments on the flow past a circular cylinder at very high Reynolds
number”, pp 345-356
• Bearman PW 1965, “Investigation of the flow behind a two-dimensional model with a blunt
trailing edge and fitted with splitter plates”, Journal of Fluid Mech. Vol. 21 pp.241–255.
• Bearman PW, Obasaju ED 1982, “An experimental study of pressure fluctuation on fixed and
oscillating square-section cylinder”, J Fluid Mech. Vol.119 pp. 297–321.
• Lesage F, Gartshore IS 1987, “A method of reducing drag and fluctuating side force on bluff
bodies”, Journal of Wind Engg.vol.2, pp. 229–245.
• Sakamoto and Haniu 1994, “Optimum suppression of fluid forces acting on a circular
cylinder”, ASME Journal of Fluids Eng. Vol.116, pp. 221–227.
• Williamson and Prasad, 1997, “A method for the reduction of bluff body drag” Journal of
Wind Engineering and Industrial Aerodynamics, vol. 69- 71, pp.155 167.
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various corner shapes”, Journal of Wind Engineering and Industrial Aerodynamics, pp- 531-
542.
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various corner shapes” Journal of Wind Engineering and Industrial Aerodynamics vol. 74-76,
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• Lemay and Bouak, 1997, “Passive control of the aerodynamic forces acting on a circular
cylinder” Experimental thermal and fluid sciences, vol.16, Pages 112-121.
42. References
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Journal of Wind Engineering and Industrial Aerodynamics, vol. 67, pp-141-153.
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tandem arrangement” Journal of Wind Engineering and Industrial Aerodynamics, vol. 90, pp.
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