LAMINAR, TURBULENT AND VORTEX FLOW

 

  LAMINAR, TURBULENT AND VORTEX FLOW

Introduction

       Fluid dynamics is "the branch of applied science that is concerned with the movement of liquids and gases," according to the American Heritage Dictionary. Fluid dynamics is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them. (The other branch is fluid statics, which deals with fluids at rest.)

       The movement of liquids and gases is generally referred to as "flow", a concept that describes how fluids behave and how they interact with their surrounding environment — for example, water moving through a channel or pipe, or over a surface. Flow can be either steady or unsteady. The main types of flow namely Laminar, Turbulent and Vortex flow and can be easily identified in our real life. Let’s have a brief idea about these types of flows

 Laminar Flow

          In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers’ slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

           When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. The velocity is determined by a dimensionless parameter characterizing the flow called the Reynolds number, which also depends on the viscosity and density of the fluid and dimensions of the channel. Turbulent flow is a less orderly flow regime that is characterized by eddies or small packets of fluid particles, which result in lateral mixing.

          

          In non-scientific terms, laminar flow is smooth, while turbulent flow is rough. laminar flow, type of fluid (gas or liquid) flow in which the fluid travels smoothly or in regular paths, in contrast to turbulent flow, in which the fluid undergoes irregular fluctuations and mixing. In laminar flow, sometimes called streamline flow, the velocity, pressure, and other flow properties at each point in the fluid remain constant. Laminar flow over a horizontal surface may be thought of as consisting of thin layers, or laminae, all parallel to each other. The fluid in contact with the horizontal surface is stationary, but all the other layers slide over each other. A deck of new cards, as a rough analogy, may be made to “flow” laminarly.

    Properties-

• R_e < 2000
• ‘low’ velocity
• Fluid particles move in straight lines
• Layers of water flow over one another at different speeds with virtually no mixing between layers.
• The flow velocity profile for laminar flow in circular pipes is parabolic in shape, with a maximum flow in the center of the pipe and a minimum flow at the pipe walls.
• The average flow velocity is approximately one half of the maximum velocity.
• Simple mathematical analysis is possible.
• Rare in practice in water systems.

 

 Turbulent flow

        This is the type of fluid (gas or liquid) flow in which the fluid undergoes irregular fluctuations, or mixing, in contrast to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction. The flow of wind and rivers is generally turbulent in this sense, even if the currents are gentle. The air or water swirls and eddies while its overall bulk moves along a specific direction. Most kinds of fluid flow are turbulent, except for laminar flow at the leading edge of solids moving relative to fluids or extremely close to solid surfaces, such as the inside wall of a pipe, or in cases of fluids of high viscosity (relatively great sluggishness) flowing slowly through small channels. Common examples of turbulent flow are blood flow in arteries, oil transport in pipelines, lava flow, atmosphere and ocean currents,

The flow through pumps and turbines, and the flow in boat wakes and around aircraft-wing tips.

    Properties-

• Re > 4000
• ‘high’ velocity
• The flow is characterized by the irregular movement of particles of the fluid.
• Average motion is in the direction of the flow
• The flow velocity profile for turbulent flow is fairly flat across the center section of a pipe and drops rapidly extremely close to the walls.
• The average flow velocity is approximately equal to the velocity at the center of the pipe.
• Mathematical analysis is very difficult.
• Most common type of flow.

 

Vortex Flow

           In fluid dynamics, a vortex (plural vortices/vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.

Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterize vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis.

          In the absence of external forces, viscous friction within the fluid tends to organize the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carries with it some angular and linear momentum, energy, and mass.

What is a vortex flow? When a cylindrical vessel, containing some liquid, is rotated about its vertical axis, the liquid surface is depressed down at the axis of its rotation and rises up near the walls of the vessel on all sides.

This type of flow is known as vortex flow. It is of the following two types:

1. Forced vortex flow: In this type of flow, the vessel containing the liquid is forced to rotate about the fixed vertical axis with the help of some external torque.

2. Free vortex flow: In this type of flow, the liquid particles describe circular paths about a fixed vertical axis, without any external torque acting on the particles. The flow of water through the hole in the bottom of a wash basin is an example of free vortex flow.

The following important points may be noted for vortex flow:

(a) When a cylindrical vessel containing liquid is revolved, the surface of the liquid takes the shape of a paraboloid.

(b) The rise of liquid along the walls of a revolving cylinder about the initial level is same as the depression of the liquid at the axis of rotation.

 

(c) The total pressure on the bottom of a closed cylindrical vessel completely filled up with a liquid is equal to the sum of the total centrifugal pressure and the weight of the liquid in the vessel.

(d)The total pressure (P) on the top of a closed cylindrical vessel of radius (r) completely filled up with a liquid of specific weight (w) and rotating about its vertical axis is given by

(e)The increase in pressure at the outer edge of a drum of radius (r) completely filled up with liquid of mass density (p) is

(f) The tangential velocity (v) of the water element having a free vortex is inversely proportional to its distance from the center.