Study of Laminar, Turbulent and Vortex fluid flow

In fluid dynamics, it is necessary to identify which type of fluid flow it is? Because of this the further study of fluid, its properties, and all starts. So, one must be very clear about the concepts of flow type. 

    There are various types of flows such as :

• Steady and Unsteady
• Uniform and Non-Uniform
• Laminar and Turbulent
• Compressible and In-compressible
• Rotational and Ir-rotational and
• One, Two, and Three -dimensional Fluid Flow

  In this blog, we are going to start with Laminar and turbulent fluid flow types. And one thing we also discuss What is Vortex Flow? Before going to study this thing we take a look at its history how it starts, 

History

       The distinction between laminar and turbulent regimes was first studied and theorized by Osborne Reynolds in the second half of the 19th century. His first publication on this topic is considered a milestone in the study of fluid dynamics.

This work was based on the experiment used by Reynolds to show the transition from the laminar to the turbulent regime.

The experiment consisted of examining the behavior of water flow in a large glass pipe. In order to visualize the flow, Reynolds injected a small vein of dyed water into the flow and observed its behavior at different flow rates. When the velocity was low, the dyed layer remained distinct through the entire length of the pipe. When the velocity was increased, the vein broke up and diffused throughout the tube’s cross-section, as shown in figure 

     Figure: Reynolds’ experimental observation of the transition phase showing the streamlined dye gradually transitioning to eddies and swirls.

Thus, Reynolds demonstrated the existence of two different flow regimes, called laminar flow and turbulent flow, separated by a transition phase. He also identified a number of factors that affect the occurrence of this transition.

So, this is how it starts. Let's see the further part.

Laminar Flow

In fluid dynamics, laminar flow is characterized by smooth or regular paths of particles of the fluid, The fluid flows in parallel layers (with minimal lateral mixing), with no disruption between the layers. Therefore the laminar flow is also referred to as streamline or viscous flow.

When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of any types of flow  may occur depending on the velocity, viscosity of the fluid and the size of the pipe.

 Laminar flow tends to occur at lower velocities and high viscosity.

Turbulent Flow

In fluid dynamics, turbulent flow is characterized by the irregular movement of particles of the fluid. In contrast to laminar flow the fluid does not flow in parallel layers, the lateral mixing is very high, and there is a disruption between the layers. Turbulence is also characterized by recirculation, eddies, and apparent randomness. In turbulent flow, the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction.

In the above part, many times we read the term Reynolds number, so let's see what is this Reynolds number?

   Reynolds number

    The Reynolds number is the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It can be interpreted that when the viscous forces are dominant (slow flow, low Re) they are sufficient enough to keep all the fluid particles in line, then the flow is laminar. Even very low Re indicates viscous creeping motion, where inertia effects are negligible. When the inertial forces dominate over the viscous forces (when the fluid is flowing faster and Re is larger) then the flow is turbulent.

        It is a dimensionless number comprised of the physical characteristics of the flow. An increasing Reynolds number indicates increasing turbulence of flow.
It is defined as:

   

           Characteristic Of Laminar Flow

1.Laminar is characterized by smooth streamlines and highly ordered motion. Under most practical conditions, the flow in a circular pipe is laminar for Re < 2000. In fully developed laminar flow, each fluid particle moves at a constant axial velocity along a streamline and the velocity profile remains unchanged in the flow direction.
2.The steady laminar flow of an incompressible fluid with constant properties in the fully developed region of a straight circular pipe.
3.Laminar flow in a straight pipe may be considered as the relative motion of a set of concentric cylinders of fluid, the outside one fixed at the pipe wall and the others moving at increasing speeds as the center of the pipe is approached.

4.Smoke rising in a straight path from a cigarette is undergoing laminar flow. After rising a small distance, the smoke usually changes to turbulent flow, as it eddies and swirls from its regular path.

Characteristics of Turbulent Flow

     1.  Turbulent flow tends to occur at higher velocities, low viscosity, and at higher characteristic linear dimensions.

2.  If the Reynolds number is greater than Re > 3500, the flow is turbulent.

3.     Irregularity: The flow is characterized by the irregular movement of particles of the fluid. The movement of fluid particles is chaotic. For this reason, turbulent flow is normally treated statistically rather than deterministically.

4.     Diffusivity: In turbulent flow, a fairly flat velocity distribution exists across the section of pipe, with the result that the entire fluid flows at a given single value and drops rapidly extremely close to the walls. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow are called “diffusivity”.

5.     Rotationality: Turbulent flow is characterized by a strong three-dimensional vortex generation mechanism. This mechanism is known as vortex stretching.

6.     Dissipation: A the dissipative process is a process in which the kinetic energy of the turbulent flow is transformed into internal energy by viscous shear stress.

Difference between Laminar and Turbulent Flows 

Laminar flow	Turbulent Flow
Re < 2000	Re > 4000
‘low’ velocity	‘high’ velocity
Fluid particles move in straight lines	The flow is characterized by the irregular movement of particles of the fluid.
Layers of water flow over one another at different speeds with virtually no mixing between layers.	Average motion is in the direction of the flow
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 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 one half of the maximum velocity.	The average flow velocity is approximately equal to the velocity at the center of the pipe
Simple mathematical analysis is possible.	Mathematical analysis is very difficult
Rare in practice in water systems.	A most common type of flow.

 

Example :

Laminar Flow 

• Oil flow through a thin tube or blood flow through capillaries is laminar. Most other Kinds of fluid flow are turbulent except near solid boundaries, where the flow is often laminar, especially in a thin layer just adjacent to the surface.

•       When water leaves a tap with little force, it first exhibits laminar flow, but as acceleration by the force of gravity immediately sets in, the Reynolds number of the flow increases with speed and the laminar flow can transition to turbulent flow. Optical transparency is then reduced or lost entirely.

•       Another example is the flow of air over an aircraft wing. The boundary layer is a very thin sheet of air lying over the surface of the wing (and all other surfaces of the aircraft). Because air has viscosity, this layer of air tends to adhere to the wing. As the wing moves forward through the air, the boundary layer at first flows smoothly over the streamlined shape of the airfoil. Here, the flow is laminar and the boundary layer is a laminar layer. Prandtl applied the concept of the laminar boundary layer to airfoils in 1904.

Turbulent Flow

• The flow conditions in many industrial equipment (such as pipes, ducts, precipitators, gas scrubbers, dynamic scraped surface heat exchangers, etc.) and machines (for instance, internal combustion engines and gas turbines).
• The external flow over all kinds of vehicles such as cars, airplanes, ships, and submarines.
• The motions of matter in stellar atmospheres.
• A jet exhausting from a nozzle into a quiescent fluid. As the flow emerges into this external fluid, shear layers originating at the lips of the nozzle are created. These layers separate the fast moving jet from the external fluid, and at a certain critical Reynolds number they become unstable and break down to turbulence.

Water Falls:-     

Combination of laminar and turbulent flow at a waterfall. Laminar (exactly over the ridge) and turbulent flow (immediately downstream with white foam) of the Victoria Falls.

Smoke rising from a cigarette or an incense stick :-

For the first few centimetres, the flow is certainly laminar. However, at some point from the leading edge the flow will naturally transition to turbulent flow

as its Reynolds number increases. The Reynolds number increases as its flow velocity and characteristic length are both increasing.

Power-law velocity profile – Turbulent velocity profile

The velocity profile in turbulent flow is flatter in the central part of the pipe (i.e. in the turbulent core) than in laminar flow. The flow velocity drops rapidly extremely close to the walls. This is due to the diffusivity of the turbulent flow.

In the case of turbulent pipe flow, there are many empirical velocity profiles. The simplest and the best known is the power-law velocity profile:

Where the exponent n is a constant whose value depends on the Reynolds number. This dependency is empirical. In short, the value n increases with increasing Reynolds number. The one-seventh power-law velocity profile approximates many industrial flows.

Let's see the next state of fluid flow i.e Vortex flow From the following information you get an idea about how it is.

Vortex Flow

vortex  is a region in a fluid in which the flow revolves around an axis line, which 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.

For example,

- Vortices formed by milk when poured into a cup of coffee.

- 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 is 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.

PROPERTY OF VORTEX - ( Vorticity )

A key concept in the dynamics of vortices is the vorticity, a vector that describes the local rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it. Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center. The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the right-hand rule) while its length is twice the ball's angular velocity.

Types of Vortex flow

 1.) Irrotational vortices 

In the absence of external forces, a vortex usually evolves fairly quickly toward the irrotational flow pattern, where the flow velocity u is inversely proportional to the distance r. Irrotational vortices are also called free vortices.

                                                                                    

                                             Fig. - An irrotational vortex

In a free vortex mechanics, overall energy flow remains constant. There is no energy interaction between an external source and a flow or any dissipation of mechanical energy in the flow. Fluid mass in this flow rotates due to the conservation of angular momentum. In Irrotational vortices the velocity inversely proportional to the radius. In free vortex flow, Bernoulli’s equation can be applied.

Examples include a whirlpool in a river, water flows out of a bathtub or a sink, flow in the centrifugal pump casing, and flow around the circular bend in a pipe.

 

                                    Whirlpool in river

2.) Rotational vortices:- 

A rotational vortex – one which has non-zero vorticity away from the core – can be maintained indefinitely in that state only through the application of some extra force, that is not generated by the fluid motion itself.

The surface profile of the vortex flow is parabolic.

Tangential velocity is directly proportional to the radius.

                 v = r ω         

                 ω = Angular velocity.

                 r = Radius of fluid-particle from the axis of rotation.

For example,

 if a water bucket is spun at constant angular speed w about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity u equal to w*r. In that case, the free surface of the water will assume a parabolic shape.

The reasoning for the above-mentioned  example - In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure gradient in the water, directed inwards, that prevents the evolution of the rigid-body flow to the irrotational state.

Conclusion

From this blog, we have seen that what is the laminar, turbulent, and vortex flows along with their characteristics, examples, and practical significance.

 I hope you may clear with this concept now! If not please go and check this video to see how it works. 

Do share your precious views in the comments section and give it alike!

Thank you!
 

This blog is written by -

Kiran Ranmale

Mayur Rathod

Shivam Rathod

Shrusti Rathod

Under the guidance of - Prof.Nitin Borse Sir

jk