What is Fluid Dynamics?

Fluid dynamics is "the branch of applied science that is concerned with the movement of liquids and gases. 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.) 

Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns. Some important technological applications of fluid dynamics include rocket engines, wind turbines, oil pipelines and air conditioning systems.

Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.

Steady vs Unsteady flow:

Hydrodynamics simulation of the Rayleigh-Taylor Stability.

A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady.

Turbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary.

The random field U(x,t) is statistically stationary if all statistics are invariant under a shift in time.

This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.

Steady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.

What is flow?

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."If all properties of a flow are independent of time, then the flow is steady; otherwise, it is unsteady." That is, steady flows do not change over time. An example of steady flow would be water flowing through a pipe at a constant rate. On the other hand, a flood or water pouring from an old-fashioned hand pump are examples of unsteady flow. 

Flow can also be either laminar or turbulent. Laminar flows are smoother, while turbulent flows are more chaotic. One important factor in determining the state of a fluid’s flow is its viscosity, or thickness, where higher viscosity increases the tendency of the flow to be laminar. "By laminar flow we are generally referring to a smooth, steady fluid motion, in which any induced perturbations are damped out due to the relatively strong viscous forces. In turbulent flows, other forces may be acting the counteract the action of viscosity." 

Laminar flow is desirable in many situations, such as in drainage systems or airplane wings, because it is more efficient and less energy is lost. Turbulent flow can be useful for causing different fluids to mix together or for equalizing temperature. Most flows of interest are turbulent; however, such flows can be very difficult to predict in detail, and distinguishing between these two types of flow is largely intuitive.

An important factor in fluid flow is the fluid's Reynolds number (Re), which is as "the ratio of inertial to viscous forces." The inertial force is the fluid's resistance to change of motion, and the viscous force is the amount of friction due to the viscosity or thickness of the fluid.

NOTE: Re is not only a property of the fluid; it also includes the conditions of its flow such as its speed and the size and shape of the conduit or any obstructions. 

At low Re, the flow tends to be smooth, or laminar, while at high Re, the flow tends to be turbulent, forming eddies and vortices. Re can be used to predict how a gas or liquid will flow around an obstacle in a stream, such as water around a bridge piling or wind over an aircraft wing. The number can also be used to predict the speed at which flow transitions from laminar to turbulent. 

Liquid flow 

The study of liquid flow is called hydrodynamics. While liquids include all sorts of substances, such as oil and chemical solutions, by far the most common liquid is water, and most applications for hydrodynamics involve managing the flow of this liquid. That includes flood control, operation of city water and sewer systems, and management of navigable waterways.

Hydrodynamics deals primarily with the flow of water in pipes or open channels. The main difference between pipe flow and open-channel flow: "flows in closed conduits or channels, like pipes or air ducts, are entirely in contact with rigid boundaries," while "open-channel flows, on the other hand, are those whose boundaries are not entirely a solid and rigid material." Open-channel flows are rivers, tidal currents, irrigation canals, or sheets of water running across the ground surface after a rain."

Due to the differences in those boundaries, different forces affect the two types of flows. While flows in a closed pipe may be driven either by pressure or gravity, flows in open channels are driven by gravity alone. The pressure is determined primarily by the height of the fluid above the point of measurement. For instance, most city water systems use water towers to maintain constant pressure in the system. This difference in elevation is called the hydrodynamic head. Liquid in a pipe can also be made to flow faster or with greater pressure using mechanical pumps.  

Gas flow 

The flow of gas has many similarities to the flow of liquid, but it also has some important differences. First, gas is compressible, whereas liquids are generally considered to be incompressible. "If the density of the fluid changes appreciably throughout the flow field, the flow may be treated as a compressible flow." Otherwise, the fluid is considered to be incompressible. Second, gas flow is hardly affected by gravity. 

One area of particular interest is the movement of objects through the atmosphere. This branch of fluid dynamics is called aerodynamics, which is "the dynamics of bodies moving relative to gases, especially the interaction of moving objects with the atmosphere,"

Bernoulli's principle

Generally, fluid moving at a higher speed has lower pressure than fluid moving at a lower speed. This phenomenon was first described by Daniel Bernoulli in 1738 and is commonly known as Bernoulli's principle. It can be applied to measure the speed of a liquid or gas moving in a pipe or channel or over a surface. 

Geometrical Dimensions of the cylinder:

D = 0.02m

L = 0.05m

Fluid Properties:

V = 10m/s

Rho = 1.225kg/m^3

Density= 1.81 * 10^-5kg/m.s

R = 13535.91  (Reynold’s Number)

Behavior of fluid across the cylinder is shown below:

With Mesh Refinement:

Animation Link: https://www.youtube.com/watch?v=DMGUYLZkPx4

Now, we increase the Reynold's Number by 20%, so our new Reynold's Number becomes

R = 16243.92

V = 11.99m/s

Behavior of fluid across the cylinder is shown below:

With Mesh Refinement:

Animation Link: https://www.youtube.com/watch?v=mhPtuEuL7pk

If, we increase the Reynold's Number by 40%, so our new effective Reynold's Number becomes

R = 18950.27

V = 13.99m/s

Behavior of fluid across the cylinder is shown below:

With Mesh Refinement:

Animation Link: https://www.youtube.com/watch?v=D2lPa24yIw4

If, we increase the Reynold's Number by 100%, so our new effective Reynold's Number becomes,

R = 27071.82

V = 19.99m/s

Behavior of fluid across the cylinder is shown below:

With Mesh Refinement:

Animation Link: https://www.youtube.com/watch?v=hmmkzLmnHO4

Variation of Pressure with the change in velocity:

1. V = 10m/s

Animation Link: https://www.youtube.com/watch?v=OpqzOmkFgFk

2. V = 11.99m/s

Animation Link: https://www.youtube.com/watch?v=y3OSpM8Vqgg

3. V = 13.99m/s

Animation Link: https://www.youtube.com/watch?v=1R8kxK9udXE&feature=youtu.be

4. V = 19.99m/s

Animation Link: https://www.youtube.com/watch?v=ttPO-TdFkdI

OBSERVATIONS:

1. As we know that if R> 2000, then the flow is considered to be turbulent. So, the flow in each of these cases are turbulent.

2. As Reybols Number increases, the flow velocity increases. It is seen that the velocity is maximum at the top surface of the cylinder.

3. A very high pressure region is created when the velocity hits the cylinder, and gradually there is a low pressure created at the backend of the cylinder.

4. The pressure variation in all the cases are almost the same.

5. In the Trajectory flow analysis it is observed that a vortex is created at the back side of the cylinder.