# What is Turbulence ?

Most of the engineering flow problems are turbulent in nature. So knowledge in turbulence is imperative for an engineer. In this video lesson we will see how to predict and quantify effect of turbulence.

Summary of above lecture along with applications of turbulence are described below.

## Why Turbulence ?

There is no universally accepted answer for reason behind turbulence. Many scientific searches to find out reason behind turbulence of flow have ended up in vain. Take a look at a famous witticism made by Heisenberg regarding this.

But engineers and scientists have developed a good understanding on nature of turbulence and way to quantify effect of it. So here we will learn ‘How Turbulence’ instead of ‘Why Turbulence’.

## How to distinguish a Turbulent flow ?

All turbulent flows have got following 3 characteristics

1. 3 dimensional
2. Fluctuating
3. Chaotic - With eddies and vortices
So if a fluid flow under consideration has got all 3 above characteristics it is turbulent in nature, otherwise flow is laminar.

## A Daily Life Experience to Predict Turbulence

To understand nature of turbulence we will consider a daily life experience, a tap water problem. Consider following 3 cases, where in each case flow rate of water increases. It is clear that as flow rate increases turbulence of flow also increases. So finding number one turbulence increases with increase in flow velocity.

 Fig.1 Increase in turbulence of flow as flow rate of water is increased
If you replace water in tap by a fluid which is more viscous in nature(oil), you will find that flow is not turbulent even at high flow rate. So finding number two turbulence decreases with increase in fluid viscosity.
 Fig.2 Decrease in turbulence of flow as flow as viscosity of fluid is increased

From above findings it can be summarized that turbulence increases with increase in flow velocity and decrease in fluid viscosity. Flow velocity increases with increase inertial force on the fluid and if fluid viscosity is high viscous force in fluid will also be high. So it can be summarized that turbulence increases with increase in inertial force and decrease in viscous force.

## Concept of Reynolds number

Ratio of inertial force to viscous force is know as Reynolds number .

It is clear that when Reynolds number increases turbulence increases. So Reynolds number is the criterion which decides whether a flow is laminar or turbulent. For this pipe problem Reynolds number can be represented as
Where D is diameter of pipe. So you can define a Critical Reynolds number for a particular problem above which flow is turbulent and below which flow is laminar

## More analysis - Concept of Averaging

Consider a turbulent tap water case with constant flow rate input. If you measure velocity at tap outlet for this case you will find that velocity is highly unsteady as shown in figure below.

 Fig.3 Fluctuating velocity field at outlet of a turbulent flow problem
This is one big characteristic of turbulent flow, strictly speaking all flow variables in a turbulent flow are unsteady in nature. But if you do a mathematical operation called averaging in this case on flow velocity, the result becomes steady in nature. So you could say a turbulent flow is in steady state if averaged flow variable is in steady state.
 Fig.4 Result of averaging operation in constant flow input flow problem

## Averaging operation

Averaging is defined as follows

Where time interval used for integration should be carefully chosen. It should be small enough to take care of any unsteadiness in flow, at the same time it should be big enough to take care of any fluctuation in the flow.

An engineer always speak about averaged quantities when he comes across a turbulent flow. Because averaged quantities are pretty enough for his purpose. Knowledge of actual fluctuating value of a turbulent flow might be useful in scientific world, but for an engineer it is of no use most of the time. Figure below shows averaging operation in a turbulent-unsteady flow.

 Fig.5 Averaging operation on a turbulent-unsteady problem
It is clear from above figure that actual velocity can have 2 components, one average component and another fluctuating component. Similarly one can define averaging for any other flow variable say pressure,temperature,other components of velocity etc.

## Shear stress in a Turbulent Flow & Turbulence Modeling

Let us consider a turbulent pipe flow case, if you want to determine shear stress near pipe wall, first thing you have to obtain is averaged velocity profile near wall as shown in figure below.

 Fig.6 Average velocity profile and inter layer mixing in a turbulent flow
Assuming this is 2 dimensional flow case one can express shear stress parallel to flow direction as
Thus shear stress has got 2 components. First component which is similar to shear stress in a laminar case is known as laminar shear stress. Second component arises due to mixing of different fluid layers in a turbulent flow as shown in figure above. This is known as turbulent shear stress or Reynolds stress. So shear stress in a turbulent flow can be represented as
One can note Reynolds stress is in terms of fluctuating parts of velocity components, which are unknown to the user. Determination of Reynolds stress in terms of known quantities (averaged quantities)is considered to be one of the toughest problem in fluid mechanics. And this is known as Turbulence Modeling.

## Applications Utilizing Effect of Turbulence

Most of the time turbulence has positive effect on engineering devices. It increases convective heat transfer, it increases mixing and reduces drag around a body.

1. ### Heat Transfer Enhancement

2. Convective heat transfer coefficient increases drastically when the flow becomes turbulent, due to effective mixing of different fluid layers in the flow. This behaviour is shown in following figure.So it is a common practice among designers to covert laminar flows into turbulent by introducing suitable vortex generators in the flow.
 Fig.7 Increase in heat transfer coefficient due to  turbulence
3. ### Drag reduction

4. Coefficient of drag around a body reduces by a huge amount when flow changes from laminar to turbulent.This phenomenon is shown in following figure.This is the reason why golf ball has got lot of dimples on it.This irregularities on surface of the ball will help in transforming laminar flow into turbulent and reduces drag, with low drag ball can travel more distance.
 Fig.8 Change in drag coefficient over a sphere when flow changes from laminar to turbulent

# Fuel Cell Technology

Fuel cells are magic devices which convert fuel directly into electricity. In this video lecture we will understand physics and technology behind fuel cells. Sit back and enjoy the lecture.

## Summary of the Lecture

• H2-O2 reaction - Most of the time Hydrogen and Oxygen react together and forms water molecule spontaneously.

• Internal electron transfer - During this reaction internal electron transfer (electricity) takes from Hydrogen atoms to Oxygen atoms. But since this transfer is internal, it is of no use.

• Physics of Fuel cell - Fuel cells force electrons to move through an external path, by introduction of a barrier in between. A barrier which will transfer only Hydrogen ions, but not electrons.

• So electrons flow through the external circuit and produces electricity in a fuel cell, In the meantime Hydrogen ions which are capable to sneak through the barrier moves and combine with Oxygen ions. Here same chemical reaction happens but in a different fashion.

• Membrane Electrolyte - Most common barrier used for H2-O2 fuel cell is Membrane electrolyte.

• Anode & Cathode - Every fuel cell requires one anode and one cathode, which are acting as catalysts. Function of anode is to aid dissociation of H atom into H ion. Cathode helps in combining Oxygen and Hydrogen ions together in order to form water molecule.

• GDL - Such a fuel cell will require Gas Diffusion Layer (GDL) at both sides, main function of which is to allow passage of gas at both the sides, provide a compartment for product water removal and conduct electricity and heat out of the system.

• Stacking different Fuel cells - Bipolar plates help in stack different fuel cells together, thus augments voltage of fuel cell. It also helps in distributing gases on both sides of the plate.

• Compression plates - GDL works well under high pressure, so 2 compression plates are used increase pressure of the system.

• Electricity collectors are used to transfer electricity produced inside the system to external circuit.

• Electro Chemical Mechanism – H2 and O2 which are supplied at both ends of bipolar plates pass through GDL and reach anode and cathode respectively. At anode H atoms become H+ ions and electrons. Electrons which are not able to pass through membrane electrolyte flow through the external circuit and produces electricity. It then combines with O atom and produce O2- ion. H+ ions which can penetrate through the membrane, travels through it combine with O2- ion at the anode side and produces water. Due to high temperature of Fuel cell this water produced will be in vapor state and can be carried away by a blowing air supply.Step by step electro chemical mechanism of fuel cell is shown in video link below

• PEM Fuel cells - This kind of fuel cells is known as Proton Electrolyte Membrane fuel cells. PEM fuel cells are considered to be the most versatile one for industrial use.

Some advantages of fuel cell are listed below
• Green Energy - H2 powered fuel cells are green source of energy, since they do not emit CO2 as in conventional internal combustion engines.
• Quite operation - Since there are no rotating parts in fuel cell it is always quite in operation.
• High power density - Fuel cells produce high amount of power for same weight of equipment compared to other conventional source of energy. This makes fuel cells preferred method in space applications.
• High Conversion Efficiency - Since Fuel cells convert chemical energy directly into electricity their efficiency is not constrained by 2nd law of thermodynamics. In effect fuel cells have got good conversion efficiency, they can convert 60-70% chemical energy into electrical energy.

## What is Impeding Fuel Cell Technology?

So many advantages for Fuel cells, but still this technology hasn't made way through industrial and technical applications as it should have. So what is impeding this technology from getting into your life?
Main reason which impede fuel cells technology is its high cost.High cost incurred mainly due to cost of membrane electrolyte and other accessories. But recent developments to cut cost of Fuel cell are positive.It is expected that in 20 years Fuel cell technology will be able compete other power generation technologies commercially.

# What is Von Mises Stress ?

Von Mises stress is widely used by designers to check whether their design will withstand a given load condition. In this lecture we will understand Von Mises stress in a logical way.

A detailed webpage version of the video lecture along with the industrial applications of Von Mises stress are listed below.

## Use of Von Mises stress

Von Mises stress is considered to be a safe haven for design engineers.Using this information an engineer can say his design will fail, if the maximum value of Von Mises stress induced in the material is more than strength of the material. It works well for most cases, especially when the material is ductile in nature. In the folowing sections we will have a logical understanding of Von Mises stress and why it is used.

## When does a material fail?

One of the most easy way to check when a material fails is a simple tension test. Here the material is pulled from both ends. When the material reaches the yield point (for ductile material) the material can be considered as failed. The simple tension test is a unidirectional test, this is shown in the first part of Fig.1.

Now consider the situation in second part of Fig.1, an actual engineering problem with a complex loading condition. Can we say here also, that the material fails when the maximum normal stress value induced in the material is more than the yield point value ?. If you use such an assumption, you would be using a failure theory called 'normal stress theory'. Many years of engineering experience has shown that normal stress theory doesn’t work in most of the cases. The most preferred failure theory used in industry is ‘Von Mises stress’ based. We will explore what Von Mises stress is in the coming section.

## Distortion energy theory

The concept of Von mises stress arises from the distortion energy failure theory. Distortion energy failure theory is comparison between 2 kinds of energies, 1) Distortion energy in the actual case 2) Distortion energy in a simple tension case at the time of failure. According to this theory, failure occurs when the distortion energy in actual case is more than the distortion energy in a simple tension case at the time of failure.

## Distortion energy

It is the energy required for shape deformation of a material. During pure distortion, the shape of the material changes, but volume does not change. This is illustrated in Fig.2.

 Fig.2 Representation of a pure distortion case
Distortion energy required per unit volume, ud for a general 3 dimensional case is given in terms of principal stress values as:
Distortion energy for simple tension case at the time of failure is given as:

## Expression for Von Mises stress

The above 2 quantities can be connected using distortion energy failure theory, so the condition of failure will be as follows.

The left hand side of the above equation is denoted as Von Mises stress.
So as a failure criterion, the engineer can check whether Von Mises stress induced in the material exceeds yield strength (for ductile material) of the material.So the failure condition can be simplified as

## Industrial Application of Von Mises Stress

Distortion energy theory is the most preferred failure theory used in industry. It is clear from above discussions that whenever an engineer resorts to distortion energy theory he can use Von Mises stress as a failure criterion.Let's see one example:

Suppose an engineer has to design a cantilever beam using mild steel as the material, with a load capacity of 10000 N. The materials properties of mild steel are also shown in the figure. The yield stress value of mild steel is 2.5x108 Pa. He wants to check whether his design will withstand the design load.

 Fig.3 A design problem, the cantilever should be able to withstand design load
The following figure shows the Von Mises stress distribution obtained by FEA analysis of the beam.
 Fig.4 Distribution of Von Mises stress in the beam obtained from FEA analysis
One can note that Von Mises stress is at maximum towards the fixed end of the beam, and the value is 1.32x108 Pa. This is less than the yield point value of mild steel. So the design is safe. In short an engineer's duty is to keep the maximum value of Von Mises stress induced in the material less than its strength.

# What is Second Law of Thermodynamics ?

Second law of thermodynamics is law of nature, unarguably one of the most valuable find of mankind. But this topic is somewhat confusing for most of the students and engineers. This video is aimed at describing 2nd law in an engineer's point of view.

Summary of the above lecture along with application of 2nd law in engineering life are described below.

## Uses of Second Law

We will start our discussion by going through uses of 2nd law. They are listed below.

• ### Direction of a Process

• Most important use of second law is to determine direction of a process. First law of thermodynamics tells the user only about energy transfer, it does not specify in which direction energy transfer will happen for a given condition. Consider following examples.According to first law hot tea can gain heat, mass can go up and mixed gas can become unmixed spontaneously. It is 2nd law of thermodynamics which comes in between and tells in which direction a process is possible spontaneously.

 Fig.1 Second law is used to determine in which direction above processes will happen spontaneously
Well, you could argue that you can find out direction of all this processes without using second law (from your intuition). Then what about following process, a chemical reaction.  Fig.2 Second law can even check whether the chemical reaction above is spontaneous or not
Can you say in which direction reaction will go spontaneously from your intuition ? Using 2nd law you can predict even this, you can predict whether the blue atoms and yellow atoms combine together to form a new molecule spontaneously.

• ### Maximum Possible Thermal Efficiency

• Another main use of 2nd law is in determining maximum possible thermal efficiency of a given system. 2nd law of thermodynamics puts a limit for maximum performance a system can achieve. For example you can find whats the maximum thermal efficiency possible for a car engine or refrigerator just by knowing its heat interaction temperatures.

## Classical Statements of 2nd Law

2nd law has got 2 classical statements, they are self-similar.

1. ### Clausius Statement

2. According Clausius statement heat cannot flow from a hot body to cold body without any external work.This is depicted in following figure.

 Fig.3 Clausius statement does not permit the process shown here

3. ### Kelvin-Planck Statement

Accoriding to Kelvin-Planck statement a heat engine cannot produce work without rejecting some heat to the surrounding. This is depicted in following figure.

 Fig.4 Kelvin-Planck statement does not premit the process shown in figure

## Clausius Inequality - 2nd Law in a Useful form for Engineers

Clausius and Kelvin-Planck are 2 classical statements of 2nd law, but they are not in a form which is directly useful for engineers.Most useful form of 2nd law is Clausius inequality, It states that cyclic integral of dQ/T along boundary of a cycle will always be less than or equal to zero.

Here temperature T should be in Kelvin.Right hand side of this equation becomes zero when there is no irreversibility present in the cycle, irreversibilities like friction or vertices. Consider following example, a power production cycle.
 Fig.5 Clausius inequality applied on a power plant cycle, dotted line represents boundary of the cycle
Here there are 2 heat interactions in the cycle, one at condenser represented by 'c' next is at boiler represented by 'b'. Assuming there are no irreversibilities present and heat interactions are in uniform temperature, then Clausius inequality reduces to

## Concept of Carnot Engine

When heat interactions are happening at uniform temperature and irrevesibilities in cycle are zero, such cycle will give maximum possible thermal efficiency.This cycle is known as Carnot cycle. In this aspect the power cycle we just discussed above is an example of Carnot cycle. So thermal efficiency of such a cycle can be written as

Or 2nd law states that a cycle which gives thermal efficiency more than Carnot efficiency is impossible. If somebody approaches you claiming a very high efficiency engine, with efficiency greater than Carnot efficiency you can send him back immediately.

## Second Law for a Process - Concept of Entropy

If you want to apply 2nd law for a process the statements derived above which are for cycles are not useful. Consider following cyclic processes, 1st cycle passes through paths A & B and 2nd cycle passes through paths A & C.

 Fig.6 Two cyclic processes used to define 2nd law for a process, here process A same for both the cycles
If there is no irreversibitly in the cycle Clausius inequality for the first cycle cycle can be written as
Similarly Clausius inequality for 2nd cycle can be written as
Comparing these two equations one can write
So irrespective of path taken integration of the quantity dQ/T for a reversible process remains same. This is exactly how a property is defined, properties are independent of path taken. We will call this property entropy, denoted by S.So for a reversible process change in entropy can be represented as

## Second Law for an Irreversible Process

One can extend 2nd law equation derived for reversible process to an irreversible. In this case a term called entropy production should be added to the equation. Entropy production signifies degree of irreversibilities during the process. So entropy change equation for an irreversible process is

So there could be 2 components for entropy change in an actual process.
1. Entropy transfer - due to heat interaction
2. Entropy production - due to effect of irreversibilites
Value of entropy transfer can be either positive or negative, but value of entropy production is always positive.

## Increase of Entropy Principle

Consider following case, where system is losing some heat to surroundings. We can approach this problem in 2 ways.

 Fig.7 Two approaches in solving same problem, second approach states that entropy transfer of universe is zero
In first approach we consider object as system, so system is losing some entropy due to entropy transfer. In second approach we are considering the object and surrounding of the object together as system, means we are considering the universe together. In such an approach there will not be any heat loss from it. Whatever heat interactions are happening is within the universe. So there is no entropy transfer from universe. The general entropy change equation will be simplified as
Since entropy production term is always positive, from above equation it is clear that change of entropy of universe always positive or entropy of universe always increases. This is increase of entropy principle. We will do a sample problem to demonstrate increase of entropy principle. Consider the following case, a hot tea which is in a surrounding whose temperature is less than temperature of tea. Now the question is whether the tea will gain heat or lose heat ?

 Fig.8 Whether this tea will gain hear or lose heat ?
First assume the tea is gaining 10J of heat, then change in entropy of universe is
Substituting values in it

This shows that entropy change of universe is negative, that is against 2nd law of thermodynamics. But if the tea loses 10J of heat this will lead to increase in entropy of universe, which means this is a feasible process.

## Concept of Gibbs Free Energy

While using increase of entropy principle engineer has to calculate entropy change of surrounding also.In order to over come this difficulty a new property is introduced - Gibbs free energy.

 Fig.9 Use of Gibb's free energy change in determining whether this chemical reaction is spontaneous or not
Consider the example shown above, here we want to determine whether the given chemical reaction will occur spontaneously. For this purpose we have to determine entropy change of universe as we did in earlier case. Here entropy change of system and enthalpy change of system are given, so entropy change of surrounding is given by
So entropy change of universe is
This process is spontaneous if
Since T is always positive we can write process is spontaneous if
We will call L.H.S of this equation as another property called Gibbs free energy. So in short a process is spontaneous if
Most of the time it is also convenient to talk in terms of Gibbs free energy. When Gibbs free energy change of system is less than zero it implies entropy change of universe is greater than zero.

## Industrial Applications of 2nd Law

Second law of thermodynamics is extensively used in industry to determine direction of a process or a reaction. Most common method to check whether a reaction is spontaneous is to find out change in Gibbs free energy. If this term is negative for a reaction then the process is spontaneous.

## Does Entropy Mean Disorder?

The discussions we have done so far were in macroscopic point of view. But there exists a whole different field of thermodynamics where things are viewed microscopically, called as Statistical thermodynamics.Boltzman relation is considered to be one of the pillar statement of statistical thermodynamics, at the same time it is one of the most controversial too. According to this entropy, S and thermodynamic probability, w are related by the relation

The term thermodynamic probability, w deserves special attention. It represents total number of possible microscopic states available to a system, it often referred to as disorder of the system. So according to Boltzman relation as disorder of the system increases entropy increases, or if during a process disorder of the universe increases that process is spontaneous.But always remember statistical thermodynamics is not free of controversies, especially Boltzman relation. For an engineer thermodynamics in classical point of view is enough for his needs.

# Theories of Failure

A good understanding of theories of failure are imperative in the design of civil structures or types of mechanical equipment. This lecture will give you a conceptual introduction on the theories of failure. So sit back and Enjoy

A detailed webpage version of the above lecture along with the industrial application of Failure Theories are given below.

## The Weight Lifter Analogy

Consider a weight lifter problem.

 Fig.1 A weight lifter analogy
In the first case he is able to lift maximum up to 50 k.g in a relatively simple fashion. Now consider a second case, here he is lifting the same amount of weight in a different manner.Is it true to say here also his maximum lifting ability is 50 k.g?. Answer to this question could be Yes or No. If you assume that, his lifting ability is same in the second case also , then this can be considered as a failure theory for a weight lifter.

## The Backbone of Failure Theories

In materials also we can apply the same concept of weight lifter failure theory.Here material will undergo a simple force test(simple tension test), so one can determine what's the maximum load capability the material has. Now, we will assume that in a complex loading condition also, the material has the same capability. This assumption forms the backbone of Failure theories.Concepts of Simple tension test and Principal stresses are the main 2 prerequisites to understand the Failure theories effectively.

## Simple Tension Test

In Simple tension test material is pulled from both the ends, the elongation of material(strain) with respect to the load is noted. From such an observation one can easily determine maximum strength of the material. For ductile material upper yield point is considered to be maximum strength of material, while for brittle material it is taken as ultimate strength of the material. From the maximum strength value of the material, values of various other parameters can easily be calculated.Simple tension graph and upper yield point value for a ductile material case is shown in the figure below.

 Fig.2 Simple tension test

## Principal Stress

Principal stress is the maximum normal stress occurring at a given point. In order to find out this value easy way is to do a Mohr circle analysis. Once you know Principal stress values you can go ahead with failure theories.Figure below shows principal stress values induced at point in a 3 dimensional complex loading case.

 Fig.3 Principal stresses and planes

## The Failure Theories

The interesting thing in the Failure theories is that, just by looking at the name of the theory you will be able to formulate condition of failure in an actual case. Just make sure that your concept of STT and Principal stresses are clear. The theories along with its usability is given below.

1. Maximum principal stress theory - Good for brittle materials*
2. According to this theory when the maximum principal stress induced in a material under complex load condition exceeds the maximum normal strength in a simple tension test the material fails. So the failure condition can be expressed as

3. Maximum shear stress theory - Good for ductile materials
4. According to this theory when the maximum shear strength in actual case exceeds maximum allowable shear stress in simple tension test the material case. Maximum shear stress in actual case in represented as

Maximum shear stress in simple tension case occurs at angle 45 with load, so maximum shear strength in a simple tension case can be represented as
Comparing these 2 quantities one can write the failure condition as

5. Maximum normal strain theory - Not recommended
6. This theory states that, when the maximum normal strain in actual case is more than maximum normal strain occurred in simple tension test case the material fails. The maximum normal strain in actual case is given by

Maximum strain in simple tension test case is given by
So condition of failure according to this theory is
Where E is Youngs modulus of the material

7. Total strain energy theory - Good for ductile material
8. According to this theory when the total strain energy in actual case exceeds the total strain energy in simple tension test at the time of failure, the material fails. The total strain energy in actual case is given by
The total strain energy in simple tension test at time of failure is given by
So failure condition can be simplified as

9. Shear strain energy theory - Highly recommended
10. According to this theory when the shear strain energy in the actual case exceeds shear strain energy in simple tension test at the time of failure the material fails. Shear strain energy in the actual case is given by

Shear strain energy in simple tension test at the time of failure is given by
So the failure condition can be deduced as
Where G is shear modulus of the material

Out of the 5 theories discussed, the Shear strain energy theory or Von-mises theory is the most valuable one.

*Since brittle materials does not have yield point, you can use ultimate tensile stress as failure criterion.

## Industrial Applications of Failure Theories

Nowadays FEA based solvers are well integrated to use failure theories. User can specify kind of failure criterion in his solution method. Shear strain energy theory is the most commonly used method. These softwares can produce Von-mises stress along material,which is based on Shear strain energy theory. So user can check whether maximum Von-mises stress induced in the body crosses maximum allowable stress value. It is a common practice to introduce Factor of Safety(F.S) while designing, in order to take care of worst loading scenario. So the engineer can say his design is safe if following condition satisfies.