# Back Work Ratio: What, How, Formula, Several Cycles

This article discusses about back work ratio. The name itself will take you to its meaning and we shall discuss about it in this article.

The compressor requires to work for its operation whereas turbine produces work after operation. Due to this, the compressor work is said to be negative and turbine work is considered positive. In this article we shall discuss about the back work ratio and the different types of devices used in thermal power plants.

## What is back work ratio?

The term ratio implies that back work ratio is a ratio of two quantities. The term back work represents that it is something related to negative work that is compressor work.

Hence, we can define back work ratio as the ratio between the work done by the compressor to the work done by turbine in the thermal power plant. The compressor work is derived from the turbine itself, that is around thirty percent of the turbine work is translated to compressor work.

## Back work ratio formula

In the above section we have discussed about the definition of back work ratio. Let us see the formula of the same.

Mathematically, back work ratio can be given as –

BWR= Compressor Work / Turbine Work

## Rankine cycle

Rankine cycle is an example of an idealized thermodynamic cycle in which various thermal devices are used to extract mechanical energy from the working fluid.

In Rankine cycle, a boiler, condenser, compressor and a turbine is used and the working fluid that is used is steam. The turbine gives out the work output that is used to generate electricity using a generator. The efficiency of the Rankine cycle is given by, efficiency= Output/Input= Total work done/Turbine work

## Working of Rankine Cycle

In the above section we have introduced ourselves with the concept of Rankine cycle. Now let us consider a Rankine cycle whose thermodynamic processes are given below, then we shall understand the working of Rankine cycle.

• 1-2: Adiabatic expansion :This represents adiabatic expansion in turbine. The steam from the boiler enters the turbine and rotates the turbine shaft.
• 2-3: Isoethermal heat rejection– The condenser extracts the heat out of the low pressure steam, this way the steam turns into liquid. The phase change of steam occurs at constant temperature.
• 3-4: Compressor work– Compressor is driven with the help of work done by the turbine. Compressor compresses the liquid and increases the pressure of the liquid. The compressed liquid is forced into the boiler.
• 4-1 Isothermal heat addition– The heat is added into the boiler in such a way that the liquid turns into vapour. The heat addition process takes place isothermally that is the temperature does not changes.

Image credits: ​Wikipedia (user:andrew.ainsworth) user [[:User:Andrew.Ainsworth:User:{{{3}}}|{{{3}}}]], Rankine cycle layoutCC BY-SA 3.0

## Back work ratio of Rankine cycle

Let us consider the above discussed Rankine Cycle. The turbine work is represented by h2-h1 and compressor work is represented by h4-h3. The total work done is represented by h1-h4.

Hence the back work ratio is given by the following-

Back work ratio = Compressor work/Turbine work = (h4-h3)/(h2-h1)

## Otto Cycle

Otto cycle is an example of idealized thermodynamic cycle which is used to describe the functioning of spark ignition engines. Spark ignition engines are those engines which ignite the compressed charged with the help of electric spark plug.

The working fluid used here is petrol, spark ignition engines are used in light weighted vehicles such as two wheelers. This cycle contains two isentropic expansion and compression process and two constant volume processes (heat addition and heat rejection).

## Working of Otto Cycle

In the above section we have discussed what an Otto cycle is. Now let us consider an Otto cycle in which following thermodynamic processes are taking place and see the working of Otto cycle-

• 1-2 Isentropic compression: The charge is compressed isentropically. This happens when the piston moves from bottom dead center to top dead center.
• 2-3 Constant volume heat addition: The heat is added to the system at constant volume. The piston is at the top dead center when heat addition takes place.
• 3-4 Isentropic expansion: Due to heat addition, the piston moves from top dead center to bottom dead center. This way expansion takes place at constant entropy.
• 4-1 Constant volume heat rejection: The heat is rejected during this process. The entire procedure takes place at constant volume. The piston is at the bottom dead center.

## Back work ratio of Otto cycle

Let us consider the same Otto cycle as discussed in the above section. The back ratio of Otto cycle is given as follows-

Back work ratio= Compression work/Turbine work= (T2-T1)/(T3-T4)

Where T1 is the temperature at 1st point

T2 is the temperature at 2nd point

T3 is the temperature at 3rd point

T4 is the temperature at 4th point

## Back work ratio significance

We have clearly understood the meaning of back work ratio. The back work indicates the amount of work needed by the compressor to run. It has a negative value because compressor runs at the expense of work and does not produce any work.

This work in most cases is provided by the turbine itself. The back work ratio indicates the amount of work needed by the compressor in terms of work done by the turbine. It tells us how much work the turbine has to provide the compressor to work.

## How to calculate back work ratio?

The back work ratio is defined as the ratio of compressor work to turbine work. To calculate the back work ratio we simply find the ratio between these two terms. We have already this in the above sections of this article.

First we find the compressor work using the enthalpy values at points 3 and 4. Then we find the turbine work using the enthalpy values at points 1 and 2. The enthalpies are subtracted (h2-h1 and h4-h3) to find the work done by compressor and turbine. Later we divide the values of compressor work and turbine work to find the back work ratio.

The formula is given by-

Back work ratio or BWR= Work done by compressor/ Work done by turbine

Abhishek

Hi ....I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.