STEADY FLOW ENERGY EQUATION FOR A TURBINE AND A COMPRESSOR

We were discussing the basic concepts in thermodynamics such as “steady flow process” and also we have seen “First law of thermodynamics for a closed system undergoing in a cycle” in our recent post. Today we will see here the steady flow energy equation for turbine and compressor with the help of this post.

Before writing and understanding the concept of steady flow energy equation for turbine and compressor, let us first brief here steady flow energy equation and after that we will analyze the steady flow energy equation for turbine and compressor.

Brief introduction of steady flow energy equation

For steady flow process, net quantity of energy contained within the system will never change with respect to time. Therefore according to the principle of conservation of energy, we will have following statement and energy equation for a steady flow process.

Net quantity of energy entering to the control volume = Net quantity of energy leaving the control volume

For more detail about steady flow energy equation, please find the post “Mass balance and energy balance for a steady flow process”.

Now let us come to the point i.e. Steady flow energy equation for a turbine

Turbine is basically defined as one prime mover where thermal energy of the high pressure fluid will be converted in to mechanical energy in terms of rotation of turbine shaft. Mechanical energy developed by turbine will be finally converted in to electrical energy.

Turbine is also designated as mechanical device that will provide the work energy through the expansion of fluid.

Let us see here the following figure, where high pressure fluid enters at inlet 1-1 and low pressure fluid leaves the turbine at its outlet section i.e. 2-2.

Let turbine is well insulated and hence there will no heat energy interaction between system and surrounding and therefore we can say that Q =0.

When fluid flows through a turbine, change in kinetic energy could be assumed as zero as velocity of fluid flow will be small and we can neglect the small change in kinetic energy of the fluid. Therefore, we will have ΔKE =0

We have also assumed here that change in potential energy is zero or we can say that ΔPE =0

Let us implement above data that we have mentioned above in steady flow energy equation for a steady flow process and we will have following equation

H₁ - W = H₂

We have taken work energy as positive because turbine is producing the work energy and this work is being done over the surrounding by the system. Therefore according to the “Sign convention for heat and work transfer in thermodynamic system” work energy will be positive.

W = H₁ – H₂

We can also say that, work energy produced by the turbine during the process will be the result of drop in enthalpy.

Now, let us see steady flow energy equation for a compressor

Compressor is basically defined as one mechanical device which is used for increasing the pressure of fluid by securing the work energy from the surrounding. Work energy will be supplied to the system i.e. compressor from surrounding with the help of a rotating shaft.
 
Let us see here the following figure of compressor, where low pressure fluid enters at inlet1 and high pressure fluid leaves the compressor at its outlet section i.e. 2.

We must note it here that for a compressor, work will be done over the system by the surrounding and hence work energy will be taken here with negative sign. Therefore by considering the same assumption that we have made above, we will have following energy equation for an adiabatic compressor as mentioned here.

H₁ – (-W) = H₂

W = H₂ – H₁

Or we can say that work done on compressor by surrounding during the process will provide the result of increment in enthalpy.

Do you have suggestions? Please write in comment box. 

We will see another topic i.e. "Steady flow energy equation for a heat exchanger"and Reciprocating pump working principle in our coming post.

Reference:

Engineering thermodynamics by P. K. Nag

Image Courtesy: Google

Also read

Steady flow energy equation for a nozzle and diffuser

Steady flow energy equation for throttling process

Wind turbine project

Principle of design

Working principle and types of milling machine