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MEEN-4350/5350

Turbomachinery Efficiency

Xianchang Li, Ph.D.

Associate Professor

Department of Mechanical Engineering

Lamar University

Spring 2015

Lamar University

Objectives:

To define different efficiencies for compressors and

turbines

To describe the relationship between them.

Turbomachinery Efficiency

Assignments/Notice:

Read Chapter 1

Homework: Please check the blackboard

Efficiency of Turbines

Overall efficiency, ho

Efficiency of Turbines (2)

Isentropic efficiency(ht) or hydraulic efficiency (hh)

Mechanical efficiency (hm)

Due to flow patterns and friction with solid surface

Due to mechanical friction (lubrication system)

Maximum Fluid Work of Steam/Gas Turbines

Adiabatic process with potential energy ignored

Energy conservation equation of steady-flow with one inlet

and one outlet

Adiabatic + isentropic process

Here it is assumed that the kinetic energy @ outlet can be

employed. Expanding with the same stagnation pressure

Total-to-Total Efficiency of Steam/Gas Turbines

2

Total-to-Static Efficiency of Steam/Gas Turbines

Here it is assumed that the kinetic energy @ outlet is

entirely wasted Ideal expansion: State 2 has a ZERO

velocity

In what case,

can hts be 1?

Adiabatic &

isentropic &

c2=0

Maximum Fluid Work of Hydraulic Turbines

Energy conservation equation of steady-flow with one

inlet and one outlet

h1-h2 = (p1-p2)/r when r=const

Adiabatic + Isentropic process

Efficiency of Hydraulic Turbines

Total-to-Total or

Total-to-Static ?

Example: Water flows at a rate of 100 m3/s

and the elevation difference between the

reservoir and turbine is 20m. The water left

the turbine has a velocity of 1.0 m/s, and

the turbine has an efficiency of 80%. Ignore

the water velocity in the reservoir. What is

the power output? (hm=90%)

(20*9.8-0.5)*100*1000*.8*.9

=14.076 MW

Efficiency of Compressors/Pumps

Efficiency of Compressors/Pumps (2)

Pumps

Total-to-Total or

Total-to-Static ?

Compressor

Small Stage or Polytropic Efficiency

Question: If each stage of a 10-stage compressor has an

isentropic efficiency of 0.85, what will be the compressor efficiency if

p2/p1=10?

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Small Stage or Polytropic Efficiency (2) Small Stage or Polytropic Efficiency (3)

Small Stage or Polytropic Efficiency (4)

For ideal gas (or perfect gas)

Small Stage or Polytropic Efficiency (5)

Small Stage or Polytropic Efficiency (6)

For turbines (with ideal gas)

For steam turbines (steam is not ideal gas)

RH, reheat factor, =1.03~1.08

Small Stage or Polytropic Efficiency (7)

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Example

Example: Air @ 15 atm and 1000oC expands to 1 atm and 350oC in a gas

turbine. If the inlet velocity is 75 m/s and the outlet velocity is 125 m/s,

find the total-to-total efficiency, total-to-static efficiency, and polytropic

efficiency for this turbine. (Consider air as perfect gas)

Solution: (with Section 1.10)

Find p01 with p1 and c1

Find p02 with p2 and c2

Find T01 with T1 and c1

Find T02 with T2 and c2

Find T02s with p01, p02, and T01

Find the efficiency

Example (2)

For incompressible fluid

For compressible fluid

h0=h+c2/2

The End

Questions and comments ?