Thermodynamics and Heat Engine4 (3+1)

LESSON - 36 PERFORMANCE CRITERIA FOR STEAM ENGINES

For a single acting engine  

Power is developed on one side of the piston.

From equation (35.2a), the mean effective pressure, p_m (bars) is given by

P_m =     or       p_m =

Therefore,  work done/cycle =  100 p_m  . V_s    =  100 p_m  . A . L, kJ/cycle

 where,     A = area of cross-section of piston, m²   ;      L = stroke of engine, m  

Actual work done/min = (work done/cycle) x (No of cycles per min)

Actual work done/min = (100 p_m  . A . L) x (n), kJ/min

where ‘n’ is No of power cycles per min

In steam engine  number of power cycle per min ‘n’ is equal to number of crankshaft revolutions per min (rpm) ‘N’,

Therefore, actual work done/min = (100 p_m  . A . L) x (N),  kJ/min

Indicated Power Output of engine =  _, kW                    ......................……….. (36.1)  

or                                                       =  , hp

 For a double acting engine 

 Power is developed on both side of the piston.

Let P_m,1, A₁ and P_m,2, A₂ be the mean effective pressures and effective piston areas of head end and crank end sides of the piston, respectively, then from equation (36.1)

Indicated Power Output of engine on the head end side   =  , kW    

Indicated Power Output of engine on the crank end side   = , kW    

Total indicated power output of the engine

                                                                        ........................…..(36.2)

or                            ,hp          

                   where,     A₁ =  and   

                                  A₂ =         

                        where, ‘D’ and ‘d’ is diameter of piston and piston rod, respectively.

If the power developed on both side of the piston is same and area of piston rod is neglected

then     A₁ = A₂ = A   and P_m1 = P_m2  = P_m

From equation (36.2)

Total indicated power output of the engine

                              =   kW           

Therefore, Indicated Power Output of engine =    _, kW    

or                                                                         = ,  hp

36.1.2. Brake Power

The actual power produced at the crank shaft may be termed shaft power (sp) or Brake power (bp). It is equal to the indicated power minus the power spent to overcome the mechanical friction in the engine and to drive the auxiliary mechanisms attached to the engine.

The power absorbed due to mechanical friction in the engine and to drive the auxiliary mechanisms called friction power (fp).

So    bp = ip – fp

The brake power (bp) is measured by dynamometer with the following relation:

Brake power (bp)        =           (kW or kJ/s)    

For detail of brake power refer section “Performance Criteria for IC Engines” in lesson 46 of module IX.

36.2. EFFICIENCY OF STERAM ENGINE

There are several efficiencies which are to be considered for the performance of a steam engine.

36.2.1. Mechanical efficiency:

It is the ratio of brake power (bp) to indicated power (ip) ;  

      i.e.       η_m =           (normally = 80 - 94%)

As it depends primarily on engine mechanism, so it may be called the efficiency of the engine mechanism.

36.2.2. Thermal efficiency

It is the ratio of output energy as work to the heat energy supplied by the steam in the cylinder. If the output is indicated work, it will be indicated thermal efficiency (η_ith)  and if it be brake work it will be brake thermal efficiency (η_bth).

Indicated Thermal Efficiency (η_ith)  =                      (normally = 17 - 24%)      

Brake thermal efficiency (η_bth)         = ;                      (normally = 14 - 21%)

where M  is mass of steam admitted in per min into the engine

           h_g    is enthalpy of dry steam at the inlet of the engine (from steam table)

           h_f  is enthalpy of  water at saturation temperature of exhaust pressure (from steam table).

36.2.3. Overall efficiency

The overall efficiency (η_o) of a steam engine power plant is defined as the ratio of work available at the crank shaft of steam engine to the heat energy supplied by the fuel in boiler.

Overall efficiency (η_o) =

 where  is mass of fuel supplied per min

            CV is calorific value of fuel.

36.2.4. Relative efficiency

The relative efficiency of a steam engine is the ratio between the indicated thermal efficiency and Rankine efficiency

Relative efficiency =