Mumbai University > Mechanical Engineering > Sem 7 > Power Plant Engineering

Marks : 10M

Year: Dec 2015

Generally, the thermal efficiency of the simple open cycle is only about 16 to 23% as lot of heat energy goes waste in the exhaust gases. Moreover the cycle efficiency directly depends upon the temperature of the inlet gases to the turbine. And as the metallurgical limitations do not permit the use of temperatures higher than about 1000°C, a sizeable increase in efficiency cannot be expected through the increased temperature of the gases. Of course, this efficiency handicap can be overcome by incorporating thermal refinements in the simple open cycle e.g. regeneration, reheating. But the plant will become complex in contrast to the simple open cycle plant which is compact, occupies very little space, does not need any water and can be quickly run up from cold. The thermal refinements can raise the plant efficiency to over 30% and thereby obliterate the advantage of fuel efficiency possessed by diesel or condensing steam power plants. These refinements are discussed below:

REGENERATION

In regeneration, the heat energy from the exhaust gases is transferred to the compressed air before it enters the combustion chamber. Therefore, by this process there will be a saving in fuel used in the combustion chamber if the same final temperature of the combustion gases is to be attained and also there will be a reduction of waste heat. Figure shows a regenerative cycle.

For regeneration to take place T5 should be greater than T2. In the heat exchanger, the temperature of air is increased from T2 to T3, and the temperature of the exhaust gases is reduced from T5 to T6. If the regeneration is perfect, the air would be heated to the temperature of the exhaust gases entering the H.E. the effectiveness of the regeneration is defined as:

ϵ=effectiveness

=$\frac{(Rise in air tremperature)}{(Max.possible rise)}=\frac{(T_3-T_2)}{(T_5-T_2 )}$

For ideal regeneration,

T3 = T5 and T6 = T2

The common values of effectiveness would be from 70 to 85%. The heating surface of the generator, as well as the dimensions and price of the gas turbine increases with the regeneration fraction. But to justify the regeneration economically, the effectiveness should at least be 50%. The regenerative cycle has higher efficiency than the simple cycle only at low-pressure ratios. If the pressure ratio is raised above a certain limit, then the regenerator will cool the compressed air entering the combustion chamber instead of heating it and the efficiency of the regenerative cycle drops shown in graph figure.

It is clear from T-s plot Figure, that the compressor turbine works are not affected by regeneration. However, the heat to be supplied in the combustion chamber is reduced and also it is added at higher temperature as compared to the cycle without regeneration. Thus, the thermal efficiency of the cycle increases. It will be equal to,

$n_f=\frac{C_p(T_4-T_5)-C_p(T_2-T_1)}{C_p(T_4-T_3)}$

For ideal regeneration, T3 = T5

$n_f=1-\frac{(T_2-T_1)}{(T_4-T_5)}$

This equation will get reduced to,

$n_t=1-[\frac{T_1}{T_4}](\frac{1}{n_ac n_at }.(r_p )^\frac{(k-1)}{k})$

For ideal open cycle, $n_ac=n_at=1$

$n_t=1-[\frac{T_1}{T_4 }].(r_p )^\frac{(k-1)}{k}$

The regenerator should be designed properly to avoid any substantial. Pressure loss in it,which might cancel out any gain in thermal efficiency. Because of some pressure loss in the regenerator, the turbine output and the net output will be slightly less than for the simple cycle.

REHEATING

In reheat cycle, the combustion gases are not expanded in one turbine only but in two turbines. The exhaust of the high-pressure turbine is reheated in a re-heater and then expanded in a low-pressure turbine. By reheating, the power output of the turbine is increased but the cost of additional fuel may be heavy unless a heat exchanger is also used. A reheat cycle is shown in Fig. 9.13. Considering the adiabatic expansions, the total work done in the two turbines will be equal to: (I3 – I4a) + (I5 – I6a).

If the combustion gases were expanded in one turbine only down to point 7a for the same pressure ratio, then the work output would have been: (I3 – I7a). Now the constant pressure lines on the H-chart diverge away from the origin and converge towards the origin. Therefore the line 5–6a will be greater than 4a–7a. Hence reheating is increases the power output. By reheating, the average temperature of heat addition is raised resulting in higher output and efficiency of the cycle. If reheat cycle is to be adopted then the pressure ratio must be high as at low pressure ratios, the thermal efficiency is lowered by reheating Fig. Reheating reduces the airflow through the cycle resulting in decreased input to the compressor. For ideal reheating; the working fluid temperature after reheating is equal to the maximum permissible turbine inlet temperature. That is, T5 = T3 The efficiency of the cycle will be given as,

$n_f=\frac{(T_3-T_4)+(T_5-T_6)-(T_2-T_1)}{(T_3-T_2)+(T_5-T_4)}$