Chapter 9 Practical cycles

Transcription

1 Prof.. undararajan Chater 9 Practical cycles 9. Introduction In Chaters 7 and 8, it was shown that a reversible engine based on the Carnot cycle (two reversible isothermal heat transfers and two reversible adiabatic work rocesses) rovides the highest level of conversion from heat to work, for given maximum and minimum temerature limits. In common ractice, we often find that when heat is added to a substance, its temerature starts increasing. Only during a hase change rocess, it is ossible to have isothermal heat transfer to the working substance. herefore, one may consider the otion of carrying out the entire cycle within the saturated liquid- vaor mixture regime as shown in Fig. 9.. Fig. 9. Carnot engine cycle with hase change substance Here, rocess - corresonds to the boiling of saturated liquid into saturated vaor by reversible heat addition in a boiler; rocess - reresents the exansion of the saturated vaor reversibly and adiabatically in a turbine; rocess - reresents the artial condensation of vaor into liquid by isothermal heat rejection in a condenser; rocess - reresents the adiabatic comression of the mixture in a um. Although theoretically the above Carnot cycle seems feasible, there are some ractical difficulties in carrying out the cycle comletely within the saturated liquid- vaor dome. Indian Institute of echnology Madras

2 Prof.. undararajan When a um is oerated in the liquid vaor mixture regime, it suffers from the roblem of cavitation which severely affects the erformance and oerational life of the um. herefore, it is referable that the adiabatic comression rocess - be shifted to the left (outside the mixture regime) into the sub-cooled liquid region. Furthermore, when the um oerated with liquid only, the work inut needed will be small because of the small liquid volume. In the case of the turbine, the turbine blades will be severely eroded when a large number of liquid drolets iminge on their surface at high seed. herefore for long oerational life of the turbine blades, it is essential to shift the adiabatic exansion rocess - to the right, comletely into the suerheated vaor regime. In any case, even if the vaor at the turbine exit is slightly wet (with a few drolets), the mixture quality should be very close to one. Now, with state lying in the sub-cooled regime and state lying in the suerheated vaor regime, it is not ossible to have isothermal heat addition in the boiler. In fact, rocess - is better aroximated as constant ressure heat addition, since boiler is essentially a constant ressure device. imilarly, the condenser is also a constant ressure device; however, unlike in the case of boiler, the non-isothermal heat transfer art in a ractical condenser is almost negligible. Relacing the isothermal heat addition and heat rejection rocesses of Carnot cycle by corresonding constant ressure heat addition and constant ressure heat rejection, results in a new cycle known as the Rankine cycle for steam ower lants. 9. Rankine Cycle he simlest form of Rankine cycle that could be used for converting from heat to work, is made u of the following rocesses: (i) Reversible adiabatic comression rocess - (in Pum) (ii) Reversible constant ressure heat addition rocess - (in Boiler) (iii) Reversible adiabatic exansion rocess - (in team urbine) Indian Institute of echnology Madras

3 Prof.. undararajan (iv) Reversible constant ressure heat rejection rocess - (in Condenser) A schematic diagram indicating the various devices of this ower lant cycle was shown in Fig. 7.. Water- steam substance is emloyed as the working fluid in this cycle. he basic Rankine cycle in - coordinates is shown in Fig. 9.. In the ractical Rankine cycle of thermal ower lants, additional comlexities such as the reheating of steam after artial exansion in the turbine, regenerative heating of water before entry to the boiler with the hel of some wet steam bled from turbine (after artial exansion), are also incororated. Fig. 9. Basic Rankine cycle Neglecting KE and PE changes, the I law alication to each device gives: (i) Rate of heat inut in boiler = { } m h h (9.) Q H (ii) urbine ower outut = { } m h h (9.) W (iii) Rate of heat rejection in condenser = { } (9.) (iv) Power inut to um W P m { h h } Q C m h h = m ~ (9.) ρ Indian Institute of echnology Madras

4 Prof.. undararajan While evaluating the um ower, since is negligible across the um, we can aroximate h ~ /ρ. Net ower = W = m { h h } m { h h } = Q Q = m { h h ) ( h )} (9.5) net H C ( h he enthaly values at different states of the water-steam substance can be obtained from the steam tables, for evaluating the heat and work interactions in the cycle. 9. Gas urbine (Brayton) cycle he Brayton cycle is based on the closed cycle gas turbine ower lant shown in Fig. 7.. It uses air as the working fluid. he simlest form of the Brayton cycle in - coordinates is shown in Fig. 9.. imilar to the Rankine cycle, the industrial Brayton cycle may include additional rocesses such as reheating after artial exansion, regenerative heating with turbine exhaust etc. Fig. 9. Basic Brayton Cycle he cycle consists of reversible adiabatic comression -, constant ressure ( = ) reversible heat addition rocess -, reversible adiabatic exansion - and constant ressure ( = ) reversible heat rejection -. In order to find the roerties of the working fluid (air), we can emloy ideal gas relations. hus, the heat and work interactions can be evaluated as: Indian Institute of echnology Madras

5 Prof.. undararajan = (i) Power inut to comressor Wcom m{ h h } = mcp ( ) (9.6) (ii) Rate of heat inut in heater Q = m { h h } = mc ( ) (9.7) H P (iii) urbine ower outut W m{ h h } = mc ) (9.8) = P ( (iv)rate of heat rejection in cooler Q m{ h h } = mc ) (9.9) C = P ( In addition to the above relations, for the reversible adiabatic rocesses - and -, the ressure ratios and temerature ratios are related as follows: = γ γ = = γ γ (9.0) hus, if the ressure ratio ( / ), comressor inlet temerature ( ) and the turbine inlet temerature ( ) are available, all the heat and work interactions can be calculated. 9. Vaor Comression Refrigeration cycle A Carnot refrigeration (or heat um) cycle based on a hase change substance as working fluid, is shown in Fig. 9.. he working substances used in refrigerators are some refrigerant fluids with commercial names such as R-, R-a etc. Although the reversible heat um/ refrigerator cycle also consists of two isothermal heat transfer and two adiabatic rocesses, it is traversed in the anti-clockwise sense, contrary to the reversible heat engine cycle. his is in view of the fact that here heat absortion takes lace at low temerature and heat rejection takes lace at high temerature. Indian Institute of echnology Madras

6 Prof.. undararajan 9. Reversible Heat Pum/ Refrigerator cycle he ractical refrigerator cycle differs from the reversible Carnot cycle in two imortant ways. Firstly, the adiabatic comression rocess has to be shifted to the suerheated vaor regime, since the comressor cannot handle liquidvaor mixture. Additionally, the reversible exansion rocess - would require a frictionless adiabatic turbine or iston- cylinder device which are actually not necessary- considering the fact that the work that can be delivered by this rocess will be negligibly small (because of the low mass flow rate of the refrigerant and also the small volume of the redominantly liquid mixture). herefore, instead of using a work-roducing exansion device, in a ractical refrigerator, a very chea throttle valve can be used to carry out irreversible exansion. In fact, with the hel of friction, a very large ressure dro is introduced in the refrigerant flow which results in flashing (raid hase change from liquid to vaor hase because of sudden decrease in ressure). Due to flashing, the temerature of the mixture will reduce significantly, because the latent heat needed for evaoration is derived from the sensible heat of the refrigerant itself. he throttling rocess occurring in the throttle valve is an isenthalic rocess, as exlained in Chater 6. herefore, for the irreversible exansion rocess -, h = h. With the two changes described above, the basic cycle of a ractical refrigerator is shown in Fig Indian Institute of echnology Madras

7 Prof.. undararajan Fig. 9.5 Basic Vaor Comression Refrigeration Cycle he cycle consists of the following rocesses. (i) Reversible adiabatic comression of the refrigerant vaor - (ii) Reversible constant ressure heat rejection in condenser - (iii)adiabatic exansion in throttle valve (irreversible) - (iv) Reversible constant ressure heat absortion in evaorator - he heat and work interactions can be evaluated as: Power inut to comressor = { } (9.) W com m h h Rate of heat rejection in condenser = { } (9.) Q H m h h Rate of heat absortion in evaorator = { } (9.) Q C m h h For the throttle valve, h = h. (9.) In all the three cycles resented above, although the ideal cycle may consider the adiabatic rocesses to be reversible (i.e. isentroic), in reality, there may be entroy roduction because of irreversibilities such as friction. he erformance of the associated device can be exressed in terms of isentroic efficiency as discussed in Chater 8. Indian Institute of echnology Madras