Gas turbine with a free power turbine

Transcription

1 Gas turbine with a free power turbine A light oil gas turbine plant operates with a free power turbine. The power output is 7 MW when the abient conditions are 308 and 0.9 bars. The turbine inlet teperature is 0. The pressure ratio of the copressor is 8. and the isentropic efficiencies of the copressor and copressor-turbine are 0.8 and 0.8 respectively. The isentropic efficiency of the power turbine is The echanical efficiency on the power turbine shaft is The cobustion pressure loss is %. Calculate the required flue gas ass flow through & FUEL the gas turbine and the specific fuel consuption ( β. The following is also & AIR given: Ratio of specific heat for copression in the copressor: κ air.39 Ratio of specific heat for expansion in the power turbine κ power turbine.33 copressor turbine qg turbine 3 air fuel

2 HINTS: Hint (-p The flue gas ass flow can be found through a heat balance over the free power turbine, which has a power output of 7 MW. el 7MW qg ( h h * η Hint (-p To find h and h we have to find the teperatures t and t. We know that turbine operates the copressor, i.e. T Or with a heat balance: c * ( * * + β ct T Fro this heat balance we can find T as we do not know the pressure ratios over respective turbine. β is the specific fuel consuption and is found through a heat balance over the cobustion chaber. Hint 3 (-3p The pressure ratio over Turbine is found fro 67 T T3 * ηt[ ( κ κ T [ κ ( κ T T T3 * ηt Now we are able to calculate the pressure ratio over the power turbine, T, and thus the outlet teperature t.

3 SOLUTION The flue gas ass flow can be found through a heat balance over the free power turbine, which has a power output of 7 MW. el 7MW qg ( h h * η We have to find the enthalpies h and h. These are directly correlated to the teperatures, that is, we have to find the teperatures T and T. To find T with have to look for the teperature decrease in the first turbine. As we do not know the pressure ratios in respective turbine, we cannot use the teperature decrease equation with pressure ratio. However, we know that turbine operates the copressor, i.e. T Or with a heat balance: c * T ( + * ct * T β [A Here we can find T. We start in calculating on the copressor. The teperature increase is: T η κ κ 39 *[ *[ We can calculate t. We can find the enthalpy (or we can as well work with c p for exaple in L Wester s Tables and Diagras, year 99 p 9. In the copressor we have pure air, therefore x 0. t h 360kJ kg If we work with the Cp value, it is found on p 63 for the average teperature in the copressor. c 0 J ( kg, _ at _ t 9 C _ in _ copressor c We can now put the values for the copressor into Eq. A. However, the specific heat for turbine, C pt is a function of the outlet teperature T. The function in diagra for can be found on page 6 in L. Wester Tables and Diagras. We have to iterate by guessing an outlet teperature, finding a C p and recalculate the teperature. However, Cp for the turbine is also a function of the flue gas content x. So in order to find T we first have to calculate the specific fuel consuption, β. This paraeter is also included in Eq A. β is calculated with a heat balance on the cobustion chaber. Heat balance on cobustion chaber (on flow free basis: h + β*h i (+β*h 3 [

4 H i,3 MJkg for light oil. h 3 is a function of the gas content, and thus a function of β. For light oil the gas content is: β x,* [ + β The enthalpy h 3 is h 3 h 3 (air + x*dh [3 The enthalpy for air at C (L. Wester page 0: h 3 (air 06 kjkg and DH 99,3 kjkg. Cobining [ and [3 into [ gives: β H i h h 3air 3air h. DH ( t So the specific fuel consuption is.77%. Now we are able to calculate T for the turbine according to Eq. A: x. * β ( + β * 36.9 T Guess _ t 700 C t 80 C 67 t 70 C.077 * c T c 9 J kg, t 70 C T kj h h ( t air + x * DH ( t * kg In order to find T we have to know which are the pressure ratios on respective turbine. The pressure ratio on first turbine is found fro: 67 T3 * ηt[ ( κ T κ T Solving for the unknown pressure ratio T : κ ( κ T [ T T3 * ηt κ T is found for exaple in Tables and diagras L. Wester. With t t ( C and x 0.7, we get κ T,37. Thus

5 T The pressure ratio on the power turbine can now be found, taking into account the cobustion pressure loss: *0.9* T The teperature decrease in the power turbine is: T * ηt *[ ( κ T κ T T 983*0.87 *[ 7 t 39 C ( The enthalpy for the outlet teperature of the power turbine is h h ( t + x * DH ( t air s * kj kg The electrical power output heat balance gives the ass flow: el 7000 qg 88.kg s ( h h * η ( * 0.98