Ministry of education and science of ukraine
National Aviation University
Explanatory note
For course paper
“Thermodynamic and gasdynamic calculations of compressors and gas-turbine power plant”
Performed by student of 307 group AF
Julija Andreeva
Checked by F.I. Kirchu
Kiev 2013
1. Thermodynamic calculation of gas-turbine power plant
Calculation of working body parameters.
Principal scheme of gas-turbine power plant (GTPP) with power turbine is shown on Figure 1, where there are cross sections in which working body parameters are determined.
Determination of air parameters in section 1-1 (at the entrance of the power plant)
Т1* = Тн* = Тн = 288 К, р1* = рн*in = 101325 ∙ 0.975 = 98791.875 (Pa),
w
Fig.
1. Principal
scheme
of
gas-turbine
power
plant
and
graphs
of the pressure and temperature
changes
along it sections.
Determination of work, that is necessary to compress of 1 kg air, in compressor and air parameters in the section 2-2 (at the exit from the compressor)
(J/kg)
,
where k = 1,4, R = 287,2 J/(kg·К); *c.s = 0,89–0,91 – compressor stage efficiency.
Air temperature and pressure at the exit from the compressor are calculated according to the formulas:
Т*2 = Т*1 + Lc/[kR/(k – 1)] = 288 + 421131.357 ∙ (1.4 - 1) / 1.4 / 287=
= 707.245 (K);
р*2 = р*1*∑C = 98791.875 ∙ 17 = 1679461.875 (Pa)
Determination of working body parameters in the section 3-3 (before turbine)
Thermal capacity of combustion product in the temperature range Т*3 - Т*2. With high accuracy average thermal capacity of gases near combustion chamber GTPP is determined by generalized equation:
сp = 848 + 0,208(Т*3 + 0,48Т*2) = 848 + 0,208 ∙ (1445 + 0,48 ∙
∙ 707.245) = 1219.171 (J/(kg∙K))
Relative fuel loss in combustion chamber is calculated in such way :
gfuel = сp(Т*3 – T*2)/(Hucc) = 1219.171∙(1445 – 707.245)/(43∙106∙ ∙0.98) = = 0.0213,
where
Нu
– lower
fuel
combustion
heat;
cc
– coefficient,
that
takes
into
account
incompleteness
of fuel burning and heat losses through the combustion section walls.
Usually
cc
=
0,97–0,98.
For liquid hydrocarbonic fuels Нu = (42,5–43,5)106 J/kg,
Specific supplied heat in the combustion chamber:
q1 =cp(Т*3 – Т*2)= 1219.171 ∙ (1445 – 707.245) = 899449.501 (J/kg)
Pressure on the exit from the combustion section:
р*3 = р*2cc = 1679461.875 ∙ 0.98 = 1645872.638 (Pa)
Value cc = 0,97–0,99 characterizes total pressure losses in the combustion chamber.
Air amount, theoretically needed for combustion of 1 kg liquid hydrocarbonic fuels is determined from the equation:
L0 = [(8/3)C + 8H]/0,232,
where, С, Н – mass portions of carbon and hydrogen in 1 kg fuel. By the way, for standard liquid fuel С = 0,85, Н = 0,15. Then:
L0 = [(8/30,85) + 80,15]/0,232 = 14,9 [kg air/kg fuel].
Total coefficient of excess air in combustion chamber:
= 1/gfuelL0 = 1 / (0.0213 ∙ 14.9) = 3.144
Determination of expansion work of 1 kg gas in turbine, that drives compressor and gas parameters in section 4-4 (after compressor turbine or compressors in case when it is two-shafted)
(J/kg)
where gcooling – value of specific air waste, that is extracted at the exit from the compressor for turbine elements cooling ; gexchange – specific air waste, that is extracted for technological necessities GTPP (choosing in range 0,01–0,02); mech – mechanical efficiency of turbocompressor (choosing in range 0,99–0,995).
Value gcooling is determined according to temperature level at the exit from the combustion chamber and chosen cooling way.
Value gcooling = 0.08
Temperature and pressure at the exit from the compressor turbine are determined with the help of following equations:
(K),
(Pa)
where kg = 1,33, Rg = 288 J/(kg·К), *t = 0,9–0,91 – compressor turbine efficiency.
Determination of expansion work in power turbine and gas parameters at the exit from it.
Pressure at the exit from the power turbine is equal
р*5 = (1,03–1,05)рн*= 1.04 ∙ 101325 = 105378 (Pa).