An ideal double-reheat steam turbine is a sensitive machinery that requires utmost care and precision in terms of its operation. In this article, we will discuss a theoretical case where an ideal double-reheat steam turbine receives 300,000 kg/h of steam at 10 MPa and 400°C. After expansion from high pressure turbine shell, it is reheated twice from saturated vapor condition back to its initial temperature. The steam entering the condenser should be 97% dry. We need to determine (a) engine work, (b) engine thermal efficiency, and (c) steam rate for this system.
To calculate the engine work provided by the turbo machine, we use the equation: W = m × hin − hout Where m represents mass flow rate of the working fluid passing through the turbine per unit time; hin and hout represent specific enthalpy across inlet and outlet respectively. For our purposes here, let’s assume that there are two stages – during each stage of expansion let us take specific enthalpies as follows High Pressure Stage :hin=3300 kJ/kg , hout1=3000kJ/kg . Reheating Stage 1:hin1=3000kJ/kg , hout2=3150kJ/kg . Reheating Stage 2 :hin2=3150 kJ/kg , hout3=3300 kj / kg Thus, Engine Work can be approximated as: W = 300000×(3300−3000)+300000×(3050−3150)+300000×(3300−3150)=45000000 kj / hr
The thermal efficiency indicates how much useful energy is derived from a given amount of heat input into a system or cycle. Theoretically speaking it can be expressed as η th = (T 2 − T 3 )/(T 1 − T 4 ) where T 1 – Initial Temperature before Expansion in HP Turbine Shell; T 2 – Saturation Temperature after Expansion ; T 3 – Final Temperature after Condensation ; T 4 – Final Temperature before Heating .For our purposes here let’s assume that all temperatures remain constant i.e.,400°C throughout hence ηth=(400–400)/(400–400)=100%. Thus engine thermal efficiency for this system would come out to be 100%.
Next we need to calculate Steam Rate which is defined as total heat supplied over time divided by total work output which can further be expressed mathematically as SR=(hm-hl)/W . Where hm represents mass flow rate of feedwater per unit time;hl represents specific enthalpy at exhaust side from condenser;W represents energy available or generated due to conversion process within turbo machine itself Taking values according to our example case i.e.,hm = 3000kj / kg ,Hl = 1000kj / kg , W = 45000000 Kj / hr thus Steam Rate comes out to be SR=(3000-1000)/45000000Kj /hr ≈ 0.67 % Hence Steam Rate for this particular example would turn out to approximately 0.67%.
In conclusion, after analyzing an ideal double-reheat steam turbine receiving 300 000 kg/h at 10MPa & 400°C along with reheat twice back up to same temp value coupled with 97% dryness level on exiting end indicated following results obtained viz.(A)Engine Work came out roughly @ 45 000 000 Kj / Hr ;(B) Thermal Efficiency @ 100%; & lastly (C)Steam Rate @0 67 %
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