22-Mec-A1 Applied Thermodynamics and Heat Transfer · May 2016
Question 2 of 8: Combined Reheat / Regenerative Steam Cycle
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Reference texts: Çengel & Boles, Thermodynamics: An Engineering Approach (9th ed., McGraw-Hill) — closed- and open-system energy balances, steam tables, vapour and gas power cycles, and vapour-compression refrigeration; Çengel & Ghajar, Heat and Mass Transfer (6th ed.) and Incropera, DeWitt, Bergman & Lavine, Fundamentals of Heat and Mass Transfer (8th ed., Wiley) — cylindrical composite-wall conduction, internal-flow and cross-flow convection correlations, natural convection with radiation, and the ε–NTU heat-exchanger method. Freon-12 property data are taken from the appendix supplied with the exam; steam, air and engine-oil data from standard tables.
Paper format: National Examination 07-Mec-A1, 3 hours, open book. Part A — Thermodynamics (Q1–4); Part B — Heat Transfer (Q5–8). Each answer carries equal value; a complete paper is any five (three from one part, two from the other). All eight questions are solved in full below.
Figure 2 — T–s schematic: 1→2 HP expansion to 0.8 MPa (fraction $y$ extracted), 2→3 constant-pressure reheat to 350 °C, 3→4 LP expansion to 0.2 MPa (fraction $z$ extracted), 4→5 continued expansion to the 10 kPa condenser. The two open feedwater heaters return the extractions to the boiler feed line.
Given. A reheat–regenerative cycle: HP inlet 3.5 MPa/350 °C, extraction and reheat at 0.8 MPa back to 350 °C, LP extraction at 0.2 MPa, condenser 10 kPa, two open feedwater heaters. Find. The extraction fractions, the net work per kilogram of boiler steam, and the thermal efficiency.
Approach. Take 1 kg through the boiler; two open-feedwater-heater energy balances fix the extraction fractions $y$ and $z$, after which the turbine work, pump work, and boiler heat give the efficiency and net work per kilogram of boiler steam.
Turbine states (ideal, isentropic). From $s_1$ at 0.8 MPa, $h_2=2767.6$; after reheat $s_3$ gives $h_4=2825.7$ at 0.2 MPa and $h_5=2348.4$ at 10 kPa (quality $x_5=0.90$).
Feed-line states. Condensate $h_6=191.8$; the pumps add $w_{p1}=v_f\Delta P=0.19$, $w_{p2}=0.64$, $w_{p3}=3.0$ kJ/kg, giving $h_7=192.0$, $h_9=505.3$, $h_{11}=723.9$ kJ/kg. Heater exits are saturated liquid: $h_8=504.7$, $h_{10}=720.9$ kJ/kg.
Net work per kilogram of boiler steam. Turbine $w_t=(h_1-h_2)+(1-y)(h_3-h_4)+(1-y-z)(h_4-h_5)=337.2+304.4+380.6=1022.2$ kJ/kg; pumps $w_p=w_{p3}+ (1-y)w_{p2}+(1-y-z)w_{p1}=3.7$ kJ/kg, so $$w_\text{net}=1022.2-3.7=\boxed{1018\ \text{kJ/kg}}.$$
Steam properties are evaluated from IAPWS-IF97; a ±0.1 % table sensitivity at the 0.8 MPa/350 °C reheat point shifts $y$, $z$ and $\eta$ by well under half a percent. The turbines are taken as ideal (isentropic) since no component efficiency is stated; adding realistic 85 % stages would lower $\eta$ to roughly 31–32 %.
