22-Mec-A1 Applied Thermodynamics and Heat Transfer · December 2014
Question 2 of 8: Part-Load Steam Turbine by Throttle Governing
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Open-book, 3-hour paper. Part A (Thermodynamics, Q1–Q4) and Part B (Heat Transfer, Q5–Q8); the rubric grades any five (three from one part, two from the other), all of equal value. All eight questions are solved in full. Freon-12 property values are read from the saturated and superheated tables printed in the exam appendix (pages 4–5). Reference texts: Çengel & Boles, Thermodynamics: An Engineering Approach (9th ed.); Çengel & Ghajar, Heat and Mass Transfer (6th ed.); Incropera et al., Fundamentals of Heat and Mass Transfer (8th ed.).
Question 2: Part-Load Steam Turbine by Throttle Governing (equal value)
Given. Line steam $P_0=1.4\ \text{MPa}$, $T_0=300\ ^\circ\text{C}$ ($h_0=3040.9\ \text{kJ/kg}$, $s_0=6.9563$); exhaust fixed at $10\ \text{kPa}$; turbine isentropic; throttle isenthalpic.
Find. Throttle pressure $P_t$ giving 75 % of full work.
Figure 3 — Throttle governing on an $h$–$s$ chart. Throttling shifts the turbine-inlet state right at constant $h$ (higher entropy), so the isentropic drop to 10 kPa is shorter and the work is smaller.
Approach. Compute the full isentropic work from line conditions to 10 kPa. Set the part-load turbine work to 75 % of that; since throttling preserves enthalpy, the turbine still enters at $h_0$, so the required exit enthalpy fixes the exit entropy, which equals the post-throttle entropy — and that entropy at $h_0$ locates $P_t$.
Full work. $w_\text{full}=h_0-h_{2s}=3040.9-2203.6=837.3\ \text{kJ/kg}$; target $w_t=0.75(837.3)=628.0\ \text{kJ/kg}$.
Part-load exit enthalpy. The throttle keeps $h=h_0$ at turbine inlet, so $h_\text{exit}=h_0-w_t=3040.9-628.0=2412.9\ \text{kJ/kg}$; at 10 kPa $x_\text{exit}=\dfrac{2412.9-191.81}{2392.1}=0.929$.
Post-throttle entropy. $s_\text{exit}=0.6492+0.929(7.4996)=7.613\ \text{kJ/kg}\cdot\text{K}$; this is the entropy of the throttled steam (still $h=h_0$).
Throttle pressure. Searching the superheated tables at $h=3040.9$, $s=7.613$ falls between 0.30 MPa ($s\approx7.651$) and 0.40 MPa ($s\approx7.520$): $P_t=\boxed{\approx0.33\ \text{MPa}}$ (330 kPa).
Throttle governing is deliberately wasteful: the enthalpy the throttle "spends" raising entropy is unavailable to the turbine, which is why dropping the inlet from 1.4 MPa to about 0.33 MPa cuts the output by a quarter. It is simple and cheap but thermodynamically inferior to nozzle (partial-arc) governing.
Check: The throttle pressure is read by double interpolation of the superheated table (in $h$ then $s$); a ±0.1 % shift in the tabulated entropies moves $P_t$ by roughly ±10 kPa. The value 0.33 MPa is robust to that band.
