Questions: Regenerative Cycles and Efficiency Improvements

Question 1

A Rankine power plant uses steam extracted from intermediate turbine stages to preheat condensate in feedwater heaters. A technician argues this extraction must reduce plant efficiency because it takes steam out of the turbine before it has finished expanding and producing work. What is wrong with this reasoning?

• A. Extracted steam continues to produce work inside the feedwater heater, compensating for the lost turbine work
• B. The extraction does reduce turbine work output, but it reduces the heat that must be supplied to the boiler by a proportionally larger amount, so the efficiency ratio (work/heat input) increases
• C. Feedwater heaters recover more work from extracted steam than the turbine would have, because mixing is more efficient than expansion
• D. Efficiency is unaffected because the extracted steam is returned to the boiler at the same enthalpy as it left

Answer: (B)

The technician is right that extraction reduces turbine work — but efficiency is work/heat input, not just work. When feedwater is preheated by extracted steam, the feedwater enters the boiler at a higher temperature, so the boiler needs to add less heat (especially at low temperatures where the thermodynamic penalty is largest). This reduction in heat input is proportionally greater than the reduction in turbine work, so the efficiency ratio improves. The cycle is using 'free' internal heat transfer instead of purchasing heat with additional fuel — exactly what regeneration is designed to accomplish.

Question 2

Why does regeneration move a power cycle's efficiency closer to the Carnot limit, even though it adds no heat from outside the cycle?

• A. Regeneration raises the peak cycle temperature T_H by preheating steam before it enters the high-pressure turbine
• B. Regeneration lowers the cold reservoir temperature T_L by pre-cooling exhaust before it reaches the condenser
• C. Regeneration reduces irreversibilities caused by large temperature differences during heat addition, making actual heat exchange closer to the reversible ideal
• D. Regeneration captures work from turbine exhaust that would otherwise be wasted, directly adding it to the cycle output

Answer: (C)

Carnot efficiency depends only on T_H and T_L. Regeneration does not change these boundary temperatures. What it changes is the process of heat addition. In a simple Rankine cycle, cold subcooled water enters the boiler and is heated at low temperatures before reaching saturation — thermodynamically wasteful because adding heat at low temperature is far from the reversible ideal of adding all heat at T_H. Feedwater heaters bring water closer to saturation temperature before it enters, so a greater fraction of heat is added at higher temperatures. This reduces the temperature mismatch (and therefore the irreversibility) during heat addition, moving the cycle toward the Carnot ideal.

Question 3

In a regenerative Rankine cycle, the feedwater heaters add heat to the feedwater from an external source such as a separate auxiliary boiler or heat exchanger, independent of the main turbine.

• T. True
• F. False

Answer: False

Feedwater heaters use steam extracted (bled) from intermediate stages of the main turbine — an internal heat transfer within the cycle, not external heat input. Open feedwater heaters mix extracted steam directly with feedwater; closed heaters keep the streams separate but still use turbine extraction steam as the heat source. The entire efficiency benefit of regeneration comes from this internal transfer: heat already in the cycle is reused rather than purchased with additional fuel. If the heat came from an external source, it would be thermodynamically no different from simply adding more heat in a larger boiler.

Question 4

A recuperator in a Brayton gas turbine cycle improves thermal efficiency by transferring heat from the hot turbine exhaust to the cooler compressor outlet air, reducing the fuel required to reach the combustor peak temperature.

• T. True
• F. False

Answer: True

In a simple Brayton cycle, compressed air enters the combustor at relatively low temperature (say 300°C) and turbine exhaust leaves at high temperature (say 550°C). Without a recuperator, this hot exhaust is discarded to the atmosphere — a major waste of exergy. A recuperator intercepts this exhaust and transfers heat to the compressed air before combustion, raising the air inlet temperature (say to 480°C). The combustor only needs to add the remaining temperature rise, requiring less fuel. Turbine work output is unchanged; only heat input decreases. Therefore thermal efficiency (W_net / Q_in) improves.

Question 5

Why does adding more feedwater heaters to a Rankine cycle yield diminishing efficiency returns, and what is the theoretical upper limit to how many heaters would be thermodynamically beneficial?

Model answer: Each feedwater heater reduces the temperature mismatch during heat addition by preheating feedwater closer to saturation temperature. The first heater eliminates the largest mismatch (heating very cold condensate) and gives the greatest efficiency gain. Each successive heater operates over a smaller temperature range, yielding a smaller marginal gain. The theoretical limit is an infinite number of infinitesimally small heaters that preheat feedwater continuously from condenser exit to boiler entry, approximating isothermal heat addition at saturation temperature and approaching the Carnot efficiency for the given T_H and T_L. In practice, 5–8 heaters capture most of the achievable theoretical gain economically.

The thermodynamic ideal of regeneration is to add all heat at T_H (Carnot-like). With a finite number of heaters, feedwater temperature rises in discrete steps and heat is still added over a range of temperatures below T_H in the boiler. More heaters make the steps smaller and the approach to the Carnot ideal closer, but with diminishing returns — each additional heater recovers a smaller temperature interval at increasing mechanical complexity and capital cost. Engineers balance the efficiency gain per heater against these costs, which is why practical plants use 5–8 heaters rather than dozens.