A steady-flow system operating on the ideal Ericsson cycle can achieve the Carnot efficiency. One of the salient features of this cycle is the isothermal expansion through a heated turbine, as shown in Fig. a. Heat is added to the turbine such that the outlet temperature is equal to the inlet temperature, i.e. T₁=T₂, and the overall pressure ratio for this process is rₚ=P₁/P₂. However, an isothermal expansion through a heated turbine is very difficult to achieve in practical engineering applications. An alternate approach is two use a multi-stage expansion process with reheating. In this approach, the gas expansion process is carried out in multiple stages with reheating in between each stage. Consider the two-stage turbine expansion with reheating shown in Fig. b. The gas enters the first stage of the turbine at state A1, is expanded isentropically to an intermediate pressure Pₐ₂, is reheated at constant pressure to state B1, and is expanded in the second stage isentropically to the final pressure Pᵦ₂. The overall pressure ratio remains Pₐ₁/Pᵦ₂=rₚ. In this concept, the work output is minimized if the gas is reheated to the initial temperature Tᵦ₁=Tₐ₁, and the pressure ratio is equal across each turbine stage such that Pₐ₁/Pₐ₂=Pᵦ₁/Pᵦ₂=√rₚ. For the same inlet temperature T₁=Tₐ₁, the same mass flow rate m˙, the same overall pressure ratio rₚ, and an ideal monoatomic gas as the working fluid for both scenarios.  Sketch the two expansion scenarios a the T−s diagram.

Elements Of Electromagnetics
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A steady-flow system operating on the ideal Ericsson cycle can achieve the Carnot efficiency. One of the salient features of this cycle is the isothermal expansion through a heated turbine, as shown in Fig. a. Heat is added to the turbine such that the outlet temperature is equal to the inlet temperature, i.e. T₁=T₂, and the overall pressure ratio for this process is rₚ=P₁/P₂.

However, an isothermal expansion through a heated turbine is very difficult to achieve in practical engineering applications. An alternate approach is two use a multi-stage expansion process with reheating. In this approach, the gas expansion process is carried out in multiple stages with reheating in between each stage. Consider the two-stage turbine expansion with reheating shown in Fig. b. The gas enters the first stage of the turbine at state A1, is expanded isentropically to an intermediate pressure Pₐ₂, is reheated at constant pressure to state B1, and is expanded in the second stage isentropically to the final pressure Pᵦ₂. The overall pressure ratio remains Pₐ₁/Pᵦ₂=rₚ. In this concept, the work output is minimized if the gas is reheated to the initial temperature Tᵦ₁=Tₐ₁, and the pressure ratio is equal across each turbine stage such that Pₐ₁/Pₐ₂=Pᵦ₁/Pᵦ₂=√rₚ.

For the same inlet temperature T₁=Tₐ₁, the same mass flow rate m˙, the same overall pressure ratio rₚ, and an ideal monoatomic gas as the working fluid for both scenarios. 

Sketch the two expansion scenarios a the T−s diagram.

Qreheat
Reheater
士。
- PA2, TA2
PB1, TB1
PB2, TB2
P2, T2 = T1
PA1, TA1"
P1, T1
WT.B
WTA
Turbine B
Turbine
Turbine A
T=const.
Qin
b) Two-stage turbine expansion with reheating
a) Isothermal turbine
Transcribed Image Text:Qreheat Reheater 士。 - PA2, TA2 PB1, TB1 PB2, TB2 P2, T2 = T1 PA1, TA1" P1, T1 WT.B WTA Turbine B Turbine Turbine A T=const. Qin b) Two-stage turbine expansion with reheating a) Isothermal turbine
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