šŸ­ Steam Rankine Cycle Calculator

Analyze steam power plant cycles ā€” simple and reheat configurations with efficiency and power output calculations.

Boiler Turbine Condenser Pump 3: Superheated Steam 4: Low-P Mixture 1: Sat Liquid 2: High-P Liquid

Vapor Power Loop Schematic

The Rankine thermodynamic cycle represents the ideal working model of a steam turbine power plant. Reheating steam between turbine stages prevents excessive moisture accumulation, protecting the turbine blades from erosion.

ā€¢ Simple Cycle: Standard 4-component loop (Boiler, Turbine, Condenser, Pump).
ā€¢ With Reheat: Expands steam in HP stage, returns to boiler to reheat, expands in LP stage.

šŸ“ Configuration

Operating Pressures

Typical: 4000-16000 kPa
Typical: 5-15 kPa
Typical: 400-600 Ā°C

Component Efficiencies

Rankine Cycle States:
1ā†’2: Pump (isentropic compression)
2ā†’3: Boiler (constant P heat addition)
3ā†’4: Turbine (isentropic expansion)
4ā†’1: Condenser (constant P heat rejection)

Ī·_th = W_net / Q_in
BWR = W_pump / W_turbine

šŸ“Š Results & Visualization

Configure the inputs and click Calculate to see results.

ā„¹ļø About the Rankine Cycle

The Rankine cycle is the fundamental thermodynamic cycle for steam power plants. It converts heat into work using water as the working fluid.

Components:
ā€¢ Boiler: heats water to superheated steam
ā€¢ Turbine: expands steam to produce work
ā€¢ Condenser: rejects heat, condenses steam
ā€¢ Pump: pressurizes liquid water

Reheat improves efficiency by reheating partially expanded steam.

šŸ“˜ Calculation Methodology

Mathematical Model & Theory

The Rankine cycle thermal efficiency ($\eta_{th}$) is determined by turbine work, pump work, and heat input rate:

$$\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_{turb} - W_{pump}}{Q_{in}}$$ $$W_{turb} = \eta_t (h_3 - h_{4s}), \quad W_{pump} = \frac{v_1 (P_2 - P_1)}{\eta_p}$$

Assumptions & Idealizations

  • Isentropic expansion in turbines with efficiency $\eta_t$
  • Isentropic compression in water pumps with efficiency $\eta_p$
  • Negligible friction and pressure losses in piping loops
  • Constant boiler and condenser pressures

References & Literature

  1. Cengel, Y. A., & Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill.
  2. Moran, M. J., Shapiro, H. N., Boettner, D. D., & Bailey, M. B., Fundamentals of Engineering Thermodynamics, Wiley.

Worked Engineering Example

Problem Statement:
An ideal Rankine cycle operates between boiler pressure 8 MPa and condenser pressure 10 kPa. Steam leaves the boiler superheated at 500Ā°C. Calculate thermal efficiency. (Enthalpy values: $h_1 = 191.8$, $h_2 = 199.9$, $h_3 = 3399.5$, $h_4 = 2100$ kJ/kg).

Step-by-step Solution:
1. Calculate net work:
$$W_{turb} = h_3 - h_4 = 3399.5 - 2100 = 1299.5 \text{ kJ/kg}$$ $$W_{pump} = h_2 - h_1 = 199.9 - 191.8 = 8.1 \text{ kJ/kg}$$ $$W_{net} = W_{turb} - W_{pump} = 1291.4 \text{ kJ/kg}$$ 2. Calculate heat input:
$$Q_{in} = h_3 - h_2 = 3399.5 - 199.9 = 3199.6 \text{ kJ/kg}$$ 3. Calculate efficiency:
$$\eta_{th} = \frac{1291.4}{3199.6} = 0.4036 \quad (40.36\%)$$
Final Result:
Thermal efficiency is 40.36%.