An impulse reaction turbine is a type of thermal turbine that extracts energy from a fluid by both impulse and reaction principles. In such a turbine, the working fluid, typically steam or gas, undergoes an enthalpy (heat) drop in both the stationary (fixed) blades and the rotating (moving) blades. The problem asks us to determine the degree of reaction for a specific turbine stage given the individual heat drop values for the fixed and moving blades.

Turbine Stage Heat Drop Definition

The heat drop in a turbine stage refers to the total decrease in the enthalpy of the working fluid as it passes through that stage. This energy conversion drives the turbine rotor. The total heat drop within a stage is divided between two main components:

• Heat drop in fixed blades: This occurs in the stationary passages (often called nozzles or guide vanes) where the fluid's pressure energy is converted into kinetic energy.
• Heat drop in moving blades: This occurs as the fluid flows over the rotating blades, leading to a further reduction in pressure and enthalpy, which directly results in work being done on the rotor.

Degree of Reaction Concept Explained

The degree of reaction (R) is a fundamental parameter in turbine design that quantifies the proportion of the total enthalpy drop (or static heat drop) that takes place within the moving blades, relative to the total enthalpy drop across the entire stage. It helps classify turbines and understand their operating characteristics. For an impulse reaction turbine, the degree of reaction is defined as:

\[ \text{Degree of Reaction (R)} = \frac{\text{Heat drop in moving blades}}{\text{Total heat drop in the stage}} \]

The total heat drop for the entire stage is the sum of the heat drops in both the fixed and moving blades:

\[ \text{Total heat drop in the stage} = \text{Heat drop in fixed blades} + \text{Heat drop in moving blades} \]

Reaction Calculation for the Impulse Reaction Turbine

To find the degree of reaction for this impulse reaction turbine stage, we will use the provided heat drop values:

• Given heat drop in fixed blades = \(15 \, \text{kJ/kg}\)
• Given heat drop in moving blades = \(30 \, \text{kJ/kg}\)

Heat Drop Total Calculation

First, we calculate the total heat drop for the entire turbine stage:

\[ \text{Total heat drop in the stage} = 15 \, \text{kJ/kg} \, (\text{fixed blades}) + 30 \, \text{kJ/kg} \, (\text{moving blades}) \]

\[ \text{Total heat drop in the stage} = 45 \, \text{kJ/kg} \]

Degree of Reaction Step-by-Step Calculation

Now, we can substitute the calculated total heat drop and the given heat drop in moving blades into the formula for the degree of reaction:

\[ \text{R} = \frac{\text{Heat drop in moving blades}}{\text{Total heat drop in the stage}} \]

\[ \text{R} = \frac{30 \, \text{kJ/kg}}{45 \, \text{kJ/kg}} \]

To simplify the fraction, we find the greatest common divisor of 30 and 45, which is 15:

\[ \text{R} = \frac{30 \div 15}{45 \div 15} = \frac{2}{3} \]

Degree of Reaction Final Result

The calculated degree of reaction for this impulse reaction turbine stage is \(\frac{2}{3}\).

This result implies that two-thirds of the total enthalpy drop in this particular turbine stage occurs within the moving blades, highlighting the significant reactive nature of this turbine stage.