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Degree of Reaction of Turbine with Right Angled Outlet Blade Calculator

Degree of Reaction Formula:

\[ R = 1 - \frac{\cot(\alpha_f)}{2 \times (\cot(\alpha_f) - \cot(\theta_i))} \]

radians
radians

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1. What is Degree of Reaction?

Degree of Reaction is defined as the ratio of pressure energy change inside a runner to the total energy change inside the runner. It's a crucial parameter in turbine design that indicates how much of the total energy conversion occurs in the rotor versus the stator.

2. How Does the Calculator Work?

The calculator uses the Degree of Reaction formula:

\[ R = 1 - \frac{\cot(\alpha_f)}{2 \times (\cot(\alpha_f) - \cot(\theta_i))} \]

Where:

Explanation: The formula calculates the proportion of energy conversion that occurs due to pressure changes within the turbine runner, using trigonometric relationships between the guide blade angle and vane angle at inlet.

3. Importance of Degree of Reaction

Details: The degree of reaction is fundamental in turbine design as it affects efficiency, pressure distribution, and overall performance. A proper reaction degree ensures optimal energy conversion and prevents issues like cavitation.

4. Using the Calculator

Tips: Enter guide blade angle and vane angle at inlet in radians. Both values must be positive and valid angles. The calculator will compute the degree of reaction between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What does a Degree of Reaction of 0.5 mean?
A: A reaction degree of 0.5 indicates that half of the total energy conversion occurs in the rotor and half in the stator, which is typical for many impulse turbines.

Q2: How does guide blade angle affect reaction degree?
A: The guide blade angle directly influences the velocity triangles and thus affects how energy is distributed between pressure and kinetic energy components.

Q3: What are typical values for Degree of Reaction?
A: For Francis turbines, the reaction degree typically ranges from 0.4 to 0.6, depending on the specific design and operating conditions.

Q4: Why is Degree of Reaction important in turbine design?
A: It helps determine the pressure distribution along the blade, affects efficiency, and influences the likelihood of cavitation occurrence.

Q5: Can Degree of Reaction be greater than 1?
A: In theory, reaction degree can approach 1 for pure reaction turbines, but values greater than 1 are not physically meaningful as they would imply more pressure drop in the rotor than available.

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