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Exit swirl in rotor blade dynamics refers to the rotational component of velocity at the rotor blade's exit, measured along the pitchline at a certain radial position. Calculating the exit swirl involves understanding the angular velocity of the rotor and the mean radius of the blade.
To compute the exit swirl at the pitchline, we use the formula:

• \( C_{θ_{2m}} = ω \times r_m \)

where \( ω \) is the angular velocity calculated as \( \frac{2\pi N}{60} \), followed by substituting \( N = 6000 \) revolutions per minute (rpm). The mean radius \( r_m \) is given as \( 0.3 \text{ m} \).
This equation captures how fast the rotor is spinning and reflects it as a swirl component at the exit, revealing energy conversion efficacy in flow dynamics.

The downstream swirl distribution is crucial in rotor blade design and performance, often assessed under specific design conditions like a free-vortex assumption. This concept describes how the swirl carries energy downstream along the radius. The key principle here is that, under a free-vortex design, the upstream swirl \( C_{θ2} \) is determined as a function of radius \( r \) using the relationship:

• \( C_{θ2} = C_{θ_{2m}} \times \frac{r_m}{r} \)

This implies that as the radius changes from hub to tip, the swirl's influence varies - generally reducing as one moves towards the blade tip.
Graphing \( C_{θ2} \) as a function of \( r \) allows engineers to visualize how swirl diminishes, aligning with goals of efficient exit flow profiles and minimizing energy loss.

The degree of reaction in rotor dynamics signals how evenly energy extraction is divided between the rotor and stator sections, critical for predicting efficiency. It indicates the proportion of pressure energy converted in the rotor.
The mathematical expression for the degree of reaction \( R \) is derived as follows:

• \( R = - \frac{C_{θ_{2}}^{2}}{2U^{2}} = - \frac{C_{θ2}}{2C_{a_{2}}} \)

where \( C_{θ2} \) is the tangential velocity at exit and \( C_{a_{2}} \) is the axial velocity at exit.
Understanding \( R \) along the blade span reveals where in the rotor stator there is maximum change and how design adjusts to enhance total flow efficiency. With the axial velocity given, this calculation becomes straightforward along the blade span.

In rotor dynamics, the diffusion factor distribution provides insight into the deceleration of flow as it passes through the blade passages. The distribution of diffusion factors along the radial span is vital for analyzing how efficiently the blade decelerates flow and manages boundary layer growth.
For calculating radial distribution:

• \( D_{r}(r) = 1 - \frac{r_{2}}{r_{1}} \)

Where \( r_{1} \) and \( r_{2} \) are the radial positions at entry and exit respectively.
By plotting \( D_{r}(r) \) against the radial span, one can observe how effectively the blade diffuses the flow, ensuring balanced pressure and velocity profiles - crucial for optimizing rotor performance and reducing stall risks.