Stream Function For Flow Over Rankine Oval Calculator

Rankine Oval Stream Function:

\[ \psi_r = V_{\infty} \times r \times \sin(\theta) + \frac{\Lambda}{2\pi} \times (\theta_1 - \theta_2) \]

Freestream Velocity:

m/s

Radial Coordinate:

Polar Angle:

rad

Source Strength:

m²/s

Polar Angle from Source:

rad

Polar Angle from Sink:

rad

Rankine Oval Stream Function:

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1. What is the Rankine Oval Stream Function?

The Rankine Oval Stream Function describes the flow pattern around an oval-shaped object in potential flow theory. It combines uniform flow with a source-sink pair to create a closed streamline that represents the oval body shape.

2. How Does the Calculator Work?

The calculator uses the Rankine Oval Stream Function equation:

\[ \psi_r = V_{\infty} \times r \times \sin(\theta) + \frac{\Lambda}{2\pi} \times (\theta_1 - \theta_2) \]

Where:

\( V_{\infty} \) — Freestream velocity (m/s)
\( r \) — Radial coordinate (m)
\( \theta \) — Polar angle (rad)
\( \Lambda \) — Source strength (m²/s)
\( \theta_1 \) — Polar angle from source (rad)
\( \theta_2 \) — Polar angle from sink (rad)

Explanation: The equation combines the stream function for uniform flow with that of a source-sink pair to describe the flow around a Rankine oval.

3. Importance of Stream Function Calculation

Details: Stream functions are fundamental in potential flow theory for analyzing fluid flow patterns, determining streamlines, and solving flow problems around various body shapes in aerodynamics and hydrodynamics.

4. Using the Calculator

Tips: Enter all values in appropriate units. Angles should be in radians. Ensure all input values are valid and within reasonable physical ranges for the specific flow scenario.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rankine oval?
A: A Rankine oval is a theoretical body shape formed by combining uniform flow with a source-sink pair in potential flow theory, resulting in a closed streamline that resembles an oval shape.

Q2: What are the applications of Rankine ovals?
A: Rankine ovals are used in aerodynamics and hydrodynamics to model flow around streamlined bodies, analyze pressure distributions, and study flow separation patterns.

Q3: How does source strength affect the oval shape?
A: Higher source strength increases the size and thickness of the oval body, while the distance between source and sink affects the length-to-width ratio of the oval.

Q4: What are the limitations of this model?
A: The model assumes inviscid, incompressible, irrotational flow and may not accurately represent real fluid behavior, especially near boundaries or in turbulent flow conditions.

Q5: Can this be used for three-dimensional flow analysis?
A: The Rankine oval stream function is primarily for two-dimensional flow. Three-dimensional flow around similar shapes requires more complex modeling approaches.