Flow Deflection Angle Due To Expansion Wave Calculator

Flow Deflection Angle Formula:

\[ \theta_e = \sqrt{\frac{\gamma_e+1}{\gamma_e-1}} \cdot \tan^{-1}\left(\sqrt{\frac{(\gamma_e-1)(M_{e2}^2-1)}{\gamma_e+1}}\right) - \tan^{-1}\left(\sqrt{M_{e2}^2-1}\right) - \left[ \sqrt{\frac{\gamma_e+1}{\gamma_e-1}} \cdot \tan^{-1}\left(\sqrt{\frac{(\gamma_e-1)(M_{e1}^2-1)}{\gamma_e+1}}\right) - \tan^{-1}\left(\sqrt{M_{e1}^2-1}\right) \right] \]

Flow Deflection Angle (θe):

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1. What is Flow Deflection Angle Due To Expansion Wave?

The Flow Deflection Angle Due To Expansion Wave represents the angle by which a flow turns when passing through an expansion wave in supersonic flow. It's a fundamental concept in gas dynamics and compressible flow theory.

2. How Does the Calculator Work?

The calculator uses the expansion wave deflection angle formula:

Where:

\( \theta_e \) — Flow Deflection Angle (degrees)
\( \gamma_e \) — Specific Heat Ratio Expansion Wave
\( M_{e1} \) — Mach Number Ahead of Expansion Fan
\( M_{e2} \) — Mach Number Behind Expansion Fan

Explanation: This formula calculates the turning angle of flow through an expansion fan based on the specific heat ratio and Mach numbers before and after the expansion.

3. Importance of Flow Deflection Angle Calculation

Details: Accurate calculation of flow deflection angles is crucial for designing supersonic nozzles, analyzing flow around corners in supersonic flow, and understanding expansion wave behavior in various aerospace applications.

4. Using the Calculator

Tips: Enter the specific heat ratio (typically 1.4 for air), Mach number ahead of expansion fan, and Mach number behind expansion fan. All values must be greater than 1 for supersonic flow conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for specific heat ratio?
A: For most gases, specific heat ratio ranges from 1.3 to 1.67. For air at standard conditions, it's approximately 1.4.

Q2: Why must Mach numbers be greater than 1?
A: Expansion waves only occur in supersonic flow, so both upstream and downstream Mach numbers must be supersonic (greater than 1).

Q3: What are practical applications of this calculation?
A: This calculation is used in designing supersonic aircraft nozzles, analyzing flow in wind tunnels, and studying supersonic flow around obstacles.

Q4: How accurate is this formula?
A: The formula provides exact solutions for ideal gas flow through expansion waves and is widely used in compressible flow analysis.

Q5: Can this be used for subsonic flow?
A: No, expansion waves and this specific formula only apply to supersonic flow conditions where Mach numbers exceed 1.