Rearward Mach Angle of Expansion Fan Calculator

Formula Used:

\[ \mu_2 = \arcsin\left(\frac{1}{M_{e2}}\right) \]

Rearward Mach Angle (μ₂):

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1. What is Rearward Mach Angle of Expansion Fan?

The Rearward Mach Angle (μ₂) is the angle formed between the rearward Mach line and the downstream flow direction across an expansion fan in supersonic flow. It represents the direction of propagation of disturbances in the flow field behind the expansion fan.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \mu_2 = \arcsin\left(\frac{1}{M_{e2}}\right) \]

Where:

\( \mu_2 \) — Rearward Mach angle (degrees)
\( M_{e2} \) — Mach number behind expansion fan

Explanation: The arcsine function calculates the angle whose sine equals the reciprocal of the Mach number behind the expansion fan, which defines the Mach angle in the downstream flow region.

3. Importance of Rearward Mach Angle Calculation

Details: Calculating the rearward Mach angle is essential for analyzing supersonic flow fields, designing aerodynamic surfaces, and understanding wave propagation patterns in expansion fans. It helps determine the direction of characteristic lines in method of characteristics calculations.

4. Using the Calculator

Tips: Enter the Mach number behind the expansion fan. The value must be greater than or equal to 1 (supersonic flow). The calculator will compute the corresponding rearward Mach angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of the rearward Mach angle?
A: The rearward Mach angle represents the angle at which disturbances propagate relative to the flow direction in the region behind an expansion fan in supersonic flow.

Q2: Why must the Mach number be ≥1 for this calculation?
A: Mach angles only exist in supersonic flow (M≥1). For subsonic flow, disturbances propagate in all directions and Mach lines don't form.

Q3: How does the rearward Mach angle relate to the forward Mach angle?
A: Both are calculated using the same formula μ = arcsin(1/M), but they represent Mach lines propagating in opposite directions relative to the flow.

Q4: What units are used for the rearward Mach angle?
A: The angle is typically measured in degrees, though radians may be used in some theoretical calculations.

Q5: Can this formula be used for any supersonic Mach number?
A: Yes, the formula is valid for all Mach numbers ≥1, though extremely high Mach numbers will produce very small Mach angles approaching 0°.