What Is the Prandtl-Meyer Supersonic Expansion Fan Calculator?
A Prandtl-Meyer expansion fan is an isentropic centered expansion process in supersonic gas dynamics.
Unlike compression shocks, expansion waves accelerate supersonic gas while maintaining total pressure and total temperature.
How Does the Prandtl-Meyer Supersonic Expansion Fan Calculator Work?
The upstream Prandtl-Meyer angle nu(M1) is evaluated.
Adding corner deflection angle theta gives the downstream Prandtl-Meyer angle nu(M2).
The downstream Mach number M2 is iteratively inverted from nu(M2) using Newton-Raphson method.
Isentropic relations compute static pressure and temperature drops.
Prandtl-Meyer Supersonic Expansion Fan Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Prandtl-Meyer function relates supersonic Mach number to the cumulative isentropic turning angle.
How to Use the Prandtl-Meyer Supersonic Expansion Fan Calculator
- Enter upstream Mach number (strictly greater than 1.0).
- Enter the convex turn angle in degrees.
- Set the specific heat ratio gamma (default 1.4 for air).
Step-by-Step Example Calculation
Supersonic Airfoil Expansion
Input Values:
Understanding Your Result
Mach number increases downstream (M2 > M1).
Static pressure and static temperature drop significantly across the expansion fan.
Total pressure is preserved since the flow is completely isentropic (entropy change = 0).
Factors That Affect the Result
- Specific heat ratio: Monatomic gases (gamma=1.67) expand with different Mach gradients than air.
- Turn angle: Larger turns produce higher exit Mach numbers and lower static pressures.
When Should You Use This Calculator?
- Designing supersonic aircraft cowlings, diamond and biconvex airfoils.
- Analyzing rocket nozzle bell expansions and scramjet inlets.
Assumptions & Limitations
- Assumes steady, two-dimensional, inviscid, calorically perfect gas flow.
- Only valid for convex turns without flow detachment or boundary layer separation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Iterative solution converges to 1e-7 relative tolerance on Mach number.