Supersonic Corner Expansion Test Duct
Optical supersonic channel with interchangeable convex corner blocks from theta = 3.0 to 18.0 degrees.
Aerospace & Aeronautical Engineering / Prandtl-Meyer Expansion Fan
FREE TO EXPLORELABORATORY 14 · AEROSPACE & AERONAUTICAL ENGINEERING
Prandtl-Meyer Centered Expansion Waves and Convex Corner Flow
Map Mach number increase and static pressure drop across a sharp convex expansion corner to evaluate the Prandtl-Meyer function nu(M). Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.
AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS
Your virtual aerospace engineering laboratory.
MACH INCREMENT DELTA M—
FLIGHT & TEST CELL TELEMETRY
Ready to sample with theta = 6.0 deg.
Adjust theta, then execute aerospace trial.
Aeronautical telemetry and flight states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity aerodynamic modeling.
Aeronautical assumptions and boundary condition limits
Convex corner curvature creates a localized boundary layer thinning and favorable pressure gradient that can laminarize turbulent flow. Linear regression of the Mach increment against convex turn angle yields an expansion gradient of 0.0520 deg^-1 with R^2 > 0.999999.
Aeronautical apparatus & wind tunnel sensors.
Supersonic Blowdown Air Supply
Delivers dry, heated air at stable stagnation pressure P_0 = 350 kPa and M_1 = 1.80.
Downstream Static Pressure Tap Array
Precision static taps spaced 5 mm apart along the expanded wall downstream of the corner apex.
Multi-Channel Electronic Manometer Scanner
Samples wall static pressures P_2 with 16-bit A/D resolution and temperature compensation.
Toepler Schlieren Optical System
Visualizes the leading Mach wave, centered fan rays, and trailing Mach wave of the expansion fan.
Prandtl-Meyer Data Processing Workstation
Converts static-to-total pressure ratios into local Mach numbers and evaluates the nu(M) function.
FOLLOW THE METHOD
A reason behind every step.
Map Mach number increase and static pressure drop across a sharp convex expansion corner to evaluate the Prandtl-Meyer function nu(M). Standardized parameter settings: 3.0, 6.0, 9.0, 12.0, 15.0, 18.0 deg.
01
Corner Model Alignment
Install the theta = 3.0 degree convex corner model into the optical test section, aligning the upstream floor with the nozzle exit.
02
Schlieren Wave Verification
Initiate supersonic blowdown at M_1 = 1.80, verifying through Schlieren optics that the leading expansion wave is inclined at mu_1 = arcsin(1/1.80) = 33.75 deg.
03
Upstream Baseline Acquisition
Record upstream reference static pressure P_1 and stagnation pressure P_01 ahead of the expansion corner.
04
Downstream Pressure Mapping
Acquire downstream wall static pressures P_2 at fully expanded stations for convex angles theta = 3.0, 6.0, 9.0, 12.0, 15.0, and 18.0 degrees.
05
Mach Number Computation
Compute downstream Mach number M_2 using the isentropic relation: M_2 = sqrt(5 * [(P_01/P_2)^(2/7) - 1]) and compute Delta M = M_2 - M_1.
06
Prandtl-Meyer Linear Regression
Plot Delta M versus theta, perform linear regression to determine the expansion rate dM / dtheta, and compare with the theoretical Prandtl-Meyer derivative.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into aerodynamic insight.
Points are your recorded observations. The solid regression line validates Prandtl-Meyer Expansion Fan mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
\Delta M = (M_2 - M_1) \approx m \cdot \theta_{\text{deg}} + b
| # | Convex Turn Angle theta (deg) | Mach Increment Delta M (dimensionless) | Convex Wall Turn Angle theta (deg) | Downstream Mach Increment Delta M = M_2 - M_1 | Remove |
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