Aerospace & Aeronautical Engineering / Schlieren Optical Imaging
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LABORATORY 15 · AEROSPACE & AERONAUTICAL ENGINEERING

Supersonic Wind Tunnel Calibration and Schlieren Optical Density Imaging

Calibrate supersonic test-section Mach number using static-to-stagnation pressure ratios and visualize compressible flow density gradients using Toepler Schlieren optics. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

MACH NUMBER SQUARED M^2—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with x = 0.3 dimensionless.

0.3 dimensionless
Parabolic mirror diameter: 200 mm

Adjust x, 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

Schlieren images represent an integrated optical path across the entire test section width (spanwise integration). Linear regression of M^2 against (P_0/P)^(2/7) - 1 yields an isentropic parameter slope of 5.0000 matching gamma = 1.40 with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Z-Type Schlieren Optical Test Rig

Twin 200 mm diameter parabolic mirrors (f = 2.0 m) with optical vibration isolation breadboard.

Adjustable Micrometer Razor Knife-Edge

Cut-off knife edge mounted on 3-axis micro-positioner to control optical contrast and sensitivity.

High-Power LED Pulsed Light Source

Uniform 100 W point LED light source with condenser lens and adjustable aperture slit.

Supersonic Calibration Pitot-Static Probe

Measures center-stream stagnation total pressure P_0 and local static pressure P.

Digital High-Speed CCD Imaging Camera

Records 12-bit grayscale Schlieren images of shock waves and expansion fans at 2000 fps.

Supersonic Variable-Mach Blowdown Tunnel

Delivers test airspeeds from Mach M = 1.4 to 3.0 with dry compressed air reservoir.

FOLLOW THE METHOD

A reason behind every step.

Calibrate supersonic test-section Mach number using static-to-stagnation pressure ratios and visualize compressible flow density gradients using Toepler Schlieren optics. Standardized parameter settings: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 dimensionless.

01

Optical Alignment and Collimation

Align parabolic mirrors and light source to collimate light parallel through the test section and focus onto knife-edge.

02

Knife-Edge Cut-Off Setting

Adjust the horizontal knife-edge to block approximately 50% of the focused focal spot, establishing a neutral grey background.

03

Wind Tunnel Starting and Flow Verification

Start supersonic blowdown, verifying nozzle starting via Schlieren imagery as the starting shock train sweeps out of the test section.

04

Centerline Pressure Acquisition

Sample static pressure P and stagnation pressure P_0 across nozzle area settings corresponding to parameter x = 0.10 to 0.60.

05

Mach Angle Optical Cross-Check

Measure the shock angle beta of a 5-degree reference needle wedge on Schlieren imagery to cross-check probe-derived Mach numbers.

06

Isentropic Compressibility Regression

Plot M^2 against (P_0/P)^(2/7) - 1, perform linear regression to extract slope 2/(gamma-1), and verify gamma = 1.40 for air.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Schlieren Optical Imaging mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
M^2 = \frac{2}{\gamma - 1} \left[\left(\frac{P_0}{P}\right)^{\frac{\gamma-1}{\gamma}} - 1\right] \implies M^2 = m \cdot x + b
#Pressure Ratio Parameter (dimensionless)Mach Number Squared M^2 (dimensionless)Isentropic Pressure Parameter (P_0/P)^(2/7) - 1Test-Section Mach Number Squared M^2Remove

No readings yet. Execute an aerodynamic trial and record it.

Calculate it yourself.

CHECK YOUR UNDERSTANDING

Explain what the aerodynamic metrics mean.

What physical quantity does a standard Toepler Schlieren optical system visualize directly?

For air with specific heat ratio gamma = 1.4, what is the theoretical isentropic slope 2 / (gamma - 1)?

What is the purpose of the knife-edge placed at the focal point in a Schlieren apparatus?

If an acoustic Mach wave on a Schlieren image is inclined at an angle mu = 30 degrees to the flow, what is the local Mach number?