Lab 05: Schlieren Imaging & Supersonic Wind Tunnels

Lab Overview

• Course: AE 315 – Experimental Aerodynamics, Section 04 (Robert Bryan) | April 18, 2025
• Objective: Operate the ERAU blowdown supersonic wind tunnel, use Schlieren imaging to visualize shock wave formation in the nozzle, and quantify nozzle pressure ratio, shock strength, and mass flow rate from static pressure tap data.
• Tunnel type: Blowdown, air-driven, convergent-divergent (C-D) nozzle; throat area A_th = 0.765 in², nozzle half-angle ≈4.8°
• Instrumentation: 13 static pressure taps at positions 1.5–19.5 inches along nozzle floor, Schlieren optical imaging system
• Tunnel components documented: Air dryer, compressor, storage tank, main valve, pressure regulator, quick-disconnect nozzle, Schlieren system, silencer

Schlieren Imaging & Wind Tunnel Components

Schlieren imaging is an optical technique that visualizes density gradients in a flow field by detecting how light rays refract as they pass through regions of varying refractive index — directly proportional to local density. In a supersonic nozzle, this reveals shocks and expansion fans as sharp bright or dark bands without any physical intrusion into the flow.

The ERAU supersonic tunnel uses a blowdown configuration: compressed air stored in a high-pressure tank is released through a main valve, regulated to a set stagnation pressure, and accelerated through a C-D nozzle. The divergent section expands the flow to supersonic speeds. Pressure taps along the nozzle floor sample the static pressure distribution during the run window, and the Schlieren system captures still images of the test section throughout.

Results & Analysis

• Schlieren images confirmed a clear normal shock wave positioned between tap locations 9.5 and 10.5 inches in the divergent section of the nozzle.
• The static pressure distribution showed a continuous decrease from the throat through the divergent section, followed by a sharp pressure rise at the shock location, then recovery toward back pressure.
• Nozzle Pressure Ratio: NPR = P₀ / P_exit = 3.932 — exceeding the critical NPR, confirming that the nozzle was choked and a shock was present.
• Shock strength: S = P_before / P_after = 1.6142 — classified as a moderately strong shock.
• Mass flow rate: ṁ = 6.1036 lbm/s — computed from throat conditions using the isentropic choked-flow relation.
• All uncertainties were evaluated at a 95% confidence interval using standard deviation of the steady-state pressure data window.

MATLAB Code

Raw pressure data was read from a CSV file, averaged over the steady-state window (rows 1,653–2,103), and augmented with atmospheric pressure. Total pressure was back-calculated from the throat Mach number, and the mass flow rate computed from choked-flow theory. Below is a representative excerpt; the full script is AE315_LAB5.m.

% Constants
Patm = 14.7;       % psi
T0   = 27;         % °C ambient
T    = T0*(9/5) + 491.67;   % → Rankine
y    = 1.4;
R    = 1716;       % ft·lbf/(slug·°R)
Ath  = 0.765;      % throat area (in²)

% Steady-state average + add atmospheric pressure
range_ss  = tempData(1653:2103, :);
dataframe = mean(range_ss) + Patm;    % 13-element vector (psi)

% Back-calculate total pressure from throat tap (Mach 1)
pTotal = dataframe(2);
P0     = pTotal / (1 + (y-1)/2)^(-y/(y-1));

% Nozzle pressure ratio
Pb  = mean(dataframe(11));   % back-pressure tap
NPR = P0 / Pb;               % = 3.932

% Shock strength between taps 9 and 10
shock = dataframe(10) / dataframe(9);  % = 1.6142

% Choked-flow mass rate (lbm/s)
a    = sqrt(y * R * T);
mdot = Ath * (P0/a) * sqrt(y) * ((2/(y+1))^((y+1)/(2*(y-1)))) * 32.174; % = 6.1036