Lab 02: Flow Around Cylinders

Lab Overview

• Course: AE 315 – Experimental Aerodynamics, Section 04 (Robert Bryan) | February 27, 2025
• Objective: Measure surface pressure distributions around a cylinder at two flow velocities, compute Cp, Cd, and drag force, and compare results to potential flow theory.
• Model: Circular cylinder, d = 1.4 in (0.03556 m), with a single static pressure port rotated through 24 angular positions (0°–180°)
• Ambient conditions: T = 24°C (297.15 K), P = 30.4 inHg (102,946.2 Pa), ρ = 1.207 kg/m³
• Test velocities: 10 m/s (Re ≈ 23,515) and 15 m/s (Re ≈ 35,272)

Procedure & Methodology

Ambient temperature and pressure were recorded before each run to establish air density. The cylinder's static pressure port was positioned at 24 discrete angles from 0° to 180°, and differential pressure data was collected at both 10 m/s and 15 m/s. Dynamic pressure was computed by subtracting ambient pressure from the total pressure reading, then the coefficient of pressure was calculated as C_p(actual) = P_dyn / (0.5 ρ V²).

The theoretical potential flow coefficient of pressure was computed as C_p(potential) = 1 − 4sin²(θ) for comparison. The drag coefficient was then obtained by numerically integrating the pressure distribution using MATLAB's trapz function: C_d = ∫ C_p cosθ dθ. Finally, drag force was computed as D = 0.5 ρ V² A C_d, where A is the frontal area of the cylinder.

Velocity and Cp uncertainties were propagated through partial derivatives of the governing equations, incorporating uncertainties in dynamic pressure, atmospheric pressure, and temperature.

Results & Analysis

• Both test velocities produced subcritical flow (Re < 300,000); no drag crisis was observed.
• At lower angles (<40°), experimental Cp agreed closely with potential flow theory near the stagnation point.
• Past ≈40°, actual Cp deviated significantly from potential flow as boundary layer separation occurred, creating a turbulent wake.
• At 15 m/s, flow remained attached to the cylinder longer than at 10 m/s — consistent with higher Re delaying separation.
• Cd = 1.3055 at 10 m/s (uncertainty: ±0.0043)
• Cd = 1.4239 at 15 m/s (uncertainty: ±0.0051)
• Drag force increased with velocity, confirming that drag scales with V². Deviations from the theoretical C_d vs Re curve are attributed to surface roughness and measurement error.

MATLAB Code

Pressure data was loaded from 24 .mat files per velocity, converted to Pa, and processed to extract Cp and Cd. Below is a representative excerpt; the full script is AE315_LAB2.m.

% Load and process data for 10 m/s and 15 m/s
for i = 1:filecount
  file_10ms = load(sprintf('LAB2_DATA/10ms/Experiment2_10ms_%d.mat', i));
  dp_10ms(i)       = mean(file_10ms.dp) * 248.84;  % inH2O → Pa
  currAngle_10ms(i) = file_10ms.currAngle;
  v_1 = 10;
  Cp_10ms(i) = (dp_10ms(i)) / (0.5 * density * v_1^2) + 1;  % dp relative to freestream total; +1 normalises to Cp scale
end

% Potential flow Cp for comparison
Cp_potential = 1 - 4 .* sind(currAngle_10ms(2:24)).^2;

% Drag coefficient via trapezoidal integration
theta    = deg2rad(currAngle_10ms(2:23));
freq_10  = Cp_10ms(2:23) .* cos(theta);
Cd_10    = trapz(theta, freq_10);   % = 1.3055

% Drag force
DF_10 = 0.5 * density * v_1^2 * Cd_10 * diameter;  % drag force (N)