Find/Calculate displacement thickness from a velocity profile

Manosd25 · July 27, 2023, 13:35

Hi!

This post is part of a question that I have posted here but remained unanswered (Extracting flow parameters from measured velocity profiles in wind tunnel)

I have some data simulating different types of ABL in a wind tunnel. The data are basically different velocities (u) at different height levels of the wind tunnel (y), with also known parameters to have the kinematic viscosity (v) and von Karman constant (κ).

How I could find the displacement thickness δ* for every velocity profile?

Thank you!

LuckyTran · July 27, 2023, 14:13

You just numerically integrate the formula you claim you know.

If it helps, make plots of U vs y and U^2 vs y. Find the areas under each curve. The area under U vs y is related to displacement thickness and U^2 is related to momentum thickness.

Also you can just bump your own thread next time.

Manosd25 · July 27, 2023, 14:19

So by using the trapezoidal rule I could compute delta star by that?

delta_y = y(2:end) - y(1:end-1); % Height increment
u_mid = (u(1:end-1) + u(2:end)) / 2; % Midpoint velocities
delta_star = sum((1 - u_mid / U_inf) .* delta_z); % Displacement thickness

July 27, 2023, 13:35	Find/Calculate displacement thickness from a velocity profile	#1
Manosd25 New Member Manos Dimitriadis Join Date: May 2023 Posts: 20 Rep Power: 3	Hi! This post is part of a question that I have posted here but remained unanswered (Extracting flow parameters from measured velocity profiles in wind tunnel) I have some data simulating different types of ABL in a wind tunnel. The data are basically different velocities (u) at different height levels of the wind tunnel (y), with also known parameters to have the kinematic viscosity (v) and von Karman constant (κ). How I could find the displacement thickness δ* for every velocity profile? Thank you!

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July 27, 2023, 14:13		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,761 Rep Power: 66	You just numerically integrate the formula you claim you know. If it helps, make plots of U vs y and U^2 vs y. Find the areas under each curve. The area under U vs y is related to displacement thickness and U^2 is related to momentum thickness. Also you can just bump your own thread next time.

July 27, 2023, 14:19		#3
Manosd25 New Member Manos Dimitriadis Join Date: May 2023 Posts: 20 Rep Power: 3	So by using the trapezoidal rule I could compute delta star by that? delta_y = y(2:end) - y(1:end-1); % Height increment u_mid = (u(1:end-1) + u(2:end)) / 2; % Midpoint velocities delta_star = sum((1 - u_mid / U_inf) .* delta_z); % Displacement thickness