How to calculate the turbulence velocities along three axes (x, y, z) of an airplane? The effect of turbulence is considered as disturbance to the system model. I am trying to estimate the turbulence velocities using Dryden wind model which contains power spectral density functions (There are three equations). I would like to generate the wind velocity components (u, v, w) in the body frame. Could you please tell me how to generate the wind velocity components using dryden spectral equations?
Are you looking for that?
https://www.mathworks.com/help/aeroblks/drydenwindturbulencemodelcontinuous.html
Maybe you get some key information about turbulence velocities from this paper.
Article A measuring method for three-dimensional turbulent velocitie...
There are several ways to define the turbulent velocities, but the most basic method is to make ensemble average of each the instantaneous values obtained for a certain time duration, say, one minute.
However, unfortunately we have no flow meter to measure the instantaneous velocity accurately, so such a flow meter is eagerly wanted by the fluid dynamists in the world.. Currently, we are trying to develop a novel flow meter to measure the instantaneous velocity vector accurately. We hope that this is completed very soon.
Power Spectrum Density can be described using two parameters (the dissipation rate and viscocity of the fluid). To go from dissipation to turbulent energy k (thus to rms of velocity) you need another scale and for instance a lenth scale (the integral lenth scale for example Ls) with can be related to the width of the boundary layer on the body. the dissipation can be estimates as (k**(3/2))/Ls which gives (k) and rms of velocity
See:
Chapter SMTF-Chapitre 2 : Les échelles de la turbulence
The proposed question, "How to estimate turbulent velocities ?" is indeed a critical question on turbulence research, so it is necessary to answer it. However, I should comment this question in brief here: There are several methods to define a turbulence velocity currently, but I will introduce only one that it seems to me the most appropriate in a concrete manner.: 1. Measure turbulent velocities for a specified time duration continuously, say for 5 seconds, 2. Determine the instantaneous velocity at each 1 second interval, and obtain 5 different velocities, and finally 3. Calculate the mean velocity of these 5 velocities, and this mean velocity is considered to be a turbulent velocity.
I think that the proposed averaged velocity can be one of the turbulence velocities. But, at this stage, I leave my discussion on this problem, and wait for others ' contradictory comments against the present definition of turbulent velocity.
This is to comment on the reply by Dr. Nakagawa,
If I have well understood Dr. Parabhu, he is seeking to estimate the turbulence velocities from power spectral density. How to do it ? My answer tried to respond to this question.
Dear Jamel,
I believe that "to estimate turbulent velocities from the power spectral density" is to make a detour to obtain the turbulent velocities. Because without knowing turbulent velocities, we might not to get the power spectral density.
In brief, I recommend you that you estimate turbulent velocities directly by measuring the instantaneous velocity vectors in the flow.
Dear Colleague Nakagawa,
This is true of course!
But, apart from the experimental conditions which produced the power spectrum density (not mentioned by colleague Parabhu), the question as I understood it (maybe colleague Prabhu can specify on this) is: if I have a representation of a energy spectral density (regardless to from it comes), how I can estimate the rms of the velocity? Otherwise, the question does not arise: if we have the fluctuating signal of the velocity field, it suffices in this case, as you explained it well, to determine the standard deviation of the signal
The question is clear, provided you have a certain spectral content, how to reconstruct a velocity signal? For example, that is a technique ofte used to reproduce the initial conditions in homogeneous isotropic turbulence.
Dear colleagues, Thanks for sharing your opinions. Actually I want to derive the turbulence velocities and to plot the three velocity components of turbulence (say u, v, w) using real flight data. In my state estimation problem, turbulence is considered as a disturbance (noise/uncertainty) just to show whether my filtering algorithm is performing well even in the presence of external disturbance (turbulence). This is what my objective. I have the Dryden spectra equations of translational velocities. I just want to know how to derive these translational velocity components using the Dryden equations. Could anyone share your idea please???
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