Velocity Data (15000 samples) is measured at 50Hz frequency. From these velocity data how can we compute the Turbulent Kinetic Energy Dissipation Rate?
From the definition https://www.cfd-online.com/Wiki/Turbulence_dissipation_rate you see that spatial gradients are required, therefore you need a spatial velocity field.
Dear Lalit,
Particle image velocimetry (PIV) offers a new possibility for turbulence kinetic energy dissipation rate measurements. It can be used for the estimation of the turbulent kinetic energy dissipation rate using its definitions. Dissipation rate definitions include spatial derivatives of the velocity fluctuation components.
https://engineering.purdue.edu/~chen220/doc/publications/Xu13ETFS.pdf
With my best regards
Prof. Bachir ACHOUR
Dear,
I recommend the book of Chassaing et al. « Variable density fluid turbulence« .
you can see the chapter devoted for deriving the equations of TKE transport. It is interesting if the density is varying in your problem. You can check the time-averaged terms required to accumulate during the the simulatio...
Dear Lalit,
the definition given by @Filippo Maria Denaro is correct, but, since I assume you do not have the spatial distributions that you'd need to use this approach, you might calculate the turbulence dissipation rate through the turbulence spectrum, as correctly pointed out by @Sandeep Jella.
However, you need to pay attention to your acquisition frequency and in particular be sure that you are capturing the smallest scales (Kolmogorov scales) in your flow. Otherwise you risk to severely underestimate the turbulent dissipation rate.
Tiziano, you are correct but we don't know if the problem studied by Lalit allows to transform the temporal spectra (as you stated, provided that the measurement is able to acquire all the dissipative frequencies) in the spatial counterpart. and the more general ergodicity property is valid
1. In the best scenario: you are measuring grid turbulence (isotropic turbulence) with a mean velocity, and 50Hz is more than sufficient to resolve the smallest time scales, you can esitimiate the dissipation using Taylor's frozzen hypothesis.
2. In the worst scenario: anisotropy is dominant, 50Hz is not enough to resolve the smallest time scales, you may not be able to estimate the dissipation.
3. Unless you are studying very low Reynolds number turbulence, 50Hz is a bit too small in my opinion.
In my opinion, answer by @Xingjun_Fang is more appropriate for the posted question.
TKE can be produced by fluid shear, friction or buoyancy, or through external forcing at low-frequency eddy scales. Turbulence kinetic energy is then transferred down the turbulence energy cascade, and is dissipated by viscous forces at the Kolmogorov scale . The technique uses the second-order structure function and Kolmogorov’s law for inertial subrange.
This topic is strictly related to the calculation of energy dissipation (and hence entropy generation) in turbulent flows from numerical simulations. We have come across a number of papers that estimate entropy generation by post-processing averaged or filtered simulations, forgetting that not all of the energy dissipation is resolved in their simulation. The result is that most of the entropy generation is left out from the calculation, especially in situations where the production of turbulent kinetic energy is large (high reynolds number flows, separated flows). This often leads to unphysical results (such as a decrease in entropy generation at incidence angles).
This paper tries to put some order in this topic, also through a comparison between entropy generation and drag (two quantities that are generated by the same mechanisms and hence should correlate somehow):
Article Numerical Evaluation of Entropy Generation in Isolated Airfo...
Turbulent kinetic energy (tke) dissipation will be the difference between its production and the sum of tke turbulence transport and dk/dt. tke production and turbulence transport could be usually estimated by assumed functions (refer to famous Spalding/Launder work). More recent work refer below and other similar papers. k in dk/dt is time differentiated tke, which is equal to 1/2*((u')^2+(v')^2+(w')^2). u', v', w' being the fluctuation of velocity in 3D. Remember that in your handling your velocity data to find out u', v' and w', they have to be time-averaged.
Pu J. H., 2015, Turbulence Modelling of Shallow Water Flows using Kolmogorov Approach, Computers and Fluids, 115, pp. 66-74.
Dear Jaan H Pu , I don't think we are saying quite the same thing. My comment was on the fact that if you use time averaged, or filtered data, to get turbulent energy production, dissipation or any other function, you need to have a model for the quantity that comes from the scales that are not resolved. In other words, the contribution of the mean flow is minimal, and if you "forget" to account for the part that is not resolved, you make a big underestimation. Unfortunately, this omission has been often made in scientific papers, leading to some unphysical results in important journals. This is what our paper discusses. I suggest you a quick read:
Article Numerical Evaluation of Entropy Generation in Isolated Airfo...
one of the few exact theorems of turbulence is the Kolmogorov 4/5-law. From this law, it is straightforward to obtain the averaged TKE dissipation rate.
Ferraro, D., Servidio, S., Carbone, V., Dey, S., & Gaudio, R. (2016). Turbulence laws in natural bed flows. Journal of Fluid Mechanics, 798, 540-571.
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