I am estimating the dissipation rate from (du'/dt), estimated at each time using the central differencing scheme. Some authors especially Prof. Mi (ref: Meas.Sci.Technol. 22 (2011)) have used spectral like stencil to calculate (du'/dt) from (u',t) data.Can anyone give me an idea of setting the matrix for this procedure. I tried forming a pentadiagonal matrix (A) (with the coefficients of gradient terms) in the right hand side, [A] [Grad]=[u']; This matrix is very sensitive to the boundary conditions and shows very large values compared to central differencing. How can I resolve this?
The rate of Entropy production is determined within Irreversible thermodynamics as
E = Ja Xa + Jb Xb +......, where Ji is the flux and Xi is the generalised force. In the case of fluid mecanics the rate of entropy production (dissipation) within the tube is given as E = Q (P1 - P2), where Q is volumetric flow rate, (P1 - P2) is the pressure difference at the inlet and outlet. The formula is strong for any flow, laminar and turbulent, accounts for cavitation as well if that is present.
Dear Sir,
I am working in round free jet. Yes Taylor's frozen flow approach is valid, my turbulent intensity is within the validity limits.
In case of the frozen turbulence your du'/dt and mean flow velocity give you du'/dx. After that If you can assume 3D isotropy, dissipation rate definition collapses to 15nu(du'/dx)^2. See Doron et al 2001 in JPO for details. There is also another method you can use that would involve construction of "structure functions", sorry don't remember the reference.
Dear sir,
I have already calculated Reynolds number based on Taylor's scale, it is small but the accurate calculation of Taylor's scale it self is a question. What I want to know is how to apply spectral like stencil to find the gradient du'/dt more accurately without any additionally instrumentations.
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