Module 3: Velocity Measurement
  Lecture 15: Processing velocity vectors
 

The and terms in the turbulent kinetic energy equation are termed as viscous diffusion and pressure diffusion respectively. The sum of these two terms has been obtained as the residual of the turbulent kinetic energy equation. It should be noted that the viscous diffusion can be expected to be insignificant at intermediate and high Reynolds number. Therefore the residual term is primarily due to the pressure transport.

The individual budget terms of the turbulent kinetic energy equation can be calculated from PIV measurements. It may be assumed that the total kinetic energy is 1.33 times that of that measured from two dimensions. Panigrahi et al., (2005) have validated the above assumptions from an experiment on flow past a rib using 2-component and stereo-PIV.

The dissipation term of the kinetic energy budget equation has been calculated based on the assumption of both local isotropy and axisymmetry. The assumption of local isotropy requires the eight ratios of velocity fluctuations to be equal to unity. Schenck and Jovanovic (2002) reported the eight isotropic ratios to be in the range of 0.4 to 1.7 from hotwire measurements of the plane wake of a circular cylinder and axisymmetric wake of a sphere. The diffusion term in the turbulent kinetic energy equation is calculated using the assumptions: The above assumption has also been justified by Panigrahi et al. (2005) through experiments involving flow past a rib.