Experiments in Fluids

, 46:499 | Cite as

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

  • J. de Jong
  • L. Cao
  • S. H. Woodward
  • J. P. L. C. Salazar
  • L. R. Collins
  • H. Meng
Research Article


Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Reλ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.

List of symbols


constant, from the scaling argument method


spatial spectral-filtering function


first Kolmogorov constant


second Kolmogorov constant


third Kolmogorov constant


Smagorinsky constant


longitudinal velocity structure function of order n


second-order longitudinal velocity structure function


third-order longitudinal velocity structure function


second-order transverse velocity structure function


three-dimensional energy spectrum


one-dimensional energy spectrum


large eddy length scale


longitudinal integral length scale


number of points for the Fourier transform of the velocity vector field


Taylor microscale Reynolds number


large eddy time scale


longitudinal velocity spatial correlation function


height of PIV interrogation volume


turbulent kinetic energy


three-dimensional direction vector


velocity vector separation in xi direction

\( \underline{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{r} }} \)

unit vector in the r direction


inertial range velocity vector separation in xi direction


fluctuating rate-of-strain tensor

\( \tilde{s}_{ij} \)

filtered fluctuating rate-of-strain tensor


Kolmogorov time scale


instantaneous velocity vector at a point


instantaneous velocity vector at a point in the xi direction


root mean square of the velocity fluctuations

\( u_{i}^{\prime } \)

root mean square of the velocity fluctuations in the xi direction

\( \tilde{u}_{i} \)

filtered root mean square of the velocity fluctuations in the xi direction

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u}_{j} \)

Fourier transform of the velocity vector field

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u}_{j}^{*} \)

complex conjugate Fourier transform of the velocity vector field


Kolmogorov velocity scale


width of PIV interrogation volume


three-dimensional position vector


separation between PIV vectors


“window” size over which velocity field is spatial averaged


three-dimensional velocity spectrum tensor


proportionality constant for the Lin spectrum


turbulent kinetic energy dissipation rate


Kolmogorov length scale


wavenumber vector


magnitude of wavenumber vector


wavenumber in xi direction

κi, IR

inertial subrange wavenumbers in xi direction


separation between wavenumbers


kinematic viscosity


depth of PIV interrogation volume


subgrid Reynolds stress



This work was supported by the NASA Microgravity Fluid Physics Program grants NNCO5GA45G and NNCO5GA37G, by the National Science Foundation through grants CTS-0112514 and PHY-0554675, and by the New York State Office of Science, Technology and Academic Research (NYSTAR) under contract number 3538479. J.P.L.C. Salazar acknowledges support from the Brazilian Ministry of Education through the CAPES agency.


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • J. de Jong
    • 1
  • L. Cao
    • 1
  • S. H. Woodward
    • 1
  • J. P. L. C. Salazar
    • 2
  • L. R. Collins
    • 2
  • H. Meng
    • 1
  1. 1.Mechanical and Aerospace Engineering DepartmentUniversity of BuffaloBuffaloUSA
  2. 2.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA

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