2 nd UK-JAPAN Bilateral and 1 st ERCOFTAC Workshop, Imperial College London

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  Multi-scale generated turbulence may lead to exciting new insights into turbulence theory as well as important new industrial applications: Turbulence generated by injecting energy over a range of length scales; Uncommon fast turbulence kinetic energy decay, well modeled by a self-preserving single lengthscale decay model (George and Wang, POF, 2009); About three times higher Reynolds number Re λ than turbulence generated by classical grids.  PIV can be a useful tool to obtain a better understanding of the fluid dynamics of fractal-generated turbulence.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  Despite of the geometrical complexity, the grid features are defined by a few parameters: L o an t o, i.e. length and thickness of the largest square; R L and R t, i.e. the scaling factors for the length and the thickness at each iteration (more often the thickness ratio t r between the largest and the smallest scale is considered as a main parameter). trtr RLRL RtRt σM eff [mm]

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge The grids are tested in a low turbulence level open circuit wind tunnel, with a 1,524mm long and 152.4mm wide square test section. The fractal grid is placed at the inlet of the test section, immediately after the contraction.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge The grids are tested in a low turbulence level open circuit wind tunnel, with a 1,524mm long and 152.4mm wide square test section. The fractal grid is placed at the inlet of the test section, immediately after the contraction. 385mm 600mm Measurement area ≈50mm

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Fig. from Raffel et al., Particle Image Velocimetry – A practical guide, Springer Ed. (2007)

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Optical calibration: Images of a target with equally spaced dots with diameter of 250μm and spacing of 1mm are recorded to determine the magnification map as a function of the physical space coordinates; Images of the particle distributions are taken simultaneously by two cameras in a pre-processing run to determine via disparity map computation the location of the laser sheet in the physical space to properly set the local magnification. Image acquisition (5000 samples to ensure satisfactorily statistical convergence) Image Processing IW: 32 x 32 pixels (0.63 x 0.63 mm  comparable to the laser sheet thickness) with 75% overlap; Multi-pass iterative window deformation with adoption of weighting windows in cross-correlation to enhance the spatial resolution.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge U [m/s] Mean streamwise velocity for t r =13 and Re M =3.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Mean streamwise velocity for t r =13 and Re M =3.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge tr =13 Re M =3.5∙10 3 u 2 [m 2 /s 2 ] v 2 [m 2 /s 2 ]

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge tr =13 Re M =3.5∙10 3 u 2 / v 2

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 The longitudinal correlation function changes only slightly moving downstream, suggesting that the integral lengthscale increases with the streamwise coordinate. However, the narrow field of view does not enable to estimate it with good confidence.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 x/x*=0.47 This is not equivalent to the longitudinal two-point correlation function (the velocity component is always the streamwise one).

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 x/x*=0.47 This is not equivalent to the transverse two-point correlation function (the velocity component is always the crosswise one).

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 x/x*=0.47 This is not equivalent to the longitudinal 2 nd order structure function (the velocity component is always the streamwise one).

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 x/x*=0.47 This is not equivalent to the transverse 2 nd order structure function (the velocity component is always the crosswise one).

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Space filling square fractal grids are characterized by an unusually fast decay: is it governed by an exponential law or a power law? t r =13 Re M =11.5∙10 3 B=0.526C=0.262 R 2 =0.91 B=-0.481C=-3.90 R 2 =0.91

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Exponential decay trtr BCR2R trtr BCR2R Re M =3.5∙10 3 Re M =11.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Re M =3.5∙10 3 Re M =11.5∙10 3 Power-law decay trtr BCR2R trtr BCR2R

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Re M =11.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge Re M =11.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  It is not possible to conclude if the decay law is exponential or a power law by visual inspection or using the correlation factor of the fitting law;  More confidence in specifying the decay law can be obtained by increasing the measurement area in the streamwise direction;  Even if the decay was not exponential, it is still governed by a power law with an unusually high exponent!

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  W.K. George (Physics of Fluids, 1992) showed that single length scale power law solutions of the spectral equations for the decay of isotropic turbulence is possible;  W.K. George and H. Wang (Physics of Fluids, 2009) proposed a viscous solution (exponential decay) and an inviscid one (power law decay);  An important feature is that the turbulent statistics collapse if normalized with respect u 2 and λ T.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r = 13X = 385 mm

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  DIRECT METHOD:  INDIRECT METHOD:

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  DIRECT METHOD: Very simple and straightforward application; The noise effects are amplified by the derivative operator; The data need to be filtered: the choice of the filter intensity is critical.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  INDIRECT METHOD: The peak of the two-point correlation is fitted with a parabolic function:

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  INDIRECT METHOD: The peak of the two-point correlation is fitted with a parabolic function:

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  INDIRECT METHOD: According to Adrian and Westerweel (2011):

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  INDIRECT METHOD: According to Adrian and Westerweel (2011): At least the first 3 measurement points have to be excluded in the fitting, since we are using interrogation windows with 75% overlap.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge A least square fitting may lead to a more accurate estimate of both the Taylor lengthscale and the turbulent fluctuations; A Signal to Noise criterion can be introduced by considering the ratio of the estimate peak of the two-point correlation, and the one obtained by best fitting of the peak.  INDIRECT METHOD:

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

Direct methodIndirect method t r =13 Re M =3.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3 t r =13 Re M =11.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  DIRECT METHOD:  ENERGY BALANCE: One can use the relations of the power law and exponential decay.  INDIRECT METHOD: One can use the Taylor lengthscale estimated with the indirect method.

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge t r =13 Re M =3.5∙10 3

S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge  PIV performances are assessed for measurements in nearly isotropic and homogeneous low-intensity turbulence; the results are in close agreement with the literature;  PIV complements pointwise measurement techniques by its capability of detecting inhomogeneity and anisotropy;  The results confirm the presence of a single lengthscale decay; it is not possible to conclude on the nature of the decay;  Fitting of the peak of the two-point correlation enables a more accurate estimate of the Taylor length scale and of the dissipation;  Three dimensional measurements (Tomo-PIV) are planned to get a better understanding of the underlying dynamics (QR pdf, dissipation, etc.).