An experimental study of turbulent two-phase flow in hydraulic jumps and application of a triple decomposition technique

Intense turbulence develops in the two-phase flow region of hydraulic jump, with a broad range of turbulent length and time scales. Detailed air–water flow measurements using intrusive phase-detection probes enabled turbulence characterisation of the bubbly flow, although the phenomenon is not a truly random process because of the existence of low-frequency, pseudo-periodic fluctuating motion in the jump roller. This paper presents new measurements of turbulent properties in hydraulic jumps, including turbulence intensity, longitudinal and transverse integral length and time scales. The results characterised very high turbulent levels and reflected a combination of both fast and slow turbulent components. The respective contributions of the fast and slow motions were quantified using a triple decomposition technique. The decomposition of air–water detection signal revealed ‘‘true’’ turbulent characteristics linked with the fast, microscopic velocity turbulence of hydraulic jumps. The high-frequency turbulence intensities were between 0.5 and 1.5 close to the jump toe, and maximum integral turbulent length scales were found next to the bottom. Both decreased in the flow direction with longitudinal turbulence dissipation. The results highlighted the considerable influence of hydrodynamic instabilities of the flow on the turbulence characterisation. The successful application of triple decomposition technique provided the means for the true turbulence properties of hydraulic jumps. List of symbols C Time-averaged void fraction C Decomposed time-averaged void fraction of average signal component C0 Decomposed time-averaged void fraction of low-frequency signal component C00 Decomposed time-averaged void fraction of high-frequency signal component Cmax Local maximum time-averaged void fraction in the shear flow region c Instantaneous void fraction c Decomposed instantaneous void fraction of average signal component c0 Decomposed instantaneous void fraction of low-frequency signal component c00 Decomposed instantaneous void fraction of high-frequency signal component d1 Inflow water depth immediately upstream of the jump toe (m) d2 Downstream water depth (m) F Bubble count rate (Hz) F Decomposed bubble count rate of average signal component (Hz) F0 Decomposed bubble count rate of lowfrequency signal component (Hz) F00 Decomposed bubble count rate of highfrequency signal component (Hz) Fmax Maximum bubble count rate in the shear flow region (Hz) Electronic supplementary material The online version of this article (doi:10.1007/s00348-014-1775-8) contains supplementary material, which is available to authorized users. H. Wang (&) S. Felder H. Chanson School of Civil Engineering, The University of Queensland, Brisbane, QLD 4072, Australia e-mail: [email protected] Present Address: S. Felder The University of New South Wales, Sydney, NSW 2052, Australia 123 Exp Fluids (2014) 55:1775 DOI 10.1007/s00348-014-1775-8