Hydraulic jump is a canonical complex two-phase flow problem, which is usually characterized by strong turbulence production and significant air entrainment. It is hard for experimental measurement to obtain the flow details in the gas-liquid mixture region due to intense splash droplets and entrapped bubbles. In this paper, we perform the direct numerical simulation of two-dimensional hydraulic jump. Adaptive mesh refinement technique is adopted to achieve a high grid resolution near interface. Time-averaged interface flow patterns have shown a good agreement with experimental measurement. Air entrainment mechanisms as well as energy transfer process are analyzed to gain a more comprehensive understanding of complex interface flow structures evolution in a hydraulic jump and the effect of Froude number are also discussed.


Hydraulic jumps are common phenomenon which can be observed in natural streams, open channel or man-made water conveyance systems. In general, a hydraulic jump occurs due to the sudden transition from flow with high velocity to slowly varied flow, resulting in an obvious increase in the depth of flow. Hydraulic jumps are often accompanied by strong turbulence, considerable energy dissipation and flow structures with a broad range of length scale (Xiang, et al., 2014). The typical recirculation region in hydraulic jumps are characterized by both air pockets within water and liquid droplets surrounded by air. There are also spray jets and foam laden with enormous micro-bubbles near the hydraulic jump toe. It is difficult to obtain quantitative details of flow field and bubble size distributions from laboratory experiments.

There have been extensive experimental studies on hydraulic jump, various aspects relating to turbulence production and air entrainment are the main focus of investigations. High-speed photography (Long, et al., 1991), micro acoustic Doppler velocimetry (MicroADV) (Liu, et al. 2004), particle image velocimetry technique(PIV) (Misra, et al. 2008) are widely used to study the turbulent vortex structures and velocity field at the gas-liquid mixture region of hydraulic jumps. For the complex air entrainment process, research interests are focused on the interactions between large coherent vortex with entrapped bubbles and distribution of void fraction, bubble size. Bubble image velocimetry (BIV) technique are used by Rodriguez et al. (2011) and Lin et al. (2012) to investigate the vortex evolution responsible for air entrainment and turbulent energy spectra of two phase bubbly flow of stationary hydraulic jumps. For a specific position, conductivity probes (Chanson, et al., 2000) and optical probes (Murzyn, et al., 2005) are usually arranged to measure the void fraction and bubble frequency. Then the bubble characteristics and associated turbulence-bubbles interactions were analyzed by Murzyn, et al. (2005). Although experiments can provide high-fidelity details of turbulent hydraulic jump, the accurate and comprehensive measurements of bubble characteristics at the intense jump region are limited by the measuring technique and experiment costs. Also, numerous entrained bubbles and splash droplets made a detailed measurement near jump toe very difficult.

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