# Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps

Abstract: The large-scale turbulence and high air content in a hydraulic jump restrict the application of many traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump, where the total pressure and air–water flow properties were measured simultaneously with intrusive probes, namely a miniature pressure transducer and a dual-tip phase-detection probe, in the jump roller. The total pressure data were compared to theoretical values calculated based upon void fraction, water depth and flow velocity measured by the phase-detection probe. The successful comparison showed valid pressure measurement results in the turbulent shear region with constant flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into account the void fraction distributions. The total pressure fluctuations were related to both velocity fluctuations in the air–water flow and free-surface dynamics above the roller, though the time scales of these motions differed substantially.

## Summary (1 min read)

### 1 Introduction

- The jump toe, where the upstream flow impinges into the downstream region, is a singular locus with discontinuity in velocity and pressure fields (Rajaratnam 1967).
- Any theoretical and numerical analyses of hydraulic jumps are based upon a large number of relevant equations to describe the two-phase turbulent flow motion and the interaction between entrained air and turbulence.
- The phase-detection probe was excited by an electronic system designed with a response time less than 10 µs, and scanned at 5 kHz simultaneously with the total pressure probe and an acoustic displacement meter above the probe leading tip.
- The simultaneous sampling of all instruments was performed for 180 s at each measurement location.

### 3 Results

- 1 Basic flow patterns Observations showed some enhanced flow aeration and turbulent fluctuations with increasing Froude number.
- Figure 4 shows a comparison between the vertical void fraction distributions in the present study and Wang & Chanson (2014) for identical flow conditions and longitudinal positions.
- The instantaneous bubble distribution was highly affected by the turbulent flow structures, and bubbles tended to travel in clusters rather than in randomness (Chanson 2007).
- The turbulence intensity Tu" deduced from the high-frequency signal component reflected the 'true' turbulence of the flow.

### 4 Discussion: characteristic total pressure fluctuation frequencies

- The instantaneous total pressure signals exhibited some pseudo-periodic patterns.
- The analysed characteristic total pressure fluctuation frequencies are summarised in Table 2.
- The relatively high-frequency filtered signals (0 – 25 Hz) exhibited a range of typical fluctuation frequencies Fp(H) between 8 and 12 Hz, whereas the low-frequency filtered signals (0 – 5 Hz) gave a frequency Fp(L) about 2.6 Hz.
- Figure 15a shows a smaller dimensionless frequency Fp(H)×d1/V1 for a higher Froude number, which decreased with increasing distance from the jump toe.
- The comparable decreasing trends along the roller might suggest some correlation between the detected pressure fluctuations and the turbulent air-water flow features, of which the longitudinal decay was related to the diffusion and dispersion of bubbly flow structures as well as the turbulence dissipation.

### 4 Conclusion

- The total pressure and air-water flow properties were measured simultaneously at adjacent locations in hydraulic jump rollers, together with the water level fluctuations above.
- Four Froude numbers were investigated with the same intake aspect ratio and inflow length, corresponding to partiallydeveloped inflow conditions.
- The bubble count rate was however underestimated when the Froude and Reynolds numbers were large.
- The total pressure was predicted based upon the void fraction and velocity data, and the predictions agreed well with experimental results given by the total pressure probe.
- This was supported by comparison between relative total pressure fluctuation and turbulence intensity, and a preliminary investigation of pressure fluctuation frequencies.

Did you find this useful? Give us your feedback

...read more

##### Citations

102 citations

51 citations

32 citations

27 citations

### Cites background from "Total pressure fluctuations and two..."

...Further observations include the integral turbulent length scale Lt characterising the size of large turbulent eddies advecting the bubbles in the hydraulic jump roller [34, 179]....

[...]

24 citations

### Cites background from "Total pressure fluctuations and two..."

...Hydraulic jump data gmax/d1: theoretical calculations [31], experimental data [22,26,23,27,17,28,4,35,36] (For interpretation of the references to colour in this...

[...]

##### References

20,482 citations

### "Total pressure fluctuations and two..." refers methods in this paper

...The experimental data fitted a solution of classical twodimensional diffusion equation (Crank 1956; Chanson 1995): C ¼ Cmax exp 1 4 D# y YCmax d1 2 x x1 d1 0 B @ 1 C A 0 \ y \ y ð3Þ where D# is a dimensionless diffusivity....

[...]

...The experimental data fitted a solution of classical twodimensional diffusion equation (Crank 1956; Chanson 1995): C 1⁄4 Cmax exp 1 4 D# y YCmax d1 2...

[...]

[...]

2,051 citations

347 citations

### "Total pressure fluctuations and two..." refers background in this paper

...1 below) was only observed for partially developed inflow conditions, with the shortest aeration length downstream of the toe (Chanson 1997)....

[...]

...3.2.1 below) was only observed for partially developed inflow conditions, with the shortest aeration length downstream of the toe (Chanson 1997)....

[...]

[...]

280 citations

### "Total pressure fluctuations and two..." refers background in this paper

...In a hydraulic jump, the momentum considerations demonstrated the significance of the inflow Froude number, and the selection of the Froude similitude derives implicitly from basic theoretical considerations (Lighthill 1978; Liggett 1994)....

[...]

246 citations