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Experimental study of sand-water swirling jets in stagnant water

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Abstract

A series of laboratory experiments was conducted to study particle dynamics and flow characteristics of vertically discharged sand-water swirling jets in stagnant water. The effects of swirling motion on variations of sand concentration, axial velocity, and mixing properties of sand-water swirling jets were studied by employing an advanced optical fiber probe (PV6). The axial and radial sand concentration and velocity were measured for sand-water swirling jets with limited and unlimited mass of sand particles. The availability of sand particles was quantified by the aspect ratio of sand mass to nozzle diameter. Sand mass and momentum fluxes were calculated from cross-sectional integration of sand concentration and velocity profiles to validate the measured data. A strong decay rate of momentum flux was observed along the recirculation zone and at a distance equal to 20 times the nozzle diameter. Prediction models were developed based on the measured data to estimate sand concentration and velocity of sand-water swirling jets with different swirling strengths. It was found that aspect ratio and swirling strength significantly impact the variations of axial concentration and velocity decay rates in sand-water swirling jets. Laboratory measurements indicated that the centerline sand concentration decreased at a higher rate in comparison with sand-water jets without a swirling motion. In addition, the centerline sand concentration and velocity significantly decreased by increasing the swirling strength. The spreading rate of sand-water swirling jets increased with increase in the swirling number. The radially averaged drag coefficient of particles at different cross sections was calculated by employing the momentum balance along the jet axis and the proposed models for prediction of sand velocity and concentration. It was found that the swirling motion of sand particles significantly increased the drag coefficient. The power spectral density results of sand-water swirling jets indicated that the sand phase attenuated the first peak signal in the frequency domain in comparison with the power spectral density results of single-phase swirling jets.

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Abbreviations

A p :

Projected frontal area of individual sand particle (m2)

b :

Half-width of the jet (mm)

b c :

Half-width of the jet concentration profile where c/cm = 50% (cm)

b u :

Half-width of the jet velocity profile where u/um = 50% (mm)

c :

Concentration in nozzle (%)

\(\overline{c}\) :

Average sand volumetric concentration (%)

c o :

Initial concentration at the nozzle (%)

c m :

Sand volumetric concentration at the centerline of the swirling jet (%)

C c :

Calibration concentration (% vol)

C d :

Drag coefficient

d a :

Annular nozzle diameter size (mm)

d o :

Central nozzle diameter size (mm)

d p :

Optical probe’s diodes diameter (mm)

D p :

Optical probe’s diodes detected planner surface (mm)

D 50 :

Particle size (mm)

f :

Frequency, Hz

f D :

Individual particle drag force (N)

F B :

Buoyancy force (N)

F D :

Drag force (N)

F g :

Gravitational force (N)

g :

Acceleration due to gravity (m/s2)

h c :

Planner surface elementary cubes sides (mm)

L o :

Length of sand occupied in a release tube (mm)

L s :

Size of signal overlapping

L p :

Distance between optical probe’s diodes (mm)

m :

Sand mass (g)

ṁ :

Sand mass flux (kg/s)

m o :

Initial sand mass at the nozzle (g)

\(\dot{m}_{o}\) :

Initial sand mass flux at the nozzle (kg/s)

\(\dot{M}\) :

Momentum flux of the swirling jet (kg m/s2)

\(\dot{M}_{o}\) :

Initial momentum flux at the nozzle (kg m/s2)

M p :

Number of optical probe’s detected planner surface layers

N p :

Number of particles

r :

Horizontal distance from the swirling jet axis (mm)

Re:

Reynolds number

Rep :

Particle Reynolds number

Sw:

Swirling number

S t :

Stokes number

t*:

Non-dimensional time (s)

u :

Particle velocity (m/s)

u ave :

Particle average velocity (m/s)

u m :

Sand velocity at the centerline of the swirling jet (m/s)

u o :

Initial sand velocity at the nozzle (m/s)

u ow :

Initial water velocity at the nozzle (m/s)

u rms :

Root mean square of particles velocities (m/s)

u x :

Vertical velocity component (m/s)

u az :

Azimuthal velocity (rad)

u′:

Velocity fluctuation (m/s)

r :

Horizontal distance from the jet axis, m

V c :

Calibration voltage (V)

V p :

Disk-shaped control volume (m3)

V disk :

Volume of sphere particles (m3)

x :

Distance from the nozzle (m)

µ :

Dynamic viscosity (m2/s)

ρ s :

Densities of sand particles (kg/m3)

ρ w :

Densities of water (kg/m3)

τ p :

Particle relaxation time (s)

τ f :

Time scale of the flow (s)

φ :

Sphericity ratio

ΔL s :

Size of signal segment

Δt :

Time lag

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Acknowledgements

The authors are thankful to our laboratory technician (Mr. Morgan Ellis) and (Miss. Victoria Erickson) for their supports in preparation of a part of the experimental setup and the 3D design of the nozzle.

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  1. Department of Civil Engineering, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    Fardin Sharif & Amir Hossein Azimi

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  1. Fardin Sharif
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Sharif, F., Azimi, A.H. Experimental study of sand-water swirling jets in stagnant water. Exp Fluids 63, 26 (2022). https://doi.org/10.1007/s00348-021-03379-1

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