Abstract
We present results of laboratory experiments conducted to study the evolution, growth, and spreading rate of a dispersed particle-laden plume produced by a constant inflow into a density varying environment. Particles having mean size, \(d_p=100\ \upmu \)m, density \(\rho _p=2500 \ {\text{ kg/m}}^3\), volume fraction, \(\phi _v =\) 0–0.7 % , were injected along with the lighter buoyant fluid into a linearly stratified medium. It was observed that a particle-laden plume intruding at the neutral density layer is characterized by four spreading regimes: (i) radial momentum flux balanced by the inertia force; (ii) inertia buoyancy regime; (iii) fluid-particle inertia regime, and (iv) viscous buoyancy regime. Regimes (i), (ii), and (iv) are similar to that of a single-phase plume, for which \(\phi _v = 0\,\%\). The maximum height, \(Z_m\), for \(\phi _v > 0\,\%\) was observed to be consistently lower than the single-phase case. An empirical parameterization was developed for the maximum height for particle-laden case, and was found to be in very good agreement with the experimental data. In the inertia buoyancy regime, the radial spread of the plume, \(R_f\), for \(\phi _v > 0\,\%\), advanced in time as \(R_f \propto t^{0.68 \pm 0.02}\) which is slower compared to the single-phase plume that propagates at \(R_f \propto t^{0.74 \pm 0.02}\). Due to the presence of particles, ‘particle fall out’ effect occurs, which along with the formation of a secondary umbrella region inhibits the spreading rate and results in slower propagation of the particle-laden plume. The effect of particles on spreading height of plume, \(Z_s\), and thickness of the plume, \(h_p\), were also studied, and these results were compared with the single-phase case. Overall from these experiments, it was found that the evolution, growth, and spread of dispersed particle-laden plume is very different from that of the single-phase plume, and presence of low concentration of particles (\( \phi _v < 1\,\%\)) could have significant effects on the plume dynamics.
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References
Fernando HJS (1991) Turbulent mixing in stratified fluids. Annu Rev Fluid Mech 23:455–493
Linden PF (1979) Mixing in stratified fluids. Geophys Astrophys Fluid Dyn 13(1):2–23
Peltier WR, Caulfield CP (2003) Mixing efficiency in stratified shear flows. Annu Rev Fluid Mech 35:135–167
Camilli R, Reddy CM, Yoerger DR, Van Mooy BAS, Jakuba MV, Kinsey JC, McIntyre CP, Sylva SP, Maloney JV (2010) Tracking hydrocarbon plume transport and biodegradation at deepwater horizon. Science 330(6001):201–204
Ai J, Law AWK, Yu SCM (2006) On boussinesq and non-boussinesq starting forced plumes. J Fluid Mech 558:357–386
Turner JS (1986) Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J Fluid Mech 173:431–471
List EJ (1982) Turbulent jets and plumes. Annu Rev Fluid Mech 14:189–212
Morton BR, Taylor GI, Turner JS (1956) Turbulent gravitational gonvection from maintained and instantaneous sources. Proc R Soc Lond A 234(1196):1–23
Richards TS, Aubourg Q, Sutherland BR (2014) Radial intrusions from turbulent plumes in uniform stratification. Phys Fluids 26(3):036602
Schmidt W (1941) Turbulente ausbreitung eines stromes erhitzter luft. ZAMM—J Appl Math Mech 21(6):351–363
Morton BR (1959) Forced plumes. J Fluid Mech 01:151–163
Konstantinidou K, Papanicolaou PN (2003) Vertical round and orthogonal buoyant jets in a linear density-stratified fluid. In: Ganoulis J & Prinos P (eds.) proceedings XXX IAHR Congress on water engineering and research in a learning society: modern developments and traditional concepts , Inland Waters: Research, Engineering and Management Theme, (theme C Nezu I & Kotsovinos N (eds.)) 1:293–300
Kaye NB, Linden PF (2004) Coalescing axisymmetric turbulent plumes. J Fluid Mech 502:41–63
Mott Richard W, Woods AW (2009) On the mixing of a confined stratified fluid by a turbulent buoyant plume. J Fluid Mech 623:149–165
Duo X, Chen J (2012) Experimental study of stratified jet by simultaneous measurements of velocity and density fields. Exp Fluids 53(1):145–162
Adalsteinsson DD et al. (2011) Subsurface trapping of oil plumes in stratification: laboratory investigations. A Record-Breaking Enterprise, Monitoring and Modeling the Deepwater Horizon Oil Spill, pp. 257–262
Rooney GG, Devenish BJ (2014) Plume rise and spread in a linearly stratified environment. Geophys Astrophys Fluid Dyn 108(2):168–190
Socolofsky SA, Adams EE (2002) Multi-phase plumes in uniform and stratified crossflow. J Hydraul Res 40(6):661–672
Chou Y-J, Fringer Oliver B (2008) Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model. Phys Fluids 20(115):103
Wang R-Q, Law AWK, Adams EE, Fringer OB (2011) Large-eddy simulation of starting buoyant jets. Environ Fluid Mech 11(6):591–609
Yuan LL, Street RL, Ferziger JH (1999) Large-eddy simulations of a round jet in crossflow. J Fluid Mech 379:71–104
Balachandar S, Eaton JK (2010) Turbulent dispersed multiphase flow. Annu Rev Fluid Mech 42:111–133
Balasubramanian S, Voropayev SI, Fernando HJS (2008) Grain sorting and decay of sand ripples under oscillatory flow and turbulence. J Turbul 9(17):1–19
Leah SR (1994) An experimental comparison of bubble and sediment plumes in stratified environments. Dept. of Civil and Environmental Engineering, M.s., Massachusetts Institute of Technology
Cardoso Silvana SS, Zarrebini Mehrãn (2001) Sedimentation of polydispersed particles from a turbulent plume. Chem Eng Sci 56(16):4725–4736
Mehrãn Z, Cardoso SSS (2000) Patterns of sedimentation from surface currents generated by turbulent plumes. AIChE J 46(10):1947–1956
Ernst GGJ et al (1996) Sedimentation from turbulent jets and plumes. J Geophys Res: Solid Earth 101(B3):5575–5589
Carey SN, Sigurdsson H, Sparks RSJ (1988) Experimental studies of particle-laden plumes. J Geophys Res: Solid Earth 93(B12):15314–15328
Graham V, Woods AW (2002) Particle recycling in volcanic plumes. Bull Volcanol 64(1):31–39
Chow AC (2004) Effects of buoyancy source composition on multiphase plume behavior in stratification. Dept. of Civil and Environmental Engineering, M.s., Massachusetts Institute of Technology
Chan GKY (2013) Effects of droplet size on intrusion of sub-surface oil spills. Dept. of Civil and Environmental Engineering, M.s., Massachusetts Institute of Technology
Jessop D, Jellinek M (2013) The effect of fine particles on ash cloud and plume dynamics. AGU Fall, Meeting Abstracts p C2860
Oster G, Yamamoto M (1963) Density gradient techniques. Chem Rev 63(3):257–268
Mehta RD, Bradshaw P (1979) Design rules for small low-speed wind tunnels. Aeronaut J 83(827):443–449
Masutami SM, Adams EE (2004) Experimental study of multi-phase plumes with application to deep ocean oil spills. In: Technical report, U.S. Department of the Interior, Minerals Management Service
Kotsovinos N (2000) Axisymmetric submerged intrusion in stratified fluid. J Hydraul Eng 126(6):446–456
Huppert HE, Simpson JE (1980) The slumping of gravity currents. J Fluid Mech 99:785–799
Holasek RE, Self S, Woods AW (1996) Satellite observations and interpretation of the 1991 mount pinatubo eruption plumes. J Geophys Res: Solid Earth 101(B12):27635–27655
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The authors acknowledge funding from Indian Institute of Technology Bombay and Ministry of Earth Sciences for the present research work.
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Appendix
Appendix
The density profile measured using the conductivity probe in the stratified tank (T2) is shown in Fig. 15.
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Mirajkar, H.N., Tirodkar, S. & Balasubramanian, S. Experimental study on growth and spread of dispersed particle-laden plume in a linearly stratified environment. Environ Fluid Mech 15, 1241–1262 (2015). https://doi.org/10.1007/s10652-015-9412-5
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DOI: https://doi.org/10.1007/s10652-015-9412-5