A direct numerical simulation of single plume flow in thermal convection with polymers was carried out in a domain with 1:3 as the width to height ratio. The heat transport ability is weakened by adding polymers within the here-investigated governing parameter range. However, it is promoted when the maximum polymer extension L is increased. The distribution of vertical velocity and temperature indicates that the plume in the polymer solution case is speeded up and widens bigger as compared to that in the Newtonian fluid case. Inside the plume, polymer chains tend to release energy at the position where the velocity is decelerated. The ratio of Nusselt numbers (Nu/) shows the power-law scaling relation with the governing parameter L2/Wi in polymer solution cases, which is only applicable for moderate Wi and small L. The present study can give direct insight into the observation about plumes in turbulent thermal convection experiments. It is therefore useful for the analysis of heat transport in thermal convection with polymers.
REFERENCES
1.
G.
Ahlers
, S.
Grossmann
, and D.
Lohse
, “Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection
,” Rev. Mod. Phys.
81
, 503
(2009
).2.
D.
Lohse
and K.-Q.
Xia
, “Small-scale properties of turbulent Rayleigh-Bénard convection
,” Annu. Rev. Fluid Mech.
42
, 335
(2010
).3.
H.-D.
Xi
, S.
Lam
, and K.-Q.
Xia
, “From laminar plumes to organized flows: The onset of large-scale circulation in turbulent thermal convection
,” J. Fluid Mech.
503
, 47
(2004
).4.
K.-Q.
Xia
, C.
Sun
, and S.-Q.
Zhou
, “Particle image velocimetry measurement of the velocity field in turbulent thermal convection
,” Phys. Rev. E
68
(6
), 066303
(2003
).5.
X.-D.
Shang
, X.-L.
Qiu
, P.
Tong
, and K.-Q.
Xia
, “Measured local heat transport in turbulent Rayleigh-Bénard convection
,” Phys. Rev. Lett.
90
, 074501
(2003
).6.
X.-D.
Shang
, X.-L.
Qiu
, P.
Tong
, and K.-Q.
Xia
, “Measurements of the local convective heat flux in turbulent Rayleigh-Bénard convection
,” Phys. Rev. E
70
, 026308
(2004
).7.
Y.
Dubief
, “Heat transfer enhancement and reduction by polymer additives in turbulent Rayleigh-Benard convection
,” e-print arXiv:1009.0493v1 [physics.flu-dyn] (2010
).8.
R. B.
Bird
, O.
Hassager
, R. C.
Armstrong
, and C. F.
Curtis
, Dynamics of Polymeric Liquids
(Wiley-Interscience
, New York
, 1987
).9.
G.
Boffetta
, A.
Mazzino
, and S.
Musacchio
, “Effects of polymer additives on Rayleigh-Taylor turbulence
,” Phys. Rev. E
83
, 056318
(2011
).10.
G.
Ahlers
and A.
Nikolaenko
, “Effect of a polymer additive on heat transport in turbulent Rayleigh-Bénard convection
,” Phys. Rev. Lett.
104
, 034503
(2010
).11.
P.
Wei
, R.
Ni
, and K.-Q.
Xia
, “Enhanced and reduced heat transport in turbulent thermal convection with polymer additives
,” Phys. Rev. E
86
, 016325
(2012
).12.
T.-Z.
Wei
, W.-H.
Cai
, C.-Y.
Huang
, H.-N.
Zhang
, W.-T.
Su
, and F.-C.
Li
, “The effect of surfactant solutions on flow structures in turbulent Rayleigh-Bénard convection
,” Therm. Sci.
22
, 507
–515
(2018
).13.
W.-H.
Cai
, T.-Z.
Wei
, X.-J.
Tang
, Y.
Liu
, B.
Li
, and F.-C.
Li
, “The polymer effect on turbulent Rayleigh-Bénard convection based on PIV experiments
,” Exp. Therm. Fluid Sci.
103
, 214
(2019
).14.
Y.-C.
Xie
, S. D.
Huang
, D.
Funfschilling
, X.-M.
Li
, R.
Ni
, and K.-Q.
Xia
, “Effects of polymer additives in the bulk of turbulent thermal convection
,” J. Fluid Mech.
784
, R3
(2015
).15.
M.
Lappa
and H.
Ferialdi
, “Multiple solutions, oscillons, and strange attractors in thermoviscoelastic Marangoni convection
,” Phys. Fluids
30
, 104104
(2018
).16.
T.
Ukai
, H.
Zare-Behtash
, and K.
Kontis
, “Suspended liquid particle disturbance on laser-induced blast wave and low density distribution
,” Phys. Fluids
29
, 126104
(2017
).17.
G. K.
Batchelor
, “Heat convection and buoyancy effects in fluids
,” Q. J. R. Meteorol. Soc.
80
, 339
–358
(1954
).18.
T.
Fuji
, “Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source
,” Int. J. Heat Mass Transfer
6
, 597
–606
(1963
).19.
R. S.
Brand
and F. J.
Lahey
, “The heated laminar vertical jet
,” J. Fluid Mech.
29
(2
), 305
–315
(1967
).20.
B.
Gebhart
, L.
Pera
, and A.
Schorr
, “Steady laminar natural convection plumes above a horizontal line heat source
,” Int. J. Heat Mass Transfer
13
, 161
–171
(1970
).21.
M. G.
Worster
, “The axisymmetric laminar plume: Asymptotic solution for large Prandtl number
,” Stud. Appl. Math.
75
(2
), 139
–152
(1986
).22.
D. J.
Shlien
, “Some laminar thermal and plume experiments
,” Phys. Fluids
19
(8
), 1089
–1098
(1976
).23.
E.
Moses
, G.
Zocchi
, and A.
Libchaberii
, “An experimental study of laminar plumes
,” J. Fluid Mech.
251
, 581
–601
(1993
).24.
E.
Kaminski
and C.
Jaupart
, “Laminar starting plumes in high-Prandtl-number fluids
,” J. Fluid Mech.
478
, 287
–298
(2003
).25.
A.
Davaille
, L.
Angela
, T.
Floriane
, K.
Ichiro
, and V.
Judith
, “Anatomy of a laminar starting thermal plume at high Prandtl number
,” Exp. Fluids
50
(2
), 285
–300
(2011
).26.
M. C.
Rogers
and S. W.
Morris
, “Natural versus forced convection in laminar starting plumes
,” Phys. Fluids
21
, 083601
(2009
).27.
R. J.
Whittaker
and R. L.
John
, “Steady axisymmetric creeping plumes above a planar boundary. Part 1. A point source
,” J. Fluid Mech.
567
, 361
–378
(2006
).28.
S.
Paillat
and E.
Kaminski
, “Entrainment in plane turbulent pure plumes
,” J. Fluid Mech.
755
, R2
(2014
).29.
B.
Vajipeyajula
, T.
Khambampati
, and R. A.
Handler
, “Dynamics of a single buoyant plume in a FENE-P fluid
,” Phys. Fluids
29
, 091701
(2017
).30.
G. S.
Gunasegarane
and B. A.
Puthenveettil
, “Dynamics of line plumes on horizontal surfaces in turbulent convection
,” J. Fluid Mech.
749
, 37
–78
(2014
).31.
R.
Sureshkumar
and A. N.
Beris
, “Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows
,” J. Non-Newtonian Fluid Mech.
60
, 53
(1995
).32.
C. D.
Dimitropoulos
, R.
Sureshkumar
, and A. N.
Beris
, “Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: Effect of the variation of rheological parameters
,” J. Non-Newtonian Fluid Mech.
79
, 433
(1998
).33.
E.
De Angelis
, C. M.
Casciola
, and R.
Piva
, “DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms
,” Comput. Fluids
31
, 495
(2002
).34.
Y.
Zhang
and Y.
Cao
, “A numerical study on the non-Boussinesq effect in the natural convection in horizontal annulus
,” Phys. Fluids
30
, 040902
(2018
).35.
J.-P.
Cheng
, H.-N.
Zhang
, W.-H.
Cai
, S. N.
Li
, and F.-C.
Li
, “Effect of polymer additives on heat transport and large-scale circulation in turbulent Rayleigh-Bénard convection
,” Phys. Rev. E
96
(1
), 013111
(2017
).36.
T.
Ye
, D.
Pan
, C.
Huang
, and M.
Liu
, “Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications
,” Phys. Fluids
31
, 011301
(2019
).37.
B.
Yu
and Y.
Kawaguchi
, “Direct numerical simulation of viscoelastic drag-reducing flow: A faithful finite difference method
,” J. Non-Newtonian Fluid Mech.
116
, 431
(2004
).38.
B. P.
Leonard
, “A stable and accurate convective modelling procedure based on quadratic upstream interpolation
,” Comput. Methods Appl. Mech. Eng.
19
, 59
–98
(1979
).39.
F.
Xu
and J. C.
Patterson
, “Temperature oscillations in a differentially heated cavity with and without a fin on the sidewall
,” Int. Commun. Heat Mass Transfer
37
(4
), 350
–359
(2010
).40.
M.-M.
Qiao
, F.
Xu
, and C. S.
Suvash
, “Scaling analysis and numerical simulation of natural convection from a duct
,” Numer. Heat Transfer, Part A
72
(5
), 355
–371
(2017
).41.
A. I. P.
Miranda
and P. J.
Oliveira
, “Start-up times in viscoelastic channel and pipe flows
,” Korea-Aust. Rheol. J.
22
(1
), 65
–73
(2010
).42.
R.
Benzi
, E. S. C.
Ching
, and V. W. S.
Chu
, “Heat transport by laminar boundary layer flow with polymers
,” J. Fluid Mech.
696
, 330
–344
(2012
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.