We study characteristics of miscible displacement flows in inclined pipes with density-stable configuration, meaning the lighter fluid is pumped to displace the heavier fluid downward along the pipe. Experiments have been completed in a pipe covering a broad range of inclination angles, flow rates, and viscosity configurations. Viscosity contrast between the fluids is obtained by adding xanthan gum to water, while glycerol is used to achieve density difference. Novel instabilities appear in the case of shear-thinning displacements. Numerical simulations are performed using the finite volume package OpenFOAM. The unsteady three-dimensional Navier-Stokes equations are used with the volume of fluid method to capture the interface between the fluids. A number of numerical cases are compared against the experiments to benchmark the model favourably. The code allows us to examine in detail the 3D structure of the propagating front and other secondary flows.
REFERENCES
1.
C. Y.
Chen
and E.
Meiburg
, “Miscible displacements in capillary tubes. Part 2. numerical simulations
,” J. Fluid Mech.
326
, 57
–90
(1996
).2.
P.
Petitjeans
and T.
Maxworthy
, “Miscible displacements in capillary tubes. Part 1. Experiments
,” J. Fluid Mech.
326
, 37
–56
(1996
).3.
N.
Goyal
and E.
Meiburg
, “Miscible displacements in Hele-Shaw cells: Two-dimensional base states and their linear stability
,” J. Fluid Mech.
558
, 329
–355
(2006
).4.
N.
Goyal
, H.
Pichler
, and E.
Meiburg
, “Variable-density miscible displacements in a vertical Hele-Shaw cell: Linear stability
,” J. Fluid Mech.
584
, 357
–372
(2007
).5.
J.
Fernandez
, P.
Kurowski
, P.
Petitjeans
, and E.
Meiburg
, “Density-driven unstable flows of miscible fluids in a Hele-Shaw cell
,” J. Fluid Mech.
451
, 239
–260
(2002
).6.
E.
Lajeunesse
, J.
Martin
, N.
Rakotomalala
, and D.
Salin
, “3D instability of miscible displacements in a Hele-Shaw cell
,” Phys. Rev. Lett.
79
, 5254
–5257
(1997
).7.
E.
Lajeunesse
, J.
Martin
, N.
Rakotomalala
, D.
Salin
, and Y.
Yortsos
, “Miscible displacement in a Hele Shaw cell at high rates
,” J. Fluid Mech.
398
, 299
–319
(1999
).8.
E.
Lajeunesse
, J.
Martin
, N.
Rakotomalala
, and D.
Salin
, “The threshold of the instability in miscible displacements in a Hele-Shaw cell at high rates
,” Phys. Rev. Lett.
13
, 799
–801
(2001
).9.
S. M.
Taghavi
, T.
Seon
, D. M.
Martinez
, and I. A.
Frigaard
, “Influence of an imposed flow on the stability of a gravity current in a near horizontal duct
,” Phys. Fluids
22
, 031702
(2010
).10.
S. M.
Taghavi
, T.
Seon
, K.
Wielage-Burchard
, D. M.
Martinez
, and I. A.
Frigaard
, “Stationary residual layers in buoyant Newtonian displacement flows
,” Phys. Fluids
23
, 044105
(2011
).11.
S. M.
Taghavi
, K.
Alba
, T.
Seon
, K.
Wielage-Burchard
, D. M.
Martinez
, and I. A.
Frigaard
, “Miscible displacement flows in near-horizontal ducts at low Atwood number
,” J. Fluid Mech.
696
, 175
–214
(2012
).12.
K.
Alba
, S. M.
Taghavi
, and I. A.
Frigaard
, “Miscible density-unstable displacement flows in inclined tube
,” Phys. Fluids
25
, 067101
(2013
).13.
A.
Etrati
, K.
Alba
, and I. A.
Frigaard
, “Two-layer displacement flow of miscible fluids with viscosity ratio: Experiments
,” Phys. Fluids
30
, 052103
(2018
).14.
S. M.
Taghavi
, K.
Alba
, M.
Moyers-Gonzalez
, and I. A.
Frigaard
, “Incomplete fluid-fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory
,” J. Non-Newtonian Fluid Mech.
167-168
, 59
–74
(2012
).15.
K.
Alba
, S. M.
Taghavi
, and I. A.
Frigaard
, “Miscible density-stable displacement flows in inclined tube
,” Phys. Fluids
24
, 123102
(2012
).16.
C. E.
Hickox
, “Instability due to viscosity and density stratification in axisymmetric pipe flow
,” Phys. Fluids
14
, 251
–262
(1971
).17.
D. D.
Joseph
, M.
Renardy
, and Y.
Renardy
, “Instability of the flow of two immiscible liquids with different viscosities in a pipe
,” J. Fluid Mech.
141
, 309
–317
(1984
).18.
H. H.
Hu
and D. D.
Joseph
, “Lubricated pipelining: Stability of core-annular flow. Part 2
,” J. Fluid Mech.
205
, 359
–396
(1989
).19.
B.
Selvam
, S.
Merk
, R.
Govindarajan
, and E.
Meiburg
, “Stability of miscible core-annular flows with viscosity stratification
,” J. Fluid Mech.
592
, 23
–49
(2007
).20.
C.
Gabard
and J.-P.
Hulin
, “Miscible displacement of non-Newtonian fluids in a vertical tube
,” Eur. Phys. J. E
11
, 231
–241
(2003
).21.
N.
Rashidnia
, R.
Balasubramaniam
, and R. T.
Schroer
, “The formation of spikes in the displacement of miscible fluids
,” Ann. N. Y. Acad. Sci.
1027
, 311
–316
(2004
).22.
R.
Balasubramaniam
, N.
Rashidnia
, T.
Maxworthy
, and J.
Kuang
, “Instability of miscible interfaces in a cylindrical tube
,” Phys. Fluids
17
, 052103
(2005
).23.
J.
Scoffoni
, E.
Lajeunesse
, and G. M.
Homsy
, “Interface instabilities during displacements of two miscible fluids in a vertical pipe
,” Phys. Fluids
13
, 553
–556
(2001
).24.
T.
Soori
and T.
Ward
, “Stable and unstable miscible displacement of a shear-thinning fluid at low Reynolds number
,” Phys. Fluids
30
, 103101
(2018
).25.
H. E.
Huppert
and M. A.
Hallworth
, “Bi-directional flows in constrained systems
,” J. Fluid Mech.
578
, 95
–112
(2007
).26.
F. M.
Beckett
, H. M.
Mader
, J. C.
Phillips
, A. C.
Rust
, and F.
Witham
, “An experimental study of low-Reynolds-number exchange flow of two Newtonian fluids in a vertical pipe
,” J. Fluid Mech.
682
, 652
–670
(2011
).27.
D.
Picchi
, A.
Ullmann
, and N.
Brauner
, “Modeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes
,” Int. J. Multiphase Flow
103
, 43
–60
(2018
).28.
J.
Suckale
, Z.
Qin
, D.
Picchi
, T.
Keller
, and I.
Battiato
, “Bistability of buoyancy-driven exchange flows in vertical tubes
,” J. Fluid Mech.
850
, 525
–550
(2018
).29.
T.
Ranganathan
and R.
Govindarajan
, “Stabilization and destabilization of channel flow by location of viscosity-stratified fluid layer
,” Phys. Fluids
13
, 1
–3
(2001
).30.
P.
Ern
, F.
Charru
, and P.
Luchini
, “Stability analysis of a shear flow with strongly stratified viscosity
,” J. Fluid Mech.
496
, 295
–312
(2003
).31.
R.
Govindarajan
, “Effect of miscibility on the linear instability of two-fluid channel flow
,” Int. J. Multiphase Flow
30
, 1177
–1192
(2004
).32.
M.
d’Olce
, J.
Martin
, N.
Rakotomalala
, D.
Salin
, and L.
Talon
, “Pearl and mushroom instability patterns in two miscible fluids’ core annular flows
,” Phys. Fluids
20
, 024104
(2008
).33.
B.
Selvam
, L.
Talon
, L.
Lesshafft
, and E.
Meiburg
, “Convective/absolute instability in miscible core-annular flow. Part 2. Numerical simulations and nonlinear global modes
,” J. Fluid Mech.
618
, 323
–348
(2009
).34.
L.
Talon
and E.
Meiburg
, “Plane Poiseuille flow of miscible layers with different viscosities: Instabilities in the Stokes flow regime
,” J. Fluid Mech.
686
, 484
–506
(2011
).35.
K. C.
Sahu
and R.
Govindarajan
, “Linear stability analysis and direct numerical simulation of two-layer channel flow
,” J. Fluid Mech.
798
, 889
–909
(2016
).36.
R.
Govindarajan
and K. C.
Sahu
, “Instabilities in viscosity-stratified flow
,” Annu. Rev. Fluid Mech.
46
, 331
–353
(2014
).37.
K. C.
Sahu
, H.
Ding
, P.
Valluri
, and O. K.
Matar
, “Pressure-driven miscible two-fluid channel flow with density gradients
,” Phys. Fluids
21
, 043603
(2009
).38.
M.
Mishra
, A.
De Wit
, and K. C.
Sahu
, “Double diffusive effects on pressure-driven miscible displacement flows in a channel
,” J. Fluid Mech.
712
, 579
–597
(2012
).39.
S. H.
Vanaparthy
and E.
Meiburg
, “Variable density and viscosity, miscible displacements in capillary tubes
,” Eur. J. Mech.: B/Fluids
27
, 268
–289
(2008
).40.
H. G.
Weller
, G.
Tabor
, H.
Jasak
, and C.
Fureby
, “A tensorial approach to computational continuum mechanics using object-oriented techniques
,” Comput. Phys.
12
, 620
–631
(1998
).41.
A.
Etrati
and I. A.
Frigaard
, “A two-layer model for buoyant inertial displacement flows in inclined pipes
,” Phys. Fluids
30
, 022107
(2018
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
