Analysis of ﬂow characteristics in an annular ﬂume: Implications for
erosion and deposition of cohesive sediments
Mariano Cantero1 , Silvina Mangini2 , Francisco Pedocchi1 , Yarko Ni˜o3 and Marcelo
Ven Te Chow Hydrosystems Laboratory, Dept. of Civil Engrg.,University of
Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
ıa ıdricas, Universidad del Litoral, Argentina
Facultad de Ingenier´ y Ciencias H´
Departamento de Ingenier´ Civil, Univeridad de Chile, Chile
Criteria for developing operating curves for annular ﬂumes and deﬁning appropri-
ate values for shear stress for erosion and deposition experiments are proposed.
The work of several authors is reviewed and new large eddy simulations (LES) are
presented for the annular ﬂume in the Ven Te Chow Hydrosystems Laboratory at
the University of Illinois at Urbana-Champaign (VTCHL), USA.
The CFD simulation methodology is validated with experimental data by Petersen
and Krishnappan (1994). Then, the code is used to address the ﬂow characteristics
in the VTCHL annular ﬂume. Two diﬀerent pairs of operating curve and shear
stress deﬁnitions are proposed based in this study: one for erosion experiments
and one for deposition experiments.
The use of annular ﬂumes has been adopted for the study of cohesive sediments
because of its advantages over the traditional straight recirculating ﬂumes since
1966 (Partheniades et al., 1966; Partheniades & Kennedy, 1966).
An annular ﬂume is basically composed of a channel and a lid, and the ﬂow is
established by the rotation of the ﬂume itself (see ﬁgure 1) avoiding the use of
recirculating pumps. This guaranties that the aggregate structures are not ex-
ternally disturbed and that all the processes that they undergo are only due to
the ﬂow. Another advantage of the use of annular ﬂumes is that ones the ﬂow
has been established it is fully developed in the entire ﬂume, producing uniform
distributions of bed shear stresses in the direction of ﬂow. On the other hand,
strong secondary ﬂows develop in the ﬂume and lead to uneven distributions of
shear stresses in the radial direction (Peterson & Krishnappan, 1994). This re-
circulation currents also make the aggregates sample diﬀerent regions of the ﬂow
with diﬀerent shear stresses (Maa, 2001).
The secondary currents in the ﬂume can be minimized by allowing the lid to rotate
in the opposite direction that the channel does (Partheniades et al., 1966). In this
way operation curves, which set the lid angular velocity (for example clockwise) as
a function of the channel angular velocity (counter-clockwise), can be developed
for every annular ﬂume in particular. However, diﬀerent criteria exist to do this
and the appropriate one must be used according to the type of experiment that
it is going to be performed.
Deciding the values of critical shear stresses that are going to be reported for
erosion and deposition experiments constitutes also a complication. The exis-
tence of uneven shear stress distributions in the radial direction and the fact that
the particles sample diﬀerent ﬂow regions with diﬀerent characteristics during the
experiment make it necessary to have clever and studied deﬁnitions of a represen-
tative shear stress value for each type of experiment.
In this work the ways in which diﬀerent authors dealt with these problems in the
past are reviewed, and new criteria are proposed and evaluated for the VTCHL
annular ﬂume. To this end, large eddy simulations were carried out and analyzed
taking into account these past experiences.
Partheniades et al. (1966) reported the ﬁrst use of annular ﬂumes for the study
of cohesive sediments. This pioneering work has served as model for several ex-
perimental facilities in the world. Table 1 summarizes the main information and
characteristics of these facilities, all of them having rotating channel and rotating
Operating curves. Patheniades et al. (1966) developed operating curves by
observing the deposition of plastic beds in the bottom of the channel. These
researchers considered that the secondary ﬂow was minimum when the particles
deposited at the center of the channel. In this way, they produced curves that
set the lid angular velocity (ωl ) as a function of the channel angular velocity (ωc )
for diﬀerent depths. They reported the use of the same operation curve for both
Table 1: Main annular ﬂume facilities in the world with rotating channel and
Reference Mean radius [m] Width [m] Reported depths [m]
Partheniades et al. (1966) 0.409 0.097 0.08 - 0.12 - 0.16
Partheniades and Kennedy (1971) 0.762 0.203 0.152 - 0.229 - 0.305
Krishnappan (1993) 2.5 0.28 0.2 - 0.16 - 0.12 - 0.1
Spork and K¨ngeter (1999) 1.625 0.25 0.175 - 0.25 - 0.325
Booij (1994) 1.85 0.3 0.157 - 0.196 - 0.297
Yang et al. (2000) 0.67 0.42 0.4
Cantero et al. (actual work) 0.65 0.2 0.2
erosion and deposition experiments.
Krishnappan (1993) and Petersen and Krishnappan (1994) performed a detailed
analysis of the ﬂow and presented a new criterion for minimizing secondary ﬂows.
They proposed that secondary currents are minimal when the speciﬁc secondary
kinetic energy, Es ,
Es = Vr2 + Vz2 dA (1)
is minimal. Here A is the cross sectional area of the ﬂume. These authors also
reported the use of the same operating curves for both erosion and deposition
Booij et al. (1993) proposed diﬀerent criteria for the determination of the optimum
values of the ratio ωl /ωc depending on the nature of the experiment, i.e.
• erosion experiments: uniform distribution of bottom shear stress,
• deposition experiments: minimum secondary ﬂow velocities.
It is worth noting that Booij (1994) indicated that secondary current velocities
are of the same order of magnitude of settling velocities of ﬁne sediments (even
with optimal ratio ωl /ωc ). He concluded that the 3-D complex pattern ﬂow should
be studied carefully when performing deposition experiments in order to not mis-
interpret the results. On the other hand, Booij (1994) showed that the bottom
shear stress does not depend strongly on the ratio ωl /ωc , which, in addition to
the uniformity of the bed shear stress achieved for optimal angular velocity ratios,
makes the annular ﬂume a suitable tool to study erosion and entrainment-into-
Spork et al. (1994) also mentioned the necessity of having diﬀerent operating
curves for erosion and deposition experiments (same as those suggested by Booij
et al. (1993)). Spork and K¨ngeter (1999) commented in a later work that al-
though they minimized the secondary ﬂow in the ﬂume, the upward velocities in
some regions of the ﬂow were of the same order of magnitude than the sediments
settling velocities and suggested a limited application of annular ﬂumes for depo-
Yang et al. (2000) proposed to use two diﬀerent criteria for developing operating
curves in accordance with Booij et al. (1993) and Spork et al. (1994). They pre-
sented two implementations for the criterion of minimum secondary ﬂow. The
ﬁrst one is to minimize the secondary ﬂow kinetic energy in comparison to the
tangential kinetic energy
where Es is deﬁned in equation (1) and Et is deﬁned in a similar way. The second
implementation is to minimize the maximum secondary velocity relative to the
maximum tangential velocity
max Vr2 + Vz2
Rv = . (3)
max | Vθ |
These authors reported that the two implementations are equivalent.
Reported shear stress. From the work of Partheniades et al. (1966) and Parthe-
niades and Kennedy (1966) it can be inferred that the researchers used a mean
value for the shear stress based on a force balance, deﬁned as the average of the
values at the bottom and at the walls of the channel, i.e.
d Rout d
τb = τ (Rin , z)dz + τ (r, 0)dr + τ (Rout , z)dz . (4)
0 Rin 0
Here τb is the averaged bed shear stress, τ (r, z) is the shear stress distribution, R in
is the inner radius and Rout is the outer radius of the ﬂume (see ﬁgure 1). They
reported the use of the same deﬁnition of bed shear stress for the both erosion
and deposition experiments.
Petersen and Krishnappan (1994) also proposed to use the same deﬁnition for
the shear stress for erosion and deposition experiments. However, they used a
torque-based deﬁnition based only on the bottom shear stress distribution
τb = τ (r, 0)dr. (5)
R3 − R 3
Booij (1994) and Spork et al. (1994) reported the use of the shear stress averaged
over the channel bottom as a representative value of shear stress for erosion exper-
iments. From their work, it can also be inferred that they used a bottom-averaged
shear stress value for deposition experiments, as well.
Partial conclusions. Several conclusions can be drawn from the literature pe-
rusal above. Firstly, it can be concluded that two diﬀerent criteria are necessary
for developing operations curves: one for erosion experiments and one for deposi-
tion experiments (Booij et al., 1993; Spork et al., 1994).
Secondly, upward velocities in the annular ﬂume may be of the order of magnitude
of the sediment settling velocities even when secondary currents are minimized
(Booij, 1994; Spork & K¨ngeter, 1999; Yang et al., 2000). Besides, the shear
stress distribution is uneven in the ﬂume walls reaching the maximum at the lid
(Maa, 2001). These two main issues suggest that the use of annular ﬂumes facili-
ties for deposition experiments should be done very carefully.
Thirdly, it seems clear that two diﬀerent deﬁnitions are necessary for represen-
tative mean shear stress values: one for erosion experiments, and another for
deposition experiments. A representative value of the critical shear stress for ero-
sion experiments should be related to the bottom shear stress distribution, while
a representative value for critical shear stress for deposition experiments should
be related to the shear distributions of the ﬂow regions that the aggregates sample.
Description of the VTCHL annular ﬂume facility. The VTCHL annular
ﬂume was constructed by Engineering Laboratory Design, Inc. of Lake City, Min-
nesota. The channel is made of laminated ﬁberglass and it has one Plexiglas
window. It is supported by a ﬁve-leg frame of welded steel structural tubing. The
channel rests on an aluminum board with a steel ring that runs on ﬁve rollers.
The channel has an inner radius Rin =0.55 m, an outer radius Rout =0.75 m, and is
0.45 m deep. Seven taps were installed at 5-cm intervals on the outer wall of the
channel in order to take water samples at heights ranging from 5 to 35 cm. An-
other tap installed at a height of 18 cm was used to add clean water to the ﬂume
after samples were taken so that the volume of water inside the ﬂume remained
The lid is made of Plexiglas bolted to a steel frame mounted on a threaded shaft.
The lid can be moved up and down on this shaft to allow for ﬂow depths between
0.2 and 0.4 m, and a large nut holds it at the desired vertical position. Three
holes were cut into the lid in order to insert various measuring devices into the
ﬂow. The holes are sealed with Plexiglas caps when not in use. A painted wooden
shelf is mounted on the support arms of the lid to hold a laptop computer and
the data logger for the velocimeter.
The channel and the lid are free to rotate independently of each other and move-
ment is transmitted by two electric motors. The speed of each motor is controlled
by a control system implemented in a PC with Labview. Two magnetic sensors
that measure the channel and lid angular velocities for feedback complete the
control system. The maximum speed of the channel is 10 revolutions per minute,
while the maximum speed of the lid is 16 rpm.
CFD simulations. CFD computations were carried out using the commercial
code FLOW3D. The code is a ﬁnite volume code that allows for viscous and turbu-
lent ﬂows computations and has been widely used and shown to be a very reliable
tool. More details about the code can be found in the FLOW3D users manual
For the CFD simulations the ﬂow was assumed three dimensional, incompressible
and turbulent. The Navier-Stokes equations were solved in a cylindrical coordi-
nate system and turbulence closure was done using the Smagorinsky model (LES).
Although large eddy simulations are more CPU consuming compared to k − sim-
ulations, they are preferred when simulating these type of ﬂows because they have
shown to produce better results (Booij, 2003). The CFD simulations were per-
formed in a periodic domain in the tangential direction long enough to allow for
three of the largest ﬂow structures to exist in the domain. Periodic boundary
conditions were used in the tangential direction, while the smooth wall law was
used for wall boundary conditions (in radial and vertical directions). Once the
CFD simulation reached a statistically steady state 200 seconds were simulated in
order to compute the statistical values (mean velocity and shear stress). All the
simulations were grid independent.
The CFD methodology was validated by reproducing experimental results by Pe-
tersen and Krishnappan (1994) (experiment PK1 in table 2). Figure 2 shows
the comparison of the mean tangential velocity isolines between Petersen and Kr-
ishnappan (1994) experiment and the CFD simulation. This ﬁgure shows good
agreement both qualitatively and quantitatively. Observe that the isolines from
the CFD simulation follow the same pattern as experiments and also agree well
with the measured values. Figure 3 shows the bed shear stress computed from the
CFD simulation in comparison to the values measured by Petersen and Krishnap-
pan (1994). The agreement is also good. Although the CFD simulation seems to
underestimate the bed shear stress values, the error (about 15%) is within what
is expected for these type of simulations.
Several large eddy simulations were performed for the VTCHL annular ﬂume fa-
cility in order to evaluate the criteria for the operating curves and shear stress
deﬁnitions. Only the main results will be presented here because of space reasons.
Next subsection summarizes these results.
Operating curves. In erosion experiments the goal is to ﬁnd water-sediment
interface shear stress values for which erosion begins, and to produce relations
between the erosion rate and the water-sediment interface shear stress. With this
idea in mind the criterion we propose to develop operating curves for these type
of experiments is to have a uniform shear stress distribution at the bottom wall
Table 2: Experimental conditions and CFD simulations for validation.
Reference ID ωl [rpm] ωf [rpm] Rm [m] b [m] d [m]
Petersen and Krishnappan (1994) PK1 1 -1 2.5 0.28 0.16
CDF simulation 1, (actual work) CFD1 1 -1 2.5 0.28 0.16
CDF simulations for – 0 to 10 -2.9, -4, -5, -6 0.65 0.2 0.2
calibration (actual work)
(Booij et al., 1993; Spork et al., 1994). The optimum ratio for erosion experiments
for the annular ﬂume in the VTCHL is ωl /ωc =-2.75.
On the other hand, in deposition experiments the goal is to evaluate the critical
shear stress for which deposition occurs. Experiments are started with a homoge-
neous sediment concentration in the water column and the ﬂow velocity is lowered
stepwise in order to promote ﬂocculation. Due to this process aggregates form,
which have larger size and larger settling velocities that the original particles, and
the process of deposition begins. This suggests that the criterion for deposition
experiments should be to minimize the vertical currents velocities (regardless of
the radial velocity), i.e. max | Vz | must be minimum. The optimum ra-
tio for deposition experiments for the annular ﬂume in the VTCHL is ωl /ωc =-0.75.
Shear stress deﬁnitions. Deﬁning representative values of the shear stress for
erosion and deposition experiments is very important in order to produce results
that can be used for modeling purposes. For erosion experiments a representative
value of shear stress is an average along the bottom, i.e.
τb = τ (r, 0)dr. (6)
In deposition experiments deposition is completely controlled by the aggregate
sizes, which depend on the shear stress to which the aggregate has been exposed
to. Due to the secondary ﬂow the aggregates sample diﬀerent values of shear
stress because the uneven shear stress distributions along the walls and because
the shear stress values vary from wall to wall. Then, an appropriate value for the
shear stress is an average of the shear stress along the four walls, i.e.
τb = Rin τ (Rin , z)dz + Rout τ (Rout , z)dz (7)
(Rout + Rin )d + R2 − R2
+ rτ (r, 0)dr + rτ (r, d)dr .
A complete literature review of the main facilities in the world has been presented.
Based in that experience and in the authors experience an operational strategy
for developing operating curves and suitable deﬁnitions for representative values
of shear stress for erosion and deposition experiments in annular ﬂumes has been
Large eddy simulations have been carried out and used to calibrate the annular
ﬂume facility at the VTCHL at the University of Illinois at Urbana-Champaign,
USA using the proposed strategy.
The use of the annular ﬂume for deposition experiments must be done carefully
because secondary currents in the ﬂow are important, even in operation condi-
tions. However, the annular ﬂume can be used to study the process of aggregate
formation where upward and downward currents are not of importance.
The ﬁnancial support from the Metropolitan Water Reclamation District of Greater
Chicago is gratefully acknowledge.
Booij, Robert. 1994. Measurements of the ﬂow ﬁeld in a rotating annular ﬂume.
Tech. rept. 94-2. Delft University of Technology.
Booij, Robert. 2003. Measurements and large eddy simulations of the ﬂows in
some curved ﬂumes. Journal of Turbulence, 4.
Booij, Robert, Visser, Paul, & Melis, Helma. 1993 (August). Laser Doppler Mea-
surements in a Rotating Annular Flume. In: Laser Anemometry - Advances
Flow3D. 2004. http://www.ﬂow3d.com/.
Krishnappan, Bommanna. 1993. Rotating circular ﬂume. Journal of Hydraulic
Engineering, 119(6), 758–767.
Maa, Jerome. 2001. Discussion on the article ”Numerical modeling of ﬂow char-
acteristics in a rotating annular ﬂume” by Yang, Z., Baptista, A., Darland,
J. Dynamics of Atmospheres and Oceans, 33, 321–323.
Partheniades, Emmanuel, & Kennedy, John. 1966 (September). Depositional be-
haviour of ﬁne sediment in a turbulent ﬂuid motion. vol. 1. Proceedings of
the 10th Conference on Coastal Engineering, Tokio, Japan.
Partheniades, Emmanuel, & Metha, Ashish. 1971. Deposition of ﬁne sediments
in turbulent ﬂow. Tech. rept. U.S. Environmental Protection Agency, Wash-
ington, DC, USA.
Partheniades, Emmanuel, Kennedy, John, Etter, Robert, & Hoyer, Richard. 1966.
Investigation of the depositional behavior of ﬁne cohesive sediments in an
annular rotating channel. Tech. rept. 96. M.I.T., Cambridge, Massachusetts,
Peterson, O., & Krishnappan, B. 1994. Measurements and analysis of ﬂow char-
acteristics in a rotating circular ﬂume. Journal of Hydraulic Research, 32(4),
Spork, V., & K¨ngeter, J. 1999. Optimisation of experimental conditions for
annular ﬂumes by LDV measurements. Pages 329–335 of: Jayawardena,
A., Lee, J., & Wang, Z. (eds), River Sedimentation. Proceedings of the 7th
international symposium on river sedimentation, Hong Kong, China.
Spork, Volker, Ruland, Peter, Schneider, Barbara, & Rouv´, Gerhard. 1994. A
New Annular Flume for Investigations on Sediment Transport. International
Journal of Sediment Research, 9(Special issue Dec.), 141–147.
Yang, Zhaoqing, Baptita, Antonio, & Darland, Jeﬀrey. 2000. Numerical modeling
of ﬂow characteristics in a rotating annular ﬂume. Dynamics of Atmospheres
and Oceans, 31, 271–294.
Top view Cross section AA
Figure 1: Geometry of the annular ﬂume. Nomenclature.
0.2 0.175 0.15
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28
Distance from inner wall [m]
Figure 2: Tangential velocity isolines. Symbols: data by Petersen and Krishna-
pann (1994); lines: CFD simulation.
Figure 3: Bed shear stress. Symbols: data by Petersen and Krishnapann (1994);
line: CFD simulation.