Craig 2013
Craig 2013
Craig 2013
Article history: A computational fluid dynamics (CFD) model that evaluates mechanical mixing in a full-
Received 2 March 2013 scale anaerobic digester was developed to investigate the influence of sewage sludge
Received in revised form rheology on the steady-state digester performance. Mechanical mixing is provided through
25 April 2013 an impeller located in a draft tube. Use is made of the Multiple Reference Frame model to
Accepted 5 May 2013 incorporate the rotating impeller. The non-Newtonian sludge is modeled using the Hershel
Available online 21 May 2013 eBulkley law because of the yield stress present in the fluid. Water is also used as modeling
fluid to illustrate the significant non-Newtonian effects of sewage sludge on mixing pat-
Keywords: terns. The variation of the sewage sludge rheology as a result of the digestion process is
CFD considered to determine its influence on both the required impeller torque and digester
Digester mixing patterns. It was found that when modeling the fluid with the HersheleBulkley law,
HersheleBulkley law the high slope of the sewage stress-strain curve at high shear rates causes significant
Impeller mixing viscous torque on the impeller surface. Although the overall fluid shear stress property is
Viscous torque reduced during digestion, this slope is increased with sludge age, causing an increase in
Sludge rheology impeller torque for digested sludge due to the high strain rates caused by the pumping
impeller. Consideration should be given to using the Bingham law to deal with high strain
rates. The overall mixing flow patterns of the digested sludge do however improve slightly.
2013 Elsevier Ltd. All rights reserved.
pumped mixing, and Yu et al. (2011) who considered me- nature of the mechanical mixing configuration does determine
chanical mixing using an axial flow impeller and a helical the influence of an MRF implementation. E.g., Bakker et al.
ribbon. Their modeling fluid was a non-Newtonian sludge (2009) modeled a pitch-blade turbine impeller agitating a
modeled by a power law whose coefficients were determined non-Newtonian slurry (modeled as a HersheleBulkley law
by a rheological experiment. Bridgeman (2012) modeled a cy- fluid) with a straight-bladed stator located in close proximity to
lindrical digester stirred by two six-blade paddles, again using the impeller. Because of the small gap between the impeller
the same dairy cow liquid manure properties as Wu (2010a). and stator, they found that the MRF approach couldnt capture
Wu (2010a), Yu et al. (2011) and Bridgeman (2012) used the MRF the strong time-dependent interaction between the two as the
(Multiple Reference Frame) approach in ANSYS Fluent (2010) SMM could. In the current application, the impeller is situated
to model the relative rotation of the impellers/stirrers in the in a stationary draft tube providing a constant axi-symmetric
computational domain. Meroney (2009) used water (Newto- boundary that enhances the ability of the MRF method to
nian) as modeling fluid for dilute sludge and simplified the accurately model the steady-state situation. Wu (2011) used
effect of impellers in draft tubes using fan boundary condi- the SMM for the LES simulations in that study, and since large-
tions. Terashima et al. (2009) used an imposed body force to eddy simulations are inherently transient, the additional cost
simulate the effect of a downward-pumping screw located in a of the SMM was not that much of a factor. Although the LES-
draft tube. Their study is the only digester CFD simulation in SMM results were better than the RANS-MRF results in that
the literature that assumed laminar flow. study, the slight increase in accuracy was judged not to be
Wu (2011) asserted that most digester applications are justified by the considerable increase in computational effort.
turbulent and used Large Eddy Simulation (LES) (Wu, 2012) This paper evaluates an anaerobic digester situated in a
and a range of 12 turbulence models (Wu, 2010b) to evaluate municipal waste water treatment plant. The work was
different turbulence closure methods. Of the Reynolds- prompted by the retrofitting of existing, old digesters with
Averaged NaviereStokes (RANS) models, the standard k-u new mixing equipment. It is therefore important that the CFD
performed the best. The high cost of LES limited the investi- modeling provides confidence of the mixing performance of
gation as to the improved turbulent resolution that can be the digester as well as gives an indication of the power
obtained with this model (Wu, 2010b). In evaluating a gas- required by the impeller/draft tube combination. Because of
mixed digester, Wu (2010a) decided on the SST k-u turbu- the fact that the digester modification has not been imple-
lence model for modeling gas mixing. Bakker et al. (2009) mented, full-scale validation is not possible. Of the CFD
found that the SST k-u turbulence model performed the best digester studies in literature, only Terashima et al. (2009)
in the modeling of an agitated non-Newtonian slurry. report full-scale results in the form of a tracer experiment.
When modeling the motion of an impeller or stirrer in a Lab-scale digester validation has been performed by other
bioreactor or chemical reactor, the incorporation of the me- researchers using CFD simulation (e.g., Bridgeman, 2012;
chanical mixer can be done in different ways. Apart from the Meroney, 2009; Yu et al., 2011) or through the use of simpler
MRF approach and simplified actuator plane methods (e.g., fan geometries like non-Newtonian pipe flow (Wu and Chen, 2008)
boundary condition, imposed body force) mentioned above, a or water agitated in a tank with a Rushton turbine (Wu, 2010c).
more accurate but more computationally intensive method is In general, these validation exercises show that CFD modeling
the Sliding Mesh Model (SMM), as implemented, e.g., in ANSYS is capable of predicting digester mixing and performance
Fluent (2010). Kritzinger (2010) compared the MRF method to provided that modeling features like grid independency,
the SMM and found that the MRF method provided reliable proper rheological treatment and impeller rotation are treated
engineering answers in a much shorter time (mainly because correctly.
the MRF allows for a steady-state solution while the SMM Domestic sewage or sludge exhibits yield stress behavior
method is inherently transient). In that study, the impeller (Monteiro, 1997) and as such is better modeled using the
interacted with stationary blades in a stirrer reactor. The exact HersheleBulkley or Bingham laws. The power law used for
w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 4 4 8 5 e4 4 9 7 4487
liquid manure in the CFD studies mentioned above is there- consistency coefficient (k), plastic viscosity (mp) and power-law
fore not applicable in that it assumes zero yield stress in the index (n) are determined experimentally. It can be seen that
non-Newtonian fluid. In addition, Monteiro (1997) showed the Bingham law corresponds to the HersheleBulkley law
that the rheological properties of sewage sludge change dur- with n 1.
ing the digestion process. For batch operation, this means that In the implementation in ANSYS Fluent (2010), a critical
the power consumed by the impeller will change during shear rate parameter, g_ c , is added to avoid infinite apparent
operation and for sizing purposes, the maximum torque and viscosities at very low shear rates (due to the discontinuity at
power needs to be known. For continuous feed digesters, the g_ 0 in equation (3)). It is implemented via a switch between
sludge in the digester has a variation in age. For this reason, the linear stress-strain region and the shear-thinning/thick-
rheological properties ranging from raw to digested sludge are ening portion in the following manner:
used in the study to investigate this effect. g_
sy 2
The paper starts with describing the theoretical model used g_ c g_
For g_ g_ c : h k 2 n n 1 (4)
for the CFD simulation, followed by a description of the rheo- g_ c g_ c
logical properties implemented. The geometric description
n1
and meshing strategy used is explained next, thereafter CFD sy g_
For g_ > g_ c : h k (5)
model settings like turbulence modeling, boundary conditions g_ g_ c
used and the MRF approach are discussed. After a presentation Equation (4) reduces to equation (3) at g_ g_ c . Some re-
of mixing criteria, results are presented. These take the form of searchers assume a constant value for the apparent viscosity
a grid independence study, an evaluation of free-surface mo- below the critical shear rate instead of the linear relationship
tion on the results, the effect of sewage sludge age on the tor- shown in equation (4). E.g., Bakker et al. (2009) adjust this
que required for turning the impeller, and an overall discussion critical apparent viscosity (and hence the shear rate) until
of digester mixing patterns. Conclusions conclude the paper. their simulated results correspond to experimental pre-
dictions. As the data measured in Monteiro (1997) extend
down to a lower shear rate limit of 0.01 s1, this value is used
2. Theoretical model
for the critical shear rate in the current study, except for the
first case listed in Table 1, where 0 s1 is used, implying that
The commercial CFD code ANSYS Fluent (v.13.0, v.14.0 and
only equation (5) is used in the model. To illustrate the dif-
v.14.5) is used to determine the steady-state iso-thermal tur-
ference between the Monteiro (1997) data (for 3e4% total
bulent flow in the digester through solution of the Naviere-
solids (TS) by weight when raw) and the 5.4% TS liquid dairy
Stokes equations (continuity and conservation of momentum).
cow manure used by Wu (2010a), refer to Fig. 1 where the
The following sections discuss different aspects of the theo-
shear stress versus shear rate is plotted on a logelog scale.
retical model.
Both raw (0 days) and digested (40 days) sludge data from
2.1. Rheological properties Monteiro (1997) are shown together with HersheleBulkley law
fits that most closely resemble the single experiment
Domestic sludge seems to be better described by the Her- measured data (coefficients also presented in Table 1). At
sheleBulkley law (Monteiro, 1997), which is a combination of diminishing shear rates (as found in the body of the digester),
the power law and the Bingham law. The HersheleBulkley law the sewage sludge reaches a constant yield stress that de-
allows for shear-thinning or shear-thickening after yield, creases with sludge age. For liquid manure, the shear stress
depending on the power law index being less or more than required diminishes toward zero as the shear rate is reduced
one, respectively. Both the HersheleBulkley and Bingham (similar to that shown in Fig. 1 for water at 20 C, for com-
laws have a yield stress that needs to be overcome before the parison). At high shear rates however (as are found on the
fluid comes into motion. surfaces of the impeller and draft tube), a high shear stress is
required to bring the non-Newtonian fluid into motion. The
Bingham law : s sy mp g_ (1) slope of this curve at high shear rates increases with sewage
sludge age (Monteiro, 1997), implying that digested sludge
Hershel Bulkley law : s sy kg_ n (2) remains difficult to pump using an impeller but that the bulk
digester fluid that experiences low shear rates is more easily
h sy kg_ n1 (3) kept in motion (lower shear stress required). Data from
g_
Baudez et al. (2011) who only consider digested sewage sludge
where s is the shear stress, g_ the strain or shear rate and h the are also plotted in Fig. 1. Their 1.85% total solids concentration
apparent viscosity. The parameters yield stress (sy), (when digested) data match very well with that of Monteiro.
Table 1 e HersheleBulkley law coefficients for sewage sludge (based on Monteiro (1997)).
Sludge age [days] Yield stress, Power-law Consistency index, Critical shear rate,
sy [Pa] index, n k [Pa.sn] g_ c [s1]
100
Hershel-Bulkley n=0.66,k=0.75,ty=0.7
Hershel-Bulkley n=1.15,k=0.0017,ty=0.3
Water @20C
0.1
Critical
shear rate
0.01
0.001
0.001 0.01 0.1 1 10 100 1000
shear rate [1/s]
Fig. 1 e Rheological properties of sewage sludge (Monteiro, 1997), liquid manure (Achkari-Begdouri and Goodrich, 1992),
digested sludge (Baudez et al., 2011) and water with HersheleBulkley law fits for sewage sludge.
Table 1 also lists the HersheleBulkley coefficient data for discussed under the Results section). To allow more gradual
raw sludge based on Monteiros own data fits for both his turning of the flow, a bellmouth-shaped rotating flow
experiments (the raw sludge total solids concentration deflector was also considered (Fig. 4).
differed for the two experiments listed (Monteiro (1997)). This The domain was meshed with mixed cells (hexahedral,
coefficient set was used for all simulations except those tetrahedral and prisms). Cells were concentrated in the impeller
evaluating the effect of sludge age (see Results section). area and draft tube inlet and outlet where the highest gradients
Fig. 3 e Impeller in draft tube with cone-shaped deflector. 2.3. Turbulent closure
rND2
Reimpeller water
m
rVa2n Dn
Redrafttube sludge
k0:75 0:25=nn 8n1
rVa D
Redrafttube water
m
Fig. 5 e Difference between coarse, medium and fine mesh models at impeller outlet for cone-shaped deflector (note
thickness of draft tube, as well as differing mesh distributions on impeller and digester faces) a) Fine mesh, b) Medium
mesh, and c) Coarse mesh.
domain (rest of draft tube and digester). The extent of the MRF 2.5. Boundary conditions and convergence
zone has an influence on the solution because of the treat-
ment of the interface between the zone that is rotating rela- The free surface of the digester was treated as a slip wall (i.e.,
tive to the zones that are stationary. The lower interface of the zero shear stress specified on this boundary). All the other walls
MRF was chosen to be 195 mm below the rotating impeller. were treated as no-slip smooth walls. As the digester is modeled
The upper interface of the MRF was chosen to be in the throat with no inlets or outlets, the flow patterns are established
of the impeller draft tube exit as indicated in Figs. 3 and 4a). through application of a rotation to the impeller MRF zone. The
The effect of the size of the MRF zone was not investigated.
Fig. 6 e Fine mesh in the region of the impeller (inserts Fig. 7 e Velocity magnitude contours on solid surfaces of
showing difference between medium and coarse mesh impeller, shaft and stationary cone-shaped flow deflector
models). (N [ 500RPM).
w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 4 4 8 5 e4 4 9 7 4491
would have f1, f2 and f3, with f1 associated with the finest
mesh. The order of convergence, p, can then be calculated as
f3 f2
p ln lnr (6)
f2 f1
f1 f2 rp f1 f2
fh0 f1 p (7)
rp 1 r 1
The Grid Convergence Index (GCI ) of the fine grid is defined
as
Fs jj
GCIfine (8)
rp 1
Fig. 8 e Velocity contours on solid surfaces of impeller, where Fs is a factor of safety (Fs 1.25 when a minimum of 3
shaft and rotating bellmouth-shaped flow deflector solutions are available (Roach, 1998)) and the relative error, ,
(N [ 500RPM). is
f2 f1
(9)
f1
impeller rotation direction is set to provide upward pumping in When 3 solutions are available, we can calculate GCI12 and
normal operation. The surface velocities of the impeller and flow GCI23 in a dimensionless form, as
deflector are shown in Figs. 7 and 8 for the two draft tube con-
f2 f1 f3 f2
Fs F
figurations considered. In Fig. 7, the cone deflector is stationary, f1 f
s
2
while in Fig. 8, it can be seen that the bellmouth-shaped flow GCI12 and GCI23 (10)
rp 1 rp 1
deflector is rotating. Convergence is obtained when normalized
If we are in the asymptotic range of convergence, then
residuals have stabilized (typically all residuals less than 1E-3
except for u, less than 5E-3) and when the draft tube mass flow GCI23 zrp GCI12 : (11)
rate and impeller torque had stabilized.
Therefore, if
Draft tube mass flow rate [kg/s] 1091 1078 1078 1076
Steady-state operating impeller torque [Nm] 264 260 284 279
Volume turnover time [min] 19.1 19.3 19.3 19.3
Velocity gradient (G-value) [s1] 105 104 109 108
Power dissipated per unit volume/Mixing 11.1 10.9 11.9 11.7
Energy Level [W/m3]
Draft tube mass flow rate [kg/s] 1091 1078 1076 2.374 1076 0.042 0.271 0.988
Steady-state operating impeller 264 284 279 1.758 277 0.734 3.157 1.076
torque [Nm]
As discussed in Sections 1 and 2.6, the SST k-u turbulence of revolution was formed. A 3D steady-state simulation with
model is chosen for this study based on previous experience this perturbed but fixed free surface was performed to
and recommendations from other authors. To provide addi- investigate this influence on the impeller performance pa-
tional support for this choice, the Reynolds Stress turbulence rameters. The free-surface shape modeled is displayed in
model (RSM) was evaluated for the coarse mesh using water as Fig. 10. A sample result (see Fig. 11) for non-Newtonian
modeling fluid. The RSM uses 7 additional equations instead sludge shows that an unrealistic flow pattern is obtained.
of the 2 equations used for the SST k-u turbulence model. As The fixed free-surface slip wall causes the impeller jet to be
illustrated in Table 3, this higher-order turbulent closure deflected downward and attach to the outer surface of the
provides results that are within 1.5% of the coarse mesh SST draft tube before ingestion at the bottom of the draft tube.
result, justifying the use of the cheaper SST k-u turbulence This flow pattern was obtained for both water and non-
model for the rest of the results in this paper. Newtonian sludge. The impeller torque and draft tube
mass flow rate estimates were not influenced substantially
for water (less than 6%) implying that the draft tube flow is
3.2. Effect of free-surface assumption largely unaffected by the digester flow pattern. In order to
obtain a more physically realistic representation of the free-
Because of the close proximity of the free surface of the surface behavior, a transient VOF simulation incorporating
digester to the draft tube outlet (approximately 300 mm), it is both sludge and air would need to be performed on the 3D
expected that the impeller jet stream will interact with the geometry. An added complexity in such a model could be
free surface during operation. The question is how much the the treatment of a crust (should it form) in terms of its
deviation in the free-surface level from horizontal will characteristics (motion, break-up. etc.). Such an analysis is
impact the performance estimate of the impeller or the outside the scope of the present study. For the remainder of
digester mixing performance. The free-surface boundary is
modeled as a slip wall, i.e., no resistance (zero shear stress) is
imparted by the air above the fluid level to the fluid motion. If
the free surface is forced to remain horizontal, then the fluid
flow of the jet is forced to turn in a horizontal direction once
it impacts this surface. Apart from resulting in an incorrect
jet momentum (direction and magnitude), this could cause
an increase in the back pressure of the impeller.
To test the effect of this flat slip-wall assumption, a 2D
axi-symmetric CFD simulation was performed with the
Volume of Fluid (VOF) method (ANSYS, 2010) to get an esti-
mate of the free-surface movement for the average draft
tube velocity obtained with the 3D CFD model. This transient
simulation reached a steady-state free-surface position after
about 4 s (see Fig. 9 for a snapshot at 5.4sec). This position Fig. 9 e Free-surface position at t [ 5.4s (2D Axi-symmetric
(exported from ANSYS Fluent as a surface) was imported model, no swirl, HersheleBulkley non-Newtonian fluid
and parameterised as a spline curve in GAMBIT and a body model, 1000 kg/s mass flow rate).
w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 4 4 8 5 e4 4 9 7 4493
Fig. 12 e Effect of draft tube exit shape on draft tube flow patterns, HersheleBulkley (n [ 0.5, k [ 0.5 Pa.sn, sy [ 0.9 Pa),
N [ 500RPM: a) Straight cone (stationary deflector), and, b) Bellmouth (rotating deflector).
4494 w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 4 4 8 5 e4 4 9 7
Fig. 13 e Effect of draft tube exit shape on overall flow patterns, HersheleBulkley (n [ 0.5, k [ 0.5 Pa.sn, sy [ 0.9 Pa),
N [ 500RPM: a) Straight cone (stationary deflector), b) Bellmouth (rotating deflector), and c) Water, stationary straight cone
deflector e All velocity scales clipped at 0.3 m/s.
Table 5 e Comparison of integrated quantities for different draft tube exit geometries.
Straight cone deflector Bellmouth rotating deflector
Draft tube mass flow rate [kg/s] 1070 1076 1111 1112
Steady-state operating impeller torque [Nm] 306 279 249 237
Volume turnover time [min] 19.4 19.3 18.7 18.7
Velocity gradient (G-value) based on viscosity of water [s1] 113 108 102 99.6
Power dissipated per unit volume/Mixing Energy Level [W/m3] 12.8 11.7 10.4 9.92
Fig. 14 e Effect of sludge age on overall flow patterns, N [ 500RPM: a) Raw sludge, and, b) Digested sludge e All velocity
scales clipped at 0.3 m/s.
Fig. 15 e Strain rate plots, N [ 500RPM: a) Raw sludge (single experiment), b) Digested sludge (single experiment), and c)
Raw sludge (averaged data) e All scales clipped at 3000 sL1.
4496 w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 4 4 8 5 e4 4 9 7
Bingham law fits to his data. Fig. 16 compares the high strain
rate behavior of the two laws (HersheleBulkley and Bingham)
based on Monteiros averaged data for raw (0 days) and
digested (40 days) sludge. Note how the two HersheleBulkley
curves cross over at around 1700 s1 strain rate, while the
Bingham curves remain parallel on the logelog plot because of
the constant plastic viscosities of the two fluids.
4. Conclusions
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tube mass flow rate. The second effect was detrimental in Reactor (PhD thesis). Technical University Delft.
that the torque required to turn the rotating bellmouth flow Meroney, R.N., 2009. CFD simulation of mechanical draft tube
mixing in anaerobic digester tanks. Water Research 43 (4),
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1040e1050.
impeller. The main reason for this is the large diameter of Metzner, A.B., Reed, J.C., 1955. Flow of non-Newtonian fluids-
the bellmouth. A solution to this problem could be to correlation of laminar, transition and turbulent-flow regions.
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Monteiro, P.S., 1997. The influence of the anaerobic digestion
process on the sewage sludges rheological behaviour. Water
Science and Technology 36 (11), 61e67.
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