5th-6th Thermal and Fluids Engineering Conference (TFEC)
May 26–28, 2021
*Corresponding Author: email@example.com
SMART ATOMIZATION: IMPLEMENTATION OF PID CONTROL IN
D. M. Wilson1*, W. Strasser1
1Liberty University, Virginia, USA
We introduce a novel implementation of a proportional integral derivative (PID) control algorithm in CFD
simulations for a biosludge atomizer to accommodate dynamically changing fluid properties. Direct spray
injection of a highly concentrated non-Newtonian biosludge into a steam boiler is sought as a method to
efficiently convert human waste to usable energy. We model biosludge atomization using a twin-fluid atomizer
design with steam as the assisting gas. Difficulties arise because the viscosity of biosludge varies widely; if
viscosity levels are too high, an undesirable pressure drop restricts the flow, and atomization quality suffers. To
improve the robustness of the atomization process, two PID controllers were added. The first automates the flow
of biosludge based on pressure drop across the atomizer. The second compensates for phase momentum ratio
and controls the flow of steam based on droplet size. We demonstrate the efficacy of this coupled controller
system by maintaining efficient atomization with a simulated 100-fold increase in biosludge viscosity.
KEY WORDS: Atomization, Biosludge, PID, CFD, Multiphase, Energy Conversion
Ever increasing energy demands and scarcity of resources drive the need for alternatives to conventional energy
production. Human waste is nothing if not plentiful and is already harnessed for energy by means of digestion
gasification, and pyrolysis. An alternative and more efficient means of energy conversion is direct spray
injection of a highly concentrated, non-Newtonian biosludge (human waste sludge) into a steam boiler.
Compared to other methods of energy conversion that require dilution and/or drying, using a highly concentrated
biosludge increases energy conversion efficiency, reduces water usage, and reduces fossil fuel emissions by
decreasing the transportation load. Effective atomization of a highly concentrated biosludge for combustion is of
great interest for this energy conversion process. Additionally, it is known that shear has cleansing effects for
manure slurries, and atomization is generally a high-shear process .
We model biosludge atomization with a twin-fluid atomizer using steam as the assisting gas. Steam shear
facilitates biosludge atomization by creating instabilities that lead to droplet formation. Additionally, interfacial
unsteadiness leads to a pulsing flow, which further amplifies the growth of instabilities . Steam is also useful
in that it reduces the viscosity of the biosludge by transfer of thermal energy, enabling more effective
atomization. However, steam reduces boiler efficiency as a heat sink and source of non-combustibles.
Preliminary assessment of steam-assisted viscous waste atomizer designs  led to the current configuration.
Quality atomization of biosludge (small droplets) is important for energy conversion due to the effect of
increased interfacial surface area with smaller droplets. However, difficulties arise because the viscosity of
biosludge varies widely, affecting both atomization quality and pump requirements. High biosludge viscosity
restricts the flow, straining the pump. Moreover, viscosity’s restraining force reduces atomization quality.
We introduce a “smart atomization” system that incorporates a proportional integral derivative (PID) control
algorithm into CFD simulations to adjust for dynamically changing biosludge viscosity. PID control is widely
used in industrial processes and can be incorporated into CFD models for testing . Two independent
controllers are incorporated into our CFD model as a coupled system. The first, henceforth referred to as “C1”,
adjusts the flow of biosludge based on biosludge pressure drop across the atomizer. Its objective is to maintain a
consistent pressure drop in the face of widely changing viscosity, which translates to biosludge pump
requirements. The second, henceforth referred to as “C2”, compensates for the phase momentum ratio and
adjusts the flow of steam based on droplet size. Its objective is to maintain consistent droplet sizes while the
atomizer experiences widely varying 1) sludge viscosity and 2) sludge flows resulting from C1 influences. In
short, a coupled system is required to protect atomization quality while ensuring feed pump reliability. The
efficacy of this coupled controller system for PID-assisted atomization is evaluated through a 100-fold step-
increase in biosludge viscosity. Higher fidelity CFD models provide a preliminary assessment of mesh
refinement and atomization characteristics.
2.1 Computational Methods
The atomizer CFD model employed an unconventionally coarse mesh, shown partially in Figure 1, strictly for
our PID controller proof-of-concept. No attempts were made to assess grid or time step independence, and it is
understood that this model is not intended to predict accurate droplet sizes. Again, we emphasize that the
purpose of this work is to develop and demonstrate a robust “smart atomization” process. For computational
efficiency, the full, azimuthally symmetric atomizer geometry was reduced to a 1/32 (11.25°) wedge with
periodic boundary conditions on both azimuthal bounding faces. Almost all of the nearly 250,000 cells are
hexahedral and swept in the general flow direction. The steam pipe and biosludge annulus inlets, denoted by
“Steam Flow” and “Biosludge Flow” in Figure 1, respectively, both have PID-controller-varied mass flow inlets.
The outlet to the right of Figure 1 was a pressure outlet set to atmospheric pressure. Biosludge viscosity was
initially set to a constant 0.05 kg/m-s and later changed to 5 kg/m-s for the 100-fold step-increase. The biosludge
annulus is considerably longer than the steam pipe, extending around 10 times as far to the left of Figure 1. This
“long biosludge entry” strengthened the relationship between biosludge viscosity and pressure drop in the
biosludge annulus, creating a more stable realistic scenario for PID control testing. The domain to the right of
Figure 1 extends about 10 nozzle exit diameters in the axial direction. The nozzle exit and steam pipe diameters
are both 0.016 m, and the biosludge annular gap is 0.0098 m.
The methods used to solve the Reynolds-Averaged Navier-Stokes and volume-of-fluid (VOF) equations in
commercial CFD solver ANSYS Fluent 2020 R1 are described here. Our goals in choosing these methods and
(and choosing the mesh size) were primarily model stability and sufficiently resolved biosludge droplets for PID
control testing. The CFD model uses a “standard” k-ω turbulence model and SIMPLE pressure-velocity
coupling scheme. PRESTO! was used for pressure, second order upwind for momentum, and first order upwind
for turbulence quantities. Geometric reconstruction (PLIC)  was used for the volume-of-fluid (VOF) interface.
Time step was 2e-7 s for all tests, and Courant number remained around 0.5. Both steam and biosludge are
treated as incompressible, and heat transfer was ignored.
Three additional CFD models are used for preliminary characterization of the atomization system and
assessment of mesh refinement’s effect on droplet size. These models include all characteristics previously
outlined except for 1) azimuthal angle and 2) mesh refinement level. The “Base” case used the same element
size range as the 11.25° wedge model in Figure 1 but with a more complete 90° azimuth. The Base mesh was
refined once for a “Ref-1” case, cutting each cell edge length in half in all three dimensions to increase the cell
count by a factor of approximately 8. The only cells not refined were upstream in the steam pipe and biosludge
annulus, far from any steam-sludge interaction. Ref-1 was refined a second time for a “Ref-2” case. The
approximate cell counts are 1, 8, and 66 million for Base, Ref-1, and Ref-2, respectively. These models are for
preliminary assessment and are not grid or time step independent.
Fig. 1 Isometric view of surface mesh for 1/32 (11.25°) wedge atomizer model with periodic boundary
conditions. This coarse mesh was designed strictly to demonstrate proof-of-concept for PID-assisted
atomization, and no grid independence studies were performed. The full mesh contains around 250,000,
mostly hexahedral, cells.
2.2 PID Control Algorithm Implementation
A PID control algorithm was implemented as user-defined functions (UDFs) in ANSYS Fluent 2020 R1 for the
two controllers. Equation 1 is the discrete velocity PID algorithm used, where p is the controlled variable, e is the
error, n is the time stamp, Δt is the sampling time, and Kc, τI, and τD are gain, integral, and derivative constants,
respectively. The error is the difference between the measured variable and setpoint, where measured values are
time-averaged within each Δt sampling period.
( ) ( )
1 1 1 2
n n n c n n n n n n
p p p e e eK e
− − − −
− + + − +
For C1, the measured variable is biosludge pressure drop, and the controlled variable is biosludge mass flow.
Pressure at the biosludge inlet represents biosludge pressure drop, as the outlet is constant at 1 atmosphere. Since
“pressure” and “pressure drop” are functionally the same here, they are used interchangeably in referring to the
measured variable for C1 in the following discussions. For C2, the measured variable is droplet size, and the
controlled variable is steam mass flow. Droplet size is captured by a UDF as the volume-averaged Sauter mean
diameter (SMD) in a series of 10 volumes spaced axially away from the injector . For the purposes of
controller testing, C2’s measured variable is the fifth volume’s SMD, roughly 5 diameters from the nozzle exit.
Two protections are added to each controller to maintain a stable and practical system: 1) mass flow rates of
either phase cannot be set below zero and 2) measured values outside of three standard deviations are not
included in the averaging process.
3. RESULTS AND DISCUSSION
3.1 Controller Tests
To assess the efficacy of the coupled controller system, the controllers were evaluated during a 100-fold
step-increase in biosludge viscosity. Before the viscosity change, only C1 is engaged, and the steam mass
flow is held constant. This essentially results in constant biosludge and steam flows to maintain a quasi-
steady system for a low-viscosity baseline. After the viscosity change, four scenarios are evaluated, each
representing one of the four possible combinations of C1 and C2. These will be referenced simply using the
controller nomenclature as C0, C1, C2, and C12, where C0 represents no controllers engaged and C12
represents the coupled controller system, using both C1 and C2 to control biosludge and steam flow,
respectively. Figures 2-5 show the measured and controlled variables for each scenario across the viscosity
change at normalized flow time (tn) = 0. All data are non-dimensional in this manner: pressure and SMD data
are normalized by their respective setpoints, and mass flows are normalized by the starting value just before
the viscosity change. Flow time is normalized by the convective time scale for biosludge droplets to travel
roughly five diameters axially away from the nozzle exit (where SMD is measured for controller tests). The
bulk velocity is around 150 m/s, and the convective time scale is around 0.0004 s.
The biosludge inlet pressures for C1 and C12 behave similarly (Figure 2), successfully adjusting to the
dramatically higher viscosity level and remaining much lower than those for C0 and C2. Pressure initially
doubles in response to the viscosity increase but is driven back down to the setpoint as the biosludge mass
flow is decreased. For C0 and C2, pressure initially increases by a factor of about 2.5. The C0 pressure then
remains constant, while the C2 pressure continues to increase because of the decreasing steam flow. Table 1
further elucidates the controller responses with time-averaged pressure and standard deviation statistics. C1
and C12 experience no change in mean and a slight decrease in standard deviation through the viscosity shift
(the transition period has been removed for these statistics). C0 and C2 stand in stark contrast; the mean and
standard deviation increase dramatically for both. C2 represents the largest change with a 320% increase in
mean and a 530% increase in standard deviation. Interestingly, the C1 and C12 biosludge flows diverge in
the latter half of Figure 3. The C12 biosludge flow is likely increasing because C2 is decreasing the steam
flow, lowering biosludge pressure and causing C1 to increase the biosludge flow. This suggests an
interesting interplay between C1 and C2 that will be the subject of future investigation.
Fig. 2 Biosludge pressure (equivalent to pressure drop) across a 100-fold biosludge viscosity increase at tn =
0, demonstrating the need for the C1 controller to maintain a constant biosludge pump requirement. For C1
and C12, the pressure returns to setpoint as designed, but C0 and C2 maintain much higher pressures. C2 is
particularly problematic, with the highest and most widely varying pressure.
Fig. 3 Biosludge mass flow in response to a 100-fold biosludge viscosity increase at tn = 0. C1 and C12
behave similarly due to their common biosludge flow controller. After a sharp drop, the C12 biosludge flow
increases and then decreases, suggesting an interesting interplay between the C1 and C2 controllers.
C2 and C12 maintain lower and more stable SMD values compared to C0 and C1, as shown in Figure 4.
While the C2 and C12 time-averaged SMDs remain unchanged through the viscosity change, the C0 and C1
time-averaged SMDs increase by 20% and 40%, respectively (Table 1). While appreciable, we expected
stronger effects by the viscosity change on the time-averaged SMD without controller intervention. Our
preliminary results indicate a surprisingly robust system in terms of average SMD. The most notable change
in SMD, as is visually evident from Figure 4, is the large increase in variation for C0 and C1. While the
SMD standard deviation for C2 and C12 increases moderately, it increases by 450% and 520% for C0 and
C1, respectively. Using a different metric as the measured variable for C2 could improve controller
C2 and C12 adjust the steam flow in different ways because of the difference in sludge flow. C2’s behavior
is expected: the steam flow increases to decrease the SMD by increasing the momentum ratio. The C12
steam flow swings both above and below the constant C1 value. We thus arrive at a useful and obvious
conclusion: engaging C2 allows not only for increased steam usage to maintain the SMD setpoint but also
for decreased steam usage as necessary. In other words, the coupled controller system is free to use only
what steam it requires to maintain atomization quality. It is clear, however, that the C12 steam flow has not
reached quasi-steady state. The aforementioned interplay between C1 and C2 seems to be at work and will
dictate how the steam flow adjusts moving forward. Decreased steam usage is desirable, as steam reduces
boiler efficiency by adding a heat sink and as a source of non-combustibles.
Fig. 4 Biosludge SMD (equivalent to atomization quality) across a 100-fold biosludge viscosity increase at tn
= 0, demonstrating that the C2 controller is necessary to maintain atomization quality. C2 and C12 result in
more consistent SMD values with significantly low standard deviation.
Fig. 5 Steam mass flow in response to a 100-fold biosludge viscosity increase at tn = 0. The C2 steam flow
continues to increase to drive the SMD down. For C12, the biosludge flow reduction requires less assistance
from the steam to maintain atomization quality. This highlights the fact that, with C12, the steam flow can
decrease as appropriate, which increases boiler efficiency.
Table 1 Descriptive statistics for SMD and pressure in Figures 2-5 presented as the ratio of a value after the
100x biosludge viscosity change to that before the viscosity change (excluding transition regions). Thus, a
value of 1 indicates no change through the 100x viscosity increase.
Ratio of Means
Ratio of Standard Deviations
In summary, Figures 2-5 demonstrate 1) the efficacy of the coupled controller system and 2) the need for
both C1 and C2. Figures 2 and 3 demonstrate that the C1 controller is necessary to maintain a constant
biosludge pump requirement. Both C0 and C2 are problematic, as the increase in pressure may be
unacceptable. The C2 pressure increases and varies most dramatically; therefore, C2 alone is not a preferred
option despite its successfully maintaining an acceptable SMD. Figures 4 and 5 demonstrate that the C2
controller is necessary to maintain atomization quality. The dramatic decrease in biosludge flow for C12
resulted in less than the expected increase in steam flow, demonstrating the flexibility of the C2 controller. If
steam flow needs to be higher for better atomization, then it will be. If not, then it will lower, making the
boiler will be more efficient.
3.2 Mesh Refinement and Atomization Characteristics
Biosludge atomization with various meshes (preliminary assessment) is illustrated in Figures 6-9. The Base,
Ref-1, and Ref-2 cases revealed atomization differences and similarities for three mesh refinement levels.
Each case was run in the same manner as the low-viscosity baseline for controller tests: C1 was engaged and
the steam flow held constant with a biosludge viscosity of 0.05 kg/m-s. Biosludge and steam flows were
generally constant in a quasi-steady system. No attempts were made to test other controller combinations or
increase biosludge viscosity. It must be emphasized that even Ref-1 and Ref-2 do not necessarily predict
mesh-independent droplet sizes. These models are intended for preliminary assessment of mesh refinement
and atomization characteristics.
A comparison of the Base, Ref-1, and Ref-2 cases in Figure 6 show that the general characteristics of
atomization remain relatively unchanged as the mesh is refined. The Base case (left in Figure 6) represents
the mesh element size used for controller tests. While finer meshes do result in small droplet resolution, the
general atomization characteristics are largely the same through 2 refinement levels. Of particular
importance to our work is this: if a controller configuration is effective or ineffective for the Base case, it
should perform comparably for the Ref-1 or Ref-2 case. In other words, the Base mesh is sufficient for a
“smart atomization” controller proof-of-concept.
The Ref-2 case further elucidates characteristics of biosludge atomization in our system. Interfacial
instabilities lead to pulsing biosludge, where the biosludge exits the nozzle in “bursts”. A radial pulsing
sequence is illustrated in Figure 7, where a “chunk” of biosludge moves through the nozzle, pushes out
radially, and bursts to break away. A series of pictures like those in Figure 7 at sequential flow times were
studied to determine the time scale of macro biosludge pulsations as being on the order of 0.001 s. The
Ohnesorge and Weber numbers are around 0.23 and 200,000, respectively. The characteristic length used is
the droplet diameter for Ref-2 roughly five diameters axially away from the nozzle exit (where SMD is
measured for controller tests), and the velocity used is the bulk velocity of 150 m/s. Multiple other time
scales and velocities can be observed in the system, which are of interest for future study.
Fig. 6 Representative contours of biosludge (red) and steam (blue) with a biosludge viscosity of 0.05 kg/m-s,
demonstrating the change in droplet resolution as the mesh is refined. The approximate cell counts are 1, 8,
and 66 million for Base, Ref-1, and Ref-2, respectively. The Base case (left) represents the mesh element
size range used for controller tests. While refining the mesh does enable increasingly smaller droplet
resolution, the general characteristics of atomization remain largely unaltered through each level of
Fig. 7 Representative contours of biosludge (red) and steam (blue) with a biosludge viscosity of 0.05 kg/m-s
for the Ref-2 mesh, demonstrating the development of a radial pulse “burst” event. This pulsing sequence
involves a “chunk” of biosludge moving through the nozzle (left), pushing out radially after exiting the
nozzle (middle), and finally bursting radially and breaking away (right).
Figures 8 and 9 show the axial atomization development, with a clear progression of increasingly smaller
droplets further away from the nozzle. A representative iso-surface of the biosludge for the Ref-2 case (90°
wedge) was duplicated 4 times for the full 360° visualization in Figure 8. The axial SMD profiles for the
Base, Ref-1, and Ref-2 cases are plotted in Figure 9. Each axial curve shows droplet size generally
decreasing as distance from the nozzle increases, which corresponds to what is visually evident from Figure
8. Increasing mesh refinement results in smaller droplets, as is shown in Figure 6. The difference in droplet
size between Ref-1 and Ref-2 is smaller than that between Base and Ref-1, indicating a movement towards
mesh independence. Each axial SMD curve has roughly the same shape except for the “humps” in Ref-1 and
Ref-2, which are present because the models likely need more run time to fully reach quasi steady state. The
similarity in profile confirms the conclusion of Figure 6: while mesh refinement decreases droplet size, the
general characteristics of atomization are preserved.
Increasing Flow Time
Increasing Mesh Refinement
Fig. 8 Representative iso-surfaces of the biosludge (blue) with a viscosity of 0.05 kg/m-s for the Ref-2 mesh.
The 90° wedge model is duplicated 4 times to visualize the full azimuth.
Fig. 9 Preliminary axial SMD profiles for the Base, Ref-1, and Ref-2 cases. Distance from the orifice is
normalized by the orifice diameter. As expected, Ref-1 and Ref-2 show increasingly lower droplet sizes.
Each curve has roughly the same shape except for the “humps” in the two lower curves, which are present
because the models likely need more time to fully reach quasi steady state.
A proof-of-concept computational study was conducted to assess coupled PID control as a viable means for
consistently atomizing viscous biosludge with dynamically changing fluid properties. We refer to this novel
implementation of PID control algorithms as “smart atomization”. Atomization of highly concentrated, non-
Newtonian biosludge is of interest for efficient energy conversion via direct spray injection into a boiler. Our
method is designed to protect atomization quality and supply system reliability under the influence of
dramatically changing biosludge properties. Two PID controllers (C1 and C2) were included as user-defined
functions in a CFD model for a twin-fluid biosludge atomizer with steam as the assisting gas. C1 controlled
the flow of biosludge to maintain a constant pressure drop (pump requirements), and C2 controlled the flow
of steam to maintain consistent droplet size (atomization quality).
We evaluated controller performance for two scenarios across a 100-fold increase in biosludge viscosity.
Having no controllers engaged significantly increased pressure drop and SMD, in terms of both time
averages and standard deviations. Engaging only C1 resulted in a consistent pressure drop but increased the
SMD time average and standard deviation by 20% and 520%, respectively. Engaging only C2 maintained a
consistent SMD but drove the pressure drop time average and standard deviation up by 320% and 530%,
respectively. Engaging both C1 and C2 as a coupled controller maintained both pressure drop and SMD at
their respective setpoints. Additionally, steam usage decreased on average with both controllers engaged,
which is desirable for boiler efficiency. Preliminary assessment of refined meshes showed a decrease in
droplet size but a general maintenance of atomization characteristics, justifying a coarse mesh for a “smart
atomization” proof-of-concept. In summary, our preliminary tests demonstrate that a coupled controller
system can maintain reasonably constant atomization quality and biosludge pump requirements through a
100-fold increase in biosludge viscosity while reducing steam usage to improve boiler efficiency. Future
work will include more mesh refinement analyses, modeling the biosludge as non-Newtonian, and modeling
energy effects, as the steam will reduce biosludge viscosity.
C0 No controllers ( - )
C1 Biosludge flow controller ( - )
C2 Steam flow controller ( - )
C12 Coupled controller system ( - )
e Controller error ( - )
Kc Controller gain ( - )
n Time stamp ( - )
p Controlled variable ( - )
SMD Sauter mean diameter (m)
Δt Controller sampling time (s)
τD Controller derivative constant ( - )
τI Controller integral constant ( - )
tn Normalized flow time ( - )
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