Content uploaded by Wayne Strasser

Author content

All content in this area was uploaded by Wayne Strasser on Aug 20, 2021

Content may be subject to copyright.

5th-6th Thermal and Fluids Engineering Conference (TFEC)

May 26–28, 2021

Virtual Conference

TFEC-2021-36753

*Corresponding Author: dwilson221@liberty.edu

1

SMART ATOMIZATION: IMPLEMENTATION OF PID CONTROL IN

BIOSLUDGE ATOMIZER

D. M. Wilson1*, W. Strasser1

1Liberty University, Virginia, USA

ABSTRACT

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

1. INTRODUCTION

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 [1].

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 [2]. 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 [3] 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.

TFEC-2021-36753

2

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 [4]. 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. METHODS

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) [5] 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.

TFEC-2021-36753

3

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

2

D

n n n c n n n n n n

Ie

t

p p p e e eK e

te

− − − −

− + + − +

=

=−

(1)

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 [6]. 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.

TFEC-2021-36753

4

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.

TFEC-2021-36753

5

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

effectiveness.

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.

TFEC-2021-36753

6

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.

TFEC-2021-36753

7

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

Case

SMD

Pressure

SMD

Pressure

C0

1.4

2.5

5.5

1.8

C1

1.2

1.0

6.2

0.9

C2

1.0

4.2

1.5

6.3

C12

1.0

1.0

1.8

0.9

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.

TFEC-2021-36753

8

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

refinement.

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.

Burst Event

Increasing Flow Time

Increasing Mesh Refinement

TFEC-2021-36753

9

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.

Injector

Biosludge

Atomization

TFEC-2021-36753

10

4. CONCLUSION

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.

NOMENCLATURE

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 ( - )

REFERENCES

[1] Liu, Z., Carroll, Z.S., Long, S.C., Roa-Espinosa, A., Runge, T., “Centrifuge separation effect on bacterial indicator reduction in

dairy manure,” Journal of Environmental Management, 191, pp. 268-274, (2017).

[2] Strasser, W., Battaglia, F., “The Effects of Prefilming Length and Feed Rate on Compressible Flow in a Self-Pulsating

Injector,” Atomization and Sprays, 27(11), pp. 929-947, (2017).

[3] Strasser, W., “Towards Atomization for Green Energy: Viscous Slurry Core Disruption By Feed Inversion,” Atomization and

Sprays, (2020). (In Revision)

[4] Wong, S., Zhou, W., Hua, J., “Designing process controller for a continuous bread baking process based on CFD modelling,”

Journal of Food Engineering, 81, pp. 523-534, (2007).

[5] Strasser, W., Battaglia, F., “The effects of pulsation and retraction on non-Newtonian flows in three-stream injector

atomization systems,” Chemical Engineering Journal, 309(1), pp. 532-544, (2017).

[6] Strasser, W., “Oxidation-assisted pulsating three-stream non-Newtonian slurry atomization for energy production,” Chemical

Engineering Science, 196, pp. 214-224, (2019).