Annular Ultraviolet Reactor with Particle Tracing

In this example, the sterilization of water in a simple ultraviolet (UV) water purification reactor is modeled using a combination of optical ray tracing, computational fluid dynamics (CFD), and Lagrangian particle tracking methods.

The model consists of three studies. In the first study, the fluence rate in the annular region surrounding a UV lamp is solved for, using the Geometrical Optics physics interface. The fluence rate represents the amount of radiation that a small spherical detector would absorb per unit time, divided by the cross sectional area of such a detector. It has the same units as irradiance (SI unit: W/m2), but is a volume quantity and can be defined at any arbitrary point in space, not just on surfaces.

In the second study, the velocity profile of water flowing through the reactor is solved for, using the Turbulent Flow, k-ε interface. The reactor in this example is a U-shape with inlet and outlet tubes running perpendicular to the orientation of the lamp.

In the third study, particles are traced through the reactor using the Particle Tracing for Fluid Flow interface. The particle velocity is based on the velocity of the water solved for in the second study. As the particles move through the reactor, the accumulated dose along their trajectories is computed, based on the fluence rate solved for in the first study.

The results show that all particles arriving at the outlet have been exposed to a certain minimum dose. A small number of particles, mostly those passing very close to the lamp, are subject to a substantially higher dose. This model could be used as a starting point to develop more energy-efficient UV water purification reactors by seeking designs with a more uniform accumulated dose.

This model requires the Ray Optics Module, CFD Module, and Particle Tracing Module.

Model Definition

The model geometry consists of the annular region between a cylindrical UV lamp and the cylindrical reactor that surrounds it, along with inlet and outlet tubes. All of the domains contain flowing water at room temperature.

Ultraviolet Lamp Model

The surface of the lamp is treated as a diffuse (Lambertian) emitter using the node. Rays are released at the lamp surface with uniform spatial density, and the initial direction of each ray is sampled according to the cosine law. The total power of the lamp is specified; in this example the power distribution over the lamp surface area is assumed to be uniform, although it is also possible to define a weighting factor.

As rays propagate through the water, away from the lamp surface, the power of each ray is attenuated based on the internal transmittance of the water, which in this example is taken to be 70% per centimeter of propagation. For distilled water, the internal transmittance of germicidal UV radiation is approximately 98%, so the value of 70% used here could represent that the water is less pure.

As rays propagate through the water, the volumetric fluence rate is computed using the dedicated node. To obtain an accurate distribution of the fluence rate, it is important to release a sufficiently large number of rays and to use a sufficiently fine mesh in the domain. In this example, 100,000 rays were released in order to balance accuracy with solution time and file size considerations, but in some publications the number of rays could be orders of magnitude greater (Ref. 1).

Rather than releasing rays diffusely at the lamp surface, a possible extension of this model would be to release rays from positions inside the lamp. At the lamp surface, then, the light could be refracted into the water domain according to Snell’s law and the Fresnel equations. Another possible extension is to use the boundary condition on the exterior surfaces of the reactor, rather than an absorbing boundary condition.

Fluid Flow

The Turbulent Flow, k-ε physics interface was used to solve for the fluid velocity and pressure in the reactor. At the boundary, the built-in option was used to define the inflow velocity profile.

The default mesh is controlled by the Turbulent Flow, k-ε interface in this model, which causes boundary layers to grow on surfaces with the boundary condition. Note that a mesh was used to reduce solution time in this example model, so the results should be verified using a finer mesh. The mesh also controls the resolution of the fluence rate computed by the Geometrical Optics interface, which uses constant shape functions.

Particle Tracing

The Particle Tracing for Fluid Flow interface was used to track particles as they flow past the lamp. The fraction of deactivated or killed bacteria was predicted using a simple exponential decay model with a fixed inactivation constant k (SI unit: m2/J),

where N is the number or concentration of active bacteria at any point along a particle trajectory and N0 is the initial number or concentration. The variable E0 appearing in the time integral is the fluence rate obtained from the study.

To integrate the fluence rate along each particle trajectory, an was defined with time derivative equal to E0. At any time, the value of E0 for any particle is found by evaluating the volumetric fluence rate at the particle’s instantaneous position.

Simulations of particles in a fluid are prone to numerical stiffness when the particles are small and the fluid velocity is large. This is because accelerations of small particles in response to drag by the surrounding fluid occur over the time scale τp given by

where

•

ρp (SI unit: kg/m3) is the density of the particle,

•

dp (SI unit: m) is the particle diameter, and

•

μ (SI unit: Pa s) is the dynamic viscosity of the surrounding fluid.

For a micron-sized particle in water, this time scale is on the order of 10-7 seconds. A full inertial treatment of the particle motion would require time steps close to this order of magnitude, whereas the maximum time for particles to cross through the reactor is on the order of 10 seconds. It would therefore be possible to include the effects of particle inertia but the model would be significantly more time-consuming. For a similar reason, the effects of turbulent dispersion have been neglected in this example; each model particle follows a streamline of the mean fluid velocity. In an inertial particle tracing simulation with very small time steps, it would also be possible to get a more realistic solution by enabling turbulent dispersion in the settings for the .

Results and Discussion

A plot of the fluence rate is shown in Figure 1. The fluence rate is greatest in the region adjacent the lamp, and significantly smaller at the outermost extents of the reactor volume. Thus, particles passing through the center of the reactor are subjected to more intense UV radiation compared to particles moving along the outer edges.

The fluid velocity is shown in Figure 2 and the particle trajectories in Figure 3. The in the trajectory plot shows the fraction of bacteria yet to be inactivated, starting at 1 and with 0 representing complete inactivation.

In Figure 4 a plot shows the accumulated dose of particles that reach the outlet by the final time. All particles receive a dose of at least 10 mJ/cm2, but for some particles the accumulated dose is substantially higher.

Figure 1: Fluence rate distribution in a cross section of the UV reactor.

Figure 2: Slice plot of the fluid velocity norm, with arrows indicating the velocity direction.

Figure 3: Particle trajectories in the UV reactor. The color expression shows the fraction of surviving bacteria.

Figure 4: Histogram of the accumulated dose along particle trajectories. The plot was filtered to exclude particles that did not reach the outlet by the final time.

References

1. Y.M. Ahmed, M. Jongewaard, M. Li, and E.R. Blatchley III, “Ray Tracing for Fluence Rate Simulations in Ultraviolet Photoreactors,” Environ. Sci. Technol., vol. 52, no. 8, pp. 4738–4745, 2018.

2. D.A. Sozzi and F. Taghipour, “UV Reactor Performance Modeling by Eulerian and Lagrangian Methods,” Environ. Sci. Technol., vol. 40, no. 5, pp. 1609–1615, 2006.

Ray_Optics_Module/Ultraviolet_Sterilization/annular_ultraviolet_reactor_particle

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select ε .

Click .

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
r_lamp	1[cm]	0.01 m	Lamp radius
r_reac	5[cm]	0.05 m	Reactor radius
L_reac	100[cm]	1 m	Reactor length
L_lamp	80[cm]	0.8 m	Lamp length
d_lamp	L_reac-L_lamp	0.2 m	Lamp displacement
mid_lamp	d_lamp+L_lamp/2	0.6 m	Lamp midplane location
P	40[W]	40 W	Total source power
r_inl	3[cm]	0.03 m	Inlet radius
L_inl	30[cm]	0.3 m	Inlet length
z_inl	5[cm]	0.05 m	Inlet z-coordinate
k_inact	0.1[cm^2/mJ]	0.01 s²/kg	Inactivation rate constant

Geometry 1

Reactor

In the toolbar, click

In the window for , type Reactor in the text field.

Locate the section. In the text field, type r_reac.

In the text field, type L_reac.

Inlet Pipe

In the toolbar, click

In the window for , type Inlet Pipe in the text field.

Locate the section. In the text field, type r_inl.

In the text field, type L_inl+r_reac.

Locate the section. In the text field, type z_inl.

Locate the section. From the list, choose .

Outlet Pipe

In the toolbar, click

In the window for , type Outlet Pipe in the text field.

Locate the section. In the text field, type r_inl.

In the text field, type L_inl+r_reac.

Locate the section. In the text field, type L_reac-z_inl.

Locate the section. From the list, choose .

Union 1 (uni1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select all objects.

In the window for , locate the section.

Clear the check box.

Lamp

In the toolbar, click

In the window for , type Lamp in the text field.

Locate the section. In the text field, type r_lamp.

In the text field, type L_lamp.

Locate the section. In the text field, type d_lamp.

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Find the subsection. Click to select the

toggle button.

Select the object only.

In the toolbar, click

Geometrical Optics (gop)

In the window, under click .

In the window for , locate the section.

In the text field, type 0.

Select the check box.

Locate the section. From the list, choose .

Ray Properties 1

In the window, under click .

In the window for , locate the section.

In the λ0 text field, type 254[nm]. A low-pressure mercury vapor lamp would emit most of its UV radiation at this wavelength (Ref. 1).

Medium Properties 1

In the window, click .

In the window for , locate the section.

From the n list, choose . In the associated text field, type 1.38. This is approximately the refractive index of water at 254 nm (Ref. 1).

From the list, choose .

From the τi,10 list, choose . In the associated text field, type 0.7. Different values of the internal transmittance of water can be used here, depending on the clarity of the water. For pure water, the internal transmittance of germicidal UV radiation is about 0.98 per centimeter (Ref. 1). The value of 0.7 shown here indicates that the water is less clear.

Release from Boundary 1

In the toolbar, click

and choose .

Select Boundaries 5, 6, 9, and 10 only. These are the curved surfaces of the inner cylinder. Use the middle mouse wheel to select an interior boundary in the Graphics window. You can also make it easier to view the interior boundaries by enabling wireframe rendering.

In the window for , locate the section.

From the list, choose .

In the N text field, type 100000.

Locate the section. From the list, choose .

Select the check box.

In the Nw text field, type 1.

Specify the r vector as


0	t1
0	t2
1	n

From the list, choose .

These settings will cause rays to be released from the lamp surface with uniform spatial density, with a distribution of initial directions following the cosine law with respect to the surface normal at each release position. To ensure that the surface normal points in the outward direction rather than the inward direction, look for the arrows in the Graphics window.

Locate the section. In the Psrc text field, type P.

Fluence Rate Calculation 1

In the toolbar, click

and choose .

Select Domain 1 only.

Wall 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Turbulent Flow, k-ε (spf)

In the window, under click ε .

Inlet 1

In the toolbar, click

and choose .

Select Boundary 20 only.

In the window for , locate the section.

From the list, choose .

Locate the section. Click the button.

In the V0 text field, type 25[gal/min].

Outlet 1

In the toolbar, click

and choose .

Select Boundary 21 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Particle Tracing for Fluid Flow (fpt)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Drag Force 1

In the toolbar, click

and choose .

Select Domain 1 only.

In the window for , locate the section.

From the u list, choose .

Particle Properties 1

In the window, click .

In the window for , locate the section.

From the ρp list, choose . The default value of the particle density will be used.

Inlet 1

In the toolbar, click

and choose .

Select Boundary 20 only.

In the window for , locate the section.

From the list, choose .

In the N text field, type 1000.

In the ρ text field, type spf.U.

Outlet 1

In the toolbar, click

and choose .

Select Boundary 21 only.

Particle Counter 1

In the toolbar, click

and choose .

Select Boundary 21 only.

Absorbed Dose

In the toolbar, click

and choose .

In the window for , type Absorbed Dose in the text field.

Locate the section. In the text field, type dose.

In the R text field, type gop.frc1.E0.

Locate the section. Click

In the table, enter the following settings:


Dependent variable quantity	Unit
Custom unit	J/m^2

Definitions

Variables 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
rs	exp(-k_inact*dose)		Survival rate

Mesh 1

In this example a mesh is used. To get higher resolution of the radial dependence of the fluence rate, a structured mesh could be created, although this may require the addition of mesh control surfaces to the geometry sequence.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click

Study 1

Step 1: Ray Tracing

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type 0 0.2.

Locate the section. In the table, enter the following settings:


Physics interface	Solve for	Equation form
Geometrical Optics (gop)	√	Automatic (Time dependent)
Turbulent Flow, k-ε (spf)		Automatic (Stationary)
Particle Tracing for Fluid Flow (fpt)		Automatic (Time dependent)