COMSOL 6.4 - Vdara® Caustic Surface

When the Vdara® hotel first opened in Las Vegas, visitors relaxing by the pool would experience intense periods of heat at certain times of the day and at certain times of the year. This intense heat was caused by the reflection of solar radiation from the curved, reflective surface on the South-facing side of the hotel. This model shows how a caustic surface is generated in the pool area around the time and date the problems were first reported.

This application also requires the CAD Import Module.

Figure 1 below shows a small area of the CityCenter® complex which is the subject of this model. The concave surfaces of the Vdara® hotel are illuminated by sunlight, indicated by red arrows, at certain times of the day. The direction of the reflected rays depends on the direction of the incident solar radiation and the surface normal of the hotel.

Figure 1: A solar flux incident on the concave surface of the Vdara® hotel is reflected down to the pool area beneath.

The Geometrical Optics interface can compute the intensity along individual ray paths by computing the principal radii of curvature of the associated wavefronts. When plane waves are reflected by the surface of the hotel, these principal radii of curvature are changed. When the rays are reflected by a concave surface, the radius of curvature decreases in magnitude thereafter and eventually approaches zero. A continuous set of points at which either principal radius of curvature equals zero is called a caustic surface. In lens systems, the caustic surface often demarcates an envelope of rays. In the limit of geometrical optics, the ray intensity is infinite on a caustic surface. Practically, this corresponds to locations where the incident heat flux is extremely high, which can cause severe burns.

Model Definition

The model geometry includes the Vdara® hotel and several nearby buildings in the CityCenter® complex.

Figure 2: Imported CAD geometry of a section of the CityCenter® complex. The Vdara® hotel is shown at the top.

In order to avoid having to trace rays from the sun onto the surface of the hotel, a special boundary condition called the is employed. This boundary condition allows rays to be released from the surface of the hotel directly, significantly reducing the simulation time. The direction at which the rays are released from the surface of the hotel depends on the incoming ray direction vector n and the outward surface normal ns, according to the formula

The principal radii of curvature of the released rays are also computed based on the radii of curvature of the incident wavefront and the curvature of the surface of the hotel. More details can be found in the Ray Optics Module User’s Guide.

When the rays arrive at the swimming pool area, the intensity value of each ray is projected onto the surface mesh. This allows for more convenient visualization of the intersection of the caustic surface with the boundary. The feature is used to accomplish this by implementing the following equation:

where Rj is the value of an arbitrary source term for the jth incident ray, qj is the position of the jth ray when it strikes the pool area, and rb is the value of the accumulated variable on a given boundary mesh element. Any expression for the source term Rj may be defined; for this example, Rj=log(Ij) is used, where Ij is the intensity of the jth ray. The sum is taken over all rays that reach a given boundary element. The logarithm is used to better visualize changes in the order of magnitude of the ray intensity.

The selections for the boundary conditions are shown below. The curved, reflective surfaces of the hotel that face the sun are shown in orange. The other surfaces of the hotel are shown in gold. The pool and the surrounding area are shown in blue.

Figure 3: Close-up view of the Vdara® hotel.

Results and Discussion

The trajectories of the rays can be seen in Figure 4. The rays begin to cross each other after they reflect off the surface of the hotel. The color represents the intensity, which becomes very high at specific locations, indicated by the green and red coloring.

Figure 4: Ray trajectories reflecting off the Vdara® hotel in September at 11:45 am. The arrows indicate the direction vector of the solar radiation.

The projection of the high-intensity regions onto the swimming pool area is plotted in Figure 5. As expected, for this specific time of month and day, there is a clearly visible caustic surface cutting directly across the pool yard.

Figure 5: Plot of the log of the intensity projected onto the swimming pool area. There is a region of very high intensity right across the swimming pool.

Reference

1. M. Vollmer and K-P. Möllmann, “Caustic effects due to sunlight reflections from skyscrapers: simulations and experiments,” Eur. J. Phys., vol. 33, pp. 1429–1455, 2012.

Ray_Optics_Module/Solar_Radiation/vdara_caustic_surface

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

This example uses an imported CAD geometry. Check that is selected from the list.

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file vdara_caustic_surface.x_b.

Click

Compare the imported geometry to Figure 2.

Disable the analysis of the geometry as the remaining small geometric details can be kept.

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Definitions

Create a selection that contains all of the surfaces of the hotel.

Hotel Surfaces

In the toolbar, click

In the window for , type Hotel Surfaces in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type 0.475.

In the text field, type 0.52.

In the text field, type 0.38.

In the text field, type 0.5.

In the text field, type 0.01.

In the text field, type 0.2.

All of the surfaces of the hotel should be selected, including the orange and gold surfaces in Figure 3.

Geometrical Optics (gop)

In the window, under click .

In the window for , locate the section.

Click

Locate the section. In the text field, type 0.

Locate the section. From the list, choose .

Selecting the checkbox causes a variable for the final ray status available for postprocessing; this will be used to filter rays so that only the rays that reach the pool are viewed.

Locate the section. Select the checkbox.

Illuminated Surface 1

In the toolbar, click

and choose .

Select boundaries 351, 356, and 359, the curved surfaces of the hotel that face the sun. These surfaces are colored orange in Figure 3.

In the window for , locate the section.

From the list, choose .

In the N text field, type 50000.

Locate the section. From the list, choose .

From the list, choose .

In the table, enter the following settings:


Day	Month	Year
01	9	2014

In the table, enter the following settings:


Hour	Minute	Second
11	45	0

Wall 1

In the toolbar, click

and choose .

Select boundaries 321, 331, and 345, the pool and the surrounding area. These surfaces are colored blue in Figure 3.

Accumulator 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

In the R text field, type gop.logI.

The text field will turn yellow and a tooltip warning will appear, indicating that the deduced unit does not match the expected unit. Fix this by specifying the dependent variable quantity.

Locate the section. Click

In the table, enter the following settings:


Dependent variable quantity	Unit
Custom unit	m^-2

Wall 2

In the toolbar, click

and choose .

The second condition allows rays to be reflected multiple times at different surfaces of the building.

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Mesh 1

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 .

Click

In the dialog, type 10 in the text field.

In the text field, type 200.

Click .

In the toolbar, click

Results

Ray Trajectories (gop)

In the window for , click to expand the section.

From the list, choose .

In the text area, type Reflected Rays and Ambient Solar Radiation.

Grid 3D 1

The default plot shows the paths of the reflected rays. The direction of the incident solar radiation is also shown as a vector field. First, adjust the dataset so that the vectors are closer together.

In the window, expand the > node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.4.

In the text field, type 0.48.

Find the subsection. In the text field, type 0.4.

In the text field, type 0.48.

Find the subsection. In the text field, type 0.05.

In the text field, type 0.15.

Ray Trajectories (gop)

Now resume editing the plot.

In the window, expand the > node.

Color Expression 1

In the window, expand the > > node, then click .

In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

Filter 1

Plot only the rays with final status gop.fs==2. This is true for all rays that have hit a with the condition; that is, all rays that have reached the pool. Filtering the rays makes the solution easier to visualize.

In the window, click .

In the window for , locate the section.

From the list, choose .

In the text field, type gop.fs==2.

Ray Trajectories (gop)

Add a plot to the building and poolside to make them appear solid.

Surface 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .