Technical Manager Andy Fulcher explores 'Radiation in Flow Simulation, Part 1 : Reflection'

Radiation
in Flow Simulation – Part 1: Reflection

Recently I helped a customer who needed to simulate water
being heated by the sun. The water was flowing in a pipe at the centre
of a parabolic reflector. This is a great way of heating fluids or solids and
surprisingly high temperatures are possible – provided the sun shines!

Naturally, I set up a test in SOLIDWORKS Flow Simulation as
it handles all three heat transfer mechanisms – conduction, convection and
radiation. What I had not appreciated was the capabilities of Flow for ray-tracing
and so I will share what I learnt.

The example is a 250 mm x 300 mm deep parabolic solar trough
– to show you how the sun’s rays can be reflected form shiny surfaces.
These types of device are commercially available and have
implications for the environment and cooking in the third world …

The basic shape I chose is shown below. This was
conveniently created using the SOLIDWORKS ‘Parabola’ sketch entity. The reason
for the shape is that parabolas have a special optical property: if they are
made of material that reflects light, then light which travels parallel to the
axis of symmetry of the parabola and strikes its concave side is reflected
to its focus, regardless of where on the parabola the reflection occurs.
In other words, all the solar
energy is focussed at a single point.

The geometry is therefore very simple: an extruded thin
walled parabola and a pipe at the focus …

The Flow set up is also straightforward – provided you know
how to define a mirror-like shiny surface.

I set up an External project with ‘Heat Conduction in Solids’,
‘Solar Radiation’ and ‘Gravity’ enabled (to account for the effect of natural
convection cooling). I used London as the location and set the date to the end
of May.

I added a ‘Blackbody’ Radiative Surface to the
pipe. This has an emissivity = 1; i.e. it is a perfect absorber of radiation.
Now here is the trick! Initially I applied a ‘Whitebody’
Radiative Surface to the parabolic surface as I wanted a perfect reflector
of radiation.

This was partially correct. However, after running I did not get
the high temperatures I expected. I called SOLIDWORKS and they explained that
the crucial factor I was missing was the surface specularity i.e. shininess. My
parabola was reflecting the radiation – but diffusively and therefore
scattering the solar radiation. To correct this, they recommended I use the
radiative surface called ‘Symmetry’. This is a special
surface that has perfect specularity – a mirror!

With my whitebody and specular surface in place, the
temperatures jumped to realistic values as the radiation became concentrated on
the pipe.
Here is a temperature plot – note the parabola is at room
temperature but the pipe is over 200 deg C.
A hand calculation proves that the majority of solar energy
impinges on the pipe: the sun’s radiation rate in this study is 0.07 Watts / cm2
and the ‘collection area’ (i.e. the horizontal open area of the parabola) is 25
cm x 30 cm = 750 cm2. This gives a total wattage of 52.5 Watts.

Theoretically, the 1 cm dia pipe receives all this heat –
but spread over its outer surface which is 94.6 cm2. Therefore, the
solar radiation rate on the pipe should be 52.5/94.6 Watts per cm2 =
0.55 Watt per cm2.

Here are Flow results …

The negative values indicate heat being absorbed into the
pipe.

The 4% difference can be explained by the fact that the pipe
causes a thermal shadow on the parabola immediately below the pipe. If this
area (30 cm2) is removed from the calculations, the predicted
wattage = 50.4 Watts and the
radiation rate = 0.534 Watts per cm2
– almost identical to Flow.

This confirms that the ray tracing in Flow is accurately
reflecting the solar rays that are then heating the pipe.

This can also be run as a Transient Study. This is very helpful as the parabola only works
efficiently when the sun’s rays are directly overhead. How sensitive is this?
Over what period of time will the parabola work? How does efficiency change
over time? These are crucial questions to anyone designing this type of solar
device – and in Flow the sun can always shine! Even if it does not you can set
a ‘Cloudiness’ Index!

Here is the set-up of radiation. The start time is 9.00 am
and I set it to run for 4 hours …

Below is an animation using the 2017 ‘Transient Explorer’
capability. This shows that the parabola is only effective between 2.6 hours
and 3.6 hours after 9.00 am i.e. 11.30 am – 12.30 pm. Outside this range the
parabola will not work so would need a means of positioning it to face the sun.

Parabolic Reflector Transient Heating

Flow never ceases to amaze me with the depth of capabilities
and ease of use. It has inspired me to design a frame, rapid prototype it, buy
a sheet of mirrored plastic and build my own barbeque for the long hot summer!

What else can we do with radiation in Flow? How about a
magnifying glass and some refraction? Is that possible? Take a look at Part 2
of this blog where I will show you some more cool stuff.

By Andy Fulcher
Technical Manager
Solid Solutions
Management Ltd

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