Radiative Heat Transfer by View Factors

[dgerosasotelo]

Dear community,

I hope you are doing well.

I am having some problems with my Final Engineering Project: I am trying to simulate the heat loss from a cattle trough to the environment in order to understand the freezing mechanism and provide a solution to this problem.
My simulation consists of a 2D domain to reduce simulation time, where I have two flow regions. The first one, which looks like half of a circle, represents the water in the trough, the material I have assigned to it is a solid with water properties to avoid natural convection. The other flow region represents part of the environment surrounding the trough and I attribute the properties of air to it. However, to minimize the effects of convection in the air I change the specific heat to 1.
The assigned boundary conditions are described in the following image:

Face 423: Slip, Adiabatic, Opaque (Emissivity = 0)
FAce 937: No Slip (solid), Adiabatic, Opaque (Emissivity = 0)
Faces 2, 548, 27: Slip, Fixed temperature=-10°C, Opaque (Emissivity =1)
Face NONE: No slip, Fixed Heat Flux = 10W/m^2), Opaque (Emissivity= 0,95 (water))
Note that Face 33 has not been asigned any boundary condition because it is an interface.

I ran the simulation for 86.400 seconds (24 hours).
The problem appears when I obtain the area integral of the faces bordering the environment: unexpectedly the faces parallel to the interface face are the ones that exchange the most radiative heat (Qr). Naturally, the face opposite to the interface should be the one receiving the most radiative heat and that puzzles me a lot.

The energy balance between the two flow regions is correct, since the amount of heat introduced by Face NONE is the same that enters in Face 33. However, inside the air flow region the distribution is not phically correct as I mentioned before.
I will also post some images of the solution fields to help you understand the whole scenario.

I hope you can help me,

Best regards,
Dante.

[RicardoParis]

Hello!

Quick comments:

• Since your water material is currently opaque, the radiation will never be able to make its way to the bottom-most face, since the transmissivity for opaque materials is 0.
  
  

In other words: as far as the water domain goes, from a radiation perspective, currently only the air/water interface will play a role. Maybe you want to try one of the other radiative behaviors?

• Given that you have a steady-state simulation, this simulation control configuration does not mean that you are running the simulation for 36000 seconds of real life time. It just means that you are requesting 36000/10 = 3600 iterations from the solver.

• Radiation is not available for transient studies, so only steady-state simulations would work with these exact physics.

Cheers

[dgerosasotelo]

Hi Ricardo! Thank you for your response.

I choosed the radiative opaque behaviour for water because what I want to simulate is the heat loss from the water surface to the ambient. I am not interested in the radiative heat transfer in the water domain. Knowing this do you still think that I should try other radiative behaviour for the water?

Also, I investigated in Simscale documentation about the methods used to simulate radiation heat transfer: for Conjugate Heat Transfer the Discret Ordinates Method (DOM) is used. Knowing this I am suspecting that the strange distribution of the radiative heat transfer in the faces of the ambient domain is a consecuence of the radiation scattering due to the participating medium. Do you think that if I run the simulation with more iterations the distribution of radiative heat will follow a more natural behaviour? What number of iterations do you recommend for this problem?

Hope you still fine. Thank you in advance for your help!

BR

[RicardoParis]

Hi!

I guess it depends on what behavior you’re looking to get. If you go “opaque” for water, then the interface between water/air does not allow any rays through it (transmissivity = 0). If you go “transparent” or “semi-transparent”, then you will allow rays through the interface. To me, since water is not opaque, this option doesn’t seem a good one, but it depends on what you are trying to emulate.

Water will still exchange heat with the surrounding air by means of convection regardless of what option you choose for the radiative behavior.

PS: there’s no participating medium options at the moment in SimScale - radiation will be a face-to-face exchange.

[dgerosasotelo]

Hi, Ricardo! Thanks again for your reply.

In my simulation, I wanted to demonstrate how much heat water loses due to radiation, without taking into account the effects of convection with air (for this, I changed the CP of air to 1). Based on your comments, I think that perhaps another radiative behavior might work better for water, since I am using a surface heat flux at the bottom of the duct. By doing so, I expect the water to heat up by convection until it reaches an equilibrium temperature, at which point the heat input from the bottom should be equal to the heat exchanged by radiation, since this is the only heat transfer mechanism available at the outlet of the water domain (convection with air is neglected, as mentioned above).

Finally, the Simscale documentation states that in conjugate heat transfer simulations, the DOM is used to calculate the behavior of radiation, while in convective heat transfer simulations, the face-to-face method is used. That is why I am considering that my simulation, being a conjugate heat transfer, uses the DOM. However, I would be interested in using the face-to-face method to validate my simulation by measuring the radiative heat on each wall of the environment and verifying that the sum of all these flows is equal to the heat lost at the interface.

Radiation Behavior | Heat Modelling Documentation | SimScale

BR