RadMod2D

Radiation modelling for two-dimensional geometries (RadMod2D)

RadMod2D provides a model for calculating view factors of arbitrary two-dimensional surfaces. With these view factors the additional application of the net radiation method for calculating exchanged heat fluxes can be used.

With a set of basic tools like edges, circles etc arbitrary two dimensional geometries can be build and discretized. Complex geometries can be build externally and transfered into the model format. The view factor matrix for the model's elements get calculated with the area integration method and newly developed blocking algorithm. After applying boundary conditions for each element the heat fluxes due to radiation exchange can be calculated.

A detailed discription of the model is given in the following publication by the contributors:

Büschgens, D., Schubert, C. & Pfeifer, H. Radiation modelling of arbitrary two-dimensional surfaces using the surface-to-surface approach extended with a blocking algorithm. Heat Mass Transfer (2022). https://doi.org/10.1007/s00231-022-03203-4

In order to give credit to the RadMod2D contributors, we simply ask you to cite the reference in any publication in which you have made use of the RadMod2D project.

Setup and Usage

RadMod2D is written in the Julia programming language.

Tested with julia 1.6.1

All files should be run from within the project folder!

./src contains the essential code of the model

Setup julia and package

1. Download and install Julia
2. Open a Terminal
3. Setup enviroment
   1. Go to the folder of this project containing the Project.toml file.
   2. Open Julia
   3. Switch to package mode with ]
   4. In pkg mode activate current environment with activate .
   5. Use instantiate to install packages defined in the Project.toml file (first time only)
4. Check if RadMod2D is working properly
   1. Switch back to julia REPL mode (backspace) or open new terminal with julia
   2. Run script with include("./test/run_test_vf.jl")
   3. Check if RadMod2D is working properly with comparing analytical and numerical results of the calculation

Run custom script

For using RadMod2D and ensuring the right enviroment start the script with:

using Pkg
Pkg.activate(".")
using RadMod2D

A collection of predefined models can be found in test/models2D.jl. One example is a small rectangle (r1) centered inside a bigger rectangle (r2):

include("./models2D.jl")
r1x = 0.8 # length of one side of r1
r1y = 0.8 # length of other side of r1
r2x = 1.2
r2y = 1.2
elemsize = 0.05 # element size used for discretization
m = model_rect_in_rect(r1x, r1y, r2x, r2y, elemsize)

The view factors for the discretized geometry get calculated with:

vfmat = zeros(Float64, m.nelem, m.nelem)
existing_vf!(m, vfmat)
n = 15
dx, dy = create_tiles(m, n)
t_occ = check_tile_occupation(m, dx, dy, n)
blocking_vf_with_tiles!(m, vfmat, dx, dy, n, t_occ)
calculating_vf!(m, vfmat, normit = true)

Afterwards the heat flows per element Q can be calculated with the net radiation method:

epsilon = zeros(m.nelem,1) # emissivities for elements
set_bc_part!(m, epsilon, 1, 0.3)
set_bc_part!(m, epsilon, 2, 0.6)
temp = zeros(m.nelem,1) # temperature boundary conditions per element
set_bc_part!(m, temp, 1:2, 300)
temp[79:106,1] .= 600 # temp bc for specific elements
Q, G = tempsolver(m, vfmat, temp, epsilon)

With the areas of the elements the heat flux density can be determined:

area = [m.elem[i].area for i = m.elem2par[1].first:m.elem2par[end].last]
q = Q[:] ./ area[:]

The plots are made with a plotting toolbox available at test/plot2D.jl. The examples are presented in in test/run_example2.jl.