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A. Bhattacharya
of the PCM. Heat transfer occurs due to heating from the bottom boundary and at
first sensible energy absorption occurs. Subsequently, the PCM starts melting and
energy is absorbed as latent heat.
Geometry creation model. For simulating the stated problem a coupled method is
used (Dinesh and Bhattacharya 2019). The method combines a geometry creation
model with a melting and solidification solver. The geometry creation model assumes
that the 3-dimensional cuboidal domain is filled with overlapping pores of different
sizes. The entire geometry creation process is performed using the following algorithm.
• At first, the cuboidal domain is created based on the length of its three sides.
• Pores are represented by spheres. Each sphere is defined by its radius (r) and
co-ordinates of its center (x c , y c , z c ). The minimum and maximum sphere radius
(r min , r max ) are input parameters specified by the user. To insert a sphere in the
domain, a random location within the domain is selected as the center coordinates
for the sphere. The radius of the sphere is randomly selected using a random
number generator subjected to the upper and lower bounds of r max and r min , i.e.
r min ≤ r ≤ r max . After the coordinates of its center (x c , y c , z c ) and radius (r) are
fixed, a sphere can be considered to be generated in the domain.
• To insert the subsequent sphere, another parameter, the sphere overlap, needs to
be defined. The sphere overlap parameter denotes whether two spheres intersect
each other or not. The distance between the centers of the two spheres can be
calculated using d =
(x n − x c ) 2 + (y n − y c ) 2 + (z n − z c ) 2 where x n , y n , z n are
the coordinates of the center of the new sphere. Sphere overlap is defined as
q = d/(r + r new ) where r new is the radius of the new sphere. If q is less than 1, it
means that the two spheres intersect each other. This type of interaction between
the spheres will lead to open cell type foam structure. If q is greater than 1, it
means that the two spheres do not intersect each other leading to closed cell foam
structure. At the limiting value of 1, the two spheres touch each other at a single
point. For the geometry creation model, the minimum and maximum values of
pore overlap are specified by the user.
• To insert a second sphere, the sphere radius is randomly assigned using the criteria
r min ≤ r new ≤ r max and a random location is selected as the coordinates for the
center of the second sphere with random overlap subjected to the minimum and
maximum overlap bounds specified previously.
• Subsequently, spheres are generated one by one in a sequential manner following
the same procedure. For each sphere, its overlap with all the existing spheres has
to be checked. However, to make the algorithm computationally efficient, only the
spheres within a certain distance from the center of the new spheres are considered
for this overlap calculation.
• After generation of each sphere, the total volume occupied by the spheres is calculated and the resultant porosity is checked. If the resultant porosity reaches or
exceeds the specified foam porosity, the generation of spheres is stopped.
A. Bhattacharya
of the PCM. Heat transfer occurs due to heating from the bottom boundary and at
first sensible energy absorption occurs. Subsequently, the PCM starts melting and
energy is absorbed as latent heat.
Geometry creation model. For simulating the stated problem a coupled method is
used (Dinesh and Bhattacharya 2019). The method combines a geometry creation
model with a melting and solidification solver. The geometry creation model assumes
that the 3-dimensional cuboidal domain is filled with overlapping pores of different
sizes. The entire geometry creation process is performed using the following algorithm.
• At first, the cuboidal domain is created based on the length of its three sides.
• Pores are represented by spheres. Each sphere is defined by its radius (r) and
co-ordinates of its center (x c , y c , z c ). The minimum and maximum sphere radius
(r min , r max ) are input parameters specified by the user. To insert a sphere in the
domain, a random location within the domain is selected as the center coordinates
for the sphere. The radius of the sphere is randomly selected using a random
number generator subjected to the upper and lower bounds of r max and r min , i.e.
r min ≤ r ≤ r max . After the coordinates of its center (x c , y c , z c ) and radius (r) are
fixed, a sphere can be considered to be generated in the domain.
• To insert the subsequent sphere, another parameter, the sphere overlap, needs to
be defined. The sphere overlap parameter denotes whether two spheres intersect
each other or not. The distance between the centers of the two spheres can be
calculated using d =
(x n − x c ) 2 + (y n − y c ) 2 + (z n − z c ) 2 where x n , y n , z n are
the coordinates of the center of the new sphere. Sphere overlap is defined as
q = d/(r + r new ) where r new is the radius of the new sphere. If q is less than 1, it
means that the two spheres intersect each other. This type of interaction between
the spheres will lead to open cell type foam structure. If q is greater than 1, it
means that the two spheres do not intersect each other leading to closed cell foam
structure. At the limiting value of 1, the two spheres touch each other at a single
point. For the geometry creation model, the minimum and maximum values of
pore overlap are specified by the user.
• To insert a second sphere, the sphere radius is randomly assigned using the criteria
r min ≤ r new ≤ r max and a random location is selected as the coordinates for the
center of the second sphere with random overlap subjected to the minimum and
maximum overlap bounds specified previously.
• Subsequently, spheres are generated one by one in a sequential manner following
the same procedure. For each sphere, its overlap with all the existing spheres has
to be checked. However, to make the algorithm computationally efficient, only the
spheres within a certain distance from the center of the new spheres are considered
for this overlap calculation.
• After generation of each sphere, the total volume occupied by the spheres is calculated and the resultant porosity is checked. If the resultant porosity reaches or
exceeds the specified foam porosity, the generation of spheres is stopped.