aiming beyond infinity: GSoC

Showing posts with label GSoC. Show all posts

Friday, September 27, 2013

Python Software Foundation - SfePy : GSoC 2013 : The Begining!

Hi Pythonistas,

GSoC finally comes to an end.
It was a wonderful experience.
My projects and docs are available on my repo.
It was an awesome experience going through the wonderful projects of other pythonistas.

Adios & Cheers!
Ankit

Monday, September 16, 2013

Python Software Foundation - SfePy : GSoC 2013 : The Final Lap

Hi Pythonistas,

So finally I am heading into the final lap of GSoC 2013.
Just a few more steps away from complete integration and need to update the doc strings.

Pushed my latest codes.
Feeling awesome!

Regards,
Ankit

Liquid Fraction

Temperature

Velocity

Thursday, September 12, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 12 & 13

Hi Pythonistas,

PS: I will get a bit informal in today's report. Do forgive me for that.

Past 14 days have given me the best coding experience of my lifetime. After doing rigorous research I had formalized my problem statement earlier and started working on it. I realised the true intricacies in my problem when I started searching for methods by which phase change simulations are implemented. I had to change my earlier timeline and jump to my project problem directly. This field is a relatively new field and the algorithms have been developed surrounding the legacy SIMPLE algorithm by Patankar. From Brent, A.D., Voller, V.R. and Reid, K.J.(1988) to Chakraborty, P R and Dutta, P (2011), people have developed the enthalpy update scheme for accounting phase change keeping Patankar's algorithm as the base. I was familiar with SIMPLE algorithm earlier so I have developed a phase change solver for SfePy using Semi-Implicit Method for Pressure Linked Equations (Revised) or SIMPLER algorithm which is much more robust than SIMPLE algorithm.

The solver code is located here.
Download test problem file here.

Run python brent_test.py
You will get an output dir containing the vtk files which can be viewed using
./postproc.py <file>.vtk

Sample:

The entire group can be loaded in Paraview and you can get the animation.

The code has been validated for the melting gallium experiment performed by Gau and Viskanta(1986) & Brent et al.(1988).

You can see that the code is following the trend and the difference is due to the slight change in thermophysical properties of Gallium taken in the code which might be different while performing the experiments.

Do leave your views in the comments below.

Regards,
Ankit

Phase Change Solver - SfePy GSoC 2013

Hi Pythonistas,

Here are some videos of the final result I obtained using the new solver I developed for Phase Change Effect Simulation.
A more detailed blogpost will follow soon.
Right now just enjoy the videos. :)

Regards,
Ankit

Tuesday, September 3, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 10 & 11

The ﬁnal problem accounting convection-diﬀusion along with phase change has been deﬁned below along with the governing equations and validation case studies.

Problem
Heat transfer in the processing of materials involving solid-liquid phase transformations (melting and solidiﬁcation) is commonplace in such ﬁelds as metallurgy, crystal growth from melts and solutions, puriﬁcation of materials, and solidiﬁcation of metals. The associated density gradients in a gravitational ﬁeld can induce natural convection ﬂows. Convection in the liquid phase inﬂuences the process in two diﬀerent ways, one of which is beneﬁcial and the other of which can be detrimental. During melting convection increases the overall transport rate and, hence, the growth rate of the new phase, which is desirable. On the other hand, during solidiﬁcation convection decreases the growth of the new phase and also seems to aﬀect the morphology of the solid-liquid interface adversely. The nature of the solid is largely determined by what occurs in the vicinity of the solid-liquid interface. The heat release (absorption), density change, and other processes that take place in the vicinity of the transformation front result in nonuniformities along the front that cause its shape to change. The resulting density gradients in the liquid generate buoyancy-driven convection that can aﬀect the transport of heat, constituent chemicals, and the growth rate.
The physical domain considered is shown in the ﬁgure. The vertical side walls of the enclosure are maintained at uniform temperatures, while the connecting horizontal walls are adiabatic. The govering equations are written for the entire domain assuming constant thermophysical properties, Boussinesq approximation, laminar, incompressible, and Newtonian two-dimensional ﬂow. The solid-liquid interface motion due to volume change upon melting or solidiﬁcation is neglected through the assumption

ρ_{s} = ρ_{l}

Nomenclature

$ρ$	Density	kg/m $^{3}$
$μ$	Viscosity	Pa.s
$c_{p}$	Speciﬁc heat capacity	J/kg.K
$k$	Thermal conductivity	W/m.K
$β$	Thermal expansion coeﬃcient	1/K
$L$	Latent heat of fusion	J/kg
$H$	Enthalpy	J/kg
$f$	Volume fraction
$T$	Temperature	$^{\circ}$ C
$t$	Time	s
$\vec{u}$	Velocity	m/s
$p$	Pressure	Pa
$S$	Source term	m/s $^{2}$

Subscript

$l$	Liquid
$s$	Solid
$r e f$	Reference
$e f f$	Eﬀective
$h o t$	Hot
$c o l d$	Cold
$i n t$	Initial
$m e l t$	Melting

Governing Equations

The continuum relations:

g_{l} + g_{s} = 1

f_{l} + f_{s} = 1

f_{l} = \frac{g_{l} ρ_{l}}{ρ}

f_{s} = \frac{g_{s} ρ_{s}}{ρ}

ρ = g_{l} ρ_{l} + g_{s} ρ_{s}

\vec{u} = f_{l} {\vec{u}}_{l} + f_{s} {\vec{u}}_{s}

k_{e} f f = g_{l} k_{l} + g_{s} k_{s}

c_{p} = f_{l} c_{p_{l}} + f_{s} c_{p_{s}}

1. Continuity

\nabla \cdot (\vec{u}) = 0

2. Momentum

ρ "["\frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \nabla \vec{u}"]" = - \nabla p + μ \nabla^{2} \vec{u} + ρ \vec{g} β (T - T_{r e f}) + B \vec{u}

Now the key lies in modelling the source term. The coeﬃcient

B

which should tend to 0 as the liquid volume fraction

g_{l}

approaches unity, and should become a large negative number to anhilate the motion in the ﬂuid region at

g_{l} = 0

. Whereas these asymtotic conditions can be satisﬁed by several functions, we adopt the suggestion of Brent et al. :

B = \frac{- C {(1 - g_{l})}^{2}}{(g_{l}^{3} + b)}

where

C = 1.6 \times 1 0^{6}

b = 0.001

2. Energy
Writing a general equation for conservation of thermal energy for all the zones in the domain is facilitated by focusing on an element undergoing phase change. Below are the energy equation of solid and liquid phases under the thermal equilibrium condition

T_{l} = T_{s} = T

:
Solid

\frac{\partial (ρ_{s} g_{s} H_{s})}{\partial t} + \nabla \cdot (ρ_{s} g_{s} \vec{u_{s}} H_{s}) = \nabla \cdot (g_{s} k_{s} \nabla T) + S_{s}

Liquid

\frac{\partial (ρ_{l} g_{l} H_{l})}{\partial t} + \nabla \cdot (ρ_{l} g_{l} \vec{u_{l}} H_{l}) = \nabla \cdot (g_{l} k_{l} \nabla T) + S_{l}

where

S_{s}

and

S_{l}

are the interphase energy terms, having the same magnitude but being opposite in sign.
A single governing enthalpy equation results:

\frac{\partial (ρ H_{m})}{\partial t} + \nabla \cdot ρ (f_{s} \vec{u_{s}} H_{s} + f_{l} \vec{u_{l}} H_{l}) = \nabla \cdot (k_{e f f} \nabla T)

where

H_{m} = f_{s} H_{s} + f_{l} H_{l} = H_{s} + f_{l} (H_{l} - H_{s})

The latent heat content of the element is due to the fraction of liquid converted to, or from, the corresponding quantity of solid. Hence we write

Δ H = f_{l} (H_{l} - H_{s}) = f_{l} L

H_{m} = H_{s} + f_{l} L

H_{s} = c_{p} T

H_{l} = H_{s} + L

where L is the latent heat of fusion.
The zones where

T > T_{m e l t}

, the entire element is in the liquid state and

f_{l} = 1

.
The zones where

T < T_{m e l t}

, the entire element is in the liquid state and

f_{l} = 0

.
It is the elements undergoing phase change at

T = T_{m e l t}

, where

f_{l}

varies between 0 and 1. Substituting

H_{m}

and

H_{l}

in equation we get

\frac{\partial (ρ H)}{\partial t} + \nabla \cdot (ρ \vec{u} H) = \nabla \cdot (\frac{k_{e f f}}{c_{p}} \nabla H) S_{e}

where

\vec{u} = f_{l} \vec{u_{l}}

S_{e} = - \frac{\partial (ρ Δ H)}{\partial t} = - ρ L \frac{\partial (f_{l})}{\partial t}

Initial Conditions

f_{l} = 0

everywhere

T = T_{i n t}

everywhere

\vec{u} = 0

everywhere.

Boundary Conditions

f_{l} = 1

Left wall

f_{l} = 0

Right wall

f_{l} [i] [j] = f_{l} [i - 1] [j]

Top

f_{l} [0] [j] = f_{l} [1] [j]

Bottom

T = T_{h o t}

Left wall

T = T_{c o l d}

Right wall

\vec{u} = 0

Walls

Validation Cases
Melting Gallium : Gau and Viskanta
Melting Gallium : Brent et al.
Melting Calcium chloride : Zivkovic and Fujii

References

Zivkovic, B., Fujii, I., 2001. “An Analysis of Isothermal Phase Change of Phase Change Material within Rectangular and Cylindrical Containers”. Solar Energy, 70, pp. 51-61.
Brent, A.D., Voller, V.R., Reid, K.J., 1988. “Enthalpy-porosity Technique for Modeling Convection-diﬀusion Phase Change: Application to the Melting of a Pure Metal”. Numerical Heat Transfer, 13(3), pp. 297-318.
Gau, C., Viskanta, R., 1986. “Melting and Solidiﬁcation of a Pure Metal on a Vertical Wall”. Journal of Heat Transfer, 108(1), pp. 174-181.
Rajeev, K., Das, S., 2010. “A Numerical Study for Inward Solidiﬁcation of a Liquid Contained in Cylindrical and Spherical Vessel”. Thermal Science, 14(2), pp. 365-372.
Vreeman, C. J., Krane, M. J. M., Incropera, F. P. , 2000. “The Eﬀect of Free-Floating Dendrites and Convection on Macrosegregation in Direct Chill Cast Aluminum Alloys. Part 1: Model Development”. Int. J. Heat Mass Transfer, 43, pp. 677-686.
Flemings, M. C., 1974. Solidiﬁcation Processing. McGraw-Hill, New York.
Kumar, A., Walker, M. J., Sundarraj, S., Dutta, P., 2011. “Grain Floatation During Equiaxed Solidiﬁcation of an Al-Cu Alloy in a Side-Cooled Cavity: Part II-Numerical Studies”. Metallurgical and Materials Transactions, 42(B), pp. 783-799.
Voller, V.R., 2006. Handbook of Numerical Heat Transfer, 2nd ed.. Wiley, New York, NY, pp. 593-622.

Wednesday, August 28, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 8 & 9

Hi Pythonistas,

It has been quite busy lately and I have done some extensive research in this period to come up with the final set of equations of my problem.

Btw,
Have a look at an awesome example I tried out which is a legacy 'mixing elbow' problem using SfePy.

Regards,
Ankit

Wednesday, August 14, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 7

Hi,

This week was spent on midterm evaluation.
The next biweekly report (Week 8&9) is coming soon.

Cheers.

Tuesday, July 30, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 6

Hi Pythonistas,

This week I spent coupling steady Navier Stokes Equation with the Energy Equation.

First Navier-Stokes Eq is solved to get the velocity field then this result is used to calculate the temperature field.

Code:

https://github.com/animator/sfepy/blob/phase_change/examples/phase_change/convective_diffusive/convective_diffusive.py

Monday, July 22, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 4&5

Hi Pythonistas,

Week 4&5 went of really well.

- Firstly after huge amount of discussions we finalised the Navier-Stokes solver and have started development on it.

- In parallel, working on the coupled convective-diffusive problem that I have selected: Laminar Heat Transfer to a Steady Couette Flow
between parallel plates. Where first the Navier Stokes Equation will be solved to determine the velocity and pressure field and then that will be used to determine the temperature field using the Energy Equation.

- I have also added new examples:

Steady Axial convection and diffusion in parabolic flow with maximum velocity U in an insulated pipe.

Commit - 1 2

Also benchmarked our solver based on the four cases mentioned in the paper Laminar Heat Transfer to a Steady Couette Flow
between parallel Plates

Case A

Case B

Case C

Case D

Except for one plot in Case D (Psi = 0.200) all other graphs obtained were in accordance with the paper.

Commit - Link

This week I will focus on obtaining the result of coupling the equations.

Adios!

Sunday, July 7, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 3

Hi Pythonistas,

This week kicked off with the hunt for a robust Navier-Stokes solver for SfePy.
I went through huge amount of resources.

To summarise the journey:

For our Navier-Stokes currently we use the Newton method with backtracking line-search. in OpenFoam and most of the CFD code the linearization approach is based on Patankar's SIMPLE algorithm.[1][2]
I talked to my professor who told me that SIMPLE is used in commercial softwares like FLUENT too.

I found few papers which tells us some other approaches:

[1]: http://www.cfd-online.com/Forums/openfoam-solving/60167-how-nonlinear-discretised-equations-linearised-openfoam.html
[2]: http://web.cecs.pdx.edu/~gerry/class/ME448/notes/pdf/SIMPLEslides.pdf

I did some more digging from the implementation point of view and came across some interesting things:

This tutorial demonstrates the solution of Incompressible Navier-Stokes Equations using Fenics. it uses Chlorin's method[3] to solve the problem.
http://fenicsproject.org/documentation/dolfin/1.2.0/python/demo/pde/navier-stokes/python/documentation.html

Other Implementations:

Parallel Spectral Numerical Methods/The Two- and Three-Dimensional Navier-Stokes Equations - http://en.wikibooks.org/wiki/Parallel_Spectral_Numerical_Methods/The_Two-_and_Three-Dimensional_Navier-Stokes_Equations
2D Navier-Stokes solver implemented as a Python package with Python modules and C++ extension modules. It uses the finite difference method on a uniform, rectangular grid. It handles single- and two-phase incompressible, Newtonian, laminar flow with obstacles. -https://code.google.com/p/kmkns/
Finite Volume Based - http://www.ctcms.nist.gov/fipy/

Here is a list of Open Source CFD codes. Maybe we can fork a repo and use it or learn from it:
http://www.cfd-online.com/Wiki/Codes

According to people iNavier and dolphyn are promising:
http://www.cfd-online.com/Forums/main/13529-colver-code-c-c.html

Someone was using PyAMG to develop Jacobian-Free Newton-Krylov code to solve the Navier Stokes equations : https://groups.google.com/forum/#!topic/pyamg-user/HXrXTyvXPpw

[3] http://en.wikipedia.org/wiki/Projection_method_%28fluid_dynamics%29

This is everything I could harness this week. There is a lot of things to take care to lock the final solver to be used which I would do the current week. Also I am currently narrowing down and rigorously searching a way to implementing SIMPLE in the FE context.

On a side note I have also been working on a SfePy version for Python 3 and benchmarking the simulation results.

This journey is surely turning out to be awesome!

Cheers!

Tuesday, July 2, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 2

Hi Pythonistas,

After developing more understanding of SfePy I moved towards implementation.
The first phase of my project involved implementation of convective-diffusive equations.

So with the help of my mentor R (Robert. He is awesome!), energy equations were implemented.

The sample problem taken was:

r"""
Steady Axial convection and diffusion in slug flow with velocity :math:`U _0`
in an insulated pipe.
It is subjected to specified temperature at the entry and exit lengths -
:math:`T _0 for x \leqslant 0`
:math:`T _1 for x \geqslant L`
:math:`\alpha \frac {\partial T}{\partial n} = 0 on the lateral surface of the pipe`
Find :math:`T` such that:
.. math::
\int_{\Omega} c \nabla v \cdot \nabla T =
- \int_{\Omega_L} (\vec{u} \cdot \nabla T) v
"""

Now the results were pretty interesting :

The results were in accordance with the Peclet number graph which predicts the Temperature distribution in a convective-diffusive case.

We have realised that a robust Navier-Stokes solver is necessary for the project compared to the present solver so our next task is to get that in place and then move ahead with the coupling of the two equations.

Cheers!

Up Next: Navier-Strokes Eq. Solver

Python Software Foundation - SfePy : GSoC 2013 : Week 1

Hello Pythonistas,

I am Ankit and this week I kickstarted my GSoC 2013 Project - Enhancing the solver to simulate solid-liquid phase change phenomenon in convective-diffusive situations. I am a dual-degree undergrad pursuing my masters in phase-change material simulation.

Previously I had worked on the post processor of Abaqus, a commercial software, in my internship and always dreamed of working on a solver. Surely it was an honour when I was given a chance to work on SfePy as my GSoC project.

This project is pursued under :

Click Here to know more about SfePy

"Briefly, SfePy is a software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 2D and 3D. It can be viewed both as black-box PDE solver, and as a Python package which can be used for building custom applications. The word 'simple' means that complex FEM problems can be coded very easily and rapidly."

This week ended with:

Finalizing the weak form of the equations to be implemented.
Tinkering with the examples and code-base to know the entire architecture which is very modular and powerful.

I realised that lots of challenges are awaiting ahead, but the interesting part is that SfePy falls under the umbrella organisation - Python Software Foundation

And you know I Love Python!

So the adventure has already begun ...

Up Next: Energy Equation Implemented

Pages

Friday, September 27, 2013

Monday, September 16, 2013

Thursday, September 12, 2013

Tuesday, September 3, 2013

Wednesday, August 28, 2013

Wednesday, August 14, 2013

Tuesday, July 30, 2013

Monday, July 22, 2013

Sunday, July 7, 2013

Tuesday, July 2, 2013