Smoothed Particle Hydrodynamics discretization

[ronin777]

Hi all,

I want to use SPH discretization for my cooling rate but i don't know if its valid.

So, this is the equation i want to discretize.

L = (1/dT/dt) . ∫v(T) dT

So,

dT/dt = (1/L) . ∫v(T) dT

dT/dt = (1/L). Ʃv(T) dT (with dT →0)


The limits of the above integral are

Tini: Initial temperature at which columnar grain nucleates
Tnuc: Nucleation temp. of equiaxed grain
L: Average length of the appearing columnar grain
during solidification

dT/dt: The cooling rate caused by diff. in mould and melt temperature

The above transition is columnar to equiaxed in grain structures which takes place during solidification of the melt.

Background of the problem: I have a situation in the form where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. So, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature or temperature gradient across the fluid in the mould or the cooling rate because of the temperature gradient with the viscosity situation in the melt.

Cheers
Ronin

 

[eljose79]

Hi Ronin,

Using the SPH (Smoothed Particle Hydrodynamics) discretization method for your cooling rate equation is definitely valid. SPH is a widely used method in computational fluid dynamics for simulating fluid flows and heat transfer. It is a mesh-free method that can handle complex geometries and large deformations, making it suitable for simulating solidification processes like the one you described.

Your discretized equation looks correct and the limits of the integral make sense in relation to your problem. The transition from columnar to equiaxed grain structures during solidification is a common phenomenon in metallurgy, and understanding the cooling rate is crucial for controlling the microstructure and properties of the final product.

In terms of your background problem, the relationship between temperature gradient and viscosity in the melt is an important one. As the temperature decreases, the viscosity of the melt increases, affecting the solidification process and the final microstructure. By using your discretized equation, you can analyze the effect of different temperature gradients on the cooling rate and ultimately on the microstructure of your alloy.

Overall, using SPH discretization for your cooling rate equation is a valid and effective approach for studying the solidification process in your alloy. I hope this helps and good luck with your research!