Dendrite tip velocity

[CharMIC]

Dear Bernd,

Just need to clarify some confusion with the dendrite tip undercooling.

The alloy that I am considering has equilibrium melting temperature of 1611K. During the simulation I defined a constant temperature of 1600K (no thermal gradient).
In the simulation domain I have a single nuclei. this nuclei will grow at 1600K and achieve a steady state growth velocity (I used moving fram option). So the undercooling of 11k that I defined is the total dendrite tip undercooling that include curvature, kinetic and solutal undercooling? or am I wrong.

[Bernd]

Hi Chamara,

No, you are not wrong - that is exactly right.

The .driv output gives you the sum of the kinetic and curvature undercooling (in terms of driving force: ΔG=ΔS*ΔT).

Bernd

[cboe]

Yes,

using "front_temp" as function of time you easily can calculate the mean average front velocity (by taking the derivative and divided by the temperature gradient).
In cases without moving_frame, it is equivalent to the total fraction of solid.

Bernd

Dear CharMIC and Bernd,

I calculated the dendrite tip velocity for a concentration coupled moving frame dendritic directional solidification (boundary conditions: temp gradient G and cooling rate CR, see attached driving file).The outputs of the aforementioned calculation methods deviate.

alcu13.in

(16.66 KiB) Downloaded 211 times

In a first estimation I can calculate the growth rate R = G/CR from my boundary conditions. However, this relation is only valid for equlibrium conditions in a bridgman-type solidification, correct?

As you two have already discussed here, the dendritic tip velocity can be derived from Micress output in multiple ways with different grades of accuracy:
i) *vel.mcr output can give me an estimate of the growth rate R (=2.03 cm/2)
ii) growth rate R equal to the derivative of TabL output d(Front Pos * CellDimension) / d(Simulation Time) (see figure left)
iii) The dendrite tip cooling rate can be estimated with the TabL output ( d(Front Temp) / d(Simulation Time) ) / (TabL temperature gradient) (see figure right)

In comparison, R calculated boundary conditions = 2250 / 950 = 2.37 cm/s

i) and ii) result in a more or less equal dendrite velocity. However, iii) underestimates the growth rate by a factor of ca. 7. In my simulation the cooling rate is decreasing further and further. This makes me wonder if my simulation is set up correctly.

Is it possible that my diffusion rates are chosen too low, which then leads to a temperature limited growth (as I would expect it in equiaxed solidification) rather than a diffusion limited growth? Or am I on the wrong track?

Thank you for your time and your suggestions.

Cheers
Constantin

[CharMIC]

Dear Constantin,

You have mentioned that you calculate the growth rate using R = G/CR. However shouldn't it be R = CR/G. Later you have shown that you have calculated it in the correct way

From the above method what you get is the velocity of the liquidus isotherm. Dendrite tip velocity will differ from it.

In addition, from my experience, the R that is calculated using MICRESS is very sensitive to the grid resolution, kinetic and mobility coefficients.

I am not sure if you can calculate the R using (iii) since at two different times your tip is at two different locations. but you are not using location specific temperature to calculate the instantaneous cooling rate. When you use R = CR/G,then you will use location specific instantanious data to calculate R. This is how in FEM software calculate cooling rate and based on the location of liquidus isotherm we will be able to get cooling rate at the liquidus isotherm.

BR
Chamara

[Bernd]

Dear Constantin,

Sorry that I confused you. My statement which you cited was clearly wrong, and I just corrected it: What I meant was of course the front position ("Front Pos.") which is given in the .TabL file and which gives you the position of the highest point of the dendrite front in cells relative to the bottom of the domain. As Chamara just explained, the average front temperature ("Front Temp.") cannot be used for calculating the front velocity, even if you have a temperature gradient, because it gives you the average temperature of all interface regions which are in your domain. "Front Temp." is typically used to get the average undercooling of a planar or eutectic front.

Bernd