Quenching (update)

Schematic showing stages of Quenching

Heat transfer during quenching into liquid is complicated when the quench medium forms a gas when heated to high temperatures.

The quenching process is usually split into 3 -5 stages.

Stage 1. Vapour blanket.
Depends upon surface roughness, quenchant temperature, quenchant type, oxidation. Heat transfer by radiation through vapour layer into quenchant.

Stage 1b. Partial film boiling.

Stage 2. Nucleate boiling.
Conduction and Convection.

Stage 3. Convection.
Dominated by heat transfer in the quenchant by convection which can be natural, forced with turbulence or forced with lamellar flow.

Hala Salman-Hasan has been investigating heat transfer problems, a series of experiments have been made for quenching using an experimental rig we built at Cambridge. Here we can see a video of a 2 mm probe made from steel which has a thermocouple embedded. Data logging is from a computer with data logger. I think data logging at these speeds could also be achieved using an Oscilloscope, that would probably need an electrical engineer, and more importantly a trigger to start logging at the correct time.

Quenching into water

Quenching curve for water at 42 Celcius, Heat Transfer as a function of temperature.

Installing gnuplot on Windows

[updated Sep 2012]

If you are still stuck with using windows for whatever reason, don’t despair you can still use gnuplot to plot your graphs! You can get gnuplot from the gnuplot project page on sourceforge.

Browse versions to go to directory with latest updates.

Download gp443win32.zip (or latest version) which is a self extracting zip file, click on it and follow the instructions. (you don’t need to have winzip installed). You just have to copy the files to a directory on your computer, then make a shortcut to wgnuplot.

It is also useful to install ghostview, you need gs860w32.exe and gs49w32.exe (or higher?) which allows you to view postscript graphs made with gnuplot, you can copy from ghostview to the windows clipboard to insert into your word document if you so desire.

Instructions for installing ghostview can be found here;
http://pages.cs.wisc.edu/~ghost/gsview/

Fitting polynomial equations with gnuplot

I wanted an equation to summarise the following data so that it could conveniently be used for some calculations, after many attempts I found that I could fit the data using 2, 6 order polynomials. One was fitted on the data between x = 0-200 and another in the range x = 200-900.

1 polynomial equation after fitting.

Second polynomial equation after fitting.

Final polynomial equations after fitting.

Source files


set terminal png
set output "HH.png"

#set cntrparam cubicspline
#set cntrparam order 2

#plot "HH.DAT" using 1:2:(1.0) smooth acsplines title "acsplines"
#sw(x,S)=1/(x*x*S)
#plot "HH.DAT" using 1:2 smooth csplines title "csplines"
#plot "HH.DAT" using 1:2 smooth bezier title "bezier"
#plot "HH.DAT" using 1:2 smooth sbezier title "sbezier"
#plot "HH.DAT" using 1:2 smooth unique title "unique"
#plot "HH.DAT" using 1:2 smooth frequency title "frequency"

# Linear Regression
#f(x) = m*x+c
#fit f(x) "HH.DAT" via m,c
#plot "HH.DAT", f(x)
#f(x) = a + b*x + c*x**2 + d*x**3 + e*x**4 + f*x**5
#fit f(x) "HH.DAT" via a,b,c,d,e,f
#plot "HH.DAT" ps 0.1, f(x)

a = 100
f(x) = a + b*x + c*x**2 + d*x**3 + e*x**4 + f*x**5 + g*x**6
fit [200:900] f(x) "HH.DAT" via a,b,c,d,e,f,g
plot "HH.DAT" ps 0.1 , f(x)

#g(x) = h * exp (((x-j)*(x-j))/(2*i*i))
#g(x) = h + j*x + i*x**2
g(x) = h + i*x + j*x**2 + k*x**3 + l*x**4 + m*x**5 + n*x**6

fit [0:200] g(x) "HH.DAT" via h,i,j,k,l,m,n
set yrange [-2000:10000]
set output "HH2.png"
plot "HH.DAT" ps 0.1, g(x)

set output "HH3.png"
h(x) = (x<200 ? g(x) : f(x))
plot "HH.DAT" ps 0.1, h(x)

show variables

Mtdata example 2


:example by Mathew Peet Nov07
multiphase
define system 'Fe,Mn,C' source tcfe !
:using tcfe database - other options are sol, ssol, plus, pluss, sub_sgte etc
set w 100 !
:set total weight of system to 100 kg
set w(1) undefined w(2) 1 w(3) 0.1 !
:this means 1 weight percent manganese and 0.1 weight percent carbon
:iron is calculated as the balance
classify absent phase(*) !
classify normal phase(BCC_A2,FCC_A1) !
:in this calculation we want to allow only ferrite and austenite phases
step temp 973 1373 20 !
:we want to calculate the equilibrium for this system
:from around 700 to 1100 centigrade
compute print mole_fraction_table !
:we want the calculation to produce the results as a table of mole fractions


Writing the results to a file
To output the fraction of the phase to a file we can use something like;


compute print graphics_output !
ordinate mass fraction_of_phases !
units temperature celsius !
plot tabulate spreadsheet !


Mtdata will then tell us where the file “def1.gtb” is written. This file can then be opened in your spreadsheet software or plotted using gnuplot, etc.

Plotting the output with gnuplot
The file is output as a spreadsheet with comma delimiters. If we want to plot this in gnuplot, it’s useful to switch these to spaces. This can be done with the following incantation;

sed 's/,/ /g' def1.gtb > file.ssv

The following is the commands needed in gnuplot to produce a suitable graph. This can either be written in gnuplot used interactively, or placed in a file and executed as a script.

Copy the following to a text file, for example called plot_mtdata.gnu, and run the script with the command gnuplot plot_mtdata.gnu in this case we will produce a graph in postscript format, although other formats are also available in gnuplot.


#example by Mathew Peet Nov07
set term postscript enhanced eps 22
set title "Equilibrium between austenite and ferrite for Fe-1Mn-0.1C Wt. \%"
set xlabel "TEMPERATURE / ^oC"
set ylabel "CONSTITUENTS / Wt. \%"
set output "graph.eps"
plot "file.ssv" using 1:($2*100) title "BCC" w lp, \
"file.ssv" using 1:($3*100) title "FCC" w lp


This should produce a graph something like this (converted to jpg using ‘convert graph.eps graph.jpg” command in linux)

Simple Math: Quadratic Equation

Gnuplot script