Hi,
I am attempting to dynamically model the behaviour of granular solids in a rotary kiln using known equations, however i am having trouble setting up the following ODEs in mathCAD for the model....can anyone help. I have included the key points i am trying to model in Mathcad.
boundary condition:
where h0 is a fixed value (say 10% of the value of R).
From the above i'm looking to be able to determine the bed height (h) at any axial location (z) along the kiln tube.
Subsequently equations for Cross section area of the granular bed and residence time of the granular transport through the kiln (as a function of bed depth (h)) follow on from this...
Cross section area:
Residence time
So essentially i am looking to use MatCAD to find the residence time (t), given fixed values for: n (rotation speed in rpm), R (radius of kiln in m), D (diameter of kiln in m), angle of repose of the material (beta), angle of inclination of the kiln (theta), mass flow rate (ms) , bulk density of material (rho), axial length of the kiln tube (z).
My initial attempt using ODEsolver block did not get that far and with limited success (see attached) and seems very temperamental depending on what values are used and cannot utilise units for the variables (hence why they are all unitless.
Hmmm interesting... trying your example out for myself i get this:
is this correct? it still looks like it has defaulted to metres i.e 2ft = 0.61m?
The unitless values are dependent on the unit system chosen.
With unit system "U.S."you get:
But with unit system set to "S.I." you get:
Success!
Luc
Your rotational speed may be a litle low. 1/3 of a rotation per minute apparently isn't enough, 333 rotations per minute does give a solution.
Mind that you don't have to use the UnitsOf function to cancel units, and 'rad' is a unitless 'unit' anyway. You can also divide the units out directly.
See below.
Then, with Dw reduced to 0.5 m,and the minus sign in front of the derivative removed, I get:
Success!
Luc
Concerning the odesolve block it should make no difference if you define your constants inside the solve block or above. But if you define them inside, the values are not available below and outside of the solve block. So it may be a good idea anyway to define those constants above the block.
The reason for your solve block failing is the value of your variable R.w.
Compared to your Mathcad sheet you used different values for m.s and R.w in your Prime attempt.
Especially the low value 0.25 for R.w compared to the value 2 you had in Mathcad seems to make the solve block fail. It looks like (with the other values unchanged) R.w must be at least 0.502 or larger.
- The initial conditions must be given with the appropriate units. Its not necessary to write 0m instead of just 0, but its good habit to do so, too
- The solve block fails if R is lower than 1.97 m. You'll have to check your equation or the other values assigned if you think that R=0,5m should yield a valid result. I notice that you changed several values compared to the file I posted (where R must had a value of at least 0.502).
- To plot with units on the abscissa you need to define a range variable. I have chosen z.plot as the name for this variable which is only to be used for plotting, but you can chose any name you like (even simply z :-).
@Pyros1111 wrote:
Hi,
thanks for this - i see how that works now.
I was also trying to alter the initial condition for Hz as its not correct and should be Hz(L)=0.01 rather than Hz(0)=0.01 however this doesn't seem to work? does something else need to be changed?
Alan already solved that. Its as simple as writing the desired inital condition in the solve block and set the "end" value to zero. No R can be a higher value, too.
sorry to be a bother again but when i try and put this in it still doesn't seem to work properly for the last bit - says variable undefined??? any pointers on what im doing wrong?
hi again,
thanks again for your previous reply - i have been looking over it and trying to use the more accurate values to see what comes out and noticed i had initially described the inmitial condition for the ODEsolver as Hx(0)=0.01, whereas what i wanted to do was define it as Hx(L) = 0.01. However, when i do this in the Mathcad (See attached) it doesn't work and says the endpoints cannot be the same in the solve block?
can you explain why and how to make it work for this end constraint please?
