time transit code for heaa transfer

[swainw]

We are doing some calcs on cyclinders filled with 5000psi air. the cyclinder is installed in an aircraft and using thermal flight profiles (dT/dt) functions, I am trying to see what the effect of the cylinder housing will have on thermal lag to effecting the internal temperature of the air. Since its a constant volume process, our concerns are the pressurization rise anbd fall over the temperature range. If it hits a certain high pressure, a relief valve lets out m.dot amount of gas, so the total mass is reduced. We need to set this venting pressure point to a suitable level to prevent gas loss, and understand the max operating pressure.

I tried this in excell using finite difference and as long as the T.infinity stays the same the cells converge to temerature time profiles, but as soon as I start varing the t.infinity as a function of aircraft flight altitude profiles, the system crashes. My thoughts are that an inner loop needs to resolve the transient temperature points at each time step, then advance to the next T.infinity point and re-run the convergence algorithm.

In my mind I have just a thought that a.) the metal housing probably conducts very rapidly and the inner wall becomes the same as the outerwall fairley quickly, Then the convective transfer to the stored gas takes x amount of time to stabilize, considering that air enclosed acts as a nice energy barier, Similar to fiberglass insulation with loosely filled air pockets.

Any assistance with the code structure or availability of off the shelf modules that can be dropped in would be helpful.

Regards,
Bill

Bill Swain
Ultra Electronics Precison Air Systems
Technical Coordination Manager-US Programs
swainw@asme.org

 

[magicme]

hello

it sounds like you are extremely close using EXCEL....i assume you tried a *very* small time step....? and it isnt clear what you mean by "the system crashes".


also.....in EXCEL, you may need to go into TOOLS>OPTIONS>CALCULATIONS and set the number of iteration to 100 or so...... this way, the cells that recursively reference each other (like t.infinity - q.out - t.inside-q.out - t.inside - q.out...etc...etc..) iterate to an answer row by row.

daveleo

 

[chicopee]

Have you though of insulating the cylinders and see what happens to your excell calculations when you replace the thermal conductivity of the shell material with that of insulating material?

 

[chicopee]

Have you though of insulating the cylinders and see what happens to your excell calculations when you replace the thermal conductivity of the shell material with that of insulating material?
Second question- are these cylinders(filled w/ air) portable so that crew members can walk around depressurized compartments of airplanes w/ their respirator hoses hooked to the cylinder valves?

 

[swainw]

Thank you,

But I have some more questions and problem definition. I'm not sure what the excel setting does on the calculation you mentioned, but the way I've set up the excel spread sheet is the LH column represents the T.infinity of the outside air Temp. The next 7 columns to the right are the nodes of the 1D matrix. to the center of the cylinder using finite differences equations.

When all of the left hand cells are set to a constant temperature, the rows represent the time step and the convergence happens around row 11. Hence the spreadsheet is actually the inner loop function to find a steady state solution.

As I moved to the transient analysis what I mistakenly did was modify the LH column to the ambient air as a function of the mission altitude/temp profile where each row represents about 5 mins time. The LH column is the inputs for the outer loop time step. Hence, The outerloop of the analysis.

What I was trying to do was not solve to convergence for a solution over many iterations as in stready state. Meaning when the LH column Temp is all the same. This implies the time step resolution only has to meet the delta time criteria to cause convergence and a solution to the steady state problem.

However, when doing transient analysis the center nodes may not actually see the temp change due to thermal lag and hence the equation needs converge to the temporary solution in the inner loops before moving onwards to the outerloops next time step.

Treating the bottle as insulating, nothing would happen as the thermal resistance would be too high (very large time lag) to cross into the cylinders inner surface.
P.S. these are not cylinders for air crew breathing chicopee.


Again any more information would be very beneficial.

Bill

Bill Swain
Ultra Electronics Precison Air Systems
Technical Coordination Manager-US Programs
swainw@asme.org

 

[chicopee]

It seems to me that you do not have a good feel as to which equations are being used in the finite difference analysis which is necessary to understand the spread sheet. T infinity is an expression for ambient temperature but you have not stated its value because i am certain that it is one of the initial values; you also have not stated what value is being used in the delta theta(time increment). Without knowing the above equations and initial conditions, it is difficult to understand what is happening to your spreadsheet.

 

[swainw]

Yes you are correct that I do not have a good feel for what is happening in my spreadsheet. When the temperature stayed constant I thought understood what the rows were iterating on as they were the execution of the finite difference convergence. I believe that in all of the rows prior to 11th where the rows start repeating, hence convergence on the steady state solution, the previous rows depicted true node temperatures at time step (t) as the amount of heat transfer during those particular time steps. That was sort of how I thought it worked, but then I assumed I could say at row 5 have the T.infinity changed and because the boundry condition changed, the rows would simply readjust. However, they did not and within two rows the method got way out of range at the face node.

Because now that its a continuous transient situation throughout the flight profile, I am having problems visualizing the "innerloop" which I think is to determine each nodes temperature at each particular time. It now seems to me the finite difference method needs several rows to come to a quasi steady state for each node based on the new BC at that particular time step. Then it also seems that we need to increment the "outerloop" which is a change in the t.infinity property at time step (t2).

All this said was why I posted this thinking I needed to go to maybe coding the problem in maybe C or something to get the iterative capability to solve the "innerloop" heat transfer or be able to do a matrice inversion method, gauss-seidel, or something else to determine the transient system state before the change in BC occurs with the proscribed BC time step change.

Again,
Thanks in advance. This is slowly helping me get my head around the problem. I only hope I'm not too far off base as you suggest bacause I am still a bit confused right now.


Bill

Bill Swain
Ultra Electronics Precison Air Systems
Technical Coordination Manager-US Programs
swainw@asme.org

 

[magicme]

hello again

are you really doing a time-step transient analysis (which means that material specific heats, mass or thermal diffusivity is somewhere in the equations) or are you just doing incremental steady state solutions for various boundary conditions?

if its the former (a true transient analysis), then the equations on one row would somehow refer to cells on the previous row and if time steps are too large and the changes in some cell is too large, the calculation will go unstable....use smaller time steps.

if you are doing the latter, it is not going unstable because of time steps (there are no time steps!). my guess then is that you made some error in click-dragging the eqautions down row by row or something simple like that. also need to set the iterations per my previous message.

you are correct in thinking that C or fortran would handle the looping process better.....excel can do it but its very klutsy and probably best done using the VBA embedded in excel, but i wouldnt know how to do that.

ohh....i just recalled that excel has a SOLVER add-in that will find iterate the value of a specified cell (in other words solve for an unkown)....check it out in TOOLS>ADDINS>SOLVER you may have to do some stuff to add it in (its in your computer just not necessarily called up yet in excel)....ive used that before and it is very handy....but you would have to solve each row manually with SOLVER but it would work.

daveleo

 

[swainw]

Thanks Dave,

You are correct that the spreadsheet uses the row above to calculate the next time step. As mentioned before as long as the boundry condition stays the same, the initial node and those through do fine. But, again reading about the time step, the real world data is set to a 1 minute intervals for a 120 minute profile. Hence the time step is one minute when we do change the boundry condition.

Second, the finite difference does not have all of the diffusivity, specific heats, etc. in them. It is a steady state equation with h and k at the boundry node and [(T+1.node) + (T-1.node)-2T.node] for the material on the internal nodes. Any assistance with the form of the transient finite differnce would be very helpful. Also, on the internal edge of the cylinder, is the node form back to a convection form involving a film h layer, even though the cylinder has no air movement. Then the Air nodes are of what form till it is uniformally heated.

The biggest question in my mind is for the given time step, and the reason for the transient analysis about thermal lag, is: will the diffusivity through the cylinder wall and then into the air volume happen too quickly in the time step, or is there a real thermal lag and the external time changes be sufficient that some extremes are never hit.

Regards,
Bill

Bill Swain
Ultra Electronics Precison Air Systems
Technical Coordination Manager-US Programs
swainw@asme.org

 

[corus]

I would be surprised if there was no air movement in the cylinder as natural convection would occur. In the cylinder itself I'd expect radiation between all the surfaces in the enclosed space to be a factor. In addition heat loss from the top and bottom surfaces would be different from the sides of the cylinder. You also have to consider that you're solving an axisymmetric problem and the differential isn't in cartesian co-ordinates d^2T/dx^2. I believe it's k/r.dT/dr + kd^2T/dr^2 (for k constant). For a transient that is equal to pCdT/dt. There are two ways of solving that, an explicit method or an implicit method. The explicit method is generally unstable and you should use an implicit method which tends to be more stable for a given time step. An implict method would use pC(T(i)-T(i-1))/t where T(i) is the temperature at the current time t.
I'd consider using finite elements to look at the problem.

corus