Non-steady flow simplified for use in Vissim
I need some help. Flow dynamics is not my thing. I added an attachment that shows the flow simulation throu a verry simplified valve. That is no restricition to flow through valve. It is to test the response to the pressure change when a valve opens and closes. The pressure from the tube section are ploted. The source driving steam pressure is 1480 PSIA at 850F and the drop is to 1200 PSIA when valve opens. I am after the resonent pressure fluctions as the valve opens and closes and the effect on engine at verious RPM.
I have searched high and low on info on how to do something like this. I can't find anything that really takes into acount the acceleration that produces the pressure waves. So I did this on my own. I fuged the gravity factor to make the resonent frequincy match the speed of sound of the steam resonent frequency for the tube length. If this the wrong forum to ask this question please let me know. I may be way off base on this as I basicly treated the gas as a mass being accelerated by the pressure differances between sections. Intragate that to get velocity. I calculate that in both directions to get a flow to or away from the calculation point so it winds up as a mass flow to or away from the calk point and figure the rate of density dd/dt. I intergrate dd/dt to get density, multiply dd/dt by dT/dd to get dT/dt and intergrate that to get T which drives the steam State Point change. Hopefullt this explains so some one can tell me I have screwed this up on I am on the right track. Or maybe I am posting to the wrong group here. I can explain the steam engine I am designing if that would help. I am trying to develop an engine that will have around a 216:1 power range needed to get a 6:1 speed range in a vehical. It is to simplyfied a constant expansion ratio engine that is controled by cutoff. It does so be varing it clearance and cutoff together to maintain a constant end of expansion pressure whil vaing exhaust timming to compress residule steam in the cylander to inlet pressure eleminating the clearance loss. But with real engine dynamics there has to be pressure differances for flow and valve lead etc. Because of constrants on minum clearance and minum opening close of valves I have had to plane on at least 3 stages of expansion and maybe 4. Each stage needs to run between constant pressure points os each stage needs to use at least steam or more then previous. extra steam usage can be made up be regulating higher pressure into inter stage recievers. But pressure build up between stages would necessate higher loss releasing it to maintain pressure. So I need to model the dynamics in order to figure expander sizing etc. Hopefully I have explained what I need help on here.
I am trying to do a simpliflied flow throu a tube. I am developing a steam property plugin for Vissim and trying to model a piston steam engine. I wont a model that can model flow to the engine. And through the entire system at some point. Right now an trying to get tube flow from a constant pressure source through tubes into the engine through a valve. It needs to model bulk flow and harmonic oscillation in the tubes as the valve opens and closes.
I started out using a Newton mass fource acceleration model where the mass if figured from the steam density between tube sections. It figures acceleration in both directions and intergrates to get velocity. I had some problems with mass continuity though. And after considering the problem it doesn't apply to a point. There can be a case where flow is moving away in both directions. Looking at the pressure fluctuation I did however come out very close with the right frequence for the closed tube length.
Acceleration if figured as
a = P * v/l i.e (force)lb/in^2 * in^3/lb / in in Gs
pressure * specific volume / tube length
It may bother you that area is not part of the acceleration. At first I scritched my head. But it works out
Pressure is force/area
specific volume,(1/density) is area*length/mass
so a = force/area * area*length/mass / length = force/mass
I am using the IAPWS-95 formulations to figure steam properties. It is vary fast as all properties are figured from temperature and density. So I intergrate the acceleration and use that to get the rate of change of density I have added a property that I figure from the speed of sound property and the isentropic temperature-density coefficient to get dT/dd|s the rate of change of temperature with respect to density constant entropy. * dd/dt gives dT/dt|s intergrating dT/dt and dd/dt I get the inputs to the IAPWS T,V state point. dT/dd|s comes from that state point. Image of tube section in Vissim attached.
The State Point block there is from my plugin. as are the property-conversion blocks. I have all of the IAPWS-95 properties available. I am playing a bit of game in outputing a C++ class from the state point block. The blocks connected to it I call retrival blocks. The retrival blocks call class methods that calculate the property. So only thoes properties needed are calculated. Internally I cash common sub parts of the formulations for use in later property calculations. The State Point class contains 10 user variables. In the diagram I am using one "x" to pass the "calculated rate of change of density from the previous block to this one" back to the previous block. This block also retrieves that some calculation passed back from the next block. The pass back block has two inputs one being the previous state point block and the valus to be put into the previous block. The var index is set as a block parameter. It's output is the previous value of that var. Kp is a damping factor. I figure that it will be computed to figure in Renonalds number at some point.
This is being done as an isentropic flow, if you can not tell from the attachment.
I need to do this in a general simulation package as there are combined mechanical, electronic and therodynamic simulations involved.
Comments sugestions questions welcomed.
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