VacTran 3 Manual (779748), страница 37
Текст из файла (страница 37)
Mass flow is often called throughput. This additional gas has the effect ofreducing the delivered pump throughput from the vessel.The figure below is the gas load palette used to insert gas loads into a system model. In VacTran, gas loadthroughput is the summation of gas load elements in a system model.
A gas load element can be an out gassource, permeation, leak, or raw data.See also:Out gas calculationsPermeation calculationsExponential out gas calculationsAffect of decay time on out gas calculations© 2011 Professional Engineering ComputationsCalculation Formulas36518.4.1 Out gas calculationsReference 1, eqn 6.2Outgassing rate (Q)qnt nCombining out gas constantsNote that 1 and 10 refer to the negative slope of the log-log outgassing curve at one hour and tenhours, respectively, while q1 and q10 refer to the outgassing rates at these times.At exactly one hour, the outgassing rate is q1for time < 1 hour, Q is in torr - liters/secondNote that at one hour (3600 seconds), the above equation degenerates into Q1for time >1 hour and <10 hoursfor time > 10 hoursNote that at ten hours (36000 seconds), the above equation degenerates into Q10t is in second units© 2011 Professional Engineering Computations366VacTran 318.4.2 Permeation calculationsReference 14WhereQ = rate of flowKp= Permeation constantA= Area normal to flow of gasP= Pressure differentialD= Thickness of material (length of flow path)unitsunitsunitsunitsunits:::::pressure-volume/timearea/time/pressureareapressurelengthSee also:PermeationPermeation entry dialogPermeation dialog description© 2011 Professional Engineering ComputationsCalculation Formulas36718.4.3 Exponential out gas calculationsThe exponential out gas model is used when a single rate of decay (alpha) and known starting point (at1 second) is available.
For example, if q 1 second is 1e-3 torr-liters/second, and alpha is 0.5, the followout gas curve will result.© 2011 Professional Engineering Computations368VacTran 318.4.4 Affect of decay time on out gas calculationsOut gas values decay exponentially with time, as inIn calculating a gas load curve that is added to the system model, the user has the ability to choose the base timevalue that is applied to the outgassing equation. For example, if decay time is 1 second, the exponential out gascurve will be calculated from time = 1 second as shown previously.If decay time is 100 seconds, the exponential out gas curve will look like this:© 2011 Professional Engineering ComputationsCalculation Formulas369Note that time starts at 100 seconds instead of 1 second.
The decayed gas curve will be applied tosystem models starting at the Gas Load Start time. This effectively means a lower gas load at thebeginning of pump down calculations.Change the decay time using the Environment dialog as shown:© 2011 Professional Engineering Computations37019VacTran 3Hand calculating a pump down curveThe tedious nature of performing hand calculations for vacuum systems is probably why most people purchaseVacTran in the first place. This section lets you verify the nature of the calculations by following a hand calculationin detail.This section is highly recommended for anyone who has not done vacuum calculations before.
As with anyengineering analysis software, the user should have some experience with the basic formulas that can lend someconfidence to the results from the computer program.Although this exercise is designed to show a manual calculation, you can model it in VacTran. Thisexample is provided in two files on the VacTran Data Disk. The pump model is the file "HANDCALC.VTPMP", and the system model is in the file "HANDCALC.VTSYS". These files are in the Examplesfolder.Assume the following system:• Start pressure = 1000 torr, Target pressure = 10-4 torrNote: 1000 torr is used to simplify this example. Atmospheric pressure is nominally 760 torr at sea level.• Vessel volume = 100 liters• Pipe radius = 1 cm, length = 10 cm• The gas in the vessel is air, with the following propertiesmolecular diameter: 3.72e-8 cmdynamic Viscosity: 1.708e-4 poisegas temperature: 273.15 degrees Kelvinmolecular weight: 28.966 grams/moleGases are individually stored on disk.
You can open the file AIR.VTGAS from within VacTran to see this data.• The pump for this example has the following performance data:pressure (torr)speed (l/sec)1000501007510100115010-115010-210010-35010-410© 2011 Professional Engineering ComputationsHand calculating a pump down curve371Open the pump file HANDCALC.VTPMP, which contains the data above. The graph of this pump is shown below:© 2011 Professional Engineering Computations37219.1VacTran 3Hand calculation steps - no gas loadStep 1) Calculate the pressure incrementsStep 2) Calculate conductancesStep 3) Calculate average pump speedsStep 4) Calculate delivered speedStep 5) Calculate pump down time© 2011 Professional Engineering ComputationsHand calculating a pump down curve37319.1.1 Calculate pressure incrementsStep 1) Calculate the pressure incrementsPumping of a vacuum vessel is a continuous process.
As the vessel pressure decreases, the delivered speed andconductance are continually changing. Most pump performance curves vary widely pressure. An approximationcan be made by calculating the pump down incrementally. If the calculations are made with small enoughincrements of pressure, continuous pump down will be approximated. Twenty increments are usually enough to geta reasonably accurate answer, but make for lengthy hand calculations. To simplify this example calculation, sevenincrements will be used, one for each decade of pressure from 1000 to 10-4 torr.The average pressure in each increment is shown below.
For example, the first pressure increment = (1000+100)/2= 550 torr.pressureincrementsincrementaverageincrementpressure1E+0311E+025.50E+0221E+015.50E+0131E+005.50E+0041E-015.50E-0151E-025.50E-0261E-035.50E-0371E-045.50E-04In subsequent calculations for conductance and delivered speed, we will use the average pressure for each pressureincrement. Note again that in the real world, most calculations would start the first increment at 760 torr instead of1000 torr.© 2011 Professional Engineering Computations374VacTran 319.1.2 Calculate conductancesStep 2) Calculate conductancesThe conductance of the pipe can be calculated from the following two equations.
Because viscous flow andmolecular flow conductance results are orders of magnitude different at most pressures, they can be added toapproximate total conductance at any pressure.For viscous flow,whereD = diameter of conductance element in cmh = dynamic viscosity of gas in poiseL = equivalent length of cylindrical pipe in cmP = average pressure in TorrFor molecular flow,whereCTMa= transmission probability= molecular flow conductance in liters/second= temperature in Kelvin= molecular weight of gas in grams/mole= equivalent cylinder radius in cmRather than getting into calculations of transmission probability now, let’s use the simplified long tube conductanceformula given by Roth, equation 3.93:The difference between the simplified long tube formula and the transmission probability formula diminishes as thelength/diameter ratio increases.
For our case of L/D = 5, this formula gets us through the example with a smallerror introduced because we are somewhere between the short tube and long tube flow formulas.Conductance calculations are summarized below:incrementpressureviscous flowconductancemolecular flowconductancetotal15.50E+02168477.89.2 168487.025.50E+0116847.89.216857.035.50E+001684.89.21694.045.50E-01168.59.2177.755.50E-0216.89.226.165.50E-031.79.210.975.50E-040.29.29.4© 2011 Professional Engineering ComputationsHand calculating a pump down curve375Open the system model HANDCALC.VTSIS, and graph Conductance vs.
Pressure. The following data is shown inthe Main Text Window:Note that the slope of the curve in viscous flow, plotted on a log-log scale, is constant. In molecular flow, the slopeis always zero.© 2011 Professional Engineering Computations376VacTran 3© 2011 Professional Engineering ComputationsHand calculating a pump down curve37719.1.3 Calculate average pump speedsStep 3) Calculate average pump speedsFor each increment of pressure, interpolate the pump speed.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
