VacTran 3 Manual (779748), страница 31
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The gas load valueswill be calculated based on this elapsed time. Most gas loads decrease with time, so a higher value for the starttime will result in a lower gas load in the calculation.Rate of rise stop time: Specifies the end point for the pressure rise calculation.Rate of initial vessel pressure: Specifies the pressure from which the pressure rise calculation will start.Vessel volume: Total volume of the chamber to be evacuated, not including the conductance elements connectingto the vacuum pumps.© 2011 Professional Engineering ComputationsCalculation Formulas18301Calculation FormulasVacTran uses formulas that have proven to be reliable under a wide range of operating conditions.
These formulashave been widely published in text books and papers, and accepted in the vacuum and fluid flow industries for manyyears.See also:Choked FlowConductances in seriesConductance in parallelDelivered speedElbow volume calculationFlow regimeGas load throughput calculationsIncremental pressure calculationsMean free pathMolecular flow conductanceOut gassingPermeationPump down timeTotal VolumeTransition flow conductanceTransmission probabilityViscous flow conductanceViscous flow equivalent length© 2011 Professional Engineering Computations30218.1VacTran 3Caveats - calculation formulasIn designing this program, no new theories in vacuum technology have been developed.
However there arelimitations:1) At extreme pipe lengths, the equations may lose accuracy.It is possible, that a long pipe could have viscous, transition, and molecular flow in at the same time. VacTranassumes only one flow regime in each conductance element at each pressure. If the delivered speed is smallfraction of the pump speed, the formulas in this version of VacTran may be inappropriate.2) Transition flow is an approximation.There are several ways in which the conductance in the transition regime can be handled.viscous and molecular conductance values to obtain the transition conductance.VacTran adds the3) Gas loads often dominate molecular flowLeaks, permeation, outgassing, pump back flow are a reality in most vacuum systems.
The extent of each of thesefactors can be controlled by design, quality control, and operational procedures. However, the exact magnitude of agas load is difficult to predict, and is best supported by measured data.4) Determination of gas load pump down is an inexact scienceVacTran's method for determining gas load pump down is one of many possible approaches. The usefulness of anycalculation, no matter how accurate, is limited by the constraints of the real world.5) Pump performance can be lower than the catalog valuesDepending on the type of vacuum pump and its operating and maintenance history, the actual observedperformance could vary greatly from the product catalog specification. In other words, pumps often degrade withuse depending on the technology.
For example, a capture pump such as a cryogenic pump will suffer reducedpumping speed as the condensation surfaces load up with ice and form an insulating boundary. Contact themanufacturer for guidance on pump speed degradation for specific use cases.© 2011 Professional Engineering ComputationsCalculation Formulas18.2303Pump down calculation hierarchyThe following chart shows the calculations or data required to perform a pump down calculation. The lowest level ofeach branch must be calculated first, feeding into the next level up.
Calculations at parallel levels of the hierarchycan be performed in any order.© 2011 Professional Engineering Computations304VacTran 318.2.1 Pump down timeConductance, pump speed, and gas load are typically highly non-linear in nature, often varying by orders ofmagnitude with pressure or time. VacTran addresses this by performing small incremental calculations so thatthese nonlinearities are captured at a reasonable resolution.for each increment,(equation 3.267, Reference 2)whereVSPHPL= total volume in liters= delivered pump speed in liters/second= high (starting) pressure in Torr= low (ending) pressure for increment in Torr18.2.2 Pump down time for gas loaded systemThe gas loaded calculation is identical to the ideal pump down calculation, except that the gas load is subtractedfrom the delivered pump speed.
The gas load value for each increment is based on the elapsed time required afterthe previous increment.If the gas load in is greater than the delivered speed, we cannot pump down that increment to the target pressureusing the above formula. However, gas loads often decrease with time. The pump down time in this case will beequal to the time it takes for the gas load to decrease sufficiently . In this case, the time to achieve a targetpressure is found by interpolating on the gas load data set using the current pump throughput.
During a givenincrement, the target pressure will be reached when the pump throughput surpasses the gas load sufficiently toachieve a pressure decrease. The time calculated for the gas load is added to the clean pump down time for theincrement. If the gas load is constant, as with a leak, it will not decrease with time and the will become a “hardstop” for the pump down calculation if it exceeds the delivered pump throughput.© 2011 Professional Engineering ComputationsCalculation Formulas30518.2.3 Total volume calculationsTotal volume consists of the user-defined vessel volume plus the volume of the conductance path between the pumpstation and the vessel.The user can select whether the volume of the conductance path is included in pump down calculations, using theAdd cond volume check box on the system model dialog box (see below).
Adding the conductance volume (bychecking the box) is equivalent to locating the vacuum valve at the pump. Excluding the conductance volume (bynot checking the box) is equivalent to having the vacuum valve located at the vessel. Depending on the actualconfiguration of the system being modeled, the conductance volume can have a significant impact on pump downtime.Volume calculations for different types of conductance elements are provided in Calculation Formulas.Note that the choice of adding the conductance volume has no effect on the gas flow conductance calculations.© 2011 Professional Engineering Computations306VacTran 318.2.4 Incremental pressure calculationsVacTran uses closed form equations for most calculations, which are often divided up into small increments toincrease accuracy.
For example, pump down time calculations use incremental calculations to divide the totalpressure range into multiple segments, so that large changes in depended variables such as pump speed andconductance can accounted for.Delta pressure for each increment:wherePs = system start pressurePt = system target pressuren = number of incrementsPLow for a given increment:where N = current increment numberPHigh for a given increment:© 2011 Professional Engineering ComputationsCalculation Formulas30718.2.5 Delivered pump speedequation 3.241, Reference 2whereS = Delivered pump speed at chamber (liters/second)Sp = Pump speed at pump inlet (liters/second)C= Combined conductance connecting pump to chamber (liters/second)Although this example uses liters/second, any consistent volume/time units can be used.In a system model, delivered speed is determined as follows at each pressure increment:1) If no pumps have data at this pressure in this pump station, the pump station is ignored.2) Conductance is calculated for each conductance element in the pump station at the current pressure, thenadded to give a total conductance for the pump station (liters/second)3) Pump speed is interpolated at the current pressure for each active pump in the pump station, then added togive a total pump speed for the station (liters/second)4) Delivered speed is then calculated for each station as in the equation above (liters/second)5) Delivered speed is converted to delivered throughput (torr-liters/second)6) Gas load is calculated and subtracted from delivered throughput to obtain net delivered throughput (torrliters/second)7) Net delivered throughput is converted back to net delivered speed for the pump down calculation© 2011 Professional Engineering Computations308VacTran 318.2.6 Conductances in seriesWhen conductances are connected in series, their combined conductance is calculated from the formula below.Note that this is an ideal combination formula that does not add transition flow losses between conductanceelements that have changes in cross section.
For example, if a rectangular pipe exits to a cylindrical pipe, therewill be an additional exit loss for the rectangle or entrance loss for the cylinder. This additional loss needs to beaccounted for by selected entrance and exit and entrance losses for each individual conductance element. VacTrandoes not make the determination of end effects.equation 3.23, Reference 2Given a series of conductance elements, Ca, Cb, … Cn,1/Cs = (1/Ca) + (1/Cb) + … + (1/Cn)whereCs = combined conductanceCa = conductance of element aCb = conductance of element bCn = conductance of element n18.2.7 Conductances in parallelThe combination of parallel conductances is the numerical sum of the individual conductance paths.Note that is is an ideal formula that assumes there is no loss associated with the physical connection ofthese parallel paths at their end points.
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