VacTran 3 Manual (779748), страница 32
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If a loss is expected at the entrance or exit of any of theindividual parallel paths, the user should select the appropriate entrance or exit loss options within thestarting and ending conductance elements. VacTran does not make the determination of end effects.Cp = Ca + Cb + ... + CnwhereCp = combined conductance for the parallel groupCa = conductance of element aCb = conductance of element bCn = conductance of element n© 2011 Professional Engineering ComputationsCalculation Formulas18.3Conductance calculationsThe concept of flow regimesMolecular flow conductanceViscous flow conductanceTransition flow conductanceSonic flow conductanceMean Free PathThe concept of flow randomizersChoosing entrance and exit loss optionsExamples of selecting entrance and exit lossesTransmission probabilityEntrance transmission probabilityBody transmission probabilityExit transmission probabilityThe concept of equivalent LengthViscous flow equivalent lengthViscous entrance equivalent lengthViscous body equivalent lengthViscous exit equivalent lengthMolecular flow equivalent lengthSummary- geometric equivalencyGeometry-specific conductance casesElbow and miter calculationsBend calculationsRectangle calculationsRectangular pipe efficiencyAnnulus calculationsAnnular pipe efficiencyTriangle calculationsTriangular pipe efficiencyEllipse calculationsElliptical pipe efficiencyConical pipe calculationsComparison of long pipe equations© 2011 Professional Engineering Computations309310VacTran 318.3.1 The concept of flow regimesThe characteristics of low pressure flow are generally described in terms of regimes that have common physicalattributes.
These regimes are generally dependent on pressure, or in the case of sonic flow, pressure ratio across aconductance.An example of a conductance curve showing all four flow regimes is shown below:Flow regimes do not have sharp boundaries, but generally transition from one to another with some overlap. Onereason for this is that pressure is based on a statistical average of molecular velocities, which have a distributionfunction throughout the gas.
This variation means that there could be more than one flow regime existing at thesame time. However, using the general guidance below is a reasonable approximation for modeling the general flowproperties at a given pressure.Viscous flowAt the higher pressures during initial pumping, the flow of gas is limited by gas molecule-gas molecule interactions(viscosity). Under these conditions of viscous flow, the cross section dimensions of the conductance paths aremany times the mean free path.© 2011 Professional Engineering ComputationsCalculation Formulas311Molecular flowAt lower pressures, the mean free path may be many times the diameter of the conductance paths. Molecular flowthen characterizes the movement of gas molecules, which is determined by gas molecule - pipe interactions.Transition flowAt some intermediate pressure range, where the molecular mean free path is nearly the same as the conductancepath diameter, flow is in a somewhat complicated transition regime, which is neither viscous nor molecular incharacter, and is generally referred to as transition flow.Choked, or sonic flowUnder conditions of a high-pressure ratio, choked flow can occur, where the speed of the gas inside a pipeapproaches that of sound.
Sonic flow is actually a special case of viscous flow, which can only occur at highenough pressures where gas molecules interact. VacTran addresses choked flow by including a choked exit optionfor pipes, elbows, miters, and bends.See also:Mean Free Path© 2011 Professional Engineering Computations312VacTran 318.3.1.1 Molecular flow conductanceAlthough the long tube equation is often used in hand calculations, VacTran uses the more general transmissionprobability formula.For any cross sectionC ge ne r al3.64TAMwhereC= conductance of any conductance element= transmission probability of the conductance elementT = temperature in KelvinM = molecular weight of gas in grams/moleA = area of cross section in cm2For a circular cross sectionwhereC= conductance of any conductance element= transmission probability of the conductance elementT = temperature in KelvinM = molecular weight of gas in grams/molea = cylinder radius in cmTransmission probability is defined in the next section, and is the principal means of calculating conductance forgeometry-based conductance elements.For a long pipe of circular cross section4D3LC longpipe4D2.863LTD2M3.81T D3M LFor the special case of a circular orificetransmission probability = 1Reference 8, equation 1whereCom = molecular flow conductance of an orifice in liters/secondThe transmission probability term ( ) is covered in more detail in a separate section.
The important point is that allconductance elements have an associated transmission probability that can be entered in the general formulaabove. The only exception is the raw data conductance, which has explicit pressure -conductance values.© 2011 Professional Engineering ComputationsCalculation Formulas31318.3.1.2 Viscous flow conductanceIn long straight pipe, vacuum systems often encounter laminar viscous flow, also called Hagen-Poiseuille flow orfully developed flow. This is characterized by a velocity profile cross section that is temporally constant. Flowstreamlines are smooth and continuous, and fluid motion is essentially parallel to the long axis of the pipe.The general form of the viscous flow equation for long pipes isC K ge om e tr yPLWhere K is a geometry-dependent constant.The classical conductance equation for laminar viscous flow for a circular pipe is given as (eqn 3.53, Ref.
2)orwhereD = diameter of conductance element in cm= dynamic viscosity of gas in poiseL = total equivalent length of cylindrical pipe in cmP = average pressure in dyne/cm2C = cm3/secondIn more common units:C0.0327D4PLwhereD = diameter of conductance element in cm= dynamic viscosity of gas in poiseL = total equivalent length of cylindrical pipe in cmP = average pressure in TorrC = liters/secondTotal equivalent length includes the entrance, body, and exit equivalent lengths.viscous flow in the following section.© 2011 Professional Engineering ComputationsThese are demonstrated for314VacTran 318.3.1.3 Transition flow conductanceTransition flow conductance = viscous conductance + molecular conductanceNote that many texts publish the transition flow conductance as:Conductance = viscous conductance + Z (molecular conductance)Where Z varies from 0.8 to 1.0, depending on Knudson’s number.
This version of VacTran uses a constantvalue of Z = 1 in the transition flow regime.18.3.1.4 Sonic flow conductanceWhereCsonic = sonic flow (also called choked flow) conductanceC0 = flow coefficient (varies from 0.85 to 1.00)T = temperature (Kelvin)= gas Cp/Cv ratio (ratio of specific heats)= 1.66 for monatomic, 1.4 for diatomic, 1.33 for polyatomic gasesD = pipe diameterM = gas molecular weightEquation from Reference 15See also:Choked flow© 2011 Professional Engineering ComputationsCalculation Formulas31518.3.1.5 Mean Free PathThe mean free path is generally defined as the distance a molecule of gas travels before it collides with anothermolecule. Comparing the mean free path of a gas to the minimum section dimension (such as inside diameter) of aconductance element will indicate the flow regime of conductance.equations 3.8, 3.9, 3.10 Reference 2viscous flowD/L > 110transition flow1 < D/L < 110molecular flow1 > D/LwhereD = equivalent cylinder diameter of the conductance elementL = mean free pathequation 2.57, Reference 2cmwhereLTeP====mean free path in centimeterstemperature in degrees Kelvinmolecular diameter of gas in cmpressure in Torr© 2011 Professional Engineering Computations316VacTran 318.3.2 The concept of flow randomizersFlow is interrupted in real systems due to geometric transitions such as exits, entrances, obstructions, andchanges in direction.
A geometric interruption is also called a randomizer, because it tends to introduce random,chaotic motion to the downstream flow field. In viscous flow, this effect is referred to as turbulence. Randomizingconductance elements include elbows, miters, and bends and pump exhausts. A large upstream volume, such asa vacuum vessel, is also considered a randomizer. Other randomizers found in real systems include obstructions toflow such as traps and valves.An entrance is used to model the effect of an upstream randomizer. An exit models the effect of sudden pressuredrop. For pipes, VacTran allows the user to selectively add an entrance or exit loss to account for thesetransitions, as shown below.
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