VacTran 3 Manual (779748), страница 33
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Note that entrances only apply to pipes because they are the only conductanceelement that is capable of fully developed flow. Since other conductances such as elbows are already randomizers,an entrance loss option would be redundant.As mentioned in the previous section, entrance and exit losses can each be expressed as an equivalent length ofpipe having the same diameter. For any given conductance element, total equivalent length is comprised of the sumof equivalent lengths for the entrance, exit, and the conductance body. When the user does not select entrance orexit losses, they are not added to the total equivalent length.© 2011 Professional Engineering ComputationsCalculation Formulas317As previously mentioned, elbows, miters, and pipe bends are inherent randomizers because they tend to interruptfully developed flow.
For this reason, an entrance loss option is not provided for these element types because it isredundant with the basic equivalent length calculations for the body geometry. Therefore, the explicit entranceequivalent length for these conductance elements is always stated as zero because it is not distinctly separatedfrom the body equivalent length.
Randomizer elements can have an exit loss in addition to their body geometricequivalent length, if they have a sudden pressure drop at the exit. For example, if an elbow is situated upstreamfrom a larger diameter pipe, the user should add the exit loss option.© 2011 Professional Engineering Computations318VacTran 3The effect of selecting entrance and exit losses on equivalent length is shown in the conductance entry dialogSummary tab.
This text field displays the underlying calculated values for the conductance element. For example,the pipe entry dialog below lists the viscous and molecular flow equivalent length calculations. The list is shownscrolled to the molecular flow section.© 2011 Professional Engineering ComputationsCalculation Formulas31918.3.2.1 Choosing entrance and exit loss optionsConductance elements have characteristic equations for flow loss in molecular and viscous flow pressure regimes.However, additional flow affects are encountered when the upstream or downstream conductance element isconsidered. The Pipe Entry dialog, for example, allows the user to select entrance and exit losses.
Otherconductance element entry dialogs have exit loss selection only. Choose the entrance or exit loss using thefollowing criteria:Select include entrance loss if the upstream conductance element1) is a vacuum vessel2) has a larger diameter3) is a randomizer, but does not already have an exit lossIn other words, molecules arrive at the entrance in a random, scattered, cosine distribution in molecularflow, or a turbulent at the entrance in viscous flow.Select no entrance loss if the upstream conductance element1) is the same diameter and is not a randomizer2) is a smaller diameterThere would be no entrance loss if there is a continuity with the upstream element because of a similarcross section or because of beaming effects.Select include exit loss if the downstream conductance element1) is a vacuum vessel with a larger cross section than the conductance element2) has a larger diameterIn other words, there is a sudden pressure drop at the interface with the downstream conductance, usuallybecause the downstream element is substantially larger in cross section.Select no exit loss if the downstream conductance element1) is the same diameter2) is a smaller diameterIn other words, there is no sudden pressure drop at the interface with the downstream conductance.Avoid double-counting:1) If an elbow is upstream from a pipe with the same diameter, the elbow does not have an exit loss, but the pipedoes have an entrance loss.2) If an elbow is upstream from a larger diameter pipe, the elbow has an exit loss, but the pipe does not have anentrance loss.© 2011 Professional Engineering Computations320VacTran 3Entrance and exit loss examples, using the Pipe Entry dialogInclude entrance loss and Include exit lossNo entrance loss and Include exit lossInclude entrance loss and No exit lossNo entrance loss and No exit loss© 2011 Professional Engineering ComputationsCalculation Formulas18.3.2.2 Examples of selecting entrance and exit lossesPipe 1: entrance loss, no exit lossPipe 2: no entrance loss, no exit lossPipe1: add entrance loss, no exit lossElbow 1: no entrance loss, no exit lossElbow 2: no entrance loss, add exit lossPipe 2: no entrance loss, no exit lossPipe 3: add entrance loss, no exit loss© 2011 Professional Engineering Computations321322VacTran 318.3.3 Transmission probabilityTransmission probability is a concept associated only with molecular flow.
It is a statistical value from 0 to 1,representing the probability that a gas molecule entering the inlet of a conductance will pass completely throughand leave through the exit. In molecular flow, some percentage of gas molecules strike the inner walls of theconductance element and emit from the walls in a cosine distribution function. This means that a given moleculecan move either upstream or downstream in the conductance element, and leave from either end. The fact that moremolecules enter the high pressure side of the conductance than those entering the low pressure side from theopposite direction creates the perception of "flow".A transmission probability of 0 means that the conductance is blocked and no molecules pass through. Atransmission probability of 1 corresponds to an aperture (no walls).
All other conductance geometries have a valuebetween 0 and 1.Reference 8 (Santeler) introduced a transmission probability equation useful for both short and long tubes(cylindrical pipe). Equation 2 from that reference highlights the classical transmission probability (Knudson) of avery long circular pipe asWhere L = length, a = radiusGiven that an orifice has a transmission probability of 1 and a long pipe has a transmission probability as describedabove, a combined equation (10) is given as follows:Notice if length L' = 0, = 1.
This allows the equation for a pipe of zero length to degenerate to that for an orifice.Also note that when L' is very large, becomes equal to the 1/(3L/8a) term. For intermediate values of L, hasbeen found to be inaccurate by as much as 12%. To address this, Reference 8 (Santeler) developed a correctionequation for L’ that covers the whole range of values for L from 0 to very large numbers.L’ is a corrected length as described in equation 12:whereaL= pipe radius= actual length of pipe, or equivalent lengthTotal transmission probability for a conductance element consists of three components associated with the threecomponents of equivalent length:1) Entrance transmission probability2) Body transmission probability3) Exit transmission probability© 2011 Professional Engineering ComputationsCalculation Formulas323Trends of the L’ formulaThe graph illustrates the affect that the L’ formula has on short and long pipe.
The length/diameter ratio (L/d) isplotted against the change in equivalent length using the L’ formula. Note that at very small L/d ratios, as Lapproaches zero length, L’ adds about 33%. At ratios greater than 10, L’ has almost no effect.© 2011 Professional Engineering Computations324VacTran 318.3.3.1 Entrance transmission probabilityBased on Reference 8 (Santeler), we can separate the equivalent length contribution for the body from the equivalentlength contribution for the entrance.Given that L’ adds the entrance equivalent length to LWe can extract the entrance equivalent length from L’ as follows:or18.3.3.2 Body transmission probabilityFor a long cylindrical pipe, excluding entrance effects18.3.3.3 Exit transmission probability=1exit equivalent length usingwhere Lexit = 8a/3© 2011 Professional Engineering ComputationsCalculation Formulas32518.3.4 The concept of equivalent LengthEquivalent length is a convenient metric that can be used to compare conductance elements that have significantlydifferent geometry.
It is a way to physically describe conductance in terms of a single geometry: straight circularpipe. When using equivalent length of pipe, we must account for the differences between flow regimes and theeffects of entrance, body, and exit losses. Once this is done, equivalent length can be used to calculateconductance at a given pressure. The element conductance can be combined with other element conductances todetermine total conductance, which then feeds into the delivered speed and pump down calculations as shown inthe figure.A conductance element can consist of up to three constituent losses associated with total equivalent length:1.2.3.An entrance lossA body loss due to the geometry of the conductance between the entrance and the exitAn exit lossEach of the above types of losses can be expressed in terms of equivalent length of straight pipe.
They can beadded to produce a total equivalent length of straight pipe for the conductance element.For conductance elements that are not cylindrical pipe, VacTran uses equivalent length as a common variable forconductance calculations. For example, the viscous flow equivalent length of a 90-degree elbow is about 30diameters of pipe. For example, a 1 cm diameter elbow would have the same viscous flow loss as a pipe that was1 cm diameter and 30 cm long.Exit loss is applicable when selected by the user. Body loss is always applicable. For example, if an elbow exitsto a downstream pipe having the same diameter, there will be no additional exit loss.
If the same elbow exits to adown stream pipe having a much larger diameter, there will be an exit loss.Similarly, the entrance loss (applicable to pipe) is appropriately selected when the conductance is connected to anupstream large cross section, such as a vacuum vessel or a larger diameter conductance. The rationale behind thisconcept is reviewed in the following section on flow randomizers.In summary, total equivalent length will potentially have an entrance, body, and exit equivalent length addedtogether, depending on upstream and downstream geometry. The user is expected examine the sequence ofconductance elements and select appropriate entrance and exit loss options when creating or editing aconductance element.Equivalent length formulas are not the same for viscous and molecular flow regimes. In otherwords, the equivalent length for a given conductance element in viscous flow will likely havea very different value in molecular flow.See also:Viscous flow equivalent lengthViscous entrance equivalent lengthViscous body equivalent lengthViscous exit equivalent lengthMolecular flow equivalent lengthSummary- geometric equivalency© 2011 Professional Engineering Computations326VacTran 318.3.4.1 Viscous flow equivalent lengthTo determine equivalent length from the friction factor and the resistance coefficient, we use the followingrelationship that is valid in any viscous flow regime:orIn turbulent viscous flow conditions, where Reynold’s number is generally greater than 2000-4000, friction factor isconstant for a given relative roughness pipe.
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