Fundamentals of Vacuum Technology (1248463), страница 7
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Surfaces free of gases cantherefore be achieved (and maintained over longer periods of time) onlyunder ultrahigh vacuum conditions.Further physical properties change as pressure changes. For example, thethermal conductivity and the internal friction of gases in the mediumvacuum range are highly sensitive to pressure. In the rough and highvacuum regimes, in contrast, these two properties are virtually independentof pressure.Thus, not only will the pumps needed to achieve these pressures in thevarious vacuum ranges differ, but also different vacuum gauges will berequired. A clear arrangement of pumps and measurement instruments forthe individual pressure ranges is shown in Figures 9.16 and 9.16a inChapter 9.represents an resistance to flow, the consequence of which is that theeffective pumping speed Seff is always less than the pumping speed S ofthe pump or the pumping system alone.
Thus to ensure a certain effectivepumping speed at the vacuum vessel it is necessary to select a pump withgreater pumping speed. The correlation between S and Seff is indicated bythe following basic equation:11 1= +Seff S CHere C is the total conductance value for the pipe system, made up of theindividual values for the various components which are connected in series(valves, baffles, separators, etc.):1 1 1 11= + + + . . .C C1 C2 C3CnThe effective pumping speed required to evacuate a vessel or to carry outa process inside a vacuum system will correspond to the inlet speed of aparticular pump (or the pump system) only if the pump is joined directly tothe vessel or system. Practically speaking, this is possible only in raresituations. It is almost always necessary to include an intermediate pipingsystem comprising valves, separators, cold traps and the like.
All this(1.25)Equation (1.24) tells us that only in the situation where C = ∞ (meaningthat the flow resistance is equal to 0) will S = Seff. A number of helpfulequations is available to the vacuum technologist for calculating theconductance value C for piping sections. The conductance values forvalves, cold traps, separators and vapor barriers will, as a rule, have to bedetermined empirically.It should be noted that in general that the conductance in a vacuumcomponent is not a constant value which is independent of prevailingvacuum levels, but rather depends strongly on the nature of the flow(continuum or molecular flow; see below) and thus on pressure.
Whenusing conductance indices in vacuum technology calculations, therefore, itis always necessary to pay attention to the fact that only the conductancevalues applicable to a certain pressure regime may be applied in thatregime.1.5.3 Conductance for piping and orificesConductance values will depend not only on the pressure and the nature ofthe gas which is flowing, but also on the sectional shape of the conductingelement (e.g. circular or elliptical cross section).
Other factors are thelength and whether the element is straight or curved. The result is thatvarious equations are required to take into account practical situations.Each of these equations is valid only for a particular pressure range. This isalways to be considered in calculations.a) Conductance for a straight pipe, which is not too short, of length l, witha circular cross section of diameter d for the laminar, Knudsen andmolecular flow ranges, valid for air at 20 ¡C (Knudsen equation):C = 1351.5.2 Calculating conductance values(1.24)d4d 3 1 + 192 · d · pp +12.1 ·`/sl 1 + 237 · d · pl(1.26)wherep=p1 + p22dlp1p2Pipe inside diameter in cmPipe length in cm (l ³ 10 d)Pressure at start of pipe (along the direction of flow) in mbarPressure at end of pipe (along the direction of flow) in mbar====16HomeVacuum physicsfor δ ³ 0.528If one rewrites the second term in (1.26) in the following form3C = 12.1·d· f (d · p )l(1.26a)with(1.29)Cvisc = 76.6 · δ 0.712 · 1 − δ 0.288A `·1− δ sfor δ ² 0.5281 + 203 · d · p + 2.78 ·10 3 · d 2 · p 2f (d · p ) =1 + 237 · d · p(1.27)it is possible to derive the two important limits from the course of thefunction f (d á –p):d4· p `/ sland for δ ² 0,03(1.29b)`sδ = 0.528 is the critical pressure situation for air(1.28a)Limit for molecular flow(d · –p < 10Ð2 mbar · cm) :d3C = 12.1 ·` /slA `1− δ sCvisc = 20 · ALimit for laminar flow(d · –p > 6 · 10Ð1 mbar · cm):C = 135 ·C visc = 20 ·(1.29a)(1.28b)In the molecular flow region the conductance value is independent ofpressure!The complete Knudsen equation (1.26) will have to be used in thetransitional area 10Ð2 < d · –p < 6 · 10Ð1 mbar · cm.
Conductance values forstraight pipes of standard nominal diameters are shown in Figure 9.5(laminar flow) and Figure 9.6 (molecular flow) in Chapter 9. Additionalnomograms for conductance determination will also be found in Chapter 9(Figures 9.8 and 9.9).p 2 p1 critFlow is choked at δ < 0.528; gas flow is thus constant. In the case ofmolecular flow (high vacuum) the following will apply for air:Cmol = 11,6 · A · l · s-1 (A in cm2)(1.30)Given in addition in Figure 1.3 are the pumping speeds S*visc and S*molrefer-enced to the area A of the opening and as a function of δ = p2/p1.The equations given apply to air at 20 ¡C. The molar masses for the flowinggas are taken into consideration in the general equations, not shown here.l á sÐ1 á cmÐ2b) Conductance value C for an orifice A(A in cm2): For continuum flow (viscous flow) the following equations(after Prandtl) apply to air at 20 ¡C where p2/p1 = δ:Fig.
1.2Flow of a gas through an opening (A) at high pressures (viscous flow)Fig. 1.3 Conductance values relative to the area, C*visc, C*mol, and pumping speed S*visc andS*mol for an orifice A, depending on the pressure relationship p2/p1 for air at 20 ¡C.17HomeVacuum physicsWhen working with other gases it will be necessary to multiply theconductance values specified for air by the factors shown in Table 1.1.Gas (20 ¡C)Molecular flowLaminar flowAir1.001.00Oxygen0.9470.91Neon1.0131.05Helium2.640.92Hydrogen3.772.07Carbon dioxide0.8081.26Water vapor1.2631.73The technical data in the Leybold catalog states the conductance values forvapor barriers, cold traps, adsorption traps and valves for the molecularflow range.
At higher pressures, e.g. in the Knudsen and laminar flowranges, valves will have about the same conductance values as pipes ofcorresponding nominal diameters and axial lengths. In regard to right-anglevalves the conductance calculation for an elbow must be applied.In the case of dust filters which are used to protect gas ballast pumps androots pumps, the percentage restriction value for the various pressurelevels are listed in the catalog. Other components, namely the condensateseparators and condensers, are designed so that they will not reducepumping speed to any appreciable extent.Table 1.1 Conversion factors (see text)Nomographic determination of conductance valuesThe conductance values for piping and openings through which air andother gases pass can be determined with nomographic methods.
It ispossible not only to determine the conductance value for piping at specifiedvalues for diameter, length and pressure, but also the size of the pipediameter required when a pumping set is to achieve a certain effectivepumping speed at a given pressure and given length of the line. It is alsopossible to establish the maximum permissible pipe length where the otherparameters are known.
The values obtained naturally do not apply toturbulent flows. In doubtful situations, the Reynolds number Re (seeSection 1.5.) should be estimated using the relationship which isapproximated belowRe = 15 ·qpVdAxial lengthThe following may be used as a rule of thumb for dimensioning vacuumlines: The lines should be as short and as wide as possible. They mustexhibit at least the same cross-section as the intake port at the pump. Ifparticular circumstances prevent shortening the suction line, then it isadvisable, whenever this is justifiable from the engineering and economicpoints of view, to include a roots pump in the suction line. This then acts asa gas entrainment pump which reduces line impedance.(1.31)Here qpV = S · p is the flow output in mbar l/s, d the diameter of the pipein cm.A compilation of nomograms which have proved to be useful in practice willbe found in Chapter 9.1.5.4 Conductance values forother elementsWhere the line contains elbows or other curves (such as in right-anglevalves), these can be taken into account by assuming a greater effectivelength leff of the line.
This can be estimated as follows:leff = laxial +133. ·θ·d180°(1.32)Wherelaxial : axial length of the line (in cm)leff: Effective length of the line (in cm)d: Inside diameter of the line (in cm)θ: Angle of the elbow (degrees of angle)18HomeVacuum generation2. Vacuum generationwhich the first three classes belong to the compression pumps and wherethe two remaining classes belong to the condensation and getter pumps:2.1.
Vacuum pumps: A survey1. Pumps which operate with periodically increasing and decreasing pumpcham-ber volumes (rotary vane and rotary plunger pumps; also trochoidpumps)Vacuum pumps are used to reduce the gas pressure in a certain volumeand thus the gas density (see equation 1.5). Consequently consider the gasparticles need to be removed from the volume.
Basically differentiation ismade between two classes of vacuum pumps:a) Vacuum pumps where Ð via one or several compression stages Ð thegas particles are removed from the volume which is to be pumped andejected into the atmosphere (compression pumps). The gas particles arepumped by means of displacement or pulse transfer.b) Vacuum pumps where the gas particles which are to be removedcondense on or are bonded by other means (e.g. chemically) to a solidsurface, which often is part of the boundary forming volume itself.A classification which is more in line with the state-of-the-art and practicalapplications makes a difference between the following types of pumps, of2. Pumps which transport quantities of gas from the low pressure side tothe high pressure side without changing the volume of the pumpingchamber (Roots pumps, turbomolecular pumps)3.
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