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Eirini KoutantouSupervisor: Prof. D. ValougeorgisHolweck pumpmodelingDepartment of Mechanical Engineering,University of Th...
Presentation contents:1) Introduction2) Statement of the problem3) Computational scheme4) Results and discussion5) Conclud...
3Vacuum:the pressure of thegas is much lowerthan the one of itsenvironmentPump:device that is usedto move fluidsVacuum pum...
General Terminology:4• Pressure:• Ideal gas equation:• Mean free path:• Reynolds number:• Knudsen number:mfp:FpABmRTpV Nk ...
5Vacuum Terminology:• Mass flow:• Pumping speed:• Pump throughput:• Conductance/Conductivity:• Compression ratio:mMt [kg/...
6vacuum(mfp range)rough vacuum:mfp << 10-4 mmedium vacuum:10-4 m - 10-1 mhigh vacuum:10-1 m - 103 multra high vacuum:mfp >...
7fluid displacedby a space and isforwarded toanothergases are removedby extracting themin the atmospherechange of thekinet...
Gas transfer: Positive displacement8• Diaphragm pump:- Well known forenvironmental reasons- low maintenance cost- noiseles...
9Gas transfer: Kinetic- 1913 :Gaede - molecular- 1957 :Dr.W.Becker - turbomolecular• (Turbo) molecular pump:Entrapment pum...
10Examples!AUDIMERCEDESBMWMEDICAL APPLICATIONAEROSPACE APPLICATIONApplications:- Refrigeration systems- Food industry- Lab...
Holweck pump:11Invented by:Fernand HolweckConstructed by:Charles BeaudouinMolecular pump:- Outer cylinder withgrooves, spi...
3D problem12Simulation: much computational effortNeglect: end effects and the curvatureof the geometry(total effect = 0.05...
Geometry:13H : distance between platesW x D : groove cross sectionW : groove widthD : groove depthL : periodIsothermal wal...
General description ofindividual problems:141. Longitudinal Couette flow2. Longitudinal Poiseuille flow3. Transversal Coue...
15Longitudinal Couette: Longitudinal Poiseuille:Fluid flow: in direction z’Cause of flow: moving wallin direction z’Cause ...
1616Fluid flow: in direction x’Cause of flow: moving wallin direction x’Cause of flow: pressure gradientin direction x’Lin...
Macroscopic quantities:17Longitudinal flows:220 01,zu x y e d d220 01, sinyzP x y e d d102 ,2zLG u y dyH/2/22( ,1)L HyzL ...
18Boundary conditions:CouettePoiseuilleeqwf f2023202wuRTeq wwnf eRT, , , , , ,2 2L Ly yH HInlet – Outlet: PeriodicInterfac...
• Discretization:- Physical space [ (x,y) or (x,z)] : (i,j)where i=1,2,…,I and j=1,2,…,J- Molecular velocity space (μm,θn)...
Algorithm:20Parameters:δ μm θn Ny_chaD (D/H) W (W/H) L (L/H)Couette: U0 / Poiseuille: Χp• Grid format :Channel and Cavity•...
• Geometries:21L = 2:L = 2.5:L = 3:• Rarefaction parameter:δ 0 10-310-² 10-¹ 1 10 100Total runs:18 geometries 7 δ=126• Res...
22Transversal Poiseuille flow:Knudsen minimum: δ=1Normalization of results:F. SharipovL=3 , W=1.5 , D=0.5δL W D 0 10-3 10-...
23Transversal Poiseuille flow:Normalization of results:F. SharipovL=3 , W=1.5 , D=0.5δL W D 0 10-3 10-² 10-1 1 10 1002 0.5...
24channel inlet:Longitudinal Couette:Transversal Couette:L=3, W=1, D=1L=3, W=1, D=1Macroscopic velocitieschannel middle:L=...
25channel inlet:Macroscopic velocitieschannel middle:cavity start:Longitudinal Poiseuille:Transversal Poiseuille:L=3, W=1,...
26Longitudinal Couette:Longitudinal Poiseuille:Macroscopic velocitiesvelocity contours:L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=1...
27Transversal Couette:Transversal Poiseuille:Macroscopic velocitiesvelocity streamlines:L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=...
• Four different flow configurations have been examined:1. Longitudinal Couette flow2. Longitudinal Poiseuille flow3. Tran...
29Thank you for your attention !!!
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Holweck pump

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Holweck pump

  1. 1. Eirini KoutantouSupervisor: Prof. D. ValougeorgisHolweck pumpmodelingDepartment of Mechanical Engineering,University of Thessaly
  2. 2. Presentation contents:1) Introduction2) Statement of the problem3) Computational scheme4) Results and discussion5) Concluding remarks2
  3. 3. 3Vacuum:the pressure of thegas is much lowerthan the one of itsenvironmentPump:device that is usedto move fluidsVacuum pump:movement of gasmolecules due to flowinduced by a vacuumsystemWas invented in:1650by:Otto von Guericke
  4. 4. General Terminology:4• Pressure:• Ideal gas equation:• Mean free path:• Reynolds number:• Knudsen number:mfp:FpABmRTpV Nk TM2 21 12 2n d n dwhere: 8kTmReudv12KndAbsolute vacuum:density ofmolecules=0
  5. 5. 5Vacuum Terminology:• Mass flow:• Pumping speed:• Pump throughput:• Conductance/Conductivity:• Compression ratio:mMt [kg/h, g/s]dVSdt[m3/s, m3/h]pVV mRTQ pt tMpVdVQ S p pdt[Pa m3/s =W]pVQCpin row:1/Ctot = 1/C1 + 1/C2parallel:Ctot = C1 + C2 + …201pKpP1: inlet pressureP2: outlet pressure
  6. 6. 6vacuum(mfp range)rough vacuum:mfp << 10-4 mmedium vacuum:10-4 m - 10-1 mhigh vacuum:10-1 m - 103 multra high vacuum:mfp >> 103 mvacuum(pressure range)rough vacuum:105 Pa - 100 Pafine vacuum:100 Pa - 10-1 Pahigh vacuum:10-1 Pa - 10-5 Paultra high vacuum (UHV):10-5 Pa - 10-10 Paextreme high vacuum(XHV):10-10 Pa - 10-12 PaDefinition of vacuumranges:Gas flow regimes:Kn > 0.5:Free Molecular-Equation of Boltzmann(without the collision term)-ultra, extreme highvacuum0.01 < Kn < 0.5:Transition regime-Equation of Boltzmann(empirical approaches)- fine, medium vacuumKn << 0.01:Viscous or continuum flow(laminar or turbulent)-Described by the equations NS- rough vacuum
  7. 7. 7fluid displacedby a space and isforwarded toanothergases are removedby extracting themin the atmospherechange of thekinetic state ofthe moving fluidcause condensationor chemicaltrapping of gasPump tree:
  8. 8. Gas transfer: Positive displacement8• Diaphragm pump:- Well known forenvironmental reasons- low maintenance cost- noiselessRotary pumps• Roots pump:- design principle was discovered:in 1848 by Isaiah Davies- implemented in practice:Francis and Philander Roots- in vacuum science: only since 1954Reciprocating pumps
  9. 9. 9Gas transfer: Kinetic- 1913 :Gaede - molecular- 1957 :Dr.W.Becker - turbomolecular• (Turbo) molecular pump:Entrapment pumps• Cryopump:- concentration on coldsurface- profitable for somegasesDrag pumps
  10. 10. 10Examples!AUDIMERCEDESBMWMEDICAL APPLICATIONAEROSPACE APPLICATIONApplications:- Refrigeration systems- Food industry- Laboratory experimentation- Mechanical vacuum- Medicine- Aerospace industry- Formula 1 andAutomotive industries
  11. 11. Holweck pump:11Invented by:Fernand HolweckConstructed by:Charles BeaudouinMolecular pump:- Outer cylinder withgrooves, spiral form- Inner cylinder withsmooth surfaceThe rotation of thesmooth cylinder causesthe gas flowFernand Holweck(1890-1941)
  12. 12. 3D problem12Simulation: much computational effortNeglect: end effects and the curvatureof the geometry(total effect = 0.05 )4 independent problems: 2D flowin grooved channelregion of solution:
  13. 13. Geometry:13H : distance between platesW x D : groove cross sectionW : groove widthD : groove depthL : periodIsothermal walls:Τ=Τ0Characteristic length:ΗBoundaries of flow domain:- Inlet: (x΄= -L/2)- Outlet: (x΄= L/2)- Top wall: (y΄= Η)- Bottom wall: (y΄=-D)
  14. 14. General description ofindividual problems:141. Longitudinal Couette flow2. Longitudinal Poiseuille flow3. Transversal Couette flow4. Transversal Poiseuille flow( , )if fQ f ft iBoltzmann equation:BGK model:( )Mif fv f ft i23[ ( , )]22 ( , )( , )2 ( , )i iBm u i tk T i tMBmf n i t ek T i tMaxwell distribution function:Steady state flow:Taylor expansion:( )Mifv f fi00n nn00T TT200 0312 2M i iuf fRT RTwhere:Polar system coordinates:2 2x yc c1tan yxcccos sinx ydc cx y x y dsLinear differentiation of distribution function
  15. 15. 15Longitudinal Couette: Longitudinal Poiseuille:Fluid flow: in direction z’Cause of flow: moving wallin direction z’Cause of flow: pressure gradientin direction z’0,0, ,zu u x y0 01oUf f hu01oUuLinearization01f f hXp z Xp 1XpxxHyyH 0xxcu 0yycu 0zzcu00Pv 00 0P Hu 02ou RTNon dimensionalvariables0zzuuU00uU 0ouU0zzuuu Xp Xp XpreducedBGK equationsafter projectionx y zc c ux ywhere:21, , , , , , , zcx y x y z z zx y c c h x y c c c c e dc12x y zc c ux yMacroscopic velocity:
  16. 16. 1616Fluid flow: in direction x’Cause of flow: moving wallin direction x’Cause of flow: pressure gradientin direction x’LinearizationxxHyyH 0xxcu 0yycu 0zzcu00Pv 00 0P Hu 02ou RTNon dimensionalvariables( , ), ( , ),0x yu u x y u x yTransversal Couette: Transversal Poiseuille:0 01oUf f hu01oUu01f f hXp x Xp 1Xp00uU 0ouU Xp Xpwhere:0xxuuU0yyuuU0xxuuu Xp0yyuuu Xp21 2 cos sinx yu ux y21 2 cos sin cosx yu ux y2x yc cx y21, , , , , , , zcx y x y z zx y c c h x y c c c e dc221 1, , , , , , ,2zcx y x y z z zx y c c h x y c c c c e dcandreducedBGK equationsafter projectionMacroscopic velocity:
  17. 17. Macroscopic quantities:17Longitudinal flows:220 01,zu x y e d d220 01, sinyzP x y e d d102 ,2zLG u y dyH/2/22( ,1)L HyzL HHCd P x dxLTransversal flows:220 01,x y e d d2220 01 2, 13x y e d d2220 01, cosxu x y e d d2220 01, sinyu x y e d d2230 01, sin cosxyP x y e d d/2/22,1LxyLHCd P x dxL102 ,2xLG u y dyHDensity deviation:Temperature deviation:Macroscopic velocity:Stress tensor:Flow rate:Drag coefficient:
  18. 18. 18Boundary conditions:CouettePoiseuilleeqwf f2023202wuRTeq wwnf eRT, , , , , ,2 2L Ly yH HInlet – Outlet: PeriodicInterface gas-wall: Maxwell - diffusion0 0ncStationary walls:Moving wall: 2 zc 0ycStationary walls:2 coswn 0ycLongitudinalTransversal Stationary walls:Moving wall:0 0nc0 0ncwnStationary walls: 0ncwhere00LongitudinalTransversalwhere nw is defined by the no-penetration condition: 0u n
  19. 19. • Discretization:- Physical space [ (x,y) or (x,z)] : (i,j)where i=1,2,…,I and j=1,2,…,J- Molecular velocity space (μm,θn) : (ζm , θn)where 0 < ζm < ∞ and 0 < θn < 2πm=1,2,…,M and n=1,2,…N19Discrete Velocity MethodDVMSet consists of:Μ × Ν discrete velocities(16 × 50 × 4)3200• Discretized kinetic equations:(e.g. transversal Couette flow), ,, , , 2, , , , , 1 2 cos sini j i ji j m nm i j m n i j i j m m x n y ndu uds, , , ,, , ,2i j m n i jm i j m nddsSet ofalgebraic equations:2 × Μ × Νequations/node
  20. 20. Algorithm:20Parameters:δ μm θn Ny_chaD (D/H) W (W/H) L (L/H)Couette: U0 / Poiseuille: Χp• Grid format :Channel and Cavity• Grid reverse:Scan of grid:1st 2nd3rd4thend of scanning
  21. 21. • Geometries:21L = 2:L = 2.5:L = 3:• Rarefaction parameter:δ 0 10-310-² 10-¹ 1 10 100Total runs:18 geometries 7 δ=126• Results:Mass flow rateDrag coefficientMacroscopic velocities
  22. 22. 22Transversal Poiseuille flow:Knudsen minimum: δ=1Normalization of results:F. SharipovL=3 , W=1.5 , D=0.5δL W D 0 10-3 10-² 10-1 1 10 1002 0.5 0.5 3,211 3,157 2,815 1,976 1,511 2,766 15,5442 0.5 1 3,212 3,158 2,814 1,975 1,509 2,752 15,4332 1 0.5 3,149 3,096 2,760 1,945 1,534 2,996 17,2282 1 1 3,159 3,106 2,769 1,953 1,539 2,984 16,6252 1.5 0.5 3,159 3,107 2,777 1,983 1,651 3,523 20,9182 1.5 1 3,159 3,107 2,775 1,978 1,641 3,514 20,8562.5 0.5 0.5 3,227 3,173 2,829 1,988 1,516 2,754 15,4502.5 0.5 1 3,227 3,173 2,828 1,986 1,513 2,740 15,3402.5 1 0.5 3,183 3,129 2,789 1,961 1,532 2,927 16,7422.5 1 1 3,191 3,137 2,796 1,968 1,535 2,914 16,6252.5 1.5 0.5 3,171 3,119 1,219 1,241 1,617 3,312 19,4122.5 1.5 1 3,173 3,120 2,785 1,980 1,610 3,301 19,3333 0.5 0.5 3,239 3,184 2,839 1,996 1,520 2,746 15,3873 0.5 1 3,239 3,184 2,838 1,993 1,517 2,732 15,2773 1 0.5 3,202 3,148 2,806 1,974 1,530 2,880 16,4283 1 1 3,208 3,154 2,811 1,978 1,533 2,867 16,3133 1.5 0.5 3,193 3,139 2,801 1,985 1,594 3,171 18,4963 1.5 1 3,196 3,142 2,802 1,984 1,588 3,160 18,4080.01 0.10 1.00 10.000.51.01.52.02.5Mass flow rate:
  23. 23. 23Transversal Poiseuille flow:Normalization of results:F. SharipovL=3 , W=1.5 , D=0.5δL W D 0 10-3 10-² 10-1 1 10 1002 0.5 0.5 0,470 0,470 0,471 0,476 0,488 0,488 0,3932 0.5 1 0,471 0,471 0,472 0,477 0,489 0,488 0,3932 1 0.5 0,436 0,436 0,438 0,449 0,483 0,499 0,4032 1 1 0,443 0,443 0,445 0,456 0,488 0,500 0,4002 1.5 0.5 0,414 0,414 0,417 0,436 0,493 0,522 0,4202 1.5 1 0,415 0,415 0,418 0,436 0,493 0,522 0,4202.5 0.5 0.5 0,476 0,476 0,477 0,480 0,490 0,487 0,3922.5 0.5 1 0,477 0,477 0,478 0,481 0,491 0,487 0,3922.5 1 0.5 0,449 0,449 0,450 0,459 0,486 0,496 0,3992.5 1 1 0,455 0,455 0,456 0,464 0,489 0,497 0,4002.5 1.5 0.5 0,431 0,431 0,434 0,449 0,494 0,513 0,4132.5 1.5 1 0,432 0,320 0,434 0,449 0,494 0,513 0,4123 0.5 0.5 0,480 0,480 0,481 0,484 0,491 0,487 0,3923 0.5 1 0,481 0,481 0,481 0,484 0,492 0,487 0,3923 1 0.5 0,457 0,457 0,459 0,466 0,488 0,494 0,3983 1 1 0,462 0,462 0,464 0,470 0,491 0,495 0,3983 1.5 0.5 0,442 0,443 0,445 0,457 0,495 0,508 0,4083 1.5 1 0,443 0,443 0,445 0,457 0,494 0,508 0,4080.010 0.100 1.000 10.0000.00.20.40.60.81.01.21.4Drag coefficient:
  24. 24. 24channel inlet:Longitudinal Couette:Transversal Couette:L=3, W=1, D=1L=3, W=1, D=1Macroscopic velocitieschannel middle:L=3, W=1, D=1L=3, W=1, D=1cavity start:L=3, W=1, D=1L=3, W=1, D=1
  25. 25. 25channel inlet:Macroscopic velocitieschannel middle:cavity start:Longitudinal Poiseuille:Transversal Poiseuille:L=3, W=1, D=1L=3, W=1, D=1L=3, W=1, D=1 L=3, W=1, D=1L=3, W=1, D=1L=3, W=1, D=1
  26. 26. 26Longitudinal Couette:Longitudinal Poiseuille:Macroscopic velocitiesvelocity contours:L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=1δ=1L=2 , W=1 , D=1δ=10L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=1δ=1L=2 , W=1 , D=1δ=10
  27. 27. 27Transversal Couette:Transversal Poiseuille:Macroscopic velocitiesvelocity streamlines:L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=1δ=1L=2 , W=1 , D=1δ=10L=2 , W=1 , D=1δ=0.1L=2 , W=1 , D=1δ=1L=2 , W=1 , D=1δ=10
  28. 28. • Four different flow configurations have been examined:1. Longitudinal Couette flow2. Longitudinal Poiseuille flow3. Transversal Couette flow4. Transversal Poiseuille flow• Results have been obtained in the whole range of Knudsen numberand for various values of the geometrical parameters: L/H , W/H, D/H.• Synthesizing these results in a proper manner designed parameterssuch as pumping speed and throughput can be obtained.• Optimization of the Holweck pump will follow soon!!!28
  29. 29. 29Thank you for your attention !!!

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