Dr. János VAD AXIAL FLOW TURBOMACHINERY Classification, restriction of topic under discussion

Transcription

1 Dr. János VAD AXIAL FLOW TURBOMACHINERY. INTRODUCTION.. Classificaion, resricion of opic under discussion Fluid: Gas (Liuid) (Muliphase fluid) ower inpu / oupu: ower inpu ransporaion of fluid from a domain of lower pressure ( sucion side ) o a domain of higher pressure ( pressure side ) (ower oupu e.g. wind urbines) Operaing principle: Euler principle (fluid mechanical principle): TURBOMACHINERY. Bladed roor in a casing. Mechanically free passing beween sucion and pressure sides. (Volumeric principle: operaing enclosure beween he sucion and pressure sides, bounded by saionary and moving walls. No mechanically free passing. E. g. pison compressors.).. Classificaion of fluid machinery for power inpu... Direcion of hrough-flow relaive o he axis of roaion: axial (radial) (mixed) (cross-flow)... ressure increase, pressure raio: p /p pressure raio A/ p /p <. (.) fans ρ consan, T 0 design, consrucional, applicaion aspecs JUTIFICATION: Isenropic approach: p /p (ρ /ρ ) χ (.)

2 Dr. János VAD AXIAL FLOW TURBOMACHINERY ubsiuing p /p., for air, he resul is ρ /ρ.07, being sill negligible according o he above aspecs. Being consan of densiy gives crieria for he fluid velociy characerising he machinery, e.g. for he circumferenial velociy of he blade ip, or for he fluid velociy developing in he conneced machinery. Le us consider a sreamline beween he poin of he sucion por and he sagnaion poin T locaed on he nose cone of he machine. Having crieria being even more sric compared o he previous relaive difference of densiy of 7 %: ρ ρ 0. 05ρ (.) T The energy euaion beween poins and T: v RMa T T χ + + TT c p c p Where he following relaionship was considered: Ma v v (.3) (.4) a κ RT Isenropic change of sae: κ ρ T TT (.5) ρ T Wih assumpion of ρt ρ 0. 05ρ and wih subsiuion of air characerisics, he combinaion of Es. (.3) and (.5) reads []: Ma < 0.3 (.6) This condiion reads, wih assumpion of air of room emperaure, ha no velociies higher han 00 m/s are allowed o develop in he machinery and in he conneced sysem. The circumferenial velociy of he blade ip characerises of he machine in a lifelike manner. ummary: FOR FAN IN GENERAL Assuming nearly amospheric pressure on he sucion side, p < 0. bar [] Blade ip circumferenial speed < 00 m/s, being in harmony wih he mechanical and acousic demands relaed o he urbomachinery. B/. < p /p < 3 blowers ρ consan, T > 0, bu cooling due o naural convecion is sill sufficien. C/ 3 < p /p compressors ρ consan, T >> 0, arificial cooling is necessary. (Mechanical and echnological aspecs)

3 Dr. János VAD AXIAL FLOW TURBOMACHINERY 3 Fig... Indusrial gas urbine [4] Fig... Airplane je combusion engine [4]

4 Dr. János VAD AXIAL FLOW TURBOMACHINERY 4.3. Work process of fans Q For ideal (inviscid) case: m Q m v p + gh + U + ρ i i (.7) For fans Q 0, U 0, and gh plays role only if he densiies of he ambien and he ranspored fluid differ (e.g. ransporaion of ho fume gas or cold air). Therefore, for fans in general v p v m + V ρ + p V pid ρ Where, due o he Euler euaion of urbomachines [3]: p id ( v u v ) u (.8) ρ (.9) Deparures from ideal (inviscid) case: A/ Due o volumeric losses, he volume flow rae VR hrough he roor is higher han he volume flow rae V uilised (a percenage circulaes inside he roor), bu exra power is o be inroduced for circulaion of he exra amoun. This effec is considered wih use of he volumeric efficiency η V : VR p id, VR > V, η V V / VR (.0) B/ The oal pressure rise is less han he ideal value, due o fricion losses. This effec is considered wih use of he hydraulic efficiency η h, also called as oal efficiency (because of is relaion o oal pressure rise): η p / p (.) h id Wih use of he above p V useful VR pid (.) ηv ηh ηvηh C/ The overall inpu power covers he mechanical losses, e.g. losses of bel drive and bearing, as well. This effec is considered wih inroducion of he mechanical efficiency: η m / overall (.3) Therefore overall useful useful (.4) η η η η V h m overall

5 Dr. János VAD AXIAL FLOW TURBOMACHINERY 5 For fans, i is usually rue ha η m, η V (no considerable pressure difference occurs; his would no be rue in he case of pumps), and herefore, η overall η h..4. Basic consrucion of axial flow fans Guide vanes Tip clearance Duc Nose cone Roor blading Hub Fig..3. kech of an axial fan [] Fig..4. Axial (mixed-flow?) fan [6] Characerisic geomerical daa: inner (hub) and ouer (ip) diameers of roor blading: D, D, respecively. Fig..5. Duced axial fan [5] Fig..6. Wall axial fan [5] RINCIAL DIFFERENCE BETWEEN RADIAL AND AXIAL TURBOMACHINE: According o Euler euaion of urbomachines (.9), in he case of axial flow machinery r r, u u. For his reason, he axial flow machines usually achieve less oal pressure rise han radial flow machines. In he case of fixed fluid mechanical performance, his also means ha axial urbomachines usually perform higher volume flow rae han radial flow urbomachines. In an axial flow urbomachine, he fluid flow deflecion is reduced compared o ha of a radial flow machine. This leads o reduced losses and increased efficiency of he axial flow urbomachine uni. In he case of an axial flow urbomachine, he hrough-flow direcion accommodaes he flow direcion in he conneced duc sysem. This leads o reduced losses no only in he urbomachine in iself bu also in he conneced sysem.

6 Dr. János VAD AXIAL FLOW TURBOMACHINERY 6.5. Axial fan arrangemens: dependen on echnology and geomery!.5.. From duc o he surroundings (exracion, induced flow, e.g. food indusry: vapour and sink exracion) v p 0 v p 0 p Fig..7. From duc o he surroundings arrangemen [5] v v v v p ρ p + 0 ρ + ( p0 p ) p + ρ ρ (.5) ( p for axial fans, because v v due o he uniformiy of he fluid cross-secion) v v ps p ρ p ρ (.6).5.. From surroundings o he duc (inflow, forced flow, e.g. boiler feed air fan, or fans providing overpressure: clean room echnology) v p 0 p 0 p Fig..8. From surroundings o he duc arrangemen [5] Wih neglec of losses on he sucion side: v v p ρ + ( p0 + p ) p0 p + ρ (.7) p s p (.8)

7 Dr. János VAD AXIAL FLOW TURBOMACHINERY From duc o duc (duced fan: upsream and downsream of i: service elemens. E.g. upsream: calorifer, downsream: jeallousie) Fig..9. From-duc-o-duc arrangemen [5] v v ρ + p ρ + p (.9) p v p s p ρ + p (.0).5.4. From surroundings o surrounding (e.g. unnel venilaion) p 0 p 0 v Fig..0. [5] v v p ρ p + 0 p0 ρ (.) v ps p ρ 0 (.) Even in absence of duc, he saic pressures may be differen on he wo sides!

8 Dr. János VAD AXIAL FLOW TURBOMACHINERY 8.6. Characerisic curve: an example Fig... Characerisic curves of a HELIO HQ 7/4 axial fan [6].7. Dimensionless characerisics, comparison User demands: p, ( p s ), V, overall (moor selecion) Machinery characerisics: D (roor ouer diameer), n Fluid characerisics: ρ, ν To compare various machines: ( u D π n ) Toal pressure coefficien: aic pressure coefficien: Flow coefficien: p Ψ (.3) ρ u p s Ψ s (.4) ρ u A v Φ (.5) char u Where A char (D ip - D hub ) π/4 D ip π/4 (-ν ) annulus cross-secion Hub-o-ip raio: ν D hub / D ip (.6) ower coefficien: λ ρ u A overall char u pv η ρ u A char u Ψ Φ η (.7)

9 Dr. János VAD AXIAL FLOW TURBOMACHINERY 9 Reynolds number for axial fans: u l Re (.8) ν Fig... Dimensionless characerisics [] Fig..3. Reynolds number dependency of hydraulic efficiency of an axial fan [7] For axial fans: he (.8) Reynolds number is o be kep above (criical Reynolds number) ( above ) Fig..4. Comparison of various fans []

10 Dr. János VAD AXIAL FLOW TURBOMACHINERY 0 LIT OF YMBOL a [m/s] sound speed c p [J/(kgK)] isobar specific hea ( 005 J/(kgK) for air) D [m] diameer g [N/kg] graviy field inensiy h [m] level, heigh i [J/kg] oal enalphy l [m] chord lengh Ma [-] Mach number n [/s] roor speed m [kg/s] mass flow rae [W] inpu shaf power useful [W] useful fluid mechanical power overall [W] oal inpu power p [a] saic pressure p [a] oal pressure p [a] oal pressure rise p s [a] saic pressure rise Q [W] hea power exraced by cooling V [m 3 /s] volume flow rae R [J/(kgK)] specific gas consan ( 87 J/(kgK) for air) r [m] radius T [K] emperaure U [J/kg] specific inernal energy u [m/s] circumferenial speed u [m/s] roor blade ip circumferenial speed v [m/s] absolue velociy ν [m /s] kinemaic viscosiy ρ [kg/m 3 ] densiy χ [-] isenropic exponen (.40 for air) η V [-] volumeric efficiency η h [-] hydraulic efficiency η m [-] mechanical efficiency η overall [-] overall efficiency difference beween characerisics of pressure and sucion sides UBCRIT: 0 characerisics of amosphere sucion side; fluid enering he roor pressure side; fluid exiing he roor id ideal (no losses)