Turbomachinery. Turbines
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1 Turboachinery Turbines Turboachinery -40 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turbine Overview Configurations (aial, radial, ied), analysis and other issues siilar to copressors Copared to copressors higher loading h o / (or specific work) and pressure ratio per stage - why? favorable pressure gradient usually uch higher teperature inlet higher teperature aterials (strength) and/or blade cooling Turboachinery -4 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Science, S
2 Turbine nalysis Siilar to copressor analysis Euler turboachinery (conservation) equations rc rc W u i c i i u c i i i Nole Rotor and cascade flow to find c nole rotor Turboachinery -4 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turbine Cascade nalysis c Now blade oves upward (flip sign convention); again fied r, u i = w c i i w c i i Therefore for rotor, and constant c c c tan c c tan c, c tan tan h o, sae for of blade loading eqn for turbine as copressor Nole c wu Rotor w Turboachinery -4 Copyright 04,05 by Jerry M. Seitan. ll rights reserved.
3 Stage Pressure Ratio For adiabatic turbine with TPG/CPG po To To ho, Prt p0 st T o st RTo > as written c h o,, p p o st RT o c o, Stage pressure ratio still depends on. = f(= r, c ). blade M=f(r, T o ). st <0 for turbine Turboachinery -44 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. ial Turbine Maps Larger stage pressure ratios and efficiencies then copressors Peak efficiency on-design For fied RPM, larger pressure change (drop) at higher ass flowrate ore work etracted per unit ass t high (corrected) ass flowrate, nole becoes choked Turboachinery -45 Copyright 04,05 by Jerry M. Seitan. ll rights reserved.
4 Turboachinery -46 Blade Design: Degree of Reaction We have TWO blade paraeters to design rotor trailing edge (atch ) nole trailing edge (atch ) How to do this?.degree of reaction, R c c.stage eit condition constraint ( ) tan tan c c w Copyright 04,05 by Jerry M. Seitan. ll rights reserved. c tan c c tan c w c c, w,, c tan tan Siilar issue for copressor; we just ignored designing Turboachinery -47 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Degree of Reaction Recall R h rotor h stage allows us to distribute load (static pressure change) between rotor and nole (or stator) how to relate static enthalpy change to aiuthal velocity changes? KE!! h h v o for stationary blade, no work done h o 0 h KE e.g., nole blade h if c constant, and negligible c r h c c c c c c 4
5 c Turboachinery -48 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Degree of Reaction (Turbine) Rotor blades?? are stationary in rotor s reference frae h h w w Reaction h h h h R h h ho c ho c h w w h h o h o c c R if c c, c tan tan relates design blade angles to aiuthal KE change c w c c c w tan tan R = 0 w w c w,, c tan c, c tan Ipulse Turbine h R h all the pressure change occurs across the nole, or the nole creates high KE 0 w c tan c tan w w w, w w c tan tan Turboachinery -49 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. 5
6 So for ipulse turbine, blade loading coeff. Ipulse Turbine Relates blade loading to nole eit angle <0 ho stage tan c Fro equation, rotor blade angles given by tan tan tan c hostage c c tan Turboachinery -50 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turboachinery -5 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Ipulse Turbine To let largest power per unit ass flow rate large tends to produce high velocities and p o losses practical liit, ~70-75 Further possible constraint no eit swirl (c =0) c c c c c,, c c h o stage tan, tan c c c c c tan 6
7 50% Reaction Turbine R 0.5 c balanced p drop across stage w w, w w w w c tan c c tan tan h c ostage, c tan if no eit swirl c c, ho stage tan half loading of ipulse: less power/stage Turboachinery -5 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. tan, c c, c w w R c, tan tan Turboachinery -5 Copressor-Turbine Matching nother part of design/operational requireent Need to atch copressor and turbine stages on sae spool Steady operation atch. N (RPM).. W Iterative procedure Copyright 04,05 by Jerry M. Seitan. ll rights reserved. 7
8 Turbine Stresses/Operational Liits Turbine blades eperience large stresses: bending, theral and centrifugal (rotor: g) Materials ehibit significant loss of strength and enhanced creep at high T low strength at odern engine T o4 (high ST, th ) T o4 >400C (500F) Turboachinery -54 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turbine Inlet Teperature Evolution Solutions high teperature aterials blade cooling TBC (theral barrier coatings) Ni supers single crystal super s Turboachinery -55 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. 8
9 Turbine Blade Cooling sually use copressor (bleed) air Configurations internal passages eternal fil cooling tip cooling Heat transfer designed to focus on hot spots and initial stages iniie stress concentration Turboachinery -56 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Gas Turbine Theory, Cohen, Rogers and Saravanauttoo Turbine Blade Cooling Rotor and nole cooling configurations Gas Turbine Theory, Cohen, Rogers and Saravanauttoo Turboachinery -57 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. 9
10 Introduction to Heat Transfer Consider a siplified version of a (half) turbine blade v hot (=c or w) Q Inner cooling only neglect fil and tip cooling for now hot gas (cobustor products) flows over outer surface cold gas (bleed air) flowing over inner surface turbine blade wall in between How to analye this heat transfer proble? T outer Turboachinery -58 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turboachinery -59 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Conduction Heat Transfer Start with description of (conduction) heat transfer Q through the wall assue one-diensional top side of wall unifor tep. (T outer ) botto side of wall unifor tep. ( ) Look at energy equation d differential CV Q in cdt Q out dt steady Q in Q out Need odel for Q Q dt Fourier s Law (d) k d Theral Conductivity Q in T Q out Touter d 0
11 Conduction and Theral Conductivity For steady, unifor aterial T gradient is dt Q a constant d k so T varies linearly through wall Theral conductivity insulators like ceraics have uch lower conductivities than etals Material k (W / K) at 000C Nickel Super lloys 0-0 Ceraic TBC s - so TBC will produce uch lower heat flu for sae teperature gradient Q T outer Touter T Turboachinery -60 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turboachinery -6 Effect of dding TBC Coating 5 k =5W/K Q dt W 700K MW T k 5.5 outer =400K d K 5 700K TBC 0.5 k =.5W/K Q Q T outer Tid Tid Tinner ktbc k Eaple Ni with Now add 500 TBC T id TBC T outer T id 96K Copyright 04,05 by Jerry M. Seitan. ll rights reserved. k k Q 5 T TBC inner W K TBC k TBC TBC k TBC 6K MW. 5 Most of the teperature drop occurs across TBC, uch lower etal T and lower heat transfer T id T outer T outer Q Q TBC T id T outer T
12 Turboachinery -6 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Convective Heat Transfer Eaine heat transfer between gas flow and blade wall Convective heat transfer due to fluid oving over surface theral boundary layer develops, like oentu boundary layer shear shearre Convective Heat Transfer Coeff. Reynolds Model Q ht gas T wall h hre Pr nuber,, Prandtl nuber Theral so T wall varies downstrea Pr diffusivity k c e.g., for lainar flow over flat plate p h 0.Pr Re h 0.664Pr Re g cp v L c v Stanton Nuber g g v T wall Q T gas, pg averaged over full length Convective Heat Transfer - Eternal Eaple hot air nalysis h Turboachinery -6 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. L4c p=0at T gas =850K T wall 400K v=50/s Pr=0.7 v=0-4 /s c Pr Re 0. g v pg.0mpa s K.8 Q kw 4 g cp g kw kw K K K MW K v T wall L Q p v Re T 50 s s h T gas, 0.5 kw hl.9 K L,.MW L Q total uch higher heat load around leading edge
13 Turbine Blade nalysis In our two eaples conduction through TBC- coated ~.MW convective heat transfer into blade ~.MW 50 s 400K 96K 700K.MW So together they represent a single proble Q convection Q conduction Net step is to investigate bleed air cooling requireent TBC 850K Turboachinery -64 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Cooling Convection Internal Flow In pipe/channel flow can t T v cool assue infinite flow Q boundary layers eet and central flow changes with aial distance Q Q Now L perieter New epressions for h, e.g., for round tubes turbulent flow, profile still developing averaged over channel length h h T bulk k 0.8 d 0.06 Red Pr d L, coolant Q Tinner Bulk avg. tep. Turboachinery -65 Copyright 04,05 by Jerry M. Seitan. ll rights reserved.
14 Turbine Blade nalysis ssuing sae inforation in previous eaples ND height channels with span = 80% of blade chord, with 500K, 0 /s inlet bleed air, negligible spacing betweenchannels Q cool ht inner Tbleed h 9W Q cool 0kW Much less than the cooling requireent fro previous parts of the analysis v hot (=c or w) Q 50 s 400K 96K 700K need to enhance the coolingfil cooling.mw v hot (=c or w) TBC 850K T outer T outer Turboachinery -66 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. 4
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