Axal Turbne Analyss From Euler turbomachnery (conservaton) equatons need to Nole understand change n tangental velocty to relate to forces on blades and power m W m rc e rc uc uc e Analye flow n a plane normal to rotatonal axs (cascade plane) to fnd c Rotor Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Cascade Analyss You may have prevously analyed flow over a blade (arfol) but n blade s reference frame Here there are movng (e.g. rotor) and statonary blades e.g., for turbne nole (stator) rotor se velocty trangles to swtch between frames Nole r Mechancs and Thermodynamcs of Propulson, Hll and Peterson Rotor Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved.
Velocty Trangles Two reference frames to use for flud velocty engne s c blade s w Dfference due to blade moton c c w u u u w For cascade flow u s n drecton defne angles (,) for each ref. frame c w u Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved., Rotor Velocty Trangles Blade moves n drecton, and n cascade flow for fxed r, let u = w c w c Also have general geometrc relatons e.g., c c sn c tan Therefore c c tan c c w c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Nole Rotor c w c w u Turbomachnery - 4 Copyrght 0,07 by Jerry M. Setman. All rghts reserved.
Sngle-Stage Characterstcs (Axal Turbne) Goal - determne how turbne performance, e.g., Pr T, affected by changes n operatng condtons Start by analyng sngle-stage turbne Rotor () Euler W R m u c uc m h o ho at fxed W R m c c m h o ho radal locaton c h, o, Nole () W h h So for stage h S h 0 o o c o, o,, Turbomachnery - 5 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Axal Turbne Stage Combnng c c tan ho h, o c,, results c c tan ho, stage c tan c tan assumng constant axal velocty, stage loadng coeff. h o, stage, flow coeffcent c tan tan Hgh output power: W T, produced A nlet c nletc tan tan Turbomachnery - 6 Copyrght 0,07 by Jerry M. Setman. All rghts reserved.
Turbne Stage Pressure Rato For adabatc turbne wth TPG/CPG po To To ho, PrT p0 st T o st RTo > as wrtten c h o,, p p o st RT o c o, M blade Stage pressure rato depends on. = f(= r, c, ). blade Mach number M blade =f(r, T o ). st <0 for turbne Turbomachnery - 7 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Turbne Characterstcs For gven M b, blade desgn,, T c PrT M b st tan tan c PrT C C As ncrease flowrate through turbne (at fxed rpm), larger pressure drop (more expanson) s produced more work extracted per unt mass Pr T Hgher M b c Turbomachnery - 8 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 4
Axal Turbne Maps Typcally presented as separate curves for each rpm (M b ) x-axs - replace flow coeffcent wth corrected mass flow rate, recall m A p o RT o at hgh corrected mass flowrate, nole becomes choked Peak effcency around desgn pont Turbomachnery - 9 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. T Pr T /Pr T Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 0 Blade Desgn: Degree of Reacton We have TWO blade parameters to desgn rotor tralng edge (match ) nole tralng edge (match ) How to do ths?.degree of reacton, R c c.stage ext condton constrant ( ) tan tan c c w w Copyrght 0,07 by Jerry M. Setman. All rghts reserved. c, c tan tan c tan c c w,, c tan c Mechancs and Thermodynamcs of Propulson, Hll and Peterson 5
Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Degree of Reacton Recall R h rotor h stage allows us to dstrbute load (statc pressure change) between rotor and nole (or stator) how to relate statc enthalpy change to amuthal velocty changes? KE!! h h v o for statonary blade, no work done h o 0 h KE e.g., nole blade h f c constant, and neglgble c r h c c c c c c c Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Degree of Reacton (Turbne) Rotor blades?? are statonary n rotor s reference frame h h w w Reacton h h h h R h h ho c ho c h w w h h o h o c c R f c c, c tan tan relates desgn blade angles to amuthal KE change c c c w w c tan tan 6
R = 0 w w c w,, c tan c, c tan Impulse Turbne h R h all the pressure change occurs across the nole, or the nole creates hgh KE 0 w c tan c tan w w w, w w c tan tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Impulse Turbne So for mpulse turbne, blade loadng coeff. Relates blade loadng to nole ext angle tan ho c <0 stage From prevous & velocty trangles, rotor angles gven by tan tan tan c hostage c c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 4 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 7
Impulse Turbne To let largest power per unt mass flow rate large tends to produce hgh veloctes and p o losses practcal lmt, ~70-75 Further possble constrant no ext swrl (c =0) c c c c c,, c c h o stage tan, tan c c c c c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 5 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. R 0.5 c 50% Reacton Turbne balanced p drop across stage w w, w w w w c tan c c tan tan h c ostage, c tan f no ext swrl ho stage tan, c c tan, c less convergence n nole w w vs mpulse turbne R c, c, c tan tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 6 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 8
Rocket Turbnes Can combne results for no ext swrl condton to show R ho stage as reacton decreases, power per stage ncreases To mnme se/weght, rocket turbopumps often employ mpulse or low reacton turbnes but effcences typcally lower (<70%) for mpulse turbnes compared to hgher reacton turbnes (~90%) Can mprove effcency by decreasng flow coeffcent (c /) for gven flowrate, requres hgher blade speed, RPM hgher RPM = hgher stresses = heaver, and larger gear rato f geared to pump Turbomachnery - 7 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Velocty-Compound Impulse Turbne Can ncrease stage power even more usng velocty-compoundng multple nole/rotors n seres Example, two-row compounded mpulse turbne all p n st nole st rotor exts wth hgh swrl (so large allowed) nd nole redrects flow wthout p nd rotor extracts more work and reduces swrl stage loadng s 4x that of sngle-row mpulse stage From Sutton Turbomachnery - 8 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 9
Hghly-Loaded Turbne Effcences Can provde effcency mprovement over sngle row mpulse stage stll lower than hgh reacton turbnes From Hll and Peterson Turbomachnery - 9 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 0