Solution to 10-Minute Quiz in Aircraft Propulsion, 2 nd Edition

Transcription

1 Solution to 10-Minute Quiz in Aircraft Propulion, nd Edition Quiz No Heating M=1 M<1 Branch Cooling M>1 Branch Heating. M<1 Branch M=1 M>1 Branch 3. 3 p=contant p=contant 4 1 η th = 1 1 1

2 4. max 3 min 1 η th = 1 min max 4 Quiz No. 1. p = ρr p i ga (tatic) preure, ρ i ga (tatic) denity, R i ga contant and i ga (tatic) temperature Note: he ame equation may be written for the tagnation or total tate of the perfect ga, namely p t = ρ t R t. Denity of air at SL i 1.5 kg/m 3, it ballpark number to remember i about one kg/m 3 Abolute tatic preure at SL i kpa, with the ballpark number of 100 kpa. Alo remember that the abolute tatic preure at SL i 14.7 lbf/in (or pia). 3. c p =contant, c v =contant, therefore γ=contant 4. c p =c p (), c v =c v (), therefore γ=γ() 5. p t = p + ρv where p t i fluid total preure, p i fluid tatic preure and ρv fluid dynamic preure. he limitation of Bernoulli i that it applie to low peed flow where denity variation i negligibly mall, i.e., incompreible. Alo, if the fluid i invicid, beide being incompreible, the total preure remain contant. i Quiz No δq = de + δw. kj/kgk or BU/lbm o R 3. kg/m 4. τ xy = μ u + v or often we may write: τ y x xy μ u v where y u x y

3 5. Shear tre in the fluid and it rate of train are linearly proportional 6. Continuum i the approximation made to fluid where it MFP (mean-free path) λ i λ<<l, where L i the characteritic length of the object in motion. In continuum, fluid loe it identity a being compoed of individual molecule eparated by void 7. Average ditance travelled by ga molecule between colliion 8. MFP increae with altitude a the fluid denity drop Quiz No Re ρvl μ where ρ i fluid denity, V i the fluid peed, L i the characteritic length and μ i the fluid vicoity Reynold number i the ratio of fluid inertia to fluid vicou force. M V where V i the (local) fluid peed and a i the local peed of ound. Mach a number i a meaure of compreibility of ga due to motion 3. kj/kgk or ft.lbf/lbm o R R 4. 1 = MW the ratio of ga contant i inverely proportional to their molecular R MW 1 weight 5. a = γr /MW where R i the Univeral Ga Contant 6. Ientropic ince the wave amplitude i infiniteimally mall 7. At or near Mach 0.3, the maximum ga denity variation in the fluid flow reache ~5%. Below thi Mach number, we neglect denity variation, therefore treat the fluid a incompreible. Above thi Mach number, it i conventionally accepted to account for the effect of fluid denity variation on the preure and temperature development in the fluid. Quiz No Compreor urbine Combutor. F g = m 9V 9 + (p 9 p 0 )A 9 where tation 9 i at the nozzle exit and p 0 i the ambient tatic preure 3. D r = m 0V 0 where tation 0 i the (unperturbed) flight condition 3

4 4. Preure hrut = (p 9 p 0 )A 9 5. where p 9 = p D C B N Quiz No hermal Power Input = m fq R where Q R i the heating value of the fuel and m f i the fuel (ma) flow rate. η th KE 9 KE 0 m fq R 3. η p F n.v 0 KE 9 KE 0 4. SFC m f F n 5. Specific hrut F n In a J pecific thrut i high, i.e., we produce tremendou m 0 thrut by drawing in a mall (air) ma flow rate. In contrat, in F we produce the thrut by engaging large ma flow rate of air, thu it pecific thrut i lower than the J. 6. p 9 > p 0 and thu the penalty i in the unrealized momentum thrut at the nozzle exit, which i more than the gain in preure thrut 7. = p γ 1 γ 1 p 1 8. p t = p 1 + γ 1 γ M γ 1 Quiz No p t1 t1 t p t p p 1 1 4

5 . t0 t t0 t 0 0 a) Ideal Inlet i ientropic b) Real Inlet create Δ p t3 p t3 3. p 3 p 3 p t p p t p 4. a) Ideal Compreor i ientropic b) Real Compreor p t4 p t4 p t3 p t3 p 4 p3 p 4 p 3 5. a) Ideal Burner ha p t =contant b) Real Burner p t4 <p t3 p t4 p 4 p t4 p 4 p t5 p t5 p 5 p 5 a) Ideal urbine (un-cooled) b) Real urbine (un-cooled) 5

6 6. p t5 =p t9 p t9 p 5 p t5 p 5 p 9 p 9 a) Ideal Nozzle (un-cooled) b) Real Nozzle (un-cooled) Quiz No Intalled thrut= net (unintalled) thrut intallation drag he intallation drag i caued by nacelle inlet and aft-end aerodynamic.. he air flow that enter the inlet goe through engine core and fan bypa duct. Bypa ratio, α, i defined a the ratio of air ma flow rate in the fan bypa duct to that of the core flow, i.e. α m fan = m fan m core m 0 3. Gro thrut i max when the nozzle i perfectly expanded, i.e., p 9 =p 0 4. F n unintalled = m 0 + m f V 9 + (p 9 p 0 )A 9 + αm 0V 19 + (p 19 p 0 )A 19 (1 + α)m 0V 0 Quiz No. 9 A 1. D add 1 (p p 0 )da A 0 n. Inlet pillage drag i due to the un-cancelled part of the inlet additive drag by the nacelle lip uction force, namely D pillage = D add F lip uction 3. Cowl lip uction force i due to preure ditribution on the (blunt) inlet cowl lip, which create a component of force in the thrut direction 4. 6

7 Ga-Generator urbine Power urbine 0 6 Regenerator Quiz No Specdific hrut F n (1+α)m 0. Afterburner-off (in real engine) would expoe the turbine exhaut to the total preure lo due to boundary layer formation on the wall a well a flameholder drag. he lo of total preure in the AB-duct caue the nozzle preure ratio (NPR) to drop, which in turn caue a reduction in exhaut peed, V 9. With ideal cycle aumption, there i no penalty in AB-off (ince the fluid i aumed to be invicid). 3. SFC m f F n 4. t13 p t13 =p t19 Fan nozzle expanion Inlet and fan compreion p 19 =p 0 (perfectly-expanded fan nozzle) 0 19 Quiz No η b Q R actual Q R ideal, which i alway le than 1 due to unburned fuel 7

8 . Due to frictional loe on the combutor wall a well a burning at finite Mach number 3. NOX, CO, UHC (unburned-hydrocarbon), Soot 4. CH 4 + O CO + H O 5. heoretical (dry) air i 79% N and 1% O, which in mole fraction, it i 0.79 N O Quiz No c = η m t. hey follow ientropic relation, namely π c = τ c γ γ 1 3. c = m 0(h t3 h t ) 4. m fq R η b = m 0 + m f h t4 m 0h t3 5. kj/kg and BU/lbm 6. mg//n and lbm/hr/lbf 7. t4, which i the primary combutor exit (total) temperature and t7, which i the exit (total) temperature of the afterburner Quiz No η prop F propv 0 prop. Static preure i continuou, eentially Kutta condition impoed at a harp trailing edge (a in airfoil aerodynamic) 3. η o F prop+f core )V 0 m fq R 4. F c = m 0 + m f V 9 + (p 9 + p 0 )A 9 m 0V 0 5. he tree in the turbine, i.e., centrifugal, thermal and vibratory tree, limit τ λ wherea the component that follow the AB i the nozzle, which experience lower tree than the turbine 6. m 15h t15 + m 5h t5 = (m 5 + m 15)h t6m 8

9 Quiz No (F g ) fan = αm 0V 19 + (p 19 p 0 )A 19. f = αm 0(h t13 h t ) 3. m fabq RAB η AB = m 0 + m f + m fab h t7 (m 0 + m f)h t5 4. At the trailing edge of the duct, i.e., plitter plate, eparating the turbine exit flow from the fan duct exit flow, where we aume p 5 =p Increaing bypa ratio increae the engine propulive efficiency (a it cut down the core and the fan nozzle exhaut peed) 6. Increaing compreor preure ratio improve thermal efficiency, a the cycle look more Carnot-like Quiz No p t4 p t3 t4 t3. t0 p t0 t p t p η c π c 9

10 4. η t 1/π t 5. η AB Q RAB Actual Q RAB Ideal, which i le than 1, due to unburned hydrocarbon in the afterburner 6. t7 9 9 η n h t7 h 9 h t7 h 9 Quiz No It provide all the power to propeller, therefore the core thrut i zero. 10

11 4 5 Ga-Generator urbine 3 6 Power urbine 3 6 Regenerator 0 Ga generator turbine Inlet Shaft power Power turbine Burner Exhaut 6 Rotating matrix regenerator 3. Adiabatic flow in the inlet duct make τ d = 1 and the loe (due to friction and hock) in the inlet make π d < 1 4. Adiabatic flow in the nozzle make τ n = 1 and the friction and hock loe in the nozzle make π n < 1 Quiz No t3 Δp t t4 11

12 . t7 p t7 p t9 t9 V 9 c p 9 9 η n h t7 h 9 h t7 h 9 3. m fq R η b = m 0 + m f h t4 m 0h t3 4. Mechanical efficiency account for the lo of haft power in the bearing a well a and mechanical power extraction from the turbine, it relate the turbine and compreor power according to: η m = c t 5. t η m = c + f Quiz No η d h t h 0 h t h 0 t t. η c h t3 h t h t3 h t = Δh t Δh t 0 t3 t3 t 3. e c dh t Polytropic efficiency i mall-tage efficiency, i.e., for compreor dh t preure ratio near 1 (note that Δ in compreor adiabatic efficiency definition wa replaced by d in polytropic efficiency definition) 1

13 p t3 =p t +dp t p t 4. η t h t4 h t5 h t4 h t5 t4 t5 t5 5. η b Q R,actual Q R,ideal Quiz No Static preure recovery in a diffuer i defined a C PR p p 1, which mean the q 1 fraction of inlet dynamic preure that i converted to tatic preure rie in a diffuer. ranitory tall i the unteady boundary between the teady-tate tall and diffuer un-talled tate. ranitory tall correpond to the maximum tatic preure recovery in a diffuer, where patche of eparated flow appear at one point in the diffuer and then diappear and re-appear elewhere 3. Inlet blockage i related to the effective v. the geometric flow area at the diffuer inlet. he effective area i reduced from the phyical area by the diplacement thickne in the boundary layer. B A geo A eff A geo 4. Jet flow regime in a diffuer correpond to large wall divergence angle where the flow doe not ene the wall or i unaware of the wall, therefore, it emerge from the diffuer inlet like a jet 5. Fully-developed tall i the tate of teady tall where the talled wall() remain teady in ize of eparated flow and location of eparation 6. 13

14 Quiz No M th < he highet flight Mach number with the firt appearance of onic flow on the nacelle 3. By a) reducing cowl lip bluntne and b) reducing A max /A 1, which create limline nacelle deign, c) ue natural or hybrid laminar flow deign on the nacelle 4. c f i the local kin friction coefficient, wherea C f i the area-average of c f over a finite urface 5. he trend i hown in the following Log-Log plot c f Laminar urbulent Re ranition 14

15 6. A Mach number increae, the boundary layer thicken, therefore wall hear (or kin friction) drop 7. Between 300,000 and 500,000 depending on the factor that affect tranition, namely: free tream turbulence level, heating or cooling of the wall, wall curvature, etc. Quiz No m rc θ. w c = ω[(rc θ ) (rc θ ) 1 ] U[C θ C θ1 ] for axial flow machine 3. τ = m [(rc θ ) 3 (rc θ ) ] 4. he abolute velocity vector entering the tage remain contant, i.e., C 1 =C 3 and α 1 =α 3 5. Blade olidity, σ, i defined a c/ where c i the blade chord and i the blade pacing. o 6. R h h 1 h 3 h 1 7. About 0.5 to 0.6, depending on the airfoil type, e.g. DCA allow for higher Diffuion factor before tall Quiz No. 1. When nozzle exit (tatic) preure i higher than ambient, i.e., p 9 >p 0. When p 9 <p 0 3. Flow i parallel on the two ide (of the hear layer) and the tatic preure i continuou 4. NPR p t7 p 0 5. Critical nozzle preure i the lowet NPR that caue the nozzle throat to choke 6. Ye Quiz No η m c t. η m c t 3. η pr F propv 0 prop γec 4. π c = τ γ 1 c γ/(γ 1)e 5. π t = τ t t 6. m 15h t15 + m 5h t5 = (m 5 + m 15)h t6m Quiz No

16 1 R β W W 1 U 1 α U β 1 C C 1 α 1. ψ Δh t. φ C z U U 3. angent to MCL at E 1 φ δ angent to MCL at LE i 4. W /W 1 >

17 Quiz No m c m θ δ. N c N θ where θ t ref and δ p t p ref 3. F c F δ 0 4. Stall line DP π c N c m c Quiz No ε C θ, actual C θ, ideal. W U C 3. W C U 17

18 4. D r 1 W W 1 + C θ σw 1 Diffuion factor for a compreor rotor Quiz No Superonic external-compreion inlet have their throat at the cowl lip, where the terminal (i.e., normal) hock i located. he condition of back preure at the compreor face determine the location of thi hock. When the back preure rie, the terminal hock i puhed out onto the ramp, which i called ub-critical mode of operation. In thi mode, the hock on ramp could caue boundary layer eparation and thu inlet throat blockage. With a drop in ma flow rate, back preure drop and thu the terminal hock i brought to the throat. But thi ma flow rate wa too high to begin with and had caued an increae in back preure and puhing the normal hock onto the ramp. herefore, the NS i puhed back out again and the cycle repeat: Inlet Buzz Intability.. Near tall condition implie that the incidence angle on the rotor blade i cloe to max. One blade may experience a local incidence which i higher than the max value, thu tall. he talled paage divert, i.e., pill, the incoming flow to the neighboring blade paage, whereby the next paage experience a higher incidence angle and thu goe into tall and the preceding paage i now relieved by the pillage from the talled blade row and thu un-tall. Since the tall moved in the oppoite direction of blade rotation, it i called rotating tall. 3. A hock in the converging ection of a CD inlet i untable and move either through the throat and i tabilized downtream of the throat, where the inlet i aid to have tarted, or it move backward and out of the inlet where it i tabilized after maive pillage from the inlet, which i called inlet untart. he intability of the NS in the converging ection i due to changing corrected ma flow rate in the engine, which caue a change (i.e., drop in the tart mode and rie in the untart mode) in back preure, which dictate the poition of the terminal hock in the inlet. Quiz No τ f = m (r C θ r 1 C θ1 ). W = C U = C ωr e θ 3. w c = ω(r C θ r 1 C θ1 ) 4. ypically, there i no wirl at the inlet to the IGV, therefore, C θ0 =0. Alo, the function of rotor i to put in wirl into the flow wherea the function of tator i to take the wirl out. herefore baed on thi argument, C θ i Max. 18

19 Quiz No N R 3 W W 3 U C 1 C U C 3. 1 N R 3 C 1 W W 3 U C U C 3 3. h tr = h + W θ + C z 4. h tr = h t3r in an uncooled turbine Quiz No R h h 1 h 3 h 1. ψ h t U 19

20 3. φ C z U 4. σ c 5. 1 R W W 1 U C 1 C U U Quiz No A uperonic inlet with an internal throat, uch a Mixed-Flow Inlet and conventional C-D inlet. Starting i often accomplihed thru variable throat. It may be poible to ue overpeed if the deign Mach number i <1.6.. here i a K-D inlet that elf tart, but due to high throat Mach number, it total preure recovery i not good. 3. Bet backpreure place the terminal hock at the throat, where Mach number i the lowet, therefore total preure recovery i the highet 4. In ub-critical mode, the terminal hock i puhed out on the external compreion ramp. Shock-BL interaction could eparate the BL therefore the throat of the inlet get partially blocked with eparated flow from the ramp. hi caue a reduction in the backpreure, whereby the hock i brought to the lip gain and the cycle continue. 5. Self-tarting, fixed geometry CD inlet 6. Backpreure 7. In the divergent portion of the duct 8. In hyperonic range, i.e., M>5 9. Between 1.6 and φ f f toich Quiz No ε C θ,actual C θ,ideal. 3 r 0

21 C θ (r)~ 1 r θ ρc r (r)~ 1 r 3. N 1 R 3 W 3 U β C 3 β 3 C W U α 3 α 4. About 70 o 5. R 3 C W U W 3 C 3 U Quiz No Ratio of axial momentum thrut to that of equivalent bell-haped nozzle. 1/π t 4 Choking limit 3 Choked N / θ 4 1 m c4 1

22 3. C V V 9 V 9i 4. C D8 m 8 m 8i 5. p 9 =p 0 6. when p 9 >p 0 7. when p 9 <p 0 8. On an external compreion ramp 9. In the divergent portion of the duct 10. NS Quiz No Operating Line (teady tate) π c Stall Line t4 / t =cont. Contant hrottle Line N/θ 0.5 Increaing t4 / t m c.

23 1/π t 4 Choking limit 3 Choked N / θ 4 1 m c4 3. F c F /δ 0, N ci N θ i m ci mi θi δ i 4. ypically 0.5 to Ye, becaue corrected ma flow rate in any tation i a function of flow area and Mach number in that tation. Since Area doen t change in a Fixed-Area-urbine, and tation i choked, i.e., M=1, then corrected ma flow rate remain contant 6. = m c 4 m4 θ 4 /δ 4 m = m θ / δ c Since ma flow rate at 4 and 8 are equal, we have m c4 = m c8 θ4 / δ 4 / θ8 / δ 8 Quiz No (a) up to M 0 =1.6 3

24 (b) 1.6<M 0 <.5 (c).5<m 0 <5.0 (d) 5.0<M 0. (a) variable geometry to open the throat (b) Over-peeding (c) K-D inlet 3. (a) in the divergent ection (b) Backpreure 4. NS NS Critical Mode Subcritical Mode Supercritical Mode 5. (a) No, M th >1 in the tarted mode (b) Ye, it i choked until the tarting hock i wallowed (i.e., inlet tarted) Quiz No Surge i the compreor-combutor intability wherea tall (including rotating tall) i the compreor intability, where a eparated flow in a compreor blade paage propagate to neighboring paage in the oppoite direction to blade rotation.. Inlet ditortion deteriorate/reduce the tall margin in compreor 3. When the wirl profile follow C θ ~1/r downtream of the rotor/tator blade row 4. 0 R h h 1 h 3 h 1 5. hat the radial preure gradient i completely in balance with centrifugal acceleration, namely: p r = ρ C θ r 4

25 Quiz No he angle between the (relative to blade) flow and the tangent to the mean camber line (MCL) at the leading edge. he angle between the exit (relative) flow and the tangent to the MCL at the trailing edge 3. he camber angle i formed at the interection of the tangent to the MCL at the leading edge and the trailing edge of the blade 4. Stagger angle i between the chord line and the axi of rotation (z in our notation) ,000 i the abolute lowet, but >500,000 i what i practiced Quiz No HHV = LHV + m HO h m lg fuel 4 o C where h lg i the latent heat of vaporization for water at. N A =6.03x10 3 /mole, which i the number of molecule in one mole of a ubtance 3. he amount of ubtance with N A molecule 4. In an exothermic reaction, heat i produced along with the product of reaction. A relevant example i the chemical reaction between fuel and oxygen/air, a in combution chamber of jet engine 5. In endothermic reaction, we need to provide the reactant with external timulu/heat to make the reaction poible. An example of endothermic reaction i in phae tranformation of water from liquid to vapor, which require external heat. 6. One mole of Air, i.e., dry air, under tandard ea-level condition i compoed of: 0.79 N +0.1 O neglecting mall trace of Argonne. Quiz No When the rate of forward and revere reaction are equal. It i the time that it take to produce/caue a reaction. he reidence time hould be longer than reaction time, ince we wih to have a complete reaction inide the combution chamber 3. Particle that mainly contain carbon, hydrogen and oxygen (in olid form) 5

26 4. Mainly Carbon dioxide, but water vapor i alo included in thi category. heir preence in the atmophere trap the IR radiation and caue warming of atmophere 5. Ha to follow FAR-36 certification limit 6. he preure ignature of a uperonic aircraft on the earth urface that follow a rapid over preure due to the vehicle front hock, followed by expanion (wave) over the aircraft and finally the terminal hock at the aft of flying aircraft. 7. EPA et thee tandard 8. Caue ozone depletion Quiz No It i the magnitude of the energy exchange, to form one mole of the compound, with an iothermal reaction chamber where the naturally occurring contituent of the compound enter at reference temperature and preure of 1 bar.. zero, ince it i a naturally-occurring ubtance 3. he preure exerted on the veel, if the veel contain the ga in quetion uing the entire volume of the veel at the mixture temperature 4. Nearly at the equivalence ratio of 1, where the fuel-air mixture ratio i that of the toichiometric mixture 5. Becaue air contain nitrogen, which remain for the mot part inert and doe not react. herefore it conume/aborb energy to be raied to the temperature of the reacting mixture (it amount to energy ink) 6. It mean that the combutible mixture doe not need an external timulu, like electric park, to initiate the combution 7. Delay i caued by the vaporization time cale. herefore, the maller droplet, a in fine pray, horten the vaporization and thu reduce the autoignition delay Quiz No Humidity caue a drop in engine air ma flow rate, ince water vapor i lighter than air (MW of water vapor i 18 v. 9 for air) 6

27 . Dry air ha higher molecular weight that humid air, a the humidity i water vapor with a lower MW than air (18 v. 9) 3. Both hot and high altitude imply lower air denity, therefore ma flow rate i reduced and thu thrut i lower 4. Due to heat tranfer, i.e., a it cool the air, the denity increae and thu ma flow rate and thrut are increaed 5. It caue water vapor to be formed and mixed with dry air and thu create humid air, which ha lower MW than dry air and thu reduced ma flow rate Quiz No In it implet form, it ay local kin friction coefficient i ½ of the local Stanton number, i.e., c f =(1/) St. q y = κ y 3. W/mK 4. Convective heat tranfer, radiation heat tranfer and conductive heat tranfer 5. ~ 5 6. Adiabatic wall temperature i the temperature of an inulated wall, i.e., an adiabatic wall. It i expreed in term of tatic temperature and the kinetic energy contribution of the ga according to: aw + r V Where r i the recovery factor. Stagnation temperature i the c p ame a adiabatic temperature, but with r=1.0 Quiz No Freetream turbulence, urface roughne, urface curvature and heat trafer. Concave curvature caue Goertler intability in the boundary layer and caue rolled up pair of vortice of oppoite pin to be formed 3. Goertler vortex i formed on concave wall and increae the heat tranfer to the wall by the churning effect of rolling vortice 4. Heating promote tranition a it thicken the BL and cooling ha the oppoite effect, i.e., delay tranition ince it make the BL thinner 7

28 5. Increae in Mach number caue boundary layer to thicken and thu it promote tranition 6. Coefficient of vicoity increae with temperature in a ga, a it increae the kinetic energy of the molecule. In a liquid, an increaing temperature caue a drop in fluid vicoity a it reduce the molecular adheion (which i the ource of vicoity in a fluid) 7. Pr μc p κ Quiz No I F n where F w n i the net thrut and w p i the propellant weight flow rate. In p calculating the weight flow rate, we ue the gravitational acceleration on the urface of the earth. In airbreatjing jet engine, the fuel flow rate replace the propellant flow rate that we ue in a rocket. Rocket engine produce more vacuum thrut a the preure thrut increae with a falling ambient/atmopheric preure, while the momentum thrut remain nearly unchanged. 3. about Mach above Mach 6 5. Mach 5 6. MR m f m 0 Quiz No. 45 F C p A 1. F c th. ~ 6000 km or ~ 4000 mile 3. Chugging i the ocillation in chamber preure and thu thrut produced in a liquid rocket engine due to coupled injector-combution chamber preure fluctuation. o decouple the two unit, we create a large tatic preure drop acro the injector plate (ay 0%) 4. High frequency noie due to acoutic diturbance created in the thrut chamber by erratic, unteady mixture and combution 8

29 5. Fater burning rate 6. Fuel and/or oxidizer are ued a heat ink to keep the wall in the thrut chamber at reduced temperature by being pumped through an outer (cooling) jacket where the cryogenic liquid fuel/oxidizer aborb heat. he aborbed heat caue the liquid to change phae and become gaeou prior to injection in the combution chamber 7. q = h ) c g ( aw wg Where h g i the ga-ide film coefficient, aw i the adiabatic wall temperature (on the ga ide) and wg i the ga-ide wall temperature. 8. Inhibitor are ued to prevent burning of the olid propellant grain where it i undeirable, e.g., on the wall/caing. It i alo a mean of achieving the deired thrut-time behavior for the olid propellant motor. 9