IS THE RATIO OF VELOCITY TO SPEED OF SOUND

Transkript

1 MACH NUMBER, M HE MACH NUMBER IS HE RAIO OF ELOCIY O SPEED OF SOUND RELAES DIRECED KINEIC ENERGY O INERNAL ENERGY IS A NON-DIMENSIONAL MEASURE OF FLOW COMPRESSIBILIY. M a FLOW REGIMES SUBSONIC AND SUPERSONIC FLOW ARE EASY O ANALYZE RANSONIC FLOW IS HE MOS DIFFICUL REGIME ( because shocks (non-isentroic) form )

2 RANSONIC FLOW HE LOCAL FLOW SPEEDS UP OER A CURED SURFACE M < M > FREESREAM FLOW IS SILL SUBSONIC RANSONIC FLOW IS A MIXED FLOW REGIME; I IS PARLY SUBSONIC AND PARLY SUPERSONIC and a (non-isentroic) shock may form.

3 SAGNAION EQUAIONS RECALL, HE ENHALPY DEFINIION AND h e + v h = c AND e = c v c = cv + R OR c cv = R DIIDING BY c R R = = c = where = c c c ALSO, RECALL HE ENERGY EQUAION v c + = c c c v where o is the stagnation (a.k.a. total ) DIIDING BY AND SUBSIUING FOR c = + = + = + = + M c R R

4 EQUAION SUMMARY CONINUIY EQUAION (INCOMPRESSIBLE) BERNOULLI S EQUAION P A = A + = P + SEADY? INCOMPRESSIBLE? INISCID?. CONINUIY EQUAION (COMPRESSIBLE) ISENROPIC RELAIONS ENERGY P P A = A = = c P + = cp + EQUAION OF SAE P P = R = R BE FAMILIAR WIH ALL EMBEDDED ASSUMPIONS

5 NOW, APPLY HE ISENROPIC RELAIONS A A SAGNAION POIN FOR A PIO UBE (ISENROPIC PROCESS) DEPEND ONLY ON MACH NUMBER HE PROCESS ONLY NEEDS O BE ADIABAIC FOR O DEPEND ONLY ON MACH NUMBER SAGNAION EQUAIONS M M M = = = + = + = + and

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7 SOLING HE SAGNAION PRESSURE EQUAION FOR MACH NUMBER CONSEQUENLY, A MACHMEER IS CALIBRAED WIH PIO UBE MEASUREMENS OF AND HIS EXPRESSION SHOWS HA IF WE KNOW a OR RUE AIRSPEED IS EASILY FOUND UNFORUNAELY, NEIHER a or ARE EASILY MEASURED MACH NUMBER & RUE AIRSPEED M M = + = a =

8 CALIBRAED AIRSPEED ( CAS ) CALIBRAED AIRSPEED IS USED BECAUSE IS NO READILY MEASURED ALL HIGH SPEED (M >.3) AIRSPEED INDICAORS ARE CALIBRAED USING HE SANDARD DAY SEA LEEL SPEED OF SOUND, a s a s CAS = s ADANAGES OF CALIBRAED AIRSPEED HE ASI IS SIMPLE, ACCURAE, AND EASILY CALIBRAED CAS IS DIREC PHYSICAL USE O HE PILO: SALL SPEED, LANDING SPEED, AND HANDLING CHARACERISICS ARE DIRECLY PROPORIONAL O CAS HE ABSENCE OF A EMPERAURE ERM IN HE CAS EQUAION MEANS HA CAS test day = CAS std day

9 I C E I Indicated AirSeed (IAS) IAS IAS = CAS + PC this is the airseed read by the cockit s ASI (airseed indicator) C Calibrated AirSeed (CAS) this is the IAS, but corrected for instrument & osition error a s CAS = s E Equivalent AirSeed (EAS) this is the CAS, but without the effect of comressibility EAS = s / rue AirSeed (AS) this is the EAS, but without the effect of altitude AS = s EAS

10 he aircraft was ressurized during a ground level test. he outflow ressure regulating valves were caed off during an overhaul and not reoened. he technician who "had always done it that way" was using a homemade gauge. he gauge did not have a max "eg" for the needle, and needle went around the gauge. During the nd loo the rear hatch was blown behind a blast fence over 7 yards away.

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12 dynamic ressure (q) vs. imact ressure (q c ) From Bernoulli (incomressible) q = But, due to comressibility q < Imact ressure is defined as q c Dynamic ressure is defined as M q Imact ressure is qc = = + M

13 incomressible.8 / o imact ressure, q c / o comressibility effects (q c q) Pressure ratio.6 dynamic ressure, q/ o + q = o.4. q/ o Mach Number Mach No. Note, a ratio form is used above, where all ressures are divided by the total ressure, o.

14 COMPRESSIBILIY ERROR LOW SUBSONIC assumed incomressible M = + / ο Mach no.

15 SUPERSONIC FLOW SHOCK WAES ARE A HIN REGION OF FLOW DISCONINUIY (NON-ISENROPIC) NO ADIABAIC -- HEA IS ADDED BY FRICION NO REERSIBLE -- ENROPY INCREASES A SHOCK WAE FORMS IN FRON OF A BODY A M > M > M < M > > < < = Shock Wave otal emerature is constant! A SONIC BOOM IS A CONSEQUENCE OF HE PRESSURE JUMPS, HEN RECOERS AS HE SHOCK WAE PASSES (we hear waves)

16 SUPERSONIC FLOW A SHOCK WAE FORMS IN FRON OF A PIO UBE AND WILL LEAD O MEARSUREMEN ERRORS ( + ) M = 4M ( ) + M + SHOCK WAE HEORY GIES HE RAYLEIGH PIO FORMULA M > M < M > > < < = Pitot ube Shock Wave HIS FORMULA RELAES OAL PRESSURE (, ) BEHIND HE SHOCK O SAIC PRESSURE ( ) AHEAD OF HE SHOCK HE FORMULA CALIBRAES MACH MEERS IN SUPERSONIC FLOW

17 AREA-ELOCIY RULE SARING WIH CONINUIY DIFFERENIAING A = c ln + ln A + ln = d da d + A + = c W/ EULER S EQN : dd da d + + = d A W/ ISENROPIC: FINALLY, da A d da d + + = a A d d d da = = a = a A ( M ) d Increasing SUBSONIC Decreasing M = Increasing Increasing SUPERSONIC Now for M >, as Area increases, elocity increases interesting!

18 SUPERSONIC NOZZLE Flow x M M = M = + M = + = + M

19 A- Rule nozzles, rocket engines, suersonic wind tunnels da A ( M ) = d Subsonic, M < : as A, and as A, Suersonic, M > : as A, and as A, But, at M = da and d must both be indicates the throat ( A t ) of the nozzle Increasing SUBSONIC Decreasing M = Increasing Increasing SUPERSONIC he area of the nozzle is found by eqn 4.88, note A is indeendent of length ( + )/( ) A = M At M + +

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