E-26 Applied Computational Aerodynamics E.7 STDATM

Transcription

1 E-26 Applied Computational Aerodynamis E.7 STDATM This subroutine omputes the 1976 standard atmosphere. It is used in program FRICTION. It overs an altitude range from sea level to 86 kilometers (282,152 ft.). The results are found in either English or metri units depending on the value of one of the input flags. The 1976 and 1962 standard atmospheres are idential for the first 51 kilometers above sea level. Method of Computation Given the geometri altitude Z in (in dimensions of either meters or feet), onvert to kilometers. The geopotential altitude H is then found from: Z H = 1+ Z r 0 where r 0 = kilometers (the radius of the Earth in kilometers) and Z = C 1 Z in, where C 1 = if Z in is in meters, and C 1 = if Z in is in feet. The 1962 standard atmosphere used a muh more ompliated and slightly more aurate relationship. The inverse relation is given by Z = H 1 H r 0. One the geopotential altitude is found, the temperature is omputed. The standard day temperature profile is defined by seven layers, where within eah layer the temperature is found by the linear relation (T is given in degrees Kelvin): T = T bi + L mi ( H H bi ) T bi L mi H bi and, and are the values at the base of the partiular layer. The following table defines these onstants, as well as the ratio of pressure to sea level pressure, whih is also needed. i (Km) ( K) ( K/Km) P/Psl Z(ft.) H bi T bi L mi x , x , x , x , x , x , ,152

2 report typos and errors to W.H. Mason Appendix E: Utility Programs E-27 One the temperature is determined, the pressure is omputed using the hydrostatis equation and the perfet gas law. The resulting formulas are: P P sl = P b P sl T b T K L m Lm 0 where K = g o M 0 in onsistent units. The remaining fundamental property is the R * = density, whih is found using the equation of state as: Additional parameters of interest in aerodynamis are: P = P b e K ( H H b ) T P sl P b L m = 0 sl ρ ρ sl = P P sl T T sl. i) The speed of sound a = a sl T T sl ii) The oeffiient of visosity, found from Sutherland s Law: µ = β T3 /2 T + S where S = K and β depends on the system of units and is defined below. iii) The Reynolds number per unit length and Mah: R e M L = ρa µ iv) The atual temperature, pressure and density: T T = T sl T sl P P = P sl P sl

3 E-28 Applied Computational Aerodynamis ρ ρ = ρ sl ρ sl and v) the dynami pressure normalized by the Mah number: q M 2 = γ 2 P =.7P. The sea level properties and other required onstants are defined in the following table. Metri English T sl P sl K x10 5 N/m R lb/ft 2 ρ sl Kg/m slugs/ft 3 a sl m/se ft/se µ sl x10-5 Kg/m/se x10-6 slugs/ft/se β 1.458x10-6 Kg/m/se/K 1/ x10-8 slugs/ft/se/k 1/2 The ratio of speifi heats, γ, is defined to be User instrutions: the omments in the subroutine define the input and output argument list. If the maximum altitude is exeeded, the program returns a non zero value of the validity flag. subroutine stdatm(z,t,p,r,a,mu,ts,rr,pp,rm,qm,kd,kk) *********** 1976 STANDARD ATMOSPHERE SUBROUTINE ********** Mason's BASIC program, onverted to FORTRAN - Sept. 1, 1989 kd - = 0 - metri units <> 0 - English units kk good return 1 - error: altitude out of table, do not use output z - input altitude, in feet or meters (depending on kd) output: units: metri English t - temp. deg K deg R p - pressure N/m^2 lb/ft^2 r - density Kg/m^3 slugs/ft^3 a - speed of sound m/se ft/se mu - visosity Kg/m/se slug/ft/se ts - t/t at sea level rr - rho/rho at sea level pp - p/p at sea level rm - Reynolds number per Re/M/m Re/M/ft Mah per unit of length qm - dynami pressure/mah^2 N/m^2 lb/ft^2

4 report typos and errors to W.H. Mason Appendix E: Utility Programs E-29 real k, h, mu, ml KK = 0 K = C1 = 3.048E-04 IF (KD.eq. 0) go to 1240 TL = PL = RL = AL = ML = E-07 BT = E-08 GO TO TL = PL = RL = C1 =.001 AL = ML = E-05 BT = 1.458E H = C1 * Z / (1 + C1 * Z / ) IF (H.gt. 11.0) go to 1290 T = * H PP = ( / T) ** ( - K / 6.5) 1290 IF (H.gt. 20.0) go to 1310 T = PP = * EXP ( - K * (H - 11) / ) 1310 IF (H.gt. 32.0) go to 1330 T = (H - 20) PP = * ( / T) ** K 1330 IF (H.gt. 47.0) go to 1350 T = * (H - 32) PP = * ( / T) ** (K / 2.8) 1350 IF( H.gt. 51.0) go to 1370 T = PP = * EXP ( - K * (H - 47) / ) 1370 IF (H.gt. 71.) go to 1390 T = * (H - 51) PP = * ( / T) ** ( - K / 2.8) 1390 IF (H.gt ) THEN kk = 1 write(6,200) H return END IF

5 E-30 Applied Computational Aerodynamis T = * (H - 71) PP = E-05 * ( / T) ** ( - K / 2) 1420 RR = PP / (T / ) MU = BT * T**1.5 / (T ) TS = T / A = AL * SQRT (TS) T = TL * TS R = RL * RR P = PL * PP RM = R * A / MU QM =.7 * P 200 format(' Out of Table in StdAtm- too high!'// 1 4x,'H =',f12.3,' > km'/) return end The following sample program and output an be used to validate your subroutine: main program to hek stdatm loop is done twie to get output suitable to inlude in text(80 ol) w.h. mason, Feb. 27, 1994 real mu kd = 1 write(6,90) do 10 i = 1,21 z = 5000.*(i-1) all stdatm(z,t,p,r,a,mu,ts,rr,pp,rm,qm,kd,kk) if (kk.ne. 0) then write(6,120) stop endif write(6,100) z,t,p,r,a,mu 10 ontinue write(6,110) do 20 i = 1,21 z = 5000.*(i-1) all stdatm(z,t,p,r,a,mu,ts,rr,pp,rm,qm,kd,kk) if (kk.ne. 0) then write(6,160) stop endif

6 report typos and errors to W.H. Mason Appendix E: Utility Programs E-31 write(6,120) z,ts,rr,pp,rm,qm 20 ontinue 90 format(/3x,'1976 Standard Atmosphere'// 1 3x,' alt T P Rho', 2 2x,' a Mu', 4 /3x,' (ft) (deg R) (psf) (s/ft^3)', 5 2x,' (f/s) (slugs/ft/se)') 100 format(3x,f9.1,f8.2,f8.2,e12.4,f8.2,e12.4) 110 format(/3x,'1976 Standard Atmosphere'// 1 3x,' alt T/Tsl R/Rsl', 2 2x, 'P/Psl Re/M/ft q/m^2', 4 /3x,' (ft)',34x,'(lb/ft^2)') 120 format(3x,f9.1,3f7.4,e10.3,f10.4) 160 format(/4x,'error in return ode from stdatm - pgm stops'/) stop end Sample output: 1976 Standard Atmosphere alt T P Rho a Mu (ft) (deg R) (psf) (s/ft^3) (f/s) (slugs/ft/se) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Standard Atmosphere alt T/Tsl R/Rsl P/Psl Re/M/ft q/m^2 (ft) (lb/ft^2) E E E E E E E

7 E-32 Applied Computational Aerodynamis STOP E E E E E E E E E E E E E E