TITLE !->C:\Documents and Settings\089884.WIN\Desktop\Paris\After\ImpDuct.out !Created@15:21:30 16-Jul-2008 with DeltaEC version 6.1b2 under win32, using Win 5.1.2600 (Service Pack 2) under Python DeltaEC. !--------------------------------- 0 --------------------------------- BEGIN Idealized Driver !A classic impedance tube, treated by DeltaEC. This illustrates everything !about BL thermocoustics in familiar hardware! And also, some of the !idiosyncracies of DeltaEC itself. When source parameters !(f, p, U in this BEGIN) are adjusted to match measured quantities (e.g., !transfer function results in RPN 5), the impedance of the sample is given !by the SOFTEND segment. ! ------------------------------- !In real use, one could use BLKDATA to match data across all frequencies to !measured spectra. Also, another target placeholder (RPN) is needed to match the !a second value in the complex transfer function (i.e. magnitude, then phase). ! ------------------------------- !For lecture purposes, the first case is just to show the effective Z of a !converged HARDEND. Then I inserted RPN(f) functions to generate a typical !sample impedance spectrum (Real and Im parts), then asked DeltaEC to meet that !impedance in the SOFTEND, over a frequency plot of several octaves. !The 2-mic method for the same condition was !compared to the (Z, R, from 8,7) to the integrated result (12,11). ! ----------------------------- !For amusement, the DUCTs can be turned into STKDUCTs and given very thin plastic !walls. At sound pressures that are not unreasonable (100 Pa), a temperature gradient !will develop resutling in a few degrees K down the tube. ! ----------------------------- ww@lanl.gov; July 2008 1.0000E+05 a Mean P Pa 995.37 b Freq Hz G 300.00 c TBeg K 100.00 d |p| Pa 0.0000 e Ph(p) deg 2.3785E-05 f |U| m^3/s G 0.0000 g Ph(U) deg 0.0000 h Htot W air Gas type !--------------------------------- 1 --------------------------------- DUCT large B&K duct (to first mic) 7.8540E-03 a Area m^2 85.422 A |p| Pa 0.31416 b Perim m 179.97 B Ph(p) deg 0.5500 c Length m 7.7933E-04 C |U| m^3/s 90.287 D Ph(U) deg 0.0000 E Htot W stainless Solid type 1.8653E-04 F Edot W !--------------------------------- 2 --------------------------------- RPN Mic 1: 3.1 mv/Pa and 40 dB gain 0.0000 a G or T 26.481 A |S1|(V) 179.97 B Ph(S1) (-26.481, 1.5576E-02) C S1 p1 .0031 * 100 * # arg lstx mag !--------------------------------- 3 --------------------------------- DUCT Inter-mic section of length 's' 7.8540E-03 a Area m^2 21.646 A |p| Pa 0.19416 b Perim m 179.66 B Ph(p) deg 5.0000E-02 c Length m 1.7880E-03 C |U| m^3/s 90.055 D Ph(U) deg 0.0000 E Htot W stainless Solid type 1.3251E-04 F Edot W !--------------------------------- 4 --------------------------------- RPN Mic 2: 3.1 mv/Pa and 40 dB gain 0.0000 a G or T 6.7102 A |S2(V)| 179.66 B Ph(S2) (-6.7101, 3.9516E-02) C S2 p1 .0031 * 100 * # arg lstx mag !--------------------------------- 5 --------------------------------- RPN Transfer Fuction H 0.0000 a G or T 0.2534 A |H| -0.30371 B Ph(H) (0.25339, -1.3432E-03) C H 4C 2C / ; # arg lstx mag !--------------------------------- 6 --------------------------------- RPN Complex wavenumber approximation from ASTM std. !Set input to get imag. coeff. Nominal is .02203 !k = w/a +j0.02203*sqrt(f) / a/d 2.2030E-02 a G or T (18.012, 3.2388E-02) A cmplx k w a / ; inp i * f sqrt * a / 3b pi / / + !--------------------------------- 7 --------------------------------- RPN reflection coef Eq 8.5.3 ! H - e^[-j ks] !R=____________ e^[j 2k(s+L)] ! e^[j ks] - H 0.0000 a G or T (0.99115, -2.1484E-03) A R 5C 6A i * 3c * ~ exp - ; 9c 3c + 6A * i * 2 * exp * ; 3c 6A * i * exp 5C - / !--------------------------------- 8 --------------------------------- RPN Z from 2 mic method ! 1 + R !Z=_____ ! 1 - R 0.0000 a G or T (212.47, -51.839) A Z_2mic 1 7A + 1 7A - / !--------------------------------- 9 --------------------------------- DUCT End section, up to 'sample' sameas 3a a Area m^2 94.330 A |p| Pa sameas 3b b Perim m 2.1693E-02 B Ph(p) deg 0.1000 c Length m 5.6094E-07 C |U| m^3/s 2.1693E-02 D Ph(U) deg 0.0000 E Htot W stainless Solid type 2.6457E-05 F Edot W !--------------------------------- 10 --------------------------------- SOFTEND G +i*H is specific acoustic impedance (Z integrated) !This represents the 'sample', which does not really exist. 0.0000 a Re(z) 94.330 A |p| Pa 0.0000 b Im(z) 2.1693E-02 B Ph(p) deg 0.0000 c Htot W 5.6094E-07 C |U| m^3/s 2.1693E-02 D Ph(U) deg 0.0000 E Htot W 2.6457E-05 F Edot W 3275.7 G Re(z) -2.8542E-09 H Im(z) 300.00 I T K !--------------------------------- 11 --------------------------------- RPN Check: Refl coeff. by decomposition ! p_in =(p+rho*a*U1/area)/2 ! p_ref=(p-rho*a*U1/area)/2 !R=p_ref/p_in 0.0000 a G or T (1.0000, 4.2665E-18) A R_int p1 rho a * U1 * 9d / - 2 / ; p1 rho a * U1 * 9d / + 2 / ; / !--------------------------------- 12 --------------------------------- RPN R from Z integrated !Z - 1 !Z + 1 0.0000 a G or T (0.99939, -5.3167E-16) A Z_int 10G i 10H * + sto 1 - rcl 1 + / !--------------------------------- 13 --------------------------------- SURFACE Solid Endcap sameas 9a a Area m^2 94.330 A |p| Pa 2.1693E-02 B Ph(p) deg 4.8878E-19 C |U| m^3/s 89.528 D Ph(U) deg 0.0000 E Htot W stainless Solid type 1.9849E-19 F Edot W !--------------------------------- 14 --------------------------------- HARDEND Change Me 0.0000 a R(1/z) =14G 94.330 A |p| Pa 0.0000 b I(1/z) =14H 2.1693E-02 B Ph(p) deg sameas 0h c Htot W 4.8878E-19 C |U| m^3/s 89.528 D Ph(U) deg 0.0000 E Htot W 1.9849E-19 F Edot W 2.2903E-18 G R(1/z) 2.6600E-16 H I(1/z) !--------------------------------- 15 --------------------------------- RPN SPL (dB) !dB re 20 uPa sameas 14A a G or T 133.47 A SPL inp 2e-5 / log10 20 * ! The restart information below was generated by a previous run ! and will be used by DeltaEC the next time it opens this file. guessz 0b 0f xprecn -3.5610E-03 -2.7401E-10 targs 14a 14b ! Plot start, end, and step values. May be edited if you wish. ! Outer Loop: | Inner Loop .