Huygens' entry and descent through Titan's atmosphere ...

More documents

Recommendations

Info

1858 Runiv is the universal gas constant (8314.3 J/kmol/K). The mean molecular mass profile mðzÞ (in kg/kmol) is inferred from the measured mole fractions of nitrogen f N2 and methane f CH4 (GCMS) according to m ¼ f N2mN2 þ f CH4mCH4 , (15) where mN2 and mCH4 are the molecular masses of N2 and CH4, respectively. In Eq. (14) the compressibility factor z takes into account the deviation of the gas behavior from an ideal gas due to particle interaction (van der Waals forces) and the effect of a finite molecular volume. In the altitude ranges from the surface up to about 70 km, Titan’s atmosphere is characterized by a combination of relatively high densities (on the order of magnitude of 10 4 –10 2 g=cm3 ) and low temperatures (100–93 K) which are both drivers for a deviation of the atmosphere from an ideal gas behavior. For the computation of the compressibility we restricted ourselves to the second virial coefficient B2 and its relations to z as provided by Dymond and Smith (1992) z ¼ 1 þ B2 r . (16) m For a gas mixture of N2 and CH4 the temperaturedependent second virial coefficient is derived from B2ðTÞ ¼f 2 N 2 B2;N 2 ðTÞþf N2 f CH4 B2;CH 4 2N 2 ðTÞ þ f 2 CH 4 B2;CH 4 ðTÞ, ð17Þ where B2;N 2 , B2;CH 4 , and B2;CH 4 2N 2 are the temperaturedependent virial coefficients for the various pure gas and interaction components, which are evaluated using polynomial fits of laboratory measurements data as tabulated by Dymond and Smith (1992). Based on the measured mole fractions from the GCMS measurements and the derived virial coefficients from Eq. (17), values of the compressibility z are obtained in the range from very close to 1 (i.e., almost ideal gas behavior) at altitudes above 70 km, decreasing continuously down to values of 0.965 (i.e., a deviation of 3.5% from the ideal gas law) near the surface. Multiplying Eq. (14) by dt and integrating both sides yields Dz ¼ðzi zi 1Þ ¼ 1 g Runiv T i 1=2z m ln Pi Pi 1 . (18) The temperature T is considered to be constant throughout the altitude interval Dz and is approximated by the mean value of two consecutive measurements, i.e., T i 1=2 ¼ 1 2 ðT i þ T i 1Þ. Starting from the initial value z0 at Titan’s surface the final altitude is derived by simple addition of the subsequently derived altitude intervals Dz zi ¼ z0 þ X Dzi 1. (19) i Note that the minus sign in Eq. (18) ensures that for a reconstruction starting from the surface in an upward direction the pressure gradient has to be negative (i.e., ARTICLE IN PRESS B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 PioPi 1) and Dz therefore positive. Assuming a constant descent velocity for the descent interval Dz the descent velocity is approximated by _z Dz . (20) Dt It should also be noted that the altitude profile reconstructed from Eq. (19) provides the radial probe distance from the probe impact point neglecting Titan’s flattening. However, the integration of the equations of motion during the entry phase reconstruction [see Eq. (2)] provides the distance of the probe to Titan’s center. To obtain the altitude relative to the surface requires the assumption of Titan’s radius (2575 km). Altitude [km] above Impact Point Altitude [km] above Impact Point 180 160 140 120 100 80 60 40 20 DTWG +1 α -1 α PREDICT Drogue Impact 0 20 40 60 80 100 120 140 Time [min] past Interface Epoch: UTC: 2005 01 14T09:05:52.523 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 Flight RAU 1 RAU 2 SSP APIS 0 151.7 151.8 151.9 152 152.1 152.2 152.3 152.4 Time [min] past Interface Epoch: UTC: 2005 01 14T09:05:52.523 Fig. 12. Upper panel: reconstructed descent phase altitude profile based on the HASI P and T, GCMS mole fraction, and SSP impact epoch measurements (solid line, labeled ‘‘DTWG’’) compared to the preflight trajectory simulation (Pérez-Ayúcar et al., 2004; Kazeminejad et al., 2004) (dashed line, labeled ‘‘PREDICT’’). The lower panel shows the final portion of the reconstructed altitude profile prior to impact, compared to the RAU 1 and 2 measurements as well as to the SSP API-S (acoustic sounder) measurements (solid line with triangles).
4.2. Discussion of reconstruction results The reconstructed altitude descent profile is depicted in Fig. 12. The upper panel provides an overview of the entire descent phase altitude range from about 155 km down to the surface. The reconstructed profile (solid thick line, labeled ‘‘DTWG’’) with its 1s uncertainty envelope (solid dashed line) is compared to the preflight simulation (dashed thin line). It can be readily seen that the simulated descent trajectory predicted that the probe impact would have occurred about 14 min earlier. In large part, this difference can be attributed to the uncertainties in the main and drogue chute aerodynamic database. The lower panel shows a zoom of the very last portion of the descent phase to surface impact. In the final descent portion the SSP Descent Velocity [m/s] Descent Velocity [m/s] 80 70 60 50 40 30 20 T0 Drogue DESCENT ENTRY PREDICT 5 10 15 20 25 30 35 40 Time [min] past Interface Epoch: UTC: 2005-01-14T09:05:52.523 25 20 15 10 5 Drogue Impact 0 40 60 80 100 120 140 Time [min] past Interface Epoch: UTC: 2005-01-14T09:05:52.523 ARTICLE IN PRESS DESCENT PREDICT SSP APIS Fig. 13. Huygens descent speed profile during the first portion (upper panel) and final portion (lower part) of the descent phase. In the upper panel the dashed-dotted line (labeled ‘‘ENTRY’’) shows the descent speed derived from the entry phase (accelerometer based) reconstruction. The solid line (labeled ‘‘DESCENT’’) shows the descent speed profile derived from the reconstructed descent phase (atmosphere based) altitude profile as shown in the upper panel of Fig. 12. The triangle in the lower panel represents the descent speed derived from measurements of the SSP acoustic sounder sensor. B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 1859 acoustic sounder instrument (SSP-APIS) provided altitude measurements, which are represented as triangles. The good agreement between the SSP-APIS data and the reconstructed altitude profile (solid line) can be clearly seen. In the same panel the very last measurements of the two RAU before they saturated can also be seen. The difference between the RAU measurements and the reconstructed altitude profile is discussed in Section 4.3. The reconstructed descent speed profile is shown in Fig. 13. The upper panel zooms into the time of main chute release shown by the vertical dashed line labeled ‘‘Drogue’’. The solid line (labeled ‘‘DESCENT’’) is the reconstructed descent speed profile based on Eq. (14) and the dashed line (labeled ‘‘PREDICT’’) represents the results of the preflight simulation. It can be seen that under the main parachute the actual descent speed was about 5 m/s lower than predicted. This is also very likely the cause for the longer flight time in the actual mission. Also shown in the same panel is the descent speed profile from the entry phase reconstruction (dashed-dotted line, labeled ‘‘ENTRY’’). It can be seen that although the descent phase velocity shows some oscillations during the main chute phase, the overall trend agrees well with the smooth velocity profile from the entry phase reconstruction. The lower panel of Fig. 13 depicts the descent speed profiles during the drogue chute phase down to probe surface impact. The descent speed reconstruction predicts a probe impact speed of 4:54 m=s, consistent with the speed derived from the altitude measurements of the SSP-APIS sensor (shown as a single triangle). 4.3. Comparison to RAU measurements The residual between the reconstructed descent trajectory and the RAU measurements are shown in Fig. 14. The 1s error of the reconstructed altitude profile is evaluated and is shown as a dashed line in the same figure. Altitude Residual [m] 3500 3000 2500 2000 1500 1000 500 RES-RAU1 RES-RAU2 DTWG 1-α 0 60 70 80 90 100 110 120 130 140 150 Time [min] past Interface Epoch: UTC: 2005-01-14T09:05:52.523 Fig. 14. Residuals of the RAU 1 and 2 measured altitude profiles and the reconstructed descent trajectory. The 1s error of the reconstructed trajectory is also shown as dashed line.
Page 1 and 2: Planetary and Space Science 55 (200
Page 3 and 4: was separated from Cassini on the t
Page 5 and 6: EXPERIMENT PLATFORM FRONT SHIELD AF
Page 7 and 8: drive the mass from its displaced p
Page 9 and 10: initially thought to be entirely lo
Page 11 and 12: Altitude [km] above Ref. Surface of
Page 13: Altitude [km] Altitude [km] 1200 10
Page 17 and 18: West Longitude [deg] Latitude [deg]
Page 19 and 20: 2 km. The scales of the surface fea
Page 21 and 22: Aerodynamic Deceleration [m/s 2 ] 6
Page 23 and 24: therefore be considered as approxim
Page 25 and 26: Table 4 (continued ) ARTICLE IN PRE
Page 31 and 32: leading truncation error term. Tech

Huygens' entry and descent through Titan's atmosphere ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?