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Reentry survival analysis of tumbling metallic hollow cylinder
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Advances in Space Research 48 (2011) 914–922 www.elsevier.com/locate/asr
Reentry survival analysis of tumbling metallic hollow cylinder Hyung-seok Sim a,1, Kyu-hong Kim a,b,⇑ a
School of Mechanical and Aerospace Engineering, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea b Institute of Advanced Aerospace Technology, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea Received 9 February 2011; received in revised form 28 April 2011 Available online 7 May 2011
Abstract The survival of orbital debris reentering the Earth’s atmosphere is considered. The numerical approach of NASA’s Object Reentry Survival Analysis Tool (ORSAT) is reviewed, and a new equation accounting for reradiation heat loss of hollow cylindrical objects is presented. Based on these, a code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) has been developed, and the new equation for reradiation heat loss is validated. Using this equation in conjunction with the formulation used in ORSAT, a comparative case study on the Delta-II second stage cylindrical tank is given, demonstrating that the analysis using the proposed equation is in good agreement with the actual recovered object when a practical value for thermal emissivity is used. A detailed explanation of the revised formulation is given, and additional simulation results are presented. Finally, discussions are made to address the applicability of the proposed equation to be incorporated in future survival analyses of orbital debris. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Reentry survival; Orbital debris; Reradiation heat loss; ORSAT; SAPAR
1. Introduction Analysis of the risk from orbital objects reentering the Earth has become an important topic in recent years (Lips and Fritsche, 2005; Tewari, 2009). Several national organizations from the space-faring nations have established the Space Debris Mitigation Standards and Handbooks that stipulate risk standards for debris that survives reentry (Kato, 2001). Tools with which to analyze the survivability of reentry objects, and thus determine the potential ground risk from the objects, have been developed by several space agencies and research institutes. In practice, these tools are used to determine whether satellites or the upper stages of launch vehicles comply with the human casualty risk stan-
⇑ Corresponding author at: School of Mechanical and Aerospace Engineering and Institute of Advanced Aerospace Technology, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea, Tel.: +82 2 880 8920; fax: +82 2 880 8302. E-mail addresses: [email protected] (H.-s. Sim), [email protected] (K.-h. Kim). 1 Tel.: +82 2 880 8920; fax: +82 2 880 8302.
dards. Among these tools, Spacecraft Atmospheric Reentry and Aerothermal Breakup (SCARAB) by ESA and the Object Reentry Survival Analysis Tool (ORSAT) by NASA can provide high fidelity simulation results, and have been widely used over the last decade. Although they adopt different approaches for trajectory simulation and the calculation of drag coefficients and heating rates, both tools have shown good agreement when analyzing objects with simple shapes (Lips et al., 2005). Although as of 2010, South Korea has no explicit standards for the mitigation of space debris, South Korea is to take part in international efforts to limit the orbital debris in the near future. Hence, South Korea will inevitably need survival analysis tools such as ORSAT and SCARAB to assess the ground risk from reentry objects. Therefore, we developed a reentry survival analysis tool named the Survivability Analysis Program for Atmospheric Reentry (SAPAR), which is described in this paper. Our code uses an approach and equations almost similar to those of ORSAT because ORSAT uses relatively simple equations and straightforward approaches, and the documentation can be obtained from the public domain.
0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2011.04.036
H.-s. Sim, K.-h. Kim / Advances in Space Research 48 (2011) 914–922
The ORSAT code simulates the reentry process by integrating software modules for integrated trajectory, atmospheric, aerodynamic, aerothermodynamic and thermal modules. ORSAT has been used as a primary tool by NASA to assess the reentry risk of orbital objects over the past decade (Dobarco-Otero et al., 2005). Frequently, ORSAT has been used for a higher fidelity survivability analysis when the NASA DAS (Debris Assessment Software) (Anon., 2007), which generates conservative risk results by relatively simple approach, has raised an issue that a spacecraft might be unable to meet the safety standard. If an uncontrolled orbital object during reentry is predicted to have risk greater than the human casualty risk criteria, controlled reentries or retrievals using other vehicles must be considered at great additional cost (O’Hara and Johnson, 2001). In this light, NASA views ORSAT as a very important tool for their current space projects, and it follows that this tool must be thoroughly investigated and validated whenever required for high fidelity and accuracy. ORSAT has been validated for the cases of a Sandia fuel rod and Delta-II second stage fragments using demise data and the features of survived objects, respectively. In the fuel rod case, ORSAT predicted the demise point of the cylinder wall of a Sandia fuel rod that was almost identical to the actual measured altitude (Rochelle et al., 1999, 2004). For the case of the Delta-II second stage cylindrical tank, Rochelle et al. (1997, 1999) presented two similar results (Fig. 17 in Rochelle et al., 1997 and Fig. 16 in Rochelle et al., 1999) based on detailed survival analysis using ORSAT 5.0. These analyses coincided with real measurements in that they predicted the survival of the cylindrical propellant tank during reentry. On the other hand, for the surface temperature of the tank, the ORSAT results were different than those of Ailor et al. (2005). They performed micro-structural analysis on the recovered tank and concluded that the peak overall reentry temperature of the tank was between 1473 and 1553 K, which is much lower than the melting temperature of stainless steel (1700–1750 K). In contrast, Rochelle et al. (1997, 1999) predicted that the object would reach the melting temperature and remain at that state for more than 70 s. Assuming that the analysis of Ailor et al. (2005) is more realistic in the sense that they used real data from the reentered objects, one may question why such a discrepancy between two peak temperatures occurred. Further analysis is therefore necessary to enhance the fidelity and accuracy of ORSAT. In addition, it remains to be determined why the ORSAT analysis of the Sandia fuel rod showed excellent agreement with the actual data whereas the prediction for the Delta-II second stage cylindrical tank did not. In this light, we reviewed the formulation of the aerothermal analysis incorporated in ORSAT, and presented a revised equation to deal with the reference area of the reradiation heat loss of cylindrical objects. As a consequence, we developed the possible causes of the mismatch between the results from ORSAT and the approach of Ailor et al.
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(2005) using the graphs presented by Rochelle et al. (1997, 1999). Finally, we obtained the results of a SAPAR analysis on the Delta-II second stage cylindrical tank using a revised reference area for reradiation heat loss and thermal emissivity, thereby demonstrating that the surface temperature remained below the melting point. This paper is organized as follows: First, the SAPAR code is described in Section 2, with details of the modules and validation of the results. The ORSAT aerothermal model for a cylindrical body is examined in Section 3.1, and the ORSAT survivability analysis of the Delta-II second stage cylindrical tank is reviewed in Section 3.2. The main contribution of this study is in Section 3.3, in which the SAPAR results for the Delta-II second stage cylindrical tank case with various conditions of calculation are provided to show the validity of the proposed causes. The effects of our proposed equation for reradiation heat loss on the final simulation results are discussed in Section 4, and the conditions for which the proposed equation should be considered is addressed. Finally, the conclusions are given in Section 5. 2. The SAPAR code 2.1. SAPAR program module The SAPAR code employs integrated trajectory, aerodynamic, aerothermodynamic and thermal modules to simulate the reentry process. The SAPAR trajectory module simulates a three degree-of-freedom (DOF) trajectory by integrating the equations in terms of the ECI (Earth Centered Inertial) frame. Various Earth models including WGS84 (World Geodetic System 84) and the spherical Earth can be adopted in SAPAR whereas ORSAT uses the equations in an Earth-fixed reference frame assuming the spherical Earth. Several atmosphere models are available in SAPAR including the US Standard 1976 and the GRAM95 (NASA/MSFC Global Reference Atmospheric Model-1995). The aerodynamics module computes average drag coefficients of objects within free molecular, transitional, and continuum flow regimes as a function of Knudsen number (Rochelle et al., 1997; Klett, 1964; DobarcoOtero et al., 2003; Cropp, 1965). The heat fluxes to reentry objects are computed in the aerothermodynamics module. The average cold-wall convective heat flux ðq_cw Þ is computed based on fractions of the sphere stagnation point heat flux using the Detra, Kemp, and Riddell formula (Detra et al., 1957; Bouslog et al., 1994) for continuum flow and the relation of the accommodation coefficient, the density, and the velocity for free molecular heating (Klett, 1964; Cropp, 1965). In order to model heat fluxes in the transition regime, a variation of Stanton number versus Knudsen number (Lips and Fritsche, 2005) was used. The average heat flux to the actual hot wall ðq_hw Þ was calculated as the cold wall value multiplied by the wall enthalpy ratio (Rochelle et al., 1997). The oxidation heat fluxes were modeled using
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the equation presented by Cropp (1965). The reradiation heat loss was computed using the Stephan–Boltzmann equation with the temperature of the outer surface and the thermal emissivity. The reference area for the reradiation heat loss ðq_ rr Þ was chosen as the whole surface area contacting the surrounding air. The thermal module computes the temperature of the object using a nodal thermal math model. The one-dimensional (1-D) heat conduction equation is solved using a forward-time-central-space (FTCS) finite difference scheme. As the object absorbs the positive heat flux, the outer layers may eventually reach the melting temperature of the material. At that point, the thermal module fixes the temperatures at the melting point to track the heat load of each layer with respect to time. After the heat absorbed into the outer layer exceeds the heat of ablation of that layer, the layer is removed by an assumed shear force, and the heat fluxes are applied to the next layer. The heat of ablation of a layer is defined as the heat needed for the layer to be completely ablated (Dobarco-Otero et al., 2005). When the outer layer is removed, the resulting changes in the mass, the diameter, and the ballistic coefficient are applied to the other program modules. Fig. 1 shows a block diagram of the relationship between the modules of the SAPAR code.
(2005). The initial conditions are listed in Table 1. For these conditions, SCARAB and ORSAT have shown good agreement, although the two codes use completely different approaches for the trajectory simulation and the calculation of drag coefficients and heating rates. Figs. 2–4 show the impact masses and demise altitudes of spheres, cylinders, and boxes predicted by ORSAT, SCARAB, and SAPAR. It is noted that the profiles predicted by the SAPAR code are in excellent agreement with the results of SCARAB and ORSAT for the impact masses and the demise altitudes. The coefficient of determination (R2) presented in the figures is a statistical parameter that indicates the closeness of the points to the trend line; i.e., if all the points lie on the line, R2 should be 1.0. It can be seen that the values of R2 for the three figures are very close to unity, and that the trend lines have slopes of nearly unity. This means the SAPAR results are almost identical to those of SCARAB and ORSAT.
2.2. Code validation
3. Survival analysis of Delta-II second stage cylindrical tank
The SAPAR code was validated by comparing its analysis results for objects with simple shapes to results from ORSAT and SCARAB that were presented by Lips et al. (2005). SCARAB is a tool developed for ESA by Hypersonic Technology Go¨ttingen (HTG), and has been used as a standard code for the reentry survivability assessment of decaying satellites by ESA (Lips and Fritsche, 2005; Lips et al., 2005). Lips et al. (2005) compared survival analysis results from SCARAB and ORSAT for 120 cases: 24 spheres, 48 cylinders, and 48 boxes. In their study, the diameter of the spheres or cylinders and the width of the boxes ranged from 0.25 m to 1.0 m; the length-to-width ratios for boxes or the length-to-diameter ratios for cylinders were equal to 2.0 or 5.0; and the masses of the objects were between 10 and 3700 kg. The material properties and the dimensions for each case can be found in Lips et al.
3.1. Review of ORSAT aerothermal model for a cylindrical body
Table 1 Initial condition of simulation. Altitude Relative velocity Relative flight path angle Orbital inclination (Latitude, longitude)
122 km 7.41 km/s 0.1° 28° (0°, 0°)
The net heat flux to an object is calculated as the average hot-wall convective heat flux plus the oxidation heat flux
Aerodynamics Drag Coef.
Altitude Kundsen No
Trajectory Velocity Altitude
Ablation Ballistic Coeff.
Heat load
Mass
Heat load
Thermal analysis Surface temperature
Aerothermodynamics
Fig. 1. Program module of SAPAR code.
Fig. 2. Comparison of demise altitudes for spheres predicted by ORSAT (Lips et al., 2005) and SAPAR.
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the product of the cold-wall convective stagnation point heat flux for a sphere and a heat factor that accounts for the type and motion mode of the reentry body. The coldwall convective stagnation point heat flux for a sphere is computed in accordance with the flow regime; i.e., Knudsen number. The oxidation heat flux is calculated using the cold-wall convective heat flux and the oxidation coefficient (Cropp, 1965). The reradiation heat flux is computed using the emissivity of the material and the surface temperature of the object: q_ rr ¼ erT 4w ;
ð2Þ
where e is the thermal material emissivity, r is the Stephan– Boltzmann constant (5.67 108 W/m2 K4), and Tw is the surface temperature of the object. The net heat flux is integrated over time and multiplied by the reference surface area to yield the absorbed heat on the object (Rochelle et al., 1999): Z Qtotal ¼ Asurf q_ net dt; ð3Þ Fig. 3. Comparison of impact masses for cylinders predicted by SCARAB (Lips et al., 2005) and SAPAR.
Fig. 4. Comparison of demise altitudes for boxes predicted by SCARAB (Lips et al., 2005) and SAPAR.
minus the reradiation heat flux in ORSAT (Rochelle et al., 1997, 1999): q_ net ¼ q_hw þ q_ ox q_ rr ;
ð1Þ
_hw is the hotwhere q_ net is the net heat flux to the surface, q wall average convective heat flux, q_ ox is the oxidation heat flux, and q_ rr is the reradiation heat flux. The hot-wall aver_hw ) is a function of the average age convective heat flux (q cold-wall convective heat flux ( q_ cw ), which is computed as
where Qtotal is the total absorbed heat, Asurf is the reference surface area, and t is the time. The temperature of the object is computed using the absorbed heat, the thermal mass of the object, and the specific heat of the material. When the temperature of the object reaches the melting temperature, the temperature is fixed and the absorbed heat is tracked with respect to time until it exceeds the heat of ablation for the object. A detailed explanation of the aerothermal model and other ORSAT modules can be found in Dobarco-Otero et al. (2005), Rochelle et al. (1997, 1999). The total cold wall convective heating (Qcw) to a cylinder can be calculated by multiplying the heat factor of a cylindrical body by the sphere stagnation convective heat flux and the lateral surface area (pDL), and integrating the result over time (Cropp, 1965): Z Qcw ¼ q_ cw dt dA ¼ q_cw dt pDL Z ð4Þ ¼ F cyl q_ ss dt pDL; where q_ cw is the cold-wall convective heat flux, A is the surface area, q_cw is the cold-wall average convective heat flux, D is the diameter of the cylinder, L is the length of the cylinder, Fcyl is the heat factor for the cylinders, and q_ ss is the sphere stagnation point convective heat flux. The heat factor for a certain shape and motion mode is derived by first averaging the convective heat flux distribution over the whole surface area ðq_ cw dt dA=Asurf Þ, and then dividing it by the integrated stagnation point convective heat flux R for a sphere ð q_ ss dtÞ. In the case of a cylindrical body, the heat factor is obtained by integrating the convective heat flux distribution over the entire surface, first averaging it over the lateral surface area excluding the end caps (Dobarco-Otero et al., 2005; Klett, 1964; Cropp, 1965) and then dividing it by the stagnation point convective heat for a sphere. The heat factor for cylindrical bodies (Fcyl) can
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be divided into two parts: one for the lateral surface (Flat) and the other for the end caps (Fcaps). Thus, q_ cw dt dA q_ ss dt pDL
25
ð5Þ
_cw lat is the cold-wall average convective heat flux to where q _cw caps is the cold-wall average conthe lateral surface and q vective heat flux to the end caps. The heat factors for random tumbling cylinders with length-to-diameter ratio of unity are 0.387 and 0.382 for free molecular and continuum flow regimes respectively. In Eq. (4), it can be found that ORSAT uses pDL as the reference area for convective heating to cylindrical bodies. Because the convective heating is the major heating process of reentry objects and ORSAT uses the concept of the net heat flux in Eq. (3), there is a possibility to use pDL as the reference area for the net heat flux to cylindrical bodies in ORSAT. If ORSAT uses Eq. (3) with the reference surface area of pDL to calculate the total absorbed heat to a cylinder, the reference area for reradiation heat loss is also pDL and the absorbed heat becomes overestimated by neglecting the reradiation heat loss of the end caps. 3.2. Survival analysis of ORSAT on Delta-II second stage cylindrical tank In the analysis of the Delta-II second stage cylindrical tank made of stainless steel using ORSAT 5.0, Rochelle et al. (1999) used the following assumptions: outer diameter = 1.742 m, length = 1.853 m, thickness = 1.49 mm, and mass = 267.05 kg. With these dimensions, the thermal mass is calculated as 173 kg using the typical stainless steel density of 7800 kg/m3 (Anon., 2007). It was also assumed that the break-up altitude was 77.8 km, the flight path angle was 0.594°, the relative velocity was 7.663 km/s, the temperature was 300 K, the inclination angle was 96.6°, the latitude was 39.21°, and the longitude was 95.74° (Rochelle et al., 1999). A similar case was also simulated in Rochelle et al. (1997) with a few differences in terms of initial entry conditions, yielding almost the same results for the heating rate and the surface temperature profiles. Fig. 5 shows the heat flux components (hot-wall, oxidation, reradiation, and net) of the Delta-II second stage cylindrical tank as given in Fig. 16 of Rochelle et al. (1999). An oxidation coefficient of 0.6 was used in the analysis. The hot-wall convective heat flux was predicted to reach a maximum value of 22 W/cm2 and then drop rapidly at about 100 s. The reradiation heat flux was estimated to stay at a constant value for more than 70 s when the surface temperature was at the melting point of stainless steel.
Heat Fluxes( W/cm2 )
R 2 q_ cw caps dt 2 pD4 q_ cw lat dt pDL R R þ ¼ q_ ss dt pDL q_ ss dt pDL R R _cw lat dt 1 q _cw caps dt q R ¼ R þ D=L ¼ F lat þ F caps ; 2 q_ ss dt q_ ss dt R
.
qhw . qox . qrr . qnet
30
20 15 10 5 0 -5 -10
50
100 Time from Breakup(sec)
150
Fig. 5. Heat fluxes vs. time for Delta-II second stage cylindrical tank by ORSAT (Rochelle et al., 1999).
The peak reradiation heat flux of 15.2 W/cm2 can be obtained using Eq. (2) with a melting temperature of 1730 K and emissivity of 0.3 as given in Rochelle et al. (1997). Fig. 6 shows the total absorbed heat produced by integrating the heat fluxes over time and multiplying the result by the surface area. The first curve shows the absorbed heat presented in Fig. 17 of Rochelle et al. (1999). The second curve is the profile calculated in this study by integrating the net heat flux distribution shown in Fig. 5 over time and multiplying it by the lateral surface area (pDL), as in Eq. (3). As shown in Fig. 6, the two curves are coincident, which implies that in Rochelle et al. (1999), ORSAT might use pDL as the reference area for both the convective heat flux and the reradiation heat flux, as stated in Section 3.1. Therefore, ORSAT could neglect the reradiation heat loss via the end caps of the hollow cylinder, resulting in a higher surface temperature.
160 140
Absorbed Heat(MJ)
F cyl ¼ R
35
Result of ORSAT(Rochelle et al., 1999) Calculated heat with Fig.1 and Eq. (6) Heat of Ablation(Rochelle et al., 1999)
120 100 80 60 40 20 0 0
50
100 Time from Breakup(sec)
150
Fig. 6. Absorbed heat vs. time for Delta-II second stage cylindrical tank.
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Z
ðq_ hw þ q_ ox Þ pDL q_ rr ðpDL þ 0:5pD2 Þ dt Z 1 ¼ pDL dt: q_ net q_ rr 2L=D
Qtotal ¼
ð7Þ Another point to be noted is that the relation about the equivalent emissivity between above two equations can be established. In order for an object to absorb the same heat, that is, for Qtotal values to be the same in both equations: 1 þ1 ; ð8Þ e6 ¼ e7 2L=D where e6 is the emissivity of Eq. (6) and e7 is the emissivity of Eq. (7). 3.3. Survival analysis of SAPAR on Delta-II second stage cylindrical tank Fig. 7 shows the demise factor of the Delta-II second stage stainless steel tank predicted by ORSAT (Rochelle et al., 1999) and SAPAR with the assumption of random tumbling using an emissivity (e) value of 0.3 and an oxidation coefficient of 0.6, as given in Rochelle et al. (1997, 1999). The spherical Earth model was used in the SAPAR code, which is similar to the ORSAT calculation. The SAPAR code computation applied Eqs. (6) and (7) to evaluate the effect of reradiation heat loss via the end caps. The demise factor in Fig. 7 is defined as the ratio of the absorbed heat divided by the heat of ablation of the object. When Eq. (7) is used, the SAPAR code predicts that the demise factor reaches only 68%, whereas it reaches 95% if Eq. (6) is used. A demise factor of 95% means that the object would be almost melted. It should be noted that a large amount of heat is supposed to reradiate at the end caps (i.e., about 30% of the total absorbed heat), and that
110 100 90
Demise Factor(%)
80 70 60 50 40 30
Objedt Demise Result of ORSAT(Rochelle et al., 1999) Result of SAPAR with Eq. (6) Result of SAPAR with Eq. (7)
20 10 0
0
20
40 60 Time from Breakup(sec)
80
100
Fig. 7. Demise factor vs. time for Delta-II second stage cylindrical tank.
the neglect of the reradiation heat loss of the end caps makes a considerable difference in the final results of the analysis of this problem. Fig. 8 shows the temperature profiles predicted using the revised reference area for reradiation heat loss based on Eq. (7). The predicted temperature using a higher-fidelity Systems Improved Numerical Differencing Analyzer (SINDA) (Anon., 2005) model is also shown in Fig. 8. In the SINDA calculation, the sum of the hot-wall and the oxidation heat fluxes shown in Fig. 5 was given as the heating condition and the reradiation heat loss via the whole surface was considered based on the surface temperature calculated by the SINDA code. Both the SINDA and the SAPAR codes with Eq. (7) and the emissivity of 0.3 predicted maximum temperatures slightly below the melting point of stainless steel, 1714 and 1721 K, respectively. On the other hand, the ORSAT result showed that the tank would be at the melting temperature and continuously ablated from 40 to 120 s. Almost the same profile as that
2000
Peak temperature range by (Ailor et al., 2005) 1600
Temperature(K)
From the preceding discussion, the total absorbed heat of cylindrical bodies in ORSAT can be expressed by Eq. (6), where the lateral surface area (pDL) is used as the reference surface area. On the other hand, if we take into account the reradiation heat loss of the end caps (assuming that the temperature of the end caps is similar to that of lateral surface), the total absorbed heat of the cylindrical body can be expressed by Eq. (7). Because a 1-D heat conduction model was employed in ORSAT and SAPAR, Eq. (7) is believed to be more realistic than Eq. (6). By comparing Eqs. (6) and (7), it should be noted that the ignored heat loss in ORSAT plays a significant role when the reradiation heat flux is comparable to the net heat flux and the length-to-diameter ratio (L/D) is small. Details regarding this point are given in Section 4 Z Z Qtotal ¼ Asurf q_ net dt ¼ pDL q_ net dt Z _hw þ q_ ox q_ rr Þdt; ¼ pDL ðq ð6Þ
919
1200
ORSAT(Rochelle et al., 1999) SAPAR with Eq.(6), emissivity=0.3 SAPAR with Eq.(6), emissivity=0.8 SINDA with Eq.(7), emissivity=0.3 SAPAR with Eq.(7), emissivity=0.3 SAPAR with Eq.(7), emissivity=0.54 SAPAR with Eq.(7), emissivity=0.8
800
400
0
0
50
100
150
200
Time from Breakup(sec)
Fig. 8. Temperature vs. time for Delta-II second stage cylindrical tank.
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of ORSAT was produced by the SAPAR code with Eq. (6) and the emissivity of 0.3 as seen in Fig. 8. The temperature difference between the results of SINDA and SAPAR with Eq. (7) and the emissivity of 0.3 after 100 s from breakup can be primarily attributed to a difference in the trajectory. The SINDA code used the heat flux profiles of Rochelle et al. (1999) such that the object would be ablated during reentry and undergo greater deceleration compared to the result of SAPAR with Eq. (7), in which the ablation did not occur. The reentry survival analysis can be significantly affected by the emissivity of material (Dobarco-Otero et al., 2003). However, the prediction of the accurate emissivity of an object is very difficult because it is dependent on the temperature, the level of oxidation, and roughness of the surface etc. A case study was performed in this paper to investigate the effect of the thermal emissivity on reentry survival analyses for Delta-II second stage stainless steel tank, and to find out the emissivity for the peak temperature of this cylindrical tank to agree with that of Ailor et al. (2005). The temperature profile calculated by SAPAR with Eq. (7) and an emissivity of 0.8 is presented in Fig. 8. In this case, the maximum temperature was predicted to be 1358 K, which is lower than the maximum temperature range of 1473 to 1553 K by Ailor et al. As seen from Fig. 8, the results of SAPAR with Eq. (6) and emissivity of 0.8 shows peak temperature of 1491 K which lies in the range by Ailor et al. When Eq. (7) was used, almost identical results were produced with an emissivity of 0.54 which is equivalent to the emissivity of 0.8 in Eq. (6) as can be obtained by Eq. (8). In fact, the analyses by SAPAR with Eq. (7) and the emissivity from 0.46 to 0.57 predicted that the peak temperature would be within the peak temperature range (Ailor et al., 2005) suggested. The emissivity of 0.8 is the mean value for the oxidized stainless steel (Dobarco-Otero et al., 2003) which is well manufactured in a furnace with enough oxygen and time. Hence, the effective emissivity for Delta-II second stage stainless steel tank, which were in oxidation process in rarefied air condition for a short time, should be much lower than 0.8. In this light, it is believed that the analysis by SAPAR with Eq. (7) is reasonable in that the result agreed well with the analysis by Ailor et al., when using the emissivity from 0.46 to 0.57 as was stated above. The oxidation coefficient can also affect the reentry survival analysis (Dobarco-Otero et al., 2003). In the present analysis on Delta-II second stage stainless steel tank using SAPAR, the peak temperature did change according to the oxidation coefficient, but not significantly. When the oxidation coefficient was increased from 0.2 to 0.8 with the emissivity fixed at 0.3, the peak temperature was predicted to increase from 1691 to 1730 K. 4. Discussion As previously mentioned, the revised equation for the reference area of reradiation heat loss of cylindrical bodies
reduces the absorbed heat into the objects, resulting in a lower surface temperature and greater possibility of survival of the reentry debris. This can partly explain the discrepancy between the ORSAT analysis of the Delta-II second stage stainless steel cylindrical tank and the research on the actual recovered object by Ailor et al. (2005). However, it should be noted that the ORSAT analysis coincide with the reentry data of the Sandia fuel rod. This implies that neglect of the reradiation heat loss of the end caps of the cylindrical body can be reasonable in some cases. 4.1. Length-to-diameter ratio As previously stated, the ignored heat loss via the end caps occupies a significant portion of the total heat loss when the length-to-diameter ratio (L/D) is small. Comparing Eq. (6) and (7), it is easy to find that the added heat loss in the revised equation (Eq. (7)) is f0:5pD2 q_ rr g, which occupies the fraction of {1/(1 + 2L/D)} out of the total reradiation heat loss for cylindrical bodies. When L/D of a cylindrical body increases from 1.0 to 10.0, the neglected fraction of heat loss by Eq. (6) compared to the total heat loss decreases from 0.33 to 0.05, as shown in Fig. 9. L/D of the Sandia fuel rod was about 9.8 (Rochelle et al., 1999); that is, the heat loss from the end caps can be neglected without having a significant effect on the final result. 4.2. Reradiation heat flux versus net heat flux The ignored heat loss via the end caps can be significant when the reradiation heat flux is comparable to the net heat flux. The total heat load absorbed into the object in ORSAT is calculated by integrating the net heat flux, which is calculated as the average hot-wall convective heat flux plus the oxidation heat flux minus the reradiation heat flux, and then multiplying it by the surface area, as in Eq. (6). So, if the reradiation heat flux is small compared to the
1
Ignored Heat Fraction
920
0.8
0.6
0.4 0.33 0.2 0.05 0 0
1
2
4
6
8
10
Length to Diameter Ratio
Fig. 9. Ignored heat fraction out of total reradiation heat loss by Eq. (6).
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average hot-wall convective heat flux, neglecting some portion of the reradiation heat loss does not make much difference. The peak value of the average hot-wall convective heat flux of the Sandia fuel rod was predicted to be about 200 W/cm2 with a diameter of 0.032 m, and the reradiation heat flux was predicted to be less than 10 W/cm2 throughout the reentry (Rochelle et al., 1999). In such a case, the neglect of the heat loss via the end caps has a slight effect on the final result. On the other hand, the peak value of the average hot-wall convective heat flux of the Delta-II second stage cylindrical tank was predicted to be about 22 W/cm2 with a diameter of 1.74 m, and the peak reradiation heat flux was predicted to be about 15 W/cm2 with an emissivity of 0.3 and a melting temperature of 1730 K (Rochelle et al., 1999). In this case, the two heat fluxes are comparable with each other and the reradiation heat flux via the end caps can occupy a considerable fraction of the total net heat flux and cannot be neglected for cylindrical objects with low length-to-diameter ratio. 4.3. Material of objects Whether or not Eq. (7) should be used can be determined based on the material of objects. Due to its fourth power relation with temperature, the reradiation heat flux can vary enormously according to the surface temperature of the object. Because the melting point is the maximum temperature of the material in its solid state, the peak value of the reradiation heat flux can be determined according to the melting temperature of the object. Therefore, for typical cylindrical spacecraft components whose maximum convective heat flux can be estimated, the melting point of the objects can determine whether the reradiation heat loss via the end caps can be ignored. Assuming an emissivity of 0.5 for a certain material, the reradiation heat flux can be varied from 2.8 to 229.6 W/cm2 when the surface temperature increases from 1000 to 3000 K. The maximum average convective heat flux for a cylinder of typical size of a spacecraft component has an order of magnitude of ten or hundred in W/cm2. Therefore, if the melting temperature of the material is below 1000 K, neglecting the reradiation heat loss from the end caps rarely makes a difference. However, for materials with a melting temperature of over 3000 K, the reradiation heat loss via the end caps cannot be neglected and Eq. (7) must be used for most typical spacecraft components. When the melting point of the object is between 1000 and 3000 K, the application of Eq. (7) can be determined according to the average convective heat flux on the object. The reradiation heat fluxes for the surface temperatures are summarized in Table 2, with several materials whose melting points are near those temperatures. This table is helpful in determining if the reradiation heat flux at the end caps is important.
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Table 2 Reradiation heat fluxes according to surface temperature. Temperature, K
Reradiation heat flux, W/cm2 (e = 0.5)
Material of concern
1000 1000–1500 1500–1800
2.8 2.8–14.4 14.4–29.8
1800–2000 2000–3000
29.8–45.4 45.4–229.6
3000
229.6
Aluminum, lead Copper, gold Beryllium, stainless steel, nickel Titanium, iron Molybdenum, platinum, niobium Tungsten
5. Conclusion The ORSAT aerothermal model was reviewed, and a revised equation for reradiation heat loss for cylindrical objects was presented. A code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) was developed and used to analyze the effects of the new equation. The effect of the new equation for the reradiation heat flux was shown to increase the reradiation heat loss and decrease the surface temperature of a hollow cylinder compared to ORSAT. This result could partly explain the discrepancy between the ORSAT analyses and the research on a recovered Delta-II second stage cylindrical tank. This effect could be negligible in some cases, but it should be considered when reradiation heat flux is comparable to the convective heat flux and the length-to-diameter ratio of the cylinder is small. The effect of the emissivity and the oxidation coefficient on the reentry survival analysis of the Delta-II second state cylindrical tank was also investigated. It was shown that the emissivity of the material had significant influence on the peak temperature, while the oxidation coefficient didn’t. Using the proposed equation for reradiation heat loss with approaches similar to those used in ORSAT and applying a practical value for thermal emissivity, the SAPAR code was used to predict the maximum temperature of the Delta-II second stage cylindrical tank reentering the Earth’s atmosphere. The result showed good agreement with the analysis of the actual reentered object.
Acknowledgements This work was supported by the New and Renewable Energy Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Knowledge Economy (No. 20104010100490). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 20110001227). The authors gratefully acknowledge this assistance. Moreover, the authors would like to thank Tobias Lips for providing the detailed conditions and results of calculations from Lips et al. (2005).
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References Ailor, W., Hallman, W., Steckel, G., Weaver, M. Analysis of reentered debris and implications for survivability modeling, in: Proceedings of the 4th European Conference on Space Debris, Darmstadt, Germany, April 18–20 2005 (ESA SP-587, pp. 539-544). ESA Publications Divisions, ESTEC, Noordwijk, The Netherlands, 2005. Anon. Debris Assessment Software User’s Guide Version 2.0. NASA/JSC, JSC 64047, Houston, TX, USA, November 2007. Anon. User’s Manual, SINDA/FLUINT General Purpose Thermal/Fluid Network Analyzer-Version 4.8. Cullimore and Ring Technologies, Inc., Littleton, CO, USA, October 2005. Bouslog, S.A., Ross, B.P., Madden, C.B. Space debris reentry risk analysis, in: 32nd Aerospace Sciences meeting, Reno/NV, USA, Jan 10–13, AIAA paper 94-0591, 1994. Cropp, L.O. Analytical Methods Used in Predicting the Re-Entry Ablation of Spherical and Cylindrical Bodies. Sandia Corporation SC-RR-65-187, September 1965. Detra, R.W., Kemp, N.H., Riddell, F.R. Addendum to heat transfer to satellite vehicles reentering the atmosphere. Jet Propulsion 27 (12), 1256–1257, 1957. Dobarco-Otero, J., Smith, R.N., Marichalar, J.J., Opiela, J.N., Rochelle, W.C., Johnson, N.L. Upgrades to Object Reentry Survival Analysis Tool (ORSAT) for spacecraft and launch vehicle upper stage applications, paper IAA 03-5.3.04, in: Proceedings of 54th IAC, Bremen, Germany, September 29–October 3, 2003. Dobarco-Otero, J., Smith, R.N., Bledsoe, K.J., Delaune, R.M., Rochelle, W.C., Johnson, N.L. The Object Reentry Survival Analysis Tool (ORSAT)-version 6.0 and its application to spacecraft entry, paper IAC-05-B6.3.06, in: Proceedings of 56th IAC, Fukuoka, Japan, October 2005. Kato, A. Comparison of national space debris mitigation standards. Adv. Space Res. 28 (9), 1447–1456, 2001.
Klett, R.D. Drag coefficients and heating ratios for right circular cylinders in free-molecular and continuum flow from Mach 10 to 30. Sandia Corporation SC-RR-64-2141, December 1964. Lips, T., Wartemann, V., Koppenwallner, G., Klinkrad, H., Alwes, D., Dobarco-Otero, J., Smith, R.N., DeLaune, R.M., Rochelle, W.C., Johnson, N.L. Comparison of ORSAT and SCARAB reentry survival results, in: Proceedings of the 4th European Conference on Space Debris, Darmstadt, Germany, April 18–20 2005 (ESA SP-587, pp. 533–538). ESA Publications Divisions, ESTEC, Noordwijk, The Netherlands, 2005. Lips, T., Fritsche, B. A comparison of commonly used re-entry analysis tools. Acta Astronaut. 57 (2–8), 312–323, 2005. O’Hara, R.E., Johnson, N.L. Reentry survivability risk assessment of the extreme ultraviolet explorer (EUVE), in: Proceedings of the 3rd European Conference on Space Debris, Darmstadt, Germany, March 19–21, 2001 (ESA SP-473, pp. 541–546). ESA Publications Divisions, ESTEC, Noordwijk, The Netherlands, 2001. Rochelle, W.C., Kinsey, R.E., Reid, E.A., Reynolds, R.C., Johnson, N.L. Spacecraft orbital debris reentry aerothermal analysis, in: Proceedings of the 8th Annual Fluids Analysis Workshop: Spacecraft Analysis and Design, NASA CP 3359, USA, pp 10.1–10.14, September 1997. Rochelle, W.C., Kirk, B.S., Ting, B.C., Smith L.N., Smith R.N., Reid, E.A., Johnson, N.L, Madden, C.B. Modeling of space debris reentry survivability and comparison of analytical methods, paper IAA-99IAA.6.7.03, in: Proceedings of 50th IAC, Amsterdam, Netherlands, 1999. Rochelle, W.C., Marichalar, J.J., Johnson, N.L. Analysis of reentry survivability of UARS spacecraft. Adv. Space Res. 34 (5), 1049–1054, 2004. Tewari, A. Entry trajectory model with thermomechanical breakup. J. Spacecraft Rockets 46 (2), 299–306, 2009.
Advances in Space Research 48 (2011) 914–922 www.elsevier.com/locate/asr
Reentry survival analysis of tumbling metallic hollow cylinder Hyung-seok Sim a,1, Kyu-hong Kim a,b,⇑ a
School of Mechanical and Aerospace Engineering, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea b Institute of Advanced Aerospace Technology, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea Received 9 February 2011; received in revised form 28 April 2011 Available online 7 May 2011
Abstract The survival of orbital debris reentering the Earth’s atmosphere is considered. The numerical approach of NASA’s Object Reentry Survival Analysis Tool (ORSAT) is reviewed, and a new equation accounting for reradiation heat loss of hollow cylindrical objects is presented. Based on these, a code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) has been developed, and the new equation for reradiation heat loss is validated. Using this equation in conjunction with the formulation used in ORSAT, a comparative case study on the Delta-II second stage cylindrical tank is given, demonstrating that the analysis using the proposed equation is in good agreement with the actual recovered object when a practical value for thermal emissivity is used. A detailed explanation of the revised formulation is given, and additional simulation results are presented. Finally, discussions are made to address the applicability of the proposed equation to be incorporated in future survival analyses of orbital debris. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Reentry survival; Orbital debris; Reradiation heat loss; ORSAT; SAPAR
1. Introduction Analysis of the risk from orbital objects reentering the Earth has become an important topic in recent years (Lips and Fritsche, 2005; Tewari, 2009). Several national organizations from the space-faring nations have established the Space Debris Mitigation Standards and Handbooks that stipulate risk standards for debris that survives reentry (Kato, 2001). Tools with which to analyze the survivability of reentry objects, and thus determine the potential ground risk from the objects, have been developed by several space agencies and research institutes. In practice, these tools are used to determine whether satellites or the upper stages of launch vehicles comply with the human casualty risk stan-
⇑ Corresponding author at: School of Mechanical and Aerospace Engineering and Institute of Advanced Aerospace Technology, Seoul National University, 599 Kwanakno, Gwanak-Gu, Seoul 151-742, South Korea, Tel.: +82 2 880 8920; fax: +82 2 880 8302. E-mail addresses: [email protected] (H.-s. Sim), [email protected] (K.-h. Kim). 1 Tel.: +82 2 880 8920; fax: +82 2 880 8302.
dards. Among these tools, Spacecraft Atmospheric Reentry and Aerothermal Breakup (SCARAB) by ESA and the Object Reentry Survival Analysis Tool (ORSAT) by NASA can provide high fidelity simulation results, and have been widely used over the last decade. Although they adopt different approaches for trajectory simulation and the calculation of drag coefficients and heating rates, both tools have shown good agreement when analyzing objects with simple shapes (Lips et al., 2005). Although as of 2010, South Korea has no explicit standards for the mitigation of space debris, South Korea is to take part in international efforts to limit the orbital debris in the near future. Hence, South Korea will inevitably need survival analysis tools such as ORSAT and SCARAB to assess the ground risk from reentry objects. Therefore, we developed a reentry survival analysis tool named the Survivability Analysis Program for Atmospheric Reentry (SAPAR), which is described in this paper. Our code uses an approach and equations almost similar to those of ORSAT because ORSAT uses relatively simple equations and straightforward approaches, and the documentation can be obtained from the public domain.
0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2011.04.036
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The ORSAT code simulates the reentry process by integrating software modules for integrated trajectory, atmospheric, aerodynamic, aerothermodynamic and thermal modules. ORSAT has been used as a primary tool by NASA to assess the reentry risk of orbital objects over the past decade (Dobarco-Otero et al., 2005). Frequently, ORSAT has been used for a higher fidelity survivability analysis when the NASA DAS (Debris Assessment Software) (Anon., 2007), which generates conservative risk results by relatively simple approach, has raised an issue that a spacecraft might be unable to meet the safety standard. If an uncontrolled orbital object during reentry is predicted to have risk greater than the human casualty risk criteria, controlled reentries or retrievals using other vehicles must be considered at great additional cost (O’Hara and Johnson, 2001). In this light, NASA views ORSAT as a very important tool for their current space projects, and it follows that this tool must be thoroughly investigated and validated whenever required for high fidelity and accuracy. ORSAT has been validated for the cases of a Sandia fuel rod and Delta-II second stage fragments using demise data and the features of survived objects, respectively. In the fuel rod case, ORSAT predicted the demise point of the cylinder wall of a Sandia fuel rod that was almost identical to the actual measured altitude (Rochelle et al., 1999, 2004). For the case of the Delta-II second stage cylindrical tank, Rochelle et al. (1997, 1999) presented two similar results (Fig. 17 in Rochelle et al., 1997 and Fig. 16 in Rochelle et al., 1999) based on detailed survival analysis using ORSAT 5.0. These analyses coincided with real measurements in that they predicted the survival of the cylindrical propellant tank during reentry. On the other hand, for the surface temperature of the tank, the ORSAT results were different than those of Ailor et al. (2005). They performed micro-structural analysis on the recovered tank and concluded that the peak overall reentry temperature of the tank was between 1473 and 1553 K, which is much lower than the melting temperature of stainless steel (1700–1750 K). In contrast, Rochelle et al. (1997, 1999) predicted that the object would reach the melting temperature and remain at that state for more than 70 s. Assuming that the analysis of Ailor et al. (2005) is more realistic in the sense that they used real data from the reentered objects, one may question why such a discrepancy between two peak temperatures occurred. Further analysis is therefore necessary to enhance the fidelity and accuracy of ORSAT. In addition, it remains to be determined why the ORSAT analysis of the Sandia fuel rod showed excellent agreement with the actual data whereas the prediction for the Delta-II second stage cylindrical tank did not. In this light, we reviewed the formulation of the aerothermal analysis incorporated in ORSAT, and presented a revised equation to deal with the reference area of the reradiation heat loss of cylindrical objects. As a consequence, we developed the possible causes of the mismatch between the results from ORSAT and the approach of Ailor et al.
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(2005) using the graphs presented by Rochelle et al. (1997, 1999). Finally, we obtained the results of a SAPAR analysis on the Delta-II second stage cylindrical tank using a revised reference area for reradiation heat loss and thermal emissivity, thereby demonstrating that the surface temperature remained below the melting point. This paper is organized as follows: First, the SAPAR code is described in Section 2, with details of the modules and validation of the results. The ORSAT aerothermal model for a cylindrical body is examined in Section 3.1, and the ORSAT survivability analysis of the Delta-II second stage cylindrical tank is reviewed in Section 3.2. The main contribution of this study is in Section 3.3, in which the SAPAR results for the Delta-II second stage cylindrical tank case with various conditions of calculation are provided to show the validity of the proposed causes. The effects of our proposed equation for reradiation heat loss on the final simulation results are discussed in Section 4, and the conditions for which the proposed equation should be considered is addressed. Finally, the conclusions are given in Section 5. 2. The SAPAR code 2.1. SAPAR program module The SAPAR code employs integrated trajectory, aerodynamic, aerothermodynamic and thermal modules to simulate the reentry process. The SAPAR trajectory module simulates a three degree-of-freedom (DOF) trajectory by integrating the equations in terms of the ECI (Earth Centered Inertial) frame. Various Earth models including WGS84 (World Geodetic System 84) and the spherical Earth can be adopted in SAPAR whereas ORSAT uses the equations in an Earth-fixed reference frame assuming the spherical Earth. Several atmosphere models are available in SAPAR including the US Standard 1976 and the GRAM95 (NASA/MSFC Global Reference Atmospheric Model-1995). The aerodynamics module computes average drag coefficients of objects within free molecular, transitional, and continuum flow regimes as a function of Knudsen number (Rochelle et al., 1997; Klett, 1964; DobarcoOtero et al., 2003; Cropp, 1965). The heat fluxes to reentry objects are computed in the aerothermodynamics module. The average cold-wall convective heat flux ðq_cw Þ is computed based on fractions of the sphere stagnation point heat flux using the Detra, Kemp, and Riddell formula (Detra et al., 1957; Bouslog et al., 1994) for continuum flow and the relation of the accommodation coefficient, the density, and the velocity for free molecular heating (Klett, 1964; Cropp, 1965). In order to model heat fluxes in the transition regime, a variation of Stanton number versus Knudsen number (Lips and Fritsche, 2005) was used. The average heat flux to the actual hot wall ðq_hw Þ was calculated as the cold wall value multiplied by the wall enthalpy ratio (Rochelle et al., 1997). The oxidation heat fluxes were modeled using
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the equation presented by Cropp (1965). The reradiation heat loss was computed using the Stephan–Boltzmann equation with the temperature of the outer surface and the thermal emissivity. The reference area for the reradiation heat loss ðq_ rr Þ was chosen as the whole surface area contacting the surrounding air. The thermal module computes the temperature of the object using a nodal thermal math model. The one-dimensional (1-D) heat conduction equation is solved using a forward-time-central-space (FTCS) finite difference scheme. As the object absorbs the positive heat flux, the outer layers may eventually reach the melting temperature of the material. At that point, the thermal module fixes the temperatures at the melting point to track the heat load of each layer with respect to time. After the heat absorbed into the outer layer exceeds the heat of ablation of that layer, the layer is removed by an assumed shear force, and the heat fluxes are applied to the next layer. The heat of ablation of a layer is defined as the heat needed for the layer to be completely ablated (Dobarco-Otero et al., 2005). When the outer layer is removed, the resulting changes in the mass, the diameter, and the ballistic coefficient are applied to the other program modules. Fig. 1 shows a block diagram of the relationship between the modules of the SAPAR code.
(2005). The initial conditions are listed in Table 1. For these conditions, SCARAB and ORSAT have shown good agreement, although the two codes use completely different approaches for the trajectory simulation and the calculation of drag coefficients and heating rates. Figs. 2–4 show the impact masses and demise altitudes of spheres, cylinders, and boxes predicted by ORSAT, SCARAB, and SAPAR. It is noted that the profiles predicted by the SAPAR code are in excellent agreement with the results of SCARAB and ORSAT for the impact masses and the demise altitudes. The coefficient of determination (R2) presented in the figures is a statistical parameter that indicates the closeness of the points to the trend line; i.e., if all the points lie on the line, R2 should be 1.0. It can be seen that the values of R2 for the three figures are very close to unity, and that the trend lines have slopes of nearly unity. This means the SAPAR results are almost identical to those of SCARAB and ORSAT.
2.2. Code validation
3. Survival analysis of Delta-II second stage cylindrical tank
The SAPAR code was validated by comparing its analysis results for objects with simple shapes to results from ORSAT and SCARAB that were presented by Lips et al. (2005). SCARAB is a tool developed for ESA by Hypersonic Technology Go¨ttingen (HTG), and has been used as a standard code for the reentry survivability assessment of decaying satellites by ESA (Lips and Fritsche, 2005; Lips et al., 2005). Lips et al. (2005) compared survival analysis results from SCARAB and ORSAT for 120 cases: 24 spheres, 48 cylinders, and 48 boxes. In their study, the diameter of the spheres or cylinders and the width of the boxes ranged from 0.25 m to 1.0 m; the length-to-width ratios for boxes or the length-to-diameter ratios for cylinders were equal to 2.0 or 5.0; and the masses of the objects were between 10 and 3700 kg. The material properties and the dimensions for each case can be found in Lips et al.
3.1. Review of ORSAT aerothermal model for a cylindrical body
Table 1 Initial condition of simulation. Altitude Relative velocity Relative flight path angle Orbital inclination (Latitude, longitude)
122 km 7.41 km/s 0.1° 28° (0°, 0°)
The net heat flux to an object is calculated as the average hot-wall convective heat flux plus the oxidation heat flux
Aerodynamics Drag Coef.
Altitude Kundsen No
Trajectory Velocity Altitude
Ablation Ballistic Coeff.
Heat load
Mass
Heat load
Thermal analysis Surface temperature
Aerothermodynamics
Fig. 1. Program module of SAPAR code.
Fig. 2. Comparison of demise altitudes for spheres predicted by ORSAT (Lips et al., 2005) and SAPAR.
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the product of the cold-wall convective stagnation point heat flux for a sphere and a heat factor that accounts for the type and motion mode of the reentry body. The coldwall convective stagnation point heat flux for a sphere is computed in accordance with the flow regime; i.e., Knudsen number. The oxidation heat flux is calculated using the cold-wall convective heat flux and the oxidation coefficient (Cropp, 1965). The reradiation heat flux is computed using the emissivity of the material and the surface temperature of the object: q_ rr ¼ erT 4w ;
ð2Þ
where e is the thermal material emissivity, r is the Stephan– Boltzmann constant (5.67 108 W/m2 K4), and Tw is the surface temperature of the object. The net heat flux is integrated over time and multiplied by the reference surface area to yield the absorbed heat on the object (Rochelle et al., 1999): Z Qtotal ¼ Asurf q_ net dt; ð3Þ Fig. 3. Comparison of impact masses for cylinders predicted by SCARAB (Lips et al., 2005) and SAPAR.
Fig. 4. Comparison of demise altitudes for boxes predicted by SCARAB (Lips et al., 2005) and SAPAR.
minus the reradiation heat flux in ORSAT (Rochelle et al., 1997, 1999): q_ net ¼ q_hw þ q_ ox q_ rr ;
ð1Þ
_hw is the hotwhere q_ net is the net heat flux to the surface, q wall average convective heat flux, q_ ox is the oxidation heat flux, and q_ rr is the reradiation heat flux. The hot-wall aver_hw ) is a function of the average age convective heat flux (q cold-wall convective heat flux ( q_ cw ), which is computed as
where Qtotal is the total absorbed heat, Asurf is the reference surface area, and t is the time. The temperature of the object is computed using the absorbed heat, the thermal mass of the object, and the specific heat of the material. When the temperature of the object reaches the melting temperature, the temperature is fixed and the absorbed heat is tracked with respect to time until it exceeds the heat of ablation for the object. A detailed explanation of the aerothermal model and other ORSAT modules can be found in Dobarco-Otero et al. (2005), Rochelle et al. (1997, 1999). The total cold wall convective heating (Qcw) to a cylinder can be calculated by multiplying the heat factor of a cylindrical body by the sphere stagnation convective heat flux and the lateral surface area (pDL), and integrating the result over time (Cropp, 1965): Z Qcw ¼ q_ cw dt dA ¼ q_cw dt pDL Z ð4Þ ¼ F cyl q_ ss dt pDL; where q_ cw is the cold-wall convective heat flux, A is the surface area, q_cw is the cold-wall average convective heat flux, D is the diameter of the cylinder, L is the length of the cylinder, Fcyl is the heat factor for the cylinders, and q_ ss is the sphere stagnation point convective heat flux. The heat factor for a certain shape and motion mode is derived by first averaging the convective heat flux distribution over the whole surface area ðq_ cw dt dA=Asurf Þ, and then dividing it by the integrated stagnation point convective heat flux R for a sphere ð q_ ss dtÞ. In the case of a cylindrical body, the heat factor is obtained by integrating the convective heat flux distribution over the entire surface, first averaging it over the lateral surface area excluding the end caps (Dobarco-Otero et al., 2005; Klett, 1964; Cropp, 1965) and then dividing it by the stagnation point convective heat for a sphere. The heat factor for cylindrical bodies (Fcyl) can
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be divided into two parts: one for the lateral surface (Flat) and the other for the end caps (Fcaps). Thus, q_ cw dt dA q_ ss dt pDL
25
ð5Þ
_cw lat is the cold-wall average convective heat flux to where q _cw caps is the cold-wall average conthe lateral surface and q vective heat flux to the end caps. The heat factors for random tumbling cylinders with length-to-diameter ratio of unity are 0.387 and 0.382 for free molecular and continuum flow regimes respectively. In Eq. (4), it can be found that ORSAT uses pDL as the reference area for convective heating to cylindrical bodies. Because the convective heating is the major heating process of reentry objects and ORSAT uses the concept of the net heat flux in Eq. (3), there is a possibility to use pDL as the reference area for the net heat flux to cylindrical bodies in ORSAT. If ORSAT uses Eq. (3) with the reference surface area of pDL to calculate the total absorbed heat to a cylinder, the reference area for reradiation heat loss is also pDL and the absorbed heat becomes overestimated by neglecting the reradiation heat loss of the end caps. 3.2. Survival analysis of ORSAT on Delta-II second stage cylindrical tank In the analysis of the Delta-II second stage cylindrical tank made of stainless steel using ORSAT 5.0, Rochelle et al. (1999) used the following assumptions: outer diameter = 1.742 m, length = 1.853 m, thickness = 1.49 mm, and mass = 267.05 kg. With these dimensions, the thermal mass is calculated as 173 kg using the typical stainless steel density of 7800 kg/m3 (Anon., 2007). It was also assumed that the break-up altitude was 77.8 km, the flight path angle was 0.594°, the relative velocity was 7.663 km/s, the temperature was 300 K, the inclination angle was 96.6°, the latitude was 39.21°, and the longitude was 95.74° (Rochelle et al., 1999). A similar case was also simulated in Rochelle et al. (1997) with a few differences in terms of initial entry conditions, yielding almost the same results for the heating rate and the surface temperature profiles. Fig. 5 shows the heat flux components (hot-wall, oxidation, reradiation, and net) of the Delta-II second stage cylindrical tank as given in Fig. 16 of Rochelle et al. (1999). An oxidation coefficient of 0.6 was used in the analysis. The hot-wall convective heat flux was predicted to reach a maximum value of 22 W/cm2 and then drop rapidly at about 100 s. The reradiation heat flux was estimated to stay at a constant value for more than 70 s when the surface temperature was at the melting point of stainless steel.
Heat Fluxes( W/cm2 )
R 2 q_ cw caps dt 2 pD4 q_ cw lat dt pDL R R þ ¼ q_ ss dt pDL q_ ss dt pDL R R _cw lat dt 1 q _cw caps dt q R ¼ R þ D=L ¼ F lat þ F caps ; 2 q_ ss dt q_ ss dt R
.
qhw . qox . qrr . qnet
30
20 15 10 5 0 -5 -10
50
100 Time from Breakup(sec)
150
Fig. 5. Heat fluxes vs. time for Delta-II second stage cylindrical tank by ORSAT (Rochelle et al., 1999).
The peak reradiation heat flux of 15.2 W/cm2 can be obtained using Eq. (2) with a melting temperature of 1730 K and emissivity of 0.3 as given in Rochelle et al. (1997). Fig. 6 shows the total absorbed heat produced by integrating the heat fluxes over time and multiplying the result by the surface area. The first curve shows the absorbed heat presented in Fig. 17 of Rochelle et al. (1999). The second curve is the profile calculated in this study by integrating the net heat flux distribution shown in Fig. 5 over time and multiplying it by the lateral surface area (pDL), as in Eq. (3). As shown in Fig. 6, the two curves are coincident, which implies that in Rochelle et al. (1999), ORSAT might use pDL as the reference area for both the convective heat flux and the reradiation heat flux, as stated in Section 3.1. Therefore, ORSAT could neglect the reradiation heat loss via the end caps of the hollow cylinder, resulting in a higher surface temperature.
160 140
Absorbed Heat(MJ)
F cyl ¼ R
35
Result of ORSAT(Rochelle et al., 1999) Calculated heat with Fig.1 and Eq. (6) Heat of Ablation(Rochelle et al., 1999)
120 100 80 60 40 20 0 0
50
100 Time from Breakup(sec)
150
Fig. 6. Absorbed heat vs. time for Delta-II second stage cylindrical tank.
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Z
ðq_ hw þ q_ ox Þ pDL q_ rr ðpDL þ 0:5pD2 Þ dt Z 1 ¼ pDL dt: q_ net q_ rr 2L=D
Qtotal ¼
ð7Þ Another point to be noted is that the relation about the equivalent emissivity between above two equations can be established. In order for an object to absorb the same heat, that is, for Qtotal values to be the same in both equations: 1 þ1 ; ð8Þ e6 ¼ e7 2L=D where e6 is the emissivity of Eq. (6) and e7 is the emissivity of Eq. (7). 3.3. Survival analysis of SAPAR on Delta-II second stage cylindrical tank Fig. 7 shows the demise factor of the Delta-II second stage stainless steel tank predicted by ORSAT (Rochelle et al., 1999) and SAPAR with the assumption of random tumbling using an emissivity (e) value of 0.3 and an oxidation coefficient of 0.6, as given in Rochelle et al. (1997, 1999). The spherical Earth model was used in the SAPAR code, which is similar to the ORSAT calculation. The SAPAR code computation applied Eqs. (6) and (7) to evaluate the effect of reradiation heat loss via the end caps. The demise factor in Fig. 7 is defined as the ratio of the absorbed heat divided by the heat of ablation of the object. When Eq. (7) is used, the SAPAR code predicts that the demise factor reaches only 68%, whereas it reaches 95% if Eq. (6) is used. A demise factor of 95% means that the object would be almost melted. It should be noted that a large amount of heat is supposed to reradiate at the end caps (i.e., about 30% of the total absorbed heat), and that
110 100 90
Demise Factor(%)
80 70 60 50 40 30
Objedt Demise Result of ORSAT(Rochelle et al., 1999) Result of SAPAR with Eq. (6) Result of SAPAR with Eq. (7)
20 10 0
0
20
40 60 Time from Breakup(sec)
80
100
Fig. 7. Demise factor vs. time for Delta-II second stage cylindrical tank.
the neglect of the reradiation heat loss of the end caps makes a considerable difference in the final results of the analysis of this problem. Fig. 8 shows the temperature profiles predicted using the revised reference area for reradiation heat loss based on Eq. (7). The predicted temperature using a higher-fidelity Systems Improved Numerical Differencing Analyzer (SINDA) (Anon., 2005) model is also shown in Fig. 8. In the SINDA calculation, the sum of the hot-wall and the oxidation heat fluxes shown in Fig. 5 was given as the heating condition and the reradiation heat loss via the whole surface was considered based on the surface temperature calculated by the SINDA code. Both the SINDA and the SAPAR codes with Eq. (7) and the emissivity of 0.3 predicted maximum temperatures slightly below the melting point of stainless steel, 1714 and 1721 K, respectively. On the other hand, the ORSAT result showed that the tank would be at the melting temperature and continuously ablated from 40 to 120 s. Almost the same profile as that
2000
Peak temperature range by (Ailor et al., 2005) 1600
Temperature(K)
From the preceding discussion, the total absorbed heat of cylindrical bodies in ORSAT can be expressed by Eq. (6), where the lateral surface area (pDL) is used as the reference surface area. On the other hand, if we take into account the reradiation heat loss of the end caps (assuming that the temperature of the end caps is similar to that of lateral surface), the total absorbed heat of the cylindrical body can be expressed by Eq. (7). Because a 1-D heat conduction model was employed in ORSAT and SAPAR, Eq. (7) is believed to be more realistic than Eq. (6). By comparing Eqs. (6) and (7), it should be noted that the ignored heat loss in ORSAT plays a significant role when the reradiation heat flux is comparable to the net heat flux and the length-to-diameter ratio (L/D) is small. Details regarding this point are given in Section 4 Z Z Qtotal ¼ Asurf q_ net dt ¼ pDL q_ net dt Z _hw þ q_ ox q_ rr Þdt; ¼ pDL ðq ð6Þ
919
1200
ORSAT(Rochelle et al., 1999) SAPAR with Eq.(6), emissivity=0.3 SAPAR with Eq.(6), emissivity=0.8 SINDA with Eq.(7), emissivity=0.3 SAPAR with Eq.(7), emissivity=0.3 SAPAR with Eq.(7), emissivity=0.54 SAPAR with Eq.(7), emissivity=0.8
800
400
0
0
50
100
150
200
Time from Breakup(sec)
Fig. 8. Temperature vs. time for Delta-II second stage cylindrical tank.
H.-s. Sim, K.-h. Kim / Advances in Space Research 48 (2011) 914–922
of ORSAT was produced by the SAPAR code with Eq. (6) and the emissivity of 0.3 as seen in Fig. 8. The temperature difference between the results of SINDA and SAPAR with Eq. (7) and the emissivity of 0.3 after 100 s from breakup can be primarily attributed to a difference in the trajectory. The SINDA code used the heat flux profiles of Rochelle et al. (1999) such that the object would be ablated during reentry and undergo greater deceleration compared to the result of SAPAR with Eq. (7), in which the ablation did not occur. The reentry survival analysis can be significantly affected by the emissivity of material (Dobarco-Otero et al., 2003). However, the prediction of the accurate emissivity of an object is very difficult because it is dependent on the temperature, the level of oxidation, and roughness of the surface etc. A case study was performed in this paper to investigate the effect of the thermal emissivity on reentry survival analyses for Delta-II second stage stainless steel tank, and to find out the emissivity for the peak temperature of this cylindrical tank to agree with that of Ailor et al. (2005). The temperature profile calculated by SAPAR with Eq. (7) and an emissivity of 0.8 is presented in Fig. 8. In this case, the maximum temperature was predicted to be 1358 K, which is lower than the maximum temperature range of 1473 to 1553 K by Ailor et al. As seen from Fig. 8, the results of SAPAR with Eq. (6) and emissivity of 0.8 shows peak temperature of 1491 K which lies in the range by Ailor et al. When Eq. (7) was used, almost identical results were produced with an emissivity of 0.54 which is equivalent to the emissivity of 0.8 in Eq. (6) as can be obtained by Eq. (8). In fact, the analyses by SAPAR with Eq. (7) and the emissivity from 0.46 to 0.57 predicted that the peak temperature would be within the peak temperature range (Ailor et al., 2005) suggested. The emissivity of 0.8 is the mean value for the oxidized stainless steel (Dobarco-Otero et al., 2003) which is well manufactured in a furnace with enough oxygen and time. Hence, the effective emissivity for Delta-II second stage stainless steel tank, which were in oxidation process in rarefied air condition for a short time, should be much lower than 0.8. In this light, it is believed that the analysis by SAPAR with Eq. (7) is reasonable in that the result agreed well with the analysis by Ailor et al., when using the emissivity from 0.46 to 0.57 as was stated above. The oxidation coefficient can also affect the reentry survival analysis (Dobarco-Otero et al., 2003). In the present analysis on Delta-II second stage stainless steel tank using SAPAR, the peak temperature did change according to the oxidation coefficient, but not significantly. When the oxidation coefficient was increased from 0.2 to 0.8 with the emissivity fixed at 0.3, the peak temperature was predicted to increase from 1691 to 1730 K. 4. Discussion As previously mentioned, the revised equation for the reference area of reradiation heat loss of cylindrical bodies
reduces the absorbed heat into the objects, resulting in a lower surface temperature and greater possibility of survival of the reentry debris. This can partly explain the discrepancy between the ORSAT analysis of the Delta-II second stage stainless steel cylindrical tank and the research on the actual recovered object by Ailor et al. (2005). However, it should be noted that the ORSAT analysis coincide with the reentry data of the Sandia fuel rod. This implies that neglect of the reradiation heat loss of the end caps of the cylindrical body can be reasonable in some cases. 4.1. Length-to-diameter ratio As previously stated, the ignored heat loss via the end caps occupies a significant portion of the total heat loss when the length-to-diameter ratio (L/D) is small. Comparing Eq. (6) and (7), it is easy to find that the added heat loss in the revised equation (Eq. (7)) is f0:5pD2 q_ rr g, which occupies the fraction of {1/(1 + 2L/D)} out of the total reradiation heat loss for cylindrical bodies. When L/D of a cylindrical body increases from 1.0 to 10.0, the neglected fraction of heat loss by Eq. (6) compared to the total heat loss decreases from 0.33 to 0.05, as shown in Fig. 9. L/D of the Sandia fuel rod was about 9.8 (Rochelle et al., 1999); that is, the heat loss from the end caps can be neglected without having a significant effect on the final result. 4.2. Reradiation heat flux versus net heat flux The ignored heat loss via the end caps can be significant when the reradiation heat flux is comparable to the net heat flux. The total heat load absorbed into the object in ORSAT is calculated by integrating the net heat flux, which is calculated as the average hot-wall convective heat flux plus the oxidation heat flux minus the reradiation heat flux, and then multiplying it by the surface area, as in Eq. (6). So, if the reradiation heat flux is small compared to the
1
Ignored Heat Fraction
920
0.8
0.6
0.4 0.33 0.2 0.05 0 0
1
2
4
6
8
10
Length to Diameter Ratio
Fig. 9. Ignored heat fraction out of total reradiation heat loss by Eq. (6).
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average hot-wall convective heat flux, neglecting some portion of the reradiation heat loss does not make much difference. The peak value of the average hot-wall convective heat flux of the Sandia fuel rod was predicted to be about 200 W/cm2 with a diameter of 0.032 m, and the reradiation heat flux was predicted to be less than 10 W/cm2 throughout the reentry (Rochelle et al., 1999). In such a case, the neglect of the heat loss via the end caps has a slight effect on the final result. On the other hand, the peak value of the average hot-wall convective heat flux of the Delta-II second stage cylindrical tank was predicted to be about 22 W/cm2 with a diameter of 1.74 m, and the peak reradiation heat flux was predicted to be about 15 W/cm2 with an emissivity of 0.3 and a melting temperature of 1730 K (Rochelle et al., 1999). In this case, the two heat fluxes are comparable with each other and the reradiation heat flux via the end caps can occupy a considerable fraction of the total net heat flux and cannot be neglected for cylindrical objects with low length-to-diameter ratio. 4.3. Material of objects Whether or not Eq. (7) should be used can be determined based on the material of objects. Due to its fourth power relation with temperature, the reradiation heat flux can vary enormously according to the surface temperature of the object. Because the melting point is the maximum temperature of the material in its solid state, the peak value of the reradiation heat flux can be determined according to the melting temperature of the object. Therefore, for typical cylindrical spacecraft components whose maximum convective heat flux can be estimated, the melting point of the objects can determine whether the reradiation heat loss via the end caps can be ignored. Assuming an emissivity of 0.5 for a certain material, the reradiation heat flux can be varied from 2.8 to 229.6 W/cm2 when the surface temperature increases from 1000 to 3000 K. The maximum average convective heat flux for a cylinder of typical size of a spacecraft component has an order of magnitude of ten or hundred in W/cm2. Therefore, if the melting temperature of the material is below 1000 K, neglecting the reradiation heat loss from the end caps rarely makes a difference. However, for materials with a melting temperature of over 3000 K, the reradiation heat loss via the end caps cannot be neglected and Eq. (7) must be used for most typical spacecraft components. When the melting point of the object is between 1000 and 3000 K, the application of Eq. (7) can be determined according to the average convective heat flux on the object. The reradiation heat fluxes for the surface temperatures are summarized in Table 2, with several materials whose melting points are near those temperatures. This table is helpful in determining if the reradiation heat flux at the end caps is important.
921
Table 2 Reradiation heat fluxes according to surface temperature. Temperature, K
Reradiation heat flux, W/cm2 (e = 0.5)
Material of concern
1000 1000–1500 1500–1800
2.8 2.8–14.4 14.4–29.8
1800–2000 2000–3000
29.8–45.4 45.4–229.6
3000
229.6
Aluminum, lead Copper, gold Beryllium, stainless steel, nickel Titanium, iron Molybdenum, platinum, niobium Tungsten
5. Conclusion The ORSAT aerothermal model was reviewed, and a revised equation for reradiation heat loss for cylindrical objects was presented. A code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) was developed and used to analyze the effects of the new equation. The effect of the new equation for the reradiation heat flux was shown to increase the reradiation heat loss and decrease the surface temperature of a hollow cylinder compared to ORSAT. This result could partly explain the discrepancy between the ORSAT analyses and the research on a recovered Delta-II second stage cylindrical tank. This effect could be negligible in some cases, but it should be considered when reradiation heat flux is comparable to the convective heat flux and the length-to-diameter ratio of the cylinder is small. The effect of the emissivity and the oxidation coefficient on the reentry survival analysis of the Delta-II second state cylindrical tank was also investigated. It was shown that the emissivity of the material had significant influence on the peak temperature, while the oxidation coefficient didn’t. Using the proposed equation for reradiation heat loss with approaches similar to those used in ORSAT and applying a practical value for thermal emissivity, the SAPAR code was used to predict the maximum temperature of the Delta-II second stage cylindrical tank reentering the Earth’s atmosphere. The result showed good agreement with the analysis of the actual reentered object.
Acknowledgements This work was supported by the New and Renewable Energy Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Knowledge Economy (No. 20104010100490). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 20110001227). The authors gratefully acknowledge this assistance. Moreover, the authors would like to thank Tobias Lips for providing the detailed conditions and results of calculations from Lips et al. (2005).
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