might develop a low-cost comprehensive neural-network based on simplified deterministic models to predict whether any Targeted Space Debris (TSD) could be ...
An Efficient Computational Fluid Dynamic Model to Predict Space-Debris Burning Feasibility Malaek, S. M., Samiee, M., Zohrevandi, E. Hashemi, Z.
Sharif University of Technology-Debrix Group Tehran, Iran
Abstract This work aims to describe how commercially available Computational Fluid Dynamic (CFD) tools could effectively be employed in evaluating the feasibility of the so called space-debris “Reentry Disposal Missions (RDM)”. In general any RDM needs to be both deterministic as well as cost-effective and with the help of current approach, regardless of the possible cost; we intend to show the conditions for which RDMs remain feasible options. In the absence of precise mathematical models, and even small-scale experiments; which are extremely costly, we might develop a low-cost comprehensive neural-network based on simplified deterministic models to predict whether any Targeted Space Debris (TSD) could be burned during de-orbiting with a certain degree of confidence. We refer to this tool as “Surrogate CFD Neural Network (CFDSurNN) for not being a CFD code, but imitating its results. The CFDSurNN tool presented in this work is, in fact, a specialized neural-network that predicts temperature rise and possible melting of an object during its fall through Earth’s Dense Atmosphere (EDA). It has been developed in a systematic manner and could be expanded to cover wide variety of TSDs with different shapes, sizes and materials. The approach, with its acceptable approximation, is of great help for some immediate applications in classification of existing debris orbiting the Earth and identifying those which are suitable for RDM. At its current level we have been using commercial tools (namely, FLUENT [1] and GAMBIT [2]): nonetheless, the peculiarities of the space environment, in one hand, and the importance of reentry disposal, one the other hand, justifies developing an specialized code specifically devoted to model and analyze the reentry associated problems.
Keywords: CFD, Neural-network, Reentry Disposal, Space-debris
1. Introduction The physics of the so called “Reentry Dynamics” have not yet been profoundly studied by the existing limited scientific organizations. Yet, there are even a small portion of those limited knowledge are available as an open source. This is simply because; it has not been a sustainable market to its associated issues. It so appears that relying on such limited knowledge to develop techniques for the so called “Reentry Disposal Missions” (RDM) might be a hasty engineering approach. In fact, without a sound scientific foundation and basic understandings of the space environment, in addition to the physics of Hypersonic journeys through EDA, we might not be able to develop tools to examine whether RDM is a viable approach to eliminate (or lessen) the threats of space-debris. In the absence of such basic research, we still can come up with some novel approaches to tackle the problem. In this work, we describe a systematic approach to reach to a reliable mathematical model for “Reentry Heating” with the help of available commercial Computational Fluid Dynamics codes. Obviously, a journey from outer sky toward the Earth’s surface which goes through different layers of atmosphere can be studied from different angles. As far is “Debris Reentry Disposal” (DRD) is concerned, we are interested in heat being generated an radiated on the object’s surface and transferred within its volume that would contribute to its melting, disintegrating and burning; while the object is travelling toward the Earth’s surface. This is, indeed, a very complex problem that must be tackled from different standpoints to reach an acceptable computational model. In this stage of the work, we describe the achievements regarding computing surface temperature of the object; which by itself has been the outcome of tremendous amount computational time in hypersonic down to supersonic and even subsonic flow regimes. It is noted that any individual case takes considerable amount time to reach an acceptable solution. So we can do such computations in only limited cases. A neural network that, on the other hand, plays the role of the surrogate system is expected to deliver the results in other cases, based on those precisely modeled and computed by the CFD toolset. So, starting with relatively simpler models that only deals with the objects’ surface temperature is justified. Obviously, we are interested in predicting the possibility of destroying an object via the reentry journey with an acceptable level of confidence. In this line of thought, if the current model could, in fact, predict that a piece of Targeted Space Debris (TSD) could be burned then we classify that TSD as a “Suitable Candidate” for RDM planning. On the other hand, if our surrogate system suggests that the selected (TSD) could reach beyond its melting point, then we still have a chance to model the reentry journey of that piece of TSD with better accuracy or otherwise that TSD is marked as “Unsuitable Candidate” for RDM. We further note that any RDM planning might vary due to the TSD characteristics; including its size, material, insulated coating or cost as well as safety associated factors. Any actual attempt to grab and deorbit such debris, therefore, requires careful contributions on the part of all engineering disciplines involved. This simply means that engineering models serving to plan DRD missions rely heavily on the validity of the Computational Fluid Dynamic (CFD) Models that serve to predict the TSD burning process. On the other hand, precise CFD models could be quite expensive, based on degrees of validation one might need for a specific application. To avoid undue cost and save time, here, we describe a new approach that employs CFD results in neural network architecture to eliminate the need for many cumbersome CFD computations required to classify TSDs for RDM planning. We refer to this tool as Surrogate CFD Neural Network (CFDSurNN). To have a viable tool, we systematically examine the steps that need to be taken for such a development and how each step could be started and later-on enhanced. The following sub-sections describe the essential steps to develop CFDSurNN and issues related to both the space-environment as well as diversities we encounter when it comes to space debris.
2. CFD Model Development for an Isolated Space-Debris
Existing space-debris come with different characteristics, such as: (1) shape, (2) size and (3) material types which are freely orbiting the Earth in a wide range of orbits, in terms of height and inclination. Planning a general DRD mission, therefore, seems extremely difficult, if not impossible. So, the challenge is to develop and verify a set of tools to evaluate a DRD mission: the first of which is the ability to compute object temperature rise during reentry. This has been done with the help of commercial CFD software ANSYS Fluent 14 [1]. However, computational fluid dynamic is among those disciplines which require powerful resources to provide dependable results. Nonetheless, they are still known as the simplest way to simulate different fluid flows; especially for reentry problems. With the help of a qualified grid, we are able to compute the temperature as well as debris velocity along its trajectory. In general, we need to find numerical solutions to an Axisymmetric, Turbulent, and Hypersonic down to Supersonic. This section describes the steps have been taken in this work:
(a) On the TSD Shape Different case studies with CFD models reveal that, for fairly small sized TSDs, regardless of the initial shape, the burning process together with chaotic tumbling during reentry will eventually turn a TSD to a fairly spherical shape. Of course, for very large TSDs, they need to be broken to small pieces, for this scenario to remain valid. This line of judgment allows us to study only spherical shapes in our CFD models, that is, we do not really need to know and model the actual TSD shape. Figure 1, schematically shows the concept of the so called TSD “Equivalent Sphere Diameter (ESD)”. All we need is its Equivalent Spherical Shape Diameter (TSDESD) that carries the same amount of mass as its relevance with the original TSD size (Figure 2). The TSDESD can simply be estimated by equating TSD mass with its equivalent spherical shape. For TSDs composing of more than one type of material we might use equivalent energy produced through burning; instead of the TSD mass. The current version assumes the material to be aluminum or its alloys The current CFDSurNN tool, therefore, considers only spherical shapes with different diameters. Figures 3 and 4 show some typical results for a different sphere sizes of 2.0, 5.0 and 10.0 cm in radius entering the EDA with different Mach numbers of M= 5 and M=10. We could simply repeat such calculations with other spherical shapes having different diameters and other Mach numbers. Obviously, we need to examine whether CFDSurNN can properly predict other diameters (TSD shapes).
(b) On the TSD Material Current version of CFDSurNN assumes all debris to be made of aluminum or its alloys. This simply, suggests that we could start RDM planning for those TSDs which are made of aluminum and its alloys only. Other debris which are a combination of aluminum alloys together and materials such as silicon or steel that have a greater melting point compare to that of aluminum (1600o C ) are not subject to the DRD missions; simply, because there is no guarantee that they could melt during the process. For TSDs composing of more than one type of material we might use equivalent energy produced through burning process; instead of the TSD mass.
(c) On the TSD Environment & Initial Orbit There are two distinguished characteristics that bind all varieties of TSDs together ;if we succeed to deorbit any. The first characteristic is related to the TDS tumbling; especially during its burning process as it falls down through EDA; which was described earlier.
The second characteristic is related to its journey down to the Earth’s surface. This journey has two distinctive parts of: (1) the part that starts from TSD’s initial orbit down to the start of Thermosphere (end of Mesosphere); and (2) the part that starts from edge of Mesosphere down to the Earth’s surface, known as Earth’s Dense Atmosphere (EDA). This segment covers a thickness approximately equal to 86 km above the Earth’s surface. The first part of the TDS journey until it reaches to the Mesosphere constitutes the initial conditions for the second phase of the journey within EDA; nonetheless, it is the second phase that contributes the most to the melting process and in-turn is affected by the initial conditions imposed on it by the first part. With Figure (6), the initial conditions that affect the validity of the model as well as precision of the results are: I-
The TSD entrance angle to the EDA with respect to an arbitrary reference
II-
The TSD Mach number while entering EDA
III-
The ambient temperature depending on Sun position
Extensive case studies conducted so far reveal that any deorbited TSD could enter EDA with a Mach number varying between M=12 to M=16 based on necessary imposed on the TSD for de-orbiting initiation; with the entrance angle varying between 90.0 down to 30.0 degrees (Figure 6) On the other hand, among all that could affect the results, the most important one is the ambient temperature; which could easily amount to 250 degrees Celsius depending on the Sun position. Nonetheless, due to the uncertainties involved we only consider the first and second parameters to develop the network. It is noted that Full Navier-Stokes equations keeps their authenticity (Knudesn number < 0.1) for EDA and we have prepared a UDF for the purpose of adjusting both forces and boundary conditions in each time step. Table (1) shows the setup used for computations.
(d) On the Effect of Trajectory in Initiating the Deorbiting Process It is well noted that any TSD orbiting the Earth has a total energy equivalent to the sum of its potential and kinetic ones. During the deorbiting, it is this energy that converts to heat and the non-conservative atmospheric frictional forces help the process. To extract the most heat out of TSD’s energy, we need to carefully investigate all possible trajectories. In general, relatively smaller initial de-orbiting angles result in longer trajectories which, in-turn, affect the heat-transfer within the TSD medium. Therefore, we must aim for conditions which results in the lengthiest possible trajectory that is achievable during deorbiting (Figure 6). Nonetheless, different investigations reveal that such trajectories are very hard to achieve (see Figure 7). Therefore, the current version of CFDSurNN ignores the effect of heat-transfer and time-dependency of the problem. However, we have been able to generate modest trajectories that match the range of preselected Mach numbers and entrance angles and we use them for the current work. Nonetheless, to assign boundary conditions we need to have initial temperature and velocity of the body while entering Mesosphere. Here, DSMC can be used as a useful and efficient numerical method in modeling fluid flows of rarefied gas and can provide results for hypersonic part of the journey above Mesosphere. The resulting Mach is then used to compute temperature in EDA.
(e) On the Turbulence Modeling Turbulence modeling is always a key issue in CFD simulations; especially in the reentry applications where the flow is turbulent and hence requires a turbulence model. In this work, we use Realizable k-ε which is considered not suitable for hypersonic flow regimes. AS a matter of fact, k-omega SST could be more justifiable for recognizing
separation point on the wall and its superior performance in both high and Reynolds number, but it hardly converges; which has not been acceptable for many cases we had to investigate. Obviously, any realistic experiment would be quite necessary to properly finalize the turbulence model.
(f) Grid Generation and Refinement: Grid refinement has been shown during the grid development process through examining the resulting convergence. This level was chosen to be less than 0.2% change in the convergence parameters, C D and CL. To achieve such goal, the grids had to be modified many times (Table 1). Case Id 1 2 3
Table (1) : Grid Refinement Number of Nodes Pressure force 32421 2488805 86310 1184082 167367 1245601
Error 50 % 4% < 0.5%
(g) Convergence Problem Another issue in CFD related problems is the so called “convergence problem”. This is especially critical for hypersonic regime as reentry journeys are and must be properly addressed with that mesh refinement to reach meaningful results. In order to prevent divergent problems, we exploited FMG initialization which is computationally inexpensive. (h) Verification of the CFD Model Table (2) shows the setup used for ANSYS-FLUENT. Verifying a CFD model set-up is a critical step that requires either experiments or rigorous analytical approach. Figures (8), (9) and 10-(a) through 10-(h) serves to fulfill this purpose. Table (2)- ANSYS FLUENT Setup Solver Solver Type Density-Based Energy On Realizable k-e, Standard wall Viscous function Material (air) Density Ideal-gas CP Polynomial Thermal Conductivity Polynomial Viscosity Sutherland Solution Methods Pressure velocity coupling SIMPLE Gradient Least Square Cell Based Pressure Standard Momentum First Order Upwind Energy First Order Upwind
Figure 1- Burning of a sharped edge object in EDA would lead to a spherical shape
Figure 2- Space-Debris Equivalent Circumventing Sphere Concept
Figure 3- FLUENT Results for different sphere diameters entering EDA with M=5
Figure 4- FLUENT Results for different sphere diameters entering EDA with M=10
Figure 5- Any TSD Journey has two phases above and below Mesosphere
Figure 6- Geometry definitions of journey through EDA
Figure 7- A realistic case of reentry with 5 degrees angle requires many trial and error for a given TSD
Figure 8- Verification of pressure and temperature over sphere comparing with analytical solution
Figure 9- Temperature, Pressure contours and streamlines of a sphere obtained by DSMC due to Swisscube situation in ionosphere.
a: Mach number contour for M=3
b: Temperature contour for M=3
c: Mach number contour for M=7
d: Temperature contour for M=7
e: Mach number contour for M=12
f: Temperature contour for M=12
g: Mach number contour for M=15
h: Temperature contour for M=15
Figure 10 (a-h) - Different Cases Tested to Validate Temperature Contours
3. CFDSurNN General Architecture Figure (11) shows the general architecture of investigating a burning process used to develop CFDSurNN. And Figure (12) shows how CFDSurNN is used to eliminate the need for such computations for an arbitrary TSD. Obviously, the main dilemma is whether the results of the developed CFDSurNNare dependable enough to be used for planning an RDM. Obviously, Swisscube cannot be considered as a good test-case due to its small size and we need to set-up experiments here on the Earth to gain enough confidence in our approach. On the other hand, besides the validity of the concept, there are many enhancements that could be built-into CFDSurNN to make it more dependable. Section 6 describes the possible enhancements.
Figure 11- The Architecture of the Burning Process at isolated case
Figure 12- The General Architecture of the RDM planning
4. Constructing Temperature Contours With CFDSurNN With Figure (6) and Table (2) the CFD toolset has been used to compute the surface temperature of the object travelling through EDA toward the Earth’s surface. In addition to the results out of ANFIS tool embedded in CFDSurNN, we could fairly easily construct temperature contours. These contours are then used to conclude whether a TSD is, in fact, suitable for forced-reentry.
Figure (12) shows typical temperatures computed with the help of ANSYS-FLUENT and Figure (13) shows the associated temperature contours generated by the CFDSurNN. Table (3)- Temperature Output Resulting from ANSYS-FLUENT Entrance Angle = 90 Mach = 15 Time 0 1.31 3.67 6.18 9.37 17.25 28.95 36.79 45.83
Temp. (k)
5200 2780 2017 1421 1022 779 639 412 362
Mach = 12 Mach 15.00 7.87 7.04 5.22 4.09 2.55 1.96 1.75 1.60
Time 0 1.64 3.9 6.9 10.7 20.05 33.69 42.25 52
Temp. (k)
3880 2384 1500 1077 935 580 497 438 258
Mach = 7 Mach 12.00 8.36 5.86 4.35 3.44 2.19 1.79 1.62 0.66
Time 0.00 2.77 6.50 11.92 20.29 39.45 61.45 72.45 83.66
Temp. (k)
1633 1034 814 577 404 402 468 394 367
Mach = 5 Mach 7.00 4.99 3.26 1.99 1.68 1.36 1.45 1.41 1.37
Time 0 3 8 15 24 34 55 77 87
Mach 7.00 5.03 3.67 2.76 2.16 1.51 1.34
Time 0.00 6.47 15.40 26.02 38.04 64.04 84.24 97.84 111.9
Mach 7.00 5.42 4.39 3.76 3.56 3.63 3.90
Time 0.00 8.46 22.54 62.22 96.70 111.7
Mach 7.00 6.56 6.78 9.77 13.61 14.33
Time 0.00 3.00 8.00 18.00 23.00 25.00
Temp. (k)
464 457 385 357 329 349 382 397 377
Mach 3.00 2.63 2.15 1.88 1.57 1.47 1.32 1.43 1.46
Entrance Angle = 70 Mach = 15 Time 0.00 1.40 3.45 6.45 11.55 31.55 41.55 51.55
Temp. (k)
5465 3275 2138 1460 1017 626 546 481
Mach = 12 Mach 15.00 10.37 7.45 5.50 4.14 2.87 2.70 2.90
Time 0.00 1.75 4.31 8.18 15.03 35.03 50.03 60.03
Temp. (k)
3880 2351 1661 1031 729 477 391 312
Mach = 7 Mach 12.00 8.31 5.94 4.29 3.19 2.22 1.91 1.89
Time 0.00 2.95 7.16 13.28 22.69 42.69 57.69
Temp. (k)
1633 1041 786 561 462 383 358
Mach = 5 Temp. (k)
464 386 339 327 337 380 386 370 357
Mach 3.00 2.11 1.72 1.48 1.41 1.35 1.50 1.50 1.53
Entrance Angle = 50 Mach = 15 Time 0.00 1.40 3.45 8.45 13.55 18.55 21.55
Temp. (k)
5465 3736 2833 2330 2525 3599 5595
Mach = 12 Mach 15.00 11.28 8.93 7.84 8.78 11.46 13.92
Time 0.00 1.75 5.75 11.75 18.60 23.60 26.60
Temp. (k)
3880 2668 1825 1784 1967 2450 4928
Mach = 7 Mach 12.00 9.03 6.67 6.33 7.85 9.82 12.65
Time 0.00 2.95 7.16 13.28 22.69 32.69 37.69
Temp. (k)
1633 1169 937 863 670 643 660
Mach = 5 Temp. (k)
464 377 343 292 224 227
Mach 3.00 2.34 1.82 1.23 1.10 1.13
Entrance Angle = 20 Mach = 15 Time 0.00 3.00 6.00 7.00
Temp. (k)
5465 5083 6787 9500
Mach = 12 Mach 15.00 13.94 17.27 18.41
Time 0.00 3.00 6.00 9.00
Temp. (k)
3880 3438 3983 5685
Mach = 7 Mach 12.00 10.85 12.25 15.39
Time 0.00 3.00 8.00 18.00 23.00 24.00
Temp. (k)
1633 1472 1549 2787 5231 6288
Mach = 5 Temp. (k)
464 451 425 426 428 429
Mach 3.00 2.91 2.79 2.76 2.80 2.83
Figure (13)- Computing TSD Surface Temperature at Specific Conditions with ANSYS-FLUENT
Figure (14)- Temperature Contours Resulting from CFDSurNN Based on Table (3) Data
5. Initial Investigation on Melting Contours Modeling a melting process in hypersonic regime is indeed a very cumbersome task. Moreover, available commercial CFD tools come short to be helpful to model such cases in a straightforward manner. Nonetheless, references [9] through [11] have been consulted for this purpose. In general, a complete model, which can predict temperature rise as well as burning during the reentry must regard (1) Two-phase flow, (2) Emerging porous zones and (3) Material Evaporations. Such a model is not only costly but requires enough resources to deliver acceptable results. In the absence of such resources, the current work, concentrates on the essential parts that helps us compare the effects of the reentry angles for a specific TSD. In fact, we have found that considering the “Conduction effects”
with moving boundaries to be sufficient for the relative evaluation of the reentry angles. Table (4) shows some results completed for TDS reentry angle of 30 and 90 degrees. As it is seen, high reentry angles are not as effective as low reentry ones for destructing a TSD through reentry burning. This is, in fact, an important achievement and clearly indicates that for more elaborate CFD models, we only need to investigate reentry angles less than 30 degrees.
Time (sec) 0 0.5 1 1.9 2.4 2.9
Altitude (m)
80000 78925 77988 76507 75825 75207
Table 4: Comparing debris burning possibilities for two different reentry angle TDS Entrance Mach = 15 Entrance Angle degree= 30 Entrance Angle Degree = 90 Total Heat Generated (KJ) Melted Volume (%) Time (sec) Altitude (m) Total Heat Generated (KJ) Melted Volume (%) 0.00 80000 0 1578960 0.00 1578960 17.28 78098 43.75 1125203 0.50 877654.4 33.10 69327 48.98 877654 3.50 81737 46.63 61102 49.39 596835 8.50 3213 61.87 49963 52.50 285043 18.50 30460 44129 53.05 237899 98.56 26.50 2046 30492 53.39 Object Melted 47.50 1463 22572 53.52 65.50 1029 18458 53.76 75.50 1854 14615 54.27 85.50 2700 10952 54.63 100.50 5561 9655 54.84 105.50 5644 9162 55.21 108.50 4737 8541 55.94 114.50 5747 Object Not Melted 7363 56.88
6. Discussion Space debris orbiting the Earth are currently seen as some potential threats to the future and to some extent to the existing satellites. Any forced-reentry of these objects, on the other hand, could also pose a threat to both human and facilities on Earth. Therefore, current version of CFDSurNN must be seen as the first step toward understanding of what a forced-reentry could actually offer. In this work, we are mainly concern to with the approach used to develop CFDSurNN and how it is used to provide temperature contours for a given TSD. To authenticate the CFD computations, however, we need to set-up some experiments to simulate some of hypersonic flows studied numerically. It so appears that technologies, such as Laser Induced Fluorescence (LIF), Low-Noise LiquidNitrogen-Cooled CCD and hypersonic wind tunnels are quite essential for final verification of the approach presented here. Besides, a thorough investigation regarding flow formulations for different layers of atmosphere from Ionosphere down to the Troposphere (Figure 5), with corresponding solver seem to be necessary for the serious role that reentry disposal encounter in the near future. We devote the final section to possible enhancements that could be considered.
7. Enhancements to the Existing CFDSurNN Considering the many hours of working with CFD tools to explore the difficulties of the reentry problem has resulted in many ideas to enhance the existing tool developed so far. These enhancements are discussed in the following subsections.
(a) Use of Calories instead of Temperature The existing CFDSurNN considers maximum temperature achieved in the reentry trajectory and ignores the effects of any insulating materials and in general heat-transfer between internal debris elements. As an enhancement, we could modify the model to consider material type together with effect of any insulating material while and heat
transfers within the debris. This enhances CFDSurNN to consider quite a wide variety of disposable elements released in the space environment.
(b) Enhancements to consider partial burning One of the important issues related to the reentry disposal is the consequence of incomplete burning of a deorbited space-debris. In fact, CFDSurNN attempts to find those cases that correspond to a compete burning during the reentry; which is not the case in great many of cases. A NN that predicts partial burning that might lead to the disintegration of the target debris is of great importance. Such debris could have a substantial footprint on the Earth and need to be studied very carefully. Obviously, such an enhancement is, first, a challenge to the field of Computational Fluid Dynamic; before being used by a surrogate code; as CFDSurNN. Nonetheless, we need to consider such enhancement; as not all deorbited debris will burn.
(c) Enhancement to the Neural Network Architecture It is well noted that using a neural network to decrease the huge volume of computations, as proposed in this work, is a new idea. Here, we need to validate the mixed approach used here, as: C1- Validating the CFD code for the melting process C2- Validating the Neural Network architecture to predict other cases. In the current version of the work we use Adaptive Neuro-Fuzzy Inference System (ANFIS); as offered by MatLab. Nonetheless, there might be other suitable architectures for the current applications; which is quite new and at its early stages of the development.
(d) Enhancement due to the Reentry Angle & Trajectories The degree of precision needed to deorbit a target space-debris is quite a challenging issue. Obviously, deorbiting a space-debris with higher angles requires energy and that means more cost. It is clear, on the other hand, that subtle deorbiting angles lead to longer trajectories in the dense atmosphere. For such trajectories, simulating the precise path becomes important; as they interest current air corridors used by commercial aircraft. In addition, the effects of atmospheric turbulence on the trajectory will also become important. Marinating some acceptable level of safety is therefore a must; especially if the number of reentry disposal missions increases in time. So, we might envision developing a comprehensive virtual environment which simultaneously simulates the burning process in a reentry disposal. Such a virtual environment would be a great tool to analyze all factors; including risks associated with incomplete burning during disposal
(e) Enhancement to the physics of Melting and Burning In the current work, we only consider converting internal energy to heat which leads to melting and finally evaporating the material; which the debris is made of. This approach is rather conservative; which might not be suitable for many cases. During the reentry, however, there is another factor that could be considered as a source of energy for burning. In fact, the debris material can act as a fuel during the reentry, based on its thermal properties. It is worth mentioning that, Aluminum is among those materials that can release its internal energy; while burning. Bringing this source of energy in combustion model together with the CFD model, would definitely lead to much
more accurate results. To consider melting effects, a complete model must regard two-phase flow, porous zone and evaporations; which requires enough resources for an acceptable results. As specified earlier, the current work, we have found conduction with moving boundaries to be sufficient for the relative evaluation of the reentry angles.
(f) Enhancement to methods of Solution For more refined mesh with great number of iterations and smaller time-steps, parallel processing is a must to develop an enhanced version of CFDSurNN in a logical period of time. Initial investigation reveals that a server characteristics of Table 5 is, in fact, essential to compute the burning process for wide variety of cases. Table 5: Server characteristics
CPU Core Memory
2x Intel Pentium4 3.0 GHz 2 M. (Quad core) 2x4 16.0 GB RAM
8. References [1]. ANSYS- Fluent I Tutorial, www.ansys.com/ [2]. Roethlisberger, Guillaume, et al. "Advanced methods for structural machining and solar cell bonding allowing high system integration and their demonstration on a Pico-satellite." (2008). [3]. Bozovic, Gavrilo, et al. "SwissCube: Development of an Ultra-Light and Efficient Inertia Wheel for the Attitude Control and Stabilization of CubeSat Class Satellites." 59th International Astronautical Congress. 2008. [4]. O'Connor, B. "Handbook for Limiting Orbital Debris. NASA Handbook 8719.14."National Aeronautics and Space Administration, Washington, DC (2008). [5]. Ailor, W., et al. "Analysis of reentered debris and implications for survivability modeling." 4th European Conference on Space Debris.Vol. 587. 2005. [6]. Mehrholz, D., et al. "Detecting, tracking and imaging space debris." ESA Bulletin(0376-4265) 109 (2002): 128134. [7]. Flow Analysis of an Atmosphere Reentry Vehicle Dr.B.Balakrishna1, S. Venkateswarlu2, P. Ravinder Reddy, International Journal of Engineering Research and Development, Volume 3, Issue 4 (August 2012), PP. 52-57 52 [8]. Wu, Ziniu, et al. "Space Debris Reentry Analysis Methods and Tools." Chinese Journal of Aeronautics 24.4 (2011): 387-395. [9]. Hejranfar, K., Kamali Moghadam, R., Esfahanian, V., “Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric laminar flows”, J. Aerospace Science and Technology, No. 12, P. 135-149, 2008. [10]. P. S. Schneider, “Hypersonic laminar–turbulent transition on circular cones and scramjet forebodies”, J. Progress in Aerospace Science, Vol. 40, Page 1-50, 2004. [11]. V. Alexiades and A.D. Solomon, “Mathematical Modeling of Melting and Freezing Processes”, Hemisphere Publishing Corporation, Washington, 1993.
