Predict Aerodynamic Drag of Spacecraft in Very Low Earth Orbit Using Different Gas-Surface Interaction Models

JIN Xuhong ,CHENG Xiaoli ,WANG Bing ,HUANG Fei

1 China Academy of Aerospace Aerodynamics,Beijing 100074 2 School of Aerospace Engineering,Tsinghua University,Beijing 100084

Abstract:The accurate prediction for aerodynamic drag of spacecraft in very low Earth orbit (VLEO) is a fundamental prerequisite for aerospace missions in VLEO.The present work calculates aerodynamic drag of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite using the test particle Monte Carlo (TPMC) method.The primary goal is to obtain a comprehensive understanding of surface pressure and skin friction on the spacecraft surface and assess the sensitivity of aerodynamic drag to the gas-surface interaction (GSI) models.Results indicate that surface pressure is mainly distributed on the front of the satellite body and panels while skin friction is primarily distributed on the sides.In addition,as the GSI model changes from diffuse to specular reflection,the total drag coefficient is reduced at operation altitudes above 170 km.Therefore,the satellite surface should be processed so carefully that the GSI remains far from diffuse reflection from the view point of the drag-reduce design.

Key words:satellite drag,gas-surface interaction,surface pressure,skin friction,free-molecular aerodynamics

1 INTRODUCTION

Spacecraft operating in very low Earth orbits (VLEO),typically classified as orbits approximately between 200 km and 500 km in altitude,have some significant advantages over those that operate in higher altitude orbits.In terms of Earth observation missions,the most significant benefit for optical imaging systems is that a reduction in orbital altitude improves spatial resolution for a similar payload specification.Therefore,for the purpose of measuring the gravity field and steady-state ocean circulation,the European Space Agency (ESA) launched three satellites into VLEO,namely Gravity Recovery and Climate Experiment(GRACE),Challenging Mission Payload (CHAMP)and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)at the beginning of this century.To accomplish the scientific objectives,the spacecraft mentioned above had to fly as low as possible to maximize sensitivity to the gravity field.In VLEO,non-gravitational aerodynamic forces,especially the aerodynamic drag is still significant due to the thermosphere,which is a major aerodynamic problem.Therefore,a fundamental prerequisite for aerospace missions in VLEO is the availability of an accurate prediction of aerodynamic drag of spacecraft in VLEO.

The many influences that affect aerodynamic drag of spacecraft in VLEO can be divided into three major categories:spacecraft geometry,atmospheric model,and spacecraft surface properties.Geometric considerations include parameters such as angle of attack and body shape,and can be expressed in terms of drag coefficients.Atmospheric influences include parameters such as composition,density,and temperature.Surface properties include gas-surface interaction (GSI) models.The calculation of drag coefficients is within the scope of free-molecular aerodynamics and the commonly used techniques include the FMFPI method (panel integral method based on free molecular flow theory),the direct simulation Monte Carlo (DSMC) method,and the test particle Monte Carlo (TPMC) method.Significant investigations have been conducted to achieve the proper modelling for atmospheric density,and some empirical atmospheric density models based on large data sets have been developed to describe variations of the atmospheric composition,density,and temperature with altitudes,latitudes,and longitudes.

However,in the available research into the aerodynamic drag of spacecraft in VLEO,GSI models are limited to diffuse reflection with complete momentum and energy accommodations,without reporting the effect of GSI on aerodynamic drag.It has been discovered that accommodation coefficients in VLEO usually range from 0.65 to 1,and GSI becomes closer to specular reflection as orbit altitude or spacecraft speed becomes higher.Therefore,it is instructive to calculate the aerodynamic drag using various GSI models and perform a comparative research into the results.

The present work calculates aerodynamic drag of spacecraft in VLEO using the TPMC method.The primary goal is to obtain a comprehensive understanding of surface pressure and skin friction on the spacecraft surface and assess the sensitivity of aerodynamic drag to the GSI models to provide some key data for the aerodynamic design of spacecraft in VLEO.

2 COMPUTATIONAL METHOD AND VALIDATION

2.1 Test Particle Monte Carlo Method

The TPMC method was pioneered by Davisin 1960 for calculation of molecular flow rates through pipes.Each test particle,representing a large quantity of real gas molecules,is sequentially fired into the computational domain.The velocity of each test particle is the vector sum of a constant free-stream velocity and a probabilistically determined thermal velocity.Intermolecular collisions are neglected,so the method is ideal for free-molecular flows.In contrast to the FMFPI method that is employed widely in satellite aerodynamics,the TPMC method can model flow shadowing and multiple reflections caused by complex spacecraft geometry.The distinguishing feature of the TPMC method is that the representative molecular trajectories are generated serially rather than simultaneously,so it has the benefits of higher computation efficiency and smaller storage requirement over the DSMC method.The TPMC method has been successfully applied to aerodynamics of spacecraft in VLEO by Klinkrad et al.and Jin et al.

By building interfaces of several state-of-the-art atmospheric models,we have integrated the atmospheric models into the TPMC codeand developed a general,parallel,and three-dimensional code,APSVLEO (Aerodynamic Properties of Spacecraft in VLEO),to predict aerodynamic properties of spacecraft operating in VLEO.The GSI model in the APSVLEO code is Maxwell model,which specifies a fraction

σ

,termed as the Maxwellian accommodation coefficient,of the incident molecules to be reflected diffusely after colliding with satellite surface;the remaining incident molecules reflect in a specular manner.The prominent features of the code include the automatic construction of a computational domain encompassing spacecraft of arbitrary geometries,the inclusion of adjustable atmospheric and GSI models,execution in a batch-processing manner,an unlimited parallel processing capability,and a comprehensive output of visual aerodynamic data.

2.2 Validation Case

Consider the GOCE satellite,it is composed of a satellite body,solar panel and stabilization panel.The GOCE satellite is the first Earth Explorer Core Mission of ESA’s Living Planet Program,whose mission objectives are the determination of the global field of geoid heights with an accuracy of 1 cm and of gravity anomalies with an accuracy of 10m/s,as well as to achieve this with a spatial resolution of 100 km half wavelength.The GOCE geometry and the coordinate system of reference are shown in Figure 1,with the origin in the center of mass.The lowest altitude at which GOCE operated was as low as 200 km,so free-stream conditions are determined by atmospheric parameters at this altitude,which are provided by the US Standard Atmosphere,1976.The free-stream and surface parameters are listed in Table 1.

Figure 1 The GOCE geometry

Table 1 The free-stream and surface parameters

The most important aerodynamic property of engineering interest in satellite aerodynamic design is the aerodynamic drag.Due to the uncertainty in GSI models,we consider two Maxwellian accommodation coefficients,i.e.,

σ

=1 and 0.6.Specifically,

σ

=1 means that all incident gas molecules reflect diffusely after colliding with satellite surface while

σ

=0.6 signifies that 60% of incident gas molecules undergo perfect diffuse reflections and the remaining 40% reflect specularly.Usually,aerodynamic drag is expressed in a dimensionless fashion as the drag coefficients C,i.e.,

where D is the aerodynamic drag,

ρ

is the free-stream density,

v

is the orbit speed.In addition,

A

=3.784 mrepresents the reference area and is equal to the projected area in the flying direction.Figure 2 shows the variation of aerodynamic drag with orbit speed ranging of 2 -17 km/s.It is evident that,for the two Maxwellian accommodation coefficients,i.e.,

σ

=1 and 0.6,drag coefficients decrease monotonically with orbit speed and converge asymptotically at a steady value when the orbit speed is large enough.Note that our results compare well with those of Koppenwallnerin Hypersonic Technology Gottingen (HTG),indicating the reliability of TPMC method.

Figure 2 The variation of drag coefficient of GOCE with orbit speed

3 AERODYNAMIC DRAG OF GOCE

After validating the TPMC method in this work,we now focus on the aerodynamic drags on the GOCE,aiming at gaining insight into the sensitivity of satellite drag to GSI models.In order to analyze the effect of the GSI model,we employ five Maxwellian accommodation coefficients,i.e.,

σ

=1,0.75,0.5,0.25,and 0.In addition,we consider a wide range of orbit altitudes from 120 to 600 km,which cover the orbit of most of spacecraft operating in VLEO and low Earth orbit (LEO).Freestream conditions are determined by atmospheric parameters at these altitudes,which are provided by the US Standard Atmosphere,1976.The specific orbit and surface parameters are tabulated in Table 2.

Table 2 The orbit and surface parameters

3.1 Surface Pressure and Friction Force Distribution

In this subsection,we analyze the surface pressure and the component of skin friction in the x-axis direction.Note that we consider the pressure coefficient and skin friction coefficient,which are the dimensionless quantities of surface pressure and skin friction,respectively.The two dimensionless quantities are defined as:

where

p

is the surface pressure,and

f

is the component of surface skin friction in the x-axis direction.The distributions of these two surface quantities at an altitude of 200 km are plotted in Figure 3.

Figure 3 Distributions of surface pressure and the component of skin friction in x-axis direction

According to Figure 3,the surface pressure is mainly distributed on the front surfaces of the satellite body and panels as a consequence of the intense collision between free-stream gas molecules and these surfaces.In addition,as GSI changes from diffuse to specular reflection,the aforementioned collision becomes stronger,producing a higher pressure on the front of the satellite.On the contrary,the skin friction on the sides of the satellite body and panels is dominant resulting from the strong friction between free stream and these sides.Similar to the surface pressure,GSI models also have an important relationship with skin-friction magnitude and distribution.With the reduction of the Maxwellian accommodation coefficient,the viscous friction between the free stream and satellite sides becomes weaker.Ultimately,as GSI turns to the pure specular reflection,all the collisions between the gas molecules and satellite surfaces are elastic and viscous friction disappears,so surface skin friction becomes zero.

3.2 Aerodynamic Drag

We now examine the aerodynamic drag of the GOCE for a variety of operational altitudes as the satellite travels through different altitudes.Figure 4 shows the variations of the total drag coefficient,pressure-drag coefficient and skin-friction-drag coefficient with operational altitudes from 120 to 600 km.The total drag coefficient is defined in Equation (1),and the pressure-drag coefficient and skin-friction-drag coefficient are defined as:

where

D

is drag component resulting from the surface pressure and

D

is drag component resulting from the surface skin friction.

According to the aforementioned definitions,it is evident that we have the relations as follows:

At first,we analyze the variations of drag coefficients with operational altitudes.Referring to Figure 4(a),it is apparent that pressure-drag coefficient is almost invariable with different operational altitudes,and the reason for this is that the free stream remains a free-molecular flow in the range of 120 -600 km.However,according to Figure 4(b),when the GSI is not the pure specular reflection,i.e.,

σ

＞ 0,the skin-friction-drag coefficient shows a considerable increase with operational altitudes,and this is attributed to the larger free-stream temperature with higher altitudes.Therefore,as the sum of pressure-drag coefficient and skin-friction-drag coefficient,the total drag coefficient increases monotonically with rising operational altitudes when the GSI is not the pure specular reflection,as is shown in Figure 4(c).Now,we turn to the effects of GSI models on drag coefficients.Figure 3(a),(c) and (e) show that the surface pressure on the satellite fronts experiences a substantial growth as the Maxwellian accommodation coefficient

σ

is lessened.Consequently,as the GSI model changes from diffuse to specular reflection,the pressure-drag coefficient rises steadily.On the contrary,as the GSI alters from diffuse to specular reflection,surface skin friction on the satellite sides shows a gradual increase,producing a smaller skin-friction-drag coefficient.Specially,in the case of pure specular reflection,i.e.,

σ

=0,skin-friction-drag coefficient will stay at zero,and this is an expected result because there is no exchange in tangential momentum.The aforementioned behavior indicates that the increase in Maxwellian accommodation coefficient

σ

has an opposite influence on pressure-drag and skin-friction-drag coefficients.Therefore,as the GSI model changes from diffuse to specular reflection,the total drag coefficient grows at lower altitudes (H＜165 km),while it is reduced at higher altitudes (H＞170 km).The orbits of most of spacecraft operating in VLEO and LEO are higher than 170 km,so from the view point of a drag-reduce design,the satellite surface should be processed carefully so that the GSI remains far from diffuse reflection.

Figure 4 Variations of aerodynamic drag with operational altitudes for different GSI models

4 CONCLUSION

In this work,the TPMC method is applied to the GOCE satellite to obtain a comprehensive understanding of surface pressure and skin friction on spacecraft surface and assess the sensitivity of aerodynamic drag to the GSI models.Some conclusions are drawn as follows:

1) In terms of aerodynamic drag,our TPMC result compares well with those reported in the literature,indicating that the TPMC method that we have developed has the ability to calculate the aerodynamic drag of the GOCE satellite.

2) Surface pressure is mainly distributed on the fronts of the satellite body and panels,and as GSI changes from diffuse to specular reflection,it becomes larger.

3) Skin friction is primarily distributed on the sides of the satellite body and panels,and with the alteration of GSI from diffuse to specular reflection,it is reduced.

4) As the GSI model changes from diffuse to specular reflectional,the total drag coefficient is reduced at operational altitudes above 170 km.From the view point of a drag-reduce design,the satellite surface should be processed carefully so that the GSI remains far from diffuse reflection.