a comprehensive numerical model investigating the thermal-dynamic performance of scientific balloon

Available online at www.sciencedirect.com

www.elsevier.com/locate/asr

ScienceDirect

Advances in Space Research 53 (2014) 325–338

A comprehensive numerical model investigating thethermal-dynamic performance of scientific balloon

Q. Liu *, Z. Wu, M. Zhu, W.Q. Xu

School of Aeronautic Science and Engineering, Beihang University, 37 Xueyuan Road, Beijing 100191, China

Received 21 June 2013; received in revised form 1 November 2013; accepted 6 November 2013Available online 18 November 2013

Abstract

The increase of balloon applications makes it necessary for a comprehensive understanding of the thermal and dynamic performanceof scientific balloons. This paper proposed a novel numerical model to investigate the thermal and dynamic characteristics of scientificballoon in both ascending and floating conditions. The novel model consists of a dynamic model and thermal model, the dynamic modelwas solved numerically by a computer program developed with Matlab/Simulink to calculate the velocity and trajectory, the thermalmodel was solved by the Fluent program to find out the balloon film temperature distribution and inner Helium gas velocity and tem-perature field. These models were verified by comparing the numerical results with experimental data. Then the thermal and dynamicbehavior of a scientific balloon in a real environment were simulated and discussed in details.� 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Scientific balloon; Thermal performance; Dynamic performance; Numerical model

1. Introduction

Scientific balloon is the ideal platform to carry out com-munication and observation missions in near-space envi-ronment (Colozza, 2003). A comprehensive and preciseunderstanding of the ascending velocity, ascending trajec-tory and the temperature distribution of the balloon filmis of vital importance for the designer and operator. Itcan help the designer to shorten the design time and reducecost, and assist the operator in determining the causes offailure and malfunctions during flight experiment anddeveloping the remedial actions.

Many investigations have been carried out on the ther-mal and dynamic performance of the scientific balloons.Kreith and Kreider (1974) established a simple but excel-lent numerical model to calculate the average temperature

0273-1177/$36.00 � 2013 COSPAR. Published by Elsevier Ltd. All rights rese

http://dx.doi.org/10.1016/j.asr.2013.11.011

* Corresponding author. Tel.: +86 010 82338049.E-mail addresses: [email protected] (Q. Liu), [email protected]

du.cn (Z. Wu), [email protected] (M. Zhu), [email protected](W.Q. Xu).

of skin and lifting gas, predict the trajectory of balloon andvalidate this model with experiment data. This model wasmarked as the starting point for the subsequent research.Carlson and Horn (1983) developed a new trajectory andthermal model to analyze the average temperature of bal-loon skin and lifting gas during ascending, investigate theflight trajectory with the impact of ballasting, ventingand valving. Stefan (1983) further studied the thermalbehavior of a high-altitude airship by dividing it into atop half and a bottom half, and obtained the average tem-perature of these two parts. Farley (2005) constructed themotion model for a high altitude balloon and predictedits ascent trajectory in both vertical and horizontal direc-tions. Dai et al. (2012) investigated the thermal perfor-mance of a high altitude balloon with higher accuracy bydividing the balloon film into small elements and buildinga thermal model for each of the elements.

As for the temperature distribution of the scientific bal-loon, Louchev (1992) developed a steady-state thermalmodel of hot air balloon to calculate the shell temperaturefield and the average temperature of the lifting gas in

rved.


mailto:[email protected]






http://crossmark.crossref.org/dialog/?doi=10.1016/j.asr.2013.11.011&domain=pdf

326 Q. Liu et al. / Advances in Space Research 53 (2014) 325–338

different conditions. Kenya et al. (2003) conducted anumerical and experimental investigation on the tempera-ture distribution of different airships at different altitude.A thermal performance model on NASA’s (National Aero-nautics and Space Administration of American) scientificballoons was proposed by Franco and Cathey (2004) forinvestigating the temperature distribution of balloon filmat floating conditions neglecting the convection effect. Xiaet al. (2010) established a transient numerical model forcalculating the temperature distribution on balloon filmsat floating conditions. The model employed a simplifiedradiation model and experiential convective heat transfercoefficients. Wang and Yang (2011) proposed a transientnumerical method to study the temperature distributionalong an airship envelop and evaluate natural convectioninside the airship.

However, little work has been done to examine the ther-mal and dynamic characteristics of the scientific balloon inone model. The primary purpose of this study is to developa comprehensive numerical model that can investigate thethermal-dynamic performance of scientific balloon in bothascending and floating conditions. The work includingdeveloping the dynamic and thermal models, creation ofthe simulation platform, simulation of ascent velocity,analysis of ascent trajectory, investigates the film tempera-ture distribution and exploration of the Helium gas flowinside the balloon. The dynamic model was calculatednumerically by a computer program developed withMatlab/Simulink, and the thermal model is solved by theComputational Fluid Dynamic (CFD) method. The accu-racy of these models is verified by comparing the simula-tion data with the experimental data. Then the dynamicand thermal performance of a scientific balloon in a realenvironment were simulated and discussed in details.

Fig. 1. Solar radiation direction.

2. Environment model

2.1. Atmosphere model

The scientific balloon will floats at height 30 km. Temper-ature, pressure and density of the atmosphere changes withaltitude. Atmosphere model (The U.S. Standard Atmo-sphere, 1976) employed in this paper uses the followingsea-level values that have been standard for many decades:

Temperature – 288.15 K, Pressure – 101325 Pa, Density– 1.225 kg/m3

The temperature and pressure of the atmosphere fromthe sea-level up to 32 km were calculated by the followingformulas, while the density of the air is determined by theideal gas law.

Temperature:

T air ¼288:15� 0:0065 � h 0 < h 6 11000m

216:65 11000m < h 6 20000m

216:65þ 0:0010 � ðh� 20000Þ 20000m < h 6 32000m

8><>:

ð1Þ

Pressure:

P air ¼101325 � ðð288:15� 0:0065 � hÞ=288:15Þ5:25577 0 < h 6 11000m

22632 � expð�ðh� 11000Þ=6341:62Þ 11000m < h 6 20000m

5474:87 � ðð216:65þ 0:0010 � ðh� 20000ÞÞ=216:65Þ�34:163 20000m < h 6 32000m

8><>:

ð2Þ

2.2. Solar radiation model

The position of the sun in the sky is expressed in termsof the solar altitude angle b above the horizontal and thesolar azimuth angle / measured from the south. The coor-dinate system was shown in Fig. 1. The solar radiationdirection unit vector ns could be described as (ASHRAEHandbook, 2001):

ns ¼ �cosbcos/ � i� cosbsin/ � j� sinb � k ð3Þ

where i, j, and k are the positive unit vector along the direc-tions of south, east and top, respectively. The solar altitudeangle b and the solar azimuth angle / could be calculatedby:

b ¼ arcsinðcos L cos d cos H þ sin L sin dÞ ð4Þ

/ ¼ arccossin b sin L� sin d

cos b cos Lð5Þ

Here L denotes the local latitude, d and H represents the so-lar declination and hour angle.

The direct solar irradiation ID at the earth’s surface on aclear day is given by:

ID ¼ A=eB= sin b ð6Þ

where A indicates the apparent solar irradiation above theatmosphere, B is the atmospheric extinction coefficient(ASHRAE Handbook, 2001).

The atmosphere diffuse irradiance IAtm is given by:

IAtm ¼ C � ID � 1þ cosrð Þ=2 ð7Þ

where C is a constant within a period of one month (ASH-RAE Handbook, 2001), r is the tilt angle of the surfacefrom horizontal.

The earth’s surface reflected irradiance IRef is given by:

IRef ¼ ID � ðC þ sinbÞ � Re � 1� cosrð Þ=2 ð8Þ

Q. Liu et al. / Advances in Space Research 53 (2014) 325–338 327

where Re is the reflectivity of the earth’s surface (ASHRAEHandbook, 2001).

Fig. 2. Thermal environment and loaded forces of the balloon.

3. Dynamic and thermal models

During the ascending process, the atmospheric pressuredecreases with altitude, this leads to the volume of theballoon expanding before reaching its maximum value.Balloon inner gas volume obeys the ideal gas law asdescribed below:

V ¼ mHeRHeT He=P He ð9Þ

As the volume of the balloon is identical to that of the in-ner gas, the diameter of the balloon can be calculated as:

d ¼ 1:383V 1=3 ð10Þ

When the balloon reaches its maximum volume, there willbe a differential pressure between inside and outside of theballoon, and then the Helium gas in the balloon will bevent through a valve regularly to keep the differential pres-sure acceptable. The flow of the gas through the valvedepends on the differential pressure across the area inter-face DP valve, the area of the valve cross section Avalve, thedensity of the gas, and the discharge coefficient C. Thevelocity of the gas is given by the following equation:

V flow ¼ Cð2DP valve=qHeÞ0:5 ð11Þ

This leads to the mass differential equation of the inner He-lium gas as follows:

dmHe

dt¼ �CAvalveð2DP valve � qHeÞ

0:5 ð12Þ

Here, the discharge coefficient C should be less than 1.0and is approximately 0.6 for a sharp edged hole (Farley,2005).

3.1. Dynamic models

The main loaded forces of the balloon are buoyantforce, aerodynamic drag force and gravity force, whichare diagramed in Fig. 2.

The buoyant force F , aerodynamic drag force D, andgravity force G can be calculated as following:

F ¼ qairVg

D ¼ �1=2qairCdAtopvrjvrjG ¼ ðmfilm þ mHe þ mpayloadÞg

ð13Þ

where qair is the density of the air which can be determinedby the ideal gas law, g represents the gravitational acceler-ation, Cd is the drag coefficient, vr depicts the relative veloc-ity between the balloon and wind, and mfilm, mHe, mpayload

represents the mass of the film, Helium and payload,respectively. Atop is the reference area of the balloon andcan be calculated from (Farley, 2005):

Atop ¼ p=4 � d2 ð14Þ

After launch, the scientific balloon begins to fly freely. Ifvwlon, vwlat, vwh are the wind’s absolute velocity componentsin longitude, latitude and altitude directions, and vlon, vlat,vh are the balloon’s absolute velocity components in thesethree directions, then the relative velocity components inthese three directions between the balloon and wind canbe calculated by (Farley, 2005):

vrlon ¼ vwlon � vlon

vrlat ¼ vwlat � vlat

vrh ¼ vwh � vh

ð15Þ

The magnitude of the relative velocity is:

vr ¼ ðv2rlon þ v2

rlat þ v2rhÞ

1=2 ð16Þ

Compared to the volume of the balloon, the payload canbe treated as a mass point, and the influence of the swingof the payload exerted on the balloon can be neglected.So the dynamic differential equations of the balloon in lon-gitude, latitude and altitude directions are:

Mtot€Slon ¼ D � mrlon=mr

Mtot€Slat ¼ D � mrlat=mr

Mtot€h ¼ F þ D � mrh=mr � G

ð17Þ

Here the Slon, Slat and h denotes the displacement of theballoon in longitude, latitude and altitude directions,respectively. Mtot is the total mass of the balloon systemwhich is made up of two parts, the real mass and virtualmass. The virtual mass is to take into account the massof air that is dragged along with the balloon, with a virtualmass coefficient. The total mass is defined by:

Mtot ¼ mfilm þ mHe þ mpayload þ CvirqairV ð18Þ

Here Cvir is the virtual mass coefficient and usually assumedfrom 0.25 to 0.5 (Farley, 2005).

The relationship between the displacement and absolutevelocity of the balloon are:


€Slon ¼ dvlon=dt€Slat ¼ dvlat=dt€h ¼ dvh=dt

ð19Þ

3.2. Thermal models

The balloon will confront a complicated thermal envi-ronment at different altitudes from ground to the ceilingaltitude. The main factors that will influence the thermalperformance of the balloon are diagrammed in Fig. 2. Theyare the Sun, the Earth, the Space and the Atmosphere.

The external heat fluxes include the direct solar radia-tion, atmosphere diffuse solar radiation, solar radiationreflected by the Earth’ surface, the infrared radiation fromthe outer film to the space and the Earth’ surface, and theconvective heat transfer between the outer film and air.Inside the balloon, heat fluxes include the convective heattransfer between the inner film and Helium gas, the infra-red radiation among the balloon film elements.

3.2.1. The balloon film thermal model

The balloon film can be divided into N surface elements,and each element can be treated as a gray and diffuse radi-ation plane. The temperature change rate of the film ele-ment i can be derived from the transient energy-balanceequation (Dai et al., 2012):

dT f ;i

dt¼

QD;i þ QAtm;i þ QRef ;i þ QIRE;i þ QIRI ;i þ QCE;i þ QCI ;i

Mf ;icf

ð20Þ

where Mf ;i is the mass of the film element i, cf is the specificheat for film material. QD;i is the absorbed direct solar radi-ation flux, QAtm;i is the absorbed diffuse solar radiation flux,QRef ;i is the absorbed reflected solar radiation flux, QIRE;i isthe net gain of external infrared radiation flux, QIRI ;i is thenet gain of internal infrared radiation flux, QCE;i is the netgain of external convective heat transfer flux, and QCI ;i isthe net gain of internal convective heat transfer flux.

3.2.1.1. Direct solar radiation. The absorbed direct solarradiation of the surface element i is given by:

QD;i ¼ d1 � a � Af ;i � ID � jns � nf j ð21Þ

where a is the solar absorptivity of the film material, Af ;i isthe area of the element, ns is the solar irradiation unit vec-tor, nf is the normal vector of the outer surface of the filmelement and d1 is the index which takes into account theself-shadowing of the balloon film from the direct solarradiation, which is defined as:

d1 ¼1 ns � nf < 0

0 ns � nf P 0

�ð22Þ

The absorbed diffuse solar radiation:

QAtm;i ¼ a � Af ;i � IAtm ð23Þ

The absorbed reflected solar radiation:

QRef ;i ¼ d2 � a � Af ;i � IRef ð24Þ

Here, d2 is the index which takes into account the self-shad-owing of the balloon film from the reflected solarirradiation.

d2 ¼1 ne � nf < 0

0 ne � nf P 0

�ð25Þ

where ne is the normal unit vector of the earth’s surface. Itis assumed that the curvature effect of the earth’s surface inview is ignored and the surface is treated as an immenseplane with the normal unit vector ne towards upward.

3.2.1.2. Infrared radiation. The net gain of external infra-red radiation includes earth and atmospheric infrared con-tributions. It can be calculated by the following equation:

QIRE;i ¼ eAf ;ir½uðT 4e � T 4

f :iÞ þ ð1� uÞðT 4b � T 4

f :iÞ� ð26Þ

where e is the emissivity of the film material, r is the Ste-fan–Boltzmann constant, u is the view factor from the ele-ment to earth, T e is the temperature of earth’s surface in K,T b is the sky equivalent temperature in K, which can be cal-culated from (Shi et al., 2009):

T b ¼ 0:052T 1:5Atm ð27Þ

where T Atm is the temperature of atmosphere.The net gain of internal infrared radiation:

QIRI ;i ¼ Af ;iðGi � J iÞ ð28Þ

where Gi is the infrared radiation falling on element i, J i isthe infrared radiation away from element i. And J i can beexpressed as the sum of radiation emitted from the internalsurface and the irradiated energy reflected by it. Gi and J i

can be calculated as:

Gi ¼ ðJ i � erT 4f ;iÞ=ð1� eÞ ð29Þ

J i ¼ erT 4f ;i þ ð1� eÞ

XN

j¼1

J jX i;j ðj ¼ 1; 2; :::;NÞ ð30Þ

Here, X i;j is the view factor from the internal surface of ele-ment i to element j.

3.2.1.3. Convective heat transfer. The external convectiveheat transfer between the outer surface of the elementand atmosphere can be forced convection if there is windor natural convection if there is no wind. The internal con-vective heat transfer between the inner surface of the ele-ment and internal gas is natural convection.

The external convective heat transfer of the element ican be expressed as:

QCE;i ¼ hCEAf ;iðT Atm � T f ;iÞ ð31Þ

With the heat transfer coefficient calculated by (Incroperaand DeWitt, 1996):


hCE ¼ð2þ 0:47Re0:5Pr1=3

air Þkair=d Re 6 5� 104

ð0:0262Re0:8 � 615ÞPr1=3air kair=d 5� 104 < Re 6 108

(

ð32Þ

The internal convective heat transfer of the element i canbe expressed as:

QCI;i ¼ hCIAf ;iðT He � T f ;iÞ ð33Þ

With the heat transfer coefficient calculated by (Morris,1975):

hint ¼0:59 � kHe=d � Ra1=4 104

6 Ra 6 109

0:13 � kHe=d � Ra1=3 109 < Ra 6 1012

(ð34Þ

where kair and kHe represent the thermal conductivity coef-ficient of air and Helium, respectively, Prair denotes thePrandtl number of air. Take the diameter of the balloond as the reference length.

3.2.2. Helium thermal model

The temperature change rate of the internal Helium isformulated on the adiabatic expansion response modifiedwith internal convection with the balloon film (Farley,2005):

dT He

dt¼

QCI ;He

cvmHeþ ðc� 1ÞT He

1

mHe� dmHe

dt� 1

V� dV

dt

� �ð35Þ

Here, QCI;He is the internal convective heat gain of theHelium and can be calculated by:

QCI;He ¼ �XN

i¼1

QCI ;i ð36Þ

Here, c is specific heat ratio, cp and cv denote specific heatat constant pressure, specific heat at constant volume ofHelium, respectively.

4. Simulation method

The simulation platform consists of two parts. One is aprogram developed with Matlab/Simulink to solve thegeometry model, the dynamic model, the thermal modeland calculates the ascending velocity and trajectory of theballoon. The other is based on CFD/Fluent to solve thegoverning equations in the computational zone to calculatethe balloon film temperature distribution and Helium gasvelocity and temperature field.

The flow chart of the simulation platform is shownin Fig. 3. When the Matlab/Simulink program is run-ning, it can output environment conditions, balloongeometry, solar position, radiation heat fluxes, andconvective heat transfer coefficient as boundary condi-tions to CFD/Fluent. The CFD/Fluent program thendiscretizes the computational zone, loads boundaryconditions, and solves governing equations and postprocess results.

4.1. Matlab/Simulink simulation

The classic fourth-order Runge–Kutta scheme isemployed to solve the energy equations of the balloon filmand Helium gas.

The flow chart of the program for the dynamic model isshown in Fig. 3. Firstly, suppose that at altitude h, the vol-ume of the balloon is V , the temperature of Helium gas wascalculated by solving the thermal equations of balloon filmelements and Helium gas. Secondly, calculate the velocityand displacement of the balloon according to the dynamicmodel of the balloon. Finally, solve the geometry modeland get the volume of the balloon at a new altitude. Duringthe iterative process, the temperature of the Helium gas issupposed to be unchanged in a time step, but the pressureof the Helium gas changes with altitude.

4.2. Computational Fluid Dynamic simulation

The control volume method was adopted in the CFD/Fluent simulation and hexahedral meshes were used to dis-cretize the calculation zone.

The transient energy, mass and momentum governingequations in the calculation zone were described as follows:

Transient energy:

@ðqcpT Þ@t

þ divðqcpuT Þ ¼ divðk � grad T Þ þ ST ð37Þ

Mass:

@q@tþ divðquÞ ¼ 0 ð38Þ

Momentum:

@ðquÞ@tþ divðqu � uÞ ¼ divðl � grad uÞ � @P

@Xþ Su ð39Þ

where T is temperature; q is density; cp represents the spe-cific heat at constant pressure; t represents time; u depictsthe velocity vector of fluid; k denotes the thermal conduc-tivity; ST indicates the source energy; l denotes the fluidviscosity; P is the pressure and X denotes the coordinatesvector.

The coupled equations were solved by the Semi-ImplicitMethod for Pressure-Linked Equations (SIMPLE) algo-rithm which is based on density (Patankar, 1980). Forthe convection term and diffusion term, the spatial discret-ization method was second order, and this could provideefficient accuracy (Leonard, 1997).

5. Model validation

5.1. Dynamic model validation

Flight experimental data from a 56,790 m3 super pres-sure balloon developed by National Aeronautics and SpaceAdministration’s Balloon Program Office (Cathey, 2009)was used for validating the accuracy of the dynamic model.

Fig. 3. Flow chart of the simulation platform.

Fig. 4. Altitude comparison of the predicted data with experiment data.


The flight experiment took place on June 22, 2008 from Ft.Summer, New Mexico. The balloon was designed to flightat about 30.5 km with a suspended load of 295 kg, at thefloating altitude the balloon is 54.47 m in diameter and33.36 m in height, and a total of 109 kg of ballast weredropped in several increments to adjust the altitude asthe balloon loses buoyance due to outgassing.

It was assumed that the atmosphere environment is thestandard atmosphere with fair sunshine conditions and thepartially inflated balloon remains a scaled pumpkin shape.The balloon film is divided into 9254 surface elements bythe software ICEM CFD. The balloon film solar absorptiv-ity is 0.06 and the infrared emissivity is 0.24. Given that thesmall area of the load is too small compared to the area ofthe balloon, the effect of the load area was neglected andthe load was treated as a mass point.

Fig. 4 compares the present model predicted altitudedata with the experiment measured data. The picture showsthat in the ascending process there exist some discrepancybetween them, but in floating conditions they agree wellwith each other.

The discrepancy between the data in the ascending pro-cess may be attributed to the assumptions and simplifica-tions of the model. Firstly, the atmosphere above thelaunch site may not be identical to the standard conditions.Secondly, there were a number of undeployed areas in theballoon as it ascended, but the model assumed that the bal-loon was fully deployed during the ascending process, thisassumption may cause errors in calculating the balloondiameter which directly affect the buoyant and aerody-namic drag force of the balloon, and introduce error tothe velocity and trajectory of the balloon. In the floating

process, the balloon was pressurized and fully deployed,this makes the calculation of buoyant and aerodynamicdrag force of the balloon correct with high accuracy, sothe two sets of data agree well with each other.


5.2. Thermal model validation

The ground experiment data of a 35 m long airshipequipped with 130 m2 photovoltaic arrays, developed byAerospace Laboratory of Japanese (Kenya et al., 2003),were used to validate the accuracy of this thermal model.

The ground test was performed in June 2003, with thin-film thermocouples used to measure the temperatures ofenvelope and inner gas at various locations. The tempera-ture of the outside air was 299 K, and wind speed wasabout 1 m/s to 7 m/s.

The same boundary conditions for the ground experi-ment were employed in this simulation, the solar absorptiv-ity of the envelope is 0.33 and the IR emissivity is 0.88, thesolar absorptivity of the photovoltaic arrays is 0.93 and theIR emissivity is about 0.9, the ground reflectivity is about0.3 (Min and Guo, 1998). Hexahedral meshes were usedto discretize the computational zone, and a transient simu-lation was performed using the thermal model developedabove.

Solar radiation and wind velocity are the major factorsthat influence the temperature of the airship, as theychanges with time, the location and temperature value ofthe maximum temperature area of the airship changesaccordingly. The number of the thermocouples is limitedand their locations are fixed, so they cannot provide suffi-cient information about the temperature changes of the air-ship. But the numerical model can present detailedinformation of the temperature distribution of the airship,it can trace the temperature value and location of the high-est temperature area.

Fig. 5 shows the temperature data calculated by thismodel and the experimental results, the calculated data

Fig. 5. Temperature comparison of the

matched well with the measured results in trend.However, there exist some discrepancies between thetwo sets of results. Firstly, the fluctuations of experimentdata are larger than that of the numerical data. Secondly,the numerical and experimental deviations of the maxi-mum temperature data are larger than the averagetemperature data. Thirdly, for the maximum temperaturedata, the deviations of the PV-array are larger than theenvelope.

The thermocouple was put on the airship with a piece ofenvelope material covered, this introduces errors in mea-suring the temperature data, as the material thicknessand radiation properties of the PV-array and envelopehas changed. But these parameters can be set to be uniformin the simulation model, so the fluctuations of the experi-mental data are larger than the numerical data.

When the maximum temperature area changes withtime, the fluctuations of measured data are large, whilethe numerical data are accurate and steady, so thedeviations between the numerical and experiment dataof the maximum temperature are large. The averagingprocess of the measured maximum temperature data canreduce the fluctuations, so the deviations between thenumerical and experiment data of the average tempera-ture are small.

The absorptivity of PV-array is larger than the envelope,and a layer of 7 mm thick insulation boards are installedbetween the PV-arrays and the envelope, so the tempera-ture of the PV-array is higher than the envelope. As theenvironment changes, the temperature fluctuations of thePV-arrays will be larger than that of the envelope. So forthe maximum temperature data, the deviations of thePV-array are larger than the envelope.

calculated data with measured data.

Fig. 6. Measured atmosphere temperature.

Fig. 7. Measured atmosphere pressure.


6. Performance in a real environment

6.1. Real environment

A real environmental model is needed to calculate thethermal-dynamic performance of the scientific balloon.The atmosphere temperature, atmosphere pressure andwind data were measured above Beijing and covered analtitude range from ground to 32 km, at 8 am on August15th 2010.

6.1.1. Real atmosphere modelThe measured temperature and pressure data of the

atmosphere are slightly different from the standard atmo-

sphere (The U.S. Standard Atmosphere, 1976) because ofthe location and weather conditions of the test site. Themeasured atmosphere temperature and pressure data areshown in Figs. 6 and 7, respectively.

6.1.2. Real wind model

The magnitude and direction of wind varies with thealtitude. In general, wind velocity can be divided into lon-gitude and latitude components, and the components werecalculated according to the magnitude of the wind and theangle to the south. For longitude component, the southdirection wind is defined as positive, and for latitude com-ponent, the west direction wind is defined as positive. Thewind data is shown in Fig. 8.

Fig. 8. The measured wind data.

Table 1Parameters of the scientific balloon.

Parameters Value

Maximum volume, m3 1,132,674Diameter, m 144.2Area, m2 53678Floating altitude, km 30Absorptivity 0.09Emissivity 0.28

Fig. 9. Hexahedral meshes and coo


6.2. Results and discussion

After validation of the dynamic model and thermalmodel, these models are used to investigate the thermal-dynamic performances of a zero pressure scientific balloon.The balloon film is made of polyethylene, the designparameters of the balloon are shown in Table 1. Assumethat the balloon was launched in Beijing, China at 8 amon August 15, 2010.

Before simulation, a grid-independence test had beenperformed for two computational meshes with 192,075

rdinate system of the balloon.

Fig. 10. Ascent velocity.

Fig. 11. Ascent 3-D trajectory.

Fig. 12. Helium gas average and film maximum temperature.


Fig. 13. Temperature distribution on balloon film. (a) 8 am (b) 9 am (c) 10 am (d) 11 am.


and 330,799 hexahedral cells, respectively. The differencesin both maximum temperature and minimum temperatureof the film were less than 0.6%. Therefore, the mesh with192,075 hexahedral cells was employed for the simulation.Fig. 9 shows the meshes and coordinate system used in thissimulation, the positive X direction denotes south and posi-tive Y direction denotes east.

6.2.1. Ascending velocity and trajectory

Fig. 10 shows the velocity profile of the balloon in bothascending and floating processes. The average climb rateduring ascending is about 4.2 m/s. The rate of climbincreases extremely rapidly from zero to 4 m/s at the begin-ning, then decrease to 3.5 m/s in about 10 min because thehigh velocity of the balloon causes the aerodynamic dragforce increases strongly. After that, the velocity increases

slowly to 4.3 m/s at 8:40 am, this is because of the decreaseof air density which caused the increase of the aerodynamicdrag force less than the increase of the buoyant force. Afteranother velocity decrease and increase, the balloonapproached the design altitude at peak velocity 4.8 m/sand then dropped drastically to nearly zero. Acted by theinertia and aerodynamic drag forces, the balloon velocityoscillates with decreasing in amplitude and finally reachessteady state at 10:30 am.

Fig. 11 shows the 3-D trajectory of the balloon duringascending. The position of the balloon has changed fromthe launch site (40�N, 116�E, 0 km) to floating point(39.84�N, 117.01�E, 30 km) when it reaches the design alti-tude. Because of the large volume of the balloon and theaerodynamic drag force, it drifts with the wind in a nearlyhorizontal direction. The trajectory of the balloon turns at

Fig. 14. Average velocity of Helium inside the balloon.


an altitude near 20 km because the wind changes its direc-tion there.

6.2.2. Film temperature distribution

Solar radiation and environment conditions change withtime, which makes the temperature of the balloon film andthe Helium gas change correspondently. Fig. 12 presentsthat the maximum film temperature changes in the sametrend with the average Helium temperature in the wholeprocess, but much higher than the latter one.

The maximum temperature area locates at the upperpart of the balloon and moves from east to south as thesolar position changes with time. Fig. 13(a)–(d) shows thetemperature distribution of the balloon film at 8, 9, 10and 11 am of the day. For quick readability, the size ofthe balloon in those four pictures had been set equal,though they are not equal actually.

At 8 am, the balloon was placed at the launch site andready to launch. Fig. 13(a) depicts that the maximum tem-perature was 304 K and the temperature difference was10 K. At 9 am, the balloon reached the altitude of 13 kmwith the volume expanding swiftly. Fig. 13(b) reveals thatthe maximum temperature was 230 K, which is the lowestone in those four situations, but the temperature differencewas 14 K, the highest one among them. At 10 am, the bal-loon approached 30 km with velocity near 4.8 m/s.Fig. 13(c) shows that the maximum temperature of the bal-loon film was 259 K. At 11 am the balloon floats at 30 km,Fig. 13(d) shows that the maximum temperature of the bal-loon film was 280 K.

Compare the boundary conditions at 10 am and 11 am,the solar altitude angle is smaller, but the relative velocitybetween balloon film and air is larger, so the highest temper-ature at 10 am was about 21 K lower than that of the 11 am.

6.2.3. Helium velocity and temperature fieldThe internal Helium flow and temperature field were

strongly affected by the film temperature distribution, the

volume of the balloon and the volume expansion rate.The larger the temperature difference of the balloon, thelarger the volume and the volume expansion rate can resultin stronger Helium flow. Fig. 14 demonstrates the averagevelocity magnitude of the Helium gas inside the balloon inthe whole process. The average Helium velocity was about0.22 m/s at 8 am when the volume of the balloon wassmallest; the average Helium velocity was about 0.62 m/sat 9:30 am when the balloon volume was relatively largerand experiencing a rapid volume expansion. In the floatingprocess from 10 am to 11 am, the average Helium velocitywas about 0.53 m/s and increases slowly with time.

The Helium gas was heated through convective heattransfer with the balloon film, and then was forced to flowalong the balloon film by the buoyancy, to form flow circleinside the balloon. As the temperature distribution of theballoon film and the volume of the balloon changes, theHelium gas temperature and velocity field distributionchanges as well.

Fig. 15(a)–(d) shows the cross section velocity and tem-perature field of the balloon at 8, 9, 10 and 11 am of theday. This cross section area is the OYZ plane in Fig. 9,and the X component is invisible from this view angle.For quick readability, the size of the balloon cross sectionin those four pictures had been set equal, though they arenot equal actually.

Fig. 15(a) shows that at 8 am, the maximum tempera-ture of the Helium gas was 304 K, and the higher temper-ature zone located at the east side of the upper part. TheHelium gas in the high temperature zone expands andwas forced to flow along the film to form a big counter-clockwise circle inside the balloon. Fig. 15(b) reveals thatat 9 am, the maximum temperature of the Helium gaswas about 230 K, and the velocity was rather chaotic, thismay be attributed to the fact that the balloon was experi-encing a high ascend speed and a rapid volume expansion.Fig. 15(c) and (d) shows the maximum temperature ofHelium gas at 10 am and 11 am was 259 K and 279 K,

Fig. 15. Velocity distribution on cross section of the balloon. (a) 8 am (b) 9 am (c) 10 am (d) 11 am.


respectively, the high temperature zone located at the cen-tral and upper part inside the balloon. The Helium gas inthe high temperature zone expands and was forced to flowdown, where near the balloon film the fluid was forced toflow up along the film. In this way, two flow circles inreverse direction were formed inside the balloon. The tem-perature of the Helium gas rise about 20 K because of thetemperature rise of the balloon film.

7. Conclusion

A comprehensive numerical model was developed toinvestigate the detailed thermal and dynamic performancesof scientific balloon in both ascending and floating condi-tions. The dynamic and thermal models have been vali-

dated separately. Our results proved that this model isable to provide accurate results in complicated boundaryconditions. Detailed simulation has been carried out for azero pressure scientific balloon launched from Beijing ina real environment. From the simulation results, the mainconclusions were drawn:

1. The balloon drifts with the wind in nearly horizontaldirection, so the ascending trajectory of the balloon shallturn when the wind direction changes. Once the windmodel above the launch site is known, it is possible tomanipulate the balloon to reach the desired floatingzone when approaching the ceiling altitude by controlthe ascending velocity through gas venting and ballast-ing drops.


2. Solar radiation angle and intensity, environment tem-perature, the relative velocity with atmosphere are themajor factors that affect the temperature distributionof the balloon film. During ascending process, the max-imum temperature of the balloon could decrease to aslow as 230 K with a peak temperature difference of14 K. When floating at the design altitude, the maxi-mum temperature of the balloon could be 280 K andkept a temperature difference of 10 K.

3. Balloon film temperature distribution, volume and thevolume expansion rate can exert great influence on theHelium gas flow. During ascending, when the balloonvolume is close to its maximum value and still expandingrapidly, the Helium flow is the strongest, with the aver-age velocity at about 0.65 m/s. At floating conditions,the average velocity of Helium gas is 0.55 m/s

The future research should be focused on the validationof this model with more experimental data and to integratethis model into the Multidisciplinary Design Optimizationof balloon and airships, such integration could be help indesigning balloon and airships.

Acknowledgements

This work was supported by the National Natural Sci-ence Foundation of China under Grant No. 51307004and Shanghai Aerospace Science and Technology Innova-tion Fund (SAST201268).

References

American Society of Heating, Refrigerating and Air-Conditioning Engi-neers, 2001. ASHRAE Handbook: 2001 Fundamentals, AmericanSociety of Heating, Refrigerating and Air-Conditioning Engineers,Atlanta.

Morris, A. (Ed.), 1975. Scientific Ballooning Handbook. NCAR TN/1A-99, National Center for Atmospheric Research, Boulder CO.

Carlson, L.A., Horn, W.J., 1983. New thermal and trajectory model forhigh altitude balloons. J. Aircraft 20 (6), 500–507.

Cathey, H.M., 2009. The NASA super pressure balloon-a path to flight.Adv. Space Res. 44 (1), 23–38.

Colozza, A., 2003. Initial feasibility assessment of a high altitude longendurance airship. NASA/CR-2003- 212724.

Dai, Q.M., Fang, X.D., Li, X.J., Tian, L.L., 2012. Performance simulationof high altitude scientific balloons. Adv. Space Res. 49 (6), 1045–1052.

Farley, R.E., 2005. BalloonAscent: 3-D simulation tool for the ascent andfloat of high-altitude balloons. In: AIAA 5th Aviation, Technology,Integration, and Operations Conference. AIAA 2005-7412.

Franco, H., Cathey, H.M., 2004. Thermal performance modeling ofNASA’s scientific balloons. Adv. Space Res. 33 (10), 1717–1721.

Incropera, F.P., DeWitt, D.P., 1996. Fundamentals of Heat and MassTransfer, fourth ed. John Wiley & Sons.

Kenya, H., Kunihisa, E., Masaaki, S., Shuichi, S., 2003. Experimentalstudy of thermal modeling for stratospheric platform airships. AIAA2003-6833.

Kreith, F., Kreider, J.F., 1974. Numerical prediction of the performanceof high altitude balloons. NCAR Technical Note NCAR-IN/STR-65.

Leonard, B.P., 1997. Bounded higher-order upwind multidimensionalfinite volume convection–diffusion algorithm. In: Minkowycz, W.J.,Sparrow, E.M. (Eds.), Advances in Numerical Heat Transfer. Taylor& Francis, New York.

Louchev, O.A., 1992. Steady state model for the thermal regimes of shellsof airships and hot air balloons. Int. J. Heat Mass Transfer 35 (10),2683–2693.

Min, G.R., Guo, S., 1998. Thermal Control in Spacecraft, second ed.Science Press, Beijing (in Chinese).

Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. Hemi-sphere Publishing Corporation, Washington.

Shi, H., Song, B.Y., Yao, Q.P., 2009. Thermal performance of strato-spheric airships during ascent and decent. J. Thermophys. HeatTransfer 23 (4), 816–820.

Stefan, K.H., 1983. Thermal effects on a high altitude airship. AIAA 83–1984.

U.S. Standard Atmosphere, 1976. U.S. Government Printing Office,Washington, D.C.

Wang, Y.W., Yang, C.X., 2011. A comprehensive numerical modelexamining the thermal performance of airships. Adv. Space Res. 48,1515–1522.

Xia, X.L., Li, D.F., Sun, C., Ruan, L.M., 2010. Transient behavior ofstratospheric balloons at float conditions. Adv. Space Res. 46, 1184–1190.

http://refhub.elsevier.com/S0273-1177(13)00695-9/h0015






























a comprehensive numerical model investigating the thermal-dynamic performance of scientific balloon

Documents