- Email: [email protected]
Ascending performance analysis for high altitude zero pressure balloon
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2017) xxx–xxx www.elsevier.com/locate/asr
Ascending performance analysis for high altitude zero pressure balloon Sherif Saleh, Weiliang He ⇑ School of Astronautics, Beihang University, 37Xueyuan Road, Beijing 100191, China Received 14 May 2016; received in revised form 12 January 2017; accepted 24 January 2017
Abstract This paper describes a comprehensive simulation for high altitude zero pressure balloon trajectories. A mathematical model was established to simulate the ascending process which considers the atmospheric conditions and thermodynamic variations. Influences of launch parameters on ascending performance were analyzed. The necessary quantity of initial lift gas was estimated and optimized, so that ensures no ballast consuming during the ascending process. The climbing rate was a governing parameter to evaluate the ascending performance. Based on the simulation, results revealed the apparent different effect on climbing rate at troposphere and stratosphere layers. Change in launch time and site mainly affect the climbing rate at the stratosphere and have no significant effect at the troposphere and tropopause altitudes. Meanwhile, change in launch date has a negligible effect on both layers. Due to the earth’s declination angle, the influence of the same launch latitude and the same launch longitude is not identical within a year. Also, results showed that the optimum lift gas quantity improved the climbing rate stability to obtain an accurate simulation. Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: High altitude balloons; Ascending trajectory; Lift gas
1. Introduction Zero pressure balloons are scientific balloons that carry different payloads such as scientific data collection, reconnaissance devices, and radars to high altitudes. The differential pressure of these balloons is almost zero between the inner lift gas and atmosphere. Moreover, it requires throwing out ballast masses at nighttime to keep its float altitude level. The desirable floating altitude assists operators to select the adequate ascending design parameters of scientific balloons. Uncertainties on ascending trajectory represent a vital challenge for high altitude balloon simulation such as launching conditions, wind velocity forecast, drag model, and atmospheric conditions. The climbing rate is the most significant factor in the ascending process and faces variations due to ascending uncertainties. Overcom⇑ Corresponding author.
E-mail addresses: [email protected] (S. Saleh), [email protected] (W. He).
ing these uncertainties leads to an accurate simulation supporting a successful real flight, saving the design time, and reducing the failure reasons and costs for the balloon design (Palumbo et al., 2009). Many comprehensive thermal and dynamic simulations have been done to describe the high altitude balloon performance. Baginski and Winker (2004) investigated the basic concepts and background of zero pressure balloons such as geometry, shape, balloon design parameters, film weight density, payload, and buoyancy at the float level. Palumbo et al. (2007) implemented a new tool analysis code to accurately simulate the flight trajectory with an error less than 1% and a mean error of the climbing rate less than 0.5 m/s. Rotter and Marquez (2007) analyzed the influences of balloon volume and gross inflation during ascending. Also, they referred that the randomness of gross inflation is the most effective uncertainty on the climbing rate. Palumbo et al. (2009) introduced the influence of gas inflation on the ascending performance of zero pressure
http://dx.doi.org/10.1016/j.asr.2017.01.040 0273-1177/Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
2
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
balloon trajectories. Cathey (1997) and Cho and Raque (2002) presented a significant effect of thermal loads such as solar irradiance, albedo, and earth IR flux on balloon film and lift gas temperatures. Franco and Cathey (2004) discovered the influence of convection factor around balloon during ascending as a thermal load. Liu et al. (2014) established the thermal and dynamic numerical model for zero pressure balloons to investigate the ascending and floating performances. Xiong et al. (2014) developed the analytical thermal model to describe the gas and film temperatures, and heat transfer correlations during ascending. Kayhan and Hastaoglu (2014) studied the absorptivity to emissivity ratio; which is important to show the influence of heat transfer during day and night times on the floating altitude stability. Wu et al. (2015) adopted a blackball model for infrared heat radiation in high altitudes to describe the thermal radiation analysis of high altitude bal-
Pair
2. Governing equations of high altitude balloon ascending 2.1. Environment description 2.1.1. Atmospheric model The atmospheric model is categorized by three parameters: pressure, temperature, and density. These parameters are calculated from sea level to 32 km altitude (U.S. St. Atmosphere, 1976) as follows: 8 0 < z 6 11000 m > < 288:150:0065z Tair ¼ 216:65 11000 m < z 6 20000 m > : 216:65þ0:0010ðz20000Þ 20000 m < z 6 32000 m ð1Þ
8 5:25577 > < 101325 ðð288:15 0:0065 zÞ=288:15Þ ¼ 22632 eððz11000Þ=6341:62Þ > : 34:163 5474:87 ðð216:65 þ 0:0010 ðz 20000ÞÞ=216:65Þ
loons. Zhang and Liu (2015) presented the thermal and dynamic models to describe the ascending performance for high altitude balloons. Influences of launch conditions were analyzed, and inflating quantity is a significant effective factor on the balloon ascent speed. Morani et al. (2009) optimized the ascending design parameters to get the best flight trajectory with minimum error. So´bester et al. (2014) interested in minimizing the errors in ascending simulation and developed an accurate drag coefficient model compared to the empirical flight data. Lew and Grant (1994) aimed to reduce the effect of ballast masses useless weight in zero pressure balloons and extended the floating time endurance. The preceding discussion concluded that the researchers seek to an accurate simulation for the balloon trajectory compared to the real flight (Garde, 2005). Further, improving the climbing rate stability by reducing ascending uncertainties such as drag coefficient model, blackball radiation model, initial lift gas mass, launch time, launch site, and wind velocity forecast is important. These attempts are performed to develop zero pressure balloon performance practically. This paper concerns on four aspects: (1) Providing an accurate simulation for zero pressure balloons, (2) Investigating the influence of launch parameters on the ascending velocity, (3) Removing uncertainty of the launch inflation quantity, and (4) Optimizing the necessary inflating quantity to improving the ascending performance. In brief, the present work aims to promote the ascending performance of the high altitude zero pressure balloons and overcomes some of the trajectory uncertainties.
0 < z 6 11000 m 11000 m < z 6 20000 m
ð2Þ
20000 m < z 6 32000 m
Based on the ideal gas law, the air density can be calculated at different altitude as follows: qair ¼
Pair Rair Tair
ð3Þ
where Pair, Rair and Tair are the pressure, specific gas constant and temperature of the air, respectively, and z is the balloon altitude. 2.1.2. Solar elevation angle model The elevation angle of the sun radiation represents the angular height of the sun measured from the horizontal. This angle changes during daytime depending on latitude and the arrangement of this day in the year (Cooper, 1969). The sun elevation angle aELV can be addressed as follows: aELV ¼ sin1 ½sin d sin u þ cos d cos u cosðHRAÞ
ð4Þ
d is the declination angle which depends on the day of the year, u is the location latitude, and HRA is the hour angle. 360 d ¼ sin1 sinð23:45 Þ sin ð5Þ 365ðd 81Þ d is the day number of the year, example: d = 1 for 1st January. HRA ¼ 15 ðLST 12Þ
ð6Þ
LST is the local solar time [hour].
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
2.2. Balloon geometry Zero pressure balloons consider Pgas ¼ Pair and the balloon shape is assumed to be spherical. The balloon volume: V¼
mgas Rgas Tgas Pair
ð7Þ
where mgas, Rgas, Tgas and Pgas are the mass, specific gas constant, the temperature in K and pressure of the lift gas, respectively. The balloon diameter: 1
D ¼ 1:24V3
ð8Þ
The surface area of the balloon: 2
Aeff ¼ pD2 ¼ 4:83V3 The top projected area: p 2 Atop ¼ D2 ¼ 1:21V3 4
3
dTfilm Qfilm ¼ dt cfilm mfilm
ð11Þ
where cfilm, mfilm and Qfilm are specific heat capacity, mass, and heat of the balloon film, respectively. Qfilm ¼ Qcon;ext þ QIR;int þ QIR;e&s þ Qsun Qcon;int QIR;emit ð12Þ where Qcon;ext is the total external convection heat, QIR;int is the total internal infrared radiation, QIR;e&s is the earth and sky infrared radiation, Qsun is the total direct and reflected sun radiation, Qcon;int is the total internal convection heat, and QIR;emit is the heat emission of the balloon film.
ð9Þ
ð10Þ
2.3. Thermal models The thermal model of stratospheric balloons should express on two systems: the balloon film and the inner lift gas temperatures. The heat transfers between air, balloon film, and inner lift gas as shown in Fig. 1. The following subsections describe the heat transfer relationships of the balloon skin and inner lift gas.
2.3.1.1. External convection. External convection of the ascending balloon occurs between the air and external balloon film. It depends on two kinds (Carlson and Horn, 1981). Firstly, free convection which heats transfer to skin from the warmer surrounding air. Secondly, forced convection is excited from the relative velocity between the air and ascending balloon. The external free convection heat transfer coefficient: HCfree ¼
Nuair;free Kair D
ð13Þ
where Nuair;free and Kair are a Nusselt number free convection and thermal conductivity of the air, respectively. 1
2.3.1. Heat transfer on balloon film skins There are several factors that transfer heat to the balloon skin. These factors are external and internal convection between air, outer and inner balloon skin, direct and reflected sun radiation, IR radiation, and heat emissivity to the surrounding air. The differential equation of the balloon skin temperature:
Nuair;free ¼ 2 þ 0:6ðGrair Prair Þ4 0:9 Tair Kair ¼ 0:0241 273:15 Grair ðGrashof number for airÞ ¼ lair ðair dynamic viscosityÞ ¼
ð14Þ ð15Þ q2air gjTfilm Tair jD3 Tair l2air
,
1:458:106 T1:5 air , Tair þ110:4
Prair ðPrandtl number for airÞ ¼ 0:804 3:25:104 Tair , and g is the gravitational acceleration (Morris, 1975). The external forced convection heat transfer coefficient: HCforced ¼
Nuair;forced Kair D
ð16Þ
where Nuair;forced is a Nusselt number forced convection of the air. Nuair;forced ¼ 0:37 Re0:6
ð17Þ
jvz jDqair ; lair
Re ¼ Re is the Reynolds number, and vz is a relative vertical velocity between the surrounding air and balloon. Hence, the effective external convection heat transfer coefficient is the greatest value of free and forced convection. So, the total heat of the external convection: Qcon;ext ¼ HCexternal Aeff ðTair Tfilm Þ Fig. 1. Heat sources for high altitude balloon.
ð18Þ
where HCexternal is the effective external convection coefficient.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
4
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
2.3.1.2. Internal convection. Heat expands throughout the inner balloon film to lift gas losing temperature. The internal free convection heat transfer coefficient: HCinternal
Nugas Kgas ¼ D
ð19Þ
Here Nugas and Kgas are a Nusselt number and thermal conductivity of the gas, respectively. Carlson and Horn (1981) introduced the correlation and Nusselt numbers that avoid a delay in the lift gas temperature rise. Consequently, avoid a reduction in balloon climbing rate. By applying different forms in the present simulation model, the selected form was the best. Nusselt number of the gas: Nugas ¼
8 < 2:5 2 þ 0:6 ðGrgas Prgas Þ14 Grgas Prgas < 1:5 108 :
1
0:325ðGrgas Prgas Þ3
Kgas ¼ 0:144:
Tgas 273:15
ð25Þ
TBB is the blackball radiation temperature in K. 2.3.1.5. Solar thermal radiation. The solar radiation model consists of direct and reflected (albedo) solar radiations. Direct solar radiation depends on different factors as balloon altitude, sun elevation angle, air transmission, cloud appearance, sun declination angle and balloon launching day. On the other hand, the earth and sky surfaces reflect the sun radiation depending on the reflection factor and cloud forecast (Farley, 2005). The direct solar radiation on the balloon film: ð26Þ
ð20Þ
ð21Þ q2gas gjTfilm Tgas jD3 Tgas l2gas
lgas ðgas dynamic viscosityÞ ¼ 1:895:105
, 0:647
Tgas 273:15
, 4
Prgas ðPrandtl number for gasÞ ¼ 0:729 1:6 10 Tgas , and qgas is the lift gas density. Hence, the total heat of the internal convection: Qcon;int ¼ HCinternal Aeff ðTfilm Tgas Þ
ð22Þ
2.3.1.3. Film radiation emissivity. The infrared emission of the balloon film can be classified into two parts as shown in Fig. 1. The first part is the external thermal radiation emission from balloon film to surrounding atmosphere as described in this subsection. The second part is the internal thermal radiation emission where the balloon film reabsorbs the reflected heat on the balloon inner skin as described in the following subsection. Balloon film emits heat radiation as follows (Morris, 1975): QIR;emit ¼ eeff Aeff r
QIR;e&s ¼ eeff r Aeff T4BB
Qdirect;s ¼ a Atop qsun ð1 þ s ð1 þ reff ÞÞ
Grgas Prgas P 1:5 108
0:7
Grgas ðGrashof number for gasÞ ¼
The effective infrared radiation absorbance of the film:
T4film
ð23Þ
eeff is the effective emissivity factor of the balloon film and r is Stephan-Boltzmann constant (5:67 108 Þ. 2.3.1.4. Film radiation absorbance. The infrared radiation of sky and earth emits heat to the balloon film. Furthermore, the heat interchange between the lift gas and inner balloon skin by the internal reflected infrared radiation (Section 2.3.1.3). The film radiation absorbance can be divided into two parts as follows (Carlson and Horn, 1981): The thermal interchange of the film: QIR;int ¼ eint r Aeff ðT4gas T4film Þ eint is the interchange effective emissivity factor.
ð24Þ
a is balloon film absorption factor for the sun radiation, qsun is the net gain direct solar intensity and s is the balloon film transmission factor for the sun radiation, and reff is the effective reflectivity factor of the balloon film. The intensity of the sun radiation can be formulated as follows: Isun;z ð1 CFÞ z 6 11000 m qsun ¼ ð27Þ Isun;z z > 11000 m Isun;z ¼ Isun satm
ð28Þ
Isun;z is the resultant solar intensity at a certain altitude, CF is the cloud factor (CF 0.15 to 1), Isun is the total solar intensity, and satm is the atmospheric transmittance. Isun ¼
1358 1þecosðTAÞ ; 1e2 R2AU
satm ¼ 0:5ðe0:65Airmass þe0:95Airmass Þ; and Airmass ðair mass ratioÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pair 2 ¼ 1229þð614sinðaELV ÞÞ 614sinðaELV Þ : P0
e is the orbital eccentricity, RAU is the mean orbital radius; for Earth, e ¼ 0:016708, RAU ¼ 1. MA is a mean number , TA is a true anomaly, anomaly, MA 2p day 365 TA MA þ 2 e sinðMAÞ þ 54 e2 sinð2 MAÞ, and P0 is the air pressure at launch surface. The effective balloon film reflectivity: reff ¼ r þ r2 þ r3 þ . . . ; r is balloon film reflectivity: The reflected sun radiation is defined as follows: Qreflected;s ¼ a Aeff qalbedo ViewFactor ð1 þ s ð1 þ reff ÞÞ ð29Þ qalbedo is the allowable albedo intensity, and ViewFactor is the balloon subjected surface area to the reflected radiation depending on the balloon view angle.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
ViewFactor ¼ h i 1cosðhalf cone view angleÞ 1 Rearth , half cone view angle ¼ sin , Rearth þz 2 where
and Albedo ¼
qalbedo ¼ Albedo Isun sinðaELV Þ,
(
Albedoground ð1 CFÞ
QIR;e&s ¼ eeff;gas r Aeff T4BB
ð36Þ
So, the total infrared thermal radiation is: QIR;gas ¼ QIR;int;gas QIR;e&s
z 6 11000 m
5
ð37Þ
Albedoground ð1 CFÞ2 þ ðAlbedocloud CFÞ z > 11000 m
Rearth is the radius of the earth (6,371,000 m), Albedoground and Albedocloud are the reflected radiation factors for earth ground and cloud, respectively. Herein, the total solar heat can be expressed by a summation of the direct and reflected solar radiation at the time of sun appearance as follows: Qsun ¼ Qdirect;s þ Qreflected;s
ð30Þ
2.3.2. Heat transfer on lift gas The variation of lift gas temperature causes its compression and expansion which influences seriously on the balloon buoyancy. The internal convection, direct and reflected sun radiation, IR radiation, and heat emissivity to the inner balloon film are the heat sources for the balloon lift gas. The differential equation of the lift gas temperature is: dTgas 1 g mgas Rgas Tgas vz ¼ Qgas ð31Þ c cv mgas dt Rair Tair c is the heat capacity ratio, cv is specific heat capacity of the lift gas at constant volume, and Qgas is the total heat of the inner lift gas. Qgas ¼ Qsun;gas QIR;gas Qcon;int;gas QIR;emit;gas
ð32Þ
where Qsun;gas is the total solar thermal radiation, QIR;gas is the net infrared thermal radiation, Qcon;int;gas is the internal convection heat, and QIR;emit;gas is the infrared radiation emission of the lift gas. Heat transfers from/to lift gas according to the following relations (Carlson and Horn, 1981). 2.3.2.1. Internal convection. The internal free convection between lift gas and inner skin is: Qcon;int;gas ¼ HCinternal Aeff ðTgas Tfilm Þ
ð33Þ
2.3.2.2. Lift gas radiation emissivity. Lift gas loses its temperature by adiabatic expansion to the balloon film. The total heat emission of the lift gas: QIR;emit;gas ¼ eeff;gas Aeff r T4gas
ð34Þ
eeff;gas is the effective gas emissivity factor. 2.3.2.3. Gas radiation absorbance. The between lift gas and inner balloon film is: QIR;int;gas ¼ eint r Aeff ðT4gas T4film Þ IR radiation from sky and earth is
interchange ð35Þ
2.3.2.4. Solar radiation model. The impact of solar radiation on the lift gas can be divided into direct solar radiation and reflected solar radiation as mentioned before in the thermal equations of the balloon film. The total heat of solar radiation is: Qsun;gas ¼ aeff;gas Aeff qsun ð1 þ AlbedoÞ
ð38Þ
where aeff;gas is the effective solar absorption factor of the balloon gas. 2.4. Lift gas mass differential equation During ascending process, the differential pressure between lift gas and atmosphere is almost zero resulting in a negligible change in the lift gas mass. In contrast at float altitude, two main reasons lead to a reduction in the lift gas mass. While balloon reaches floating level, volume becomes maximum; then balloon continues ascending process by its momentum and inertia. Herein the differential pressure grows up, and gas should leak gradually out to prevent the balloon explosion achieving the first reason. The second reason is the acquired heat for the lift gas during the daytime that supports lift gas expansion. Lift gas mass tends to escape from the balloon keeping its maximum volume. Therefore, the differential equation of the lift gas mass: dmg ¼ qgas DV_ dt
ð39Þ
DV_ is a volumetric flow rate, DV_ ¼ ValtitudeDtVmax ; Valtitude is the balloon volume at altitude level, and Vmax is the maximum allowable balloon volume. 2.5. Dynamic model The dynamic model represents the force that helps balloon ascent such as the buoyant force and the forces that resist it such as the gross weight and drag force. Buoyant force (free lift) is the balloon lifting gas force (gross inflation) against the gravitational force due to a gross weight where gas density lighter than air density. The drag force is the aerodynamic force that resists the ascending balloon depending on the balloon shape, volume, velocity, and drag coefficient. The dynamic equation of motion (Morris, 1975): mvirtual
dvz 1 ¼ g V ðqair qgas Þ g mgross Cd qair Atop v2z 2 dt ð40Þ
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
6
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
The left term represents the inertia force of the ascending balloon. The three right terms are the gross inflation, the gravitational, and the drag forces, respectively. Where mvirtual is the total balloon mass including lift gas mass, in addition to the air virtual mass that represents load above the ascent balloon head (mvirtual ¼ mgross þ mgas þ Cvirtual qair V), Cvirtual is the virtual mass coefficient, Cvirtual 0:5 (Farley, 2005). mgross is the gross mass (payload + film + ballast). Cd is the drag coefficients. 2.6. Altitude differential equation The differential equation of altitude depends on a relative vertical velocity as follows: dz ¼ vz dt
ð41Þ
3. Uncertainties in ascending process Trajectory simulation is a manner to predict the balloon design parameters using the governing equations of ascending process at different altitudes. Usually, an accurate simulation results in a successful real flight. Uncertainties of the ascending governing equations represent the challenges that face this simulation. The initial lift gas quantity, drag coefficient model, wind velocity forecast, cloud cover, launch time and site are the most significant uncertainties imposed to a high altitude zero pressure balloon trajectories. These uncertainties seriously affect the climbing rate. Therefore, the following sections discuss the influence of some parameters on ascending velocity which is the major common factor between the real flight and simulation. 4. Modeling and simulation
4. Releasing ballast masses at nighttime (Yajima et al., 2009). 5. Next hours/days until the time of no ballast masses or no enough buoyancy of the balloon system. 4.2. Genetic algorithm The genetic algorithm (GA) toolbox estimates the necessary lift gas quantity and minimizes the ascending acceleration. Fig. 2 describes the algorithm linking between the ascending simulation and optimization mathematical relations. GA is a global search technique. It strikes a reasonable balance between exploiting the available information and searching through unexplored regions. GA operation close to the laws of nature uses a population of potential solutions represented by a string of binary digits (chromosomes or individuals). Then, genetic operations such as selection, crossover, and mutation enhance the optimization process. GA initiates the initial random individuals that converge the solution of optimization problem according to supposed constraints. Genetic operations selection, crossover, and mutation are the random selection, keeping diversity, and checking the best selection for the allowable individuals, respectively. The basic structure of GA mainly consists of the following steps: 1. Selection random initial population. 2. Evaluation of the individuals. 3. Applying the genetic operators (selection, crossover, and mutation). GA minimizes the nonlinear constrained objective function as follows: f min ðxÞ ¼
ðqair V xð1Þ mgross Þ g 0:5qair Cd ATop v2z mvirtual ð42Þ
4.1. Matlab M-File Matlab M-file program is used to simulate the high altitude zero pressure balloon model predicting its ascending performance. This program consists of the main program and two subroutines. Firstly, the main program includes the built-in solver function (ode45) which is the fourth orders Runge-Kutta numerical method and the initial conditions such as lift gas mass, lift gas temperature, balloon film temperature, altitude, and velocity. Then, subroutines describe the ascending constant parameters and thermodynamic nonlinear ordinary differential equations as shown in Section 2, respectively. It predicts the balloon design parameters every second comprising the following: 1. Initial conditions at launching. 2. Ascending altitudes considering the solar position and cloud cover effects. 3. Floating altitude.
Start Main Program Call Thermo-dynamic model Solve 5 differential equa tions using RungeKutta numerical solution to get “lifting gas mass – volume – lifting gas temperature – altitude – film temperature” Optimization Program Fitness evaluation of each generated individual with respect to a given objective function
Objective function of Acceleration with one variable “lifting gas mass” Nonlinear constraints Acceleration is the minimum
Stopping code at a minimum value of fitness function “acceleration” with nonlinear constraints END
Fig. 2. Integrated simulation using Matlab and Genetic Algorithm.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Variable is xð1Þ ¼ mgas . The constraints are: 1. Positive free lift all the time of ascending. 2. Velocity is almost constant (5 m/s). 3. No consuming of the ballast masses. The optimization method seeks the necessary lift gas quantity that maintains approximately constant climbing rate at all ascending altitudes. Linking between the simulation and optimization methods predicts the optimum launch lift gas quantity and the corresponding drag coefficient model which achieve an accurate simulation as shown in Fig. 13. Hence, the uncertainty of the launch lift gas quantity can be removed enhancing the ascending performance of the high altitude zero pressure balloon trajectories. 5. Results and analysis 5.1. Model validation Thermtraj NASA model and real flight 167N data were compared to validate this code (Horn and Carlson, 1983).
7
The high altitude zero pressure balloon had a maximum volume of 66,375 m3, was designed to float at an altitude of 36.7 km and carried a payload of 196.82 kg. The balloon’s gross mass and initial lift gas mass (helium) were 381 kg and 69.221 kg, respectively. The local time of launching was 11:35 am from Palestine, Texas on July 24, 1980. This code represents a complete flight simulation comprising the buoyancy compensation by ballast dropping at nighttime. And it predicts the balloon trajectory for several days and nights until the descending at no ballast masses. The code has the capability of adding several subroutines to precise simulation. Figs. 3 and 4 represent the balloon trajectories in the ascending phase and the flight throughout the first day and night, respectively. Real flight data, ThermTraj, and present model are almost close to each other at the desired float altitude and the troposphere ascending altitudes. At the desired float altitude, that is owing to the ascending velocity tends to zero, but at the troposphere may be attributed to the few effective uncertainties. The discrepancy at some points belongs to the climbing rate instability. The following sections discuss influences some of these parameters on the ascending performance in details.
Fig. 3. Balloon ascending validation.
First Ballast Drop
Fig. 4. Balloon trajectory prediction simulation.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
8
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
5.2. Climbing rate discrepancy in different layers Figs. 5–8 show the influence of the launch time, date, and site on the climbing rate at different layers. Results investigate these influences at the troposphere (from the launch position to the ceiling of tropopause about 11 km) and the stratosphere (from the ceiling of tropopause to floating altitude). Average vertical velocity at the troposphere and stratosphere represent the mean ascending
velocity between launch to 11 km and 11 km to float, respectively. 5.2.1. Launch time and date effects Fig. 5 presents the average ascending velocity profiles at different launching time in one day (24 h) at the troposphere and stratosphere. Fig. 5(a) deduces that no significant effect on the average ascending velocity at the troposphere at different launching time. Meanwhile,
Fig. 5. Variation in average vertical velocity at different launch times within a day. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
9
Fig. 6. Variation in average vertical velocity at different launch days within a month.
Fig. 5(b) appears the significant effect at the stratosphere. So, the resultant variation in ascending velocity in 24 h as shown in Fig. 5(c) belongs mainly to the influences of the launching time at the stratosphere. On the other hand, the solar radiation intensity and its angle during daytime cause the notable variation in the average ascending velocity between day and night times. Therefore, the average ascending velocity increases gradually from the sunrise to the maximum peak at midday and decreases again to the sunset. Otherwise, the average ascending velocity is almost constant and low because of the sun absence. Fig. 6 shows that the launch date does not have a significant effect on the average velocity neither at the troposphere nor the stratosphere because of the change in the earth declination angle is very small compared to the solar radiation intensity. 5.2.2. Launch site effect Figs. 7 and 8 describe the influence on the average ascending velocity at 11:35 am in July and September due to the change in latitude and longitude of the launch position, respectively. Figs. 7(a) and 8(a) indicate that the changes in latitude and longitude have no significant effect at the troposphere, but the effect significantly appears at the stratosphere in Figs. 7(b) and 8(b). Figs. 7(c) and 8(c) are the resultants average vertical velocity at the ascending process. Due to earth declination angle and sun position, the influence of the same latitude is not identical as shown in Fig. 7(c). In fact, the earth declination angles at this time of September and July are about 0° and 20°, respectively. Consequently, Fig. 7(c) distributes the average ascending velocity in September equally at both earth poles and maximum at the earth equator. But in July, Fig. 7(c) appears the minimum effect at the South Pole and increases gradually until the equator, then be almost stable until the North Pole. Due to the earth rotation and the sun relative position, Fig. 8(c) shows that the effect of the change in longitude is same as the effect of the launch time within a day in Fig. 5(c). Moreover, the maximum peak at midday is at 95o as the actual launch longitude position in the real flight. The small difference between two months at the same
longitude belongs to the same reason of the earth declination angle. The previous discussions concluded that the changes in the launch time and site influence seriously on the climbing rate at the stratosphere. Meanwhile, the launch date effect is negligible. It means that the uncertainties at the troposphere are limited such as the launch lift gas quantity, and other parameters mainly affect at the stratosphere. Consequently, the following section explains physically the reasons cause variation in the climbing rate during the ascending process. 5.3. Ascending velocity 5.3.1. Ascending performance Variation of ambient temperature and pressure at the different altitudes is the key point that describes the reasons cause the variation in the ascending velocity. The dynamic equation of motion (Eq. (40)) represents a variation in the climbing rate obeying to two major terms: the first term is a buoyant force; the second is a drag force. The following section demonstrates the variation and influences of these forces on the climbing rate. Fig. 9(c) classifies the variation of the ascending velocity to: 5.3.1.1. Ascending velocity between 0 and 11 km. At the beginning of ascent, balloon strongly ascends in high buoyant force because of the difference in density between the air and gas, but after few seconds, the buoyant force decreases gradually because of the reduction in density difference between air and gas as shown in Fig. 9(b). The initial drag force on ascending balloon is high because the flow around balloon is laminar separation causing highpressure drag (Carlson and Horn, 1983). Gradually decreasing in the drag force belongs mainly to the reduction of the air density at higher altitudes compared to slowly increasing in a volume. So, the conclusion is the resultant buoyant force overcomes drag force on the balloon volume resulting in gradually increasing in a climbing rate at troposphere. On the other hand, the ambient tem-
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
10
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Fig. 7. Variation in average vertical velocity at different launch latitude. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
perature decreases while the balloon ascends; even the lift gas and balloon film temperatures are relatively high but lose temperature by adiabatic expansion and IR emissivity to the surrounding. So, the main reason of slowly increasing of volume in Fig. 9(a) not belongs to gas temperature but owing to the reduction in the ambient pressure. This stage concludes that the lift gas quantity represents a significant parameter at the troposphere more than other parameters as mentioned in advance.
5.3.1.2. Ascending velocity between 11 and 20 km. At the beginning of this stage, the difference in density between air and gas decreases resulting in an observable reduction in the buoyant force; that is considered the main reason to reduce climbing rate as shown in Fig. 9(c). Drag sharply decreases due to the reduction in climbing rate where drag force directly proportional to the squared vertical velocity, rather than the ambient temperature changes slightly, but the lift gas and film temperatures have been reduced con-
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
11
Fig. 8. Variation in average vertical velocity at different launch longitude. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
tinuously by adiabatic expansion and IR emissivity; and volume still slowly increases. At the second part of this stage, temperatures of lift gas and balloon film increase gradually to be balanced with ambient air temperature leading to obvious increasing in balloon volume that causes the stop of the buoyant force reduction. Meanwhile, flow around volume starts to be not fully laminar and reduces relatively the pressure drag effect resulting in a little bit increasing in climbing rate.
increases but the climbing rate also highly increases due to the low air density and low drag coefficient. The drag coefficient decreases because the flow is turbulent reducing the pressure drag while the friction drag is prevailing. Even though volume grows up but drag coefficient reduces drag force totally. And the buoyant force supports the climbing rate rising. Therefore, lift gas quantity is the decisive parameter of the balloon ascent. So, the next section reveals the effect of the launch lift gas inflation on the ascending velocity.
5.3.1.3. Ascending velocity between 20 – float altitude km. This altitude of the stratosphere is quite different. Ambient temperature increases, also lift gas and film temperatures sharply increase leading to the gas expansion and rapidly growing the volume up. Although the volume
5.3.2. Lift gas inflating quantity effect It is the most significant parameter of the high altitude zero pressure balloon trajectories in accordance to the preceding arguments, especially, at the troposphere. So, GA optimization method is established to estimate the best
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
12
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Fig. 9. Ascending vertical velocity description in midday. (a) Volume–Altitude relation, (b) Buoyant/Drag forces–Altitude relations, (c) Time–Vertical velocity relation.
lift gas quantity during the whole ascent, so that ensures reasonable ascending time and velocity with no ballast consuming. GA estimates the necessary lift gas quantity relevant to selected drag coefficient model, and initial lift gas and balloon film temperatures.
Drag coefficient model, initial lift gas and balloon film temperatures are important parameters in the thermal and dynamic models of the balloon ascending. Some operators considered drag coefficient a constant value 0.5–1.3 (Farley, 2005; Kreider and Kreith, 1975) and others
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
considered it a function of Reynolds number term (Carlson and Horn, 1981, 1983; So´bester et al., 2014) as follows: 8 > 2400 Re < 102 > > > > > 102 < Re 6 100 > > 24=Re > > > 24 Re0:757 100 < Re 6 101 > > > < 16:04 Re0:582 101 < Re 6 102 Cd ¼ > 6:025 Re0:369 102 < Re 6 103 > > > > > 0:47 103 < Re 6 105 > > > > > 0:5 105 < Re 6 2:5 106 > > > : 6:7297 1020 Re2:9495 2:5 106 < Re Or a function of both of Reynolds number term and Froude dependent term (Conrad and Robbins, 1991; Palumbo et al., 2007) as follows: vz Froude number ðFRÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ; gD 4 Rair Tair 1 Cd;Froude ¼ 3 FR Rgas Tgas
mgross ðmgross þ Cvirtual qair VolumeÞ dvz 1þ þ mgas g mgas dt So, Cd ¼ Cd;Froude þ Cd;Renolds The balloon drag changes according to the volume, shape, air density, and velocity. So, it is not easy to represent a drag on the balloon at different altitudes, but it
13
should be selected carefully due to its significant effect on the balloon ascending velocity. Figs. 10 and 11 show the influence of the change in drag coefficient model, initial lift gas and balloon film temperatures on average ascending velocity. Fig. 10 observes that the references used Froude dependent term in addition to Reynolds number term express on higher drag coefficient according to zero pressure balloon shape and its attachments. So, Froude dependent and Reynolds number terms together represent the most accurate model. Fig. 11 deduces that the influence of initial lift gas temperature more than initial balloon film temperature. Also, the variation sensitivity of both temperatures converges at about 290 K which is valid to be as an initial condition of launch temperatures. Fig. 12 clarifies influences of low and high gas inflation quantity on the climbing rate leading to the altitude variation. At low initial gas inflation quantity, the balloon system should throw out ballast masses early and consumes very long time to reach the float altitude. On the other hand, long ascending time leads to inaccurate simulation because of the variations of atmospheric conditions according to the ascent time. At high initial gas inflation quantity, the balloon reaches rapidly to float altitude which refers to the high climbing rate that may cause failure criteria in the balloon film material. Fig. 12 concludes that inadequate climbing rate causes inaccurate simulation affecting the ascending performance. So, optimizing lift gas quantity at the whole ascending process is a trend to get the necessary quantity
Fig. 10. Influence of drag coefficient model on average ascending velocity.
Fig. 11. Influence of initial lift gas and film temperatures on average ascending velocity.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
14
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
First Ballast Drop
Fig. 12. Variation in altitude at different initial lift gas mass.
Fig. 13. Variation in altitude due to optimum and real flight launch lift gas quantity.
that achieves an adequate and stable climbing rate enhancing the ascending performance as shown in the next figure. Fig. 13 establishes the comparison between the real flight and simulation using optimum lift gas quantity. Ascending trajectories illustrate both curves are too close to each other. Furthermore, this method estimated the lift gas mass of 69.63 kg almost near the real flight of 69.22 kg. The optimum simulation in Fig. 13 reveals somewhat stable climbing rate during the ascending process, especially, at the troposphere where the most effective parameter on ascending velocity is the lift gas quantity. Also, optimum value controls well the climbing rate near the floating altitude improving the ascending performance. On the other hand, it attains the ascending trajectory without consuming ballast masses saving these masses at float altitude to compensate the losing altitude during nighttime as long as possible. 6. Conclusions This paper presented the thermal and dynamic simulation of high altitude zero pressure balloons. Nonlinear ordinary differential equations of zero pressure balloons were numerically modeled to describe the ascending performance. Influences of launch conditions on the ascending
velocity at troposphere and stratosphere layers were analyzed. The significant effect on ascending velocity due to different launch lift gas quantity was analyzed. Optimization subroutine using genetic algorithm was implemented to predict the necessary inflation quantity. By using optimum inflation quantity, the simulation results approached real flight data. Based on the simulation results, the conclusions are summarized as follows: 1. Different launch time and launch site have no significant effect on ascending velocity at the troposphere, but the main effect appears at the stratosphere. Meanwhile, the influence of the change in launch date is negligible. 2. Sun emergence and its intensity have the most significant thermal effect on balloon ascent. 3. The same longitude and latitude have a seasonally different effect on ascending velocity owing to the declination angle of the earth. 4. Optimum inflation quantity improves the ascending performance, especially, at the troposphere, and controls well the climbing rate near the floating altitude. 5. Optimum inflation quantity achieves balloon ascent without ballast masses consumption which supports the floating performance.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Finally, the present work strived to promote the ascending performance of the high altitude zero pressure balloons keeping the pace in this field. The future aspirations should focus on the research at the stratosphere layer enhancing the real flight. References Baginski, F., Winker, J., 2004. The natural shape balloon and related models. Adv. Space Res. 33, 1617–1622 (Science direct). Carlson, L.A., Horn, W.J., 1981. A Unified Thermal and Vertical Trajectory Model for the Prediction of High Altitude Balloon Performance. NASA-CR156884, Texas, USA. Carlson, L.A., Horn, W.J., 1983. New thermal and trajectory model for high-altitude balloons. AIAA J. Aircraft 20 (6), 500–507. Cathey Jr., H.M., 1997. Transient Thermal Loading of Natural Shaped Balloons. AIAA-31338, USA. Cho, C., Raque, S., 2002. Influence of the infrared radiation on a highaltitude scientific balloon. In: 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, USA. Conrad, G.R., Robbins, E.J., 1991. Determination of Balloon Drag. AIAA-91-3666-CP. Cooper, P.I., 1969. The absorption of radiation in solar stills. Sol. Energy 12, 333–346 (Science direct). Farley, R.E., 2005. Balloon ascent: 3-D simulation tool for the ascent and float of high-altitude balloons. In: AIAA 5th Aviation Technology Integration and Operations Conference, Arlington, Virginia. Franco, H., Cathey Jr., H.M., 2004. Thermal performance modeling of NASA scientific balloons. Adv. Space Res. 33, 1717–1721 (Science direct). Garde, G.J., 2005. Comparison of two balloon flight simulation programs. In: AIAA 5th Aviation Technology Integration and Operations Conference, Arlington, Virginia. Horn, W.J., Carlson, L.A., 1983. THERMTRAJ: A FORTRAN Program to Compute the Trajectory and Gas Film Temperature of Zero Pressure Balloon. NASA-CR-168342. Kayhan, O., Hastaoglu, M.A., 2014. Modeling of stratospheric balloon using transport phenomena and gas compress–release system. J. Thermophys. Heat Transfer 28, 534–541.
15
Kreider, J.F., Kreith, F., 1975. Numerical prediction of high altitude zeropressure balloon vertical motion. J. Heat Transfer 97, 155–157. Lew, T.M., Grant, D.A., 1994. Gas temperature control for long duration balloons. AIAA 94-0745. In: 32nd Aerospace Sciences Meeting & Exhibit, Reno, USA. Liu, Q., Wu, Z., Zhu, M., Xu, W.Q., 2014. A comprehensive numerical model investigating the thermal-dynamic performance of scientific balloon. Adv. Space Res. 53, 325–338 (Science direct). Morani, G., Palumbo, R., Cuciniello, G., Corraro, F., Russo, M., 2009. Method for prediction and optimization of a stratospheric balloon ascent trajectory. J. Spacecraft Rockets 46, 126–133. Morris, A.L., 1975. Scientific Ballooning Handbook, Balloon Design Considerations. NCAR-TN/IA-99, Colorado. Palumbo, R., Morani, G., Corraro, F., 2009. An effective approach to characterization of prediction errors for balloon ascent trajectories. In: AIAA Balloon Systems Conference, Seattle, Washington. Palumbo, R., Russo, M., Filippone, E., Corraro, F., 2007. ACHAB: analysis code for high-altitude balloons. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hilton Head, South Carolina. Rotter, J., Marquez, M.P., 2007. Zero pressure balloon reliability factors. In: AIAA Balloon Systems Conference, Williamsburg, VA. So´bester, A., Czerski, H., Zapponi, N., Castro, I., 2014. High altitude gas balloon trajectory prediction: a Monte Carlo model. AIAA J. 52, 832– 842. U.S. St. Atmosphere, 1976. U.S. Government Printing Office, Washington, D.C. Wu, J., Fang, X., Wang, Z., Hou, Zh., Ma, Zh., et al., 2015. Thermal modeling of stratospheric airships. Prog. Aerosp. Sci. 75, 26–37 (Science direct). Xiong, J., Bai, J.B., Chen, L., 2014. Simplified analytical model for predicting the temperature of balloon on high-altitude. Int. J. Therm. Sci. 76, 82–89 (Science direct). Yajima, N., Izutsu, N., Imamura, T., Abe, T., 2009. Scientific Ballooning, Technology and Applications of Exploration Balloons Floating in the Stratosphere and the Atmospheres of Other Planets: Engineering Fundamentals of Balloons, 1-213, Tokyo, Japan. Springer Science (Chapter 2). Zhang, Y., Liu, D., 2015. Influences of initial launch conditions on flight performance of high altitude balloon ascending process. Adv. Space Res. 56, 605–618 (Science direct).
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
ScienceDirect Advances in Space Research xxx (2017) xxx–xxx www.elsevier.com/locate/asr
Ascending performance analysis for high altitude zero pressure balloon Sherif Saleh, Weiliang He ⇑ School of Astronautics, Beihang University, 37Xueyuan Road, Beijing 100191, China Received 14 May 2016; received in revised form 12 January 2017; accepted 24 January 2017
Abstract This paper describes a comprehensive simulation for high altitude zero pressure balloon trajectories. A mathematical model was established to simulate the ascending process which considers the atmospheric conditions and thermodynamic variations. Influences of launch parameters on ascending performance were analyzed. The necessary quantity of initial lift gas was estimated and optimized, so that ensures no ballast consuming during the ascending process. The climbing rate was a governing parameter to evaluate the ascending performance. Based on the simulation, results revealed the apparent different effect on climbing rate at troposphere and stratosphere layers. Change in launch time and site mainly affect the climbing rate at the stratosphere and have no significant effect at the troposphere and tropopause altitudes. Meanwhile, change in launch date has a negligible effect on both layers. Due to the earth’s declination angle, the influence of the same launch latitude and the same launch longitude is not identical within a year. Also, results showed that the optimum lift gas quantity improved the climbing rate stability to obtain an accurate simulation. Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: High altitude balloons; Ascending trajectory; Lift gas
1. Introduction Zero pressure balloons are scientific balloons that carry different payloads such as scientific data collection, reconnaissance devices, and radars to high altitudes. The differential pressure of these balloons is almost zero between the inner lift gas and atmosphere. Moreover, it requires throwing out ballast masses at nighttime to keep its float altitude level. The desirable floating altitude assists operators to select the adequate ascending design parameters of scientific balloons. Uncertainties on ascending trajectory represent a vital challenge for high altitude balloon simulation such as launching conditions, wind velocity forecast, drag model, and atmospheric conditions. The climbing rate is the most significant factor in the ascending process and faces variations due to ascending uncertainties. Overcom⇑ Corresponding author.
E-mail addresses: [email protected] (S. Saleh), [email protected] (W. He).
ing these uncertainties leads to an accurate simulation supporting a successful real flight, saving the design time, and reducing the failure reasons and costs for the balloon design (Palumbo et al., 2009). Many comprehensive thermal and dynamic simulations have been done to describe the high altitude balloon performance. Baginski and Winker (2004) investigated the basic concepts and background of zero pressure balloons such as geometry, shape, balloon design parameters, film weight density, payload, and buoyancy at the float level. Palumbo et al. (2007) implemented a new tool analysis code to accurately simulate the flight trajectory with an error less than 1% and a mean error of the climbing rate less than 0.5 m/s. Rotter and Marquez (2007) analyzed the influences of balloon volume and gross inflation during ascending. Also, they referred that the randomness of gross inflation is the most effective uncertainty on the climbing rate. Palumbo et al. (2009) introduced the influence of gas inflation on the ascending performance of zero pressure
http://dx.doi.org/10.1016/j.asr.2017.01.040 0273-1177/Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
2
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
balloon trajectories. Cathey (1997) and Cho and Raque (2002) presented a significant effect of thermal loads such as solar irradiance, albedo, and earth IR flux on balloon film and lift gas temperatures. Franco and Cathey (2004) discovered the influence of convection factor around balloon during ascending as a thermal load. Liu et al. (2014) established the thermal and dynamic numerical model for zero pressure balloons to investigate the ascending and floating performances. Xiong et al. (2014) developed the analytical thermal model to describe the gas and film temperatures, and heat transfer correlations during ascending. Kayhan and Hastaoglu (2014) studied the absorptivity to emissivity ratio; which is important to show the influence of heat transfer during day and night times on the floating altitude stability. Wu et al. (2015) adopted a blackball model for infrared heat radiation in high altitudes to describe the thermal radiation analysis of high altitude bal-
Pair
2. Governing equations of high altitude balloon ascending 2.1. Environment description 2.1.1. Atmospheric model The atmospheric model is categorized by three parameters: pressure, temperature, and density. These parameters are calculated from sea level to 32 km altitude (U.S. St. Atmosphere, 1976) as follows: 8 0 < z 6 11000 m > < 288:150:0065z Tair ¼ 216:65 11000 m < z 6 20000 m > : 216:65þ0:0010ðz20000Þ 20000 m < z 6 32000 m ð1Þ
8 5:25577 > < 101325 ðð288:15 0:0065 zÞ=288:15Þ ¼ 22632 eððz11000Þ=6341:62Þ > : 34:163 5474:87 ðð216:65 þ 0:0010 ðz 20000ÞÞ=216:65Þ
loons. Zhang and Liu (2015) presented the thermal and dynamic models to describe the ascending performance for high altitude balloons. Influences of launch conditions were analyzed, and inflating quantity is a significant effective factor on the balloon ascent speed. Morani et al. (2009) optimized the ascending design parameters to get the best flight trajectory with minimum error. So´bester et al. (2014) interested in minimizing the errors in ascending simulation and developed an accurate drag coefficient model compared to the empirical flight data. Lew and Grant (1994) aimed to reduce the effect of ballast masses useless weight in zero pressure balloons and extended the floating time endurance. The preceding discussion concluded that the researchers seek to an accurate simulation for the balloon trajectory compared to the real flight (Garde, 2005). Further, improving the climbing rate stability by reducing ascending uncertainties such as drag coefficient model, blackball radiation model, initial lift gas mass, launch time, launch site, and wind velocity forecast is important. These attempts are performed to develop zero pressure balloon performance practically. This paper concerns on four aspects: (1) Providing an accurate simulation for zero pressure balloons, (2) Investigating the influence of launch parameters on the ascending velocity, (3) Removing uncertainty of the launch inflation quantity, and (4) Optimizing the necessary inflating quantity to improving the ascending performance. In brief, the present work aims to promote the ascending performance of the high altitude zero pressure balloons and overcomes some of the trajectory uncertainties.
0 < z 6 11000 m 11000 m < z 6 20000 m
ð2Þ
20000 m < z 6 32000 m
Based on the ideal gas law, the air density can be calculated at different altitude as follows: qair ¼
Pair Rair Tair
ð3Þ
where Pair, Rair and Tair are the pressure, specific gas constant and temperature of the air, respectively, and z is the balloon altitude. 2.1.2. Solar elevation angle model The elevation angle of the sun radiation represents the angular height of the sun measured from the horizontal. This angle changes during daytime depending on latitude and the arrangement of this day in the year (Cooper, 1969). The sun elevation angle aELV can be addressed as follows: aELV ¼ sin1 ½sin d sin u þ cos d cos u cosðHRAÞ
ð4Þ
d is the declination angle which depends on the day of the year, u is the location latitude, and HRA is the hour angle. 360 d ¼ sin1 sinð23:45 Þ sin ð5Þ 365ðd 81Þ d is the day number of the year, example: d = 1 for 1st January. HRA ¼ 15 ðLST 12Þ
ð6Þ
LST is the local solar time [hour].
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
2.2. Balloon geometry Zero pressure balloons consider Pgas ¼ Pair and the balloon shape is assumed to be spherical. The balloon volume: V¼
mgas Rgas Tgas Pair
ð7Þ
where mgas, Rgas, Tgas and Pgas are the mass, specific gas constant, the temperature in K and pressure of the lift gas, respectively. The balloon diameter: 1
D ¼ 1:24V3
ð8Þ
The surface area of the balloon: 2
Aeff ¼ pD2 ¼ 4:83V3 The top projected area: p 2 Atop ¼ D2 ¼ 1:21V3 4
3
dTfilm Qfilm ¼ dt cfilm mfilm
ð11Þ
where cfilm, mfilm and Qfilm are specific heat capacity, mass, and heat of the balloon film, respectively. Qfilm ¼ Qcon;ext þ QIR;int þ QIR;e&s þ Qsun Qcon;int QIR;emit ð12Þ where Qcon;ext is the total external convection heat, QIR;int is the total internal infrared radiation, QIR;e&s is the earth and sky infrared radiation, Qsun is the total direct and reflected sun radiation, Qcon;int is the total internal convection heat, and QIR;emit is the heat emission of the balloon film.
ð9Þ
ð10Þ
2.3. Thermal models The thermal model of stratospheric balloons should express on two systems: the balloon film and the inner lift gas temperatures. The heat transfers between air, balloon film, and inner lift gas as shown in Fig. 1. The following subsections describe the heat transfer relationships of the balloon skin and inner lift gas.
2.3.1.1. External convection. External convection of the ascending balloon occurs between the air and external balloon film. It depends on two kinds (Carlson and Horn, 1981). Firstly, free convection which heats transfer to skin from the warmer surrounding air. Secondly, forced convection is excited from the relative velocity between the air and ascending balloon. The external free convection heat transfer coefficient: HCfree ¼
Nuair;free Kair D
ð13Þ
where Nuair;free and Kair are a Nusselt number free convection and thermal conductivity of the air, respectively. 1
2.3.1. Heat transfer on balloon film skins There are several factors that transfer heat to the balloon skin. These factors are external and internal convection between air, outer and inner balloon skin, direct and reflected sun radiation, IR radiation, and heat emissivity to the surrounding air. The differential equation of the balloon skin temperature:
Nuair;free ¼ 2 þ 0:6ðGrair Prair Þ4 0:9 Tair Kair ¼ 0:0241 273:15 Grair ðGrashof number for airÞ ¼ lair ðair dynamic viscosityÞ ¼
ð14Þ ð15Þ q2air gjTfilm Tair jD3 Tair l2air
,
1:458:106 T1:5 air , Tair þ110:4
Prair ðPrandtl number for airÞ ¼ 0:804 3:25:104 Tair , and g is the gravitational acceleration (Morris, 1975). The external forced convection heat transfer coefficient: HCforced ¼
Nuair;forced Kair D
ð16Þ
where Nuair;forced is a Nusselt number forced convection of the air. Nuair;forced ¼ 0:37 Re0:6
ð17Þ
jvz jDqair ; lair
Re ¼ Re is the Reynolds number, and vz is a relative vertical velocity between the surrounding air and balloon. Hence, the effective external convection heat transfer coefficient is the greatest value of free and forced convection. So, the total heat of the external convection: Qcon;ext ¼ HCexternal Aeff ðTair Tfilm Þ Fig. 1. Heat sources for high altitude balloon.
ð18Þ
where HCexternal is the effective external convection coefficient.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
4
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
2.3.1.2. Internal convection. Heat expands throughout the inner balloon film to lift gas losing temperature. The internal free convection heat transfer coefficient: HCinternal
Nugas Kgas ¼ D
ð19Þ
Here Nugas and Kgas are a Nusselt number and thermal conductivity of the gas, respectively. Carlson and Horn (1981) introduced the correlation and Nusselt numbers that avoid a delay in the lift gas temperature rise. Consequently, avoid a reduction in balloon climbing rate. By applying different forms in the present simulation model, the selected form was the best. Nusselt number of the gas: Nugas ¼
8 < 2:5 2 þ 0:6 ðGrgas Prgas Þ14 Grgas Prgas < 1:5 108 :
1
0:325ðGrgas Prgas Þ3
Kgas ¼ 0:144:
Tgas 273:15
ð25Þ
TBB is the blackball radiation temperature in K. 2.3.1.5. Solar thermal radiation. The solar radiation model consists of direct and reflected (albedo) solar radiations. Direct solar radiation depends on different factors as balloon altitude, sun elevation angle, air transmission, cloud appearance, sun declination angle and balloon launching day. On the other hand, the earth and sky surfaces reflect the sun radiation depending on the reflection factor and cloud forecast (Farley, 2005). The direct solar radiation on the balloon film: ð26Þ
ð20Þ
ð21Þ q2gas gjTfilm Tgas jD3 Tgas l2gas
lgas ðgas dynamic viscosityÞ ¼ 1:895:105
, 0:647
Tgas 273:15
, 4
Prgas ðPrandtl number for gasÞ ¼ 0:729 1:6 10 Tgas , and qgas is the lift gas density. Hence, the total heat of the internal convection: Qcon;int ¼ HCinternal Aeff ðTfilm Tgas Þ
ð22Þ
2.3.1.3. Film radiation emissivity. The infrared emission of the balloon film can be classified into two parts as shown in Fig. 1. The first part is the external thermal radiation emission from balloon film to surrounding atmosphere as described in this subsection. The second part is the internal thermal radiation emission where the balloon film reabsorbs the reflected heat on the balloon inner skin as described in the following subsection. Balloon film emits heat radiation as follows (Morris, 1975): QIR;emit ¼ eeff Aeff r
QIR;e&s ¼ eeff r Aeff T4BB
Qdirect;s ¼ a Atop qsun ð1 þ s ð1 þ reff ÞÞ
Grgas Prgas P 1:5 108
0:7
Grgas ðGrashof number for gasÞ ¼
The effective infrared radiation absorbance of the film:
T4film
ð23Þ
eeff is the effective emissivity factor of the balloon film and r is Stephan-Boltzmann constant (5:67 108 Þ. 2.3.1.4. Film radiation absorbance. The infrared radiation of sky and earth emits heat to the balloon film. Furthermore, the heat interchange between the lift gas and inner balloon skin by the internal reflected infrared radiation (Section 2.3.1.3). The film radiation absorbance can be divided into two parts as follows (Carlson and Horn, 1981): The thermal interchange of the film: QIR;int ¼ eint r Aeff ðT4gas T4film Þ eint is the interchange effective emissivity factor.
ð24Þ
a is balloon film absorption factor for the sun radiation, qsun is the net gain direct solar intensity and s is the balloon film transmission factor for the sun radiation, and reff is the effective reflectivity factor of the balloon film. The intensity of the sun radiation can be formulated as follows: Isun;z ð1 CFÞ z 6 11000 m qsun ¼ ð27Þ Isun;z z > 11000 m Isun;z ¼ Isun satm
ð28Þ
Isun;z is the resultant solar intensity at a certain altitude, CF is the cloud factor (CF 0.15 to 1), Isun is the total solar intensity, and satm is the atmospheric transmittance. Isun ¼
1358 1þecosðTAÞ ; 1e2 R2AU
satm ¼ 0:5ðe0:65Airmass þe0:95Airmass Þ; and Airmass ðair mass ratioÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pair 2 ¼ 1229þð614sinðaELV ÞÞ 614sinðaELV Þ : P0
e is the orbital eccentricity, RAU is the mean orbital radius; for Earth, e ¼ 0:016708, RAU ¼ 1. MA is a mean number , TA is a true anomaly, anomaly, MA 2p day 365 TA MA þ 2 e sinðMAÞ þ 54 e2 sinð2 MAÞ, and P0 is the air pressure at launch surface. The effective balloon film reflectivity: reff ¼ r þ r2 þ r3 þ . . . ; r is balloon film reflectivity: The reflected sun radiation is defined as follows: Qreflected;s ¼ a Aeff qalbedo ViewFactor ð1 þ s ð1 þ reff ÞÞ ð29Þ qalbedo is the allowable albedo intensity, and ViewFactor is the balloon subjected surface area to the reflected radiation depending on the balloon view angle.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
ViewFactor ¼ h i 1cosðhalf cone view angleÞ 1 Rearth , half cone view angle ¼ sin , Rearth þz 2 where
and Albedo ¼
qalbedo ¼ Albedo Isun sinðaELV Þ,
(
Albedoground ð1 CFÞ
QIR;e&s ¼ eeff;gas r Aeff T4BB
ð36Þ
So, the total infrared thermal radiation is: QIR;gas ¼ QIR;int;gas QIR;e&s
z 6 11000 m
5
ð37Þ
Albedoground ð1 CFÞ2 þ ðAlbedocloud CFÞ z > 11000 m
Rearth is the radius of the earth (6,371,000 m), Albedoground and Albedocloud are the reflected radiation factors for earth ground and cloud, respectively. Herein, the total solar heat can be expressed by a summation of the direct and reflected solar radiation at the time of sun appearance as follows: Qsun ¼ Qdirect;s þ Qreflected;s
ð30Þ
2.3.2. Heat transfer on lift gas The variation of lift gas temperature causes its compression and expansion which influences seriously on the balloon buoyancy. The internal convection, direct and reflected sun radiation, IR radiation, and heat emissivity to the inner balloon film are the heat sources for the balloon lift gas. The differential equation of the lift gas temperature is: dTgas 1 g mgas Rgas Tgas vz ¼ Qgas ð31Þ c cv mgas dt Rair Tair c is the heat capacity ratio, cv is specific heat capacity of the lift gas at constant volume, and Qgas is the total heat of the inner lift gas. Qgas ¼ Qsun;gas QIR;gas Qcon;int;gas QIR;emit;gas
ð32Þ
where Qsun;gas is the total solar thermal radiation, QIR;gas is the net infrared thermal radiation, Qcon;int;gas is the internal convection heat, and QIR;emit;gas is the infrared radiation emission of the lift gas. Heat transfers from/to lift gas according to the following relations (Carlson and Horn, 1981). 2.3.2.1. Internal convection. The internal free convection between lift gas and inner skin is: Qcon;int;gas ¼ HCinternal Aeff ðTgas Tfilm Þ
ð33Þ
2.3.2.2. Lift gas radiation emissivity. Lift gas loses its temperature by adiabatic expansion to the balloon film. The total heat emission of the lift gas: QIR;emit;gas ¼ eeff;gas Aeff r T4gas
ð34Þ
eeff;gas is the effective gas emissivity factor. 2.3.2.3. Gas radiation absorbance. The between lift gas and inner balloon film is: QIR;int;gas ¼ eint r Aeff ðT4gas T4film Þ IR radiation from sky and earth is
interchange ð35Þ
2.3.2.4. Solar radiation model. The impact of solar radiation on the lift gas can be divided into direct solar radiation and reflected solar radiation as mentioned before in the thermal equations of the balloon film. The total heat of solar radiation is: Qsun;gas ¼ aeff;gas Aeff qsun ð1 þ AlbedoÞ
ð38Þ
where aeff;gas is the effective solar absorption factor of the balloon gas. 2.4. Lift gas mass differential equation During ascending process, the differential pressure between lift gas and atmosphere is almost zero resulting in a negligible change in the lift gas mass. In contrast at float altitude, two main reasons lead to a reduction in the lift gas mass. While balloon reaches floating level, volume becomes maximum; then balloon continues ascending process by its momentum and inertia. Herein the differential pressure grows up, and gas should leak gradually out to prevent the balloon explosion achieving the first reason. The second reason is the acquired heat for the lift gas during the daytime that supports lift gas expansion. Lift gas mass tends to escape from the balloon keeping its maximum volume. Therefore, the differential equation of the lift gas mass: dmg ¼ qgas DV_ dt
ð39Þ
DV_ is a volumetric flow rate, DV_ ¼ ValtitudeDtVmax ; Valtitude is the balloon volume at altitude level, and Vmax is the maximum allowable balloon volume. 2.5. Dynamic model The dynamic model represents the force that helps balloon ascent such as the buoyant force and the forces that resist it such as the gross weight and drag force. Buoyant force (free lift) is the balloon lifting gas force (gross inflation) against the gravitational force due to a gross weight where gas density lighter than air density. The drag force is the aerodynamic force that resists the ascending balloon depending on the balloon shape, volume, velocity, and drag coefficient. The dynamic equation of motion (Morris, 1975): mvirtual
dvz 1 ¼ g V ðqair qgas Þ g mgross Cd qair Atop v2z 2 dt ð40Þ
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
6
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
The left term represents the inertia force of the ascending balloon. The three right terms are the gross inflation, the gravitational, and the drag forces, respectively. Where mvirtual is the total balloon mass including lift gas mass, in addition to the air virtual mass that represents load above the ascent balloon head (mvirtual ¼ mgross þ mgas þ Cvirtual qair V), Cvirtual is the virtual mass coefficient, Cvirtual 0:5 (Farley, 2005). mgross is the gross mass (payload + film + ballast). Cd is the drag coefficients. 2.6. Altitude differential equation The differential equation of altitude depends on a relative vertical velocity as follows: dz ¼ vz dt
ð41Þ
3. Uncertainties in ascending process Trajectory simulation is a manner to predict the balloon design parameters using the governing equations of ascending process at different altitudes. Usually, an accurate simulation results in a successful real flight. Uncertainties of the ascending governing equations represent the challenges that face this simulation. The initial lift gas quantity, drag coefficient model, wind velocity forecast, cloud cover, launch time and site are the most significant uncertainties imposed to a high altitude zero pressure balloon trajectories. These uncertainties seriously affect the climbing rate. Therefore, the following sections discuss the influence of some parameters on ascending velocity which is the major common factor between the real flight and simulation. 4. Modeling and simulation
4. Releasing ballast masses at nighttime (Yajima et al., 2009). 5. Next hours/days until the time of no ballast masses or no enough buoyancy of the balloon system. 4.2. Genetic algorithm The genetic algorithm (GA) toolbox estimates the necessary lift gas quantity and minimizes the ascending acceleration. Fig. 2 describes the algorithm linking between the ascending simulation and optimization mathematical relations. GA is a global search technique. It strikes a reasonable balance between exploiting the available information and searching through unexplored regions. GA operation close to the laws of nature uses a population of potential solutions represented by a string of binary digits (chromosomes or individuals). Then, genetic operations such as selection, crossover, and mutation enhance the optimization process. GA initiates the initial random individuals that converge the solution of optimization problem according to supposed constraints. Genetic operations selection, crossover, and mutation are the random selection, keeping diversity, and checking the best selection for the allowable individuals, respectively. The basic structure of GA mainly consists of the following steps: 1. Selection random initial population. 2. Evaluation of the individuals. 3. Applying the genetic operators (selection, crossover, and mutation). GA minimizes the nonlinear constrained objective function as follows: f min ðxÞ ¼
ðqair V xð1Þ mgross Þ g 0:5qair Cd ATop v2z mvirtual ð42Þ
4.1. Matlab M-File Matlab M-file program is used to simulate the high altitude zero pressure balloon model predicting its ascending performance. This program consists of the main program and two subroutines. Firstly, the main program includes the built-in solver function (ode45) which is the fourth orders Runge-Kutta numerical method and the initial conditions such as lift gas mass, lift gas temperature, balloon film temperature, altitude, and velocity. Then, subroutines describe the ascending constant parameters and thermodynamic nonlinear ordinary differential equations as shown in Section 2, respectively. It predicts the balloon design parameters every second comprising the following: 1. Initial conditions at launching. 2. Ascending altitudes considering the solar position and cloud cover effects. 3. Floating altitude.
Start Main Program Call Thermo-dynamic model Solve 5 differential equa tions using RungeKutta numerical solution to get “lifting gas mass – volume – lifting gas temperature – altitude – film temperature” Optimization Program Fitness evaluation of each generated individual with respect to a given objective function
Objective function of Acceleration with one variable “lifting gas mass” Nonlinear constraints Acceleration is the minimum
Stopping code at a minimum value of fitness function “acceleration” with nonlinear constraints END
Fig. 2. Integrated simulation using Matlab and Genetic Algorithm.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Variable is xð1Þ ¼ mgas . The constraints are: 1. Positive free lift all the time of ascending. 2. Velocity is almost constant (5 m/s). 3. No consuming of the ballast masses. The optimization method seeks the necessary lift gas quantity that maintains approximately constant climbing rate at all ascending altitudes. Linking between the simulation and optimization methods predicts the optimum launch lift gas quantity and the corresponding drag coefficient model which achieve an accurate simulation as shown in Fig. 13. Hence, the uncertainty of the launch lift gas quantity can be removed enhancing the ascending performance of the high altitude zero pressure balloon trajectories. 5. Results and analysis 5.1. Model validation Thermtraj NASA model and real flight 167N data were compared to validate this code (Horn and Carlson, 1983).
7
The high altitude zero pressure balloon had a maximum volume of 66,375 m3, was designed to float at an altitude of 36.7 km and carried a payload of 196.82 kg. The balloon’s gross mass and initial lift gas mass (helium) were 381 kg and 69.221 kg, respectively. The local time of launching was 11:35 am from Palestine, Texas on July 24, 1980. This code represents a complete flight simulation comprising the buoyancy compensation by ballast dropping at nighttime. And it predicts the balloon trajectory for several days and nights until the descending at no ballast masses. The code has the capability of adding several subroutines to precise simulation. Figs. 3 and 4 represent the balloon trajectories in the ascending phase and the flight throughout the first day and night, respectively. Real flight data, ThermTraj, and present model are almost close to each other at the desired float altitude and the troposphere ascending altitudes. At the desired float altitude, that is owing to the ascending velocity tends to zero, but at the troposphere may be attributed to the few effective uncertainties. The discrepancy at some points belongs to the climbing rate instability. The following sections discuss influences some of these parameters on the ascending performance in details.
Fig. 3. Balloon ascending validation.
First Ballast Drop
Fig. 4. Balloon trajectory prediction simulation.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
8
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
5.2. Climbing rate discrepancy in different layers Figs. 5–8 show the influence of the launch time, date, and site on the climbing rate at different layers. Results investigate these influences at the troposphere (from the launch position to the ceiling of tropopause about 11 km) and the stratosphere (from the ceiling of tropopause to floating altitude). Average vertical velocity at the troposphere and stratosphere represent the mean ascending
velocity between launch to 11 km and 11 km to float, respectively. 5.2.1. Launch time and date effects Fig. 5 presents the average ascending velocity profiles at different launching time in one day (24 h) at the troposphere and stratosphere. Fig. 5(a) deduces that no significant effect on the average ascending velocity at the troposphere at different launching time. Meanwhile,
Fig. 5. Variation in average vertical velocity at different launch times within a day. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
9
Fig. 6. Variation in average vertical velocity at different launch days within a month.
Fig. 5(b) appears the significant effect at the stratosphere. So, the resultant variation in ascending velocity in 24 h as shown in Fig. 5(c) belongs mainly to the influences of the launching time at the stratosphere. On the other hand, the solar radiation intensity and its angle during daytime cause the notable variation in the average ascending velocity between day and night times. Therefore, the average ascending velocity increases gradually from the sunrise to the maximum peak at midday and decreases again to the sunset. Otherwise, the average ascending velocity is almost constant and low because of the sun absence. Fig. 6 shows that the launch date does not have a significant effect on the average velocity neither at the troposphere nor the stratosphere because of the change in the earth declination angle is very small compared to the solar radiation intensity. 5.2.2. Launch site effect Figs. 7 and 8 describe the influence on the average ascending velocity at 11:35 am in July and September due to the change in latitude and longitude of the launch position, respectively. Figs. 7(a) and 8(a) indicate that the changes in latitude and longitude have no significant effect at the troposphere, but the effect significantly appears at the stratosphere in Figs. 7(b) and 8(b). Figs. 7(c) and 8(c) are the resultants average vertical velocity at the ascending process. Due to earth declination angle and sun position, the influence of the same latitude is not identical as shown in Fig. 7(c). In fact, the earth declination angles at this time of September and July are about 0° and 20°, respectively. Consequently, Fig. 7(c) distributes the average ascending velocity in September equally at both earth poles and maximum at the earth equator. But in July, Fig. 7(c) appears the minimum effect at the South Pole and increases gradually until the equator, then be almost stable until the North Pole. Due to the earth rotation and the sun relative position, Fig. 8(c) shows that the effect of the change in longitude is same as the effect of the launch time within a day in Fig. 5(c). Moreover, the maximum peak at midday is at 95o as the actual launch longitude position in the real flight. The small difference between two months at the same
longitude belongs to the same reason of the earth declination angle. The previous discussions concluded that the changes in the launch time and site influence seriously on the climbing rate at the stratosphere. Meanwhile, the launch date effect is negligible. It means that the uncertainties at the troposphere are limited such as the launch lift gas quantity, and other parameters mainly affect at the stratosphere. Consequently, the following section explains physically the reasons cause variation in the climbing rate during the ascending process. 5.3. Ascending velocity 5.3.1. Ascending performance Variation of ambient temperature and pressure at the different altitudes is the key point that describes the reasons cause the variation in the ascending velocity. The dynamic equation of motion (Eq. (40)) represents a variation in the climbing rate obeying to two major terms: the first term is a buoyant force; the second is a drag force. The following section demonstrates the variation and influences of these forces on the climbing rate. Fig. 9(c) classifies the variation of the ascending velocity to: 5.3.1.1. Ascending velocity between 0 and 11 km. At the beginning of ascent, balloon strongly ascends in high buoyant force because of the difference in density between the air and gas, but after few seconds, the buoyant force decreases gradually because of the reduction in density difference between air and gas as shown in Fig. 9(b). The initial drag force on ascending balloon is high because the flow around balloon is laminar separation causing highpressure drag (Carlson and Horn, 1983). Gradually decreasing in the drag force belongs mainly to the reduction of the air density at higher altitudes compared to slowly increasing in a volume. So, the conclusion is the resultant buoyant force overcomes drag force on the balloon volume resulting in gradually increasing in a climbing rate at troposphere. On the other hand, the ambient tem-
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
10
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Fig. 7. Variation in average vertical velocity at different launch latitude. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
perature decreases while the balloon ascends; even the lift gas and balloon film temperatures are relatively high but lose temperature by adiabatic expansion and IR emissivity to the surrounding. So, the main reason of slowly increasing of volume in Fig. 9(a) not belongs to gas temperature but owing to the reduction in the ambient pressure. This stage concludes that the lift gas quantity represents a significant parameter at the troposphere more than other parameters as mentioned in advance.
5.3.1.2. Ascending velocity between 11 and 20 km. At the beginning of this stage, the difference in density between air and gas decreases resulting in an observable reduction in the buoyant force; that is considered the main reason to reduce climbing rate as shown in Fig. 9(c). Drag sharply decreases due to the reduction in climbing rate where drag force directly proportional to the squared vertical velocity, rather than the ambient temperature changes slightly, but the lift gas and film temperatures have been reduced con-
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
11
Fig. 8. Variation in average vertical velocity at different launch longitude. (a) At the troposphere, (b) at the stratosphere, (c) the resultant of both layers.
tinuously by adiabatic expansion and IR emissivity; and volume still slowly increases. At the second part of this stage, temperatures of lift gas and balloon film increase gradually to be balanced with ambient air temperature leading to obvious increasing in balloon volume that causes the stop of the buoyant force reduction. Meanwhile, flow around volume starts to be not fully laminar and reduces relatively the pressure drag effect resulting in a little bit increasing in climbing rate.
increases but the climbing rate also highly increases due to the low air density and low drag coefficient. The drag coefficient decreases because the flow is turbulent reducing the pressure drag while the friction drag is prevailing. Even though volume grows up but drag coefficient reduces drag force totally. And the buoyant force supports the climbing rate rising. Therefore, lift gas quantity is the decisive parameter of the balloon ascent. So, the next section reveals the effect of the launch lift gas inflation on the ascending velocity.
5.3.1.3. Ascending velocity between 20 – float altitude km. This altitude of the stratosphere is quite different. Ambient temperature increases, also lift gas and film temperatures sharply increase leading to the gas expansion and rapidly growing the volume up. Although the volume
5.3.2. Lift gas inflating quantity effect It is the most significant parameter of the high altitude zero pressure balloon trajectories in accordance to the preceding arguments, especially, at the troposphere. So, GA optimization method is established to estimate the best
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
12
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Fig. 9. Ascending vertical velocity description in midday. (a) Volume–Altitude relation, (b) Buoyant/Drag forces–Altitude relations, (c) Time–Vertical velocity relation.
lift gas quantity during the whole ascent, so that ensures reasonable ascending time and velocity with no ballast consuming. GA estimates the necessary lift gas quantity relevant to selected drag coefficient model, and initial lift gas and balloon film temperatures.
Drag coefficient model, initial lift gas and balloon film temperatures are important parameters in the thermal and dynamic models of the balloon ascending. Some operators considered drag coefficient a constant value 0.5–1.3 (Farley, 2005; Kreider and Kreith, 1975) and others
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
considered it a function of Reynolds number term (Carlson and Horn, 1981, 1983; So´bester et al., 2014) as follows: 8 > 2400 Re < 102 > > > > > 102 < Re 6 100 > > 24=Re > > > 24 Re0:757 100 < Re 6 101 > > > < 16:04 Re0:582 101 < Re 6 102 Cd ¼ > 6:025 Re0:369 102 < Re 6 103 > > > > > 0:47 103 < Re 6 105 > > > > > 0:5 105 < Re 6 2:5 106 > > > : 6:7297 1020 Re2:9495 2:5 106 < Re Or a function of both of Reynolds number term and Froude dependent term (Conrad and Robbins, 1991; Palumbo et al., 2007) as follows: vz Froude number ðFRÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ; gD 4 Rair Tair 1 Cd;Froude ¼ 3 FR Rgas Tgas
mgross ðmgross þ Cvirtual qair VolumeÞ dvz 1þ þ mgas g mgas dt So, Cd ¼ Cd;Froude þ Cd;Renolds The balloon drag changes according to the volume, shape, air density, and velocity. So, it is not easy to represent a drag on the balloon at different altitudes, but it
13
should be selected carefully due to its significant effect on the balloon ascending velocity. Figs. 10 and 11 show the influence of the change in drag coefficient model, initial lift gas and balloon film temperatures on average ascending velocity. Fig. 10 observes that the references used Froude dependent term in addition to Reynolds number term express on higher drag coefficient according to zero pressure balloon shape and its attachments. So, Froude dependent and Reynolds number terms together represent the most accurate model. Fig. 11 deduces that the influence of initial lift gas temperature more than initial balloon film temperature. Also, the variation sensitivity of both temperatures converges at about 290 K which is valid to be as an initial condition of launch temperatures. Fig. 12 clarifies influences of low and high gas inflation quantity on the climbing rate leading to the altitude variation. At low initial gas inflation quantity, the balloon system should throw out ballast masses early and consumes very long time to reach the float altitude. On the other hand, long ascending time leads to inaccurate simulation because of the variations of atmospheric conditions according to the ascent time. At high initial gas inflation quantity, the balloon reaches rapidly to float altitude which refers to the high climbing rate that may cause failure criteria in the balloon film material. Fig. 12 concludes that inadequate climbing rate causes inaccurate simulation affecting the ascending performance. So, optimizing lift gas quantity at the whole ascending process is a trend to get the necessary quantity
Fig. 10. Influence of drag coefficient model on average ascending velocity.
Fig. 11. Influence of initial lift gas and film temperatures on average ascending velocity.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
14
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
First Ballast Drop
Fig. 12. Variation in altitude at different initial lift gas mass.
Fig. 13. Variation in altitude due to optimum and real flight launch lift gas quantity.
that achieves an adequate and stable climbing rate enhancing the ascending performance as shown in the next figure. Fig. 13 establishes the comparison between the real flight and simulation using optimum lift gas quantity. Ascending trajectories illustrate both curves are too close to each other. Furthermore, this method estimated the lift gas mass of 69.63 kg almost near the real flight of 69.22 kg. The optimum simulation in Fig. 13 reveals somewhat stable climbing rate during the ascending process, especially, at the troposphere where the most effective parameter on ascending velocity is the lift gas quantity. Also, optimum value controls well the climbing rate near the floating altitude improving the ascending performance. On the other hand, it attains the ascending trajectory without consuming ballast masses saving these masses at float altitude to compensate the losing altitude during nighttime as long as possible. 6. Conclusions This paper presented the thermal and dynamic simulation of high altitude zero pressure balloons. Nonlinear ordinary differential equations of zero pressure balloons were numerically modeled to describe the ascending performance. Influences of launch conditions on the ascending
velocity at troposphere and stratosphere layers were analyzed. The significant effect on ascending velocity due to different launch lift gas quantity was analyzed. Optimization subroutine using genetic algorithm was implemented to predict the necessary inflation quantity. By using optimum inflation quantity, the simulation results approached real flight data. Based on the simulation results, the conclusions are summarized as follows: 1. Different launch time and launch site have no significant effect on ascending velocity at the troposphere, but the main effect appears at the stratosphere. Meanwhile, the influence of the change in launch date is negligible. 2. Sun emergence and its intensity have the most significant thermal effect on balloon ascent. 3. The same longitude and latitude have a seasonally different effect on ascending velocity owing to the declination angle of the earth. 4. Optimum inflation quantity improves the ascending performance, especially, at the troposphere, and controls well the climbing rate near the floating altitude. 5. Optimum inflation quantity achieves balloon ascent without ballast masses consumption which supports the floating performance.
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040
S. Saleh, W. He / Advances in Space Research xxx (2017) xxx–xxx
Finally, the present work strived to promote the ascending performance of the high altitude zero pressure balloons keeping the pace in this field. The future aspirations should focus on the research at the stratosphere layer enhancing the real flight. References Baginski, F., Winker, J., 2004. The natural shape balloon and related models. Adv. Space Res. 33, 1617–1622 (Science direct). Carlson, L.A., Horn, W.J., 1981. A Unified Thermal and Vertical Trajectory Model for the Prediction of High Altitude Balloon Performance. NASA-CR156884, Texas, USA. Carlson, L.A., Horn, W.J., 1983. New thermal and trajectory model for high-altitude balloons. AIAA J. Aircraft 20 (6), 500–507. Cathey Jr., H.M., 1997. Transient Thermal Loading of Natural Shaped Balloons. AIAA-31338, USA. Cho, C., Raque, S., 2002. Influence of the infrared radiation on a highaltitude scientific balloon. In: 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, USA. Conrad, G.R., Robbins, E.J., 1991. Determination of Balloon Drag. AIAA-91-3666-CP. Cooper, P.I., 1969. The absorption of radiation in solar stills. Sol. Energy 12, 333–346 (Science direct). Farley, R.E., 2005. Balloon ascent: 3-D simulation tool for the ascent and float of high-altitude balloons. In: AIAA 5th Aviation Technology Integration and Operations Conference, Arlington, Virginia. Franco, H., Cathey Jr., H.M., 2004. Thermal performance modeling of NASA scientific balloons. Adv. Space Res. 33, 1717–1721 (Science direct). Garde, G.J., 2005. Comparison of two balloon flight simulation programs. In: AIAA 5th Aviation Technology Integration and Operations Conference, Arlington, Virginia. Horn, W.J., Carlson, L.A., 1983. THERMTRAJ: A FORTRAN Program to Compute the Trajectory and Gas Film Temperature of Zero Pressure Balloon. NASA-CR-168342. Kayhan, O., Hastaoglu, M.A., 2014. Modeling of stratospheric balloon using transport phenomena and gas compress–release system. J. Thermophys. Heat Transfer 28, 534–541.
15
Kreider, J.F., Kreith, F., 1975. Numerical prediction of high altitude zeropressure balloon vertical motion. J. Heat Transfer 97, 155–157. Lew, T.M., Grant, D.A., 1994. Gas temperature control for long duration balloons. AIAA 94-0745. In: 32nd Aerospace Sciences Meeting & Exhibit, Reno, USA. Liu, Q., Wu, Z., Zhu, M., Xu, W.Q., 2014. A comprehensive numerical model investigating the thermal-dynamic performance of scientific balloon. Adv. Space Res. 53, 325–338 (Science direct). Morani, G., Palumbo, R., Cuciniello, G., Corraro, F., Russo, M., 2009. Method for prediction and optimization of a stratospheric balloon ascent trajectory. J. Spacecraft Rockets 46, 126–133. Morris, A.L., 1975. Scientific Ballooning Handbook, Balloon Design Considerations. NCAR-TN/IA-99, Colorado. Palumbo, R., Morani, G., Corraro, F., 2009. An effective approach to characterization of prediction errors for balloon ascent trajectories. In: AIAA Balloon Systems Conference, Seattle, Washington. Palumbo, R., Russo, M., Filippone, E., Corraro, F., 2007. ACHAB: analysis code for high-altitude balloons. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hilton Head, South Carolina. Rotter, J., Marquez, M.P., 2007. Zero pressure balloon reliability factors. In: AIAA Balloon Systems Conference, Williamsburg, VA. So´bester, A., Czerski, H., Zapponi, N., Castro, I., 2014. High altitude gas balloon trajectory prediction: a Monte Carlo model. AIAA J. 52, 832– 842. U.S. St. Atmosphere, 1976. U.S. Government Printing Office, Washington, D.C. Wu, J., Fang, X., Wang, Z., Hou, Zh., Ma, Zh., et al., 2015. Thermal modeling of stratospheric airships. Prog. Aerosp. Sci. 75, 26–37 (Science direct). Xiong, J., Bai, J.B., Chen, L., 2014. Simplified analytical model for predicting the temperature of balloon on high-altitude. Int. J. Therm. Sci. 76, 82–89 (Science direct). Yajima, N., Izutsu, N., Imamura, T., Abe, T., 2009. Scientific Ballooning, Technology and Applications of Exploration Balloons Floating in the Stratosphere and the Atmospheres of Other Planets: Engineering Fundamentals of Balloons, 1-213, Tokyo, Japan. Springer Science (Chapter 2). Zhang, Y., Liu, D., 2015. Influences of initial launch conditions on flight performance of high altitude balloon ascending process. Adv. Space Res. 56, 605–618 (Science direct).
Please cite this article in press as: Saleh, S., He, W. Ascending performance analysis for high altitude zero pressure balloon. Adv. Space Res. (2017), http://dx.doi.org/10.1016/j.asr.2017.01.040