Effect of flight parameters on thermal performance of a hybrid air vehicle for cargo transportation

Applied Thermal Engineering 168 (2020) 114807

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Effect of flight parameters on thermal performance of a hybrid air vehicle for cargo transportation

T

⁎

Junhui Menga,b, , Moning Lia, Lanchuan Zhangc, Mingyun Lvc a

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing 100081, PR China c School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China b

H I GH L IG H T S

combination simulation of the HAV is carried out to investigate its thermal performance. • AEffects of flight time, location, attitude and relative wind speed on temperature and output power of the HAV are researched. • An example of airline flight of the HAV during long distance transport across longitude and latitude is put forward. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Hybrid air vehicle Thermal property Solar cells Output power Flight performance

With the growth of global trade, the market of global freight transportation is increasing. Due to the combination of aerodynamic and buoyant lift, the hybrid air vehicle (HAV) is very suitable for long-distance transport of heavy loads. To achieve a long distance transportation, the HAV is designed to own large size and surface area, which causes the HAV to receive a lot of solar radiation and the resulting thermal effects have an important impact on its flight performance and safety. Meanwhile, complex configuration and solar array covered on the surface of HAV also affect its thermal performance. A co-simulation of thermal model, output power model and dynamic model of the HAV is carried out to investigate effects of flight time, location, attitude and relative wind speed on its temperature and output power during long-distance transportation across different latitudes and longitudes. The results are expected to provide references for future development of the HAV using in longdistance transport of large cargoes.

1. Introduction The globalization of world economy has led to a rapid growth in the demand for international long-distance freight transportation, especially at the stage of rapid development of Internet Commerce. According to the relevant investigation, 99% of the containerized transoceanic transport is undertaken by ships because of their low-cost and the remaining 1% is picked up by airplanes when speed is valuable [1,2]. The eclectic solution with mid-speed and relatively low cost has a great prospect, which makes the hybrid air vehicle (HAV) become a research hotspot. The HAV is one kind of aircraft that combines the characteristics of heavier-than-air (HTA) (fixed-wing aircraft or helicopter) and lighter-than-air (LTA) vehicles [3], as shown in Fig. 1. The combination of aerodynamic and buoyant lift leads to an aircraft that is a “best of both worlds” combination with the high speed characteristics of HTA and the heavy lifting capacity of LTA [4]. Because of the large

⁎

capacity and relatively good controllability, the HAV has great potential applications in the cargo transportation industry [5,6]. There are multiple advantages to using the HAV to be a tool for the long-distance transport of large cargoes. The addition of aerodynamic lift and vectoring engines has improved operational safety and buoyancy control sufficient to eliminate issues that have plagued airships of the past. There will be less constrained by geography and infrastructure gaps for the international business and trade because the HAV owns the ability of vertical take-off and landing with little or no ground support. In addition, the cost of conventional transportation is increasing because of fuel costs and the likelihood of carbon taxes. The utilization of fuel cells and photovoltaic solar modules makes it possible for the HAV to operate with little engine exhaust and zero Greenhouse Gas (GHG) emission. The first record of a sustained research on the concept of combining HTA and LTA aircraft can date back to 1960s [7]. In the early few

Corresponding author at: School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China. E-mail address: [email protected] (J. Meng).

https://doi.org/10.1016/j.applthermaleng.2019.114807 Received 29 September 2018; Received in revised form 3 July 2019; Accepted 16 December 2019 Available online 16 December 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Tg mr , air p Tw

Subscript

i j k SC LAT LST env_ He _dir _sca _ref _IR_gh _IR_ex _IR_in _conv_ex _conv_in atm sa _cond add

an arbitrary envelope unit an arbitrary solar array unit the envelope unit beneath solar array solar cell local apparent time local standard time envelope material helium direct solar radiation scattered radiation reflected radiation infrared radiation from the earth surface infrared radiation emitted from envelope outside infrared radiation emitted from envelope inside external convection heat internal convection heat atmosphere solar array conductive heat additional inertia force

Ta u Q m c T α A Is Itop λam

τh FSr ph p0 αDIP λ3 → ng → n

Variable

env

L/D ID I0n ISC E0 Γ dn

d0 θ ϕ β γ δ ω

Et tLAT tLST Ls

Le TR

lift-drag ratio solar radiation, W/m2 solar radiation intensity, W/m2 solar constant, W/m2 eccentricity correction factor day angle of the sun, radian day number of the year, ranging from 1 on January 1 to 365 on December 31 correction term of the day number angle of incidence of arbitrarily oriented planes, degree local geographic latitude, north positive, degree slope angle of an arbitrarily oriented plane, degree plane azimuth angle, degree solar declination angle, north positive, degree angle between the meridian of the inclined plane and the sun, degree equation of time, hour local apparent (solar) time, hour local standard time, or local clock time, hour longitude of the standard meridian for the local time zone, degree local longitude, degree attenuation of solar energy by Rayleigh scattering

IR re θele IIRgh IIRsh IIR _in

hex hfree hforce Nuatm katm L0 Reatm kHe ρHe PrHe μHe Psa, j ηj

attenuation of solar energy by permanent gas absorption relative optical air mass at a pressure of 101.3 kPa pressure, kPa transmission on the surfaces of the Earth after water vapor absorption transmission on the surfaces of the Earth after aerosol scattering and absorption precipitable water vapor, cm different kinds of heat flux, W mass, kg specific heat, J/(kg·K) temperature, K absorption coefficient area, m2 scattered radiation for a unit area, W/m2 direct solar radiation at the top of the atmosphere, W/m2 air mass ratio when sunlight passes through the atmosphere transmissivity of atmosphere correction factor factored into the air mass ratio atmosphere pressure at altitude h, KPa atmosphere pressure at the sea level, KPa angle of view at altitude h, radian relative position coefficient of the envelope unit and ground surface normal vector of ground surface normal vector of envelope unit reflected solar radiation, W/m2 reflectivity, be adopted as 0.18 for clear sky and 0.57 for overcast sky solar elevation angle, radian absorbed infrared radiation heat flux from ground, W/m2 emitted infrared radiation heat flux from outside and inside of envelope, W/m2 emitted infrared radiation heat flux from inside of envelope, W/m2 external convective heat transfer coefficient free convection coefficient forced convection coefficient Nusselt number for free convection conductivity of ambient air characteristic length Reynolds number thermal conductivity of the internal helium density of the internal helium Prandtl number of the internal helium dynamic viscosity of the internal helium output power of the solar array unit, W/m2 efficiency of the solar array unit,

Fig. 1. The sources of lift for the HAV.

Static buoyancy

Aerodynamic lift

Total lift

Vector thrust

hybrid lift aircraft. They also suggested that any hybrid lift aircraft with payload higher than 200 tons can be designed to be operated at a cost lower than 15 cents/ton-mile with a speed of at least 70 knots. Jeremy Agte et al. [12] made a summary of work performed in the conceptual design of hybrid aircraft as part of a larger endeavor to develop an

decades, researches on the HAV had been mainly focused on the feasibility of the design until the prototype of SkyCat completed its maiden flight in 2000 [8–10]. In recent years, more and more important studies on the HAV have been developed. Alexander Donaldson et al. [11] demonstrated a program that can be used for the parametric design of a 2

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By contrast, thermal property of the HAV for transportation differs to the spheroid stratospheric airship. Basically, the HAV is designed to be larger because of the demand for hundreds of tons of freight transportation. The HAV combines two or three lobes to compose a relatively unconventional a relatively unconventional with a high lift-drag ratio, which leads to unpredictable and complex heat effects from the environment. Besides, the solar cells are laid along the shape of the HAV's upper surface, which causes a dramatic difference in the incidence angle of solar radiation. Although the HAV suffers from weaker solar radiation because it has a lower cruising altitude compared with the stratospheric airship, forced convection heat transfer around the HAV's external surface is more complex because the wind field at low altitude is far from regular. Furthermore, unlike fixed-point observation of the stratospheric airship, long-distance transportation across latitudes can increase the complexity of thermal properties of the HAV with solar array [26,27]. Unfortunately, the relevant investigations are rare. This paper developed a numerical analysis model to investigate thermal properties of the HAV using in long-distance transport of large cargoes. Effects of flight time, location, attitude and relative wind speed on the temperature and output power of the HAV are explored based on the co-simulation of thermal model, output power model and dynamic model of the HAV. The numerical model is verified by a ground test at first and an airline flight of the HAV from Harbin to Guangzhou is illustrated. The results are expected to provide references for future development of the HAV using in long-distance transport of large cargoes.

economically feasible intra-regional air transportation system. Tensys design group developed finite element analysis tools to permit the modeling of HAVs’ hulls [13]. Carichner and Nicolai gave a detailed performance and design analysis on the HAV, which mainly refer to design methods of the traditional airship [14]. In addition, China and France also signed a development contract to design a novel configuration airship for heavy weight transportation together [15]. To achieve a long distance transportation, the hybrid energy with photovoltaic (PV) cell and fuel cell is considered one of the crucial technologies, as it provides power source by converting other forms to electrical energy without environmental pollution [16]. As buoyant lift is governed by volume directly, while aerodynamic lift is governed by projected area or volume to the two-thirds power [6], the HAV is designed to own large size and surface area, which cause the HAV to receive a lot of solar radiation. Unfortunately, the conversion efficiency of thin film flexible solar array is around 10% in the engineering application nowadays [17]. It means that only a portion of sunlight energy received by the solar array is converted to electric energy, and considerable energy is transformed into heat, which puts the HAV a great disadvantage. The heat generated by the solar array will increase the pressure of the helium inside the hull and age the envelope material underlaid the PV modules. In addition, the thermal performance of a HAV can have a big effect on output performance of the solar array [18]. Many researches and developments have been in progress in thermal analysis on the high altitude airships in the past decades. Li et al. [19] developed the thermodynamic models of PV array and stratospheric airship, based on which the three-dimensional temperature profile and output power of PV array were also presented. Liu et al. [20] proposed a numerical model to simulate the thermal performance of a stratospheric airship with solar array and analyzed the temperature field and flow field distribution by a computational fluid dynamics (CFD) method. Zhu et al. [21] investigated effects of the transmissivity of external encapsulation layer of solar array and wind speed on the thermal performance and output power of solar array. Wu et al. [22] presented a comprehensive literature review on thermal issues of stratospheric airships, in which the research activities and results on the main thermal issues were surveyed, including solar radiation models, environmental longwave radiation models, external convective heat transfer, and internal convective heat transfer. It could be concluded that solar radiation has great influence on the thermal properties of the inflatable vehicles as well as the output performance of solar cells [23–25].

2. Theoretical model 2.1. Basic assumptions It is well known that thermal properties of the HAV and output performance of the solar array are coupled with each other and affected by flight regime of the HAV. To investigate influences of flight conditions on thermal properties and output performance, a numerical model including dynamic model, thermal model and solar array model is developed in this paper. Based on the general model of fixed-wing aircraft and stratospheric airship, some specific features are introduced into the HAV model. And in order to simplify the model, some reasonable assumptions are made as follows: (1) The HAV is assumed as a rigid body in the model for the purpose of simplification. Therefore, the geometric deformation of the HAV is neglected and the volume is constant.

50m

39m

35m

52m

x

z y

117m Fig. 2. Configuration and dimensions of the HAV. 3

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ID = I0n TR Tg Tw Ta cos θ

(2) The thickness of the envelope material and solar array is quite small compared to the diameter of the HAV, so the curvature radii of the envelope and solar array at the same position are treated as equal. (3) Similarly, the assumption is made that temperatures of envelope and solar cells at same position are same because the flexible solar cells are coated on the surface of envelope.

(1)

where I0n is the intensity of the extraterrestrial normal solar radiation which can be obtained as:

I0n = ISC (r0 r )2 = ISC E0

(2)

ISC is solar constant that has a value of 1367 W/m2 and E0 is the eccentricity correction factor of the Earth’s orbit which can be received as:

2.2. Geometric model and parameters of the HAV

E0 The transportation vehicle explored in this paper is a liftbody-type buoyancy-lifting hybrid vehicle with the solar array on the top surface. This study is part of a project aimed to investigate feasibility of the application of HAVs in the transportation industry, which funded by Beijing Institute of Technology Research Fund Program for Young Scholars. According to the previous concept design, a prototype model with a three-lobe shape and four tails distributed symmetrically on the hull is constructed, which can be seen in Fig. 2. Several basic parameters of the HAV are listed in Table 1. The HAV is designed to achieve a range of 3260 km and loading capacity of 1960 kg with external dimensions of 117 m × 52 m × 39 m. The solar array is made up of flexible amorphous silicon PV cells, which is covered on the surface of HAV using network splicing technology, with 50 m length and 35 m width. It is worth noting that there is a substrate layer between PV module and envelope material for thermal protection and they are assumed to be an integrity with an equivalent thermal conductivity in this study.

= 1.000423 + 0.032359 cos Γ + 0.000086 sin 2Γ + 0.000086 sin 2Γ − 0.008349 cos Γ + 0.000115 cos 2Γ

(3)

Γ is described as the day angle of the sun which can be calculated as follows in radian [2]. (4)

Γ = 2π (dn − d 0) 365.2422

where dn is the day number in a year, i.e., dn = 1 when the date is the first day of January and dn = 366 when the date is December 31 in an ordinary year, and d 0 is correction term of the day number which can be received as [30]

d 0 = 79.6764 + 0.2422·{year − 1985 − INT[(year − 1985) 4]}

(5)

Because of the combination of buoyancy and aerodynamic lift, the HAV is huge and owns curved surface. The incidence angle of solar radiation affects heat received by the surface of the HAV and efficiency of solar cells, which can be described as angular losses. The incidence angle θ in Eq. (1) is the angle between the incident solar ray and normal direction of the curved surface of the HAV, in degrees, which can be calculated as [31]:

2.3. Thermal model of the HAV Thermal model of the HAV is used to calculate the temperature both of the envelope material and the internal helium. It is necessary to develop an exact thermal model for investigating the effects of these factors on the flight state. The thermal environment of the HAV is shown in Fig. 3, including external and internal environments. As shown in the figure, the external thermal environment of the HAV includes convection heat transfer and external thermal radiation, which vary according to time, location, altitude, weather and so on. The internal thermal environment of the HAV mainly includes convection between envelope and internal helium, infrared radiation of envelope and diaphragm [28,29]. During flight of the HAV, a thermal balance can be received and the energy equation can be obtained by the law of conservation of energy.

cos θ = (sin ϕ cos β − cos ϕ sin β cos γ ) sin δ + (cos ϕ cos β + sin ϕ sin β cos γ ) cos δ cos ω + cos δ sin β sin γsinω

(6)

where, ϕ is the local latitude, β is the slope angle of an arbitrarily oriented plane as shown in Fig. 4, γ is the plane azimuth angle, which represents the angle between local meridian line and the projection line of the normal direction of the curved surface. Particularly, the solar declination angle δ can be received as (in degrees):

δ = (180 π )(0.006918 - 0.399912 cos Γ + 0.070257 sin Γ − 0.006758 cos 2Γ + 0.000907 sin 2Γ− 0.002697 cos 3Γ + 0.001480 sin 3Γ)

(7)

The hour angle ω is the angle between the meridian of the inclined plane and the sun, which can be obtained as follows.

2.3.1. Solar radiation received by an arbitrarily oriented plane There are several heat sources of radiation received by the HAV in flight, including direct solar radiation, solar scattering radiation, infrared radiation and cloud layer albedo radiation, of which the direct solar radiation is the most critical factor. On account of cruise within the atmosphere of the Earth, there are a number of factors that affect solar radiation, such as atmospheric constituents, day of year, time of day, operating latitude and operating longitude. The solar radiation on the arbitrarily oriented envelope unit on the HAV can be received as follows.

ω=

360 E ⎛12 + t − tLAT ⎞ 24 + Et ⎝ 2 ⎠

(8)

where Et is the equation of time and can be received as [31]

Et =

229.18 (0.000075 + 0.001868 cos Γ − 0.032077 sin Γ − 0.014615 cos 2Γ 60 − 0.040890 sin 2Γ)

(9)

Table 1 Relevant parameters of the HAV, PV module and envelope material. The HAV Max Payload Range at Max Payload Length Width Height Gross Weight Aerodynamic L/D Design Cruise Speed

PV module 1960 kg 3260 km 117 m 52 m 39 m 20050 kg 6.4 50 m/s

Type Area density Size Conversion efficiency Temperature coefficient Thickness

Envelope material Amorphous silicon 300 g/m2 330 mm × 330 mm 7.5% under STC −0.01%/K 0.2 mm

4

Type Area density Poisson ratio Elasticity modulus Thickness Thermal conductivity of substrate layer

Flexible fiber-reinforced composite 190 g/m2 0.3 7GPa 0.15 mm 0.22 W/(m/K)

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Direct Solar Radiation

External Spontaneous Infrared Emission

Solar Scattering Radiation

Internal Natural Convection

Internal Spontaneous Infrared Emission

External Forced Convection

Ground Albedo Radiation

External Natural Convection Ground Infrared Radiation

Fig. 3. The thermal environment of the HAV.

absorbed heat includes direct solar radiation Qenv _dir , i , scattered radiation Qenv _sca, i , reflected radiation Qenv _ref , i and infrared radiation from the earth surface Qenv _IR _gh, i and the emitted heat include infrared radiation emitted from envelope outside and inside Qenv _IR _ex, i , Qenv _IR _in, i , external and internal convection heat Qenv _conv _ex , i Qenv _conv _in, i . Therefore, the energy equation can be given as [24]

menv, i ·cenv·

dTenv, i dt

= Qenv _dir , i + Qenv _sca, i + Qenv _ref , i + Qenv _IR _gh, i − Qenv _IR _ex , i − Qenv _IR _in, i − Qenv _conv _ex , i − Qenv _conv _in, i (13) where menv, i , cenv and Tenv, i are the mass, specific heat and temperature of the envelope unit. The absorbed direct solar radiation heat flux Qenv _dir , i mentioned above can be received as

Fig. 4. Position of the sun relative to an arbitrarily oriented solar cell.

and tLAT is the local apparent time which can be converted to the local standard time tLST as follows.

tLAT = tLST +

1 (Ls − Le ) + Et 15

Qenv _dir , i = α env·Aenv, i ·ID

where α env is the absorption coefficient of envelope material, Aenv, i is the area of envelope unit i . The absorbed scattered radiation heat flux Qenv _sca, i can be gotten as

(10)

In the equation, Ls and Le are longitude of the standard meridian for the local time zone and local longitude, respectively. The attenuation of solar energy by Rayleigh scattering, permanent gas absorption can be received as [32]

TR Tg = 1.021 − 0.084 × [mr , air (949p × 10−5 + 0.051)]1

2

(14)

Qenv _sca, i = α env·Aenv, i ·Is

(15)

where Is is scattered radiation for a unit area at the HAV’s altitude, which can be calculated with

Is = 0.5·Itop·sin α·λam ·(1 − τh) (λam − 1.41·τh)

(11)

(16)

λam is the air mass ratio when sunlight passes through the atmosphere, which can be given by

The other two main factors causing energy decrement is water vapor and aerosol, and the transmission on arbitrary planes can be given as

Tw Ta (12)

α>0 ⎧ FSr ·(ph p0 )·[ 1229 + (614·sin α )2 − 614·sin α ] ⎨ ph p0 ·(1 + α αDIP ) − αDIP ⩽ α < 0 ⎩ (17)

2.3.2. Thermal balance of the envelope exposed to environment As for an arbitrary envelope i not underneath the solar array, the

where FSr is a correction factor factored into the air mass ratio to account for fog and smoke, or for a different planet’s atmosphere. αDIP is the angle of view at the HAV’s altitude. For the envelope, the absorbed reflected radiation heat flux in Eq.

λam =

= [1 − 0.077(umr , air (949p × 10−5 + 0.051))0.3] [0.935mr , air (949p × 10

−5

+ 0.051) ]

The relevant parameters are detailed in the literature [33].

5

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2 hin = 0.13·kHe·(ρHe ·g·|Tenv − THe|·(PrHe THe )·μHe )1

(13) can be received as [16]

Qenv _ref , i

= λ3·α env·Aenv, i ·IR·|→ n g ·→ nenv|

where λ3 is the relative position coefficient of the envelope unit and ng and → nenv are normal vector of ground surface and ground surface, → envelope unit, respectively. The reflected solar radiation IR can be obtained as

2.3.3. Thermal balance of the solar array Similarly, absorbed heat sources of an arbitrary solar array unit j come from direct solar radiation Qsa _dir , j , scattered radiation Qsa _sca, j and reflected radiation Qsa _ref , j , while the consumed energy mainly includes infrared radiation Qsa _IR _ex , j , external convection heat flux between solar array and external atmosphere Qsa _conv _ex , j , conductive heat flux transferred to the envelope beneath solar array Qsa _cond, j and electricity power converted from solar energy Psa, j . The energy equation can be expressed as [16]

(19)

The absorbed infrared radiation heat flux from ground can be given as

Qenv _IR _gh, i = Aenv, i ·IIRgh

(20)

The emitted infrared radiation heat flux from outside and inside of envelope can be given as

Qenv _IR _ex , i = Aenv, i ·IIRsh

msa, j ·csa·

(21)

Qenv _IR _in, i = Aenv, i ·IIR _in

where Tenv and Tatm are temperatures of envelope material and ambient environment, respectively, and hex is the external convective heat transfer coefficient which can be divided into free convection and forced convection as follows

Psa, j = ηj ·Qj

(29)

ηj is the efficiency of PV unit and related to temperature and solar irradiation. As for amorphous silicon PV module, ηj can be received from the test under standard condition of Q0 = 1000 W m2 , T = 25 °C and λam0 = 1.5.

(24)

⎧ hfree = Nuatm ·katm L0 0.55 ⎨ hforce = (katm L0)·(2 + 0.41·Reatm ) ⎩

(28)

where msa, j , csa and Tsa, j are the mass, specific heat and temperature of the solar array unit. If Qsa _dir , j + Qsa _sca, j + Qsa _ref , j ≜ Qj , the output power of the PV unit can be described as

(23)

3

dt

− Psa, j

According to the heat transfer theory, external convection heat flux between envelope outside and ambient environment can be received as

3 3 hex = (hfree + hforce )1

dTsa, ij

= Qsa _dir , j + Qsa _sca, j + Qsa _ref , j − Qsa _IR _ex , j − Qsa _conv _ex , j − Qsa _cond, j

(22)

Qenv _conv _ex , i = hex ·Aenv, i ·(Tenv − Tatm)

ηj (25)

= 0.3602·[−0.7576(Qj Q0) + (Qj Q0 )0.6601]· 1.0322 ⎤ ⎡1 − 0.02863 Tsa, j − 1.1432 λam + ⎛ λam ⎞ ⎥ ⎢ T0 λam0 ⎝ λam0 ⎠ ⎦ ⎣

where Nuatm is the Nusselt number for free convection, katm is the conductivity of ambient air, L0 is the characteristic length, and Reatm is the Reynolds number of the HAV. Furthermore, internal convection heat flux inside the hull Qenv _conv _in, i is given by [16]

Qenv _conv _in, i = hin ·Aenv ·(Tenv − THe )

⎜

⎟

(30)

2.3.4. Thermal balance of the envelope beneath solar array There are some differences between the envelope material exposed to the environment and under solar array. The main heat source of the envelope beneath solar array is transferred from solar cells. In consequence, the energy equation of the envelope unit k beneath solar

(26)

and the internal free convective heat transfer coefficient can be gotten as

z

Conventional configuration

Solar array

r

r

y Three multi -lobed configuration

l0 y

(27)

where kHe , ρHe , THe , PrHe and μHe are the thermal conductivity, density, average temperature, Prandtl number and dynamic viscosity of the internal helium, respectively.

(18)

IR = re (ID sin(θele ) + Is )

3

j

z

r

x One tilted plane

Fig. 5. Envelope and solar array configuration. 6

dx

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dTenv, k = Qenv _cond, k − Qenv _IR _in, k − Qenv _conv _in, k dt

(31)

where menv, k , cenv and Tenv, k are the mass, specific heat and temperature of the envelope unit beneath solar array, Qenv _cond, k Qenv _IR _in, k Qenv _conv _in, k are the conductive heat transferred from solar array, internal infrared radiation and convection heat inside the HAV, which can be received as

Qenv _cond, k = A env ·ksa·

Tsa − Tenv dsa

(32)

Qenv _IR _in, k = Aenv ·IIR _in

(33)

Qenv _conv _in, k = hin ·Aenv ·(Tenv − THe )

(34)

10

330

8

325 6 320 Theoretical Prediction Experimental Measurement Relative Error

315

4

2

310

305

Relative Error (%)

menv, k ·cenv·

Temperature of solar array (K)

array can be obtained as [16]

8

9

10

11

12

13

14

15

0 16

Time (h)

2.4. Output power of the solar array

Fig. 7. Comparison of temperatures between predicted and measured data.

The transportation vehicle studied in this paper is a three lobes configuration, which can be considered as three conventional body paralleled with the photovoltaic array on the top surface as shown in Fig. 5. Referring to the traditional ellipsoid configuration, solar array installed on the upper surface of lobes can be divided into three portions with a symmetric form. The geometric equation of the solar array can be described as

y 2 + z 2 = r 2 (x ) 0 ⩽ x ⩽ L

solar array can be expressed by

Aarray = NL ∑ ∑ Aj x

where, the NL is the number of lobes. In order to balance calculation efficiency and accuracy, the solar array on one lobe of the HAV can be divided into 450 × 5000 small elements in this paper. Therefore, the total output power of solar array on the HAV can be given by

(35)

A sufficiently small curved surface of PV modules j is chosen to investigate, which can be described as a tilted plane. The length of this titled plane is dx along the flight direction and the width can be represented as the length of small circular arcs along the circumferential direction. The area of tilted element j is defined as Aj , which can be described as [34,35]

Aj = rdθdx 1 +

r ′ (x )2

Ptotal = Aarray ·Psa, j

(38)

2.5. Dynamic model of the HAV In order to investigate the coupling relationship of attitude and thermal properties of the HAV, the dynamic model is constructed in this paper. The external forces acting on the vehicle include gravity, buoyancy, aerodynamic force and added inertia force. As the gravity is always straight down, and the center of gravity does not coincide with the center of volume, the gravity and its moment are described in body

(36)

To simplify the calculation model, assuming θ0 is the central angle of solar array for each lobes and the solar array is only laying on the top surface, l0 is the length of the solar array atop the hull, the total area of Thermal environment of HAV

Thermal environment of solar array

UDF program

UDF program

HAV

Solar array

Temperature and grid data of envelope under solar array

Heat flux and grid data behind solar array

Output

Initial thermal flux

(37)

θ

Output

IDW

Thermal flux

No

Temperature

Thermal flux of envelope under solar array

Temperature of solar array

Is thermal flux balanced?

Is temperature balanced?

Yes

No

Output thermal flux

Output temperature

Yes

Fig. 6. Diagram of the thermal data using IDW approach. 7

Initial temperature

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340

290

320

280

Tail-1 Tail-2 Tail-3 Tail-4

M N

300

270

T (K)

Temperature (K)

Fig. 8. Temperature distribution of the HAV on summer solstice day.

280 260

260 250

Helium(without solar cells) Envelope(without solar cells) Helium Envelope Solar Cells

240 220

240 230

200

0

2

4

6

8

10

12

14

16

18

20

22

24

0

2

4

6

8

Time

12

Time

Fig. 9. Average temperature-time curves of each part of the HAV.

axis system as follows

− G sin θ ⎤ ⎡ FG, x ⎤ ⎡0⎤ ⎡ FG = ⎢ FG, y ⎥ = bRg ⎢ 0 ⎥ = ⎢ G cos θ sin ϕ ⎥ ⎢ ⎥ ⎥ ⎣G ⎦ ⎢ ⎣G cos θ cos ϕ ⎦ ⎣ FG, z ⎦

10

(39)

8

14

16

18

20

22

24

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Fig. 10. Temperature distribution of the middle cross-section of the HAV on summer solstice day. 100 350

Time=8h Time=12h Time=16h Time=24h

80

120

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Fig. 11. The temperature distribution trend of the middle cross-section at different time.

Fig. 12. Average temperature of each part of the HAV at different dates.

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W30°

W90°

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24

Fig. 15. Effects of longitude on the thermal performance and output power of the HAV.

Time (h) Fig. 13. Output power-time curves of the solar array on the HAV in different seasons.

{fi }T = {Fadd, x , Fadd, y , Fadd, z , Madd, x , Madd, y , Madd, z }T

(43)

The general formula calculated additional inertia force can be written as follows.

⎡ MG, x ⎤ ⎡ 0 − z c yc ⎤ ⎡ − G sin θ ⎤ 0 − x c ⎥ ⎢ G cos θ sin ϕ ⎥ MG = ⎢ MG, y ⎥ = ⎢ z c ⎢ ⎥ ⎢− y x ⎥ ⎢ 0 ⎥ M c ⎦ ⎣G cos θ cos ϕ ⎦ ⎣ G, z ⎦ ⎣ c ⎡ yc mg cos θ cos ϕ − z c mg cos θ sin ϕ ⎤ = ⎢ − z c mg sin θ − x c mg cos θ cos ϕ ⎥ ⎥ ⎢ ⎣ x c mg cos θ sin ϕ + yc mg sin θ ⎦

fi = −ρair

At the same time, the buoyancy is always straight up opposite to the gravity. The center of volume coincide with the center of buoyancy and the moment of buoyancy is zero.

(41)

MB = [ LB MB NB ]T = [0 0 0]T

(42)

duj (44)

dt

where {αij} represents the additional inertia tensor matrix. As the symmetry of the HAV and the property of tensor, the relationship can be received

(40)

B sin θ ⎡ FB , x ⎤ ⎤ ⎡ 0 ⎤ ⎡ FB = ⎢ FB , y ⎥ = bRg ⎢ 0 ⎥ = ⎢ − B cos θ sin ϕ ⎥ ⎢ ⎥ ⎥ ⎣− B ⎦ ⎢ ⎣− B cos θ cos ϕ ⎦ ⎣ FB , z ⎦

∑ αij

αij = αji = 0, i ≠ j

(45)

Therefore, the additional inertia force and moment can be expressed as follows ∼

⎧ Fadd = − d (ρfadd vo) = −ρfadd d vo − ω × ρfadd vo dt dt ⎨ M = − d (ρmadd ω) = −ρm d∼ω − ω × ρm ω − v × ρf v add o add dt add o dt ⎩ add

(46)

Considering the forces and moments on the vehicle, and their relationships between vehicle’s own characteristics, its dynamical equations are obtained

Aerodynamic forces are calculated by computational fluid dynamics. Due to the large volume to weight ratio, the added mass effects should be taken into account. The HAV drives the surrounding air to accelerate with it, and the air would has opposite effect to HAV which is additional inertia force. It can be described into six generalized force components

− mS (rc ) ⎤ νȯ m (ω × vO +ω×(ω×rC )) ⎤ F ⎡ mI ⎡ ⎤+⎡ =⎡ ⎤ Mo ⎦ ⎥ ⎢ ⎥ ⎢ × + × × ( ) ( ) ( ) ω ω ω v m S r I I m r ̇ w c o o c o ⎣ ⎣ ⎦ ⎦ ⎣ ⎦ ⎣ (47) 225

340

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0° 40° S 40° N

200

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240 50°S

30°S

10°S

10°N

30°N

150 125 100 75 50 25 0

50°N

0

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4

6

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Fig. 14. Effects of latitude on the thermal performance and output power of the HAV. 10

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Head for West Head for SW45° Head for South Head for SE45° Head for East

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Heading for SW45° Heading for SE45° Heading for West Heading for South Heading for East

75 50 25

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Fig. 16. Effects of yaw angle on temperature of envelope and output power of solar array.

300

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Fig. 17. Effects of pitch angle on temperature of helium gas and envelope. 340

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320

collaborative simulation using MATLAB and FLUENT is carried out. Relationship between flight environment and attitude of the HAV is received by MATLAB simulation. The mixed boundary conditions of the HAV in FLUENT can be defined according to the MATLAB simulation results and a user defined function (UDF) program is developed to receive heat transfer coefficient and external radiation temperature. It can be seen from the previous analysis that the heat exchange of the HAV includes radiation, conduction, convection and coupled heat transfer. The thermal effects of the HAV with solar array are simulated using CFD and discrete tetrahedral meshes are used for the computing domain. The control volume method in this paper is selected to discretize governing equations of the model and non-staggered grids and SIMPLE algorithm are introduced to simplify the program during the discretization. The basic governing equations can be described as follows. The mass governing equation is

0

5

10

15

20

25

170 30

Airspeed (m/s) Fig. 18. Effects of wind speed on thermal performance and output power of the HAV.

∂ρ + div (ρ u) = 0 ∂t

3. Simulation analysis and validation

(48)

The momentum governing equation is

3.1. Simulation model and boundary conditions

∂ (ρ u) ∂P + div (ρ u·u) = div (μ·grad u) − + Su ∂t ∂X

In order to investigate the coupling effects of flight dynamic and thermal performance of the HAV during long distance transportation,

The energy governing equation is 11

(49)

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Harbin (45°N,125°E) Beijing (40°N,117°E)

Zhengzhou (35°N,114°E)

Wuhan (30°N,113°E)

Airline From Harbin to Guangzhou

Guangzhou (23°N,112°E)

Fig. 19. Airline flight from Harbin to Guangzhou.

∂ (ρcp T ) f ∂t

+ div (ρcp uT ) f = div (k ·gradT ) f + STf

analyzed before simulation. Four different computational meshes with 1520358, 2038794, 2594321 and 3189487 grids are briefly contrasted and analyzed. The results indicate that the simulation model with 2038794 grids is accurate enough since the difference of the calculated temperature difference on HAV based on 2038794, 2594321 and 3189487 grids are less than 1.5%.

(50)

The surface to surface model (S2S) is chosen in the FLUENT software, in which the HAV’s surface is assumed to be diffuse surface and grey body radiation model is used as follows.

Qi = Af , i (Gi − Ji )

(51) 3.2. Experimental verification of the thermal model

where, Af , i is area of an arbitrary element, Gi and Ji are received and emitted heat flux, respectively.

Gi =

A ground experiment of scaling model is conducted to validate the thermal model of the HAV with solar array in Beijing in September 2016 on a cloudless day. The scaling airship with the volume of 200 m3 is tethered at about 20 m height. The maximum solar irradiation on that day is 680 W/m2 and the average wind speed is 5 m/s with the ground temperature of 290 K. The envelope material of HAV is a flexible fiber reinforced composite material, whose thermal parameters have been known. The prediction temperatures of the solar array are received by simulation model whose input parameters are based on the experimental conditions. The temperature distribution on the surface of solar array is measured by several face-stuck thermocouples. The detailed experimental setup can be seen in Refs. [16,26]. The accuracy of the simulation model can be verified by comparing predicted and measured temperatures of the solar array from 8 am to 4 pm, as shown in Fig. 7. It can be seen from the figure that temperature differences of the maximum and minimum values between the experimental data and simulation results are 6.95 K and −0.75 K at 11:00 and 13:00, respectively. The maximum relative error is 2.1% at 11:00, which can be acceptable for the theoretical model.

Ji − εσT f4, i (52)

1−ε N

Ji = εσT f4, i + (1 − ε )

∑ Ji Xi,j j=1

(53)

where, Tf , i is temperature of the arbitrary element, ε is the emissivity, Xi, j is the radiation angle coefficient from element i to j. The uneven temperature distribution of helium inside the hull of HAV will cause natural convection and the Rayleigh number, which is affected by characteristic length of the HAV and maximum temperature difference of the inside Helium, can reach to 1013. Therefore, the realizable k − ε model is selected as a turbulence model to describe the heat exchange of the HAV. It is well known that thickness of the solar cell is much smaller in comparison to length and width of the HAV and the solar array is covered on the upper surface of HAV tightly. There will be too many grids if the solar array and envelope of the HAV are treated as a whole and meshed with the same size. Therefore, the solar array and envelope of the HAV are meshed respectively and the Inverse Distance Weighted (IDW) approach [36] is used to realize coupling and exchange of corresponding thermal data. It's easy to understand that lower surface of the solar array shares the same area with upper surface of the envelope in the corresponding position and boundary conditions of the upper surface of the solar array and lower surface of the envelope are surrounding environment and helium inside the hull, respectively. The thermal data including temperature and heat flux between lower surface of the solar array and corresponding upper surface of the envelope are coupled by interpolation method with IDW approach. The flow chart can be described as Fig. 6. Furthermore, the influence of mesh size on calculation precision is

4. Numerical results and discussion The simulation model is used to investigate relationship between flight parameters and thermal performance after experimental validation. The influence of flight time, date, position, attitude and wind speed on the thermal performance of the HAV are explored respectively. 4.1. Effects of flight time and date There is a big difference of solar radiation received by the HAV in different dates or different moments of one date. Consequently, the 12

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Harbin

Beijing

Zhengzhou

Wuhan

Guangzhou

Fig. 20. The temperature distributions of the HAV passing through five positions.

rapidly after receiving solar radiation, especially for solar array, which can be illustrated in Fig. 9 in more detail. Fig. 9 is elaborated to show the change of the average temperature of inner helium Tgas , envelope Tenv , solar array Tsc and four tails of the HAV over time. The temperature rising trend of the solar array is faster than inner helium and envelope before 12:00 at noon. In addition, the solar array is like a heat source after receiving solar radiation to heat helium gas inside the hull. So the highest temperature of the inner helium is situated between the solar

thermal performance and output power of the HAV are affected by the different conditions of solar radiation. The head of the HAV is assumed to be towards west and temperature distribution graphs of the HAV on summer solstice day are shown in Fig. 8. It can be seen from the figure that the temperature distribution is uneven with the change of solar radiation angle. Because of the ground and atmospheric thermal radiation, the temperature at bottom of the HAV is higher than the temperature at the top in the night. The temperature of the HAV rises 13

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Harbin

Beijing

Zhengzhou

Wuhan

Guangzhou

Fig. 21. Temperature distributions of the middle cross-section of the HAV passing through five positions.

ones at point N. In order to illustrate the effect of time on airship temperature in more detail, the temperature distribution of the middle cross-section along length of the HAV is also shown in Fig. 10 and the distribution trend at different time is consistent with the temperature variation shown in Fig. 11. It should be noted that the particular three-lobe configuration allows the protruding part of the HAV to receive more solar radiation. Peak temperature of the HAV is on the location of 50° at

array and the envelope. The average temperature of inner helium and envelope material of the HAV without solar array is also presented in Fig. 9. By contrast, they are very close. The average temperature of four tails can be clearly divided into two groups because of the symmetry, which means that there is a similar temperature-varying trend of two tails in one side. The temperature curves of the two groups intersect with each other at point M and point N respectively at noon and the temperature of two upper tails at point M is higher than two bottom 14

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Temperature (K)

J. Meng, et al. Harbin Beijing Zhengzhou Wuhan Guangzhou

90

360 330 300 270 240 210 180 150 120

120

60

150

summer solstice day inhibits the process of photoelectric transformation. In addition, different sunrise and sunset times in the different seasons determine the time length of photoelectric transformation of the solar array. Generally, the total power generated by solar cells in summer solstice day is the largest one because of the electricity generation in the morning and evening.

30

4.2. Effects of latitude and longitude 180

120 150 180 210 240 270 300 330 360

0

210

Effects of latitude on the thermal performance and output power of the HAV are shown in Fig. 14. Theoretically, due to the revolution of the earth, the effects of latitude on thermal performance of the HAV are exactly same as changes in flight date. The HAV is assumed to fly on the location of different latitudes at their location time of noon in the summer solstice and the average temperatures of helium, envelope and solar array are shown in Fig. 14(a). It can be seen that when the sun illuminates directly in the northern hemisphere on the summer solstice day and the average temperature of each part of the HAV in the north is obviously higher than the HAV in the south. Similarly, the output power of solar array on the location of 40°S is higher than on the location of 40°N. The relationships between flight longitude and thermal performance and output power of the HAV are shown in Fig. 15. It can be seen from the comparison between Fig. 15 and Fig. 9(a) that the effect of longitude is similar to that of time. It is easy to understand that the main reason is revolution of the earth.

330

240

300 270

Fig. 22. The temperature distribution trend of the middle cross-section at different positions.

8am and the corresponding position at 4 pm is symmetrically on the location of 130°. In addition, the temperature of the solar array differs little from the rest envelope at midnight. The solar altitude and solar radiation intensity are different at different dates in one year, which affects the thermal performance and output power of the HAV. The average temperature of inner helium, envelope, solar array and four tails of the HAV at noon on four typical dates in four seasons are shown in Fig. 12. As shown in the figure, the average temperature of solar array is the highest one in all four seasons, naturally. For each part of the HAV, the temperature in the summer solstice and winter solstice are the highest one and lowest one, respectively. Four tails can also follow the two-group rules: temperature of tail one and tail three at the top is similar and temperature of tail two and tail four on the bottom is similar. It is well known that output power of the solar array is related to its received solar radiation and working temperature. The output power curves of the solar array on the HAV in different seasons are shown in Fig. 13. As can be seen from the figure, output power of the solar array increases to maximum value at noon and then decreases to the initial value. Although the solar array can receive more solar radiation, the most maximum output power at noon in summer solstice day is lower than the corresponding value in spring equinox day. The most likely possibility is that the excessive temperature of the solar array at noon in

340

Because of the 3-lobe configuration, the flexible solar cells are installed on the surface of the HAV, which is a curved surface. The solar radiation on the surface of this curved surface with great curvature is different from that on the horizontal projection plane [2] and the influence of attitude is great, which can be seen in Fig. 16 and Fig. 17. The HAV is assumed to fly at 40oN latitude region in summer solstice. As shown in Fig. 16, the temperature of envelope and output power of solar array change obviously with the heading angle of the HAV. When the HAV flies heading for north, the thermal effects and output power are both larger than that when heading for any other direction in the daytime. The main reason is that there is no obstruction between the lobes in the sun under this circumstance. It is worth noting that the temperature of envelope when the HAV is heading for southeast in the morning is larger but when the HAV is heading for southwest in the afternoon is larger. The output power curve has a similar trend because of the change in solar radiation.

Helium Envelope Solar Array

320

290

300 280 260 240

270 260 250 240

220 200

Tail-1 Tail-2 Tail-3 Tail-4

280

Temperature (K)

Temperature (K)

4.3. Effect of flight attitude

Harbin

Beijing

Zhengzhou

Wuhan

230

Guangzhou

Location

Harbin

Beijing

Zhengzhou

Location

Fig. 23. Average temperature of each part of the HAV at five different locations. 15

Wuhan

Guangzhou

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The HAV is assumed to fly heading for south and the effects of pitch angle are shown in Fig. 17. Although maximum temperatures of the helium inside the HAV with different pitch angles are similar, the HAV with +30° pitch angle reach the maximum value earlier and has a low ebb in the evening in comparison to that with any other pitch angles in the daytime. As shown in Fig. 17(b), the pitch angle has a small effect on average temperature of envelope material.

5. Conclusion In this paper, a co-simulation of thermal model, output power model and dynamic model of the HAV is carried out to investigate effects of flight time, location, attitude and relative wind speed on its temperature and output power during long-distance transportation across different latitudes and longitudes. The following conclusions can be obtained through simulation analysis:

4.4. Effect of wind speed (1) There is a great influence of the solar array on the thermal performance of the HAV. The average temperature of a solar array can reach the maximum value of 338 K at noon in the summer solstice day, which is also a heat source for the envelope material and helium gas inside of the hull. On the contrary, the solar array is the coldest part of the HAV in the night and the average temperature is 216 K. (2) The excessive temperature of the solar array at noon in summer solstice day inhibits the process of photoelectric transformation. As a consequence, the most maximum output power at noon in summer solstice day is lower than the corresponding value in spring equinox day. (3) Due to the rotation and revolution of earth, the influence of changes in longitude and latitude on thermal performance of the HAV are exactly same as changes in launch time and date. As the wind speed increases, the temperature of each part of the HAV decreases, while the output power of solar array increases at the same time. (4) The temperature of the HAV changes greatly during long distance transport across longitude and latitude. Generally, the take-off and landing locations are all determined in advance. Therefore, choice of flight airline should be made with reference to flight time for making best use of solar radiation and wind field.

The lifting-body shape of the HAV makes it owns better aerodynamic performance in comparison to the conventional airship. Nevertheless, the required power still needs to increase as the relative wind speed increases. The effects of wind speed on thermal performance and output power of the HAV can be seen in Fig. 18. As shown in the figure, with the increase of wind speed, temperatures of envelope, solar array and helium inside the HAV decrease obviously, while the output power of solar array increases at the same time. The probable reason may be that the relative airstream may cause forced thermal convection effects for the HAV. The forced convection takes the heat on the surface of envelope and solar array away to decrease their temperatures. Meanwhile, there is no drastic decline for temperature of the internal helium due to the insulation effect of envelope. The decreasing temperature of solar cell makes its photoelectric conversion efficiency increase to some extent, which causes the increase of output power. Furthermore, the energy balance between supply and demand should be reconsidered. 4.5. An example of airline flight The most likely potential application of HAV is long-distance transport of large cargoes. However, for the transport of hundreds of kilometers across longitude and latitude, there is a great impact on the thermal performance of the HAV due to the obvious change of ambient environment. An example of airline flight of the HAV is put forward in the last section of this paper. The output power model of the solar array, thermal model and dynamic model of the HAV are collaboratively simulated to investigate relationship between location, time, attitude and thermal performance. As shown in Fig. 19, a transportation airline of the HAV from Harbin (45°N, 125°E) to Guangzhou (23°N, 112°E) is illustrated in Fig. 19, and several places on the route are Beijing (40°N, 117°E), Zhengzhou (35°N, 114°E) and Wuhan (30°N, 113°E). Three Euler angles are assumed to be zero when the HAV across to five representative locations and the cruising speed and altitude are 50 m/s and 3000 m, respectively. The HAV is assumed to begin its sailing from Harbin at 8:00 on the summer solstice day. Because the HAV flies along airline, its attitude during flight is simulated by the dynamic model. The temperature distributions of the HAV passing through five locations are shown in Fig. 20. As shown in the figure, the highest temperature area of the solar array shifts from left to right when the HAV flies in daytime at Harbin, Beijing and Zhengzhou, which can be presented in more detail in Fig. 21 and Fig. 22. Particularly, the temperature of solar cell is lower than the temperature of other envelope material when the HAV flies through Wuhan to Guangzhou at night, which is consistent with Fig. 7. Detailed temperature variation curves of different parts of the HAV, including envelope, solar array, helium gas and four tails, are shown in Fig. 23. As shown in the figure, solar array has the largest temperature range from 339.3 K to 216.1 K and the variation trend of the envelope’s temperature is close to that of helium gas inside the hull. The average temperature curve of four tails can also be divided into two groups. The temperatures of tail-1 and tail-4 reach their maximum values when they are in Beijing, while tail-2 and tail-3 receive their highest temperatures when they are in Harbin. Nevertheless, temperatures of the four tails are close when the HAV is in Wuhan and Guangzhou at night and remain constant.

Acknowledgments This work was supported by the National Natural Science Foundation of China, Beijing Institute of Technology Research Fund Program for Young Scholars under Grant No. 3010011181807 and the Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies (Beihang University), Ministry of Education, China under Grant No. 2019KF004. The authors thank all the people involved in the past and present progress of the experiment. The authors also are grateful to the reviewer and the executive editor for their precious suggestions about this paper. References [1] B. Rawdon, Z. Hoisington, Air Vehicle Design for Mass-Market Cargo Transport, 2003. [2] H. Wang, B. Song, L. Zuo, Effect of high-altitude airship's attitude on performance of its energy system, J. Aircraft 44 (2007) 2077–2080. [3] G.A. Khoury, Airship Technology, Cambridge University Press, 2012. [4] K.-S. Zhang, Z.-H. Han, B.-F. Song, Flight Performance Analysis of Hybrid Airship, 2009. [5] G. Carichner, L.M. Nicolai, Hybrids...the Airship Messiah?, 2013. [6] B.T. Buerge, The Scalability of Heaviness Fraction for Large Airships, 2013. [7] R.L. Ashford, B.B. Levitt, N.J. Mayer, J.M. Vocar, D.E. Woodward, R.L. Ashford, B.B. Levitt, N.J. Mayer, J.M. Vocar, D.E. Woodward, LTA technology assessment Past and present, Musical Times 1981 (1981) 672–673. [8] R. Boyd, Performance of hybrid air vehicles, 2002. [9] M.D. Ardema, Feasibility of modern airships: preliminary assessment, J. Aircraft 14 (1977). [10] R. Mitchell, Effectiveness of Hybrid Airships as Cargo Airlifters, 2011. [11] A. Donaldson, I. Simaiakis, J. Lovegren, N. Pyrgiotis, L. Li, C. Dorbian, C. He, Parametric Design of Low Emission Hybrid-lift Cargo Aircraft, 2010. [12] J. Agte, T. Gan, F. Kunzi, A. March, S. Sato, B. Suarez, B. Yutko, Conceptual Design of a Hybrid Lift Airship for Intra-Regional Flexible Access Transport, in: Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010. [13] L. Brooke, A. Bown, Design, Analysis, and Patterning of Inflated Lifting Body Form LTA Vehicle Hulls, 2009. [14] G.E. Carichner, L.M. Nicolai, Fundamentals of Aircraft and Airship Design, Volume

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