Effect of altitude and temperature on volume control of an hydrogen airship

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EffectofAltitudeandTemperatureonVolumeControlofanHydrogenAirship

CONFERENCEPAPER·NOVEMBER2012

DOI:10.1115/IMECE2012-87575

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Proceedings of IMECE2012 2012 ASME International Mechanical Engineering Congress and Exposition

November 9-15, Huston, Texas, USA

Prof. Antonio Dumas Università di Modena e Reggio Emilia, Di.S.M.I. - Reggio Emilia, 42122, Italy

[email protected]

Dr. Michele Trancossi Phd. Università di Modena e Reggio Emilia, Di.S.M.I. - Reggio Emilia, 42122, Italy

[email protected]

Dr. Mauro Madonia Università di Modena e Reggio Emilia, Di.S.M.I. - Reggio Emilia, 42122, Italy

mauro.madonia@ unimore.it

ABSTRACT This paper analyzes the model of volume control

of an innovative stratospheric airship concept designed to use hydrogen as a buoyant gas. This paper analyzes a mathematical model which allows modelling the airship volume changes with altitude. CFD evaluation at different altitudes has been performed. CIRA and Std. Atmosphere models have been compared.

NOMENCLATURE FOV Field of View; IFOV Instantaneous Field Of View;

INTRODUCTION Different methods of altitude control applying to

airships are taken into account and examined. They are analyzed in depth and modelled by governing equations. These methods are discussed basing on atmospheric conditions and related thermodynamics. The optimum field of application is defined for each.

Emergency conditions related to balloon failures are taken into account.

This analysis has lead to an optimized buoyancy control methodology which is presented in depth. This technique has been named Multi Balloon Airship concept which will be used to guaranty the maximum safety and buoyancy control to the MAAT airship. In particular this design method allows a novel concept of open shaped airship conception with no need of air ballonets. It uses two balloons.

The first guarantees the necessary buoyancy to maintain the airship in equilibrium at sea level. The second ensures a dilatation volume for the gas till it reaches the desired operational altitude. This design is conceived to guarantee a better control and safety for airships using the more economic hydrogen instead of helium as buoyant gas. The concept is explicated, the general plants are defined and volume calculations are performed up to 21 km.

EFFECT OF ALTITUDE AND TEMPERATURE ON VOLUME CONTROL OF AN HYDROGEN AIRSHIP

Preliminary - IMECE2012-87575

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ATMOSPHERE MODELS Many atmosphere models have been presented

and discussed in literature. The most used in the aeronautic field is the US Standard Atmosphere model 1976 [1-5] because of its simplicity. Also other more complete but realistic can apply. U.S. Standard Atmosphere is based on a very simplified set of mathematic equations. It is thus very simple and easily applicable even if it can have very important differences when compared to real atmospheric data.

A more detailed model is the COSPAR International Reference Atmosphere (CIRA-86) [6-12] which has been obtained in terms of experimental values.

Standard model The model equation can be demonstrated by

hydrostatic theory and ideal gas law. The model can be divided into three zones with

separate curve fits for the troposphere, the lower stratosphere, and the upper stratosphere.

Temperature T and pressure p can be fitted by the following curves:

315.04 6.49 10T h (1)

5.256

101290288.08

Tp

(2)

The lower stratosphere starts from 11,000 meters to 25,000 meters. Different models has been created to describe this region: the simplest is the one presented below. In the lower stratosphere is constant and the pressure decreases exponentially. The metric units curve fits for the lower stratosphere are:

329,61T K (3)

1.73 0.00015722.65 hp e (4)

The upper stratosphere model is used for altitudes above 25,000 meters and is characterized by an increase of temperature and the exponential decrease of pressure:

3141.94 2,99 10T h (5)

11.388273.12.488*216.6

Tp

(6)

In each zone the density r is derived from the equation of state.

0.2869

pT

(7)

The US Standard Atmosphere, published in 1986, holds a model for the development of pressure and density with altitude over the sea level. In the US Standard Atmosphere, seven fundamental layers are defined in the lower 86 kilometres of the atmosphere. They are:

Table 1 - U.S. Atmosphere 1986 values of temperature lapse rate

h1 [km] 1 11 20 32 47 51 71 h2 [km] 11 20 32 47 51 71 84.85

L (dT/dh) [K/km] -

6.5 0.0 1.0 2.8 0.0 -

2.8 -2.0 The assumed constants are reported in the following table.

Table 2 - U.S. Atmosphere 1986 constants Sea level pressure p0 101325 N/m2 Sea level temperature T0 288.15 K Hydrostatic constant 34.1631947 K/km

CIRA-1986 Atmosphere model The COSPAR International Reference

Atmosphere [6-8] (CIRA) provides empirical models of atmospheric temperatures and densities as recommended by the Committee on Space Research (COSPAR). Since the early sixties, several different editions of CIRA have been published.

CIRA-86 models consists of tables of the monthly mean values of temperature and zonal wind with almost global coverage (80°N - 80°S). They are compiled by Fleming et al. [12] (1988), one in pressure coordinates including also the geopotential heights, and one in height coordinates including also the pressure values. These tables were generated

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from several global data compilations including ground-based and satellite (Nimbus 5, 6, 7) measurements (Oort (1983) [8] and Labitzke et al. [9] (1985)). The lower part was merged with MSIS-86 at 120 km altitude. In general, hydrostatic and thermal wind balances are maintained at all levels. The model accurately reproduces most of the characteristic features of the atmosphere such as the equatorial wind and the general structure of the tropopause, stratopause, and mesopause.

The CIRA Working Group meets biannually during the COSPAR general assemblies. A global climatology of atmospheric temperature, zonal velocity and geopotential height derived from a combination experimental measurements by satellites, radiosondes and ground-based [10, 11].

The CIRA Atmosphere model is expressed in terms of tables and presents the following main values: Pressure, Temperature (monthly and annual data), and Wind intensity with sign.

Comparison between atmospheric models A comparison between atmospheric models can

be performed and effective interpolating functions can be obtained.

Pressure Pressure data obtained both by Standard.

Atmosphere Equations and CIRA can be plotted and a good fitting of the data can be obtained (Figure 1). . Pressure data assume a quite perfect fitting in the altitude interval 020 km by a function with the following expression:

0a Hp( H ) P * expb H

(8)

p(H)=1025.1315*exp(11.4575*H/(-98.2189+H)); R²=1U.S. St. Atm. P (h Pa)CIRA-86 P (hPa)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 220

100

200

300

400

500

600

700

800

900

1000

H [m]

p (H) [Pa]

Figure 1 - Values of pressure (US Std. Atm. and CIRA-86 models) and Optimal

Interpolating Equation In particular a solution has been found with R2=1

using the following values: P0 = 1025.13; a = 11.46 and b = -98.22.

Temperature Standard Atmosphere model presents an average

value of temperature about 45° Nord . This model can be compared with the values given by CIRA-86 model both monthly and for various latitudes .

To produce an effective comparison, average annual values - presented by CIRA Model - have been taken into account for different latitudes.

By Figure 2 it can be observed that the Standards Atmosphere model can describe satisfactory upper latitudes but not lower ones. Till 30° latitude North the constant temperature zone is negligible and a sudden inversion of temperature happens above 16 km height.

By observing more in depth monthly data differences increases. It can be assumed that the Standard Atmosphere model produces good results in case of low temperatures. In particular it can be assumed that it works well between 40 and 60° latitude north.

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T (0°)T (10°)T (20°)T (30°)T (40°)T (50°)T (60°)T (70°)T (80°)Std. Atm. T (K)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

200

220

240

260

280

300

H [km]

T (H) [K]

Figure 2 - Temperature CIRA 86 average annual values vs. Standard Atmosphere

values.

Density Similar consideration can be performed on density

it is not directly plotted by CIRA and U.S. Standard Atmosphere models. It can be easily calculated by equation (4) in the case of Standard atmosphere model and plotted by values in the case of CIRA models.

In the case of Density different curves can be produced depending on temperature at various latitudes. An effective fitting function which presents a very good accordance with data can be defined as:

( H ) a b exp(-c x ) (9)

In Figure 3 density average annual values at various latitudes are plotted.

0°15°30°45°60°75°

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

H (m)

Density [kg/m^3]

Figure 3 - Density evaluation at different

latitude (CIRA model)

Daily thermal excursion Solar radiation effects present a large temperature

effect both on balloon and gas temperature, and can cause a large effect on buoyant gas density. These variations are evaluated as an effect of solar radiation by evaluating high altitude solar radiation. Thermal equilibrium of the balloon must be considered.

HYDROGEN BEHAVIOUR

Hydrogen properties Hydrogen is considered a highly flammable gas

[15-17]. For usage on airships it can be compared to other combustibles in volumetric terms. In particular it can be evaluated and compared in term of “energy density”.

The energy density is really a measure of how compactly atoms are packed in a fuel. It follows that hydro-carbons of increasing complexity (with more and more hydrogen atoms per molecule) have increasing energy density. At the same time, hydrocarbons of increasing complexity have more and more carbon atoms in each molecule so that these fuels are heavier and heavier in absolute terms.

On this basis, hydrogen’s energy density is poor (at low density) although its energy to weight ratio is the best of all fuels (because it is so light). The energy density of comparative fuels, based on the LHV, is indicated in Table 1.

Table 3 – Comparison in terms of Energy density between different gaseous fuels.

Fuel Energy Density (LHV)

10,050 kJ/m3 gas at 1 atm and 15 ºC 1,825,000 kJ/m3 gas at 200 bar and 15 ºC 4,500,000 kJ/m3 gas at 690 bar and 15 ºC

Hydrogen

8,491,000 kJ/m3 liquid 32,560 kJ/m3 gas at 1 atm and 15 ºC

6,860,300 kJ/m3 gas at 200 bar and 15 ºC Methane

20,920,400 kJ/m3 liquid 86,670 kJ/m3 gas at 1 atm and 15 ºC Propane

23,488,800 kJ/m3 liquid

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Flammability Three things are needed for a fire or explosion to

occur: a fuel, oxygen (mixed in appropriate quantities) and a source of ignition. Hydrogen, as a flammable fuel, mixes with oxygen whenever air is allowed to enter a hydrogen vessel, or when hydrogen leaks from any vessel into the air. Ignition sources take the form of sparks, flames, or high heat.

Flashpoint All fuels burn only in a gaseous or vapour state.

Fuels like hydrogen and methane are already gases at atmospheric conditions, whereas other fuels like gasoline or diesel that are liquids must convert to a vapour before they will burn. The characteristic that describes how easily these fuels can be converted to a vapour is the flashpoint. The flashpoint is defined as the temperature at which the fuel produces enough vapours to form an ignitable mixture with air at its surface.

If the temperature of the fuel is below its flashpoint, it cannot produce enough vapours to burn since its evaporation rate is too slow. Whenever a fuel is at or above its flashpoint, vapours are present. The flashpoint is not the temperature at which the fuel bursts into flames; that is the auto ignition temperature.

The flashpoint is always lower than the boiling point. For fuels that are gases at atmospheric conditions (like hydrogen, methane and propane), the flashpoint is far below ambient temperature and has little relevance since the fuel is already fully vaporized. For fuels that are liquids at atmospheric conditions (such as gasoline or methanol), the flash- point acts as a lower flammability temperature limit.

Table 4 – Flashpoint of different gaseous

combustibles

Fuel Flashpoint Hydrogen < 20 K) Methane 85 K) Propane 169 K)

Flammability Range The flammability range of a gas is defined in

terms of its lower flammability limit (LFL) and its upper flammability limit (UFL): LFL is the lowest gas concentration that will

support a self-propagating flame when mixed with air and ignited;

UFL of a gas is the highest gas concentration that will support a self-propagating flame when mixed with air and ignited.

A stoichiometric mixture occurs when oxygen and hydrogen molecules are present in the exact ratio needed to complete the combustion reaction. If more hydrogen is available than oxygen, the mixture is rich so that some of the fuel do not react although all of the oxygen is consumed. If less hydrogen is available than oxygen, the mixture is lean so that all the fuel will be consumed but some oxygen will remain. An important consequence of this considerations is that stored hydrogen (whether gaseous or liquid) is not flammable while stored due to the absence of oxygen in the cylinders.

The explosive behaviour is different from a fire. For an explosion, the combustion must be contained, allowing that pressure and temperature rise to sufficient levels which permit to violently destroy the containment. For this reason, it is far more dangerous to release hydrogen into an enclosed area (such as a building) than to release it directly outdoors. Mixtures of hydrogen and air are potentially flammable or explosive.

Explosive risk is more accentuated on storage tanks than on balloon confinement. In the case of an airship which has hydrogen balloons at pressure equal or less than atmospheric pressure at sea level it is nearly impossible to have explosive risk due to pressure.

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5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 950

100

200

300

400

500

600

700

% Hydrogen in air

Temperature [K]

Figure 4 – Flammability range of Hydrogen in air as a function of temperature

Hydrogen is flammable over a very wide range of

concentrations in air (4 – 75%) and it is explosive over a wide range of concentrations (15 – 59%) at standard atmospheric temperature. The flammability limits increase with temperature as illustrated in Figure 4. As a result, even small leaks of hydrogen are potentially inflammable or explosive. Leaked hydrogen can concentrate in an enclosed environment, increasing the risk of combustion and explosion. The flammability limits of comparative fuels are illustrated in Figure 5.

Auto ignition Temperature The auto ignition temperature is the minimum temperature required to initiate self-sustained combustion in a combustible fuel mixture without any source of ignition. In other words, it is the temperature at which the fuel must be heated until it bursts into flame. Each fuel has a unique ignition temperature. For hydrogen, the auto ignition temperature is relatively high 585 ºC. This makes it difficult to ignite a hydrogen/air mixture on the basis of heat alone without some additional ignition source. The auto ignition temperatures of comparative fuels are reported in Table 5.

Table 5 – AutoIgnition Temperature values Fuel Autoignition Temperature

Hydrogen 585 ºC Methane 540 ºC Propane 490 ºC

The auto ignition risk is nearly impossible if the balloons are separated from electrical equipments and thermal equipments. Incrementing the altitude this risk lowers dramatically due to reduction of pressure and environment temperature.

Ignition Energy Ignition energy is the amount of external energy

that must be applied to ignite a combustible fuel mixture. Energy from an external source must be higher than the auto ignition temperature and be of sufficient duration to heat the fuel vapour to its ignition temperature. Common ignition sources are flames and sparks.

Although hydrogen has a higher auto ignition temperature than methane, propane or gasoline, its ignition energy at 0.02 mJ is much lower (about an order of magnitude). Hydrogen is more easily ignitable. Even an invisible spark or static electricity discharge from a human body (in dry conditions) may have enough energy to cause ignition at sae level atmospheric conditions. Nonetheless, it is important to realize that the ignition energy for all of these fuels is very low so that conditions that will ignite one fuel will generally ignite any of the others.

Hydrogen has the added property of low electro conductivity so that the flow or agitation of hydrogen gas or liquid may generate electrostatic charges that result in sparks. For this reason, all hydrogen conveying equipment must be thoroughly grounded.

Flammable mixtures of hydrogen and air can be easily ignited.

Burning Speed Burning speed it the speed at which a flame

travels through a combustible gas mixture. Burning speed is different from flame speed. The

burning speed indicates the severity of an explosion since high burning velocities have a greater tendency to support the transition from deflagration to detonation in long tunnels or pipes. Flame speed is the sum of burning speed and displacement velocity of the unburned gas mixture.

Burning speed varies with gas concentration and drops off at both ends of the flammability range.

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Below the LFL and above the UFL the burning speed is zero.

The burning speed of hydrogen at 2.65–3.25 m/s is nearly an order of magnitude higher than that of methane or gasoline (at stoichiometric conditions). Thus hydrogen fires burn quickly and, as a result, tend to be relatively short-lived.

Quenching Gap The quenching gap (or quenching distance)

describes the flame extinguishing properties of a fuel when used in an internal combustion engine. Specifically, the quenching gap relates to the distance from the cylinder wall that the flame extinguishes due to heat losses. The quenching gap has no specific relevance for use with fuel cells.

The quenching gap of hydrogen (at 0.025 in; 0.064 cm) is approximately 3 times less than that of other fuels, such as gasoline. Thus, hydrogen flames travel closer to the cylinder wall before they are extinguished making them more difficult to quench than gasoline flames. This smaller quenching distance can also increase the tendency for backfire since the flame from a hydrogen-air mixture can more readily get past a nearly closed intake valve than the flame from a hydrocarbon-air mixture.

Flame Characteristics Hydrogen flames are very pale blue and are

almost invisible in daylight due to the absence of soot. Visibility is enhanced by the presence of moisture or impurities (such as sulfur) in the air. Hydrogen flames are readily visible in the dark or subdued light. A hydrogen fire can be indirectly visible by way of emanating “heat ripples” and thermal radiation, particularly from large fires. In many instances, flames from a hydrogen fire may ignite surrounding materials that do produce smoke and soot during combustion.

AIRSHIP MODEL

Lifting Model High airships are being pursued for their ability to

lift important payloads to great altitudes and because of their very reduced energetic consumption. They

accomplish this by displacing heavy air with a less dense gas that will rise to seek density equilibrium. A mass balance relationship can represent this principle

air air gasm g g V (10)

If the weight of a structure is less than the difference between the weight of air displaced and the gas displacing it, there will be an upward force generated. The buoyant gas is considered to be unmixed with air.

Maximum weight or “lift capacity” By equation (10) it is possible to express the maximum weight or “lift capacity” of an airship. It is a function of its lifting gas mass according to the below equation (11).

air air gasL g V (11) A design factor in developing an airship is to ensure that the pressure relationship between the gasses inside and outside the airship hull is not impacted. A certain overpressure pgas must be assured to the buoyant gas. It means a constant overpressure must exist inside the hull. The constant pressure relationship must be maintained .

gas gas airp ( H ) p p ( H ) (12)

If the pressure relationship is maintained then lifting gas pressure decreases uniformly with atmospheric pressure as the airship rises and the gas is able to expand its volume. As volume increases, gas density in the hull decreases and the buoyant force is maintained. The buoyant force will lift the airship until the hull volume is at a maximum and the pressure relationship between the hull and the environment can no longer be held constant. At this point the airship has reached its maximum or “pressure” altitude. The most important parameter which guarantee an optimal behavior of the airship is the density ratio (13):

0 0gasair

air gas

( H )( H )( H )

( ) ( )

. (13)

The density ratio permits to express the maximum lift capacity in a more effective way than equation (11).

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In particular it can be expressed as a function of zero level density as follows:

10

airgas

gas

L m g( )

(14)

Lifting gas mass usually remains constant within the envelope as the airship rises. If internal air ballonet deflation is controlled properly, the airship can rise to its maximum pressure height and maintain that altitude. If an airship rises above its pressure height the pressure difference will be exceeded and lifting gas will be vented resulting in diminished lift capacity. To prevent this from happening, some ballonet inflation must be maintained. It is a simple solution to avoid the airship from reaching its maximum altitude and the risks of over-altitude gas venting.

Maximum Volume The maximum lifting gas volume is reached when the gas density decreases without impacting the pressure differential in the hull. Since density is a ratio of the mass of a gas to its volume, the volume of a lifting gas expanded to the equivalent atmospheric density will provide rapid insight into how big an airship must be. The mass of helium used remains constant and the density of helium can be predicted as a function of altitude by taking advantage of the density ratio. The airship size can be predicted by the following equation.

0

gasmax

max air ,

mV

(15)

In this equation max is the density ratio at the desired maximum altitude and ρair0 the density of air at sea level. Taking advantage of the density scale height model, the density ratio can be rewritten as a function of altitude:

Balloon overpressure As defined above in equation (12), a certain overpressure must be granted inside the balloon to maintain the shape. This overpressure has been evaluated by Khoury and Gillett, who have defined an estimation of the overpressure required for a non-rigid airship:

2125 0 33 maxp . v

where vmax2 is the value of the maximum relative

velocity between airship and wind expressed in km/h. By this assumption the above system equations can be redefined:

gasair air air

P( H ) p P( H ) p( H )R T R T R T

gas gas gas( H ) ( H ) (16)

It is necessary to maintain at least the overpressure till when the jet streams have been overcome. By the above evaluations it is possible to express (14) as follows:

10 0

airgas

gas gas

L m g( ) ( )

(17)

and the maximum volume (15) can be expressed by

00

gasmax

gasmax air ,

gas

mV

( )

. (18)

Altitude Control mechanisms The general equation of the system is

air gasL g V( H ) ( H ) ( H ) (19) in which (H) is expressed by (13).

isothermal Volume variation The altitude control by volume variation in

isothermal conditions with atmosphere can be expressed by ideal gas equation and it can be expressed as a function of H by the following expression:

00

gas

gasair ,

gas

mV( H )

( H )( )

(20)

If the payload is Mp the general system equation becomes:

p air gasM V( H ) ( H ) ( H ) . (21)

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Temperature variations If the temperature of the buoyant gas can vary by

any cause the equation of the system becomes:

gas gas

airgas air gas

p ( H ) pL( H ) g V( H ) ( H )

R T T

(22)

and the payload is:

gas gas

p airgas air gas

p ( H ) pM V( H ) ( H )

R T T

. (23)

Ballast Variations Mass can have variations to help the airship to

reach a predefined altitude or the altitude maintenance. This system requires any kind of ballast which can be safely discharged. This ballast can be of any nature, depending on operative possibilities. The problem of this control mode is related to safe off-board evacuation: liquids such as water and compressed air do not present any danger for the environment and for people beyond.

Mass variation can be represented by a modification of mass. In particular it can be represented as:

p air gasM ( H ) M M( H ) V( H ) ( H ) ( H )

air gasM ( H ) V( H ) ( H ) ( H ) (24)

Multiple effects combination A multiple effects combination model can be

performed by combining the above equations in terms of superposition of effects. This More general equation can be expressed as follows:

gas gas

air kkgas air gas

p ( H ) pL( H ) gV( H ) ( H ) g M

R T T

(25)

or tot volume,i thermal , j pound ,ki j k

M ( H ) M M M (26)

gas gas

tot air kkgas air gas

p ( H ) pM ( H ) V( H ) ( H ) M

R T T

in which pgas=pair. By this equation the system behaviour can be

described in different operative conditions.

PRELIMINARY ASSUMPTION FOR CALCULATION

By the above model it can be possible to develop different effective parametric models of the vertical lift by buoyancy and other effect.

To realize the model it has been assumed a reference mass of 103 kg. All calculations are referred to this value. The values of temperature and density used are derived from CIRA Atmosphere Model and have been assumed to be variable in latitude from 0° to 80° with a 10° step.

For each latitude the main model has been calculated on the basis of average annual values. Then the possible variations on minimum and maximum values have been performed.

The reference data listed in Table 6 have been assumed to solve the problem.

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Table 6 – Reference data for calculations H2

Const. H2 Dens.

H2 Spec. Vol.

Air Const. Air Dens.

Air Spec. Vol. Mass

[J/kg K] [kg/m3] [m3/kg] [J/kg K] [kg/m3] [m3/kg] [kg] 4124 0.0899 11.7279 286.9 1.225 0.816 1000

VOLUME CALULATIONS

A Basic model: Volume only variation By assuming the data listed in Table 6 calculation

of the model can be performed. The first model described in Figure 5 is the model

with variation of volume only. Temperature with variation considering U.S. Standard Atmosphere data as a reference and 15 K curves to include possible variations.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22190

200

210

220

230

240

250

260

270

280

290

300

H (km)

T[K]

Figure 5 – Temperature variation only hypothesis

By the data plotted in figure 5 the following

volume values are calculated (Table 7). It can be verified that considering a volume only

variation the volume can vary between 874 m3 and 12270 m3 at 20 km. Considering the more effective condition at 16 km maximum value become 6534 m3.

This range can be acceptable and includes main differences which could be included by considering the CIRA atmospheric Model.

Table 7 – Volume variation table in the temperature range specified above

H Volume H2 Volume H2 Volume H2 Volume H2 Variation

[km] [kg/10^3 m3] [kg/10^3 m3] [kg/10^3 m3] [%] 0 0,874 0,877 0,881 1,000 1 0,963 0,967 0,971 1,102 2 1,064 1,068 1,073 1,217 3 1,178 1,182 1,188 1,347 4 1,307 1,312 1,318 1,495 5 1,454 1,460 1,467 1,664 6 1,622 1,629 1,637 1,857 7 1,815 1,823 1,832 2,078 8 2,038 2,047 2,057 2,333 9 2,294 2,305 2,317 2,627

10 2,592 2,604 2,618 2,968 11 2,939 2,953 2,970 3,366 12 3,441 3,458 3,477 3,941 13 4,029 4,049 4,071 4,614 14 4,717 4,740 4,767 5,402 15 5,523 5,550 5,581 6,325 16 6,466 6,497 6,534 7,405 17 7,571 7,607 7,650 8,670 18 8,864 8,907 8,956 10,151 19 10,378 10,428 10,486 11,885 20 12,150 12,209 12,277 13,915

An intermediate model: volume and ballast variation

A more sophisticated model can consider two possible variations during system behaviour: ballast expulsion and volume variation.

Maximum volume at upper altitude can be identical to the one calculated in the preceding simplified model.

In particular it has been supposed that a certain ballast in terms of compressed air is stored inside the cabin of the airship and it is released or recharged during system movement.

It can be modelled using alternative models: 1. low altitude ballast release/absorption; 2. high altitude ballast release absorption.

By these models similar results can be obtained. But with different volume variation laws. In particular these models can be used both for gaining altitude or reducing altitude.

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As a basis for calculation a ballast about 212 kg has been considered.

Table 8 - Volume variations with low altitude

ballast release or expulsion

H M Volume H2 Volume H2 Volume H2 Volume H2 Variation

[km] [kg] [kg/m3] [kg/m3] [kg/m3] [%] 0 1212,1 1,060 1,068 1,068 11,4331 1099,8 1,059 1,068 1,068 1,0002 1000,0 1,064 1,068 1,073 1,0003 1000,0 1,178 1,182 1,188 1,1074 1000,0 1,307 1,312 1,318 1,2295 1000,0 1,454 1,460 1,467 1,3676 1000,0 1,622 1,629 1,637 1,5267 1000,0 1,815 1,823 1,832 1,7078 1000,0 2,038 2,047 2,057 1,9179 1000,0 2,294 2,305 2,317 2,158

10 1000,0 2,592 2,604 2,618 2,43911 1000,0 2,939 2,953 2,970 2,76612 1000,0 3,441 3,458 3,477 3,23813 1000,0 4,029 4,049 4,071 3,79114 1000,0 4,717 4,740 4,767 4,43915 1000,0 5,523 5,550 5,581 5,19716 1000,0 6,466 6,497 6,534 6,08417 1000,0 7,571 7,607 7,650 7,12418 1000,0 8,864 8,907 8,956 8,34019 1000,0 10,378 10,428 10,486 9,76520 1000,0 12,150 12,209 12,277 11,433

The first model (Table 8) considers the use of

ballast in the first part of the operations, keeping constant volume balloon.

The second model (Table 9), in which the ballast is used at high altitude presents more problems connected with aerodynamic resistance in low altitude atmospheric levels.

The results of this calculation can be compared using the airship relationship which expresses the Drag as a function of Volume. So it appears less convenient than the first one, especially in the jet streams.

Altitude controls Heat exchange with exterior environment can be

evaluated when the system is at high altitude. A temperature difference between day and night must be considered. In particular, the heat necessary to

keep a constant altitude of the system can be evaluated.

Table 9 – Volume variation table in the

temperature range specified above

H M Volume H2 Volume H2 Volume H2 Volume H2 Variation

[m] kg [kg/10^3 m3] [kg/10^3 m3] [kg/10^3 m3] [%] 0 1164,0 1,018 1,021 1,026 1,000 1 1164,0 1,121 1,125 1,130 1,102 2 1164,0 1,238 1,243 1,248 1,217 3 1164,0 1,371 1,376 1,382 1,347 4 1164,0 1,521 1,527 1,534 1,495 5 1164,0 1,693 1,700 1,708 1,664 6 1164,0 1,888 1,896 1,906 1,857 7 1164,0 2,113 2,122 2,133 2,078 8 1164,0 2,372 2,382 2,394 2,333 9 1164,0 2,670 2,683 2,697 2,627

10 1164,0 3,017 3,031 3,048 2,968 11 1164,0 3,421 3,438 3,457 3,366 12 1164,0 4,006 4,025 4,048 3,941 13 1164,0 4,690 4,712 4,739 4,614 14 1164,0 5,491 5,517 5,548 5,402 15 1164,0 6,429 6,460 6,496 6,325 16 1000,0 6,466 6,497 6,534 6,362 17 1000,0 7,571 7,607 7,650 7,449 18 1000,0 8,864 8,907 8,956 8,721 19 1000,0 10,378 10,428 10,486 10,210 20 1000,0 12,150 12,209 12,277 11,954

A daily thermal excursion T has been considered

with a sinusoidal variation: ( ) ( ) cosavgT h T h T a t b (27)

The balloon is considered nearly isothermal with the exterior environment.

Considering the hydrogen as a perfect gas it can be possible to express density as a function of temperature.

2

( )( )cosH

avg

P hTR T T a t b

(28)

By these consideration a simple daily model can be defined. Most sophisticated models can be used, but for the exigency of this paper it seems sufficient.

12 Copyright © 20xx by ASME

The considered values have been certainly contained into the range described into the previous model.

So two different strategies can be adopted: 1. a variation of the mass of hydrogen to maintain

the volume, which is simple and energetically inexpensive (Figure 6);

2. An thermal exchange finalized to vary the temperature of the Hydrogen gas which is more expensive energetically (Figure 7).

Both options can be successfully used even if some problems related to Hydrogen heating are certainly possible, even if more dangerous. In terms of hydrogen variation assuming a daily thermal excursion of 10 K.

Mass 1 (Tint>Text]Mass 1 (Tint>Text]Mass Tint=Text

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 1269

70

71

72

73

74

75

76

77

78

79

80

81

delta T [K]

M (H2)

Figure 6 – Variation of Hydrogen mass to keep the volume constant

Referring to figure 6, mass variation can be expressed as a function of temperature variation as follows:

M(T)= 0.3624 T+74.792; R²=0.9998

M(T)= - 0.3624 T+74.792; R²=0.9999

It is important also to model the thermal case which is represented in figure 7. The heat which has to be transferred to hydrogen is calculated by the heat equation:

Q(T) = M cp T 1023.44 T

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.50

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

T [K]

Heat (J)

Figure 7 – Heat transferred to Hydrogen to keep the volume constant (absolute value)

CONCLUSIONS This paper has presented a model of an hydrogen

airship using different elements. It has not been taken into account the pressure model because it can be adopted only for very limited interventions. Using it for ample gains in terms of altitude is absolutely negative, because it forces to increase the structural weights of the system.

The produced results can be easily corrected considering different values of overpressure of the balloons and for different airship structures, both rigid, semi rigid and flexible.

The results have been presented for a reference mass of 1 ton in order to be easily parameterised to any effective mass.

The presented model presents a general guideline for airship designers in order to produce an effective government of the system. Even if it has been defined for a changing volume balloon it can be easily adopted also to ventilated air balloons airships.

ACKNOWLEDGMENTS Put acknowledgments here.

REFERENCES 1. N.A.S. A., U.S. Standard Atmosphere, U.S.

Government Printing Office, Washington, D.C., 1976;

13 Copyright © 20xx by ASME

2. U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962.

3. U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966.

4. International Civil Aviation Organization, Manual of the ICAO Standard Atmosphere (extended to 80 kilometers (262 500 feet)), Doc 7488-CD, Third Edition, 1993, ISBN 92-9194-004-6;

5. International Organization for Standardization, Standard Atmosphere, ISO 2533:1975, 1975;

6. CIRA 1972, A.C. Strickland (ed.), Akademie Verlag, Berlin, G.D.R., 1972.

7. CIRA 1986, Part II Middle Atmosphere Models, D. Rees, J.J. Barnett, K. Labitzke (ed.), Advances in Space Research (COSPAR), Volume 10, Number 12, 1990.

8. A.H. Oort, Global Atmospheric Circulation Statistics 1958-1983, National Oceanic and Atmospheric Administration, Professional Paper 14, 180 pp, U.S. Government Printing Office, Washington, D.C., 1983.

9. K. Labitzke, J.J. Barnett, and B. Edwards (eds.), Middle Atmosphere Program, MAP Handbook, Volume 16, University of Illinois, Urbana, 1985.

10. K. Rawer, C.M. Minnis, K.S.W. Champion, and M. Roemer (eds.), Models of the Atmosphere and Ionosphere, Advances in Space Research, Volume 5, Number 7, 1985.

11. K.U. Grossmann, K.S.W. Champion, M. Roemer, W.L. Oliver, and T.A. Blix (eds.), The Earth's Middle and Upper Atmosphere, Advances in Space Research, Volume 7, Number 10, 1987.

12. E.L. Fleming, S. Chandra, M.R. Shoeberl, and J.J. Barnett, Monthly mean global climatology of temperature, wind, geopotential height and pressure for 0-120 km, National Aeronautics and Space Administration, Technical Memorandum 100697, Washington, D.C., 1988;

13. G. A. Khoury and J.D. Gillett. Airship Technology. London, Cambridge University Press, 1999.

14. E. Lewitt., The Rigid Airship, A Treatise on the Design and Performance, London: Pitman and Sons Ltd, 1925.

15. J. Hord, Is Hydrogen Safe? National Bureau of Standards (NBS) Technical Note 690, October 1976.

16. R. D. McCarty, J. Hord and H. M. Roder, NBS Monograph 168, Selected Properties of Hydrogen (Engineering Design Data), Center for Chemical Engineering, National Engineering Laboratory, National Bureau of Standards, Boulder, CO 80303, published by U.S. Department of Commerce, U.S. Government Printing Office, Washington, D.C. 1981.

17. B. Lewis and G. von Elbe, Combustion, Flames and Explosions of Gases, 3rd ed., Academic Press, Orlando, 1987, pg. 717.

14 Copyright © 20xx by ASME

ANNEX A

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