Space Propulsion - Lecture Notes, Dispense di Ingegneria Aerospaziale

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SPACE

PROPULSION

Prof. Filippo Maggi

A.Y. 2019/

Lecture Notes by Andrea Pizzetti

Space Propulsion Page 1

In some systems propellant and energy sources are the same. The propellant is the medium which accelerates that generate the propulsion effect, using the third law of motion (action-reaction). In a rocket motor for instance, the propellant is also the energy source, while in electric not.

• Chemical energy source: energy is stored into the orbitals of the electrons.
• Nuclear energy source: energy is stored into the nuclei of the atoms, it's higher than chemical.
• Radiant energy source: photons (sun), laser, etc.

Primary energy source

• Thermal energy source.
• Electric energy source.

Transformed energy source

The transformed energy source has to be converted into mechanical energy through an acceleration device such a nozzle. Often, the device has limitations (for instance, isentropic limit of the nozzle expansion). In a rocket motor, chemical energy is transformed into thermal one and propellant and primary energy source coincide (the mix of oxidizer and fuel store the chemical energy) For an electro-static motor, instead, radiant energy is converted into electric one and propellant and primary energy source are different (the propellant is heated and expelled). We could fix the space debris problem using radiant sources: the laser. The laser would degrade the surface of the debris, generating a propulsion in the wanted direction. The problem is bringing the laser to the object through the atmosphere and in space, because the power cost is heavy.

Transformation efficiency

There is an efficiency in the conversion from the primary source to the transformed energy and another efficiency in the conversion from transformed to mechanical one (through acceleration device). The first efficiency is high for chemical and nuclear, low for radiant. The second one is high for electric, low for thermal. Therefore, at the end of the day, we have almost 0.5 efficiency for thermochemical (e.g. SP or H2/02) and thermonuclear, while 0.3 for electric.

Classification

In general, we'll classify all the rockets in thermal propulsion or electric propulsion. If time it's not a constraint, the second is better due to the higher specific impulse. Energy sources lunedì 9 marzo 2020 12:

1. Introduction Page 2

Where is the total impulse of the thrust (nothing to do with specific impulse). In the specific case of optimal condition, the formula simplifies: In non-optimal condition, we can retrieve a dynamic and static part also in the specific impulse formula: We can define c, the effective velocity , as: Resulting in a final formula for the specific impulse: It can be proven that for a thermochemical rocket the specific impulse depends only on thermodynamic properties: Some typical values for the specific impulse are:

1. Introduction Page 4

• HP: hybrid rocket propulsion (typically solid state fuel and liquid state oxidizer)
• LP bi-storable: usually kerosene RP1 and liquid oxygen
• LP bi-cry: liquid propellant brought to the critical temperature For chemical engines: Nuclear specific impulses are only theoretical.

Volumetric Specific Impulse

It's the averaged propellant density multiplied for the specific impulse: The averaged propellant density is not the mean of the densities weighted on the mass! It's not an intensive property, we cannot do this. We have to use the definition of the density, which is the total mass divided by the total volume. With a multi-propellant, we have to compute the total volume as the sum of the propellant volumes, the total mass as the sum of the propellant masses. Hydrogen has a very low density. A high volumetric specific impulse allow us to store a lot of energy in a little volume. A high (gravimetric) specific impulse, instead, allow us to have high thrust with little amount of propellant. If we want to save volume, we have to consider the first; if we want to save propellant, we should consider the second.

Total Impulse

It's used to compute the mission specific impulse.

System Specific Impulse

This impulse consider the mass as merit parameter. It's not often used.

Discharge coefficient/Characteristic velocity

It's a parameter of the combustion chamber only, it measures how well the propellant is discharged

1. Introduction Page 5

Primary Propulsion

If the Thrust/Weight ratio (referred to the planet in which we are) is larger than 1, we speak of primary propulsion, so a lift from the planet carrying the payload. Usually is performed by engines with short life time. Examples are launch missions such as Space Shuttle or planetary landing and return such as Apollo APS (Ascending Propulsion System). The former has a T/W of 3 and the latter of 2 (referred to lunar gravity field).

In-space Propulsion

In-space propulsion is used to place the S/C or keep its position on an orbit which leads to the target. Kick motors are examples of in-space propulsion. They can operate at apogee/perigee to circularize a transfer orbit or to escape a parking one. The technology used is usually SRM or LRM.

Types of mission

For fixed total impulse, In case of high thrust in short time, impulsive manoeuvres hypothesis can be assumed, while in low thrust in long time we have to consider losses. If the trajectory takes 3 days and the thrusting time is 1 hour, for instance, we can consider impulsive manoeuvre. There is no a specific number, it depends on the trajectory and the mission. In certain missions, the goal is to save propellant, which means to have high specific impulse. Indeed, in interplanetary or deep space missions, electric motors are used. In optimal case, specific impulse is the ratio between exit velocity and g0. Increasing specific impulse means increasing exit velocity: for I=300 s, we'll have an exit velocity of about 3000 m/s. If thrust is fixed, if exit velocity gets higher, propellant flow rate gets lower, so we are saving propellant when increasing specific impulse. The missions which more benefit from high specific impulse are the ones in which there is no time constraints, such as deorbiting of small satellites or orbit repositioning/correction. The satellites which can be deorbited have to be small because otherwise we should predict the point of impact to avoid possible danger. Controlled de-orbiting indeed needs high energy manoeuvres, so chemical propulsion (A). It's a matter of trade-off between the saving of propellant and the increase of losses due to the losing of impulsive manoeuvres assumption. In C, we have a series of manoeuvres all at the perigee, exploiting the fact that the effect of an impulse in that point is the best (Oberth Effect). In D, instead, the impulse is continuous and we keep using the propulsion device to accelerate.

Types of propulsion

Mission & Propulsion types mercoledì 11 marzo 2020 14:

1. Introduction Page 7

Only chemical or nuclear propulsion can be used to escape Earth's gravity, but the only feasible, with a good Technology Readiness Level are the chemical ones. Space shuttle main engine is liquid cryogenic bipropellant. It's the best ever built, by the way. The boosters are solid propellant, while there is no electric propulsion. Apart from the main engine, there are also orbital manoeuvres systems and reaction control system. The power density consider the mass occupied by the propulsion system to gain a kW of energy. Cold gases are used in jetpacks, they are simple and safe, but with low specific impulse and thrust. They can be restarted, pulsed but not throttled. Nuclear thrust values are on the same range of the chemical and provide higher specific impulse, but they are not feasible as them currently (both for development and cost). Moreover, they have low T/W ratio. Chemical have a long story behind and are been fully studied, but due to the combustion are unstable and unsafe. Regarding liquid propellant, they can be restarted, pulsed and throttled, while solid propellant neither of three. The electric thrust values instead are very low, lower even than the cold gas, but they are attractive thanks to their huge specific impulse. Looking at the System weight/Total impulse trade-off, cold gases are always worst apart from very low total impulse values. In fact their use is restricted to brief operations (jetpack). When total impulse is large, we need a large amount of propellant and bipropellant is winning. When

1. Introduction Page 8

stages at re-entry. Additive manufacturing is under development to enable new type of missions, allowing to create different shapes for the grains of solid and hybrid motors, which would be impossible to create with classical techniques. For instance, P120 boosters of the new Ariane 6 are made with composite materials and filament winding.

At last but not least, new nuclear propulsion systems and new propulsion physics are being investigated.

1. Introduction Page 10

Performance and nozzle behaviour

In a space environment the static contribution is always present, because the ambient pressure is almost zero. However, in most cases it can be neglected, but we need to SPECIFY it always in exercises. Thrust and specific impulse rise as the altitude rises, since the pressure difference gets higher. We are in under-expanded situation, the flow is full supersonic and nozzle exit conditions are not affected by external conditions. The plume shape in optimal condition (left figure) is column shaped and the slip line divides two zones with same static pressure but different velocities (no viscosity assumed). In under-expanded condition (right figure), the plume enlarges because the exit pressure is greater than the ambient one and has to lower till the ambient value. However, for the thrust it's important only what happens till the exit area. In over-expanded condition, ambient pressure is higher and the flow detaches, generating a flow separation region, where oblique shocks and Mach disks happens. In the right figure it can be also noticed a post-combustion generated from the interaction of gases which are not completely combusted. If I have optimal condition for the nozzle at the sea level, then on other altitudes it won't be optimal and the static contribution will increase, but the thrust will be lower than the thrust if it was optimal. Usually two motors are employed, one optimal at sea level and the other optimal at high altitude, to balance the two contributions. The best effect would be a hypothetical nozzle which is optimal at each altitude (variable geometry). Dynamic contribution is constant with altitude in case of optimal nozzle at z=0 because it depends only on the geometry (the nozzle is chocked), which is constant. Non reacting flows giovedì 12 marzo 2020 14:

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stop will be lower than the one computed with total temperature formula, because part of the enthalpy is accounted to make the flow reacts at high temperature. The Apollo thermal shield suffered thousands of Kelvin, but the maximum theoretical value was far beyond that value due to the fact that part of this energy was used to make the reactions of dissociations. In case of subsonic and supersonic flows, it's almost always true that total is equal to stagnation, but in case of hypersonic flows, the two are different.

Enthalpy

The kinetic energy is obtained from thermal energy produced in the combustion chamber, through an expansion. Considering a nozzle with no work and no heat exchanged, the total enthalpy is conserved. Under the hypothesis of calorically perfect gas, it can be written as: Dividing for the first term, we obtain the non-dimensional budget of reduced enthalpy and reduced kinetic energy: Through the expansion, enthalpy is transformed into kinetic energy from the static side (zero velocity) to the side in which we have the expansion. N.B. In this case in hypersonic regime there is no shifting chemistry because we assumed calorically perfect gas.

Maximum velocity

Maximum ideal velocity is obtained from the total enthalpy: Substituting typical values (1.3 for gamma, MM=10 for H2/02 propellants, T limited to 3000 K for the materials), the maximum velocity is about 4000 m/s. For pure hydrogen the molar mass is 2, and we get to a maximum velocity of about 9000 m/s.

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With shifting chemistry, assuming to have only gas phase, what is composition and effect on enthalpy?

• The formation enthalpy , relevant to composition.
• The sensible enthalpy, relevant to temperature = CpT, measured from a zero point (T=0K). The static enthalpy has to be defined as sum of two parts: In a constant composition case (frozen chemistry assumption) enthalpy of formation remains fixed and the delta enthalpy is the delta sensible enthalpy Cp(T1-T2). If composition changes, instead, the formation enthalpy can be converted into sensible enthalpy and vice versa. In the total enthalpy formula there is also the kinetic enthalpy. It's the sensible enthalpy which is transformed into kinetic one through the expansion. Considering shifting chemistry into the combustion chamber and frozen chemistry into the nozzle, we would have these exchanges of enthalpy: Since storage temperature is not the standard one, there will be a sensible enthalpy also before the combustion. During the combustion, formation enthalpy is transformed into sensible enthalpy. In the nozzle, formation enthalpy is fixed and there is exchange only between sensible and kinetic ones. For simple reactants such as hydrogen or oxygen, the standard enthalpy of formation is zero. If storage temperature is also the standard one, also the sensible enthalpy is zero, since the standard condition has been set to 0 enthalpy of formation for convention. Considering H2/02, the product is water which has a negative enthalpy of formation of - 285,8 kJ/mol. To respect the conservation of enthalpy, a heat is released, which is actually the sensible enthalpy. This is the reason why a combustion increases the temperature. In this example the total enthalpy is zero (reactants at standard state). To respect the balance, heat must generate equal to the heat of formation of the products (since sum of the two must be zero): Introduction to reacting flows mercoledì 18 marzo 2020 16:

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Quasi 1D Isentropic Nozzle

If flow is adiabatic, we can employ only total temperature relation. If flow is isentropic, we can employ all the total property functions. To design a nozzle, we first have to start from the operational ambient: Atmosphere. In general operational altitude is known, so we can obtain the pressure which will be the reference for optimal condition operation, then it's straightforward to compute the expansion ratio Ae/At.

○ Expansion ratio ○ Pressure ratio ○ Exit Mach Space. The altitude cannot help because the pressure tends to zero and an infinite area would be needed. So, we fix one of the three variables:

Fixing pressure ratio or exit Mach, we are able to obtain the expansion ratio. Once obtained expansion ratio, a check with typical values is needed, for both cases: If we have a dimensional constraint, such as a launcher diameter, we have to use a sub-optimal condition. The value of the expansion ratio depends on specific heat ratio gamma, which is deeply linked with the complexity of the molecules. If molecules are simpler (therefore gamma is high) the area ratio needed to reach the same exit Mach is lower, or alternatively with same nozzle the flow obtained is faster. Therefore it's better to work with simple gases (high gamma). On the other hand, low values of gamma means complex and more massive molecules, so the thrust coefficient is higher. The thrust coefficient chart shows indeed different behaviours of the coefficient with respect to the pressure ratio, in optimal condition, for different values of gamma: Nozzle description mercoledì 18 marzo 2020 16:

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Instead of summing the static contribution when non-optimal expansion is present, using the chart above, we can refer to expansion in vacuum (taking into account static contribution always) with this other chart: To sum up, with simpler molecules (then high gamma) it's possible to have higher exit velocity thanks to the better expansion. On the other hand, if we want high thrust and therefore high thrust coefficient, we should use complex molecules (low gamma). Thrust coefficient values are in the order of units. Since in space applications typical values of area ratio are in order of hundreds and gamma is in range 1.2-1.66, thrust coefficient is always between 1.6 and 2.

Quasi 1D Fanno flow

In this model friction is present, but area is constant and there is no heat transfer. The typical application is the loss in pipes and in the choking due to friction. For instance, when deciding where to put the combustion chamber for a fluid flowing in a pipe before exiting. The Fanning friction coefficient Cf is a quarter of the Darcy friction factor f found in the Moody diagram:

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Quasi 1D Generalized flow

The Saphiro equations enable us to approach different situations, accounting for both heat exchange and friction, together with chemical reactions and also volume forces. To solve them, however, numerical methods must be employed. In Saphiro tables we can find the influence coefficients which can be linked with the independent variables in order to obtain the dependent ones. A big advantage is the fact that Saphiro equations are ODE and can be solved easily, but the transient is not considered: they are steady-state. With Saphiro equations we can combine Rayleigh and Fanno flows effects. Could we have just summed up the two contributions? We can see from the plots that there are small differences with respect to Saphiro solution, this because the two equations are coupled. An example of case study is the modelling of a SRM:

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There is change in mass since the propellant burns and flows within the tube, but this is Quasi 1D and the Saphiro equations can be used (entire set including mass addition).

Quasi 1D non-optimal expansion

The external pressure is always the main constraint, it has to be matched. Above 3 a normal shock is generated in the divergent, the dashed line shows the conditions after the shock. Between 3 and 5 we'll have an oblique external shock attached at the lip of the nozzle (there's no way to match the BC with a normal shock inside the nozzle), in order to match the external pressure. In some cases ambient pressure is much above the critical value, nevertheless the nozzle is chocked. In order to chock, we don't need the critical pressure ratio for convergent divergent nozzle. Thanks to the fact that there is a divergent part, the environment pressure ratio can be higher with respect to the critical one, and the mass flow rate still remains fixed. The critical ratio is not the requirement to obtain a chocked flow for conv-div. It's the local critical ratio that matters! If we have only convergent nozzle, of course, the ambient pressure ratio must be equal or below to the critical one to have a chocked flow.

Viscid 2D non-optimal expansion

If we consider the flow viscid and 2D (instead of inviscid quasi 1D as done till now), the behaviour for pressure ratios above 3 is not the generation of normal shock waves, but instead a separation of the flow, due to the generation of oblique shock waves: If ambient pressure ratio is below 3 and above 5, we already saw that there will be oblique shocks outside

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