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The four expansion regimes of a de Laval nozzle: • under-expanded • perfectly expanded • over-expanded • grossly over-expanded

The most commonly used nozzle is the de Laval nozzle, a fixed geometry nozzle with a high expansion-ratio. The large bell- or cone-shaped nozzle extension beyond the throat gives the rocket engine its characteristic shape.

The exit

The most commonly used nozzle is the de Laval nozzle, a fixed geometry nozzle with a high expansion-ratio. The large bell- or cone-shaped nozzle extension beyond the throat gives the rocket engine its characteristic shape.

The exit static pressure of the exhaust jet depends on the chamber pressure and the ratio of exit to throat area of the nozzle. As exit pressure varies from the ambient (atmospheric) pressure, a choked nozzle is said to be

In practice, perfect expansion is only achievable with a variable-exit area nozzle (since ambient pressure decreases as altitude increases), and is not possi

The exit static pressure of the exhaust jet depends on the chamber pressure and the ratio of exit to throat area of the nozzle. As exit pressure varies from the ambient (atmospheric) pressure, a choked nozzle is said to be

In practice, perfect expansion is only achievable with a variable-exit area nozzle (since ambient pressure decreases as altitude increases), and is not possible above a certain altitude as ambient pressure approaches zero. If the nozzle is not perfectly expanded, then loss of efficiency occurs. Grossly over-expanded nozzles lose less efficiency, but can cause mechanical problems with the nozzle. Fixed-area nozzles become progressively more under-expanded as they gain altitude. Almost all de Laval nozzles will be momentarily grossly over-expanded during startup in an atmosphere.[5]

Nozzle efficiency is affected by operation in the atmosphere because atmospheric pressure changes with altitude; but due to the supersonic speeds of the gas exiting from a rocket engine, the pressure of the jet may be either below or above ambient, and equilibrium between the two is not reached at all altitudes (see diagram).

Back pressure and optimal expansionNozzle efficiency is affected by operation in the atmosphere because atmospheric pressure changes with altitude; but due to the supersonic speeds of the gas exiting from a rocket engine, the pressure of the jet may be either below or above ambient, and equilibrium between the two is not reached at all altitudes (see diagram).

For optimal performance, the pressure of the gas at the end of the nozzle should just equal the ambient pressure: if the exhaust's pressure is lower than the ambient pressure, then the vehicle will be slowed by the difference in pressure between the top of the engine and the exit; on the other hand, if the exhaust's pressure is higher, then exhaust pressure that could have been converted into thrust is not converted, and energy is wasted.

To maintain this ideal of equality between the exhaust's exit pressure and the ambient pressure, the diameter of the nozzle would need to increase with altitude, giving the pressure a longer nozzle to act on (and reducing the exit pressure and temperature). This increase is difficult to arrange in a lightweight fashion, although is routinely done with other forms of jet engines.

To maintain this ideal of equality between the exhaust's exit pressure and the ambient pressure, the diameter of the nozzle would need to increase with altitude, giving the pressure a longer nozzle to act on (and reducing the exit pressure and temperature). This increase is difficult to arrange in a lightweight fashion, although is routinely done with other forms of jet engines. In rocketry a lightweight compromise nozzle is generally used and some reduction in atmospheric performance occurs when used at other than the 'design altitude' or when throttled. To improve on this, various exotic nozzle designs such as the plug nozzle, stepped nozzles, the expanding nozzle and the aerospike have been proposed, each providing some way to adapt to changing ambient air pressure and each allowing the gas to expand further against the nozzle, giving extra thrust at higher altitudes.

When exhausting into a sufficiently low ambient pressure (vacuum) several issues arise. One is the sheer weight of the nozzle—beyond a certain point, for a particular vehicle, the extra weight of the nozzle outweighs any performance gained. Secondly, as the exhaust gases adiabatically expand within the nozzle they cool, and eventually some of the chemicals can freeze, producing 'snow' within the jet. This causes instabilities in the jet and must be avoided.

On a de Laval nozzle, exhaust gas flow detachment will occur in a grossly over-expanded nozzle. As the detachment point will not be uniform around the axis of the engine, a side force may be imparted to the engine. This side force may change over time and result in control problems with the launch vehicle.

Advanced altitude-compensating designs, such as the aerospike or plug nozzle, attempt to minimize performance losses by adjusting to varying expansion ratio caused by changing altitude.

For a rocket engine to be propellant efficient, it is important that the maximum pressures possible be created on the walls of the chamber and nozzle by a specific amount of propellant; as this is the source of the thrust. This can be achieved by all of:

  • heating the propellant to as high a temperature as possible (using a high energy fuel, containing hydrogen and carbon and sometimes metals such as aluminium, or even using nuclear energy)
  • using a low specific density gas (as hydrogen rich as possible)
  • using propellants which are, or decompose to, simple molecules with few degrees of freedom to maximise translational velocity

Since all of these things minimise the mass of the propellant used, and since pressure is proportional to the mass of propellant present to be accelerated as it pushes on the engine, and since from Newton's third law the pressure that acts on the engine also reciprocally acts on the propellant, it turns out that for any given engine, the speed that the propellant leaves the chamber is unaffected by the chamber pressure (although the thrust is proportional). However, speed is significantly affected by all three of the above factors and the exhaust speed is an excellent measure of the engine propellant efficiency. This is termed exhaust velocity, and after allowance is made for factors that can reduce it, the Newton's third law the pressure that acts on the engine also reciprocally acts on the propellant, it turns out that for any given engine, the speed that the propellant leaves the chamber is unaffected by the chamber pressure (although the thrust is proportional). However, speed is significantly affected by all three of the above factors and the exhaust speed is an excellent measure of the engine propellant efficiency. This is termed exhaust velocity, and after allowance is made for factors that can reduce it, the effective exhaust velocity is one of the most important parameters of a rocket engine (although weight, cost, ease of manufacture etc. are usually also very important).

For aerodynamic reasons the flow goes sonic ("chokes") at the narrowest part of the nozzle, the 'throat'. Since the speed of sound in gases increases with the square root of temperature, the use of hot exhaust gas greatly improves performance. By comparison, at room temperature the speed of sound in air is about 340 m/s while the speed of soun

For aerodynamic reasons the flow goes sonic ("chokes") at the narrowest part of the nozzle, the 'throat'. Since the speed of sound in gases increases with the square root of temperature, the use of hot exhaust gas greatly improves performance. By comparison, at room temperature the speed of sound in air is about 340 m/s while the speed of sound in the hot gas of a rocket engine can be over 1700 m/s; much of this performance is due to the higher temperature, but additionally rocket propellants are chosen to be of low molecular mass, and this also gives a higher velocity compared to air.

Expansion in the rocket nozzle then further multiplies the speed, typically between 1.5 and 2 times, giving a highly collimated hypersonic exhaust jet. The speed increase of a rocket nozzle is mostly determined by its area expansion ratio—the ratio of the area of the exit to the area of the throat, but detailed properties of the gas are also important. Larger ratio nozzles are more massive but are able to extract more heat from the combustion gases, increasing the exhaust velocity.

Vehicles typically require the overall thrust to change direction over the length of the burn. A number of different ways to achieve this have been flown:

  • The entire engine is mounted on a hinge or gimbal and any propellant feeds reach the engine via low pressure flexible pipes or rotary couplings.
  • Just the combustion chamber and nozzle is gimballed, the pumps are fixed, and high pressure feeds attach to the engine.
  • Multiple engines (often canted at slight angles) are deployed but throttled to give the overall vector that is r

    Rocket technology can combine very high thrust (meganewtons), very high exhaust speeds (around 10 times the speed of sound in air at sea level) and very high thrust/weight ratios (>100) simultaneously as well as being able to operate outside the atmosphere, and while permitting the use of low pressure and hence lightweight tanks and structure.

    Rockets can be further optimised to even more extreme performance along one or more of these axes at the expense of the others.

    Specific impulse

    For efficiency reasons, higher temperatures are desirable, but materials lose their strength if the temperature becomes too high. Rockets run with combustion temperatures that can reach 3,500 K (3,200 °C; 5,800 °F).

    Most other jet engines have gas turbines in the hot exhaust. Due to their larger surface area, they are harder to cool and hence there is a need to run the combustion processes at much lower temperatures, losing efficiency. In addition, duct engines use air as an oxidant, which contains 78% largely unreactive nitrogen, which dilutes the reaction and lowers the temperatures.[9] Rockets have none of these inherent combustion temperature limiters.

    The temperatures reached by rocket exhaust often substantially exceed the melting points of the nozzle and combustion chamber materials (about 1,200 K for copper). Most construction materials will also combust if exposed to high temperature oxidizer, which leads to a number of design challenges. The nozzle and combustion chamber walls must not be allowed to combust, melt, or vaporize (sometimes facetiously termed an "engine-rich exhaust").

    Rockets that use the common construction materials such as aluminium, steel, nickel or copper alloys must employ cooling systems to limit the temperatures that engine structures experience. Regenerative cooling, where the propellant is passed through tubes around the combustion chamber or nozzle, and other techniques, such as curtain cooling or film cooling, are employed to give longer nozzle and chamber life. These techniques ensure that a gaseous thermal boundary layer touching the material is kept below the temperature which would cause the material to catastrophically fail.

    Two material exceptions that can directly sustain rocket exhaust temperatures are graphite and tungsten, although both are subject to oxidation if not protected. Materials technology, combined with the engine design, is a limiting factor of the exhaust temperature of chemical rockets.

    In rockets, the heat fluxes that can pass through the wall are among the highest in engineering; fluxes are generally in the range of 100–200 MW/m2. The strongest heat fluxes are found at the throat, which often sees twice that found in the associated chamber and nozzle. This is due to the combination of high speeds (which gives a very thin boundary layer), and although lower than the chamber, the high temperatures seen there. (See § Rocket nozzles above for temperatures in nozzle).

    In rockets the coolant methods include:

    1. uncooled (used for short runs mainly during testing)
    2. ablative walls (walls are lined with a material that is continuously vaporised and carried away)
    3. duct engines use air as an oxidant, which contains 78% largely unreactive nitrogen, which dilutes the reaction and lowers the temperatures.[9] Rockets have none of these inherent combustion temperature limiters.

      The temperatures reached by rocket exhaust often substantially exceed the melting points of the nozzle and combustion chamber materials (about 1,200 K for copper). Most construction materials will also combust if exposed to high temperature oxidizer, which leads to a number of design challenges. The nozzle and combustion chamber walls must not be allowed to combust, melt, or vaporize (sometimes facetiously termed an "engine-rich exhaust").

      Rockets that use the common construction materials such as aluminium, steel, nickel or copper alloys must employ cooling systems to limit the temperatures that engine structures experience. Regenerative cooling, where the propellant is passed through tubes around the combustion chamber or nozzle, and other techniques, such as curtain cooling or film cooling, are employed to give longer nozzle and chamber life. These techniques ensure that a gaseous thermal boundary layer touching the material is kept below the temperature which would cause the material to catastrophicall

      Most other jet engines have gas turbines in the hot exhaust. Due to their larger surface area, they are harder to cool and hence there is a need to run the combustion processes at much lower temperatures, losing efficiency. In addition, duct engines use air as an oxidant, which contains 78% largely unreactive nitrogen, which dilutes the reaction and lowers the temperatures.[9] Rockets have none of these inherent combustion temperature limiters.

      The temperatures reached by rocket exhaust often substantially exceed the melting points of the nozzle and combustion chamber materials (about 1,200 K for copper). Most construction materials will also combust if exposed to high temperature oxidizer, which leads to a number of design challenges. The nozzle and combustion chamber walls must not be allowed to combust, melt, or vaporize (sometimes facetiously termed an "engine-rich exhaust").

      Rockets that use the common construction materials such as aluminium, steel, nickel or copper alloys must employ cooling systems to limit the temperatures that engine structures experience. Regenerative cooling, where the propellant is passed through tubes around the combustion chamber or nozzle, and other techniques, such as curtain cooling or film cooling, are employed to give longer nozzle and chamber life. These techniques ensure that a gaseous thermal boundary layer touching the material is kept below the temperature which would cause the material to catastrophically fail.

      Two material exceptions that can directly sustain rocket exhaust temperatures are graphite and tungsten, although both are subject to oxidation if not protected. Materials technology, combined with the engine design, is a limiting factor of the exhaust temperature of chemical rockets.

      In rockets, the heat fluxes that can pass through the wall are among the highest in engineering; fluxes are generally in the range of 100–200 MW/m2. The strongest heat fluxes are found at the throat, which often sees twice that found in the associated chamber and nozzle. This is due to the combination of high speeds (which gives a very thin boundary layer), and although lower than the chamber, the high temperatures seen there. (See § Rocket nozzles above for temperatures in nozzle).

      In rockets the coolant methods include:

      In all cases the cooling effect that prevents the wall from being destroyed is caused by a thin layer of insulating fluid (a boundary layer) that is in contact with the walls that is far cooler than the combustion temperature. Provided this boundary layer is intact the wall will not be damaged.

      Disruption of the boundary layer may occur during cooling failures or combustion instabilities, and wall failure typically occurs soon after.

      With regenerative cooling a second boundary layer is found in the coolant channels around the chamber. This boundary layer thickness needs to be as small as possible, since the boundary layer acts as an insulator between the wall and the coolant. This may be achieved by making the coolant velocity in the channels as high as possible.

      In practice, regenerative cooling is nearly always used in conjunction with curtain cooling and/or film cooling.

      Liquid-fuelled engines are often run fuel-rich, which lowers combustion temperatures. This reduces heat loads on the engine and allows lower cost materials and a simplified cooling system. This can also increase performance by lowering the average molecular weight of the exhaust and increasing the efficiency with which combu

      Disruption of the boundary layer may occur during cooling failures or combustion instabilities, and wall failure typically occurs soon after.

      With regenerative cooling a second boundary layer is found in the coolant channels around the chamber. This boundary layer thickness needs to be as small as possible, since the boundary layer acts as an insulator between the wall and the coolant. This may be achieved by making the coolant velocity in the channels as high as possible.

      In practice, regenerative cooling is nearly always used in conjunction with curtain cooling and/or film cooling.

      Liquid-fuelled engines are often run fuel-rich, which lowers combustion temperatures. This reduces heat loads on the engine and allows lower cost materials and a simplified cooling system. This can also increase performance by lowering the average molecular weight of the exhaust and increasing the efficiency with which combustion heat is converted to kinetic exhaust energy.

      Rocket combustion chambers are normally operated at fairly high pressure, typically 10–200 bar (1–20 MPa, 150–3,000 psi). When operated within significant atmospheric pressure, higher combustion chamber pressures give better performance by permitting a larger and more efficient nozzle to be fitted without it being grossly overexpanded.

      However, these high pressures cause the outermost part of the chamber to be under very large hoop stresses – rocket engines are pressure vessels.

      Worse, due to the high temperatures create

      However, these high pressures cause the outermost part of the chamber to be under very large hoop stresses – rocket engines are pressure vessels.

      Worse, due to the high temperatures created in rocket engines the materials used tend to have a significantly lowered working tensile strength.

      In addition, significant temperature gradients are set up in the walls of the chamber and nozzle, these cause differential expansion of the inner liner that create internal stresses.

      The extreme vibration and acoustic environment inside a rocket motor commonly result in peak stresses well above mean values, especially in the presence of organ pipe-like resonances and gas turbulence.[24]

      Combustion instabilities

      This can be caused due to insufficient pressure drop across the injectors.[26]:261 It generally is mostly annoying, rather than being damaging. However, in extreme cases combustion can end up being forced backwards through the injectors – this can cause explosions with monopropellants.[citation needed]

      ScreechingThis is the most immediately damaging, and the hardest to control. It is due to acoustics within the combustion chamber that often couples to the chemical combustion processes that are the primary drivers of the energy release, and can lead to unstable resonant "screeching" that commonly leads to catastrophic failure due to thinning of the insulating thermal boundary layer. Acoustic oscillations can be excited by thermal processes, such as the flow of hot air through a pipe or combustion in a chamber. Specifically, standing acoustic waves inside a chamber can be intensified if combustion occurs more intensely in regions where the pressure of the acoustic wave is maximal.[27][28][29][26] Such effects are very difficult to predict analytically during the design process, and have usually been addressed by expensive, time-consuming and extensive testing, combined with trial and error remedial correction measures.

      Screeching is often dealt with by detailed changes to injectors, or changes in the propellant chemistry, or vaporising the propellant before injection, or use of Helmholtz dampers within the combustion chambers to change the r

      Screeching is often dealt with by detailed changes to injectors, or changes in the propellant chemistry, or vaporising the propellant before injection, or use of Helmholtz dampers within the combustion chambers to change the resonant modes of the chamber.[citation needed]

      Testing for the possibility of screeching is sometimes done by exploding small explosive charges outside the combustion chamber with a tube set tangentially to the combustion chamber near the injectors to determine the engine's impulse response and then evaluating the time response of the chamber pressure- a fast recovery indicates a stable system.

      For all but the very smallest sizes, rocket exhaust compared to other engines is generally very noisy. As the hypersonic exhaust mixes with the ambient air, shock waves are formed. The Space Shuttle generated over 200 dB(A) of noise around its base. To reduce this, and the risk of payload damage or injury to the crew atop the stack, the mobile launcher platform was fitted with a Sound Suppression System that sprayed 1.1 million litres (290,000 US gal) of water around the base of the rocket in 41 seconds at launch time. Using this system kept sound levels within the payload bay to 142 dB.[30]

      The sound intensity from the shock waves generated depends on the size of the rocket and on the exhaust velocity. Such shock waves seem to account for the characteristic crackling and popping sounds produced by large rocket engines when heard live. These noise peaks typically overload microphones and audio electronics, and so are generally weakened or entirely absent in recorded or broadcast audio reproductions. For l

      The sound intensity from the shock waves generated depends on the size of the rocket and on the exhaust velocity. Such shock waves seem to account for the characteristic crackling and popping sounds produced by large rocket engines when heard live. These noise peaks typically overload microphones and audio electronics, and so are generally weakened or entirely absent in recorded or broadcast audio reproductions. For large rockets at close range, the acoustic effects could actually kill.[31]

      More worryingly for space agencies, such sound levels can also damage the launch structure, or worse, be reflected back at the comparatively delicate rocket above. This is why so much water is typically used at launches. The water spray changes the acoustic qualities of the air and reduces or deflects the sound energy away from the rocket.

      Generally speaking, noise is most intense when a rocket is close to the ground, since the noise from the engines radiates up away from the jet, as well as reflecting off the ground. Also, when the vehicle is moving slowly, little of the chemical energy input to the engine can go into increasing the kinetic energy of the rocket (since useful power P transmitted to the vehicle is for thrust F and speed V). Then the largest portion of the energy is dissipated in the exhaust's interaction with the ambient air, producing noise. This noise can be reduced somewhat by flame trenches with roofs, by water injection around the jet and by deflecting the jet at an angle.

      Rocket engines are usually statically tested at a test facility before being put into production. For high altitude engines, either a shorter nozzle must be used, or the rocket must be tested in a large vacuum chamber.

      Safety

      Rocket vehicles have a reputation for unreliability and danger; especially catastrophic failures. Contrary to this reputation, carefully designed rockets can be made arbitrarily reliable.[citation needed] In military use, rockets are not unreliable. However, one of the main non-military uses of rockets is for orbital launch. In this application, the premium has typically been placed on minimum weight, and it is difficult to achieve high reliability and low weight simultaneously. In addition, if the number of flights launched is low, there is a very high chance of a design, operations or manufacturing error causing destruction of the vehicle.[citation needed]

      Saturn family (1961–1975)

      The Space Shuttle Solid Rocket Booster, used in pairs, caused one notable catastrophic failure in 270 engine-flights.

      The RS-25, used in a cluster of three, flew in 46 refurbished engine units. These made a total of 405 engine-flights with no catastrophic in-flight failures. A single in-flight RS-25 engine failure occurred during Space Shuttle RS-25, used in a cluster of three, flew in 46 refurbished engine units. These made a total of 405 engine-flights with no catastrophic in-flight failures. A single in-flight RS-25 engine failure occurred during Space Shuttle Challenger's STS-51-F mission.[33] This failure had no effect on mission objectives or duration.[34]

      Rocket propellants require a high energy per unit mass (specific energy), which must be balanced against the tendency of highly energetic propellants to spontaneously explode. Assuming that the chemical potential energy of the propellants can be safely stored, the combustion process results in a great deal of heat being released. A significant fraction of this heat is transferred to kinetic energy in the engine nozzle, propelling the rocket forward in combination with the mass of combustion products released.

      Ideally all the reaction energy appears as kinetic energy of the exhaust gases, as exhaust velocity is the single most important performance parameter of an engine. However, real exhaust species are molecules, which typically have translation, vibrational, an

      Ideally all the reaction energy appears as kinetic energy of the exhaust gases, as exhaust velocity is the single most important performance parameter of an engine. However, real exhaust species are molecules, which typically have translation, vibrational, and rotational modes with which to dissipate energy. Of these, only translation can do useful work to the vehicle, and while energy does transfer between modes this process occurs on a timescale far in excess of the time required for the exhaust to leave the nozzle.

      The more chemical bonds an exhaust molecule has, the more rotational and vibrational modes it will have. Consequently, it is generally desirable for the exhaust species to be as simple as possible, with a diatomic molecule composed of light, abundant atoms such as H2 being ideal in practical terms. However, in the case of a chemical rocket, hydrogen is a reactant and reducing agent, not a product. An oxidizing agent, most typically oxygen or an oxygen-rich species, must be introduced into the combustion process, adding mass and chemical bonds to the exhaust species.

      An additional advantage of light molecules is that they may be accelerated to high velocity at temperatures that can be contained by currently available materials - the high gas temperatures in rocket engines pose serious problems for the engineering of survivable motors.

      Liquid hydrogen (LH2) and oxygen (LOX, or LO2), are the most effective propellants in terms of exhaust velocity that have been widely used to date, though a few exotic combinations involving boron or liquid ozone are potentially somewhat better in theory if various practical problems could be solved.[35]