Regenerative Cooling (rocketry)
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In
rocket engine A rocket engine is a reaction engine, producing thrust in accordance with Newton's third law by ejecting reaction mass rearward, usually a high-speed Jet (fluid), jet of high-temperature gas produced by the combustion of rocket propellants stor ...
design, regenerative cooling is a configuration in which some or all of the
propellant A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or another motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicle ...
is passed through tubes, channels, or in a jacket around the
combustion chamber A combustion chamber is part of an internal combustion engine in which the air–fuel ratio, fuel/air mix is burned. For steam engines, the term has also been used for an extension of the Firebox (steam engine), firebox which is used to allow a mo ...
or nozzle to cool the engine. This is effective because the propellants are often cryogenic. The heated propellant is then fed into a special gas-generator or injected directly into the main combustion chamber.


History

In 1857
Carl Wilhelm Siemens Sir Carl Wilhelm Siemens (4 April 1823 – 19 November 1883), anglicised to Charles William Siemens, was a German-British electrical engineer and businessman. autobiography Sir Carl Wilhelm Siemens FRS FRSA, anglicised to Charles William Sie ...
introduced the concept of regenerative cooling. On 10 May 1898,
James Dewar Sir James Dewar ( ; 20 September 1842 – 27 March 1923) was a Scottish chemist and physicist. He is best known for his invention of the vacuum flask, which he used in conjunction with research into the liquefaction of gases. He also studie ...
used regenerative cooling to become the first to statically liquefy hydrogen. The concept of regenerative cooling was also mentioned in 1903 in an article by
Konstantin Tsiolkovsky Konstantin Eduardovich Tsiolkovsky (; rus, Константин Эдуардович Циолковский, p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj, a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) was a Russi ...
.
Robert Goddard Robert Hutchings Goddard (October 5, 1882 – August 10, 1945) was an American engineer, professor, physicist, and inventor who is credited with creating and building the world's first liquid-fueled rocket, which was successfully lau ...
built the first regeneratively cooled engine in 1923, but rejected the scheme as too complex. A regeneratively cooled engine was built by the Italian researcher, Gaetano Arturo Crocco in 1930. The first Soviet engines to employ the technique were Fridrikh Tsander's OR-2 tested in March 1933 and the ORM-50, bench tested in November 1933 by
Valentin Glushko Valentin Petrovich Glushko (; ; born 2 September 1908 – 10 January 1989) was a Soviet engineer who was program manager of the Soviet space program from 1974 until 1989. Glushko served as a main designer of rocket engines in the Soviet progra ...
. The first German engine of this type was also tested in March 1933 by Klaus Riedel in the VfR. The Austrian scientist
Eugen Sänger Eugen Sänger (22 September 1905 – 10 February 1964) was an Austrian aerospace engineer best known for his contributions to lifting body and ramjet technology. Early career Sänger was born in the former mining town of Preßnitz (Příse ...
was particularly famous for experiments with engine cooling starting in 1933; however, most of his experimental engines were water-cooled or cooled by an extra circuit of propellant. The
V-2 rocket The V2 (), with the technical name ''Aggregat (rocket family), Aggregat-4'' (A4), was the world's first long-range missile guidance, guided ballistic missile. The missile, powered by a liquid-propellant rocket engine, was developed during the S ...
engine, the most powerful of its time at 25 tons (245 kN) of thrust, was regeneratively cooled, in a design by Walter Thiel, by fuel pumped around the outside of the combustion chamber between the combustion chamber itself and an outer shell that conformed to the chamber and was separated by a few millimeters. This design was found to be insufficient to cool the combustion chamber due to the use of steel for the combustion chamber, and an additional system of fuel lines were added outside with connections through both combustion chamber shells to inject fuel directly into the chamber at an angle along the inner surface to further cool the chamber in a system called film cooling. This inefficient design required the burning of diluted alcohol at low chamber pressure to avoid melting the engine. The American Redstone engine used the same design. A key innovation in regenerative cooling was the Soviet U-1250 engine designed by
Aleksei Mihailovich Isaev Aleksei Mikhailovich Isaev (also Isayev; Russian: Алексе́й Миха́йлович Иса́ев; October 24, 1908, in Saint Petersburg – June 10, 1971, in Moscow) was a Soviet engineer in the Soviet space program, working on rocket com ...
in 1945. Its combustion chamber was lined with a thin copper sheet supported by the corrugated steel wall of the chamber. Fuel flowed through the corrugations and absorbed heat very efficiently. This permitted more energetic fuels and higher chamber pressures, and is the basic plan used in all Russian engines since. American engines usually solved this problem by lining the combustion chamber with
brazed Brazing is a metal-joining process in which two or more metal items are joined by melting and flowing a filler metal into the joint, with the filler metal having a lower melting point than the adjoining metal. Brazing differs from welding in ...
copper or nickel alloy tubes. Only recently engines like the
RS-68 The RS-68 (Rocket System-68) was a liquid-fuel rocket engine that used liquid hydrogen (LH2) and liquid oxygen (LOX) as propellants in a gas-generator cycle. It was the largest hydrogen-fueled rocket engine ever flown. Designed and manufacture ...
have started to use the cheaper Russian technique. The American style of lining the engine with copper tubes is called the "spaghetti construction", and the concept is credited to Edward A. Neu at
Reaction Motors Reaction Motors, Inc. (RMI) was an early American maker of liquid-fueled rocket engines, located in New Jersey. RMI engines with thrust powered the Bell X-1 rocket aircraft that first broke the sound barrier in 1947, and later aircraft such ...
Inc. in 1947.


Mechanism

Regenerative cooling remains the predominant method for managing the thermal loads in thrust chambers. Typically the rocket fuel acts as a coolant as it enters the engine through passages at the nozzle exit. It traverses the high-heat throat region and exits near the injector face. These passages are created either by brazing cooling tubes to the thrust chamber or by milling channels along the chamber walls. The cross-sections of these passages are smaller, increasing the coolant velocity and maximizing cooling efficiency in high-heat areas.


Heat flow and temperature

The
heat flux In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density, heat-flow density or heat-flow rate intensity, is a flow of energy per unit area per unit time (physics), time. Its SI units are watts per sq ...
through the chamber wall is very high; usually in the range of 0.8–80 MW/m (0.5-50
BTU The British thermal unit (Btu) is a measure of heat, which is a form of energy. It was originally defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United Stat ...
/in-sec). A common method for estimating the heat flux flowing out from the hot combustion gases is to use the Bartz equation:
h_g = \frac \left( \frac \right) \left( \frac\right)^ \left(\frac \right)^ \left( \frac \right)^\sigma
*h_g is the
heat transfer coefficient In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the Proportional (mathematics), proportionality constant between the heat flux and the thermodynamic driving force for the Heat transfer, flow of heat ...
from the hot combustion gas to the chamber/nozzle interior wall (W/m²/K) * D_* is the diameter of the chamber throat (m) * \mu is the
dynamic viscosity Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
of the combustion gas (Pa s) * c_p is the
specific heat capacity In thermodynamics, the specific heat capacity (symbol ) of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat ...
of the combustion gas (J/kg/K) * Pr is the
Prandtl number The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:where: * \nu : momentum d ...
of the combustion gas * p_c is the chamber pressure (Pa) * c^ is the
characteristic velocity Characteristic velocity or c^*, or C-star is a measure of the combustion performance of a rocket engine independent of nozzle performance, and is used to compare different propellants and propulsion systems. It is independent of the nozzle, making ...
of the combustion reaction (m/s) * r_c is the
radius of curvature In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius ...
of the throat wall (m) * A_t is the cross sectional area of the chamber throat (m2) * A is the cross sectional area of the chamber/nozzle at the point of interest (m2) * \sigma is a dimensionless parameter accounting for variation of gas properties across the
boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces ...
:
\sigma = \frac
* T_w is the temperature of the chamber/nozzle interior wall (K) * T_c is the chamber temperature (K) * \gamma is the
ratio of specific heats In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...
of the combustion gas * M is the
Mach number The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Erns ...
of the combustion gas at the point of interest * \omega is the exponent of a viscosity-temperature power law for the combustion gas. A common estimation is 0.6. See
temperature dependence of viscosity Viscosity depends strongly on temperature. In liquids it usually decreases with increasing temperature, whereas, in most gases, viscosity ''increases'' with increasing temperature. This article discusses several models of this dependence, ranging ...
. The amount of heat that can flow into the coolant is controlled by many factors including the temperature difference between the chamber and the coolant, the
heat transfer coefficient In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the Proportional (mathematics), proportionality constant between the heat flux and the thermodynamic driving force for the Heat transfer, flow of heat ...
, the
thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...
of the chamber wall, the velocity of the fluid inside the coolant channels, the velocity of the gas flow in the chamber/nozzle as well as the
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is a ...
and incoming temperature of the fluid used as a coolant. Two
boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces ...
s form: one in the hot gas in the chamber (which is modeled with the Bartz equation above) and the other in the coolant within the channels. Very typically most of the temperature drop occurs in the gas boundary layer since gases are relatively poor conductors. This boundary layer can be destroyed however by combustion instabilities, and wall failure can follow very soon afterwards. The boundary layer within the coolant channels can also be disrupted if the coolant is at subcritical pressure and film boils; the gas then forms an insulating layer and the wall temperature climbs very rapidly and soon fails. However, if the coolant engages in
nucleate boiling In fluid thermodynamics, nucleate boiling is a type of boiling that takes place when the surface temperature is hotter than the saturated fluid temperature by a certain amount but where the heat flux is below the critical heat flux. For water, a ...
but does not form a film, this helps disrupt the coolant boundary layer and the gas bubbles formed rapidly collapse; this can triple the maximum heat flow. However, many modern engines with turbopumps use supercritical coolants, and these techniques can be seldom used. Regenerative cooling is seldom used in isolation; film cooling, transpiration cooling,
radiation cooling In the study of heat transfer, radiative cooling is the process by which a body loses heat by thermal radiation. As Planck's law describes, every physical body spontaneously and continuously emits electromagnetic radiation. Radiative cooling has b ...
are frequently employed as well.


Mechanical considerations

With regenerative cooling, the pressure in the cooling channels is greater than the chamber pressure. The inner liner is under compression, while the outer wall of the engine is under significant
hoop stress In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis. Cylinder stress patterns include: * circumferential stress, or hoop stre ...
es. The metal of the inner liner is greatly weakened by the high temperature, and also undergoes significant thermal expansion at the inner surface while the cold-side wall of the liner constrains the expansion. This sets up significant thermal stresses that can cause the inner surface to crack or craze after multiple firings particularly at the throat. In addition the thin inner liner requires mechanical support to withstand the compressive loading due to the propellant's pressure; this support is usually provided by the side walls of the cooling channels and the backing plate. The inner liner is usually constructed of relatively high temperature, high thermal conductivity materials; traditionally copper or nickel based alloys have been used. Several different manufacturing techniques can be used to create the complex geometry necessary for regenerative cooling. These include a corrugated metal sheet brazed between the inner and outer liner; hundreds of pipes brazed into the correct shape, or an inner liner with milled cooling channels and an outer liner around that. The geometry can also be created through direct metal
3D printing 3D printing, or additive manufacturing, is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer ...
, as seen on some newer designs such as the
SpaceX Space Exploration Technologies Corp., commonly referred to as SpaceX, is an America, American space technology company headquartered at the SpaceX Starbase, Starbase development site in Starbase, Texas. Since its founding in 2002, the compa ...
SuperDraco SuperDraco is a hypergolic propellant rocket engine designed and built by SpaceX. It is part of the SpaceX Draco family of rocket engines. A redundant array of eight SuperDraco engines provides fault-tolerant propulsion for use as a launch escap ...
rocket engine.


See also

*
Regenerative cooling Regenerative cooling is a method of cooling gases in which compressed gas is cooled by allowing it to expand and thereby take heat from the surroundings. The cooled expanded gas then passes through a heat exchanger where it cools the incoming com ...
*
Expander cycle Expander may refer to: *Dynamic range compression operated in reverse *Part of the process of signal compression *Part of the process of companding *A component used to connect Serial Attached SCSI#SAS expanders, SCSI computer data storage, device ...


References

{{Reflist Rocket propulsion