fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, slosh refers to the movement of

liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...

inside another object (which is, typically, also undergoing motion). Strictly speaking, the liquid must have a

free surface In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in ...

to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly. Important examples include

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 ...

slosh in

spacecraft A spacecraft is a vehicle that is designed spaceflight, to fly and operate in outer space. Spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth observation, Weather s ...

tanks and

rocket A rocket (from , and so named for its shape) is a vehicle that uses jet propulsion to accelerate without using any surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely ...

s (especially upper stages), and the

free surface effect The free surface effect is a mechanism which can cause a watercraft to become unstable and capsize. It refers to the tendency of liquids — and of unbound aggregates of small solid objects, like seeds, gravel, or crushed ore, whose behavior app ...

(cargo slosh) in ships and trucks transporting liquids (for example oil and gasoline). However, it has become common to refer to liquid motion in a completely filled tank, i.e. without a free surface, as "fuel slosh". Such motion is characterized by " inertial waves" and can be an important effect in spinning spacecraft dynamics. Extensive mathematical and empirical relationships have been derived to describe liquid slosh. These types of analyses are typically undertaken using

computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required ...

and finite element methods to solve the fluid-structure interaction problem, especially if the solid container is flexible. Relevant fluid dynamics non-dimensional parameters include the

Bond number Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Fidelity bond, a type of insurance policy for employers * Chemical bond, t ...

, the

Weber number The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named ...

, and the

Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...

. Slosh is an important effect for spacecraft, ships, some land vehicles and some

aircraft An aircraft ( aircraft) is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or the Lift (force), dynamic lift of an airfoil, or, i ...

. Slosh was a factor in the

Falcon 1 Falcon 1 was a two-stage small-lift launch vehicle that was operated from 2006 to 2009 by SpaceX, an American aerospace manufacturer. On September 28, 2008, Falcon 1 became the first privately developed fully liquid-fueled launch vehicle to s ...

second test flight anomaly, and has been implicated in various other spacecraft anomalies, including a near-disaster with the Near Earth Asteroid Rendezvous (

NEAR Shoemaker ''Near Earth Asteroid Rendezvous – Shoemaker'' (''NEAR Shoemaker''), renamed after its 1996 launch in honor of planetary scientist Eugene Merle Shoemaker, Eugene Shoemaker, was a Robotic spacecraft, robotic space probe designed by the Johns ...

) satellite.

Spacecraft effects

Liquid slosh in

microgravity Weightlessness is the complete or near-complete absence of the sensation of weight, i.e., zero apparent weight. It is also termed zero g-force, or zero-g (named after the g-force) or, incorrectly, zero gravity. Weight is a measurement of the fo ...

is relevant to spacecraft, most commonly Earth-orbiting

satellites A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scientif ...

, and must take account of liquid

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...

which can alter the shape (and thus the

eigenvalues In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

) of the liquid slug. Typically, a large fraction of the mass of a satellite is liquid propellant at/near Beginning of Life (BOL), and slosh can adversely affect satellite performance in a number of ways. For example, propellant slosh can introduce uncertainty in spacecraft attitude (pointing) which is often called

jitter In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a signifi ...

. Similar phenomena can cause

pogo oscillation Pogo oscillation is a self-excited vibration in liquid-propellant rocket engines caused by Rocket engine#Combustion instabilities, combustion instability. The unstable combustion results in variations of engine thrust, causing variations of accele ...

and can result in structural failure of a space vehicle. Another example is problematic interaction with the spacecraft's Attitude Control System (ACS), especially for spinning satellites which can suffer

resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

between slosh and

nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference fra ...

, or adverse changes to the rotational

inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...

. Because of these types of

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environ ...

, in the 1960s the

National Aeronautics and Space Administration The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the United States's civil space program, aeronautics research and space research. Established in 1958, it su ...

(NASA) extensively studied liquid slosh in spacecraft tanks, and in the 1990s NASA undertook the ''Middeck 0-Gravity Dynamics Experiment'' on the

Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...

. The

European Space Agency The European Space Agency (ESA) is a 23-member International organization, international organization devoted to space exploration. With its headquarters in Paris and a staff of around 2,547 people globally as of 2023, ESA was founded in 1975 ...

has advanced these investigations with the launch of SLOSHSAT. Most spinning spacecraft since 1980 have been tested at the Applied Dynamics Laboratories drop tower using sub-scale models. Extensive contributions have also been made by the

Southwest Research Institute Southwest Research Institute (SwRI), headquartered in San Antonio, Texas, is an independent and nonprofit applied research and development (R&D) organization. Founded in 1947 by oil businessman Tom Slick, it provides contract research and deve ...

, but research is widespread in academia and industry. Research is continuing into slosh effects on in-

space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...

propellant depot An orbital propellant depot is a cache of propellant that is placed in orbit around Earth or another body to allow spacecraft or the transfer stage of the spacecraft to be fueled in space. It is one of the types of space resource depots that ha ...

s. In October 2009, the

United States Air Force The United States Air Force (USAF) is the Air force, air service branch of the United States Department of Defense. It is one of the six United States Armed Forces and one of the eight uniformed services of the United States. Tracing its ori ...

and

United Launch Alliance United Launch Alliance, LLC (ULA) is an American launch service provider formed in December 2006 as a joint venture between Lockheed Martin Space and Boeing Defense, Space & Security. The company designs, assembles, sells and launches rockets ...

(ULA) performed an experimental on-orbit demonstration on a modified Centaur upper stage on the DMSP-18 satellite

launch Launch or launched may refer to: Involving vehicles * Launch (boat), one of several different sorts of boat ** Motor launch (naval), a small military vessel used by the Royal Navy * Air launch, the practice of dropping an aircraft, rocket, or ...

in order to improve "understanding of propellant settling and slosh", "The light weight of DMSP-18 allowed of remaining LO₂ and LH₂ propellant, 28% of Centaur’s capacity", for the on-orbit tests. The post-spacecraft mission extension ran 2.4 hours before the planned deorbit burn was executed.ulalaunch.com
; Successful Flight Demonstration Conducted by the Air Force and United Launch Alliance Will Enhance Space Transportation: DMSP-18, ''

'', October 2009, accessed 2011-01-10. NASA's

Launch Services Program The NASA Launch Services Program (LSP) is responsible for procurement of launch services for NASA uncrewed missions and oversight of launch integration and launch preparation activity, providing added quality and mission assurance to meet program ...

is working on two on-going slosh fluid dynamics experiments with partners:

CRYOTE An orbital propellant depot is a cache of propellant that is placed in orbit around Earth or another body to allow spacecraft or the transfer stage of the spacecraft to be fueled in space. It is one of the types of space resource depots that ha ...

and

SPHERES The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for t ...

-Slosh. ULA has additional small-scale demonstrations of cryogenic fluid management are planned with project CRYOTE in 2012–2014 leading to a ULA large-scale cryo-sat propellant depot test under the NASA

flagship technology demonstrations The Centennial Challenges are NASA space competition inducement prize contests for non-government-funded technology, technological achievements by United States, American teams. Origin NASA's Centennial Challenge Program (CCP) directly engages th ...

program in 2015.spirit.as.utexas.edu
; ''Propellant Depots Made Simple'', Bernard Kutter,

, FISO Colloquium, 2010-11-10, accessed 2011-01-10. SPHERES-Slosh with

Florida Institute of Technology Florida Institute of Technology (Florida Tech or FIT) is a private research university in Melbourne, Florida. The university comprises four academic colleges: Engineering & Science, Aeronautics, Psychology & Liberal Arts, and Business. Approxim ...

and

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

will examine how liquids move around inside containers in microgravity with the SPHERES Testbed on the

International Space Station The International Space Station (ISS) is a large space station that was Assembly of the International Space Station, assembled and is maintained in low Earth orbit by a collaboration of five space agencies and their contractors: NASA (United ...

Sloshing in road tank vehicles

Liquid sloshing strongly influences the directional dynamics and safety performance of highway tank vehicles in a highly adverse manner. Hydrodynamic

force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

s and moments arising from liquid

cargo In transportation, cargo refers to goods transported by land, water or air, while freight refers to its conveyance. In economics, freight refers to goods transported at a freight rate for commercial gain. The term cargo is also used in cas ...

oscillations in the tank under

steering Steering is the control of the direction of motion or the components that enable its control. Steering is achieved through various arrangements, among them ailerons for airplanes, rudders for boats, cylic tilting of rotors for helicopters, ...

and/or

braking A brake is a mechanical device that inhibits motion by absorbing energy from a moving system. It is used for slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of friction. Background ...

maneuvers reduce the stability limit and controllability of partially-filled tank vehicles. Anti-slosh devices such as baffles are widely used in order to limit the adverse liquid slosh effect on directional performance and stability of the tank vehicles. Since most of the time, tankers are carrying dangerous liquid contents such as ammonia, gasoline and fuel oils, stability of partially-filled liquid cargo vehicles is very important. Optimizations and sloshing reduction techniques in fuel tanks such as elliptical tank, rectangular, modified oval and generic tank shape have been performed in different filling levels using numerical, analytical and analogical analyses. Most of these studies concentrate on effects of baffles on sloshing while the influence of cross-section is completely ignored. The

Bloodhound LSR ''Bloodhound LSR'', formerly ''Bloodhound SSC'', is a British land vehicle designed to travel at supersonic speeds with the intention of setting a new world land speed record. The arrow-shaped car, under development since 2008, is powered by a je ...

1,000 mph project car utilizes a liquid-fuelled rocket that requires a specially-baffled oxidizer tank to prevent directional instability, rocket thrust variations and even oxidizer tank damage.

Practical effects

Sloshing or shifting

, water

ballast Ballast is dense material used as a weight to provide stability to a vehicle or structure. Ballast, other than cargo, may be placed in a vehicle, often a ship or the gondola of a balloon or airship, to provide stability. A compartment within ...

, or other liquid (e.g., from leaks or fire fighting) can cause disastrous

capsizing Capsizing or keeling over occurs when a boat or ship is rolled on its side or further by wave action, instability or wind force beyond the angle of positive static stability or it is upside down in the water. The act of recovering a vessel fr ...

in ships due to

; this can also affect trucks and aircraft. The effect of slosh is used to limit the bounce of a

roller hockey Roller hockey is a form of hockey played on a dry surface using wheeled skates. It can be played with traditional roller skates (quad skates) or with inline skates and use either a ball or puck. Combined, roller hockey is played in nearly 60 cou ...

ball. Water slosh can significantly reduce the rebound height of a ballSport ball for roller hockey; U.S. Patent 5516098; May 14, 1996; Jeffrey Aiello. but some amounts of liquid seem to lead to a

effect. Many of the balls for roller hockey commonly available contain water to reduce the bounce height.

References

Other references

* * NASA (1969),
Slosh suppression
'', May 1969, PDF, 36p * {{in lang, en NASA (1966),
Dynamic behavior of liquids in moving containers with applications to propellants in space vehicle fuel tanks
', Jan 1, 1966, PDF, 464 p Fluid mechanics Fluid dynamics

Spacecraft effects

Sloshing in road tank vehicles

Practical effects

See also

References

Other references