In
hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
, a plume or a column is a vertical body of one fluid moving through another. Several effects control the motion of the fluid, including momentum (inertia), diffusion and buoyancy (density differences). Pure ''jets'' and pure ''plumes'' define flows that are driven entirely by momentum and buoyancy effects, respectively. Flows between these two limits are usually described as forced plumes or buoyant jets. "Buoyancy is defined as being positive" when, in the absence of other forces or initial motion, the entering fluid would tend to rise. Situations where the density of the plume fluid is greater than its surroundings (i.e. in still conditions, its natural tendency would be to sink), but the flow has sufficient initial momentum to carry it some distance vertically, are described as being negatively buoyant.
Movement
Usually, as a plume moves away from its source, it widens because of
entrainment
Entrainment may refer to:
* Air entrainment, the intentional creation of tiny air bubbles in concrete
* Brainwave entrainment, the practice of entraining one's brainwaves to a desired frequency
* Entrainment (biomusicology), the synchronization o ...
of the surrounding fluid at its edges. Plume shapes can be influenced by flow in the ambient fluid (for example, if local wind blowing in the same direction as the plume results in a co-flowing jet). This usually causes a plume which has initially been 'buoyancy-dominated' to become 'momentum-dominated' (this transition is usually predicted by a dimensionless number called the
Richardson number The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term:
:
\mathrm = \frac = \frac \frac
where g is gravity, \rho is de ...
).
Flow and detection
A further phenomenon of importance is whether a plume has
laminar flow or
turbulent flow
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
. Usually, there is a transition from laminar to turbulent as the plume moves away from its source. This phenomenon can be clearly seen in the rising column of smoke from a cigarette. When high accuracy is required,
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 flows. Computers are used to perform the calculations required to simulate th ...
(CFD) can be employed to simulate plumes, but the results can be sensitive to the
turbulence model
Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow ...
chosen. CFD is often undertaken for rocket plumes, where condensed phase constituents can be present in addition to gaseous constituents. These types of simulations can become quite complex, including
afterburning
An afterburner (or reheat in British English) is an additional combustion component used on some jet engines, mostly those on military supersonic aircraft. Its purpose is to increase thrust, usually for supersonic flight, takeoff, and combat ...
and
thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, and (for example)
ballistic missile
A ballistic missile is a type of missile that uses projectile motion to deliver warheads on a target. These weapons are guided only during relatively brief periods—most of the flight is unpowered. Short-range ballistic missiles stay within the ...
launches are often detected by sensing hot rocket plumes.
Spacecraft designers are sometimes concerned with impingement of
attitude control system
Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle/satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, et ...
thruster plumes onto sensitive subsystems like
solar arrays
A photovoltaic system, also PV system or solar power system, is an electric power system designed to supply usable solar power by means of photovoltaics. It consists of an arrangement of several components, including solar panels to absorb and c ...
and
star tracker
A star tracker is an optical device that measures the positions of stars using photocells or a camera.
As the positions of many stars have been measured by astronomers to a high degree of accuracy, a star tracker on a satellite or spacecraft may ...
s, or with the impingement of
rocket engine
A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordanc ...
plumes onto
moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
or planetary surfaces where they can cause local damage or even mid-term disturbances to
planetary atmosphere
Planetary means relating to a planet or planets. It can also refer to:
;Science
* Planetary habitability, the measure of an astronomical body's potential to develop and sustain life
* Planetary nebula, an astronomical object
;People
* Planetary ...
s.
Another phenomenon which can also be seen clearly in the flow of smoke from a cigarette is that the leading-edge of the flow, or the starting-plume, is quite often approximately in the shape of a ring-
vortex
In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
(
smoke ring).
Types
Pollutants
A pollutant or novel entity is a substance or energy introduced into the environment that has undesired effects, or adversely affects the usefulness of a resource. These can be both naturally forming (i.e. minerals or extracted compounds like o ...
released to the ground can work their way down into the
groundwater
Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidate ...
, leading to
groundwater pollution
Groundwater pollution (also called groundwater contamination) occurs when pollutants are released to the ground and make their way into groundwater. This type of water pollution can also occur naturally due to the presence of a minor and unwante ...
. The resulting body of polluted water within an
aquifer
An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characterist ...
is called a plume, with its migrating edges called plume fronts. Plumes are used to locate, map, and measure
water pollution
Water pollution (or aquatic pollution) is the contamination of water bodies, usually as a result of human activities, so that it negatively affects its uses. Water bodies include lakes, rivers, oceans, aquifers, reservoirs and groundwater. Water ...
within the aquifer's total body of water, and plume fronts to determine directions and speed of the contamination's spreading in it.
Plumes are of considerable importance in the
atmospheric dispersion modelling
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that include algorithms to solve the mathematical equations that govern the pollutant ...
of
air pollution
Air pollution is the contamination of air due to the presence of substances in the atmosphere that are harmful to the health of humans and other living beings, or cause damage to the climate or to materials. There are many different types ...
. A classic work on the subject of air pollution plumes is that by Gary Briggs.
A thermal plume is one which is generated by gas rising above a heat source. The gas rises because
thermal expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.
Temperature is a monotonic function of the average molecular kinetic ...
makes warm gas less dense than the surrounding cooler gas.
Simple plume modeling
Quite simple modelling will enable many properties of fully developed, turbulent plumes to be investigated. Many of the classic scaling arguments are described in the monograph of
Stewart Turner
John Stewart Turner FAA FRS (11 January 1930 – 3 July 2022) was an Australian geophysicist.
Early life
Stewart Turner was educated at North Sydney Boys High School and Sydney University. He then joined the Cloud Physics Group, CSIRO Divisi ...
.
# It is usually sufficient to assume that the pressure gradient is set by the gradient far from the plume (this approximation is similar to the usual
Boussinesq approximation).
# The distribution of density and velocity across the plume are modelled either with simple
Gaussian distributions or else are taken as uniform across the plume (the so-called 'top hat' model).
# The rate of entrainment into the plume is proportional to the local velocity.
[Morton, B. R., Turner, J. S., and Taylor, G.I. (1956), ''Turbulent gravitational convection from maintained and instantaneous sources'', P. Roy. Soc. Lond., vol. 234, pp.1--&] Though initially thought to be a constant, recent work has shown that the entrainment coefficient varies with the local Richardson number. Typical values for the entrainment coefficient are of about 0.08 for vertical jets and 0.12 for vertical, buoyant plumes whilst for bent-over plumes, the entrainment coefficient is about 0.6.
# Conservation equations for mass (including entrainment), and momentum and buoyancy fluxes are sufficient for a complete description of the flow in many cases.
For a simple rising plume these equations predict that the plume will widen at a constant half-angle of about 6 to 15 degrees.
Gaussian plume modelling
Gaussian plume models can be used in several fluid dynamics scenarios to calculate concentration distribution of solutes, such as a smoke stack release or contaminant released in a river. Gaussian distributions are established by Fickian diffusion, and follow a Gaussian (bell-shaped) distribution.
For calculating the expected concentration of a one dimensional instantaneous point source we consider a mass
released at an instantaneous point in time, in a one dimensional domain along
. This will give the following equation:
where
is the mass released at time
and location
, and
is the diffusivity