Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and
supersonic airflow around that object.
The exact range of speeds depends on the object's
critical Mach number
In aerodynamics, the critical Mach number (Mcr or M*) of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it.Clancy, L.J. ''Aerodynamics'', Section 11.6 At t ...
, but transonic flow is seen at flight speeds close to the
speed of sound (343 m/s at sea level), typically between
Mach 0.8 and 1.2.
The issue of transonic speed (or transonic region) first appeared during World War II.
Pilots found as they approached the sound barrier the airflow caused aircraft to become unsteady.
Experts found that
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
s can cause large-scale
separation downstream, increasing drag and adding asymmetry and unsteadiness to the flow around the vehicle.
Research has been done into weakening shock waves in transonic flight through the use of
anti-shock bodies
Anti-shock body is the name given by Richard T. Whitcomb to a pod positioned on the upper surface of a wing. Its purpose is to reduce wave drag while travelling at transonic speeds (Mach number, Mach 0.8–1.0), which includes the typical cruising ...
and
supercritical airfoil
A supercritical airfoil (supercritical aerofoil in British English) is an airfoil designed primarily to delay the onset of wave drag in the transonic speed range.
Supercritical airfoils are characterized by their flattened upper surface, highly ...
s.
Most modern
jet powered aircraft are engineered to operate at transonic air speeds. Transonic airspeeds see a rapid increase in drag from about Mach 0.8, and it is the fuel costs of the drag that typically limits the airspeed. Attempts to reduce wave drag can be seen on all high-speed aircraft. Most notable is the use of
swept wings, but another common form is a wasp-waist fuselage as a side effect of the
Whitcomb area rule
The Whitcomb area rule, named after NACA engineer Richard Whitcomb and also called the transonic area rule, is a design procedure used to reduce an aircraft's drag at transonic speeds which occur between about Mach 0.75 and 1.2. For supersonic ...
.
Transonic speeds can also occur at the tips of
rotor
Rotor may refer to:
Science and technology
Engineering
* Rotor (electric), the non-stationary part of an alternator or electric motor, operating with a stationary element so called the stator
*Helicopter rotor, the rotary wing(s) of a rotorcraft ...
blades of helicopters and aircraft. This puts severe, unequal stresses on the rotor blade and may lead to accidents if it occurs. It is one of the limiting factors of the size of rotors and the forward speeds of helicopters (as this speed is added to the forward-sweeping
eadingside of the rotor, possibly causing localized transonics).
History
Discovering transonic airflow
Issues with aircraft flight relating to speed first appeared during the
supersonic era in 1941.
Ralph Virden, a test pilot, crashed in a fatal plane accident.
He lost control of the plane when a shock wave caused by supersonic airflow developed over the wing, causing it to stall.
Virden flew well below the speed of sound at Mach 0.675, which brought forth the idea of different airflows forming around the plane.
In the 40s,
Kelley Johnson became one of the first engineers to investigate the effect of compressibility on aircraft.
However, contemporary
wind tunnel
Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
s did not have the capability to create wind speeds close to Mach 1 to test the effects of transonic speeds.
Not long after, the term "transonic" was defined to mean "across the speed of sound" and was invented by NACA director
Hugh Dryden and
Theodore von Kármán
Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronaut ...
of the California Institute of Technology.
Changes in aircraft
Initially,
NACA
The National Advisory Committee for Aeronautics (NACA) was a United States federal agency founded on March 3, 1915, to undertake, promote, and institutionalize aeronautical research. On October 1, 1958, the agency was dissolved and its assets ...
designed "dive flaps" to help stabilize the plane when reaching transonic flight.
This small flap on the underside of the plane slowed the plane to prevent shock waves, but this design only delayed finding a solution to aircraft flying at supersonic speed.
Newer wind tunnels were designed, so researchers could test newer wing designs without risking test pilots' lives.
The slotted-wall transonic tunnel was designed by NASA and allowed researchers to test wings and different
airfoils in transonic airflow to find the best wingtip shape for sonic speeds.
After
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...
, major changes in aircraft design were seen to improve transonic flight.
The main way to stabilize an aircraft was to reduce the speed of the airflow around the wings by changing the
chord of the plane wings, and one solution to prevent transonic waves was swept wings.
Since the airflow would hit the wings at an angle, this would decrease the wing thickness and chord ratio.
Airfoils wing shapes were designed flatter at the top to prevent shock waves and reduce the distance of airflow over the wing. Later on, Richard Whitcomb designed the first
supercritical airfoil
A supercritical airfoil (supercritical aerofoil in British English) is an airfoil designed primarily to delay the onset of wave drag in the transonic speed range.
Supercritical airfoils are characterized by their flattened upper surface, highly ...
using similar principles.
Mathematical analysis
![Streamline Patterns for Flow Regimes](https://upload.wikimedia.org/wikipedia/commons/2/29/Streamline_Patterns_for_Flow_Regimes.png)
Prior to the advent of powerful computers, even the simplest forms of the
compressible flow equations were difficult to solve due to their
nonlinearity
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
.
A common assumption used to circumvent this nonlinearity is that disturbances within the flow are relatively small, which allows mathematicians and engineers to
linearize the compressible flow equations into a relatively easily solvable set of
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s for either wholly subsonic or supersonic flows.
This assumption is fundamentally untrue for transonic flows because the disturbance caused by an object is much larger than in subsonic or supersonic flows; a flow speed close to or at Mach 1 does not allow the
streamtubes (3D flow paths) to contract enough around the object to minimize the disturbance, and thus the disturbance propagates.
Aerodynamicists struggled during the earlier studies of transonic flow because the then-current theory implied that these disturbances– and thus drag– approached infinity as local Mach number approached 1, an obviously unrealistic result which could not be remedied using known methods.
One of the first methods used to circumvent the nonlinearity of transonic flow models was the
hodograph
A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. The position of any plotted data on such a diagram is propor ...
transformation.
This concept was originally explored in 1923 by an Italian mathematician named
Francesco Tricomi
Francesco Giacomo Tricomi (5 May 1897 – 21 November 1978) was an Italian mathematician famous for his studies on mixed type partial differential equations. He was also the author of a book on integral equations.
Biography
Tricomi was born in ...
, who used the transformation to simplify the compressible flow equations and prove that they were solvable.
The hodograph transformation itself was also explored by both
Ludwig Prandtl
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of ...
and O.G. Tietjen's textbooks in 1929 and by
Adolf Busemann in 1937, though neither applied this method specifically to transonic flow.
Gottfried Guderley, a German mathematician and engineer at
Braunschweig
Braunschweig () or Brunswick ( , from Low German ''Brunswiek'' , Braunschweig dialect: ''Bronswiek'') is a city in Lower Saxony, Germany, north of the Harz Mountains at the farthest navigable point of the river Oker, which connects it to the ...
, discovered Tricomi's work in the process of applying the hodograph method to transonic flow near the end of World War II.
He focused on the nonlinear thin-airfoil compressible flow equations, the same as what Tricomi derived, though his goal of using these equations to solve flow over an airfoil presented unique challenges.
Guderley and Hideo Yoshihara, along with some input from Busemann, later used a singular solution of Tricomi's equations to analytically solve the behavior of transonic flow over a
double wedge airfoil, the first to do so with only the assumptions of thin-airfoil theory.
Although successful, Guderley's work was still focused on the theoretical, and only resulted in a single solution for a double wedge airfoil at Mach 1.
Walter Vincenti, an American engineer at
Ames Laboratory
Ames National Laboratory, formerly Ames Laboratory, is a United States Department of Energy national laboratory located in Ames, Iowa, and affiliated with Iowa State University. It is a top-level national laboratory for research on national sec ...
, aimed to supplement Guderley's Mach 1 work with numerical solutions that would cover the range of transonic speeds between Mach 1 and wholly supersonic flow.
Vincenti and his assistants drew upon the work of
Howard Emmons as well as Tricomi's original equations to complete a set of four numerical solutions for the drag over a double wedge airfoil in transonic flow above Mach 1.
The gap between subsonic and Mach 1 flow was later covered by both
Julian Cole and
Leon Trilling, completing the transonic behavior of the airfoil by the early 1950's.
Condensation clouds
At transonic speeds
supersonic expansion fans form intense low-pressure, low-temperature areas at various points around an aircraft. If the temperature drops below the
dew point
The dew point is the temperature to which air must be cooled to become saturated with water vapor, assuming constant air pressure and water content. When cooled below the dew point, moisture capacity is reduced and airborne water vapor will cond ...
a visible cloud will form. These clouds remain with the aircraft as it travels. It is not necessary for the aircraft as a whole to reach
supersonic speeds for these clouds to form. Typically, the tail of the aircraft will reach supersonic flight while the bow of the aircraft is still in subsonic flight. A bubble of supersonic expansion fans terminating by a wake shockwave surround the tail. As the aircraft continues to accelerate, the supersonic expansion fans will intensify and the wake shockwave will grow in size until infinity is reached, at which point the bow shockwave forms. This is Mach 1 and the
Prandtl–Glauert singularity
The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows.
It is the prediction by the Prandtl–Glauert transformation that infinite pressures would be experie ...
.
Transonic flows in astronomy and astrophysics
In astrophysics, wherever there is evidence of shocks (standing, propagating or oscillating), the flow close by must be transonic, as only supersonic flows form shocks. All black hole
accretions are transonic. Many such flows also have shocks very close to the black holes.
The outflows or jets from young stellar objects or disks around black holes can also be transonic since they start subsonically and at a far distance they are invariably supersonic. Supernovae explosions are accompanied by supersonic flows and shock waves. Bow shocks formed in
solar wind
The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sol ...
s are a direct result of transonic winds from a star. It had been long thought that a bow shock was present around the heliosphere of our solar system, but this was found not to be the case according to
IBEX
An ibex (plural ibex, ibexes or ibices) is any of several species of wild goat (genus ''Capra''), distinguished by the male's large recurved horns, which are transversely ridged in front. Ibex are found in Eurasia, North Africa and East Africa ...
data published in 2012.
[.]
See also
*
Anti-shock body
Anti-shock body is the name given by Richard T. Whitcomb to a pod positioned on the upper surface of a wing. Its purpose is to reduce wave drag while travelling at transonic speeds ( Mach 0.8–1.0), which includes the typical cruising range of co ...
*
Subsonic flows
*
Supersonic flows
*
Hypersonic flows
*
Supersonic expansion fans
References
{{Reflist
Aerodynamics
Airspeed
Aircraft performance