Wingtip vortices

From Wikipedia, the free encyclopedia

This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (July 2009)

Condensation in the cores of wingtip vortices from an F-15E as it disengages from a KC-10 Extender following midair refueling.

Wingtip vortices are tubes of circulating air which are left behind a wing as it generates lift.^[1] One wingtip vortex trails from the tip of each wing. The cores of vortices spin at very high speed and are regions of very low pressure. To first approximation, these low-pressure regions form with little exchange of heat with the neighboring regions (i.e. adiabatically), so the local temperature in the low-pressure regions drops, too.^[2] If it drops below the local dew point, there results a condensation of water vapor present in the cores of wingtip vortices, making them visible.^[2] The local temperature may even drop below the local freezing point, in which case ice crystals will form inside the cores.^[2]

Wingtip vortices are associated with induced drag, an essentially unavoidable side-effect of the wing generating lift.^[3] Managing induced drag and wingtip vortices by selecting the best wing planform for the mission is critically important in aerospace engineering.

Wingtip vortices form the major component of wake turbulence.

Migratory birds take advantage of each others' wingtip vortices by flying in a V formation so that all but the leader are flying in the upwash from the wing of the bird ahead. This upwash makes it a bit easier for the bird to support its own weight, reducing fatigue on migration flights.

Some technical writers use the alternative expression "trailing vortices" because these vortices also occur at points other than at the wing tips.^[1] They are induced at the outboard tip of the wing flaps and other abrupt changes in wing planform.

[edit] Cause and effects

A wing generates aerodynamic lift by creating a region of lower air pressure above it. Fluids are forced to flow from high to low pressure and the air below the wing tends to migrate toward the top of the wing via the wingtips. The air does not escape around the leading or trailing edge of the wing due to airspeed, but it can flow around the tip. Consequently, air flows from below the wing and out around the tip to the top of the wing in a circular fashion. This leakage will raise the pressure on top of the wing and reduce the lift that the wing can generate. It also produces an emergent flow pattern with low pressure in the center surrounded by fast-moving air with curved streamlines.

Wingtip vortices only affect the portion of the wing closest to the tip. Thus, the longer the wing, the smaller the affected fraction of it will be. As well, the shorter the chord of the wing, the less opportunity air will have to form vortices. This means that for an aircraft to be most efficient, it should have a very high aspect ratio. This is evident in the design of gliders. It is also evident in long-range airliners, where fuel efficiency is of critical importance. However, increasing the wingspan reduces the maneuverability of the aircraft, which is why combat and aerobatic planes usually feature short, stubby wings despite the efficiency losses this causes.

Another method of reducing fuel consumption is the use of winglets, as seen on a number of modern airliners such as the Airbus A340. Winglets work by forcing the vortex to move to the very tip of the wing and allowing the entire span to produce lift, thereby effectively increasing the aspect ratio of the wing. Winglets also change the pattern of vorticity in the core of the vortex pattern, spreading it out and reducing the kinetic energy in the circular air flow, which reduces the amount of fuel expended to perform work by the wing upon the spinning air. Winglets can yield very worthwhile economy improvements on long-distance flights.

[edit] Visibility of vortices due to water condensation and freezing

The cores of the vortices are sometimes visible because water present in them condenses from gas (vapor) to liquid, and sometimes even freezes, forming ice particles.

The phase of water (i.e. whether it assumes the form of a solid, liquid, or gas) is determined by its temperature and pressure. For example, in the case of liquid-gas transition, at each pressure there is a special “transition temperature” Failed to parse (Cannot write to or create math output directory): T_{c}

such that if the sample temperature is even a little above Failed to parse (Cannot write to or create math output directory): T_{c}

, the sample will be a gas, but if the sample temperature is even a little below Failed to parse (Cannot write to or create math output directory): T_{c} , the sample will be a liquid; see phase transition. For example, at the standard atmospheric pressure, Failed to parse (Cannot write to or create math output directory): T_{c}

is 100 °C = 212 °F. The transition temperature Failed to parse (Cannot write to or create math output directory): T_{c}
decreases with decreasing pressure (which explains why water boils at lower temperatures at higher altitudes and at higher temperatures in a pressure cooker; see here for more information). In the case of water vapor in air, the Failed to parse (Cannot write to or create math output directory): T_{c}
corresponding to the partial pressure of water vapor is called the dew point.

The solid-liquid transition also happens around a specific transition temperature, which also decreases with decreasing pressure.

Vortex cores are regions of low pressure. As a vortex core begins to form, the water in the air (in the region that is about to become the core) is in vapor phase, which means that the local temperature is above the local dew point. After the vortex core forms, the pressure inside it has decreased from the ambient value, and so the local dew point (Failed to parse (Cannot write to or create math output directory): T_{c} ) has dropped from the ambient value. Thus, in and of itself, a drop in pressure would tend to keep water in vapor form: the initial dew point was already below the ambient air temperature, and the formation of the vortex has made the local dew point even lower. However, as the vortex core forms, its pressure (and so its dew point) is not the only property that is dropping: the vortex-core temperature is dropping also, and in fact it can drop by much more than the dew point does, as we now explain.

Here we follow the discussion in Ref. ^[2]. To first approximation, the formation of vortex cores is thermodynamically an adiabatic process, i.e. one with no exchange of heat. In such a process, the drop in pressure is accompanied by a drop in temperature, according to the equation

Failed to parse (Cannot write to or create math output directory): \frac{T_{\text{f}}}{T_{\text{i}}}=\left(\frac{p_{\text{f}}}{p_{\text{i}}}\right)^{\frac{\gamma -1}{\gamma}}.

Here Failed to parse (Cannot write to or create math output directory): T_{\text{i}}

and Failed to parse (Cannot write to or create math output directory): p_{\text{i}}
are the absolute temperature and pressure at the beginning of the process (here equal to the ambient air temperature and pressure), Failed to parse (Cannot write to or create math output directory): T_{\text{f}}
and Failed to parse (Cannot write to or create math output directory): p_{\text{f}}
are the absolute temperature and pressure in the vortex core (which is the end result of the process), and the constant Failed to parse (Cannot write to or create math output directory): \gamma
is about 7/5 = 1.4 for air (see here).

Thus, even though the local dew point inside the vortex cores is even lower than in the ambient air, the water vapor may nevertheless condense—if the formation of the vortex brings the local temperature below the new local dew point. Let us verify that this can indeed happen under realistic conditions.

For a typical transport aircraft landing at an airport, these conditions are as follows: we may take Failed to parse (Cannot write to or create math output directory): T_{\text{i}}

and Failed to parse (Cannot write to or create math output directory): p_{\text{i}}
to have values corresponding to the so-called standard conditions, i.e. Failed to parse (Cannot write to or create math output directory): p_{\text{i}}

 = 1 atm = 1013.25 mb = 101Failed to parse (Cannot write to or create math output directory): \, 325 Pa and Failed to parse (Cannot write to or create math output directory): T_{\text{i}}  = 293.15 K (which is 20 °C = 68 °F). We will take the relative humidity to be a comfortable 35% (dew point of 4.1 °C = 39.4 °F). This corresponds to a partial pressure of water vapor of 820 Pa = 8.2 mb. We will assume that in a vortex core, the pressure (Failed to parse (Cannot write to or create math output directory): p_{\text{f}} ) drops to about 80% of the ambient pressure, i.e. to about 80 000 Pa.^[2]

Let us first determine the temperature in the vortex core. It is given by the equation above as Failed to parse (Cannot write to or create math output directory): T_{\text{f}}=\left(\frac{\scriptstyle 80\,000}{\scriptstyle 101\,325}\right)^{\scriptscriptstyle 0.4/1.4}\,T_{\text{i}}= 0.935\,\times\,293.15=274\;\text{K},

or 0.86 °C = 33.5 °F.

Next, we determine the dew point in the vortex core. The partial pressure of water in the vortex core drops in proportion to the drop in the total pressure (i.e. by the same percentage), to about 650 Pa = 6.5 mb. According to a dew point calculator at this site (alternatively one may use the Antoine equation to obtain an approximate value), that partial pressure results in the local dew point of about 0.86 °C; in other words, the new local dew point is about equal to the new local temperature.

Therefore, the case we have been considering is a marginal case; if the relative humidity of the ambient air were even a bit higher (with the total pressure and temperature remaining as above), then the local dew point inside the vortices would rise, while the local temperature would remain the same as what we have just found. Thus the local temperature would now be lower than the local dew point, and so the water vapor inside the vortices would indeed condense. Under right conditions, the local temperature in vortex cores may drop below the local freezing point, in which case ice particles will form inside the vortex cores.

We have just seen that the water-vapor condensation mechanism in wingtip vortices is driven by local changes in air pressure and temperature. This is to be contrasted to what happens in another well-known case of water condensation related to airplanes: the contrails from airplane engine exhausts. In the case of contrails, the local air pressure and temperature do not change significantly; what matters instead is that the exhaust contains both water vapor (which increases the local water-vapor concentration and so its partial pressure, resulting in elevated dew point and freezing point) as well as aerosols (which provide nucleation centers for the condensation and freezing).^[4]

Condensation of water vapor in wing tip vortices is most common on aircraft flying at high angles of attack, such as fighter aircraft in high g maneuvers, or airliners taking off and landing on humid days.

[edit] Hazards

A NASA study on wingtip vortices produced these pictures of smoke in the wake of an aircraft, clearly illustrating the size of the vortices produced.

Wingtip vortices can also pose a severe hazard to light aircraft, especially during the landing and take off phases of flight. The intensity or strength of the vortex is a function of aircraft size, speed, and configuration (flap setting, etc.). The strongest vortices are produced by heavy aircraft, flying slowly, with wing flaps extended. Large jet aircraft can generate vortices which are larger than an entire light aircraft. These vortices can persist for many minutes, drifting with the wind. The hazardous aspects of wingtip vortices are most often discussed in the context of wake turbulence. If a light aircraft is immediately preceded by a heavy aircraft, wake turbulence from the heavy aircraft can roll the light aircraft faster than can be resisted by use of ailerons. At low altitudes, particularly during takeoff and landing, this can lead to an upset from which recovery is not possible. Air traffic controllers ensure an adequate separation between departing and arriving aircraft, particularly where a heavy aircraft is preceding a light aircraft.

[edit] Gallery

An EA-6 Prowler with condensation in the cores of its wingtip vortices and also on the top of its wings.	F/A-18C leaving vapor trails in the low pressure cores of its wingtip vortices.	The core of the vortex trailing from the tip of the flap of a commercial airplane with landing flap extended.	F/A-18C showing condensation in the cores of the vortices trailing from its leading edge extensions
Wingtip vortices from a Cessna 182 wind tunnel model.	Canada geese in V formation to make best use of each bird's wingtip vortices. Source: NASAexplores	Wingtip vortices shown in flare smoke left behind a C-17 Globemaster III. Also known as smoke angels.	Visible cores of vortices trailing from the propeller tips when producing high power.

[edit] References

• Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London ISBN 0 273 01120 0

[edit] Notes

[edit] See also

• Aspect ratio
• Contrail
• Helmholtz's theorems
• Horseshoe vortex
• V formation
• Von Kármán vortex street
• Vortex
• Vortex shedding

[edit] External links

Wikimedia Commons has media related to: Wingtip vortices

• Video from NASA's Dryden Flight Research Center tests on wingtip vortices:
  • C-5 Galaxy: [1]
  • Lockheed L-1011: [2]
• Wind prediction for analysis of vortex drift
• Flares released by an air force jet form a "smoke angel"