Features of vortex trace propagation for aircraft with propellers

: The article presents the results of a study of the characteristics of the wake vortex of aircraft with turboprop engines. Using the example of the An-12 aircraft, it is shown that rotating propellers make a noticeable contribution to the propagation of the vortex trail behind the aircraft. This is proved by some studies


Introduction
Nowadays the aeronautical communities of many countries face the current problem of the ever-growing airport capacity provision due to air traffic increase maintaining the objective aircraft flight safety level. Vortex safety provision [1-5] is one of main challenges for implementation of such plans. The essence of vortex safety issue is wake vortex following the aircraft [6][7][8][9][10][11]. This wake is an induced velocity and pressure field which is dangerous for aircraft following it. It is worth noticing that one should distinguish between the concepts of wake vortex and vortex path. It is correctly suggested in work [12] that there is a wake vortex following the body in motion developing lift (for example, an aircraft). Whether the body in motion does not develop lift (for example, a car), there is a vortex path following it.
The work focuses on a wake vortex following the propeller aircraft. Turboprop aircraft observation shows us that wake vortex following them is different from the one following the turbo-jet aircraft ( fig. 1). It is connected to propeller rotation influencing the aircraft wake vortex. Wake vortex following the aircraft loses its symmetry almost at once as the propeller spins one way, which can be seen in ( fig. 1).
The long-haul propeller aircraft introduction has required the research of the long-distance wake vortices following them. Wake vortex following such aircraft is also dangerous for other aircraft behind it. The question of propeller impact on long-distance wake vortex characteristics is still open so far. Analysis shows us that the research developments in this area are insufficient. The majority of them are scattered studies in the flight experiment of the USA Department of Transportation program on wake vortex following the propeller aircraft. There are almost no approaches and mathematical models for wake vortex following the propeller aircraft.
The interest in propeller aircraft has grown recently, as they are cheaper in terms of passenger and cargo transportation on equal distances, in comparison to turbo-jet aircraft. Some foreign experts estimate that service and fuel charges are reduced by about 30-40% during passenger and cargo transportation given the distance of 700-800 km. That is why some aerospace corporations are starting the turboprop aircraft development. For instance, the Canadian engineering company Bombardier is now developing and producing the twin-engine turboprop aircraft DHC-8. Airbus Military has developed the A-400M aircraft and started its manufacturing production. ATR is doing the same thing. There are also Ilyushin Il-114 and Ilyushin Il-112B in use in Russia. There is also data about other similar constructions.

Research methodology
Wake vortex following the propeller aircraft research methodology, used in this work, is described in details in paper [12] and article [13]. In this article it is integrated into a special calculating and software package [14], also based on discrete wake method [15][16][17]. The essence of integration is in the following. It was necessary to develop such a propeller mathematic model, in which its work effect record was made through discrete vortex points with the known circulations and coordinates on Trefftz plane. The fact is the long-distance wake vortex mathematical model of the calculating and software package is also based on vortex points. In this case the propeller mathematical model is inte-grated into the long-distance wake vortex mathematic model [12,18].
Let us interpolate the following designations: The following vortex model of the propeller ( fig. 2) is developed for the given mathematical model integration into the calculating and software package [14]. There is an axial flow circulation wake Г * in the middle of the propeller, the n wakes are set around the propeller circumference perimeter, modelling the propeller jet flow. The research in work [13] showed us, that n should correspond to the number of propeller  blades. Then the wake circulation around the propeller circumference will be equal to Г * /n. It is possible to define the intensity of the propeller-generated axial flow wake by formula [13], whether the propeller work regime is set - ,  ,  and the relative propeller rotor head diameter is known: Let us interpolate the axial flow nondimensional circulation according to formulae for the aircraft in general, L is a typical size, then  and   will be linked by formula Then, the vortex propeller jet flow scheme (in Trefftz plane) will look as it is shown in Fig , and spinning direction opposes the axial flow vortex spinning direction. At the same time the axial flow vortex produces spinning, which corresponds to propeller spinning direction. Thus, the purpose is achieved. The vortex points, which are modelling the propeller work, are integrated into the calculating and software package [14].

The results of the research
The characteristics of long-distance wake vortex following the C-130 aircraft at 1000 m height, at V = 51 m/s speed were calculated to confirm the effectiveness of the developed methodology and credibility of the results based on them. The flight experiment data has been obtained from paper [2] on wake vortex maximum vertical velocity measurement for this aircraft and the flight conditions. There are the vertical speed calculations behind the C-130 at distances Х = 0 and 1.4 km in Figure 2. It can be seen that the vertical speed graph is sawtooth if Х = 0 (that is fuselage longitudinal section, rhombs). It is connected with propeller rotation impact on the wake vortex behind the aircraft.
The whole spectrum of vertical velocity (squares) is calculated at distance Х = 1.4 km from C-130 aircraft. It can be seen that the calculation (squares) and flight experiment (triangles) correspond satisfactorily to each other, which confirms indirectly the credibility of the results (fig. 3).
Furthermore, the characteristics of Antonov An-12 aircraft wake vortex were also observed. It is shown that rotating propellers cause a noticeable impact on wake vortex distribution. The first stage shows us, how the vertical velocity spectrum changes in the middle of An-12 vortex without taking propeller spinning into considera-   worth noticing, that propeller rotation impact on vertical velocity almost disappears already at Х = 500 m distance. It is connected with vortex natural ease-off due to atmosphere turbulence, along with vortex dissipation and diffusion. At the second stage, the perturbed velocity fields behind the An-12 at up to 2 km distance ( fig. 6) Figure 6, which size is 10 m/s. It can be seen that the vortex symmetry from the left and the right wing is broken while X distance from the aircraft is increasing. This circumstance drastically distinguishes the wake vortex behind the turboprop and turbo-jet aircraft. The wake vortex following the turbo-jet aircraft remains symmetrical for a long time on both the left and the right wings [2, 12, [19][20][21][22][23][24][25][26]. This symmetry is broken almost at once between the turboprop aircraft due to propeller spinning impact. There are the works [12,27], in which it is shown that propellers spinning one way also cause impact on the aircraft aerodynamic characteristics. It is connected with non-symmetrical flowing around of the aircraft airframe. There is some yet noticeable yawing and roll during the turboprop flight. There are some special procedures implemented in some aircraft structure for their disposal. Nevertheless, it can lead to increase in drag, and, consequently, to extra fuel costs. There are the aircraft with left and right propellers spinning different ways which allows to dispose airframe non-symmetrical flowing around. For instance, A-400M by Airbus Military.

Conclusions
Thus, the calculation showed us that wake vortex behind the turboprop aircraft differs drastically from the one behind the turbo-jet aircraft. The reason of such a difference is propeller rotation. Propellers of almost all the used turboprop aircraft rotate one way. Wake vortex symmetry behind the aircraft is broken during propeller vortex interaction with vortices from the aircraft airframe. It is necessary for the crews of aircraft following the turboprop aircraft to consider this circumstance. Besides that, it is also necessary to consider this peculiarity while providing wake vortex safety in the vicinity of large airports, when the safe separation between the taking-off and landing aircraft should be maintained.