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Vortex-Induced Instability: A Possible Mechanism of Clear Air Turbulence Encounters

Tapan K. Sengupta*, T.T. Lim & Manojit Chattopadhyay

Department of Mech. Engg., National Univ. of Singapore, 10 Kent Ridge Crescent, Singapore 119 260

Introduction:

Almost 30% of all commercial aircraft accidents have weather as contributing factors and out of which Clear Air Turbulence (CAT) accounts for more than half of these incidents[pic]. CAT is usually referred to turbulence above the planetary boundary layer and not directly associated with convective cloud. CAT is usually associated with jet streams, internal gravity waves generated on the leeside of mountains and wake turbulence of a leading aircraft. Aircraft bumpiness by CAT is caused when it encounters eddies of size comparable to or bigger than the size of aircraft. The direct detection of such eddies is beyond the ability of grid based weather forecast models and are usually forecasted semi-empirically while a Doppler laser radar is being developed to detect atmospheric turbulence[pic]. There are many CAT diagnostics available[pic]. However the exact mechanism during CAT interactions with aircraft still remains elusive. Recent researches conducted at National Center for Atmospheric Research (NCAR)[pic] have revealed that the likely cause of the extreme turbulence encounter was due to the presence of horizontal vortex tubes (HVTs).

Wingrove & Bach[pic] and Mehta[pic] used flight recorder data and invoked fixed numbers of HVTs to explain CAT encounters. It is estimated by them that the HVTs have core diameters of 900 to 1000 ft, which is also consistent with earlier measurements reported by Browning et al[pic].

Here, we investigate experimentally and theoretically the detailed nature of a new instability mechanism by which a vortex excitation field, like an atmospheric HVT, creates severe unsteadiness on an underlying shear layer (as formed on aircraft wings). In the controlled experiment a HVT is formed to excite a flat plate shear layer to identify the parameters that lead to this severe instability. The experiment, as well as the analysis and computations show that the effect is strongest when the vortex rotation is counterclockwise. This finding may resolve the mystery of CAT encounters and opens up the possibility of early detection and remedy of such occurrences.

Results and Discussion:

To investigate how this HVTs can cause highly unsteady motion of a passing airplane, we carried out a controlled experiment in which a HVT is created whose strength and speed of translation can be fixed and made to move outside the shear layer of a flat plate at a constant height. The chosen parameters are also used for numerical simulations. The flat plate plays the role of the aircraft wing while the HVT simulates the horizontal component of vortex inside a CAT. The experimental set-up is shown in Figure 1. The plate is held vertically on its edge on the floor of the tunnel test section. The vortex is created by rotating a circular cylinder at a fixed speed with the aid of a stepper motor.

This arrangement creates a captive vortex that can be made to travel at any predetermined speed. For such rotating cylinders, Badr et al[pic] have noted that there is no vortex shedding from a cylinder that is rotating with a surface velocity greater than two times the free stream speed, when the Reynolds numbers are in the range between 10[pic] and 10[pic]. This was corroborated by Sengupta et al[pic] subsequently via numerical calculations. For the cases reported in Figures 2 and 3, the surface velocity varied between 1.71 to 3.36 times the free stream speed, ensuring the dominance of the captive vortex to shed vortex- if any.

The distance between the plate and vortex is held constant, while the vortex is translated at a constant speed along a guide- rail in the streamwise direction with the aid of a second stepper motor. To visualize the flow, food dye was injected slowly through six dye-ports of 0.25cm diameter. During the experiments, extreme care was taken to eliminate vibration of the cylinder by the motors and the traverse mechanism. Exhaustive range of parameters was investigated, and only two of them are reported here. For each case, the experiments were repeated at least three times to check for the repeatability of the results.

For the case shown in Fig 2, the cylinder rotates in counter-clockwise direction while it translates slowly in the direction of the freestream speed ([pic]). Although the vortex travels at a large distance from the flat plate and far away from the shear layer, yet one can visualize a violent growth of disturbances in the shear layer ahead of the translating cylinder. Such violent unsteady growth of disturbances will produce highly unsteady load on the plate and they only occur when the translational speed (c) is kept significantly below the freestream speed. For example when c = 0.7[pic], no growth of disturbances were seen. Such violent unsteadiness was also seen when the distance between the vortex and the plate was increased from 9cm to 12cm.

The case shown in Fig 3 is similar to that of Fig 2, except that the cylinder rotates in the clockwise direction. Two major differences are observed here: firstly, the disturbances are seen behind the translating cylinder and secondly, the unsteadiness caused are significantly lower. The situation does not change qualitatively even when the vortex travels at a larger distance from the plate or when c is marginally increased. These results indicate that the two threshold parameters for the perceived flow behavior are (i) the translational speed (c) and (ii) the rotational direction of the vortex. In the experiments, the translational speed of the vortex was carefully chosen to match real life situations. For example, the jet streams travel at 200 to 300 kmph at an altitude of 10,000 meters. If the HVTs in the jet stream travel at this speed, then with respect to the forward speed of a commercial jet liner, the translational speed of HVTs in CAT will be roughly in the same proportion to the flight speed, as is c with respect to [pic] in the experiment. The study of Mehta[pic] has indicated that the HVTs travel at a distance from the aircraft that is much lower than the core radius of HVTs. Despite much larger distance between the cylinder and the plate in the experiment, one still notices strong instability.

An outline of a theory that can explain the observed behavior of unsteady disturbance energy growth is provided. It can be shown that the disturbance energy ([pic]) of a perturbed incompressible flow is governed by the following equation,

[pic] (1)

where [pic] and [pic] represents the vorticity and velocity vectors and the subscripts ‘m’ and ‘d’ stands for the mean and disturbance flow quantities. The above equation is obtained by taking a divergence of the governing Navier- Stokes equation in rotational form. The right hand side of Eqn. (1) represents an efflux of energy around any chosen point, and if it is negative, it will lead to temporal instability. For the zero pressure gradient condition of the experiment, the last two terms can be shown to be stabilizing and thus the instability is due to the first term on right hand side of Eqn. (1). For the experimental cases, the primary flow vorticity distribution is negative within the boundary layer. The counterclockwise rotating cylinder creates a disturbance vorticity that is positive ahead and negative behind the cylinder. Whereas for the clockwise rotating vortex, the disturbance field is of opposite sign and the level of unstable response behind the cylinder is much lower.

The above vortex-induced instability can be present for both two- and three- dimensional flows. We have performed a two- dimensional simulation corresponding to a counter-clockwise vortex. The time sequences for the computed case are shown in Fig. 4 for the parameters indicated in the caption. Here, the disturbance source is a potential vortex and the strong instability causes large vortical structures near the wall. They are ejected out of the primary shear layer- as seen at t = 260- due to large induced vertical velocity. However, once the vortices are ejected, the interaction term in Eqn. (1) becomes weaker, due to the lower value of the primary vortex field at the instantaneous location of the ejected vortex. This quenches the instability, as evident from the sequence at t = 267. The instability of the disturbance energy only depends upon the product of primary and disturbance field vorticity distribution and does not depend upon the fact whether the primary flow is laminar or turbulent. In the case of turbulent primary flow- as for flow over the aircraft wing- the primary shear layer will be thicker and the vorticity values will be larger. Thus, the instability of such a flow by a convecting counterclockwise vortex will be even stronger than the laminar flow considered here in the experiment and computations.

Based on the above experimental and theoretical results, it is clear as to why some atmospheric turbulence produce severe effects while others do not. This study shows turbulence encounters as vortex induced instability between aircraft wing vorticity field and the HVT. It is also shown when the vortex circulation is of the right type the translational speed of such vortex is the most significant parameter for severe turbulence events to take place.

In the final version more details about the experiments and Eqn. (1) will be provided.

References:

[pic][pic]Sharman, R., Wiener G.,and Brown, B., “Description and verification of the NCAR Integrated Turbulence Forecasting Algorithm (ITFA)” AIAA Paper 00-0493. Jan. 2000.

[pic]Dutton, J.A. and Panofsky, H.A., “Clear air turbulence: A mystery may be unfolding.” Science, 167, 1970 pp 937-944

[pic]Ellrod, G.P. and Knapp, D.I., “An objective clear-air turbulence forecasting technique: verification and operational use.” Weather Forecasting, 7, 1992 pp 150-165

[pic]Petterssen, S. Weather Analysis and Forecasting. vol. 1, McGraw Hill, 1956

[pic]Clark, T.L., Hall, W.D., Kerr, R.M., Middleton, D., Radke, L., Ralph, F.M., Neiman, P.J. and Levinson, D. “Origins of aircraft-damaging clear-air turbulence during the 9 December Colorado downslope windstorms: Numerical Simulations and comparison with observations.” Journal of Atmospheric Science, 57, 2000, pp 1105-1131

[pic]Bull, L.C., “New Research Offers Clues To Clear Air Turbulence.” J. Of Aerospace and Defense Industry News, September 19, 2000.

[pic]Wingrove, R.C. and Bach, R.E. Jr. “Severe turbulence and maneuvering from airline flight records”. J. of Aircraft, 31, 1994, pp 753-760.

[pic]Mehta, R.S., “Modeling clear-air turbulence with vortices using parameter identification techniques.” J. of Guidance, Control, and Dynamics, 10, 1987 pp 27-31.

[pic]Browning, K.A., Watkins C.D., Starr J.R. and McPherson, A. “Simultaneous measurements of clear air turbulence at the tropopause by high-power and instrumented aircraft.” Nature, 228, Dec 12, 1970, pp 1065-1067

[pic]Badr, H.M., Coutanceau, M., Dennis, S.C.R., Menard, C., “Unsteady flow past a rotating circular cylinder at Reynolds numbers [pic] and [pic]”. J. Of Fl. Mech., 220, 1990, pp 459-484.

[pic]Sengupta, T.K., Gupta, K. and Nair, M.T., “Lift generation and limiting mechanism via unsteady flow development for Magnus-Robins Effect.” Proceedings of 8th ACFM, International Academic Publishers, Beijing, 1999, pp 413-416.

Figure Captions

Figure 1. Schematic of the experimental setup. (a) Side view showing a rotating cylinder translating over a flat plate. (b) The schematic as viewed from the top of the tunnel. Note that the distance (H) of the cylinder from the plate is adjustable. Broken line boundary in (b) indicates the computational domain. Note: U[pic] is the flow speed; c is the translational speed of the cylinder and [pic] is the angular velocity of the cylinder. This arrangement creates a captive vortex (at the center of the cylinder) that can be made to travel at predetermined speed.

Figure 2. Visualization of flow over a flat plate induced by a translating and counterclockwise rotating vortex as viewed from the side of the tunnel. In this case: U[pic]= 16.267 cm/sec; c = 0.1545U[pic]; H = 9 cm and [pic] rotations per second. The shear layer has a displacement thickness ([pic]) of 3.17 mm at the dye-port and hence the vortex is about 29[pic] from the flat plate. Dye filaments are disturbed ahead of the cylinder, and violent breakdown of dye filaments indicates strong unsteadiness of large bandwidth response. The front of the disturbances is indicated in the second and third frame and this travels at approximately twice the freestream speed. In the original experiment a blue dye was used against a white background. For better clarity and contrast the pictures are shown in the negative. In all cases, a wide-angle lens was used in the video camera. This creates a slight distortion of the captured images towards the edges.

Figure 3. Visualization of flow over the shear layer induced by a translating and clockwise rotating vortex, viewed from the side of the tunnel. Note here the disturbances are behind the translating cylinder and are weaker. Here U( = 16.267 cm/sec; H = 9 cm; c = 0.193U[pic] and [pic] rotations per second.

Figure 4. Computed streamline contours for the flow-field excited by a counterclockwise rotating vortex in the freestream, similar to the case of Fig 2. Computations are performed for the solution of Navier-Stokes equation in streamfunction – vorticity representation. All lengths are nondimensionalised by the displacement thickness of the shear layer at the inflow boundary ((*). Velocity components are nondimensionalised by U(. Here a potential vortex translates at a height of 25(* from the plate. The computational domain extends from x = 84(* to 484(* and up to y = 20(*. The Reynolds number based on (* is 250. Note that disturbances appear as vortical structures near the surface due to an instability given by interaction terms on the right hand side of Eqn. (1). The leading vortex travels at about twice the freestream speed when calculated at t = 276. The vertical arrow at the top left hand corner of each frame indicates the current position of the captive vortex.

* Professor, Dept. of Aerospace Engineering, IIT Kanpur, India.

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