The Flow About an Isolated Rotating Wheel – Effects of Yaw on Lift, Drag and Flow Structure A. P. Mears, R. G. Dominy and D. B. Sims-Williams School of Engineering, University of Durham, U.K. .
SYNOPSIS The airflow about an isolated rotating wheel has been analysed. Experimental data have been gathered in the form of surface pressure distributions on a pneumatic tyre at yaw angles of 0° and 5°. The Durham University radio telemetry system was used to measure the surface pressure data and integral lift and drag forces have shown that the lift force decreases and the drag force increases at yaw=5°. Surface pressure data provided considerable insight into the flow-field and Fackrell’s ‘jetting’ phenomenon was observed both before and after the line of contact between wheel and road, although Fackrell’s experimental results did not show any jetting after the line of contact. This prompts further investigation into this phenomenon.
NOTATION Cp:
Static Pressure Coefficient, where Cp =
D: P: Po: Ps:
P − Ps Po − Ps
Wheel Diameter (m) Local Static Pressure (Pa) Free Stream Total Pressure (Pa) Free Stream Static Pressure (Pa) ρDV∞ Reynolds No.: Re = , where symbols have the usual meanings
µ
Vb: V∞ : θ:
Belt Velocity (Rolling Road) (m/s) Free Stream Velocity (m/s) Angular Position (deg)
ω: β: CL: CD:
Angular Velocity (rad/s) Yaw Angle (deg) Lift Coefficient Drag Coefficient
1. INTRODUCTION The aerodynamic characteristics of rotating wheels have received growing attention from investigators in the last few years. This attention has mainly focused on numerical simulation of an isolated wheel, and a wheel located within a wheelhouse cavity (Axon et al [1,2], Axon [3], Skea et al [4,5]). The experimental test case used for model validation in both investigations was the work of Fackrell and Harvey [6,7]. The data presented by Fackrell and Harvey are extensive and give an enormous insight into the aerodynamics of an isolated wheel both stationary and rotating. The only limitation being that the data relate only to a wheel positioned parallel to the flow (yaw = 0°) and the external flow field study provided only an approximate indication of the outline of the wake. Previous research has shown that an exposed racing wheel generates positive lift and drag for both stationary and rotating cases. It has been found that the lift and drag forces decrease as a result of wheel rotation. For racing cars with exposed wheels the wheel drag, as a percentage of the overall vehicle drag, can be between 35 and 50 percent (Dominy [8]). A number of other authors have conducted studies into wheel aerodynamics but the t he technical difficulties associated with the measurement of the aerodynamic characteristics of wheels have usually allowed only a superficial analysis of the flowfield. Morelli [9] showed that the wheel lift forces were negative which opposes all subsequent studies, those results are more than likely due to a gap that existed between the wheel and ground. He chose this configuration to enable a conventional force balance to be used to measure both lift and drag forces. The gap under the wheel was present to eliminate the wheel–to–ground reaction force since having ground contact would have made it impossible to separate the aerodynamic lift force from the varying wheel–to–ground reaction force. Consequently leaving a gap under the wheel causes air to accelerate between the wheel and ground resulting in lower pressure, and therefore helps to explain the negative lift force. A racing wheel investigation was carried out by Stapleford and Carr [10] using a complete racing car model. A similar approach was adopted to that of Morelli [9] in terms of a force balance being used to directly measure the lift and drag forces. Again, a gap existed between the wheel and ground although attempts were made to seal the gap with strips of paper. Pressure distributions on the wheel’s surface were measured using a static pressure probe. The results presented by Stapleford and Carr did not show any of the special features of the flow field that Fackrell and Harvey [6,7] observed, such as the ‘jetting’ phenomenon (discussed later). Failure to observe this flow feature was probably due to the experimental configuration used.
Possibly the most widely referenced investigation into the aerodynamics of isolated wheels is the work of Fackrell and Harvey [6,7], which is described more thoroughly in Fackrell [11]. The method Fackrell used to obtain the wheel lift and drag forces was to measure the surface pressure distribution around the wheel and calculate the forces by integration. The pressure data were acquired from the rotating wheel through slip rings. This experimental technique allowed the wheel to rotate in contact with the ground. The Reynolds number based on wheel diameter was 5.3x105. An external flow field study gave an approximate indication of the outline of the wake. Bearman et al [12] present further flow field measurements made on the wheel used by Fackrell. Cogotti [13] demonstrated that correct wheel to ground contact is of critical importance by varying the gap between the wheel and ground. He observed a strong negative pressure until the wheel contacted the ground where the pressure suddenly became positive. How the surface pressures on rotating wheels are affected when the wheel is subjected to yawed flow is unclear and the authors are unaware of any published surface pressure data with respect to yawed flow. Understanding the flow field about rotating wheels and how yawed flow conditions affect the lift and drag forces is important, perhaps more so in the case of racing cars where the magnitude of the forces is proportionately higher than for passenger cars, and any underestimation of the forces could have significant consequences. The aims of this investigation were to measure static pressures on the surface of a pneumatic tyre/wheel assembly and to use integration to calculate the lift and drag forces. This was to be carried out at zero degrees yaw and with the wheel and rolling road axes yawed five degrees relative to the wind tunnel, thus simulating cross-wind conditions. The surface pressure distributions should give an insight into the flow field around the wheel and help establish what mechanisms are responsible for any changes in the lift and drag forces. 2. EXPERIMENTAL CONFIGURATION 2.1 Wind Tunnel Configuration The Durham University low speed (0.855m x 0.55m) open–jet wind tunnel with moving ground plane (MGP), or rolling road, facility was chosen for this investigation (see Fig. 1). This facility enables the wheel to rotate in contact with the rolling road and has a working section area of 0.468m 2. Both the free stream and rolling road velocities were matched to simulate the wheel moving forward in still air. To analyse an isolated wheel, the wheel was mounted from the side on a slender, faired sting to provide minimum interference with the flow field. The sting was securely located on the side of the rolling road and both the wheel and rolling road axes could be yawed relative to the wind tunnel axis.
Wind Tunnel V∞
Wheel Moving Groundplane
Fig.1 Wind Tunnel Configuration 2.2 Pressure Instrumentation The difficulty of separating the aerodynamic forces from the ground reaction forces precludes conventional force balance measurements for lift. An alternative method is to measure the pressure over the surface of the wheel and obtain the aerodynamic forces by integration, although acquiring such pressure data from a rotating wheel is technically difficult, especially if an aerodynamically non-intrusive approach is required. Durham University have designed and developed a uni-directional radio telemetry system that allows surface pressure data to be transmitted from an isolated rotating wheel to a local laboratory PC, where data acquisition is carried out. Fig.2 shows a schematic representation of the overall instrumentation system. The on-wheel telemetry briefly comprises of a Pressure Systems ESP-16HD miniature pressure scanner, which consists of 16 silicon piezo-resistive pressure transducers, each of which is selected sequentially. The analogue voltage output from the scanner is converted to a digital signal using a 12-bit A/D converter and read into a microcontroller. Data clocked into the microcontroller is synchronised to an external clock pulse. The microcontroller sends the pressure data to the off-wheel telemetry via a radio transmitter at a data transmission rate of 19.2kbps, this rate being fixed by the baud rate of the microcontroller. The radio receiver on the offwheel telemetry receives the pressure data and this is clocked into the microcontroller. The digital pressure data is then converted to an analogue voltage using a 12-bit D/A converter, this is done to interface with the standard software of the analogue data acquisition system. A once-per-revolution wheel position pulse is provided by the reference trigger and this is used at the data post-processing stage so that data can be grouped correctly depending on wheel position. The analogue voltages from the D/A converter and reference trigger are connected to the analogue channels of the Amplicon PC30-PGH logging card, which has a clock speed of 2MHz and allows logging of 8 12-bit differential channels.
ESP-16HD Pressure Scanner Transmitter
12-bit A/D
Microcontroller
On-Wh OnWheel eel Te Telem lemetr etr
Local PC
Ref. Trigger
Data Valid Pin
Receiver
Microcontroller
Off-W Off -Whee heell Tele Telemet metrr
12-bit D/A
4-bit Digital Address Lines
Logging Card
Fig.2 Schematic Representation of Overall Instrumentation System The card also has digital input/output channels, which are used for the 4-bit digital address information. Information relating to transducer number is also sent from the on-wheel telemetry to the off-wheel telemetry, where the digital address lines are set high or low accordingly. All data are logged at 1600Hz, which equates to pressure data approximately every 4 degrees. However, the frequency at which pressure data is transmitted via the telemetry is lower than 1600Hz at around 1200Hz. The problem with this is that data from a previous angular position is logged at a subsequent position and this affects the ensemble average. This effect is more pronounced at the contact patch where the pressure changes rapidly and any lower pressure data from a previous angular position (i.e. before the contact patch) reduces the magnitude of the peak. To resolve this problem a data valid pin has been devised and is set high by the off-wheel microcontroller on a rising edge of chip select (D/A), and this indicates that the voltage has changed on the D/A converter. On the next rising edge of chip select the pin is set low, again indicating that the voltage has changed. This cycle continues high, low, high, etc. The data valid pin is logged and used at the data reduction stage of post-processing. A rising or falling edge on the data valid channel indicates valid data. The data are also corrected for the time lag between the angular position where the pressure data were measured and the position at which the data were acquired. Since the amplitude of the signal is not affected this is treated as a simple transfer time lag. This is converted into an angular position offset since the rotational frequency of the wheel is known and corrections are made during postprocessing. 2.3 Wheel/Tyre Design A pneumatic tyre/wheel assembly was used for this investigation. The tyre chosen was a standard racing go-kart front tyre, with a smooth tread area (‘slick’ racing tyre). A pneumatic tyre was chosen to allow controlled deformation of the contact patch, although for this investigation the tyre was effectively run as a solid. At a wind speed of 15 m/s this equated to a wheel diameter based Reynolds number of 2.5x105. The wheel/tyre assembly had a diameter of 247mm and a width of 130mm giving an
aspect ratio of 0.53. Blockage effects of less than 7% were deemed adequate for an open-jet wind tunnel. Flush surface pressure tappings (OD=1.24mm, ID=0.94mm), manufactured from stainless steel hypodermic tubing, were located span-wise across one side of the tyre (Fig. 3a) and down the sidewall (Fig. 3b). The reason the tappings had an angular position offset (see Fig.3b), denoted in parentheses, was to enable easy tubing connections since having the tappings all located in line with the centreline caused the tubing to butt up against each other. This offset is dealt with at the postprocessing stage.
247m -W/D
130mm
W/D=0
+W/D
β=5° a) Tapping Location (Tread Region) b) Tapping Location (Sidewall) and Yaw Angle Notation
c) Wheel/Tyre Assembly
d) Wheel/Tyre Assembly Inner Hub View
Fig.3 Wheel/Tyre Geometry and Pressure Tapping Locations There was no need to install pressure tappings on both sides of the tyre since the tyre was turned around onto the opposite side of the wheel after one side had been logged. Figs.3c and 3d show the wheel/tyre assembly from the outer hub view and inner hub view, respectively. A flat plate (Fig.3c) was used to eliminate any through hub flow for this investigation, and Fig.3d clearly shows the cavity inside of the hub, thus being more representative of a ‘real’ wheel. Further details of the wheel/tyre assembly are given in Mears et al [14].
3. RESULTS AND DISCUSSION The data presented were obtained by computing the ensemble average from 32 sets of 2048 measurements, this corresponding to around 700 wheel revolutions. All results are therefore time-averaged over a around 700 wheel revolutions. The data have been corrected for centrifugal effects on the pressure scanner (mechanical effects) and the centrifugal pressure gradient that exists as a result of the different radial positions of the transducer and the pressure tapping. To correct the pressure data for the effects of the centrifugal pressure gradient the following correction [equation (1)] was used (after Fackrell [11]). The lift and drag coefficients were obtained using integration. ñV∞ PS = PM + 2
2
r S 2 − r M 2 2 r O
(1)
where r M is the radius of the transducer, r S is the radius of the pressure measuring hole, r O is the maximum radius of the wheel, PM is the measured pressure, PS is the actual pressure at the pressure-measuring hole. Table 1 shows the lift and drag coefficients for zero degrees yaw and five degrees yaw compared with Fackrell [11]. Comparisons with the results of Fackrell are similar, in terms of lift and drag coefficients and pressure distribution, although it must be emphasised that the results were not expected to be the same since the experimental configurations/geometry were different between the two sets of data, both in terms of aspect ratio and edge profile. Fackrell’s wheel aspect ratio was 0.41 compared with 0.53 for the pneumatic tyre/wheel assembly. Edge profile geometry is more difficult to quantify, in terms of a single numerical value, and it is thought that the edge profile of the pneumatic tyre has similarities with both edge profiles 1 and 2 used by Fackrell. Wheel/Tyre Type
Reynolds Number
Yaw Angle (deg)
P1 P1 B2 [ref.11]
2.5x105 2.5x105 5.3x105
0 5 0
Spoke Openness (%) 0 0 -
CD
CL
0.56 0.59 0.58
0.42 0.35 0.44
Table.1 Lift and Drag Coefficients for Different Wheels/Configurations A reduction in lift and an increase in drag were seen at yaw=5°. The drag increase agrees with the results presented by Cogotti [13] although he found that lift increased in a similar way to drag. However, Cogotti’s results were based on a stationary wheel so perhaps drawing any meaningful conclusions is difficult with respect to rotating wheels where the flow-field is quite different.
3 2.5 Yaw=0° 2 Yaw=5° 1.5
Fackrell Yaw=0°
1 0.5 0 p C
0
90
180
270
360
-0.5 -1 -1.5
ω
-2 -2.5
θ
V∞
-3 -3.5 Angular Position (deg)
V b
a) Centre line; Yaw = 0 and 5 degrees, c.f. Fackrell [11] 3 2.5 Yaw=0°, w/D = +/-0.18 2
Yaw=5°, w/D = 0.18 Yaw=5°, w/D = -0.18
1.5 1 0.5 0 p C
0
90
180
270
360
-0.5 -1 -1.5
ω
-2 -2.5
θ
V∞
-3 -3.5 Angular Position (deg)
V b
b) Tapping 6; Yaw = 0 and 5 degrees 3 2.5 Yaw=0°, w/D = +/- 0.27 2
Yaw=5°, w/D = 0.27 Yaw=5°, w/D = -0.27
1.5 1 0.5 0 p C
0
90
180
270
360
-0.5 -1 -1.5
ω
-2 -2.5 -3
θ
V∞
-3.5 Angular Position (deg)
V b
c) Tapping 9; Yaw = 0 and 5 degrees Fig.4 Static Pressure Distributions for a Rotating Wheel
It is not intended to present all of the data gathered from these experiments, but to focus on different regions of the wheel. Fig.4 shows static surface pressure distributions, in terms of pressure coefficients, for the centreline, tread edge and the sidewall of the wheel for both yaw angles (0° represents the front of the wheel facing the direction of the flow). Fig.4a shows that the results are very similar to Fackrell [11] for the zero yaw case. At around 285° (i.e. before the top of the wheel) the flow separates from the surface resulting in a much taller wake compared to that of a stationary wheel. At around zero degrees the pressure reaches stagnation pressure for the zero degree yaw case. This is not the case for the five degrees yaw case, which is expected since the stagnation streamline would be nearer the windward side of the wheel. The pressure is therefore lower at the centreline due to more cross flow at this location. Probably the most interesting feature of this pressure distribution is the rapid rise in pressure at the contact patch to Cp≈2.0. This is what Fackrell referred to as the ‘jetting’ phenomenon whereby work is done on the air as it is squeezed between the rotating wheel and moving ground, hence pressures that are greater than the total pressure in the working section. This rapid rise in pressure is accompanied by a sudden fall in pressure just after the line of contact between the tyre and rolling road. On close inspection it can be seen that Fackrell’s results do not show this, although his two-dimensional theoretical prediction did show a positive pressure peak followed by a negative pressure peak. His theoretical approach was based on the very small region between the tyre and rolling road where the effects of viscosity dominate the flow. It is reasonable to suggest that if a rapid increase to high pressure occurs before the contact patch due to the moving boundaries converging together, then a rapid decrease to low pressure should occur due to the divergence of the moving boundaries resulting in negative pressure just behind the line of contact. Such strong negative pressure could have a significant effect on the wake flow. A possible reason why Fackrell did not observe this negative pressure peak in his experiments could be due to the solid wheel that was used, and perhaps the correct line of contact was not achieved between the tyre and road, although since he observed jetting before the line of contact this may not be the case. The use of a pneumatic tyre could have significant benefits if the correct line of contact is to be achieved. The oscillations after the contact region are less easily explained and at this stage it is not known whether this effect is an intrinsic feature associated with rotating wheels. Further investigation is required to examine both the negative pressure peak and the oscillations after the contact region to establish whether they are an inherent flow feature, and to assess the applicability of Fackrell’s two-dimensional theoretical solution to highly three-dimensional flows. Base pressure is fairly constant for all traces. Fig.4b shows the surface pressure distribution for the tread edge (w/D = +/- 0.18, see Fig.3a for w/D details). At the front of the wheel (0°<θ<70°) the yaw=0° pressure distribution is bounded by the windward and leeward distributions for the yaw=5° case. This is expected, as the pressure will be higher on the windward side of the wheel compared to the leeward side where the flow is accelerating across the surface of the wheel.
Yaw = 0°
Yaw = 5°
a) Tread Region
0.20
0.225
Yaw = 0°
0.25
0.275
0.30
0.325
0.20
Theta/360
0.225
0.25
0.275 Theta/360
Yaw = 5°
b) Close-up of the Contact Patch
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
Yaw = 0°
0.25
Yaw = 5°
Theta/360
c) Base Region Fig.5 Contours of Constant Static Pressure
0.30
0.325
At the contact region the pressure distributions exhibit similar behaviour to those of the centreline, although for the yaw=0° case the Cp has risen to approximately 2.6 and fallen to around Cp= -2.8, and therefore the tread edge of the wheel experiences more jetting than the centreline of the wheel. This may be due to the edge profile and how the air flow at the contact patch interacts with the accelerating air flow as it turns around the corner of the wheel and down by the side of the wheel. If this were so then it would explain the greater Cp values for the yaw=0° case at the edge of the tread. The smaller rise in pressure on the windward side could also be explained in this way as the air flows more across the wheel towards the leeward side and away from the windward edge profile. The mechanism responsible for such behaviour is unknown and does require further study. Fig.4c shows the pressure distribution for the sidewall of the wheel. The graph shows the yaw=0° and yaw=5°, w/D= -0.27 (leeward) traces are almost contiguous. Both show a small peak at approximately 90° suggesting that any rise in pressure across the tread area has an effect on the sidewall as the flow moves downstream. The windward side of the wheel (w/D = 0.27) does not show any signs of any pressure rise and the pressure around the rear and top region of the wheel at this sidewall location are higher. Fig.5 shows contours of constant static pressure coefficient for a rotating wheel relating to the tread region (Fig.5a), a close-up of the contact patch region (Fig.5b) and the base region of the wheel (Fig.5c). Pressure data from all tappings were used in these contour plots. The width of the contour plots have been increased in order to improve clarity. The yaw=0° plot (Fig.5a upper) has been mirrored about y/D = 0, since only one half of the wheel was logged. The two plots in Fig.5a highlight the interesting region at the contact patch and this is discussed later. The yaw=0 ° plot shows that low pressure exists over most of the tread width between theta/360 = 0.6 to 0.85 compared to the yaw=5° case where the low pressure is of similar magnitude but is limited to the leeward side of the wheel. This would explain why the lift coefficient is reduced for he yaw=5° case compared to that at yaw=0 ° but does not explain why it should be limited to the leeward side of the wheel. Any positive pressure rise at the contact patch, which would increase the lift force, is mitigated by the negative pressure peak just after the line of contact. Highlighting the contact region (Fig.5b) shows that for both cases where a positive pressure exists before the line of contact a negative peak exists afterwards (yaw=0°: y/D=+/- 0.05, theta/360=0.24 high pressure; y/D=+/0.05, theta/360=0.275 low pressure, and yaw=5°: y/D= -0.025, theta/360=0.24 high pressure; y/D= -0.025, theta/360=0.275 low pressure). Fig. 5c shows the base region and this reveals that the base pressure is lower for the yaw=5° case, which will contribute towards the higher drag (yaw=5°: y/D= -0.1, theta/360= 0.5). The plot also shows that where a negative pressure peak exists it seems to have an effect on the flow field further around the wheel towards the rear of the wheel and therefore may not be localised to the contact patch.
4. CONCLUSIONS Surface static pressures have been measured on a rotating, isolated pneumatic tyre/wheel assembly at yaw=0° and yaw=5°. Integral lift and drag coefficients have shown that the lift force decreased and the drag force increased at yaw=5°. The pressure distributions and static pressure contour plots highlighted the reasons for such changes in the forces. A strong positive pressure peak was observed at the contact patch and this agrees with Fackrell’s ‘jetting’ phenomenon. A subsequent negative pressure peak was observed after the line of contact between the tyre and road, which Fackrell did not observe experimentally. However, his two-dimensional theoretical prediction predicted that such a strong negative peak should exist in this region. This prompts further investigation into such phenomenon. 5. REFERENCES 1. Axon, L., Garry, G. and Howell, J. An Evaluation of CFD for Modelling the Flow Around Stationary and Rotating Isolated Wheels. SAE 980032. 1998, 65-75. 2. Axon, L., Garry, K. and Howell, J. The Influence of Ground Condition on the Flow Around a Wheel Located Within a Wheelhouse Cavity. SAE 1999-01-0806. 1999, 149-158. 3. Axon, L. The Aerodynamic Characteristics of Automobile Wheels – CFD Prediction and Wind Tunnel Experiment. PhD Thesis, Cranfield University: College of Aeronautics. 1999. 4. Skea, A. F., Bullen, P. R. and Qiao, J. CFD Simulations and Experimental Measurements of the Flow Over a Rotating Wheel in a Wheel Arch. SAE 2000-010487. 2000, 115-123. 5. Skea, A. F., Bullen, P. R. and Qiao, J. The use of CFD to Predict Air Flow Around a Rotating Wheel. 2nd MIRA International Conference on Vehicle Aerodynamics. 1998. 6. Fackrell, J. E. and Harvey, J. K. The Flow Field and Pressure Distribution of an Isolated Road Wheel. In Stephens, H. S. Advances in Road Vehicle Aerodynamics. BHRA Fluid Engineering, 1973, Paper 10. 7. Fackrell, J. E. and Harvey, J. K. The Aerodynamics of an Isolated Road Wheel. In Pershing, B., editor, Proceedings of the Second AIAA Symposium of Aerodynamics of Sports and Competition Automobiles, 1975. 8. Dominy, R. G. Aerodynamics of Grand Prix Cars. Proc. Instn. Mech. Engrs, Part D, 1992, 206D, 267-274. 9. Morelli, A. Aerodynamic Effects on an Automobile Wheel. Technical Report Trans. 47/69, MIRA, 1969. 10. Stapleford, W. R. and Carr, G. W. Aerodynamic Characteristics of Exposed Rotating Wheels. Technical Report 1970/2, MIRA, 1970. 11. Fackrell, J. E. The Aerodynamics of an Isolated Wheel Rotating in Contact with the Ground. PhD Thesis, University of London. 1974. 12. Bearman, P. W., De Beer, D., Hamidy, E., and Harvey, J. K. The Effects of a Moving Floor on Wind-Tunnel Simulation of Road Vehicles. SAE 880245. 1988, 1-15. 13. Cogotti, A. Aerodynamic Characteristics of Car Wheels. Int. J. of Vehicle Design, Special Publication SP3. 1983, 173-196.
14. Mears, A. P., Dominy, R. G. and Sims-Williams, D. B. The Air Flow About an Exposed Racing Wheel. SAE 2002-01-3290. 2002.
