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Isosurfaces of total pressure for yaw and upstream turbulence cases.

Tesla aerodynamicists use CFD to evaluate yaw performance

Automotive aerodynamics ultimately resolves into the six forces and moments that a vehicle moving through an environment experiences. In wind-tunnel testing, the typical frame of reference is switched so that the vehicle is stationary and air is moved past it at a velocity to produce forces and moments of the same magnitude. The most obvious complication is in treatment of the ground plane, which on-road has the same speed as the flow around it (normally stationary) and a velocity relative to the vehicle. While stationary floor tunnels have been useful for decades of ground vehicle development, more modern wind tunnels incorporate a variety of means of boundary layer control and ground simulation. Meanwhile, having the ground plane move at a velocity matching the free stream flow in CFD simulations is trivial.

A facet of matching real-world conditions that has only recently been investigated is the effect of ambient wind and turbulence conditions. As the effects of aerodynamic forces and moments only become significant to vehicle performance at higher speeds, much of the focus thus far has been on highway driving conditions. Several of the works in this field have categorized the most typical flow fields into three categories: open terrain, road side obstacle (RSO), and urban/traffic driving. These three cases represent a broad variety of wind conditions that a vehicle will see in service. However, it is difficult to completely represent the full spectrum of turbulence scales in the laboratory environment. Passive systems can replicate small-scale turbulence, while active systems can replicate large-scale turbulence. As with ground plane replication, CFD is able to easily generate any desired turbulence level, usually specified via turbulence intensity and turbulent length scale.

Replicating steady side wind conditions, however, is easily accomplished in most wind tunnels. The importance of being able to acquire data at a variety of yaw angles means that a turntable is a requirement of any wind tunnel. Typically, data is gathered for a range of yaw angles specified by the test engineer on each vehicle configuration. It is up to the aerodynamicist to then weigh the importance of yaw performance (the six force and moment components) against other in-service conditions to ultimately make the most effective design decisions. This sort of yaw sensitivity analysis is far more resource-consuming in the digital domain, however. While not difficult to implement in the simulation setup for most commercial CFD codes, each yaw angle requires its own solution, which can vary from the order of several hours to a day or more for typical modern computing systems. Therefore, developing a complete understanding of a vehicle’s yaw performance in a CFD-led program can become very time consuming, to the detriment of exploring further design directions.

A group of aerodynamicists from Tesla chose Exa’s PowerFLOW CFD software to examine two alternative methods of simulating aerodynamic performance in the presence of realistic on-road crosswind for the Tesla Model S sedan. PowerFLOW’s inherently transient solution offers the ability to vary boundary conditions and move geometry during the simulation. These two capabilities allow for two different methods of changing the flow direction relative to the vehicle. The first is rotating the vehicle according to a time-varying function, similar to a turntable in a wind tunnel. Alternatively, the vehicle can be kept stationary while the boundary conditions, namely the magnitude direction of onset flow, are varied. With this option, the side boundaries of the domain are changed to be periodic rather than frictionless walls.

The upstream gust environments were divided into two categories: dynamic yaw achieved via time-dependent cross-flow and upstream turbulence. Analysis of the force histories showed that an instantaneous step change to onset flow angle presented no noticeable overshoot of drag or side force, mostly due to the roundness of the nose profile in the horizontal plane. Dynamic yaw with a 2-s period showed significant hysteresis in that the peak drag and side force neither reached the steady-state value nor returned to the zero degree yaw flow state. Dynamic yaw with a slower 6-s period showed very little hysteresis, with the peak drag and side force reaching similar levels as the steady-state cases.

Upstream turbulence cases showed greater force fluctuations than static cases. Overall drag values are higher with upstream turbulence, but the side forces are about equal. Upstream turbulence exerts transient yaw angle fluctuations of around ±3°.

Analysis of the force development plots for the upstream turbulence cases revealed that all three (yaw without added turbulence, no yaw with turbulence, and yaw with turbulence) showed higher drag at the rear wheels. When upstream turbulence, a yaw angle, or both are added, the front wheel wakes no longer protect the rear wheels. These cases had higher drag as well as a larger rear wheel wake. Further, at yaw, the flow accelerates over the downwind rear corner, lowering the pressure on the upper portion of the downwind corner. This increases drag as well as rear lift, a highly undesirable scenario.

Lastly, the wake analysis via total pressure isosurfaces showed that upstream turbulence produces a smearing of the coherent vortex structures found on the baseline. This is particularly apparent over the roof and the rear quarter panel shear layers.

These results demonstrate how both dynamic yaw and upstream turbulence provide added insight to the yaw performance characteristics of a vehicle. These methods allow for a more comprehensive understanding of the vehicle’s aerodynamics while significantly reducing the computational resources required to generate such information when compared to a series of traditional static yaw cases. Since the dynamic yaw case has a very similar resolution scheme to a static yaw case, 1 s of simulated time requires similar computational resources for either type of simulation. A typical static yaw simulation requires around two seconds of time simulated, and therefore generating the full yaw curve from 0 to 6° at 1° increments would require 14 s of simulated time. This is more than twice the time required for the slow, 6-s period dynamic yaw simulation. Such throughput improvement means that yaw cases can more regularly be incorporated into the design process. Ultimately, this increased understanding translates into a more robust vehicle with lower in-service energy consumption.

This article is based on SAE International technical paper 2014-01-0599 by Andrew D’Hooge, Robert Palin, and Luke Rebbeck of Tesla Motors; and Joaquin Gargoloff and Bradley Duncan of Exa Corp.

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