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By Sandeep Sovani, Senior Consulting Engineer, Fluent Inc.
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The generic ground transportation system (GTS) body
Highway trucks consume enormous quantities of fuel. In the year 2000, the cumulative fuel consumption of all heavy trucks in the U.S. was over 25 billion gallons. With an expanding economy, the volume of goods transported by truck is on the rise. In the year 2005, the cumulative heavy truck fuel consumption is expected to increase to 30 billion gallons. Assuming an average cost of $1.50 per gallon, the economic impact of heavy truck fuel is expected to be $45 billion this year. Furthermore, the billions of gallons of fuel burnt in truck engines every year ends up as millions of tons of toxic material polluting our atmosphere. Clearly, reducing truck fuel consumption has large economic and environmental benefits.
Instantaneous velocity vectors on the vertical midplane
Aerodynamic drag accounts for a significant portion of the resistive forces acting on a moving truck. Drag generally varies with the square of the velocity and has the highest impact at typical highway cruising speeds. At 68 mph (110 km/h), the power required to overcome the aerodynamic drag amounts to roughly 65% of the total fuel consumption. It is estimated that a 25% reduction in aerodynamic drag would yield an overall 10-15% reduction in fuel consumption.
A number of devices and strategies are being conceived these days to reduce truck drag. In their development it is important to understand the flow structure around a truck in detail, and have methodologies to quickly and economically evaluate the drag reduction yielded by a given design change. With the advent of powerful computational resources and efficient algorithms, CFD is being used increasingly to meet these needs, because it can provide detailed insight into the flow structure around moving trucks of various shapes and sizes.
The mesh cross section along the symmetry plane at the front of the vehicle
In the present study, the aerodynamics of a generic Ground Transportation System (GTS) at 0° yaw is studied using FLUENT. The GTS body is a largely simplified 1/8th scale model of a tractor-trailer truck. High Reynolds number wakes that form behind trucks have highly complex, time-varying turbulent structures. These structures cannot usually be captured using Reynolds-averaged Navier-Stokes (RANS) methods, even if transient simulations are performed. By contrast, the large eddy simulation (LES) turbulence model is a natural choice for simulating such cases, since it captures many of the transient details of the flow. However, even with today's high-speed computers, LES is too computationally expensive for many practical applications involving large domains, since it requires such a fine grid to be effective. Detached eddy simulation (DES), a RANS-LES hybrid approach, was therefore chosen for the GTS analysis. Using DES, the near wall region is modeled with a RANS turbulence model, the one equation Spalart-Allmaras model (1), and the regions away from the walls are modeled with LES. Compared to LES, this approach drastically reduces the cell count in the near-wall region without much loss of accuracy in the solution as a whole, thus making the computational expense of the simulation manageable. In addition, a separate unsteady RANS simulation was also conducted with the RNG k-ε turbulence model to compare and contrast with the DES results.
Velocity magnitude contours on a horizontal surface located at half the vehicle height
A mostly hexahedral mesh of nearly 14 million cells was created, with cells tightly clustered around the body (2). Wall y+ values were maintained in the range of 30 to 300. A steady state solution was first obtained with the realizable k-ε turbulence model. Using this solution for the initial condition, transient simulations were run with the segregated implicit solver for a real time of 0.55 seconds. It took 0.1 seconds for the flow structure to become dynamically stable, after which time-averaged and transient surface pressures, skin friction coefficients, and wake velocity structures were recorded. The expected complex time-varying turbulent structure was observed in the wake. A flapping shear layer became established around the trailing edge of the vehicle. The undulations of this shear layer caused vortices to shed from the rear of the truck. Timeaveraged calculations of pressure coefficient and skin friction were found to be in excellent agreement with corresponding experimental data (3).
The time averaged drag coefficient computed by DES and RNG are 0.253 and 0.250, respectively, which are just 1.3% and 0.24% greater than the corresponding experimental values.
Variation of the time-averaged pressure coefficient on the upper surface of the body, on the symmetry line
Skin friction coefficient variation at a point on the body's left vertical leading edge
The experiments also included measurements of the fluctuating voltage using a hot-film sensor, flushmounted at the mid point of the right front leading edge of the body. The voltage recorded is directly proportional to the skin friction coefficient acting on the film. In the DES and RNG computations, skin friction coefficient was recorded as a function of time at the same location. The voltage signal and the two computed skin friction coefficient traces were Fourier transformed to obtain frequency spectra. The absence of any sharp peaks in the measured frequency spectrum indicates that there is no flow separation in the experiments. DES predicts a similarly flat spectrum while the RNG spectrum shows a few short peaks. While both the turbulence models correctly indicate the absence of separation, DES does so more clearly.
The analysis demonstrated that DES is a viable tool for studying truck aerodynamics. It provides highly accurate, time-averaged pressure distribution along the vehicle, as well as insight into the transient behavior of the wake. While the time-averaged flow characteristics are important for understanding quantities such as drag, the transient behavior helps engineers assess safety issues, such as the vehicle's maneuverability and stability.
References:
- P.R. Spalart and S.R. Allmaras, LaRecherche Aerospatiale, No. 1, p. 5-21, 1994
- S.V. Unaune, S.D. Sovani, S-E. Kim; SAE paper 2005, no. 2005-01-0548
- B.L. Storms, J.C. Ross, J.T. Heineck, S.M. Walker, D.M. Driver, G.G. Zilliac; NASA Technical Report 2001, no. NASA-TM-2001-209621
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