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2009 | Book

The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains

Editors: Fred Browand, Rose McCallen, James Ross

Publisher: Springer Berlin Heidelberg

Book Series : Lecture Notes in Applied and Computational Mechanics

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About this book

It is our pleasure to present these proceedings for “The Aerodynamics of Heavy Vehicles II: Trucks, Buses and Trains” International Conference held in Lake - hoe, California, August 26-31, 2007 by Engineering Conferences International (ECI). Brought together were the world’s leading scientists and engineers from industry, universities, and research laboratories, including truck and high-speed train manufacturers and operators. All were gathered to discuss computer simu- tion and experimental techniques to be applied for the design of the more efficient trucks, buses and high-speed trains required in future years. This was the second conference in the series. The focus of the first conference in 2002 was the interplay between computations and experiment in minimizing ae- dynamic drag. The present proceedings, from the 2007 conference, address the development and application of advanced aerodynamic simulation and experim- tal methods for state-of-the-art analysis and design, as well as the development of new ideas and trends holding promise for the coming 10-year time span. Also - cluded, are studies of heavy vehicle aerodynamic tractor and trailer add-on - vices, studies of schemes to delay undesirable flow separation, and studies of - derhood thermal management.

Table of Contents

Frontmatter

Keynote Papers

Frontmatter
Bluff Body Flow Research with Application to Road Vehicles

This paper explores a number of aspects of bluff body research that may help in the understanding and advancement of the aerodynamics of heavy vehicles. The relationship between the lift and drag of bodies moving close to the ground is discussed and the unsteady trailing vortex structure of a vehicle is illustrated. The importance of the ground boundary condition and the flow structure around wheels rotating in contact with the ground are also described. Methods for the reduction of forebody and base drag are discussed and the possibilities for using flow control techniques to modify free shear layer development as a means of reducing drag are addressed. Finally the role of the natural wind, particular atmospheric turbulence, in affecting vehicle flows is examined.

Peter Bearman
Climate Change and the Energy Economy

There is a robust scientific consensus that human-induced climate change is occurring. The recently released Fourth Assessment Report of the IPCC states with “very high confidence,” that human activity has caused the global climate to warm. Many well-documented observations show that fossil fuel burning, deforestation, and other industrial processes are rapidly increasing the atmospheric concentrations of CO$

2

$ and other greenhouse gases. An increasing body of observations and modeling results shows that these changes in atmospheric composition are changing the global climate and beginning to affect terrestrial and marine ecosystems. In this talk, I’ll review observed and projected changes to the US climate, discuss the sectoral contributions to US greenhouse gas emissions and speculate about the future of the US carbon economy.

David Schimel

Flow Field Characteristics

Frontmatter
Large Eddy Simulations and Acoustic Predictions in Automotive Applications

The emergence of the computational tools capable of accurately predicting the flow properties around complex geometries has opened new opportunities in the design of automotive components and their integrations. In particular, one may now be able to predict the acoustic noise produced by the unsteady fluid motion induced by the individual parts and quantitatively evaluate their loudness and spectral (i.e. frequency content) without relying on semi-empirical models. To demonstrate this capability the flow noise produced by two configurations typical of automotive applications – namely the outside rear view mirrors and the rain gutters – are examined quantitatively. Relevant details regarding the prediction methods as well as a selection of results are discussed.

G. Iaccarino, F. Ham, Y. Khalighi, D. Bodony, P. Moin, B. Khalighi
Validation of the Immersed Boundary CFD Approach for Complex Aerodynamic Flows

Standard CFD methods require a mesh that fits the boundaries of the computational domain. For a complex geometry the generation of such a grid is time-consuming and often requires modifications to the model geometry. This paper evaluates the Immersed Boundary (IB) approach which does not require a boundary-conforming mesh and thus would speed up the process of the grid generation. In the IB approach the CAD surfaces (in Stereo Lithography –STL- format) are used directly and this eliminates the surface meshing phase and also mitigates the process of the CAD cleanup. A volume mesh, consisting of regular, locally refined, hexahedrals is generated in the computational domain, including inside the body. The cells are then classified as fluid, solid and interface cells using a simple ray-tracing scheme. Interface cells, correspond to regions that are partially fluid and are intersected by the boundary surfaces. In those cells, the Navier-Stokes equations are not solved, and the fluxes are computed using geometrical reconstructions. The solid cells are discarded, whereas in the fluid cells no modifications are necessary. The present IB method consists of two main components: 1) TOMMIE which is a fast and robust mesh generation tool which requires minimum user intervention and, 2) a library of User Defined Functions for the FLUENT CFD code to compute the fluxes in the interface cells. This study evaluates the IB approach, starting from simple geometries (flat plate at 90 degrees, backward facing step) to more complex external aerodynamics of full-scale fully-dressed production vehicles. The vehicles considered in this investigation are a sedan (1997 Grand-Prix) and an SUV (2006 Tahoe). IB results for the flat plate and the backward-step are in very good agreement with measurements. Results for the Grand-Prix and Tahoe are compared to experiments (performed at GM wind tunnel) and typical body-fitted calculations performed using Fluent in terms of surface pressures and drag coefficients. The IB simulations predicted the drag coefficient for the Grand-Prix and the Tahoe within 5% of the body-fitted calculations and are closer to the wind-tunnel measurements.

B. Khalighi, S. Jindal, J.P. Johnson, K.H. Chen, G. Iaccarino
Experimental Characterization of the Unsteady Flow Field behind Two Outside Rear-View Mirrors

The unsteady flow field behind two outside rear-view automobile mirrors was examined experimentally in order to compile a comprehensive database for the validation of the ongoing computational investigation effort to predict the aero-acoustic noise to the outside rear-view mirrors. This study is part of a larger scheme to predict the aero-acoustic noise due to various external components on automobiles. To aid with the characterization of this complex flow field, mean and unsteady surface pressure measurements were undertaken in the wake of two mirror models. Velocity measurements with particle image velocimetry were also conducted to develop the mean velocity field of the wake. Two full-scale mirror models with distinctive geometrical features were investigated.

Bahram Khalighi, James P. Johnson, Kuo-Huey Chen, Richard G. Lee
Investigation of Buoyancy Driven Flow in a Simplified Full Scale Underhood – PIV and Temperature Measurements

Results of the detailed flow measurements for an underhood buoyancy driven flow using a simplified full scale model of an engine compartment, engine block, and exhaust heaters are presented. The engine block surface temperature and exhaust heaters are kept at about 100 °C and 600 °C, respectively. This investigation reveals the complex dominant flow structures and thermal behavior of a vehicle underhood under steady state and transient states.

P. Merati, C.H. Leong, K.H. Chen, J.P. Johnson
Investigation of Buoyancy Driven Flow in a Simplified Full-Scale Underhood – Numerical Study

Transient numerical results are presented for simulating buoyancy driven flow in a simplified full-scale underhood in automobile. The flow condition is set up in such a way that it mimics the underhood soak condition, when the vehicle is parked in a windbreak with power shut-down, after enduring high thermal loads due to performing a sequence of operating conditions, such as highway driving and trailer grade loads in a hot ambient environment. For validation, several experiments were conducted to measure the temperature and velocity fields. The simplified underhood geometry, although simplified, consists of the essential components in a typical automobile underhood undergoing the buoyancy driven flow condition. It includes an enclosure, an engine block and two exhaust cylinders mounted along the sides of the engine block. The calculated temperature and velocity were compared with the measured data at different locations near and away from the hot exhaust plumes. The numerical predictions reveal a complex, transient flow structure under the buoyancy condition, and the results show very favorable comparisons with the experimental velocity and temperature measurements. The transient numerical procedure developed for the current study would pave the way for the future numerical simulations of the practical real underhood soaking.

K.H. Chen, J.P. Johnson, P. Merati, C.H. Leong
The Flow Environment of Road Vehicles in Winds and Traffic

The aerodynamic development of a new vehicle is usually performed in smooth flow EFD or CFD domains with the vehicle in isolation. However the flow environment on-road is complex due to the presence of atmospheric winds, the wakes of nearby stationary objects and, depending upon driving conditions, the wakes of other vehicles. Winds and traffic generate a turbulent flow environment and can augment or reduce the mean velocity experienced by the moving vehicle. Recent work on turbulence arising from vehicles traversing the atmospheric boundary layer is reviewed and the consequence of upstream vehicle wakes is considered. The influence of distance and rear slant angle is examined, via wind-tunnel measurements of wakes of Ahmed bodies using dynamically calibrated multi-hole probes. The effect on very closely coupled vehicles (such as may occur in future platoons) is investigated via force and surface pressure measurements on two and three vehicle Ahmed bodies of varying rear slant angle. It is argued that the typical turbulence intensity for current highway driving is about 5%, but this can be significantly augmented when in the close proximity of other vehicles and/or during high winds. Further it is shown that for some vehicle forms, close coupling can increase the total platoon drag.

Simon Watkins, Riccardo Pagliarella

Separation Control for Drag Reduction

Frontmatter
Preliminary Experiments Applying Active Flow Control to a 1/24th Scale Model of a Semi-Trailer Truck

Preliminary experiments were carried out to investigate possible benefits of using a relatively new type of fluidic actuators (Raman & Raghu [1]) in combination with attached aft bodies to reduce the drag on a standard semi-trailer truck. The actuators generate oscillating jets that cause the formation of streamwise vortices that enhance the entrainment of the shear layer significantly. Taking into account the potential feasibility of any add-ons to a trailer, seven different bodies with simple geometries were chosen for this investigation.

L. Taubert, I. Wygnanski
Large Trucks Drag Reduction using Active Flow Control

Aerodynamic drag is the cause for more than two-thirds of the fuel consumption of large trucks at highway speeds. Due to functionality considerations, the aerodynamic efficiency of the aft-regions of large trucks was traditionally sacrificed. This leads to massively separated flow at the lee-side of truck-trailers, with an associated drag penalty of at least a third of the total aerodynamic drag. Active Flow Control (AFC), the capability to alter the flow behavior using unsteady, localized energy injection, can very effectively delay boundary layer separation. By attaching a compact and relatively inexpensive “add-on” AFC device to the back side of truck-trailers (or by modifying it when possible) the flow separating from it could be redirected to turn into the lee-side of the truck, increasing the back pressure, thus significantly reducing drag. A comprehensive and aggressive research plan that combines actuator development, computational fluid dynamics and bench-top as well as wind tunnel experiments was performed. The research uses an array of 15 newly developed Suction and Oscillatory Blowing actuators housed inside a circular cylinder attached to the aft edges of a generic 2D truck model. Preliminary results indicate a net drag reduction of 10% or more.

A. Seifert, O. Stalnov, D. Sperber, G. Arwatz, V. Palei, S. David, I. Dayan, I. Fono
Flow Separation Control on Trailing Edge Radii using Single Dielectric Barrier Discharge Plasma Actuators: An Application to Vehicle Drag Control

As cruise speeds of ground vehicles has risen to as high as 70 miles per hour, overcoming the aerodynamic drag has become a significant percentage of the total power required. Engines have been increased in power and fuel tanks made larger to provide reasonable range between fuel stops. Heavy truck data in particular indicate that 2/3

rd

s of the cruise power is needed to overcome drag. This paper focuses on reducing drag on class-8 trucks, but the principles can be applied to lighter trucks, busses, pick-ups, SUVs, and many other ground vehicles. The University of Notre Dame has developed unique actuators that have shown potential to maintain unseparated airflow around corners. This technology promises to reduce drag on ground vehicles thus increase fuel efficiency and gas mileage. This paper discusses these actuators and the preliminary wind tunnel tests that have been conducted at Notre Dame in 2007. The cost of fuel has risen so rapidly in the past few years that drag is now a major contributor to the cost of moving freight and consumer goods around the country. The use of these actuators can be applied to passenger cars and as well as many other types of ground vehicles.

R. Spivey, R. Hewitt, H. Othman, T. Corke
Adaptive Control of Post-Stall Separated Flow Application to Heavy Vehicles

This paper discusses two adaptive feedback control approaches designed to reattach a massively separated flow over a NACA airfoil with minimal control effort using piezoelectric synthetic jet actuators and various sensors for feedback. One approach uses an adaptive feedback disturbance rejection algorithm in conjunction with a system identification algorithm to develop a reduced-order dynamical systems model between the actuator voltage and unsteady surface pressure signals. The objective of this feedback control scheme is to suppress the pressure fluctuations on the upper surface of the airfoil model, which results in reduced flow separation, increased lift, and reduced drag. A second approach leverages various flow instabilities in a nonlinear fashion to maximize the lift-to-drag ratio using a constrained optimization scheme – in this case using a static lift/drag balance for feedback. The potential application of these adaptive flow control techniques to heavy vehicles is discussed.

L. Cattafesta, Y. Tian, R. Mittal
Investigation of Tractor Base Bleeding for Heavy Vehicle Aerodynamic Drag Reduction

The drag reduction capability of tractor base bleeding is investigated using a combination of experiments and numerical simulations. Wind tunnel measurements are made on a 1:20 scale heavy vehicle model at a vehicle width-based Reynolds number of 420,000. The tractor bleeding flow, which is delivered through a porous material embedded within the tractor base, is introduced into the tractor-trailer gap at bleeding coefficients ranging from 0.0-0.018 for two different gap sizes with and without side extenders. At the largest bleeding coefficient with no side extenders, the wind-averaged drag coefficient is reduced by a maximum value of 0.015 or 0.024, depending upon the gap size. To determine the performance of tractor base bleeding under more realistic operating conditions, computational fluid dynamics simulations are performed on a full-scale heavy vehicle traveling within a crosswind for bleeding coefficients ranging from 0.0-0.13. At the largest bleeding coefficient, the drag coefficient of the vehicle is reduced by 0.146. Examination of the tractor-trailer gap flow physics reveals that tractor base bleeding reduces the drag by both decreasing the amount of free-stream flow entrained into the gap and by increasing the pressure of the tractor base relative to that of the trailer frontal surface.

Jason Ortega, Kambiz Salari, Bruce Storms
Drag Reduction on a Generic Tractor-Trailer using Active Flow Control in Combination with Solid Flaps

An experimental investigation was carried out to assess the drag reducing potential of active flow control in conjunction with flat panel flaps attached to the trailer of a generic tractor–trailer model. The experiments were carried out in a wind tunnel with a 1/10

th

scale generic tractor-trailer model at Reynolds numbers up to 640,000 based on the model width. Active flow control was achieved by means of constant blowing, constant suction and oscillatory blowing and suction. A secondary objective was to make short base flaps with active flow control as effective as long flaps with no active flow control. Measurement techniques such as flow visualizations, loads by means of a 6-component balance, LDA and PIV were employed. The results show that constant blowing at a momentum coefficient of 11.13% is able to achieve higher drag reduction than long flaps with no active flow control. The analysis of the flow field in the wake showed that constant blowing deflects the shear layer between the free stream and the wake region downward and hence reduces the size of the wake. The flaps at the side of the truck did not appear to have any substantial drag reducing effect.

Christian Navid Nayeri, Johannes Haff, David Greenblatt, Lennart Loefdahl, Christian Oliver Paschereit

Design Optimization Techniques Related to Vehicle Aerodynamics

Frontmatter
Advanced Aerodynamics and Cooling System Solutions for Higher Fuel Efficiency and Decreased Emissions

Auxiliary load systems, fuel and lubrication systems, and cooling systems are an integral part of any truck, and contribute to the overall design and energy use/management. Research and development appropriate to this topic include advanced aerodynamics, heat exchanger technologies, heat pipe/two-phase flow systems, advanced pumps and compressors, and other advanced thermal and fluid management concepts to improve electric powertrain cooling, enhance drivetrain performance, reduce energy usage, improve system energy management, and reduce component and system weight, volume, and aerodynamic drag in hybrid power trains and hybrid vehicle systems. The current study presents a cooling system and vehicle aerodynamics integration through the substitution of more efficient hardware and better integration with existing vehicle systems. Several aerodynamic add-on devices are tested for drag reduction. Practical vehicle designs are developed and software simulations are conducted to determine improvements in aerodynamic efficiency. Coastdown testing is conducted to determine the drag reduction achieved with aerodynamic modifications. Weight reduction and energy consumption improvements projected for a practical aerodynamic refuse vehicle are calculated. Improved aerodynamics and cooling system designs are integrated into the current vehicle technology and tested to quantify the benefits.

Ilhan Bayraktar
Optimization of Aerodynamic Properties of High-Speed Trains with CFD and Response Surface Models

A new procedure for optimization of aerodynamic properties of trains is presented. Instead of large number of evaluations of Navier-Stokes solver, simple polynomial response surface models are used as a basis for optimization. The suggested optimization strategy is demonstrated on two flow optimization cases: optimization of the train’s front for the crosswind stability and optimization of vortex generators for purpose of drag reduction. Besides finding global minimum for each aerodynamic objective, a strategy for finding a set of optimal solution is demonstrated. This is based on usage of generic algorithms onto response surface models. The resulting solutions called Pareto-optimal help to explore the extreme designs and to find tradeoffs between design objectives. The paper shows that accuracy of the polynomial response surfaces is good and suitable for optimization of train aerodynamics.

Siniša Krajnović
Design Considerations for Maximizing Cooling Package Performance

More stringent heavy vehicle emissions legislation demands considerably higher performance out of engine cooling systems. Presented is a study of various design parameters that can be used to maximize the cooling airflow for a Freightliner Class 8 truck. CFD analysis was used to analyze various fan shroud profiles, different fan immersions (overlap between the fan and fan shroud) and with two different engines. All of these design parameters lead to significantly different flow behavior inside the fan shroud and in the underhood region, in turn creating adverse or favorable pressure gradients. A series of isothermal CFD simulations are used to determine the effects of these flow characteristics on the radiator mass flow. For one of the simulation setup the predicted radiator coolant inlet temperature is compared to measured physical test data at different fan speeds. The methodology for the optimization of the cooling performance is outlined. It is shown that the presented simulation approach can provide accurate predictions of cooling airflow and coolant temperature.

Bhaskar Bhatnagar, Dan Schlesinger
Optimization and Correlation of a Class 8 Truck Cooling System

Development in engine technology to meet recent heavy vehicle emissions legislation has increased the demand on heavy vehicle cooling systems. The use of PowerFLOW®, a commercial computational fluid dynamics (CFD) software, allows a product development team to access a variety of cooling system improvements with no impact to the vehicle external appearance. This paper provides an overview of the PowerFLOW® modeling process and the results for several studies involving modifications to engine and cooling system parts. The design changes include the repositioning of the exhaust gas recirculation (EGR) cooler, changes to the fan diameter and position, and modifications to the exit shape of the shroud. Initial work focused on increasing cooling air mass flow and used a body force fan model with isothermal calculations. Results indicated only minimal changes with the EGR cooler repositioning, however, fan modifications resulted in a 13 percent cooling air massflow increase. The impact of the fan shroud exit shape on fan blade tip loss was computed with a multiple reference frame (MRF) fan model. Finally a detailed cooling system correlation study was performed involving a comparison to isothermal air mass flow rates and later thermal calculations involving heat exchangers modeled with PowerCOOL®

Clinton Lafferty, Kevin Horrigan, Ales Alajbegovic

Train Aerodynamics

Frontmatter
Aerodynamic Improvements and Associated Energy Demand Reduction of Trains

The importance for developing energy efficient rail vehicles is increasing with rising energy prices and the vital necessity to reduce the CO

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production to slow down the climate change. This study shows a comparison of different train types like regional and high-speed trains and provides estimation for improvements of the aerodynamic drag coefficient. Out of this estimation an assessment ofthe associated energy reduction is shown taking into account typical operational cycles with acceleration, constant speed and deceleration phases. Traditionally, aerodynamic improvements of high-speed trains were in the focus of the engineering community as the resistance to motion is increasing with the square of the velocity. However, this study reveals that it is necessary to consider regional and commuter applications equally. This transport sector is not only the one with the highest share in the market but exhibits also much higher potential for aerodynamic improvements then present day already optimized high-speed trains.

Alexander Orellano, Stefan Sperling
The use of Aeronautical Experimental Facilities and Measurement Techniques for the Aerodynamic Investigation of High Speed Trains

The development of future high speed trains is driven by commercial and ecological requirements which determine the increase of speed and payload while reducing weight and improving thermal and acoustical passenger comfort. To ensure the same level of safeness then for today’s rolling stock, additional issues like Reynolds-Number and Mach-Number dependencies have to be explored. The influence of unsteady flow phenomena as well as the impact of the train’s induced flow field on humans and infrastructure has to be investigated. For this purpose, special experimental facilities and techniques originally developed for aeronautical research proved to be extremely useful. For the investigation of viscous flow effects like separation and other boundary layer phenomena, a pressurized wind tunnel can realize high Reynolds numbers without entering the compressible flow regime. Validated results for the Göttingen high pressure wind tunnel show that it is possible to use extremely small models, down to a scale of 1:100, and to get good results if the accuracy of the model manufacturing process is high enough. A second possibility to increase the Reynolds number in a wind tunnel is to cool down the working fluid, thus increasing the Reynolds number up to a factor of 5.5. The main advantage of cryogenic wind tunnels is the possibility of independent adjustment of the Mach and Reynolds number. A third possibility to increase the Reynolds number is to change the working fluid of the facility, e.g. by using water instead of air. Advanced measurement techniques, which were originally developed for aeronautical research, allow a deep insight into the physical mechanisms governing the aerodynamic performance of high speed trains. A broad variety of experimental results is presented, showing that high Reynolds number facilities are in many cases an indispensable research tool for the aerodynamics of railroad vehicles.

Andreass dillmann
Reduction of Skin-Friction Drag on a Generic Train Configuration

Wind-tunnel experiments were carried out to determine the drag-reduction potential of dimpled surfaces on a generic train model as well as the influence of the dimpled surface on the flow field. Forces and moments were measured with an external six component balance. The flow field investigation was done by use of particle image velocimetry (PIV). The measurements were executed over a wide range of Reynolds numbers in a cryogenic wind tunnel. The use of this wind tunnel allows the variation of Reynolds number while the Mach number remains constant and vice versa. The experiments were undertaken with a standard set up i.e.: the models consist of a complete end car and half mid car (Model scale 1:20); a fresh boundary layer on the ground realized by splitter plate; no force closure between mid car and end car. Two similar models were investigated. The first model was manufactured with a smooth, polished surface. The second model was similar to the first but with a dimpled surface. The dimples were circularly shaped and arranged in a certain pattern. The results of force measurements show for some configuration, depending on the Reynolds number, an overall drag reduction of more than 20%. In consideration of the fact that the total drag of the investigated configurations is mainly determined by friction drag this drag reduction can only come from a decrease of skin friction drag. To ensure that this interpretation is correct, pressure measurements were done in the intercarriage gap for all configurations. The influence of the dimpled surface on the flow field is directly visible at the leeward vortex system, which is resulting from the flow under yaw angles. All characteristic values of the vortex become weaker than for the non dimpled configuration.

Sigfried loose
Head Pressure Effects of Trains and Locomotives – Engineering Calculation Approaches for Homologation Purpose

The head pressure pulse and the head pressure drop of a train are the pressure signals measured during the passage of the first few meters of the train at a fixed position in open air or in a tunnel, respectively. Train pressure pulses are part of the pressure loading on objects (like other trains) and persons. A new train is admitted to operation if measured data statistically satisfies certain threshold values. Nowadays train homologation in Europe predominantly relies on measurements, yet appropriate prediction tools are needed during the engineering process. The described pressure effects are well reported in literature and calculation methods are available providing for adequate accuracy. The methods are reviewed, examples from engineering applications and comparisons to data from full scale measurements are presented. The prevalent flow features are discussed covering a typical range of vehicle shapes and operational conditions (regional to high speed). The use of CFD methods is evaluated. The modeling error is estimated and error mitigation is attempted. A virtual homologation approach is proposed. The open fields of the issue are outlined.

Arnd Rueter
Numerical Analysis for Aerodynamics of High-Speed Trains Passing Tunnels

High-speed trains running at 200~350km/h will be operated on Chinese high-speed railways after 2010. Some of the high-speed railways in China will be built in mountainous areas. Many tunnels have to be constructed for the railways. However, the tunnel aerodynamic effect of high-speed trains is not very clear, especially the aerodynamic influence when the train is running in or out of tunnels. Examples are the effect of air pressure impulse on the train window strength and on the ear films of passengers, the relationship between the tunnel section size and the aerodynamic force acted on the train body, the relationship between the buffer structure of the tunnel entrance and the intensity of air pressure impulse, and so on. Based on Reynolds average Navier-Storkes equations of viscous incompressible fluid, and on two equation turbulent models, the aerodynamic effect of high-speed train in tunnels was investigated by means of the technology of moving grids in computational fluid dynamics method. Flow fields of high-speed train for 4 running speeds (200, 250, 300, 350km/h), 3 sizes of tunnel sections and 2 kinds of buffer structures for tunnel entrance were calculated. The results show that the aerodynamic effect of the tunnel’s blockage ratio is larger than that of train’s speed when the tunnel section size is smaller than a finite blockage ratio; the buffer structure for a tunnel entrance may reduce the aerodynamic influence effectively. Based on the simulation results of the investigation, some suggestion values between tunnel blocking ratio and train running speed were presented.

Jing Zhao, Renxian Li

Poster Session

Frontmatter
A Study of the Influence of Aerodynamic Forces on a Human Body near a High-Speed Train

A study of the influence of aerodynamic force on human body near the high-speed train was completed by the means of the technology of moving grids in computational fluid dynamics method. 60 running situations, which includes 3 types of locomotive shape, 4 running speeds of train combining 5 distances from human body to the sidewall of the train (human-train distances), were simulated. The 4 running speeds are 200km/h, 250km/h, 300km/h and 350km/h. The 5 human-train distances are 1.0m, 1.5m, 2.0m, 2.5m and 3.5m. The study results show that the aerodynamic force acting on human body strongly affected by the shape of the passing train head. The aerodynamic force produced at 1.0m human-train distance by extremely blunt train head at 350km/h speed is 7 times more than that produced by a streamline train head at the same operating condition. With an increase of human-train distance, the differences among the aerodynamic forces produced by the different shape of train head decreases. The decrease is about a quadratic function of the human-train distance, and has nothing to do with train speed. The ratio of the maximum aerodynamic force produced by train head and that produced by train tail at a given human-train distance is about a constant and independent of train speed. The ratio of the maximum aerodynamic forces for any two different human-train distances produced by train head or train tail is about a constant and has nothing to do with train speed. The direction of the aerodynamic force acting on the human body is nearly the same in different running conditions independent of train head/tail shape. The direction of the aerodynamic force changes over 300 degrees when train head or train tail passes. Based on the calculation results, formulas for calculating the aerodynamic force acting on the human body and the maximum wind speed near the human body were presented. Safety distances for people walking or working near passing train were recommended.

Renxian Li, Jing Zhao, Shu Zhang
Application of CFD to Rail Car and Locomotive Aerodynamics

CFD methods have been employed to solve a number of efficiency, safety and operational problems related to the aerodynamics of rail cars and locomotives. This paper reviews three case studies: 1) numerical models were employed to quantify the drag characteristics of two external railcar features; namely, well car side-posts and inter-platform gaps. The effects of various design modifications on train resistance and fuel usage were evaluated. 2) An operational safety issue facing railroad operators is wind-induced tip-over. A study was completed using CFD and wind tunnel tests to develop a database of tip-over tendencies for a variety of car types within the Norfolk Southern fleet. The use of this database in the development of a speed restricting system for the Sandusky Bay Bridge is also discussed. 3) Another safety issue involves the behavior of diesel exhaust plumes in the vicinity of locomotive cabs. Numerical simulations were performed for a variety of locomotives operating under a number of ambient conditions (wind speed, wind direction). The concentration of diesel exhaust at the operator cab window was quantified. Where appropriate, the studies provide information on the correlation of the CFD results with previously collected wind tunnel and field data.

James C. Paul, Richard W. Johnson, Robert G. Yates
Data Acquisition of a Tractor-Trailer Combination to Register Aerodynamic Performances

The design, production and verification of a data acquisition system to measure aerodynamic and mechanical characteristics of a tractor-trailer combination, operating in a real life environment, are presented. The main goal of this work is to derive a reference level of a truck with respect to its aerodynamic and mechanical performances. This way, if the truck is equipped with different aerodynamic aids, a correct comparison can be made between the aerodynamic drag reductions obtained by these devices. Also, a relation can be defined which links the aerodynamic drag reduction with fuel consumption savings. The acquisition system consists of an anemometer, which measures the wind speed and direction, and a two-axis inclination indicator, which is coupled to the FMS of the tractor via the CAN communication system and to the wipers to indicate if it is raining or not. The FMS of the tractor is measuring, for instance, the vehicle speed, the engine torque, the rpm, acceleration pedal position, cruise control, fuel rate, cargo weight and the like. All the measured data are registered on a hard disk and can be accessed through a simple USB connection. The processed data gives insight in the performance of the driver and in the aerodynamic behavior (C

D

value of 0.430) as well as the mechanical characteristics (power required breakdown; 47% rolling resistance, 39% aerodynamic drag and 15% mechanical losses; average speed of 75 km/h; fuel consumptio of 30 liters per 100 km) of the truck.

Gandert M.R. Van Raemdonck, Michel J.L. van Tooren
Automotive Testing in the DNW-LLF Wind Tunnel

The German Dutch Wind Tunnels is a foundation with the German Aerospace Center (DLR) and the Dutch National Aerospace Laboratory (NLR) as parent institutes. DNW operates ten aeronautical wind tunnels of DLR and NLR, located in Germany and the Netherlands. The main objective of the DNW organization is to provide the customer with a wide spectrum of wind tunnel test and simulation techniques, operated by one organization, providing the benefits of resource sharing, technology transfer, and coordinated research and development (R&D). The LLF is used for full-scale testing of trucks, buses, cars and alike. Heavy trucks are mounted in the 9.5m x 9.5m test section, whereby a wind speed of 60 m/s can be reached. The tested vehicle is connected to an external six-component balance with a resolution in drag measurement of 0.15N. In case of trucks, the front wheels and rear wheels are supported by air cushions. Flow visualization techniques (smoke, tufts, oil, laser light screen) are available, as well as PIV apparatus, pressure measurement equipment and an acoustic wall array for aerodynamic noise measurements. Smaller cars may also be tested with a moving ground plane of 10m long and 6.3m width. The belt has a maximum speed of 50 m/s. The poster will present an overview of the possibilities for automotive testing in the DNW-LLF wind tunnel.

Eddy Willemsen
An Experimental Study of Tractor Base Bleed for Heavy Vehicle Aerodynamic Drag Reduction

A significant contributor to heavy-vehicle aerodynamic drag is the tractor-trailer gap, especially when operating in a crosswind. At this condition, the freestream flow turns into the tractor-trailer gap, imparting a momentum exchange to the vehicle and subsequently increasing the aerodynamic drag. In common use today, tractor side-extenders provide significant drag reduction, but they are not without problems. Frequently damaged when the tractor pivots sharply with respect to the trailer, side extenders can incur additional costs for maintenance and repair. This issue can be alleviated by shortening extenders (thereby reducing their benefit) or devising an alternative drag-reduction concept. One such concept is tractor base bleed, in which air-flow is vented into the tractor-trailer gap through the back of the tractor. To study this concept, a wind-tunnel study was conducted for a generic 1:20-scale tractor-trailer configuration at width-based Reynolds number of 420,000. Delivered through a porous material embedded in the tractor base, the bleed flow was varied so as to generate velocities behind the tractor ranging from zero to 10% of the freestream velocity. Configurations were studied both with and without side extenders at two different tractor-trailer separation distances.

Bruce Storms, Jason Ortega, Kambiz Salari

CFD, Numerical Methods and Application

Frontmatter
Application of High Fidelity Numerical Simulations for Vehicle Aerodynamics

Interest in the use of the large eddy simulation (LES) technique for computation of turbulent flows of industrial relevance has increased considerably. This is in part due to the availability of low cost, powerful supercomputers. Today, a computer cluster capable of one TFOPS sustained performance for a complex flow LES calculation costs about one hundred thousand dollars. Another reason for the increased interest in LES is the recent added capabilities for multi-physics and integrated flow simulations. As part of Stanford’s DOE/ASC program, we have demonstrated and validated high fidelity simulations of multi-phase reacting turbulent flows in highly complex configurations in propulsion systems. The overarching problem in this program is simulation of flow through a complete jet engine, which is an extremely complex machine. LES computations of the entire engine flow are not feasible even with the most advanced supercomputers available. The Reynolds averaged Navier-Stokes (RANS) technique was used for the turbomachinery components and the combustor was simulated using LES. These simulations provided an early example of integrated simulations where different codes with different fidelity compute different portions of the system. A simulation environment had to be developed for the various codes to communicate with each other in an efficient and stable fashion. This integration technology and the associated science are suggested as the means for using LES in vehicle aerodynamics where Reynolds numbers are too high for high fidelity computation of the flow around the entire vehicle. LES can then be used in regions where RANS models are known to be inaccurate, and where LES provides access to flow quantities such as turbulent pressure fluctuations for predicting noise. Several examples of integrated simulations will be presented, including separation control for a high-lift system using synthetic jets.

Parviz Moin
Scale-Adaptive Simulation in the Context of Unsteady Flow Simulations

In the last decade, the spectrum of methodologies for the modeling of unsteady flows has significantly increased. Historically, the two choices were Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) methods. Both have severe limitations with respect to their application to engineering flows. URANS, typically produces no turbulent spectral information, even in regions, where time and space resolution would be sufficient to do so, whereas LES requires very high grid counts for modeling of wall-bounded flows at moderate to high Reynolds numbers. CFD users therefore had little choice than to concentrate on steady state RANS solutions, even for applications, where it was clear that these models are not adequate. Detached Eddy Simulation (DES) as proposed by Spalart in 1997, lead to a shift in paradigm, as it combined the elements of RANS and LES in a way that allowed the simulation of unsteady detached flows with available computing power. More recent studies by Menter and Egorov, have however shown that the inability of classical URANS models to resolve turbulent structures is not an inherent shortcoming of the URANS approach, but only related to the way the scale equations have historically been derived. After re-visiting an exact scale equation that Rotta had developed in the 1950s, it became clear that an important term was omitted in all scale equations, which resulted in the inability of classical RANS models to resolve unsteady structures. Closer inspection of Rotta’s equation shows that the second derivative of the velocity field should be included in the length scale equation. This so-called Scale-Adaptive Simulation (SAS) methodology behaves in many ways and for many applications similar to the DES formulation, but avoids some of the dangers of DES. On the other hand, it is not the goal of SAS to replace DES and it will be shown that both methods have their place in the spectrum of unsteady turbulence models. The paper will discuss the practical implications, but also the limitations of the SAS technology. Many results produced during the European research project DESIDER on external aerodynamic flow will be shown.

Florian Menter
Computational Simulation of the GCM Tractor-Trailer Configuration

Aerodynamic simulations were carried out for the Generic Conventional Model, a 1/8

th

scale tractor-trailer model, that was tested in the NASA Ames 7’x10’ tunnel. The computed forces are compared for the zero, ten and fourteen degree yaw cases while the pressure coefficients are compared to experimental data for the ten and fourteen degree cases. A DES version of the one-equation Menter SAS is used in these simulations. Overall forces as well as pressure distributions matched well for the fourteen degree case. For the ten degree case, the forces were in reasonable agreement while the pressure distributions indicated a need for tighter grid resolution as well as possibly advanced turbulence models.

K. Sreenivas, B. Mitchell, S. Nichols, D. Hyams, D. Whitfield
Full-Scale Simulations of Drag Reduction Devices for Class 8 Trucks

Computational Fluid Dynamics (CFD) simulations were performed to evaluate drag reduction devices on a modified full-scale version of the Generic Conventional Model (GCM) geometry. All simulations were performed with a moving ground plane and rotating rear wheels. A trailer base flap simulation was performed for comparison with drag reduction data from wind tunnels and track and road tests. A front spoiler and three mud-flaps with modest drag reduction potential were evaluated in view of their higher probability of adoption by truck fleet operators.

Ramesh Pankajakshan, Brent Mitchell, David L. Whitfield
Applicability of Commercial CFD Tools for Assessment of Heavy Vehicle Aerodynamic Characteristics

In preliminary validation studies, computational predictions from the commercial CFD codes Star-CD were compared with detailed velocity, pressure and force balance data from experiments completed in the 7 ft. by 10 ft. wind tunnel at NASA Ames using a Generic Conventional Model (GCM) that is representative of typical current-generation tractor-trailer geometries. Lessons learned from this validation study were then applied to the prediction of aerodynamic drag impacts associated with various changes to the GCM geometry, including the addition of trailer based drag reduction devices and modifications to the radiator and hood configuration. Add-on device studies have focused on ogive boat tails, with initial results indicating that a seven percent reduction in drag coefficient is easily achievable. Radiator and hood reconfiguration studies have focused on changing only the size of the radiator and angle of the hood components without changes to radii of curvature between the radiator grill and hood components. Initial results indicate that such changes lead to only modest changes in drag coefficient.

David Pointer, Tanju Sofu, Jimmy Chang, David Weber
Detached Eddy Simulations of a Simplified Tractor/Trailer Geometry

Detached Eddy Simulations (DES) are presented for the flow over simplified tractor/trailer geometry at zero degrees yaw angle. The simulations are conducted using a multi-block, structured computational fluid dynamics code. Coarse and fine grids of 3.8 million and 13.2 million cells, respectively, are used for the simulations. The analysis involves estimation of the period of initial flow transients as well as the period required to obtain statistical convergence, and suggests that prior DES studies for this case were not run long enough to ensure statistical independence. Time-averaged quantities compared with experimental data include vehicle drag, surface pressure and wake velocities. The drag coefficient predicted by the DES model matches closely with the experimental value; however, the DES model fails to accurately capture the details of the turbulent flow in the near wake of the trailer base. The simulations on the fine grid show significant improvement over the coarse grid results. Fourier analysis of the unsteady pressures in the base region suggests that the discrepancies in the near wake are/may be due to the improper transfer of turbulence information from the attached boundary layers (which are modeled with the Spalart-Allmaras RANS model) to the turbulent wake where LES-type modeling is used.

Christopher J. Roy, Harshavardhan A. Ghuge
A Hybrid RANS/LES Turbulence Model for use in the Simulation of Turbulent Separated Flows

Currently, there exists a lack of confidence in the computational simulation of turbulent separated flows at large Reynolds numbers. The most accurate methods available are too computationally costly for use in engineering applications. Using concepts borrowed from large-eddy simulation (LES), a two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence model is modified to simulate the turbulent wakes behind bluff bodies. This modification involves the computation of one additional scalar field, adding very little to the overall computational cost. When properly inserted in the baseline RANS model, this modification mimics LES in the separated wake, yet reverts to the unmodified form near no-slip surfaces. In this manner, superior predictive capability may be achieved without the additional cost of fine spatial resolution associated with LES near solid boundaries. Simulations using several modified and baseline RANS models are benchmarked against both LES and experimental data for a circular cylinder wake at Reynolds number 3900. These results reveal substantial improvements using the modified system and appear to drive the baseline wake solution toward that of LES, as intended. Further results include the simulation of the turbulent wake created by the Ground Transportation System (GTS), a simplified tractor-trailer geometry studied extensively by the Department of Energy for use in turbulence model validation.

Kambiz Salari, Paul Castellucci

Vehicle and Tire Spray and Vehicle Interaction

Frontmatter
Spray from Commercial Vehicles: A Method of Evaluation and Results from Road Tests

An accurate and repeatable measurement of truck-induced spray is required to develop and test spray-reducing devices. Such a system is described, based on a sequence of CCD-captured video images of a black and white chequerboard which was partially obscured by spray from a passing test truck. Images were analyzed to reveal the contrast changes, from which spray densities were inferred. Results of on-road trials are described and it was found that none of the tested wheel-mounted systems offered any statistically significant reduction in spray. Supporting track and wind-tunnel tests documented the flow vectors close to the truck; for an unmodified vehicle and when fitted with sideskirts and a cab-mounted add-on aerodynamic device. It was concluded from the flow field studies that the problem of vision impairment for a passing motorist would be significantly reduced when sideskirts and (for vehicles hauling a high load) correctly-matched cab roof deflectors were fitted. This offers the trucking industry the combined advantages of drag and spray reduction.

Simon Watkins
Experiments on Spray from a Rolling Tire

A novel laboratory apparatus has been built to understand the key mechanisms behind spray emerging from a rolling tire. Water leaving the tire from a single circumferential groove is analyzed using high-speed imaging. Visualizations reveal the formation of thin sheets of water connecting the roadway and the tire that eventually break into a droplet field. It is proposed that sheet breakup is the result of hydrodynamic instability. There is a preferred wavelength for disturbances on the sheet. After breakup, this preferred wavelength is preserved in slender ribs (or ligaments) that continue downstream until they disintegrate into droplets. Weber numbers based on the water density, tire circumferential speed and groove width vary in the range 1,900 – 60,300. The transition from sheet to spray is accelerated with increasing Weber number. Farther downstream, it is shown that droplet size and velocity distributions can be quantified as a function of Weber number.

Charles Radovich, Dennis Plocher
Computational Simulation of the Flow Field of a Filter System inside Self-Ventilated Road Tunnels due to Heavy Vehicle Traffic

This paper combines heavy vehicle aerodynamics with environmental considerations. The problem of air pollution in urban environments is strongly connected to the emissions of local traffic. Moreover, by-pass road tunnels in densely populated areas use often longitudinal ventilation systems, which produce high concentrations at the outlet portal. An EU-LIFE project started to investigate the potential and the feasibility of combining dust filters with standard noise protection systems. As part of the project one application deals with the reduction of pollutant emissions from road tunnel portals. For the investigation of the effectiveness of these filters, simulations of a simplified heavy vehicle shape were conducted using Computational Fluid Dynamics (CFD). The first part of this paper deals with the validation of the CFD tool. Therefore, the Ground Transportation System (GTS) in the NASA Ames 7feet by 10feet wind tunnel was simulated and the results were compared to measurements. The second part covers the considerations of the flow field induced by heavy vehicle traffic within a highway road tunnel equipped with filters. As a result, the amount of the volume flow through the filters for one complete heavy vehicle cycle is displayed.

Florian Iser, Raimund A. Almbauer
Experiments and Calculations Relevant to Aerodynamic Effects during Highway Passing Maneuvers

Aerodynamic effects during highway passing maneuvers are still not well documented. To better understand these effects, a 40% car-truck overtaking process has been carried out in the BMW wind tunnel. As a first step, the car aerodynamics has been measured without the truck to establish the reference pressure distribution for subsequent tests. The overtaking process has been approximated by fixing the truck model at eight stationary positions relative to the car model. This approximates the overtaking process as a quasi-stationary process. The reference calculations are performed with a new variant of ¯v

2

- f model, the so-called ζ-f model (Hanjalic et al., 2004). Furthermore, the calculations are also performed by using recently proposed Partially-averaged Navier Stokes (PANS) model (Girimaji et al., 2003, Girimaji and Hamid, 2005) in order to capture unsteady effects more correctly compared with the unsteady RANS. Because of its extensive reference database, the well-known Ahmed body benchmark (25 degrees) was computationally investigated as an introductory case with respect to the comparative assessment of the RANS and PANS approaches. A validation procedure for the PANS method is then conducted by computing the single passenger car (40% BMW model).

B. Basara, S. Girimaji, S. Jakirlic, F. Aldudak, M. Schrefl

Drag Reduction

Frontmatter
Design & Test Techniques for Drag Reduction at Swift Engineering – A Racecar Manufactures Perspective

Swift Engineering designs and builds high performance racecars and aircrafts. Techniques developed in this fast paced environment are relevant to transport industry. Experimental and analytical design example will be presented.

Mark Page
Summary of Full-Scale Wind Tunnel Tests of Aerodynamic Drag-Reducing Devices for Tractor-Trailers
Jason Leuschen, Kevin R. Cooper
A Fleet Operator’s Perspective on Commercial Vehicle Drag Reduction

The research establishment has proven the potential fuel-savings for many devices/modifications for commercial trucks, however many of these developments remain in limited use. The primary reason that these substantial fuel-savings are not being realized is that fleet operators have chosen not to adopt them in their current form. Why have roof fairings been accepted while trailer skirts haven’t? The reasoning behind the selection is logical, and often not obvious, so to succeed the development community must understand the environment of the fleet operator and respond with appropriate technology. This paper will address the considerations of a typical fleet operator when evaluating new technologies. A discussion and examples of the following issues will be given

1. Introduction to Robert Transport: size of fleet, typical equipment, types of cargo, description of routes.

2. Operating Costs: a. Cost of installation, maintenance and operation in terms of cash and lost productivity.

b. Weight of the device vs. cargo when the amount of paying cargo is limited by weight not volume.

c. How do we measure the savings from the device? Track tests are expensive and relatively inaccurate and fleet tests can be statistically irrelevant.

3. Operating Procedures: How compatible are the devices with current roads, shipping yards and loading facilities?

4. Human Resources: There is a shortage of qualified drivers so it can be difficult to retain drivers if the technology adds to the driver’s workload, is unpleasant or adversely affects driver comfort.

5. Reliability: The cost of unplanned downtime is significant, so the technology is expected to operate reliably, for 10 years or longer, in a variety of harsh conditions including extreme temperatures, wind, road salt, dust. Another consideration is resilience to damage caused by the drivers.

6. Safety: Visibility and crash worthiness.

Réjean Laflamme
Class 8 Vehicle Fuel Savings using Sealed Single and Dual Open Aft Cavities
Kenneth D. Visser, Kevin Grover
A Novel Approach to Heavy Vehicle Drag Reduction

The recent volatility of fuel prices and the potential of explicit CO

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emission control regulations have caused aerodynamic performance to become a critical component of heavy vehicle development. The use of traditional computational fluid dynamics (CFD) simulation for aerodynamic drag prediction on fully complex production geometries has not been adopted for a number of key reasons: the high level of expertise required, simulation time-to-completion, and accuracy versus experiment. This paper demonstrates that the proprietary, Lattice-Boltzmann based simulation method of EXA Corporation delivers valuable results on fully complex geometry, allowing aerodynamic optimization in the concept and design phase. Included is an overview of the simulation method and results for two fully detailed open grille Kenworth models: the T603 and T2000. Comparisons are made to full scale drag meter testing. Additional results are provided for several trailer drag reduction devices including a full gap seal, side skirts, boat tail, and wake boards. Advanced post-processing of the simulation results is used to study transient flow structures and highlight the physics involved with the drag reduction of these devices.

Alec Wong, Kevin Horrigan
European Truck Aerodynamics – A Comparison Between Conventional and CoE Truck Aerodynamics and a Look into Future Trends and Possibilities

The aerodynamic situation for trucks on the European market differs from that in North America on a number of points. Perhaps the most significant difference is that in Europe trucks are of the CoE configuration (Cab over Engine) and in North America trucks are of the conventional type with a hood. Another major difference is that trucks in Europe are speed limited to 90 km/h (56 mph) which of course means that aerodynamics as a whole has less of an impact there. These differences are primarily dictated by different legislations, which in turn have a lot of different side effects. This paper will high-light some of the differences and their impact on aerodynamics, as well as taking a look at possible future ideas such as: extended front or short nose, ride height adjustments, convoy driving, etc.

Linus Hjelm, Björn Bergqvist
Advanced Experimental Methods for the Analysis and Aerodynamic Design of Heavy Vehicles

Extensive knowledge exists in the testing of 1/8th scale, Class 8 tractor trailer models within fixed floor wind tunnels. This size of model has proven to correlate well with in a Reynolds number ranging between 1M and 6M. Prior testing is well documented on a Generic Conventional Model (GCM) in the NASA AMES 7x10ft and 12ft wind tunnels. Within this prior research into Heavy Vehicle Aerodynamics, it has been identified on numerous occasions that improved accuracy will allow for greater understanding of the flow field structure in the underbody and internal flow regions. The aim of this paper is to summarize the new research conducted at the Auto Research Center (ARC), a 50% rolling road scale wind tunnel facility in Indianapolis, Indiana. ARC has tested a rolling road 1/8th scale tractor trailer at 50m/s constant dynamic (approximately 1M Re). The model features fully articulated suspension & axle systems, engine bay detail for internal flow simulation, realistic radiator blockage, and an automated model motion system capable of controlling the model in roll, heave, pitch & yaw. To remain consistent with the previous testing conducted by NASA AMES, a replica of the GCM tractor and trailer shapes were used for the upper aerodynamic surfaces. The test objectives initially included a demonstration of correlation between the ARC and NASA wind tunnels with the rolling road switched off. This baseline is then compared to data obtained with the rolling road on, allowing the impact of 18 rotating wheels & tires on the flow structure to be visualized and analyzed. Further studies are presented on the effects of improved detail in the underbody regions, and on the effects of internal & cooling flows as applied to the GCM model. Future work at ARC will use detailed cab bodywork for analysis of specific OEM tractors & trailers.

Mike Camosy, Andre Brown, Henri Kowalczyk, Gaylord Couthier
Backmatter
Metadata
Title
The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains
Editors
Fred Browand
Rose McCallen
James Ross
Copyright Year
2009
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-85070-0
Print ISBN
978-3-540-85069-4
DOI
https://doi.org/10.1007/978-3-540-85070-0

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