Variable-Geometry Turbochargers

Thomas Veltman
October 24, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010

Turbocharger Parts and Function

Fig. 1: A cartoon schematic of a turbocharged engine. Exhaust flows through the tubine, which drives the compressor, which feeds the engine more air, allowing more fuel to be burned.

A turbocharger consists of two fundamental components, a turbine and a compressor. The function of the turbine is to scavenge waste exhaust heat and translate it into rotational motion. This rotational motion is then used to drive the compressor, which compresses air for the consumption of the engine. The purpose behind the turbocharger is to overcome the fundamental drawback of the internal combustion engine, its volumetric efficiency limit. An engine drawing air in from the atmosphere can only achieve a volumetric efficiency of up to 100%, meaning that the pressure inside an individual cylinder is equal to atmospheric pressure while the intake cycle is occurring. Since the amount of power that can be extracted from an engine is proportional to the fuel it burns, and the fuel consumption is limited by the amount of air present in a cylinder, times the number of cylinders (the so-called "displacement"), the volumetric efficiency limit effectively constrains the power of the engine. To make an engine more powerful, one must increase its displacement.

Unfortunately, the consequence to this is that the engine burns more fuel under all conditions, adversely affecting its fuel mileage. The turbocharger provides an alternative means of extracting more power from a given displacement by increasing the volumetric efficiency to points significantly above 100%. The pressure in the cylinders is greater than atmospheric, thanks to the compressor on the turbocharger. One might wonder how this improves the fuel-economy situation at all. Because of the way gasoline engines are controlled, it turns out that a turbocharger can be set up to only function when one wants additional power, so that most of the time, the turbocharger doesn't adversely affect fuel economy (perhaps a 5% reduction overall), but when needed, the engine is capable of turning out significantly more power. [1]

Fuel Economy and Turbocharging

Obviously burning more fuel will produce more power, but by producing extra power only when needed, overall fuel economy can be generally conserved. Turbocharging an engine not purpose-built for the task (i.e. bolting a turbo onto your car) will result in a slight loss of fuel economy under low-load conditions (i.e. driving along on the highway and not accelerating), but increase the power output significantly when the gas pedal is depressed. A reasonable approximation for power increase is the manifold pressure ratio (PR). This is the ratio of engine pressure to atmospheric pressure. When the turbocharger is running, it is creating a PR greater than 1. To estimate the power output of such a bolt-on setup, simply multiply the horsepower of the engine before the turbocharger was installed by the PR the turbocharger produces. A PR of 2 will generate approximately double the "factory" horsepower. Note, of course, that doubling your horsepower doubles your fuel consumption, so under load your fuel economy will be significantly worse. However, the fact that the turbocharger produces power-on-demand means that the displacement of the engine can be lowered without sacrificing power when it is desired.

An ideal solution is to produce small engines which can tolerate high pressure ratios safely, thereby allowing for the greatest reduction in fuel demand during normal operation without sacrificing maximum power production. It is a relatively straightforward engineering task to redesign the engine such that the intake pressure can be raised. It turns out that lowering the compression ratio from 11:1 to 8:1 allows a turbocharger to generate a PR of about 1.6. One could decrease the displacement of the engine by 34% and still achieve the same power. This reduction in compression ratio results in a 10% loss in efficiency. As mentioned above, the turbo itself will increase fuel consumption by approximately 5% owing to exhaust restriction.

It is now useful to examine a real-world example. The 2001 Honda Civic (ES) has a 1.67L, 127 horsepower engine (with a compression ratio of 9.9:1), yet only requires about 15 horsepower to overcome air resistance at 65 miles per hour. [2] However, the engine performance community suggests that compression ratios of over 11:1 are safe on pump gas. [3] If one reduces the engine's displacement by 34%, the approximate power over the whole range of operation will be about 34% less. At 65 miles per hour, the regular engine produces about 55 horsepower. Therefore the turbocharged engine, without the turbo running at that speed, produces only 37 horsepower. The wasted horsepower (and thus fuel) has been reduced by approximately 55% by lowering the displacement. One must then correct for the turbo restriction and the compression ratio decrease, which will result in a net 36% reduction in wasted fuel, or a 28% reduction overall.

The Drawback of Traditional Turbochargers

Fig. 2: Effect of A/R ratio on exhaust flow speed and flow capacity.

The turbines driving turbochargers are characterized by two chief parameters: A/R ratio and turbine radius. The A/R ratio is the ratio of the Area of the exhaust gas passage to the Radius from the center of the turbine wheel to the point defining the center of that area1. Turbochargers are designed such that the A/R ratio is always a constant: as the exhaust gasses are directed closer towards the turbine wheel, the area the gas flows through gets smaller. Funneling the exhaust down into a smaller area produces a higher velocity stream; a higher velocity stream imparts more power to the turbine wheel. It is clear, then, that the turbine can drive the compressor at a higher speed (and thus produce a greater pressure inside the engine) when the A/R ratio is low. Unfortunately, as gas velocity increases, so does the exhaust gas pressure. For the same exhaust flow rate from the engine, the larger A/R will build up less pressure than the smaller A/R. When designing a real-world system, both of these factors are important. Using traditional turbochargers, an engine designer would have to balance desire for high exhaust flow to drive the compressor against low back-pressure in the exhaust system, which robs the engine of efficiency, and in extreme cases, significantly reduces the amount of power that can be gained from an engine.

Effectively, this means that there is a narrow range of operation of a turbocharger/engine combination in which the system is capable of putting out significantly more power, with tails at either end where power is building up or falling off. This distribution of power is pivotal to the individuals that actually sell the cars, since they have to show people on test-drives that the car is a powerful one. Unfortunately, because of the relationship between A/R ratio and exhaust flow, a designer must choose between having a quick onset of power (which subsequently robs the engine of power at higher speeds) or a slow onset of power (which results in a more powerful car at higher speeds). Typically, manufacturers interested in selling a lot of cars will choose the former option and cripple the car at high speeds in favor of 0-30 mile-per-hour acceleration. Conversely, manufacturers interested in selling high-performance cars choose the latter option, which makes the car seem like it isn't very quick at low speeds, but once on the highway, the car shines as the turbocharger is functioning in its optimal range. However, the speeds in which you might want large amounts of power tend to be between 25 and 70 miles-per-hour, as this is a reasonable range where you would want to get up to highway speed, or alternatively pass a slower-moving car on the highway. Therefore, it is clear that not every turbocharged car is really operating in the true ideal range, but rather in a range specifically designed to sell a car to otherwise ignorant buyers.

Variable-Geometry Turbochargers Provide the Solution

Fig. 3: Diagram of Variable Geometry Mechanism in a Holset turbocharger, side-view. Inset shows the front view of the sliding plate-and-vane mechanism. The dashed line is the second fixed plate. Turbine wheel removed for clarity in both images.

The crux of the problem lies in balancing performance design with A/R ratio. However, a relatively new technology is available which obviates this need for balance. The variable-geometry turbocharger has a mechanism by which the inlet area can be varied to achieve the optimal A/R for a given flow rate. This is achieved by varying a set of aerodynamic vanes which direct the exhaust gas flow onto the turbine wheel. I recently had the opportunity to dismantle a variable geometry turbocharger manufactured by Holset, and I found that their vanes are fixed to a sliding plate. The vanes and plate can be moved as a unit so that the plate can partially obstruct the inlet to the turbine, thus reducing the A/R ratio. This plate can be moved such that the inlet is almost completely obstructed, or retracted fully to provide no resistance to flow. The fixed-position blades slide in and out of cutouts in a second, fixed plate, which is used to ensure that exhaust can only travel across the blades.

Using this variability, it is possible to keep the turbine working under virtually all engine speeds. By dropping the A/R ratio at low engine RPM (when exhaust flow is low), and then increasing gradually as RPM increases (and thus exhaust flow increases), inlet velocity can be kept high without increasing exhaust back-pressure significantly. This, in turn, means that the turbocharger can function over the entire operating range of the engine. In fact, since a real engine does not have a flat power curve with respect to RPM, the turbo could be controlled in such a way to artificially flatten out the curve so that the engine has the same power output regardless of its speed. Doing so makes designing a transmission significantly easier, and allows one to use gear ratios designed for better acceleration, which further improves the performance of a vehicle.

Fig. 4: Hypothetical power curves for an engine with and without a variable turbo. Here the turbo is used to artificially flatten out the power curve.

As discussed above, turbo size and performance are inextricably linked. Using conventional turbochargers, an engine will only produce extra power in a certain range, defined by the A/R of the turbine. This creates dead spots in performance commonly referred to as "lag". However, with the variable-geometry turbocharger used in place of a traditional turbocharger, the engine can match the power of the normally-aspirated engine instantaneously. The driver will notice no difference in acceleration between the two vehicles (the variable turbo has no "lag"), but will certainly notice the difference at the gas pump.

Drivability may seem like a trivial point, however the variable-turbo has one other main advantage related to its unique design. A turbocharger effectively scavenges waste heat from the engine, so a proper design puts the turbo as close to the engine as possible to minimize heat losses. Unfortunately, the turbo also works best when there is no restriction on the outlet, and placing the turbo right after the engine means that one must put catalytic converters and mufflers after the turbocharger, which significantly reduces the turbo's ability to operate efficiently. Instead, with the variable-turbo, one can install the unit after the catalytic converters (the turbo itself acts as a surprisingly good muffler). Even though some exhaust heat will be lost, the catalytic converter will maintain some of the heat (gasoline engine exhaust tends to be about 1500 °F, while a catalytic converter operates somewhere around 1200-1300 °), and the sections of pipe between the converter and the turbocharger can be insulated to further reduce losses. [4,5] The variable-geometry system can then more than make up for the heat losses incurred, and in fact, this situation is preferable, because lower turbo temperatures mean that the turbo needs fewer expensive materials to guard against melted components and the whole system will be more reliable. The catalytic converters will still keep the emissions under control, and the turbo can perform well under those conditions.

Math, For Those So Inclined

The treatment of the Honda Civic is an approximate one. The density of air was taken to be 1.18 kg/m3, the drag coefficient was assumed to be 0.32, which is less than the average for a passenger car, and the frontal area was approximated as a rectangle of the dimensions published in the 2001 Honda Civic owner's manual. Drag power is given by the equation [6,7]

Where ρ is the density of air, v is the vehicle speed, Cd is the drag coefficient, and A is the frontal area.

The power required to overcome air resistance works out to be about 10.3 kW (14 hp), which I rounded up to 15 hp. The power an engine produces scales approximately linearly with increasing RPM, up to the peak power. [8] Using this assumption, the Honda's power at 65 MPH was estimated based on test data from Car and Driver magazine, where the peak occurs at 6300 RPM, and 65 MPH is 3100 RPM in fifth gear. [9] Engine efficiency is given by [10]

and pre-ignition cylinder pressure is given by [11]

where CR is the engine's compression ratio, γ is the specific heat ratio (1.4 for air), and P0 is the pressure inside the cylinder at its largest volume.

Other Points to Consider

Modern engines have the benefit of electronically-controlled fuel injection and spark ignition, which means that these parameters can be varied to reduce or eliminate undesirable and destructive events which can occur inside the engine, namely spark knock. Spark knock occurs when some of the fuel/air mixture inside the piston explodes much more violently than the rest of the mixture, resulting in a large pressure spike inside the cylinder, which is extremely harmful to an engine; spark knock becomes more likely as the pressure of the cylinder increases. [12] Reducing spark knock can be achieved by lowering the compression ratio (CR, the ratio of the total cylinder volume to the compressed cylinder volume), however lowering the CR decreases an engine's efficiency. Today's engines can operate at a CR of about 11:1 while still running on regular unleaded gasoline (increasing the octane rating of gasoline also decreases knock, but at the expense of fuel price). [3,12]

Since cylinder pressure is an important factor affecting spark knock, the pre-ignition cylinder pressure can be estimated based on an engine's compression ratio, and then used as a proxy for knock threshold. For these modern engines, the resulting cylinder pressure is about 29 times atmospheric pressure. It should be noted that there are purpose-built engines that can sustain pressure ratios that are higher, but I am interested in estimating for the average engine. If the compression ratio is dropped from 11:1 to 8:1, the pressure ratio that the engine will tolerate is about 1.6, meaning that a turbo could pressurize the system to 1.6 times atmospheric pressure before knock became a problem.

© Thomas Veltman. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] C. Bell, Maximum Boost: Designing, Testing and Installing Turbocharger Systems (Bentley Publishers, 1997), pp 13, 31-33.

[2] 2001 Honda Civic Owner's Manual.

[3] S. Oldham, Sport Compact Car: Engine and Driveline Handbook (Motorbooks International, 2003) p. 124.

[4] A. E. Schwaller, Total Automotive Technology (Thomson Delmar Learning, 2005) p. 168.

[5] G. J. Barnett, Automotive Fire Analysis: An Engineering Approach (Lawyers and Judges Publishing, 2008) p. 36.

[6] S. T. Moeller, Energy Efficiency: Issues and Trends (Nova Science, 2002), p. 68.

[7] H. C. Smith, The Illustrated Guide to Aerodynamics (TAB Books, 1992), pp. 65, 119.

[8] V. Hillier and P. Coombes,Fundamentals of Motor Vehicle Technology (Nelson Thornes, Ltd., 2004) p. 45.

[9] B. Winfield, "Honda Civic EX Coupe - Road Test," Car and Driver, November 2009. (Specification Sheet available here.)

[10] V. Kadambi and M. Prasad, An Introduction to Energy Conversion, Vol. 2 (New Age International, Ltd., 1974) p. 80.

[11] J. E. Emswiler, Thermodynamics (McGraw-Hill, 1921) p. 99.

[12] C. F. Taylor, The Internal-Combustion Engine in Theory and Practice: Volume 2: Combustion, Fuels, Materials Design (MIT Press, 1977) pp. 37, 62, 144.