The turbocharger for a four-stroke gasoline engine of the Formula SAE racecar

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Introduction
In any motorsport competitions, for safety reasons, any restrictions on engines are applied: in terms of power, volume, etc. One type of limiter is an air restrictor, which is a calibrated hole in the intake manifold. The most effective and permitted way to increase the power of an engine with a restrictor is to install a turbocharger unit.

The purpose and objectives of the work
The purpose of the work is to conduct research on increasing the power of a single-cylinder, inline 4-stroke engine, with an air intake restrictor, by installing an air boost unit.
The calculation was carried out by simulating the operation of a single-cylinder, inline 4-stroke engine, with an air intake restrictor, and a boost unit. To simplify the calculation, the restrictor was taken as a direct diffuser.
The calculation was carried out in the Ricardo WAVE software package, which can perform complex calculations of various intake and exhaust systems, with and without a restrictor, with and without boost units.
Before constructing the design model of the engine without turbocharging, but with a restrictor, the design model of the engine without a restrictor was tested and compared with the characteristics of the manufacturer. When constructing and calculating the engine in the factory version of the intake elements, parameters close to those given by the manufacturer were obtained, namely power - 31 kW; torque – 34 Nm, against the calculated 32 kW in power and 35 kW in torque.

The object of the study
The object of the study is a single-cylinder 4-stroke inline engine manufactured by Austria KTM LC4. The volume is 654 cm3, the cylinder diameter is 102 mm. The piston stroke is 80 mm, the lubrication system with a dry sump, has excellent mass-dimensional characteristics and differs from similar engines in good performance in power and torque at low speeds (3).
Installing a restrictor on a turbocharged engine requires solving a number of problems. Such as: optimization of the size required to smooth out air pulsations in front of the intake valve of the air receiver; optimization of the length and shape of the inlet pipe located between the receiver and the intake valve of the engine; optimization that ensures low hydraulic losses and a uniform velocity field at the inlet to the compressor of the turbocharging unit of the nozzle shape with a restrictor. [2]
Solutions to these problems are described in the Cal Poly Turbocharging System Development project [1]. The intake system of the engine of the SAI "Cal Poly" Formula team includes an air filter, throttle valve, restrictor, compressor, receiver and inlet pipe ("pipe") (Fig.1).

Figure 1. The intake system of the engine of the SAI "Cal Poly" Formula team.
Variables Unit Value
Receiver volume 1500 cc
Pipe length (pipe-valve) 225 mm
Compressor inlet pipe length 50 mm
The length of the pipe between the compressor and the receiver is 110 mm
The angle of divergence of the restrictor nozzle is 7 degrees

Intake receiver
The Ricardo WAVE program was used to analyze the effect of the intake receiver size on the engine characteristics. The results are shown in the diagram below.
Figure 2. The effect of the volume of the intake receiver on the torque.

From the data obtained (Fig.2) it can be seen that the torque increases only to certain volumes of the receiver, then its values change slightly. It would seem that the best option in this case is about three liters. However, there is a compromise in this case, since the receiver is located between the throttle and the engine intake valve. If you make the receiver very large, the driver's feedback to the gas pedal (throttle) will suffer. [3] This means that designers have to find a balance between the efficiency of the receiver and the feedback from the motor. Based on the empirical experience of other Formula Student competition teams, a volume corresponding to 90% of the best torque and power indicators was selected, 1500 cc
. The length of the inlet pipe
The inlet pipe is responsible for resonant effects in the intake tract. In atmospheric internal combustion engines, a short branch pipe gives an increase in power at high speeds, but a loss in power at low speeds. The effect of a long pipe is exactly the opposite. Turbocharged engines are characterized by the use of a longer nozzle than atmospheric ones, since this gives, due to resonant effects, an increase at low speeds, where the turbocharger is not yet operating at full power. [4]

Figure 3. The dependence of the torque on the length of the inlet pipe.
From the data obtained (Fig.3) it can be seen that the length of 225 mm gives one of the most gentle torque curves, which allows for more efficient use of the engine on the car.
Pipe with a restrictor
The correctly calculated shape of the nozzle with a restrictor gives a significant increase in the output power and torque of the engine. In the end, the best shape was chosen to be a tapering-expanding nozzle. Together, the correctly calculated shape gave a 15% increase in power, compared with a simple washer design. Below (Fig.4) is a graph of the dependence of power on the design of the pipe with a restrictor. The gray line is a design in the form of a simple flat washer, the red line is a divergent nozzle.

Figure 4. The influence of the shape of the nozzle with a restrictor on the engine power.
An equally important parameter is the angle of expansion of the nozzle with a restrictor. The results of the simulation with different angles of expansion are shown below.

Figure 5. The effect of the divergence angle of the nozzle with the restrictor on the engine power.
It can be seen from the simulation results (Fig.5) that the nozzle expansion angle does not greatly affect the peak values of the engine characteristics, however, it has a noticeable effect in smoothing the torque curve, which has a sufficient role during driving the car on the track. For this reason, an angle of 7 degrees was chosen. [5]

The lengths of the inlet and outlet pipes of the compressor
The extreme two factors affecting the characteristics of the engine are the lengths of the inlet and outlet pipes of the compressor. The inlet pipe is located between the restrictor and the compressor, the outlet between the compressor and the receiver (however, since 2015 the scheme in the regulations has been changed – now there is a throttle valve after the compressor, and only then the receiver). However, these two parameters do not strongly affect the characteristics of the motor. Figure 6 below shows the effect of the inlet pipe on the torque of the engine. From the results obtained, a length of 110 mm was chosen, since the characteristic of the moment with it turns out to be the most smoothed.

Figure 6. The effect of the length of the inlet pipe on the torque of the engine.
Conclusion
The turbocharging unit system described above (with a restrictor) of the four-stroke engine of the Formula Student racing car has shown a significant advantage over the atmospheric version of the engine. For example, a turbocharged engine has 31 kW and a torque of 34 Nm, whereas a turbocharged engine shows characteristics of 40 kW and 54 Nm, which gives a significant increase in the dynamics of a racing car. Thus, the installation of a boost unit is able not only to solve the problems associated with the restrictor, but also to significantly improve the key performance of the engine. To further improve the boost system, and to find ways to further optimize engine parameters, three-dimensional mathematical modeling is required.

About the authors

Alexander A. Dementiev

Author for correspondence.
Email: w1941w@yandex.ru
ORCID iD: 0009-0001-2311-0849
SPIN-code: 7826-5560

Associate Professor of the Power Plants for Transport and Small Energy Department

References

Supplementary files

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2. Fig. 1. The intake system of the engine of the Cal Poly Formula SAE team.

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3. Fig. 2. Influence of the intake receiver volume on engine torque.

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4. Fig. 3. Dependence of engine torque on the intake nozzle length.

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5. Fig. 4. Influence of shape of the nozzle with a restrictor on engine power.

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6. Fig. 5. Influence of divergence angle of the nozzle with a restrictor on engine power.

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7. Fig. 6. Influence of the intake nozzle length on engine torque.

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