## 2 Materials and Methods  
As shown in Figure 1, a test bench consists of a motor-driven, a load-absorbing, and a data acquisition subsystem, and the test engine. The motor, hysteresis brake, and test engine are mounted in series on the base plate through couplings. The motor is a drive unit that drives the entire system to rotate at a specified speed. The hysteresis brake acts as a load-absorbing device that balances the test engine's output torque and the motor's driving torque. A frequency converter regulates the motor speed by changing the frequency and voltage, whose output frequency can be adjusted from 0 Hz to 600 Hz. The hysteresis brake can deliver a maximum of 200 W of braking power under the forced cooling condition and with a linear relationship between the control current and braking torque. An adjustable DC-regulated power supply is used to control the input current of the hysteresis brake for the braking torque regulation. The test bench is also equipped with a photoelectric tachometer (DT2234B, SUWEI Electronic Technology, Shenzhen, China), a K-type thermocouple (DM6801A, VICTOR Instrument, Shenzhen, China), and a micro-flow meter (MF5706-N-25, SIARGO Ltd., Mipitas, CA, USA) for measurement of the operating parameters, such as engine speed, cylinder block temperature, and intake flow. In addition, a weighing method is used to measure fuel consumption. A more detailed principle and layout diagrams for the test bench can also be found in References [18;32]. A piezoelectric crystal pressure transducer (6052B, Kistler, Winterthur, Switzerland) converts the in-cylinder combustion pressure into a charge signal. The pressure sensor has a sensitivity of \(-\)20.06 pC/bar and does not vary by more than \(\pm\) 0.5% over a temperature range of 150 \({}^{\circ}\)C to 250 \({}^{\circ}\)C. The pressure sensor can be mounted on the cylinder head of the test engine with a 5 mm threaded hole. The crank angle is identified by a 36-1 gear disc coaxially coupled to the crankshaft of the test engine. A Hall sensor (MP-935, ONO SOKKI, Yokohama, Japan) converts the change in the magnetic field due to the rotation of the toothed disc into a voltage signal that will be conditioned into a sawtooth square wave of 0.1 deg crank angle (CA) by a pulse multiplication algorithm built in a data analysis software suite that will be described later. The combustion pressure and crank angle signals are sent to a data acquisition module (SIRIUSi-HS, DEWEsoft, Ver. SP5) characterized by high-bandwidth transient recording (15 MS/s) and an ultra-high dynamic, anti-aliasing data sample. Based on the in-cylinder combustion pressure and crank angle signals, a software suite (X3, DEWEsoft, Ver. SP5) uses a zero-dimensional thermodynamic model to analyze the in-cylinder combustion in real time and calculate the combustion parameters and their statistical characteristics. Moreover, the top dead center (TDC) is thermodynamically determined from the in-cylinder pressures of the motored test engine, and pressure signal drift due to temperature changes is eliminated using a thermodynamic zero-point correction method. Table 1 gives the technical data of these measuring instruments. Figure 1: Test bench: 1—frequency converter; 2—digital multimeter; 3—micro-flow meter; 4—toothed disc; 5—high-speed motor; 6—hysteresis brake; 7—dial indicator; 8—test engine; 9—fuel weighing equipment; 10—fuel tank; 11—crank angle sensor; 12—pressure sensor; 13—data acquisition module; 14—data monitor and analysis. The test engine is a single-cylinder, air-cooled, two-stroke reciprocating piston internal combustion engine with a displacement of 0.547 cc. The cylinder bore and stroke of the test engine are 9.0 mm and 8.6 mm, respectively, in the millimeter-scale range. The test engine uses the HCCI combustion mode fueled by a mixture of 40% kerosene, 34% ether, 24% castor oil, and 2% isopropyl nitrate (isopropyl nitrate is used for ignition improper). The fuel properties are shown in Table 2. The test engine was remodeled for in-cylinder combustion diagnostics.