Johannes Trost

Schrodinger operators with complex potential but real spectrum

Abstract Several aspects of complex-valued potentials generating a real and positive spectrum are discussed. In particular, we construct complex-valued potentials whose corresponding Schrodinger eigenvalue problem can be solved analytically.

Characterization of four potential laser-induced fluorescence tracers for diesel engine applications

Four potential laser-induced fluorescence (LIF) tracers, 1-phenyloctane, 1-phenyldecane, 1-methylnaphthalene, and 2-methylnaphthalene, are characterized for diesel engine applications. These tracers, embedded in the diesel primary reference fuels n-C₁₆H₃₄ and iso-C₁₆H₃₄, match the relevant physical properties of commercial diesel fuel much better than the commonly used toluene/iso-octane/n-heptane tracer-fuel system does. The temperature and pressure dependencies of the fluorescence intensities and spectra were measured in a flow cell in nitrogen for each candidate tracer molecule. The results show that the signal intensities of the methylnaphthalenes are about two orders of magnitude higher than for 1-phenyloctane and 1-phenyldecane and show a strong temperature but no pressure, dependence. An analysis of the fluorescence spectrum of 1-methylnaphthalene shows that it also can be used for two-color detection LIF thermometry by choosing appropriate optical filters.

Solvable potentials, non-linear algebras, and associated coherent states

Using the Darboux method and its relation with supersymmetric quantum mechanics we construct all SUSY partners of the harmonic oscillator. With the help of the SUSY transformation we introduce ladder operators for these partner Hamiltonians and shown that they close a quadratic algebra. The associated coherent states are constructed and discussed in some detail.

Simultaneous two-dimensional measurement of fuel–air ratio and temperature in a direct-injection spark-ignition engine using a new tracer-pair laser-induced fluorescence technique

A planar tracer laser–induced fluorescence technique using a new tracer pair is introduced and has been utilized for the simultaneous detection of the fuel–air ratio and the temperature to characterize mixture formation inside a direct-injection spark-ignition engine. The new tracer pair consists of triethylamine and 3-pentanone, which are simultaneously added to the surrogate fuel isooctane. Triethylamine was used for the determination of the fuel–air ratio. The temperature distribution was evaluated with the two-line excitation laser-induced fluorescence technique using 3-pentanone. Prior to the internal combustion engine measurements, the tracer mixture was first investigated in a flow cell to demonstrate the spectral separability of the fluorescence signals and for the extension of the calibration data basis. As a first application, the tracer pair was applied inside a direct-injection spark-ignition engine operated with a split-injection scheme. For the late second injection, the fuel and temperature stratification was studied during the compression stroke. The measured temperature drop due to evaporative cooling effects was found to be about 100 K in the averaged data and up to 125 K in the single-shot measurements. The relation between fuel-rich areas and strong temperature drop can clearly be seen in the results. Furthermore, the suitability of the tracer pair to resolve cyclic variations is visualized.

Investigation of the chemical stability of the laser-induced fluorescence tracers acetone, diethylketone, and toluene under IC engine conditions using Raman spectroscopy

This paper reports on an investigation of the chemical stability of the common laser-induced fluorescence (LIF) tracers acetone, diethylketone, and toluene. Stability is analyzed using linear Raman spectroscopy inside a heated pressure cell with optical access, which is used for the LIF calibration of these tracers. The measurements examine the influence of temperature, pressure, and residence time on tracer oxidation, which occurs without a rise in temperature or pressure inside the cell, highlighting the need for optical detection. A comparison between the three different tracers shows large differences, with diethylketone having the lowest and toluene by far the highest stability. An analysis of the sensitivity of the measurement shows that the detection limit of the oxidized tracer is well below 3% molar fraction, which is typical for LIF applications in combustion devices such as internal combustion (IC) engines. Furthermore, the effect on the LIF signal intensity is examined in an isothermal turbulent mixing study.

Application of linear Raman spectroscopy for the determination of acetone decomposition

Acetone (CH3)2CO is a common tracer for laser-induced fluorescence (LIF) to investigate mixture formation processes and temperature fields in combustion applications. Since the fluorescence signal is a function of temperature and pressure, calibration measurements in high pressure and high temperature cells are necessary. However, there is a lack of reliable data of tracer stability at these harsh conditions for technical application. A new method based on the effect of spontaneous Raman scattering is proposed to analyze the thermal stability of the tracer directly in the LIF calibration cell. This is done by analyzing the gas composition regarding educts and products of the reaction. First measurements at IC engine relevant conditions up to 750 K and 30 bar are presented.

Fuel concentration imaging inside an optically accessible diesel engine using 1-methylnaphthalene planar laser-induced fluorescence

The performance and emissions of modern automotive diesel engines are highly dependent on the application of pilot injection technology. This technology also appears well suited for application to low-temperature combustion strategies. In this study, the first results of a new quantitative planar laser-induced fluorescence equivalence ratio measurement technique of pilot injections inside an optically accessible diesel engine are presented using 1-methylnaphthalene as a tracer in a mixture of the diesel primary reference fuels, n-hexadecane (cetane) and 2,2,4,4,6,8,8-heptamethylnonane (iso-cetane). This combination overcomes the shortcomings of mismatched fuel volatility and density associated with commonly used toluene/n-heptane/iso-octane planar laser-induced fluorescence techniques. A tracer characterization in a flow cell and a calibration in the internal combustion engine are performed. The internal combustion engine measurements illustrate the mixture formation process for a pilot injection. Even at low injection mass of 3 mg, a strong penetration of the pilot is observed; fuel hits the piston bowl wall and is redirected upward to the cylinder head. Small amounts of fuel are also found to have penetrated into the bottom of the piston bowl. At top dead center, the pilot injection is still not completely homogeneously distributed in the piston bowl, and local equivalence ratios of Φ > 1 are found in the bowl.

Simultaneous imaging of fuel vapor mass fraction and gas-phase temperature inside gasoline sprays using two-line excitation tracer planar laser-induced fluorescence

This paper reports for the first time, to the best of our knowledge, on the simultaneous imaging of the gas-phase temperature and fuel vapor mass fraction distribution in a direct-injection spark-ignition (DISI) spray under engine-relevant conditions using tracer planar laser-induced fluorescence (TPLIF). For measurements in the spray, the fluorescence tracer 3-pentanone is added to the nonfluorescent surrogate fuel iso-octane, which is excited quasi-simultaneously by two different excimer lasers for two-line excitation LIF. The gas-phase temperature of the mixture of fuel vapor and surrounding gas and the fuel vapor mass fraction can be calculated from the two LIF signals. The measurements are conducted in a high-temperature, high-pressure injection chamber. The fluorescence calibration of the tracer was executed in a flow cell and extended significantly compared to the existing database. A detailed error analysis for both calibration and measurement is provided. Simultaneous single-shot gas-phase temperature and fuel vapor mass fraction fields are processed for the assessment of cyclic spray fluctuations.

Simultaneous spatially resolved visualization of fuel/air ratio and residual gas distribution in an optically accessible SI engine

High residual gas concentrations are an efficient way to reduce consumption and emissions in part load conditions. However, exhaust gas recirculation (EGR) rates are limited due to irregular combustion at high EGR concentrations. Investigations using laser-induced fluorescence (LIF) and OH chemiluminescence have shown faster mixture formation and improved combustion for high residual gas concentrations with increased charge motion. A conventional tumble flow was overlaid with an additional swirl motion resulting in increased residual gas compatibility. For further investigations we developed a new approach using LIF to investigate simultaneously the effect of charge motion on mixture formation, temperature, and fresh air/residual gas concentration. For the simultaneous spatially resolved visualization of these parameters, two different excimer lasers were used to excite the charge (fuel, air, and residual gas) quasi-simultaneously and two intensified CCD cameras were used for detection (twoline-two-color LIF). Acetone was injected into the intake air system and used as a tracer for air when applying two-line-two-color LIF. Triethylamine was used as a tracer for fuel. The measurement technique was applied to a turbocharged singlecylinder SI engine with optical access equipped with charge movement flaps to generate a defined charge motion and a variable valve lift system on the intake and exhaust side. Different internal EGR strategies could be realized by changing the valve timing of both, inlet and outlet valves.