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Article
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We report a comprehensive speed of sound database for multi-component mixing of underexpanded fuel jets with real gas expansion. The paper presents several reference test cases with well-defined experimental conditions providing quantitative data for validation of computational simulations. Two injectant fluids, fundamentally different with respect...

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... High-pressure gaseous fuel injection generates an underexpanded jet that exhibits highly complex physics including turbulence, mixing layers, strong Prandtl-Meyer expansion fans and shock waves, as well as nonlinearly changing fluid properties at varying pressures and temperatures [5][6][7] . The jet characteristics depend on the nozzle pressure ratio, NPR, that is defined as the ratio between the upstream nozzle injection pres-sure and the ambient back pressure, NPR = P o /P ∞ 8 . ...
Article
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The flow field of an impulsively started round, confined nitrogen jet was investigated using combined high speed schlieren imaging and particle velocimetry (PIV) measurements. PIV measurements were carried out at five different, normalized times (55 ≤ t * ≤ 392) relative to jet intrusion into a constant volume chamber. Between 100 < t * < 250, the NPR linearly increased to that for a moderately underexpanded jet (NPR ≈ 3.5). Distributions of the mean flow and Reynolds normal and shear stresses revealed two different stages in jet development. In stage I (t * = 55 to 103), prior to clear shock cell appearance, the jet was characterized by a leading, toroidal vortex whose induced recirculatory motion inhibited the growth of the trailing jet's shear layer instabilities and radial spreading. In stage II (t * = 196 and 392), the jet became moderately underexpanded (NPR ≥ 2) and close to the nozzle exit, flow characteristics resembled those of a "co-annular" jet. The "co-annular" region did not extend beyond 15D. An analysis of instantaneous vortex numbers and strengths further supported the two identified stages in jet development and their connection to shear layer instability growth. Based on the distributions of mean flow and Reynolds stresses, it was shown that the static pressure gradient along the jet's centerline is mainly governed by the dynamic pressure gradient. Gradients of the Reynolds normal and shear stresses play a minor role. Important for gaseous fuel injection at high injection pressures, results point at limited mixing during stage I and enhanced mixing during stage II.
... The evaluation is conducted for n-hexane at three different pressures, namely 300 115 6.19 Comparison of the centerline concentration for the investigated n-hexane jets. Experimental speed of sound data were taken from Baab et al. [14] and Förster et al. [80] and have been post-processed using the adiabatic mixture concept. . . . . . 116 6.20 Pressure-temperature diagram of argon together with an approximated isentropic expansion path for a perfect gas (Ar: γ = 1.67) from reservoir to chamber conditions.118 ...
... Optical access is provided by three quartz windows. Recently, Baab et al. [14] and Förster et al. [80] used laser-induced thermal acoustics (LITA) to investigate the mixing process of highly underexpanded jets within this chamber. The speed of sound can be directly measured by extracting the frequency of the LITA signal and post-processing it using, for instance, the Fast Fourier transformation. ...
... The speed of sound can be directly measured by extracting the frequency of the LITA signal and post-processing it using, for instance, the Fast Fourier transformation. From these two recent measurement campaigns [14,80] a total of 14 injection experiments have been reported. The results of these experimental investigations [14,80] are summarized in Tab. ...
Thesis
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Injection, mixing and combustion under high-pressure conditions are key processes in modern energy conversion machines. Driven by the demand for higher efficiency and reduction of pollutants, intensive investments are made in recent years in the further development of especially two types of fuel-fired engines: liquid-propellant rocket engines (LREs) and gas engines (GEs). This arises from the fact, that LREs will remain an essential component for payload launchers in the foreseeable future and that GEs fired with hydrogen or natural gas are a possible solution to gradually diversify towards cleaner energy conversion machines. Computational fluid dynamics (CFD) can contribute to a better understanding of the injection, mixing and combustion processes within these types of engines. Here, especially one thermodynamic topic is of paramount interest within recent years: phase separation processes under initially supercritical conditions. This work presents a CFD tool that enables the thorough investigation of these processes. Both a pressure- and a density-based solver framework are introduced. The first comprises different formulations of the pressure equation to cover a wide range of Mach numbers. A double-flux scheme specifically tailored for real-gas flows is the core of the density-based solver. The thermodynamic framework relies on a rigorous and fully conservative description of the thermodynamic state. Cubic equations of state and the departure function concept form the basis of the thermal and caloric closure. Consequently, real-gas effects are included inherently. Multicomponent phase separation processes are considered by means of a minimization of the Gibbs energy. For the investigation of the non-premixed combustion process, a tabulated combustion model based on the flamelet concept is employed. Overall, measurement data from five different experimental test campaigns are used to validate the numerical framework. Both Large-Eddy Simulations and Reynolds-Averaged Navier-Stokes simulations are performed. Most of the simulations are conducted with the pressure-based framework. In the first step, real-gas effects in underexpanded jets are investigated. Very good agreement with experimental speed of sound measurements is found. Further investigations demonstrate the importance of the consideration of real-gas effects to correctly capture the jet mixing process. Next, the phase separation process in an underexpanded argon jet is studied. In the fully developed jet, the single-phase instabilities are found downstream of the nozzle exit and upstream of the Mach disk. This is in excellent agreement with experimental Mie scattering measurements. Next, the possibility of phase separation under GE-like operating conditions is investigated. Two different fuels - hydrogen- and methane-based - are considered. For the latter, pronounced phase separation processes are found which are triggered by a strong expansion and a mixing with the ambient gas. No two-phase effects occur in the hydrogen-based fuel as the critical temperature of the less volatile component is dramatically lower as in the methane-based fuel. For the investigation of phase separation processes under LRE-like operating conditions a combined experimental and numerical study together with the University of Stuttgart is conducted. Three different test cases are defined. The characteristics of the phase formation process agree well between experiments and simulations. The single-phase instability is caused solely by a mixing process of the injected fuel with the ambient gas. Next, the prediction capabilities of the pressure- and the density-based solver are assessed in detail. For the pressure-based approach a very good agreement with three experimental test cases is found. The density-based method, in contrast, yields possibly nonphysical states indicated by a strong entrainment into the two-phase region. Finally, phase separation effects in a hydrogen and a methane flame under LRE-typical operating conditions are studied. Single-phase instabilities are found on both sides of the flamelet caused by the low temperatures and the presence of water. For the methane flame, a Large-Eddy Simulation for a reference experiment is conducted. The results show that the region of phase separation is mostly restricted to the oxygen core. The OH* emission images indicate that both flame length and shape are in good agreement with the experimental results.
... To utilize LITA as a reliable tool for experimental investigation in jet disintegration or droplet evaporation studies, a high spatial resolution is imperative. Studies by Baab et al. (2016), Baab et al. (2018), andFörster et al. (2018) already showed the capability of acquiring quantitative speed of sound data in jet disintegration. Especially to be emphasised are the investigations by Baab et al. (2018), which demonstrated the potential of acquiring speed of sound data for multi-component jet mixing at high pressures in the near nozzle region. ...
Article
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Mixing and evaporation processes play an important role in fluid injection and disintegration. Laser-induced thermal acoustics (LITA) also known as laser-induced grating spectroscopy (LIGS) is a promising four-wave mixing technique capable to acquire speed of sound and transport properties of fluids. Since the signal intensity scales with pressure, LITA is effective in high-pressure environments. By analysing the frequency of LITA signals using a direct Fourier analysis, speed of sound data can be directly determined using only geometrical parameters of the optical arrangement no equation of state or additional modelling is needed at this point. Furthermore, transport properties, like acoustic damping rate and thermal diffusivity, are acquired using an analytical expression for LITA signals with finite beam sizes. By combining both evaluations in one LITA signal, we can estimate mixing parameters, such as the mixture temperature and composition, using suitable models for speed of sound and the acquired transport properties. Finally, direct measurements of the acoustic damping rate can provide important insights on the physics of supercritical fluid behaviour. Graphic Abstract
... In order to gain a better understanding of high-pressure fluid mixing with respect to the interplay between large scale dynamics and micro scale diffusion, in this paper we present a critical evaluation of speed of sound measurements in binary mixtures, performed by means of Laser Induced Thermal Acoustic (LITA). The experiments have been performed exclusively in regime III in both underexpanded [36,41] and subsonic high-pressure jets [42]. The advantage of fluid injection experiments in regime III is twofold. ...
... We used laser-induced thermal acoustics (LITA) to obtain quantitative jet mixing data along the centerline in binary mixtures. Several experimental studies [36,41,42] demonstrated the applicability of the technique to turbulent, mixing jets and provided a comprehensive speed of sound database. ...
... In the following sections, the already existing LITA speed of sound databases [42,41] for underexpanded and submerged turbulent jets are critically evaluated. As clarified in Section 1, the objective is twofold. ...
Article
The present work provides an overview on the possible phase transitions associated with supercritical fluid injection and a detailed evaluation of the mixing process between injectant fluid and quiescent ambience. The experiments cover superheated liquid disintegration, pseudo-boiling transition and single-phase jets under different nozzle pressure ratios. Pseudo-boiling effects emerge when rapid, subsequent changes in pressure/temperature interact with the non-linear behavior of thermodynamic response functions across the Widom line. The associated density fluctuations cause a significant increase in the scattering cross section and may lead to thermo-convective instabilities. Our analysis of the mixing process demonstrates the limited applicability of the adiabatic mixing model, which is often restricted to short residence times even in highly turbulent jets (Re=O(105)). Specifically, our findings show the importance of considering all coupled transport processes in the analysis of mixing problems at high pressures, in particular in presence of large mass concentration and temperature gradients.
... In this context, Baab et al. [8,9] and Förster et al. [10] performed supercritical injection studies in order to deliver quantitative jet mixing data. Using laser-induced thermal acoustics (LITA), they measured the local speed of sound in high-pressure injection with varying temperature and ambient pressure. ...
... Considering this, an extended analysis of the mixing data with regard to the applicability of the adiabatic mixing model is carried out. In the studies of Baab et al. [8] and Förster et al. [10], underexpanded jets followed the adiabatic mixing model quite accurately for axial distances of / below 110. However, in dense single-phase jets, deviations are expected in comparison to an analytical solution. ...
... Baab et al. [8] and Förster et al. [10] showed adiabatic and self-similar characteristics within underexpanded jets for axial distances of / < 110. Underexpansion implies high exit velocities and an eruptive discharge of the fluid. ...
Chapter
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Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model may become inappropriate for subsonic submerged jets at high-pressure conditions. Two cases are discussed where thermal and concentration driven fluxes are seen to have significant influence. To which extent the adiabatic mixing model is valid depends on the relative importance of local diffusive fluxes, namely Fourier, Fick and Dufour diffusion. This is inter alia influenced by different time and length scales. The experimental data from a high-pressure n-hexane/nitrogen jet injection were investigated numerically. Finally, based on recent numerical findings, the plausibility of different thermodynamic mixing models for binary mixtures under high pressure conditions is analyzed.
... The technique has also been successfully applied to calibration of Two-Colour Planar Laser Induced Fluorescence imaging of temperature distributions in a firing engine [10] . Recent developments have also included applications in shock tubes and high-speed fuel injection jets and mixing [11,12] . ...
Article
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Crank angle-resolved temperatures have been measured using laser induced grating spectroscopy (LIGS) in a motored reciprocating compression machine to simulate diesel engine operating conditions. A portable LIGS system based on a pulsed Nd:YAG laser, fundamental emission at 1064 nm and the fourth harmonic at 266 nm, was used with a c.w. diode-pumped solid state laser as probe at 660 nm. Laser induced thermal grating scattering (LITGS) using resonant absorption by 1-methylnaphthalene, as a substitute fuel, of the 266 nm pump-radiation was used for temperature measurements during non-combusting cycles. Laser induced electrostrictive grating scattering (LIEGS) using 1064 nm pump-radiation was used to measure temperatures in both combusting and non-combusting cycles with good agreement with the results of LITGS measurements which had a single-shot precision of ± 15 K and standard error of ± 1.5 K. The accuracy was estimated to be ± 3 K based on the uncertainty involved in the modified equation of state used in the derivation from the LIGS measurements of sound speed in the gas. Differences in the in-cylinder bulk gas temperature between combusting and non-combusting cycles were unambiguously resolved and temperatures of 2300 ± 100 K, typical of flames, were recorded in individual cycles. The results confirm the potential for LIGS-based thermometry for high-precision thermometry of combustion under compression-ignition conditions.
... There is a large body of literature on experimental investigations of underexpanded jets. Many studies have focused on the compressible features of free jets, mostly using Schlieren imaging as in the seminal article by Crist andco-workers in 1966 (Crist et al. 1966), or later using advanced laser techniques to measure temperature, velocity, pressure and recently the speed of sound (Paul et al. 1989;Naik et al. 2009;Förster et al. 2018). From a heat transfer standpoint, measurements of fluid-to-wall heat transfer rates were reported on underexpanded jets impinging on plane (Rahimi et al. 2003) or cylindrical surfaces (Vinze et al. 2017). ...
Article
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This article describes experiments to investigate the fluid-to-wall interaction downstream of a highly underexpanded jet, with a pressure ratio of 120, confined in a channel. Heat transfer induced by Joule-Thomson cooling, which is a real gas effect in such a configuration, has critical implications on the safety of pressurised gas components. This phenomenon is challenging to model numerically due to the requirement to implement a real gas equation of state, the large range of (subsonic and supersonic) velocities, the high turbulence levels and the near-wall behaviour. An experimental setup with simple geometry and boundary conditions, and with a wide optical access was designed and implemented. It consisted of a high-pressure gas reservoir at controlled temperature and pressure, discharging argon through a nozzle into a square channel. This facility was designed to allow for a steady-state expansion from over 120 bar to atmospheric pressure for over 1 min. The choice of fluid, pressure and temperature regulation system, and the implementation of a high pressure particle seeding system are discussed. The gas dynamics of this flow was then investigated by two separate optical techniques. Schlieren measurements were used to locate the position of the Mach disk, and planar particle image velocimetry (PIV) was used to measure the turbulent velocity field in the regions of lower velocity downstream. Mie scattering images also indicated the presence of a condensed argon phase in the supersonic region as expected from previous studies on nucleation. The observed location of the sharp interface at the Mach disk was found to be in excellent agreement with the Crist correlation. Rapid statistics were derived from the PIV measurements at 3 kHz. The recirculation zone was found to extend about 4 channel heights downstream, and in the region between 2 and 3 channel heights downstream, a continuous deceleration on the centerline velocity was observed in line with the narrowing of the recirculation zone. The first and second velocity moments as well as Reynold stresses were quantified, including pdf distributions. In addition, a sensitivity and repeatability analysis, an evaluation of the PIV random uncertainty, as well as an estimation of errors induced by particle inertia were performed to allow for a full quantitative comparison with numerical simulations. Graphical abstract Open image in new window
Article
The mixing process of extremely underexpanded supercritical jets into a gaseous environment is studied. The focus lies on the influence of the nonideal fluid behavior on the mixing process. Numerical simulations are conducted for eight different injection conditions where experimental sound speed measurements are available. Overall, a very good agreement between simulations and experiments is found. A comparison of the real-gas and the ideal-gas closures shows the necessity to account for nonideal fluid behavior. The application of the ideal-gas law results in an incorrect energetic state which most prominently leads to an overestimation of the post-shock temperature by 70 K. The wrong energetic state yields erroneous thermodynamic properties in the mixing region. Finally, a mixture model is deduced enabling the prediction of mixture properties. As independent measurements of mass/mole fractions are not available, this evaluation procedure is a first attempt to numerically predict the mixture composition in underexpanded jets.
Article
High-resolution direct numerical simulations are conducted for under-expanded cryogenic hydrogen gas jets to characterize the nearfield flow physics. The basic flow features and jet dynamics are analyzed in detail, revealing the existence of four stages during early jet development, namely, (a) initial penetration, (b) establishment of near-nozzle expansion, (c) formation of downstream compression, and (d) wave propagation. Complex acoustic waves are formed around the under-expanded jets. The jet expansion can also lead to conditions for local liquefaction from the pressurized cryogenic hydrogen gas release. A series of simulations are conducted with systematically varied nozzle pressure ratios and systematically changed exit diameters. The acoustic waves around the jets are found to waken with the decrease in the nozzle pressure ratio. The increase in the nozzle pressure ratio is found to accelerate hydrogen dispersion and widen the regions with hydrogen liquefaction potential. The increase in the nozzle exit diameter also widens the region with hydrogen liquefaction potential but slows down the evolution of the flow structures.