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Speed of sound measurements and mixing characterization of underexpanded fuel jets with supercritical reservoir condition using laser-induced thermal acoustics

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The four-wave mixing technique laser-induced thermal acoustics was used to measure the local speed of sound in the farfield zone of extremely underexpanded jets. N-hexane at supercritical injection temperature and pressure (supercritical reservoir condition) was injected into quiescent subcritical nitrogen (with respect to the injectant). The technique’s capability to quantify the nonisothermal, turbulent mixing zone of small-scale jets is demonstrated for the first time. Consistent radially resolved speed of sound profiles are presented for different axial positions and varying injection temperatures. Furthermore, an adiabatic mixing model based on nonideal thermodynamic properties is presented to extract mixture composition and temperature from the experimental speed of sound data. High fuel mass fractions of up to 94 % are found for the centerline at an axial distance of 55 diameters from the nozzle followed by a rapid decay in axial direction. This is attributed to a supercritical fuel state at the nozzle exit resulting in the injection of a high-density fluid. The obtained concentration data are complemented by existing measurements and collapsed in a similarity law. It allows for mixture prediction of underexpanded jets with supercritical reservoir condition provided that nonideal thermodynamic behavior is considered for the nozzle flow. Specifically, it is shown that the fuel concentration in the farfield zone is very sensitive to the thermodynamic state at the nozzle exit. Here, a transition from supercritical fluid to subcritical vapor state results in strongly varying fuel concentrations, which implies high impact on the mixture formation and, consequently, on the combustion characteristics.
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1 3
Exp Fluids (2016) 57:172
DOI 10.1007/s00348-016-2252-3
RESEARCH ARTICLE
Speed of sound measurements and mixing characterization
of underexpanded fuel jets with supercritical reservoir condition
using laser‑induced thermal acoustics
S. Baab1 · F. J. Förster1,2 · G. Lamanna1 · B. Weigand1
Received: 1 July 2016 / Revised: 4 September 2016 / Accepted: 11 September 2016 / Published online: 22 October 2016
© Springer-Verlag Berlin Heidelberg 2016
farfield zone is very sensitive to the thermodynamic state
at the nozzle exit. Here, a transition from supercritical
fluid to subcritical vapor state results in strongly vary-
ing fuel concentrations, which implies high impact on the
mixture formation and, consequently, on the combustion
characteristics.
1 Introduction
Characterization of fluid injection into a gaseous environ-
ment is of paramount interest for virtually all combustion-
based energy conversion concepts. Particularly for internal
combustion engines and gas turbines, confident knowledge
of the fuel/air mixture preparation is crucial. Fuel is com-
monly injected in a liquid state and atomizes during the
process. Vaporization of small droplets and subsequent mix-
ing of fuel vapor with ambient air results in a combustible
mixture. Here, the local mixture composition and tempera-
ture are known to influence the engine efficiency as well as
pollutant formation significantly (Idicheria and Pickett 2007;
Bougie et al. 2005; Kiefer et al. 2008). Although this clearly
illustrates the need for detailed experimental data, quantita-
tive measurements within the vapor region remain an inher-
ently challenging task. High injection velocities in combina-
tion with a small nozzle geometry lead to highly turbulent
jet disintegration phenomena on a scale of a few millimeters.
Concentration and temperature data within fuel/gas
mixtures are usually obtained with nonintrusive optical
techniques such as Rayleigh/Mie (Espey et al. 1997; Su
et al. 2010; Idicheria and Pickett 2007), LIF/LIEF (Wolff
et al. 2007; Cruyningen et al. 1990; Payri et al. 2006),
Raman (Weikl et al. 2006; Grünefeld et al. 1994; Taschek
et al. 2005) and CARS (Weikl et al. 2006; Seeger et al.
2003; Chai et al. 2007). In addition to these techniques,
Abstract The four-wave mixing technique laser-induced
thermal acoustics was used to measure the local speed of
sound in the farfield zone of extremely underexpanded jets.
N-hexane at supercritical injection temperature and pres-
sure (supercritical reservoir condition) was injected into
quiescent subcritical nitrogen (with respect to the inject-
ant). The technique’s capability to quantify the noniso-
thermal, turbulent mixing zone of small-scale jets is dem-
onstrated for the first time. Consistent radially resolved
speed of sound profiles are presented for different axial
positions and varying injection temperatures. Furthermore,
an adiabatic mixing model based on nonideal thermody-
namic properties is presented to extract mixture composi-
tion and temperature from the experimental speed of sound
data. High fuel mass fractions of up to 94 % are found for
the centerline at an axial distance of 55 diameters from
the nozzle followed by a rapid decay in axial direction.
This is attributed to a supercritical fuel state at the nozzle
exit resulting in the injection of a high-density fluid. The
obtained concentration data are complemented by existing
measurements and collapsed in a similarity law. It allows
for mixture prediction of underexpanded jets with super-
critical reservoir condition provided that nonideal ther-
modynamic behavior is considered for the nozzle flow.
Specifically, it is shown that the fuel concentration in the
* S. Baab
steffen.baab@itlr.uni-stuttgart.de
F. J. Förster
felix.foerster@physics.ox.ac.uk
1 Institute of Aerospace Thermodynamics (ITLR), University
of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
2 Atomic and Laser Physics Clarendon Laboratory, University
of Oxford, Parks Road, Oxford OX13PU, UK
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... [35], there is still an ongoing debate as to which is the most suitable mixing model to accurately describe fluid mixing at high-pressure conditions. For high-speed, turbulent jets (Re ≥ 10 5 ), there is an accredited opinion in literature that large scale flow dynamics controls the mixing process, leading to the formulation of adiabatic [8,36,23,37] or isochoric [38] mixing models. With decreasing Re numbers [Re = O(10 3 )], Masi et al. [39] pointed out that diffusive fluxes become increasingly important and control small scale transport in turbulent flows. ...
... 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. ...
... A radial piston pump or a pressurized fluid reservoir provides the required injection pressures depending on the desired NPRs in the experiments. A more detailed description of the test facilities is given in [43,36,44]. ...
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.
... 6.1 Schematic of the test chamber used at the ITLR for the experimental investigations of high-pressure mixing processes. The figure has been taken from Baab et al. [14]; reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Experiments in Fluids, Baab et al. [14], © (2016). . . . . 102 6.2 Comparison of the PR-EoS [226] with reference data taken from CoolProp [27]. ...
... 6.1 Schematic of the test chamber used at the ITLR for the experimental investigations of high-pressure mixing processes. The figure has been taken from Baab et al. [14]; reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Experiments in Fluids, Baab et al. [14], © (2016). . . . . 102 6.2 Comparison of the PR-EoS [226] with reference data taken from CoolProp [27]. ...
... 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 ...
Thesis
Full-text available
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.
... Especially for high pressures exceeding the critical value of the injected fluids, mixing and evaporation processes as well as fundamental changes in fluid behaviour are not yet fully understood. The latter have received increased attention in the past decade, as the recently published literature shows (Falgout et al. 2016;Müller et al. 2016;Baab et al. 2016Baab et al. , 2018Crua et al. 2017). Since the main objectives are evaporation and disintegration processes of liquid fluids at pressures and temperatures either close to or exceeding their critical points, quantitative data for validation of numerical simulations have recently become a research concern with increasing interest (Bork et al. 2017;Lamanna et al. 2018;Steinhausen et al. 2019;Stierle et al. 2020;Nomura et al. 2020;Lamanna et al. 2020;Qiao et al. 2020). ...
... 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. ...
... Three different atmospheres, namely nitrogen with a purity of 99.999 % , argon with a purity of 99.998 % , and carbon dioxide with a purity of 99.995 % , are studied. The optical setup is adapted from the one described in Baab et al. (2016) and Förster et al. (2015). ...
Article
Full-text available
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 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. ...
... For more detailed information the reader is referred to [8]. For the means of comparability, the axial concentration data is plotted according to a similarity law proposed by Chen and Rodi [21]. ...
Chapter
Full-text available
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.
... In another paper by this group (Baab et al. [19]), LIEGS is used to measure the local speed of sound in the farfield of an underexpanded jet (n-hexane in quiescent N 2 ). The authors present radially resolved speed of sound profiles at different axial positions and at different injection temperatures. ...
... The physical background to the formation of laser-induced gratings and their readout are described in various papers [11][12][13][14][15][16][17][18][19][20][21][22]. In the following section, the frequencies resulting from the superposition of Doppler-shifted laser beams are discussed in detail. ...
Article
Full-text available
At our institute a piston-driven shock tunnel is operated to investigate structures of space transportation systems under reentry and propelled flight conditions. For temperature measurements in the nozzle reservoir under single-shot conditions, laser-induced thermal grating spectroscopy is used to date to measure the speed of sound of the test gas. The temperature then can be calculated from this data. The existing experimental setup has already been successfully used to measure flows up to an enthalpy of 2.1 MJ/kg. Since conducting the experiments is extremely time-consuming, it is desirable to extract as much data as possible from the test runs. To additionally measure the velocity of the test gas, the test setup was extended. Besides, extensive improvements have been implemented to increase the signal-to-noise ratio. As the experiments can be conducted much faster at the double-diaphragm shock tube of the institute without any restrictions on the informative value, the development of the heterodyne detection technique is carried out at this test facility. A series of 36 single-shot temperature and velocity measurements is presented for enthalpies of up to 1.0 MJ/kg. The averaged deviation between the measured values and the values calculated from the shock equations of all measurements related to the average of the calculated values is 2.0% for the Mach number, 0.9% for the velocity after the incident shock and 4.8% for the temperature after the incident shock.
... Many studies have focused on steady underexpanded jets [13][14][15][16] while direct injection in ICE's is highly transient. In the latter case, there is a build-up of pressure within the injector as well as within the cylinder even when the injection pressure, P i , is kept constant. ...
Article
Full-text available
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.
... Furthermore, due to the limitations in space and time resolution of the measurement techniques applied, only very few data are available that can be used for model validation purposes as pointed out by Ruiz et al. (2016). However, efforts towards acquisition of detailed quantitative data in supercritical/transcritical jets have been undertaken and recently reported by Baab et al. (2016Baab et al. ( , 2018; Bassing and Braeuer (2017); Klima et al. (2020). Especially Baab et al. (2018) are the first to provide appreciable quantitative speed of sound data for high-pressure jet mixing of multiple components that can serve as a comprehensive database for validation of numerical simulations of near-critical fuel injection. ...
... The study of near-critical fluid injection has received increasing attention in the last decade, as testified by the large body of literature recently published on the subject [1][2][3][4][5][6]. Unfortunately, the understanding of the mixing process in high-pressure, heterogeneous media is still very controversial, due to the strong coupling between the transport of energy, mass and momentum across interfaces. ...
Chapter
This work analyses whether the inclusion of interfacial temperature jumps is necessary in the modelling of droplet evaporation at high pressure. The analysis is divided into two parts. First, we revise the major findings from theoretical models and molecular dynamics simulations on the conditions leading to the inception of interfacial jumps and the main parameters affecting them. Second, an evaporation model is considered that includes a diffuse transition layer (Knudsen layer), in the order of a few mean free paths around the droplet, where transport processes are described by kinetic molecular theory. The analysis shows that discontinuities in temperature and chemical potential across the interface are important when molecular collisions control transport processes and result in large heat and mass fluxes. This may occur not only at low pressures, but also at high pressures and temperatures for conditions sufficiently far from global thermodynamic equilibrium and/or for sufficiently small droplets. On a macroscopic scale, the resulting correction to the boundary conditions for classical diffusion-controlled models may be significant at high evaporation rates.
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A Direct Numerical Simulation (DNS) database was created representing mixing of species under high-pressure conditions. The configuration considered is that of a temporally evolving mixing layer. The database was examined and analyzed for the purpose of modeling some of the unclosed terms that appear in the Large Eddy Simulation (LES) equations. Several metrics are used to understand the LES modeling requirements. First, a statistical analysis of the DNS-database large-scale flow structures was performed to provide a metric for probing the accuracy of the proposed LES models as the flow fields obtained from accurate LES simulations should contains structures of morphology statistically similar to those observed in the filtered-and-coarsened DNS (FC-DNS) fields. To characterize the morphology of the large-scales structures, the Minkowski mathrmtionals of the iso-surfaces were evaluated for two different fields: the second-invariant of the rate of deformation tensor and the irreversible entropy production rate. To remove the presence of the small flow scales, both of these fields were computed using the FC-DNS solutions. It was found that the large-scale structures of the irreversible entropy production rate exhibit higher morphological complexity than those of the second invariant of the rate of deformation tensor, indicating that the burden of modeling will be on recovering the thermodynamic fields. Second, to evaluate the physical effects which must be modeled at the subfilter scale, an a priori analysis was conducted. This a priori analysis, conducted in the coarse-grid LES regime, revealed that standard closures for the filtered pressure, the filtered heat flux and the filtered species mass fluxes, in which a filtered function of a variable is equal to the function of the filtered variable, may no longer be valid for the high-pressure flows considered in this study. The terms requiring modeling are the filtered pressure, the filtered heat flux, the filtered pressure work and the filtered species mass fluxes. Improved models were developed based on a scale-similarity approach and were found to perform considerably better than the classical ones. These improved models were also assessed in an a posteriori study. Different combinations of the standard models and the improved ones were tested. At the relatively small Reynolds numbers achievable in DNS and at the relatively small filter widths used here, the standard models for the filtered pressure, the filtered heat flux and the filtered species fluxes were found to yield accurate results for the morphology of the large-scale structures present in the flow. Analysis of the temporal evolution of several volume-averaged quantities representative of the mixing layer growth, and of the cross-stream variation of homogeneous-plane averages and second-order correlations, as well as of visualizations, indicated that the models performed equivalently for the conditions of the simulations. The expectation is that at the much larger Reynolds numbers and much larger filter widths used in practical applications, the improved models will have much more accurate performance than the standard one.
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A new equation of state for the thermodynamic properties of natural gases, similar gases, and other mixtures, the GERG-2008 equation of state, is presented in this work. This equation is an expanded version of the GERG-2004 equation. GERG-2008 is explicit in the Helmholtz free energy as a function of density, temperature, and composition. The equation is based on 21 natural gas components: methane, nitrogen, carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, carbon monoxide, water, hydrogen sulfide, helium, and argon. Over the entire composition range, GERG-2008 covers the gas phase, liquid phase, supercritical region, and vapor–liquid equilibrium states for mixtures of these components. The normal range of validity of GERG-2008 includes temperatures from (90 to 450) K and pressures up to 35 MPa where the most accurate experimental data of the thermal and caloric properties are represented to within their accuracy. The extended validity range reaches from (60 to 700) K and up to 70 MPa. The given numerical information (including all of the sophisticated derivatives) enables the use of GERG-2008 for all of the various technical applications. Examples are processing, transportation through pipelines or by shipping, storage and liquefaction of natural gas, and processes to separate gas components. Comparisons with other equations of state, for example, AGA8-DC92 and Peng–Robinson equation (P-R), are also presented. GERG-2008 will be adopted as an ISO Standard (ISO 20765-2/3) for natural gases.