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In this study, we evaluate the thermodynamic structure of laminar hydrogen/oxygen flames at supercrit- ical pressures using 1D flame calculations and large-eddy simulation (LES) results. We find that the real fluid mixing behavior differs between inert (cold flow) and reactive (hot flow) conditions. Specifically, we show that combustion under trans...
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... corresponds to high Lewis numbers in near-critical fluids, consistent with results of Harstad & Bellan [58] and Lacaze & Oefelein [23] . Figure 8 demonstrates the influence of the transport model on the thermodynamic flame structure in more detail. In contrast to the noticeable effect of including the Soret term on the tempera- ture and density distributions, shown in Fig. 2 , the fuel-rich side of the flame trajectory in Fig. 8 is significantly modified. ...
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... of Harstad & Bellan [58] and Lacaze & Oefelein [23] . Figure 8 demonstrates the influence of the transport model on the thermodynamic flame structure in more detail. In contrast to the noticeable effect of including the Soret term on the tempera- ture and density distributions, shown in Fig. 2 , the fuel-rich side of the flame trajectory in Fig. 8 is significantly modified. Assuming a unity Lewis number is furthermore found to overestimate diffusive mixing towards the cryogenic oxygen ...
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... and clearly separated from the stoichiometric line. In some positions, localized regions of real mixing can be observed on the fuel-rich side of the flame. Figure 13 is the reduced state plot for the CFD shear layer, capturing the characteristics of the 1D flame solutions. The re- sult matches the unity Lewis number 1D flame solution shown in Fig. 8 , most notably in the absence of the flame loop. More impor- tantly, no significant reduction in the reduced pressure is observed during the bulk transition from real fluid to ideal gas conditions, consistent with the 1D ...
Citations
... With the increase in computing power, large-eddy simulations (LESs) have been used to predict turbulent flow [10] and combustion [11][12][13] under supercritical conditions. Unsteady turbulent flame structures in transcritical flows have also been studied using LES [14][15][16][17]. For example, Laurent et al. [18,19] studied flame-wall interactions near the injector lip and the heat release response to fuel inflow acoustic harmonic oscillations in CH 4 oxy-combustion at high pressures. ...
In this paper, a large-eddy simulation (LES) of turbulent non-premixed LO2/CH4 combustion under transcritical conditions is performed based on the Mascotte test rig from the Office National d’Etudes et de Recherches Ae´rospatiales (ONERA), and the aim is to understand the effects of differential diffusion on the flame behaviors. In the LES, oxygen was injected into the environment above the critical pressure while the temperature was below the critical temperature. The flamelet/progress variable (FPV) approach was used as the combustion model. Two LES cases with different species diffusion coefficient schemes—i.e., non-unity and unity Lewis numbers—for generating the flamelet tables were carried out to explore the effects of differential diffusion on the flame and flow structures. The results of the LES case with non-unity Lewis numbers were in good agreement with the experimental data. It was shown that differential diffusion had evident impacts on the flame structure and flow dynamics. In particular, when unity Lewis numbers were used to evaluate the species diffusion coefficient, the flame length was underestimated and the flame expansion was more significant. Compared to laminar counterflow flames, turbulence in jet flames allows chemical reactions to take place in a wider range of mixture fractions. The density distributions of the two LES cases in the mixture fraction space were very similar, indicating that differential diffusion had no significant effects on the phase transition under transcritical conditions.
... Ansatzes liegt in der expliziten Behandlung der Speziesdiffusion, die sich sehr einfach auf Lewis-Zahlen ungleich Eins erweitern lässt. Als Nachteil erweist sich allerdings die Tatsache, dass die Flameletlösungen im Ortsraum vorliegen und erst in den Mischungsbruchraum transformiert[105,12] werden müssen. Der in dieser Arbeit verwendete Ansatz [136] liefert ein System aus eindimensionalen Differentialgleichungen im Mischungsbruchraum [109, 95], wie sie z. ...
... Quantitativ sagen beide Flamelet-Löser die Maximaltemperatur und das Maximum von c p korrekt vorher, auch wenn die Position der Maxima im Mischungsbruchraum leicht verschoben ist. Besonders die genaue Darstellung des transkritischen Übergangs nahe dem Sauerstoffinjektor ist sehr wichtig, da dieser Bereich durch das Maximum in c p einen großen Einfluss auf die Strömungstopologie in der Nähe des Injektors hat[12]. Der Vergleich der Realgaserweiterung des Flamelet-Lösers mit den Flammenstrukturen aus der Literatur zeigt eine sehr gute Übereinstimmung und erlaubt somit den Flamelet-Löser als validiert zu betrachten. ...
Verbrennungsinstabilitäten in Raketenbrennkammern stellen seit Beginn des Raumfahrtzeitalters eine große Herausforderung bei der Entwicklung neuer Antriebe dar, weil der genaue Mechanismus ihrer Entstehung bis heute nicht vollständig verstanden ist. Einen wichtigen Teilaspekt bei der Entstehung von Verbrennungsinstabilitäten stellt die Wechselwirkung zwischen der Flamme und den akustischen Brennkammereigenmoden dar, die in dieser Dissertation für eine Experimentalbrennkammer numerisch untersucht wird. In dieser Arbeit wird der DLR Strömungslöser TAU zur skalenauflösenden Simulation eines Lastpunkts von Brennkammer H (BKH) des DLR Lampoldshausen verwendet, bei dem sowohl Treibstoff als auch Oxidator unter kryogenen Bedingungen eingespritzt werden. Zu diesem Zweck wurde das TAU Verfahren um ein Realgas Flameletverbrennungsmodell erweitert, das eine effiziente Behandlung der chemischen Reaktionen erlaubt. Weiterhin wurden die Dissipationseigenschaften des numerischen Verfahrens eingehend untersucht und die Anwendbarkeit von Upwind-Flusslösern für skalenauflösende Simulationen diskutiert. Ein weiterer Aspekt ist die Analyse der akustischen Eigenschaften des TAU-Codes und der Randbedingungen, die dann zur gezielten Untersuchung der Kopplung von Brennkammer- und Injektoreigenmoden verwendet wurden. Diese Arbeit präsentiert Resultate mehrerer Detached-Eddy Simulationen (DES) der Strömung in BKH bei verschiedenen Anregungszuständen und vergleicht sie mit experimentellen Daten. Die Simulationsergebnisse bei nicht-resonanter Anregung durch eine Sirene weichen weniger als 2.1 % von den experimentellen Brennkammereigenfrequenzen ab. Allerdings wird in der Simulation die instationäre Anregung durch die Sirene überschätzt, was auf Modellannahmen der numerischen Konfiguration zurückgeführt wird. Die Ergebnisse einer resonant angeregten Simulation und eines Impulsantwort-Tests zeigen eine Verschiebung der Brennkammereigenfrequenzen, die bereits in früheren experimentellen Studien von BKH beobachtet wurde. Die Positionen der verschobenen Frequenzen stimmen sehr gut mit den experimentellen Ergebnissen überein. Darüber hinaus zeigen die Simulationsergebnisse der resonanten Anregungen eine starke Schwankung des mittleren Brennkammerdrucks, die im Experiment nicht zu beobachten war. Dieser Unterschied wird durch das abrupte Anschalten der Sirene in der Simulation erklärt, was zu einer niederfrequenten Modulation der Einströmbedingungen führt. Zum Schluss dieser Arbeit wird durch gezielte Modifikation des Sauerstoffinjektors eine Kopplung zwischen Injektor- und Brennkammereigenmoden künstlich herbeigeführt, die sich in früheren Untersuchungen als notwendige Bedingung für die Entstehung von Verbrennungsinstabilitäten herausgestellt hatte. Anhand der instationären Druckdaten wird gezeigt, dass zwar eine erfolgreiche Modenkopplung erreicht werden konnte, darüber hinaus aber kein signifikanter Einfluss auf die Brennkammermoden beobachtbar war.
... We can identify the adiabatic flame temperature T ad as the maximum temperature reached in the field. Following the path of oxygen [50], it is injected with a temperature T LOX,in , heats through pseudo boiling at T pb , before mixing and reacting. With flames mostly anchored behind the LOX post [7,12], this means that the flow behind the LOX post sees a temperature increase from ≈100 K in the LOX stream to ≈3500 K in the flame, or to ≈300 K in an ambient temperature gaseous methane stream. ...
Flows in liquid propellant rocket engines (LRE) are characterized by high pressures and extreme temperature ranges, resulting in complex fluid behavior that requires elaborate thermo-physical models. In particular, cubic equations of state and dedicated models for transport properties are firmly established for LRE simulations as a way to account for the non-idealities of the high-pressure fluids. In this paper, we review some shortcomings of the current modeling paradigm. We build on the common study of property errors, as a direct measure of the density or heat capacity accuracy, to evaluate the quality of cubic equations of state with respect to pseudo boiling of rocket-relevant fluids. More importantly, we introduce the sampling error as a new category, measuring how likely a numerical scheme is to capture real fluid properties during a simulation, and show how even reference quality property models may lead to errors in simulations because of the failure of our numerical schemes to capture them. Ultimately, a further evolution of our non-ideal fluid models is needed, based on the gained insight over the last two decades.
... The Cantera-based approach ensures consistency of all thermodynamic variables with the selected equation of state. For example, the Peng-Robinson equation of state implemented and tested in Cantera [25,26] could also be used with this code. ...
The goal of this research is to study the thermoacoustic response of diffusion flames due to their relevance in applications such as rocket engines. An in-house code is extended to solve the fully compressible counterflow diffusion flame equations, allowing for a spatially- and temporally-varying pressure field. Various hydrogen-air flames with a range of strain rates are simulated using detailed chemistry. After introducing sinusoidal pressure perturbations at the inlet, the gain and phase of various quantities of interest are extracted. As the frequency is increased, the gain of the temperature source term transitions from the perturbed steady flamelet value to a first plateau at intermediate frequencies, and finally to a second plateau at the highest frequencies. At these high frequencies, the gain of the integrated heat release decays to zero, underscoring the importance of compressibility. These three regimes can be identified and explained through a linearization and frequency domain analysis of the governing equations. The validity of the low Mach number assumption and importance of detailed chemistry are assessed.
... For the purpose of the comparison, the phase distribution in the inert case is also shown in Fig. 7 . Here, as Banuti et al. [21] did, the phases are defined by using the reduced temperature and pressure ( T r = T /T crit and p r = p/p crit ), namely T r < 1 and p r > 1 for the liquid phase, T r > 1 and p r < 1 for the gas phase, and T r > 1 and p r > 1 for the supercritical phase (in this study, there is no condition of T r < 1 and p r < 1 ). It is observed that the high-temperature region almost corresponds to the gas phase region in the reactive case. ...
... In the high temperature region classified as gas phase, ˜ Y OH increases, and ˜ Y H 2 O does not reach the unity because of the thermal dissociation of H 2 O to OH . The phase around y = 0.5 mm is classified as a supercritical state because, as Banuti et al. [21] discussed, the mass fraction of H 2 O , whose critical pressure is 22 MPa, is small in that area and the critical pressure of the mixture is smaller than the chamber pressure. It is also noted that the temperature peak locates on the oxidizer side compared to the peak location of ˜ Y H 2 O , which is almost the same as the stoichiometric location at y = 0.81mm in Fig. 8 . ...
Large-eddy simulation (LES) employing a flamelet/progress-variable approach that considers the real gas effect is applied to liquid oxygen/ gaseous hydrogen (LOX/GH2) supercritical combustion, and the breakup mechanism of the LOX core is investigated in detail by comparing it to that in the inert case. The results show that in the reactive case, O2 is injected into the chamber in the liquid state; that is, LOX, successively shifts to the supercritical and gas states and then reacts with H2 in the gas state. The present LES in the reactive case generally succeeds in predicting the LOX core breakup location in the experiment. In the reactive case, the LOX core breakup location is observed to be further downstream than in the inert case. This is because in the inert case, the turbulent vortices that are produced around the injector exit act to break the LOX core, whereas in the reactive case, the turbulent vortices are suppressed by the volume dilatation and viscous forces around the LOX core. In the reactive case, the LOX core tends to be compressed and thinned by the thermal expansion caused by the combustion reaction around the LOX core, and at the same time, is stretched and broken by the shear forces caused by the thermal expansion.
... In order to investigate the transcritical transition in internal combustion (IC) engines, the high-speed shadowgraph or Schlieren imaging is generally utilized for the visualization of morphology of sprays and droplets [1][2][3] . Crua et al. [1] visualized the transcritical phenomena of the single-component hydrocarbon droplets at the microscopic scale, and they defined the transcritical time when there was little evidence of surface tension based on the morphological evolution of droplets after the end of injection. ...
In this study, the non-equilibrium evaporation and transcritical transition processes of the n-heptane/ethanol blends under the pure nitrogen condition are firstly analyzed, and a new transcritical criterion for the multi-component mixtures is suggested based on the molecular dynamics simulation. Firstly, the employed force fields for the n-heptane/ethanol blends are validated against the measured vapor-liquid equilibrium phase diagram and density. Then, the azeotropic phenomena are captured by the macroscopic distillation experiments for the n-heptane/ethanol blends. The MD simulation reveals that the near-azeotrope can occur in the thermodynamic non-equilibrium period for the 50%EtOH mixture in the nanometer scale, but not for the 12.5/25%EtOH mixtures. Because the lifetime of the small amount of ethanol molecules is smaller than the timescale of thermodynamic equilibrium in the 12.5/25%EtOH mixtures, which suppresses the near-azeotropic occurrence. This indicates that the non-equilibrium has a large effect on the near-azeotropic occurrence possibility. Besides, it is found that the increased ethanol concentration accelerates the evaporation rate of the n-heptane/ethanol blends in nanometer scale at low pressure, but shows little effect under high pressure conditions. Finally, the classical criterion with the large density gradient and little surface tension, is found to be insufficient to identify the transcritical transition. The molecular clusters with various sizes in the vicinity of high-density fluid and the short isothermal period are suggested to couple with the classical phenomenological criterion to determine the transcritical transition.
... Even though there exist several reacting flow solvers in which a complete set of real-fluid based thermophysical (THERMPHYS) models are implemented [1,6,[9][10][11][12][13][14][15][16][17][18], they are all academic in-house codes available for limited group users. Recently, OpenFOAM [19] has been highlighted as a robust open source computational fluid dynamics (CFD) platform for multidimensional numerical simulations of reacting/nonreacting flows. ...
Although OpenFOAM is a widely-used open source computational fluid dynamics (CFD) tool, it is limited to numerical simulations of multi-dimensional reacting/nonreacting flows at relatively-low pressures. This is not only because real-fluid models that can evaluate thermophysical properties at high pressures are not available in the thermophysicalModels library of OpenFOAM, but also because the existing mixing model cannot handle various mixing rules of real-fluid models. In the present study, we develop a novel algorithm applicable for a mixture model incorporating various mixing rules in OpenFOAM. Based on the new algorithm, we update the thermophysicalModels library of OpenFOAM 6.0 by implementing a set of real-fluid models such as the Soave-Redlich-Kwong/Peng-Robinson equation of state, Chung's model for dynamic viscosity and thermal conductivity, mixture averaged model for mass diffusivity using Takahashi's correction for binary diffusion coefficients at high pressure. The new library is validated against experimental data and is further assessed for compressible reacting flows by performing two-dimensional numerical simulations of axisymmetric laminar non-premixed counterflow flames and one-dimensional numerical simulations of premixed CH4/air flames at high pressures. The developed library can be used for any reacting flow solvers in OpenFOAM 6.0 that adopt a set of implemented real-fluid models.
Program summary
Program Title: Real-fluid thermophysicalModels
CPC Library link to program files: https://doi.org/10.17632/n8zb2wpjp6.1
Developer's repository link: https://github.com/danhnam11/realFluidThermophysicalModels-6
Licensing provisions: GPLv3
Programming language: C++
Nature of problem: The mixing rules required for evaluating the real-fluid based thermophysical properties of mixtures are relatively complicated and different from each other, while the existing thermophysicalModels library offers only a mixing rule based on the mass fraction weighted average of each species, for which overloading operator functions (“*” and “+=”) are utilized to update parameters for a mixture. However, this approach is not applicable for complicated mixing rules in the real-fluid models.
Solution method: To build a mixture class containing different mixing rules in different models such as the equation of states and thermodynamics/transport properties in OpenFOAM, we adopt void-type functions (parameter updating functions) to update parameters of a mixture instead of the original overloading operator functions in OpenFOAM. The parameters in the mixing rules that depend on pressure and temperature are handled by decomposition such that they can be updated in the mixture class.
... Another approach apart from DNS and LES to study non-premixed reacting flows at representative operating conditions is the analysis of one-dimensional counterflow diffusion flames. Amongst others, Ribert et al. [259], Lacaze and Oefelein [154] and Banuti et al. [22,24,23] conducted detailed investigations of LOx/H 2 flames: Ribert et al. [259] focused on the dependency of the flame thickness and the heat release on pressure and strain rate in physical space and quantified the influence of Soret and Dufour effects. Lacaze and Oefelein [154] performed a detailed analysis of strain effects, pressure and temperature boundary conditions as well as real-fluid effects on the flame structure in both physical and mixture fraction space to develop a tabulated combustion model. ...
... Inspired by the inert investigations on mixture-induced phase separation effects some of these research groups performed a posteriori analysis of possible single-phase instabilities [154,22,160,23]. All of them came to the finding that multi-phase effects do not occur and the mixture always stays in a single-phase state. ...
... In the field of reacting flows under rocket-relevant conditions, Lacaze and Oefelein [154], Banuti et al. [22,23] and Lapenna et al. [160] investigated hydrogen/oxygen and methane/oxygen flames and checked if thermodynamic states in these flames fall underneath the critical locus. In their investigations, a rapid estimate method [237] was used to calculate the mixture critical locus: Here, v c,i , T c,i and p c,i are the critical volume, temperature and pressure of the i-th species. ...
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.
... The extension of the flamelet equations to study the high-pressure counterflow diffusion flame problem has been investigated in a number of studies [10][11][12][13][14][15][16][17]. These works have revealed several key observations in the transcritical regime. ...
... This issue is treated using a pragmatic approach in which the minor species without critical-property data are eliminated from the EoS-related calculations and their partial molar enthalpies revert to the corresponding values of ideal gas. It should also be noted that our thermodynamic model, as well as the transport model discussed in the following, is based on the commonly used single-phase assumption [10][11][12]16,17], and the multi-phase equilibrium [31] is not considered. ...
... Furthermore, unlike the mixture composition and temperature of the propellants, the pressure plays a very minor role on the phase instability at these conditions. In the equilibrium branch, the change in the inlet propellant temperature directly impacts the location of pseudo-boiling, primarily on the oxidizer side [16,17], which concomitantly also impacts the phase instability [17]. This is expected since, in the equilibrium flamelet, the pseudoboiling occurs at a very small mixture fraction (Z ≈ 10 − 3 )-thus at a nearly pure oxygen composition-as a direct result of thermal diffusion in the flamelet. ...
The single-phase instability of high-pressure, steady, laminar counterflow diffusion flame is studied using the Vapor–Liquid Equilibrium (VLE) theory. The a posteriori study focuses on the identification of the potentially unstable regions emerging throughout the full combustion states represented by the high-pressure counterflow diffusion flame solution; a specific emphasis is placed on the middle branch solutions which are characteristic of intermediary combustion states. The a posteriori analysis provides useful bounds on the multicomponent phase separation. We use a mixture-fraction space flamelet formulation with real-fluid thermodynamics; the results compare favorably to both a spatial-based flamelet and a two-dimensional direct numerical simulations (DNS) solution, at high-pressure conditions. The a posteriori, single-phase instability for a high-pressure LO2/GH2 flame is investigated by investigating the effects of operating pressure and inlet temperature on the flame structure; then the analysis is extended to a LO2/GCH4 flame to evaluate the fuel effect. It is found that a single-phase instability can appear at both the fuel and oxidizer inlets, and its location and extent is determined by the water vapor concentration and, more importantly, temperature. For the flamelets in the upper burning branch, the size and location of unstable region is nearly invariant to the scalar dissipation rate, while for the flamelets in the middle branch, the instability region near the fuel inlet expands significantly with the decrease of chemical reactivity.
... During transcritical LOX-GH 2 combustion, gases in the flame and hot reaction products behave as ideal gases [22] . Real fluid effects are confined to the LOX core and mixing occurs only after the oxygen transitions to an ideal gas state; i.e. mixing occurs essentially exclusively under ideal gas conditions [23] . Then, high-fidelity thermodynamic data for pure oxygen can be tabulated, resulting in idealgas cost during runtime for a Younglove's modified Benedict-Webb-Rubin equation [24] of state, rather than being limited to cubic equations of state. ...
The response of a transcritical oxygen-hydrogen flame to transverse acoustic velocity was investigated using a combination of experimental analyses and numerical modelling. The experiment was conducted on a rectangular rocket combustor with shear coaxial injectors and continuously forced transverse acoustic field. Simultaneous high-speed shadowgraph and filtered OH* radiation images were collected and reduced using dynamic mode decomposition in order to characterise the flame response to the acoustic disturbance. CFD modelling of a representative single injector under forcing conditions was carried out to gain insights into the three-dimensional features of the reacting flow field. Invisible in the 2D projection, the model reveals that the excited LOX jet develops into a flattened and widened structure normal to the imposed acoustic velocity. The comparison of co-located structures allowed features in the imaging to be attributed to the deformation and transverse displacement of lower density oxygen surrounding the denser liquid oxygen core by the transverse acoustic velocity.
