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In this paper, a dataset of wall-resolved large-eddy simulations of cryogenic hydrogen at supercritical pressure and different values of wall heat flux is presented. The aim is to provide a reference dataset for wall-function development under trans- and supercritical conditions, such as those found in liquid rocket engine applications. The employed numerical framework is a pressure-based segregated low-Mach-number approach based on an equation-of-state independent formulation. The wall-adapting local eddy-viscosity subgrid model is used for turbulence closure. Real-gas effects are taken from the National Institute for Standards and Technology database and stored as a function of a nondimensional temperature at the considered pressure. A validation and a grid-convergence analysis are first performed on an incompressible case without imposed heat flux. The effect of axial, radial, and azimuthal refinements on first- and second-order velocity statistics is discussed and compared with direct numerical simulation data from the literature. A parametric analysis at different wall heat fluxes is then performed by keeping the inlet mass flux, temperature, and Reynolds number constant. Particular attention is devoted to turbulent pseudoboiling and its effect on the wall temperature. The latter shows a more pronounced increment as the heat flux increases, which is attributed to the pseudochange of the phase in the core flow. Correspondingly, a flattening of the probability density function of the temperature is observed, and it is associated with the pseudoboiling interface forming close to the wall and causing a more intense stratification. First- and second-order statistics for velocity and selected scalars are then presented, and the effect of pseudoboiling is discussed. The effect of the wall heat flux on the viscous and thermal resolution of the computational grid is also assessed, and considerations on the relation between turbulent pseudoboiling and near-wall gradients is finally provided.

We introduce Dynamic Constrained Grid (DCGrid), a hierarchical and adaptive grid structure for fluid simulation combined with a scheme for effectively managing the grid adaptations. DCGrid is designed to be implemented on the GPU and used in high-performance simulations. Specifically, it allows us to efficiently vary and adjust the grid resolution across the spatial domain and to rapidly evaluate local stencils and individual cells in a GPU implementation. A special feature of DCGrid is that the control of the grid adaption is modeled as an optimization under a constraint on the maximum available memory, which addresses the memory limitations in GPU-based simulation. To further advance the use of DCGrid in high-performance simulations, we complement DCGrid with an efficient scheme for approximating collisions between fluids and static solids on cells with different resolutions. We demonstrate the effectiveness of DCGrid for smoke flows and complex cloud simulations in which terrain-atmosphere interaction requires working with cells of varying resolution and rapidly changing conditions. Finally, we compare the performance of DCGrid to that of alternative adaptive grid structures.

Due to the complex interplay of various meteorological phenomena, simulating weather is a challenging and open research problem. In this contribution, we propose a novel physics-based model that enables simulating weather at interactive rates. By considering atmosphere and pedosphere we can define the hydrologic cycle - and consequently weather - in unprecedented detail. Specifically, our model captures different warm and cold clouds, such as mammatus, hole-punch, multi-layer, and cumulonimbus clouds as well as their dynamic transitions. We also model different precipitation types, such as rain, snow, and graupel by introducing a comprehensive microphysics scheme. The Wegener-Bergeron-Findeisen process is incorporated into our Kessler-type microphysics formulation covering ice crystal growth occurring in mixed-phase clouds. Moreover, we model the water run-off from the ground surface, the infiltration into the soil, and its subsequent evaporation back to the atmosphere. We account for daily temperature changes, as well as heat transfer between pedosphere and atmosphere leading to a complex feedback loop. Our framework enables us to interactively explore various complex weather phenomena. Our results are assessed visually and validated by simulating weatherscapes for various setups covering different precipitation events and environments, by showcasing the hydrologic cycle, and by reproducing common effects such as Foehn winds. We also provide quantitative evaluations creating high-precipitation cumulonimbus clouds by prescribing atmospheric conditions based on infrared satellite observations. With our model we can generate dynamic 3D scenes of weatherscapes with high visual fidelity and even nowcast real weather conditions as simulations by streaming weather data into our framework.

Clean energy generation is gaining significant attention from industries, academia, and governments across the globe. The Allam cycle is one such technology that has been under focus due to its efficiency, environmental friendliness, and economics. This is a direct-fired cycle operating at supercritical conditions using carbon dioxide as a working fluid. Fuel or oxidizer jet mixing with CO2 is a vital phenomenon that governs combustion efficiency, and it is not well understood for the Allam cycle conditions. This paper experimentally investigated the jet characteristics of a methane jet injected into a subcritical to supercritical carbon dioxide environment. A wide range of injection pressures and temperatures were targeted between subcritical to supercritical conditions. Unlike previous studies, the current work focused on injecting lower-density (methane) jets into higher-density (carbon dioxide) environments. Schlieren imaging and methane absorption measurements were simultaneously performed with a CMOS high-speed camera and a 3.39 μm infrared laser. Specifically, we looked at the classical injection parameter of jet spreading angle, which was classically established to be mainly a density ratio function. Here, the jet cone angle was obtained from the postprocessed schlieren imaging. The jet cone angle is a critical characteristic parameter that describes the entrainment rate in a jet; thus, it is a crucial parameter in understanding the nature of the jet. The laser measurements were only used as an additional check to confirm the entry time of methane into the chamber filled with carbon dioxide. Notably, this paper makes a detailed comparison between the jet cone angles of jets with a density ratio. The result showed that the classical correlations, such as Abramovich's theory applied to submerged turbulent gas jets developed for low-density ratio jets, were unsuitable for higher-density ratio jets. It was also observed that the divergence angles were dependent not only on density ratio but also on other parameters such as pressure ratios and reduced pressures.

Resulting from changing climatic conditions, wildfires have become an existential threat across various countries around the world. The complex dynamics paired with their often rapid progression renders wildfires an often disastrous natural phenomenon that is difficult to predict and to counteract. In this paper we present a novel method for simulating wildfires with the goal to realistically capture the combustion process of individual trees and the resulting propagation of fires at the scale of forests. We rely on a state-of-the-art modeling approach for large-scale ecosystems that enables us to represent each plant as a detailed 3D geometric model. We introduce a novel mathematical formulation for the combustion process of plants - also considering effects such as heat transfer, char insulation, and mass loss - as well as for the propagation of fire through the entire ecosystem. Compared to other wildfire simulations which employ geometric representations of plants such as cones or cylinders, our detailed 3D tree models enable us to simulate the interplay of geometric variations of branching structures and the dynamics of fire and wood combustion. Our simulation runs at interactive rates and thereby provides a convenient way to explore different conditions that affect wildfires, ranging from terrain elevation profiles and ecosystem compositions to various measures against wildfires, such as cutting down trees as firebreaks, the application of fire retardant, or the simulation of rain.

Clean energy generation is gaining significant attention from industries, academia, and governments across the globe. The Allam cycle is one such technology that has been under focus due to its efficiency, environmental friendliness, and economics. This is a direct-fired cycle operating at supercritical conditions using carbon dioxide as a working fluid. Fuel or oxidizer jet mixing with CO2 is a vital phenomenon that governs combustion efficiency, and it is not well understood for the Allam cycle conditions. This paper experimentally and computationally investigated the jet characteristics of a methane jet injected into a subcritical to supercritical carbon dioxide environment. A wide range of injection pressures and temperatures were targeted between subcritical to supercritical conditions. Unlike previous studies, the current work focused on injecting lower-density (methane) jets into higher-density (carbon dioxide) environments. Schlieren imaging and methane absorption measurements were simultaneously performed with a CMOS high-speed camera and a 3.39 μm infrared laser. Specifically, we looked at the classical injection parameter of jet spreading angle, which was classically established to be mainly a density ratio function. Here, the jet cone angle was obtained from the post-processed schlieren videos. The jet cone angle is a critical characteristic parameter that describes the entrainment rate in a jet; thus, it is a crucial parameter in understanding the nature of the jet. The laser measurements were only used as an additional check to confirm the entry time of methane into the chamber filled with carbon dioxide. Notably, this paper makes a detailed comparison between the jet cone angles of jets with a density ratio. The result showed that the classical correlations, such as Abramovich’s theory applied to submerged turbulent gas jets developed for low-density ratio jets, were unsuitable for higher-density ratio jets. It was also observed that the divergence angles were dependent not only on density ratio but also on other parameters such as pressure ratios and reduced pressures.

The complex interplay of a number of physical and meteorological phenomena makes simulating clouds a challenging and open research problem. We explore a physically accurate model for simulating clouds and the dynamics of their transitions. We propose first-principle formulations for computing buoyancy and air pressure that allow us to simulate the variations of atmospheric density and varying temperature gradients. Our simulation allows us to model various cloud types, such as cumulus, stratus, and stratoscumulus, and their realistic formations caused by changes in the atmosphere. Moreover, we are able to simulate large-scale cloud super cells - clusters of cumulonimbus formations - that are commonly present during thunderstorms. To enable the efficient exploration of these stormscapes, we propose a lightweight set of high-level parameters that allow us to intuitively explore cloud formations and dynamics. Our method allows us to simulate cloud formations of up to about 20 km × 20 km extents at interactive rates. We explore the capabilities of physically accurate and yet interactive cloud simulations by showing numerous examples and by coupling our model with atmosphere measurements of real-time weather services to simulate cloud formations in the now. Finally, we quantitatively assess our model with cloud fraction profiles, a common measure for comparing cloud types.

Today, modern combustion systems and advanced cycles often reach operating pressures exceeding the working fluid’s or fuel’s critical pressure. While the liquid-gas coexistence line is the dominant feature in the fluid state space at low pressures, a supercritical analog to boiling, pseudo boiling, exists at supercritical pressures. Pseudo boiling is the transcritical state transition between supercritical liquid states and supercritical gaseous states, associated with peaks in heat capacity and thermal expansion. This transition occurs across a finite temperature interval. So far, the relation between the pseudo boiling line of tabulated hi-fi p-v-T data and the behavior of efficient engineering cubic equations of state (EOS) is unclear. In the present paper, we calculate the slope of the pseudo boiling line analytically from cubic equations of state. The Redlich-Kwong EOS leads to a constant value for all species, Peng-Robinson and Soave-Redlich-Kwong EOS yield a cubic dependency of the slope on the acentric factor. For more than twenty compounds with acentric factors ranging from −0.38 to 0.57 calculated slopes are compared with NIST data and vapor pressure correlations. Particularly the Peng-Robinson EOS matches reference data very well. Classical empirical values of Guggenheim or Plank & Riedel are obtained analytically. Then, pseudo boiling predictions of the Peng Robinson EOS are compared to NIST data. Deviations in transition temperature interval, and nondimensional parameters of the distributed latent heat are compared. Especially the different caloric behavior of tabulated fluid data for H2, N2, CO2, and H2O cannot be reproduced by the Peng Robinson EOS. These results may open the way towards new EOS with specific emphasis on Widom line and supercritical transition behavior.

Accurate and robust simulations of transcritical real-fluid flows are crucial for many engineering applications. Diffuse-interface methods are frequently employed and several numerical schemes have been developed for simulating transcritical flows. These schemes can be categorized into two types, namely fully conservative (FC) and quasi-conservative (QC) schemes. In this study, numerical analysis is conducted to show that the mixing processes for isobaric systems follow the limiting cases of adiabatic and isochoric mixing models when FC and QC schemes are employed, respectively. It is shown that these distinct mixing behaviors are a consequence of numerical diffusion instead of physical diffusion, and can be attributed to insufficient spatial resolution. By considering several test cases, numerical simulations confirm these theoretical results. The analysis of experimental data suggests that the isochoric mixing provides better agreement in terms of the phase separation behavior. This analysis provides quantitative understanding on the interpretation of numerical simulation results and the mixing models that are commonly used to study transcritical flows.

We investigate the flow in planar microscale nozzles and find that design and analysis paradigms based on the assumption of a dominant isentropic core with moderate viscosity corrections are not valid. Instead, the flow downstream of the throat is dominated by boundary layers that may choke the flow to subsonic velocities. The geometrical expansion ratio is found to be essentially irrelevant, instead, the length from throat to exit plane is found to be a much more important design parameter. Full 3D simulations are required to predict the flow topology; thermophysical modeling of the expanding gas has a noticeable impact on predicted performance. An analytical estimation of the Knudsen number in the expanding flow is given, allowing to determine its values from the expansion pressure ratio. An axial thrust analysis suggests truncation of the nozzle, resulting in a predicted 30% increase in thrust and 30% increase in specific impulse compared to the baseline configuration. The work has been carried out within the European Commission co-funded PRECISE project which was focused on designing and testing a micro chemical propulsion system thruster prototype using catalytically decomposed hydrazine as propellant.

Simulations of fluid mixing occurring at high-pressures mandate the use of real-fluid equations of state to capture the effect of both intermolecular repulsive forces and attractive forces which are neglected in perfect gases. Dedicated mixing rules account for these forces by providing a generic mapping of the mixture state-space onto a pure fluid domain. However, the specific inter-species molecular forces depend on the particular characteristics of the molecular pairs under consideration, and typically require the knowledge of binary interaction coefficients kαβ . The impact of kαβ on a flow field is as of now unclear; further, kαβ is unknown for many molecular pairs and when unknown, set to be null. This study addresses the impact of kαβ on the temporal evolution of a real-fluid mixing layer and uses Direct Numerical Simulation (DNS) to explore this impact. The results show differences between augmented attraction (kαβ 0), affecting both fluid dynamics and diffusion processes. Specifically, in a binary mixing layer, it is observed that augmented attraction leads to delayed transition and mixing layer growth, manifested in the momentum layer thickness. The fractal dimension as a measure of interface corrugation likewise shows a delayed development for augmented attraction. These results provide an hitherto undocumented mechanism affecting the development of mixing layers.

In this study, we evaluate the thermodynamic structure of laminar hydrogen/oxygen flames at supercritical 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 transcritical conditions is not dominated by large-scale homogeneous real-fluid mixing: similar to subcritical atomization, the supercritical pure oxygen stream undergoes a distinct transition from liquid-like to gas-like conditions; significant mixing and combustion occurs primarily after this transition under ideal gas conditions. The joint study of 1D flame computations and LES demonstrates that real-fluid behavior is chiefly confined to the bulk LOX stream; real fluid mixing occurs but in a thin layer surrounding the LOX core, characterized by water mass fractions limited to 3%. A parameter study of 1D flame solutions shows that this structure holds for a wide range of relevant injection temperatures and chamber pressures. To analyze the mixing-induced shift of the local fluid critical point, we introduce a state-space representation of the flame trajectories in the reduced temperature and reduced pressure plane which allows for a direct assessment of the local thermodynamic state. In the flame, water increases the local mixture critical pressures, so that subcritical conditions are reached. This view of limited mixing under supercritical conditions may yield more efficient models and an improved understanding of the disintegration modes of supercritical flows.

The article discusses the notion of a supercritical latent heat during 'pseudoboiling': Experimental, numerical, and theoretical evidence show that the supercritical state space is not homogeneous, but can be divided into liquid-like and gas-like domains, separated by an extension to the coexistence line -- the Widom line. The key concept are two limit states of ideal liquid and ideal gas, characterized by constant heat capacities, and analyze the transition between them. Then, analogous to subcritical vaporization, a supercritical state transition from liquid to gaseous overcomes intermolecular attractive forces, albeit over a finite temperature interval rather than at an equilibrium temperature. This distributed latent heat is in fact approximately invariant with respect to pressure for (0 < p < 3 pcr) and is thus valid at subcritical and supercritical conditions. This view also changes the perspective on subcritical latent heat: while it is an accurate representation of the required energy at very low pressures, the contribution of the distributed latent heat dominates the equilibrium latent heat as the critical pressure is approached.

This paper derives from the cooperation between DLR and Airbus DS within the work package “CFD Modeling of Combustion Chamber Processes” conducted in the frame of the Propulsion 2020 project. In a joint strategy, DLR Göttingen and Airbus DS Ottobrunn have identified a number of test cases with gradually growing complexity where adequate test data are available for proper successive validation of the computational fluid dynamics (CFD) tools to be used in an industrial environment. This work highlights the simulation results for the Mascotte A-10 and A-60 test cases as presented at the 2nd International Workshop on Rocket Combustion Modeling in Lampoldshausen 2001 by ONERA and SNECMA [1]. These two test cases are characterized by different chamber pressures (10 and 60 bar) and, consequently, by oxygen injection conditions which are subcritical in one case and transcritical in the other case. The test cases are treated with three different CFD codes: the DLR TAU Code (only A-60 case), the Airbus DS in-house tool Rocflam3, and the commercial CFD tool ANSYS CFX incorporating several modeling extensions by Airbus DS. To the knowledge of the authors, this paper is the first one which covers both the A-10 and the A-60 test cases.

An experimental combustor, designated BKH, is operated at DLR Lampoldshausen to investigate high-frequency combustion instability phenomena. The combustor operates with liquid oxygen (LOx) and gaseous or liquid hydrogen propellants at supercritical conditions analogous to real rocket engines. An externally imposed acoustic disturbance interacts with a series of 5 coaxial injection elements in the center of the chamber. A combination of experimental analysis and numerical modeling is used to provide further insight and understanding of the BKH experiments. Optical data from the BKH experiments are analyzed to extract the response of the flame at the excitation frequency. A new method for reconstructing the acoustic field inside the chamber from dynamic pressure sensor data is used to describe the evolution of the acoustic mode and the local disturbance in the flame zone. An Unsteady Reynolds-Averaged Navier–Stokes (URANS) model of a single BKH injection element subjected to representative transverse acoustic velocity excitation has been computed using a specialized release of the DLR TAU code. The single-element model reproduces the retraction of the dense LOx core during transverse velocity excitation as observed experimentally. The model also provides further insight into the flattening and flapping of the flame. The flapping is identified as the oxygen core being transported by the transverse acoustic velocity.

Experimental, computational, and theoretical results have shown that the notion of a homogeneous supercritical state space has to be replaced with distinct liquid-like and gas-like regions, divided by a cross-over line. Several such cross-over lines have been proposed, such as the Frenkel line, the Fisher-Widom line, and the Widom line. We use thermodynamics arguments, molecular dynamics (MD) simulations, and experimental data to investigate the relation between these lines. This work proposes a new interpretation of the Widom line based on the curvature of the Gibbs free energy, showing that the supercritical cross-over can be evaluated as a projection of the subcritical phase transition from a liquid to an ideal gas state to supercritical conditions. We show that the cross-over across the Widom line should not be regarded as instantaneous, but instead as spreading over a finite temperature interval. The thermodynamic character of the Widom line becomes negligible at reduced pressures p/pcr > 3 and disappears completely at higher pressures p/pcr > 10. We find evidence that measured transitions attributed to the Widom line do in fact match the Frenkel line better. In this way, we suggest a consistent view of the supercritical state space and resolve apparent contradictions.

The accurate and robust simulation of transcritical real-fluid flows is crucial for many engineering applications. Diffused interface methods are frequently employed and several numerical schemes have been developed for simulating transcritical flows. These schemes can be categorized into two types, namely fully conservative and quasi-conservative schemes. An adaptive scheme which is a hybrid of the two is developed in this study. By considering several numerical test cases, it is shown that different schemes predict distinctly different mixing behaviors. It is shown that the mixing processes follow the isobaric-adiabatic and isobaric-isochoric mixing models for fully and quasi-conservative schemes, respectively, and the adaptive scheme yields a mixing behavior that spans both models. The distinct mixing behaviors are a consequence of numerical diffusion instead of physical diffusion and can be attributed to insufficient numerical spatial resolution. This work provides a better understanding on the interpretation of numerical simulation results and the mixing models that are commonly used to study transcritical flows., AIAA SciTech 2018, Kissimmee, FL

Recent experiments on pure fluids have identified distinct liquid-like and gas-like regimes even under supercritical conditions. The supercritical liquid-gas transition is marked by maxima in response functions that define a line emanating from the critical point, referred to as Widom line. However, the structure of analogous state transitions in mixtures of supercritical fluids has not been determined, and it is not clear whether a Widom line can be identified for binary mixtures. Here, we present first evidence for the existence of multiple Widom lines in binary mixtures from molecular dynamics simulations. By considering mixtures of noble gases, we show that, depending on the phase behavior, mixtures transition from a liquid-like to a gas-like regime via distinctly different pathways, leading to phase relationships of surprising complexity and variety. Specifically, we show that miscible binary mixtures have behavior analogous to a pure fluid and the supercritical state space is characterized by a single liquid-gas transition. In contrast, immiscible binary mixture undergo a phase separation in which the clusters transition separately at different temperatures, resulting in multiple distinct Widom lines. The presence of this unique transition behavior emphasizes the complexity of the supercritical state to be expected in high-order mixtures of practical relevance.

The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures p_{cr} and temperatures T_{cr} only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor ω and compares well with experimental data. Second, we introduce the scaled reduced pressure p_{r}^{*} to replace the previously used reduced pressure p_{r}=p/p_{cr}. We show that p_{r}^{*} is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from -0.38 (helium) to 0.34 (water), including alkanes up to n-hexane. By using p_{r}^{*}, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, p_{r}^{*} provides a theoretical foundation to compare Widom lines of different fluids.

This paper introduces a new model for real gas thermodynamics, with improved accuracy, performance, and robustness compared to state-of-the-art models. It is motivated by the physical insight that in non-premixed flames, as encountered in high pressure liquid propellant rocket engines, mixing takes place chiefly in the hot reaction zone among ideal gases. We developed a new model taking advantage of this: When real fluid behavior only occurs in the cryogenic oxygen stream, this is the only place where a real gas equation of state (EOS) is required. All other species and the thermodynamic mixing can be treated as ideal. Real fluid properties of oxygen are stored in a library; the evaluation of the EOS is moved to a preprocessing step. Thus decoupling the EOS from the runtime performance, the method allows the application of accurate high quality EOS or tabulated data without runtime penalty. It provides fast and robust iteration even near the critical point and in the multiphase coexistence region. The model has been validated and successfully applied to the computation of 0D phase change with heat addition, and a supercritical reactive coaxial LOX/GH 2 single injector.

Recent publications in the open literature have shown that supercritical fluid states are not homogeneously distributed but, in fact, can be differentiated into two distinct regions with gas-like and liquid-like properties, respectively. These regions are divided by an extension of the coexistence line, commonly called Widom line. This paper shows that a supercritical analog to subcritical phase change, pseudoboiling, does exist when crossing this demarcation. The supercritical state transition does not occur in a phase equilibrium but takes place over a finite temperature interval. While subcritical vaporization requires energy to overcome intermolecular attraction, supercritical state transitions additionally require energy to increase the temperature. It could be shown that the attractive potential is the dominant energy sink up to a reduced pressure of 1.5 for argon, nitrogen, oxygen, and water. The effect reduces with growing pressure and becomes negligible for p / p cr > 3. Furthermore, a new equation for this Widom- or pseudoboiling-line is given. It exhibits improved accuracy over previously published equations; performing a limit analysis of the Clapeyron equation allows to express its sole parameter purely in terms of thermodynamic variables. This parameter can then be evaluated from an equation of state or from fluid data - no nonphysical fitting is required.

In this paper we report on supercritical single injector computations using a new type of real gas CFD model. This Euler-Euler model is an extension to the DLR TAU CFD code. By storing fluid data in a library, we were able to decouple equation of state (EOS) accuracy from runtime performance. The library covers all fluid states effciently and robust, including gaseous, liquid, supercritical, and multiphase states. In our new multifluid mixing model, an EOS is solved for each species. Computations were carried out using a modifed Benedict-Webb-Rubin high fidelity equation of state for cryogenic oxygen, with negligible penalty in performance compared to a pure ideal gas computation. Additional species (H, H2, O, OH, H2O, H2O2) were treated as perfect gases. The immediate goal is to create a flow solver for industrial application, i.e. to support design by enabling a fast turnaround. Thus, we focus on 2D RANS modeling in this first step. The baseline model is applied to the canonical Mascotte A60 test case. The chamber pressure is well met, the flame dimensions are within the spread found among other CFD results. In accordance with experimental results, the reaction zone is very thin. Maximum OH* occurrences are correctly predicted in the shear layer, reducing in magnitude towards shoulder and flame tip. The fluid library allows to pinpoint the extent of the liquid oxygen core, the length is determined to 20 LOX injector diameters. It is found to be embedded in a gaseous oxygen shell. Within this RANS context, H2 and O2 do not coexist in a premixed form. Finally, we show that numerical OH* concentration differs significantly from OH mass fraction distributions, the latter are thus no appropriate data to compare to experiments.

Flow in micro chemical propulsion systems (µCPS) based on etched silicon deviates strongly from its conventional, macroscopic counterparts. This paper reports on peculiarities of small scale planar nozzles with a high aspect ratio, rectangular cross section. Design and analysis paradigms based on the assumption of rationally symmetric flow with a dominant isentropic core are shown to be no longer valid. We will point out insufficiencies of treating planar nozzles as two dimensional, inviscid, or assessing their performance with classical analytical isentropic 1D analysis. Instead, the resulting low Reynolds number flow is boundary layer dominated. Boundary layer build-up from the top and bottom walls threaten to choke the expansion. The geometrical expansion ratio is found to be essentially irrelevant, the length from throat to exit plane is found to be a much more important design parameter. The work has been carried out within the European PRECISE project which is focused on designing and testing a prototype using catalytically decomposed hydrazine as propellant.

In this paper, a new interpretation of cryogenic jet break-up in supercritical environments is introduced. It is firmly established that under these conditions a pure fluid will exhibit neither latent heat of vaporization nor surface tension. The jet undergoes a transition from a dense cryogenic fluid to an ideal gas as it mixes and blends with the surrounding warmer gas. Regarding the thermodynamic process, this transition is characterized by large changes in density and very small changes in temperature as energy is supplied. The state where density changes and the heat capacity are maximal is sometimes called `pseudo-boiling' in the literature. However, no clear definition of this process is available, its very existence debated. In this paper, the first quantitative pseudo-boiling analysis is presented. It can be shown that pseudo-boiling exists along a line which effectively structures supercritical uid states. An equation for this continuation of the coexistence line is given. Across this line, a continuous state transition can be identfied. The temperature at pseudo-boiling replaces the critical temperature as relevant parameter at supercritical pressures. By introducing a suitable definition for a supercritical uid boundary, supercritical jet break-up can be quantified thermodynamically. This suggests a novel, thermal, jet break-up mechanism. Experimental evidence from the literature is shown, further supported by CFD simulations. The pseudo-boiling effect is found to play a role for injection conditions of reduced pressures smaller than 3, and reduced temperatures lower than 1.2.

Certain experiments in quasi-isobaric supercritical injection remain unexplained by the current state of theory: Without developing a constant value potential core as expected from the mechanical view of break-up, density is observed to drop immediately upon entering the chamber. Furthermore, this phenomenon has never been captured in computational fluid dynamics (CFD) despite having become a de facto standard case for real fluid CFD validation. In this paper, we present strong evidence for a thermal jet disintegration mechanism (in addition to classical mechanical break-up) which resolves both the theoretical and the computational discrepancies. A new interpretation of supercritical jet disintegration is introduced, based on pseudo-boiling, a nonlinear supercritical transition from gas-like to liquid-like states. We show that thermal disintegration may dominate classical mechanical break-up when heat transfer takes place in the injector and when the fluid state is sufficiently close to the pseudo-boiling point. A procedure which allows to capture subsided cores with standard CFD is provided and demonstrated.

This paper discusses a thermodynamic rather than mechanic discussion and interpretation of cryogenic injection of nitrogen in the vicinity of the critical point. There is no concensus in the literature on how to properly interpret and treat injection phenomena at supercritical pressures. While it is clear that the supercritical fluid loses many distinct liquid properties, such as heat of vaporization and surface tension, flows are being treated like they were liquid. Liquid core lengths are being determined in experiments, distinct droplets are tracked in computational fluid dynamic studies. And in fact, these approaches prove to be very successful. Nevertheless, a more appropriate treatment is desireable, taking into account the specifics of supercritical fluids. A contribution is attempted in this paper. The concept of pseudo-boiling, a maximum in heat capacity associated with a strong increase in specific volume, is discussed. It will be shown that the ensemble of supercritical maximum heat capacity states is in fact an extension to the saturation curve. A novel interpretation of the Clapeyron equation of thermodynamics in the limit of the critical point and beyond will be given. It will be shown that this generalization is able to characterize the pseudo-boiling line. Furthermore it will be shown that the slope (d log p/dT) is constant for supercritical conditions and equals the value at the critical point. The pseudo-boiling approach is then applied to characterize injection experiments. It can be shown that the power needed to reach the pseudo-boiling state correlates with the structure of the axial density distribution.

This paper discusses features of a supersonic flow with a transversal Mach number stratification when encountering a ramp. A flow of this nature can occur for a variety of reasons around a hypersonic vehicle. Formation of a heated wall boundary layer, external fuel injection on the compression ramp, energy deposition, and film or transpiration cooling are just some of the processes that will establish a flow where a wall near layer features a distinct difference in Mach number compared to the outer flow. This paper will introduce a flow topology framework that will help to understand phenomena associated with this stratification. Shock refraction is identified as the main mechanism which causes a redirection of the flow additional to the ramp deflection. It will be shown how, depending on the Mach number ratios between the layers, shocks or expansion fans will be created that will interact with the surface. This can be the cause for undesired or unexpected temperature and pressure distributions along the wall when shock refraction is not taken into account. As a possible application, it will be shown how shock refraction can act as a virtual external compression ramp. CFD computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver.

This paper discusses the ongoing extension of the DLR TAU Code with a multiphase flow model. The reasoning behind choosing a Statistical Eulerian Eulerian (SEE) model with Interfacial Area Transport Equation (IATE) is covered. Properties of the model are introduced, especially concerning the less known IATE concept which provides information about interphasic interfacial area (IA) available in a computational cell. This allows for a more elaborate sub grid scale modeling. An general IA convection velocity is derived which holds for the limiting cases of stratified flow and disperse flow. As an exemplary application, the development of a spray injection IATE is discussed. This includes interfacial growth due to velocity gradients and a new IA detection term which resolves ambiguities with boundary conditions.

This paper discusses some general properties of energy deposition in hypersonics. Extending the flight envelope of passenger aircraft to high Mach numbers comes with problems unsolved before in civil flight, such as sonic boom, or excessive thermal and mechanical loads. Energy deposition is regarded as a possible remedy to a multitude of problems occurring in this flight regime and thus studied here. A new energy source term has been implemented into the DLR TAU CFD code which models a physical distributed heat addition. In a first step, energy deposition in free flow is investigated using this new term. Four flow topologies, dependent on the deposition energy, have been identified, ranging from negligible induced cross flow component, to a massive detached bow shock ahead of the deposition region. In a second step, ramp flow, as a precursor to flow about an airfoil, is studied under the influence of an upstream energy deposition region. An undesired low pressure region could be explained with a simplified model of wave refraction at thermally stratified ramp flow. Key of this model is a flow deflection above the ramp which is needed to balance pressure dierences. This model is discussed in detail to fully understand the physical nature of the flow structure. It predicts a way of increasing surface pressure compared to regular ramp flow at reduced total pressure loss. It furthermore predicts the occurrence of premature shock separation and oscillating shock patterns. Analyzing this model, a simple yet accurate functional formula is found for the additional deflection angle due to refraction which simplifies the calculation of the surface pressure distribution as no pressure balance iteration is needed anymore. These studies are currently carried out within the European ATLLAS project which is concerned with the development of hypersonic passenger aircraft. Computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver.

Contributions to Statistical Eulerian-Eulerian (SEE) flow models of two-phase flow are discussed in this article. Special attention is given to the Interfacial Area Transport Equation (IATE) which al-lows for sub grid scale modeling of exchange processes and a topological interpretation of continuous results. An interfacial area convection velocity is derived based on the assumption of strati-fied flow. This scheme will be shown to also hold in the limit of dilute spray. In the case of vanishing surface tension and heat of vaporization, disintegration of a supercritical jet can be described as a mixing rather than an atomization process. Following this assumption, growth of interfacial area due to stretching is dis-cussed and a new model term suggested. To resolve former diffi-culties with the interfacial area inflow boundary condition, an automatic interfacial area detection is proposed. This new term also allows for automatic creation of interfacial area in the case of unsteady injection or formation of a phase (e.g. condensation, cavitation, vaporization). The described model is implemented in the DLR finite volume TAU code.

In this paper we introduce a novel model for liquid rocket engine (LRE) propellant injection. Most academic codes today use an Eulerian-Eulerian (EE) description, i.e. all involved propellants and reaction products are regarded as continuous uids instead of discrete droplets. These models have successfully been improved and are capable of high fidelity studies of single injectors and mixing layers, using LES or even DNS. While impressive, this is prohibitive with regard to the simulation of a full thrust chamber with fast turnaround times - as required in industrial applications. Focusing on a RANS model, we decided to take a different route in terms of enhancement: the equation of state (EOS). State of the art EE models perform a runtime evaluation of the EOS. Thus, its numerical efficiency becomes a constraint. By using a precalculated library for the EOS instead, we succeeded to decouple quality of the EOS and CFD runtime. A multi fluid mixing model is developed which allows for each species to be modeled individually. The approach is embed- ded in a Eulerian-Eulerian homogeneous two phase model, i.e. a thermal and mechanical equilibrium between surrounding gaseous flow and and injected cryogenic fluid is assumed in each numerical cell. Due to the general treatment of the oxygen thermodynamics, the oxidizer phase can assume any thermodynamic state, including gaseous, supercritical, liquid, as well as multiphase vapor liquid mixtures. The model is validated with 0D vaporization processes. As a first application, the supercritical pressure single injector Mascotte A60 test case is treated where cryogenic oxygen is injected. Excellent agreement is found with experimental OH emission data. Especially, maximum OH emission is correctly placed in the hydrogen oxygen shear layer