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Thermodynamic Analysis and Numerical Modeling of Supercritical Injection

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Although liquid propellant rocket engines are operational and have been studied for decades, cryogenic injection at supercritical pressures is still considered essentially not understood. This thesis intends to approach this problem in three steps: by developing a numerical model for real gas thermodynamics, by extending the present thermodynamic view of supercritical injection, and finally by applying these methods to the analysis of injection. A new numerical real gas thermodynamics model is developed as an extension of the DLR TAU code. Its main differences to state-of-the-art methods are the use of a precomputed library for fluid properties and an innovative multi-fluid-mixing approach. This results in a number of advantages: There is effectively no runtime penalty of using a real gas model compared to perfect gas formulations, even for high fidelity equations of state (EOS) with associated high computational cost. A dedicated EOS may be used for each species. The model covers all fluid states of the real gas component, including liquid, gaseous, and supercritical states, as well as liquid-vapor mixtures. Numerical behavior is not affected by local fluid properties, such as diverging heat capacities at the critical point. The new method implicitly contains a vaporization and condensation model. In this thesis, oxygen is modeled using a modified Benedict-Webb-Rubin equation of state, all other involved species are treated as perfect gases. A quantitative analysis of the supercritical pseudo-boiling phenomenon is given. The transition between supercritical liquid-like and gas-like states resembles subcritical vaporization and is thus called pseudo-boiling in the literature. In this work it is shown that pseudo-boiling differs from its subcritical counterpart in that heating occurs simultaneously to overcoming molecular attraction. In this process, the dividing line between liquid-like and gas-like, the so called Widom line, is crossed. This demarcation is characterized by the set of states with maximum specific heat capacity. An equation is introduced for this line which is more accurate than previous equations. By analyzing the Clausius-Clapeyron equation towards the critical limit, an expression is derived for its sole parameter. A new nondimensional parameter evaluates the ratio of overcoming molecular attraction to heating: It diverges towards the critical point but shows a significant pseudo-boiling effect for up to reduced pressures of 2.5 for various fluids. It appears reasonable to interpret the Widom-line, which divides liquid-like from gas-like supercritical states, as a definition of the boundary of a dense supercritical fluid. This may be used to uniquely determine the radius of a droplet or the dense core length of a jet. Then, a quantitative thermodynamic analysis is possible. Furthermore, as the pseudo-boiling process may occur during moderate heat addition, this allows for a previously undescribed thermal jet disintegration mechanism which may take place within the injector. This thermal jet break-up hypothesis is then applied to an analysis of Mayer’s and Branam’s nitrogen injection experiments. Instead of the constant density cores as predicted by theory, the majority of their cases show an immediate drop in density upon entering the chamber. Here, three different axial density modes are identified. The analysis showed that heat transfer did in fact take place in the injector. The two cases exhibiting a dense core are the cases which require the largest amount of power to reach the pseudo-boiling temperature. After this promising application of pseudo-boiling analysis, thermal break-up is tested numerically. By accounting for heat transfer inside the injector, a non dense-core injection can indeed be simulated for the first time with CFD. Finally, the CFD model is applied to the A60 Mascotte test case, a reactive GH2/LOX single injector operating at supercritical pressure. The results are compared with experimental and other researcher’s numerical data. The flame shape lies well within the margins of other CFD results. Maximum OH* concentration is found in the shear layer close to the oxygen core and not in the shoulder, in agreement with experimental data. The axial temperature distribution is matched very well, particularly concerning position and value of the maximum temperature.
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... However, this assumption is physically justified in this work focused on supercritical oxygen-hydrogen combustion. Banuti et al. [60,65] explain that, for oxygen-hydrogen combustion at supercritical pressures, the LOx transitions from a liquid to a supercritical gas-like state under pure fluid conditions, where essentially all real fluid effects are confined to the LOx core. Thus, for the flames considered in the present work, the multi-fluid ideal-mixing model is appropriate. ...
... Computational domain[53] main features: each species has a dedicated equation of state and the properties of the mixture are determined by a multi-fluid mixing model, see[60][61][62] .Here the ideal gas equation of state is solved for H 2 , H, O, OH and H 2 O, and a real gas equation of state is solved for O 2 . The real gas properties of oxygen are computed from the high fidelity modified Benedict-Webb-Rubin (MBWR) equation of state (EOS) of Younglove ...
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... To investigate the response of the BKH study elements to an imposed acoustic disturbance, a model of a single injector under acoustic forcing has been developed. The model consists of steady and unsteady computations using a specialized version of the DLR TAU code for modeling real gas properties [9,10]. A steady-state Reynolds-averaged NavierStokes (RANS) computation is used to model the single injector under steady-state operation without acoustic forcing. ...
... To account for these real gas e¨ects, a new real gas mixture model has been developed and implemented in the DLR TAU code. The model and its validation are described in more depth in [9,10]. ...
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... Summarized [17], "The acceptance of this change in understanding is perhaps best reflected in the shift of boundary conditions posed by the Rocket Combustion Modeling (RCM) workshops 2001 [18] and 2006 [19]. For the same configuration of a single injector combustion chamber (but at a different oxidizer/fuel ratio) at supercritical pressures, the 2001 workshop specified a spectrum of oxygen droplets to be prescribed in the CFD calculation. ...
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