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This book reports on advanced theories and methods aimed at characterizing the dynamics of non-ideal compressible fluids. A special emphasis is given to research fostering the use of non-ideal compressible fluids for propulsion and power engineering. Both numerical and experimental studies, as well as simulations, are described in the book, which is based on selected contributions and keynote lectures presented at the 2nd International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power. Held on October 4-5 in Bochum, Germany, the seminar aimed at fostering collaborations between academics and professionals. The two perspectives have been gathered together in this book, which offers a timely guide to advanced fundamentals, innovative methods and current applications of non-ideal compressible fluids to developing turbomachines, and for propulsion and power generation.

### Experimental Investigations of Heat Transfer Processes in Cooling Channels for Cryogenic Hydrogen and Methane at Supercritical Pressure

Abstract
A rising demand for efficient and reusable rocket engines leads to the development of a new generation of methane fueled rocket engines. The most crucial part is the optimal design of the cooling system, with minimal hydrodynamic losses. Therefore a precise knowledge of the heat transfer processes in the combustion chamber and primarily in the cooling channels is necessary. Cooling channels with a high aspect ratio (height-to-width-ratio) in a wall material with high thermal conductivity are known to improve cooling efficiency with only moderate increase in hydrodynamic losses. In this paper tests will be presented, that were performed with a cylindrical combustion chamber. This chamber is divided into 4 sections around the circumference, each containing cooling channels with different aspect ratios (1.7, 3.5, 9.2 and 30). Cryogenic hydrogen and liquid methane at temperatures as low as 60 K for hydrogen and 130 K for methane respectively were used as cooling fluids. Results show a distinct thermal stratification for both coolants and a very high influence of changing fluid properties close to the critical point for methane.
Jan Haemisch, Dmitry Suslov, Michael Oschwald

### Efficient Handling of Cryogenic Equation of State for the Simulation of Rocket Combustion Chambers

Abstract
The simulation of cryogenic flows in rocket combustion chambers is challenging because we have to consider a reactive mixture over a wide temperature and density range. This necessitates the use of more advanced fluid models that impose additional computation overhead. In this study we compare two equation of state (EOS) mixture approximation approaches for cryogenic flows in rocket combustion chambers and present a computationally efficient implementation within a Reynolds Averaged Navier Stokes (RANS) context. The numerical study is validated with experimental results of a lab-scale rocket combustion chamber with optical access.
Stefan Fechter, Tim Horchler, Sebastian Karl, Klaus Hannemann, Dmitry Suslov, Justin Hardi, Michael Oschwald

### Non-equilibrium Model for Weakly Compressible Multi-component Flows: The Hyperbolic Operator

Abstract
We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. Each component is described by its own thermodynamic model, thus the definition of a mixture speed of sound is not required. In this work, we describe the hyperbolic operator, without considering relaxation terms. The acoustic part of the governing equations is treated implicitly to avoid the severe restriction on the time step imposed by the CFL condition at low-Mach. Particular care is taken to discretize the non-conservative terms to avoid spurious oscillations across multi-material interfaces. The absence of oscillations and the agreement with analytical or published solutions is demonstrated in simplified test cases, which confirm the validity of the proposed approach as a building block on which developing more accurate and comprehensive methods.
Barbara Re, Rémi Abgrall

### Pressure-Based Solution Framework for Non-Ideal Flows at All Mach Numbers

Abstract
In this work, we present an all Mach number pressure-based solution framework suitable for the simulation of application-relevant high-pressure flow configurations. A cubic equation of state is applied for the accurate description of the thermodynamic state. Different formulations of the pressure equation for sub- and supersonic flows are discussed. The framework is employed to simulate one sub- and one supersonic test case, where experimental data are available. The comparison of the simulation results with experimental shadowgraphy and Schlieren images shows very good agreement.
Christoph Traxinger, Julian Zips, Matthias Banholzer, Michael Pfitzner

### Towards Direct Numerical Simulations of Shock-Turbulence Interaction in Real Gas Flows on GPUs: Initial Validation

Abstract
A better understanding of turbulent flows in presence of strong compressible and real gas effects is in high demand for future improvements in engineering applications, such as turbomachines for regenerative power production. Therefore, a solver for future investigation of shock-turbulence interaction in presence of strong real gas effects by means of direct numerical simulation with multi-parameter equations of state utilizing the computational power of GPUs is carefully designed and initially validated using the example of carbon dioxide. It relies on a hybrid energy-consistent WENO scheme based on a shock sensor. The implementation is validated with a set of test cases, comprising the Shu–Osher problem, the inviscid Taylor-Green vortex and the compressible decay of homogeneous isotropic turbulence with eddy shocklets. In absence of appropriate and well documented experimental results, the test cases are adapted to real gas in regions where the gas behavior can be deemed near to the ideal limit and results are compared with the validated ideal gas configurations.
Pascal Post, Francesca di Mare

### Direct Numerical Simulation of Turbulent Dense Gas Flows

Abstract
In order to assess the specific characteristics of turbulence in dense gas flows with respect to ideal gas flows, Direct Numerical Simulations are performed for both FC-70 described using Martin-Hou Equation of State (EoS) and a reference ideal gas, in the case of a forced Homogeneous Isotropic Turbulence (HIT) configuration and of a temporal compressible mixing layer configuration. The forced HIT shows that the statistically stationary turbulent kinetic energy (TKE) spectrum follows quite closely the one obtained in the incompressible case even when the turbulent Mach number is large. It is shown that the weakening of compressible dissipation of the TKE can be related to the decoupling of the density fluctuations from the velocity as well as to the strong weakening of compression shocklets in the dense gas case. The mixing layer case at a convective Mach number $$M_c=1.1$$ shows that the well-known compressibility-related reduction of the mixing layer momentum thickness growth rate is not significantly influenced by the EoS. Yet the unstable growth leading to the self-similarity phase is enhanced by the dense gas thermodynamics.
Alexis Giauque, Christophe Corre, Aurélien Vadrot

### Numerical Investigation of Supersonic Dense-Gas Boundary Layers

Abstract
A study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.
Luca Sciacovelli, Donatella Passiatore, Xavier Gloerfelt, Paola Cinnella, Francesco Grasso

### Entropy Generation in Laminar Boundary Layers of Non-Ideal Fluid Flows

Abstract
This paper documents a numerical study on entropy generation in zero-pressure gradient, laminar boundary layers of adiabatic non-ideal compressible fluid flows. The entropy generation is expressed in terms of dissipation coefficient $$C_\mathrm {d}$$ and its dependency on free-stream Mach number, fluid molecular complexity, and flow non-ideality is investigated systematically by means of a boundary layer code extended to treat fluids modeled with arbitrary equations of state. The results of the study show that the trend of dissipation coefficient follows that of an incompressible flow for complex fluid molecules like siloxanes in all thermodynamic and flow conditions. For simpler fluids like CO$$_2$$ the trend becomes inversely proportional to the free-stream Mach number and the $$C_\mathrm {d}$$ value can significantly reduce in the non-ideal flow regime, where strong thermo-physical property gradients occur near the wall.
Matteo Pini, Carlo De Servi