Computational fluid dynamics (CFD) has proven to be an invaluable tool for the design and analysis of highspeed propulsion devices. Massively parallel computing, together with the maturation of robust CFD codes, has made it possible to perform simulations of complete engine flowpaths. Steady-state Reynolds-Averaged Navier-Stokes simulations are now routinely used in the scramjet engine development cycle to determine optimal fuel injector arrangements, investigate trends noted during testing, and extract various measures of engine efficiency. Unfortunately, the turbulence and combustion models used in these codes have not changed significantly over the past decade. Hence, the CFD practitioner must often rely heavily on existing measurements (at similar flow conditions) to calibrate model coefficients on a caseby-case basis. This paper provides an overview of the modeled equations typically employed by commercialquality CFD codes for high-speed combustion applications. Careful attention is given to the approximations employed for each of the unclosed terms in the averaged equation set. The salient features (and shortcomings) of common models used to close these terms are covered in detail, and several academic efforts aimed at addressing these shortcomings are discussed.

https://ntrs.nasa.gov/api/citations/20040035566/downloads/20040035566.pdf

Modeling of high speed reacting flows: established practices and future challenges

This article deals with high-speed turbulent combustion based on finite-rate chemistry. An assumed probability density function (PDF) approach is used to account for turbulence chemistry interaction. The PDFs employed are a clipped Gaussian distribution for temperature and a joint multivariate g -PDF for species mass fractions. The definition of both PDFs is based on higher order moments obtained from additional transport equations. The objective of this work is to compare different variance transport equations (energy, sensible energy, and temperature) from which the required temperaturevariance is recovered. Moreover, the influence of closed and unclosed correlations of these variance transport equations is investigated. It is shown that some higher order correlations as well as commonly used approximations for the temperature variance recovery may result in significant errors. This is the reason for modifications and for the use of a temperature variance transport equation. Numerical results are compar...

Investigation of an Assumed PDF Approach for Finite-Rate Chemistry

https://elib.dlr.de/75435/1/Koehler2012CF_manuscript.pdf

Experimental characterization and numerical simulation of a sooting lifted turbulent jet diffusion flame

A Reynolds-averaged Navier-Stokes-based scalar-variance model is described that extends a previous low-speed nonreacting jet model to more generalized high-speed compressible reacting flows. The model is cast in a k-e turbulence model framework. Transport equations for energy variance and its dissipation rate are solved to predict temperature fluctuations and provide a thermal time scale for use in calculating a variable turbulent Prandtl number. For multispecies problems, mixture-fraction variance and dissipation rate equations are solved that predict species concentration fluctuations and provide a species mixing time scale for use in calculating a variable turbulent Schmidt number. The formulation accounts for compressibility and near-wall damping effects. A series of high-speed flow simulations are presented for both nonreacting and reacting configurations and the predictions are compared to available measured data and companion LES calculations. Results demonstrate the models' capabilities over a range of conditions and suggest that the proposed formulation will provide improved predictions in practical high-speed aeropropulsive configurations of interest, such as scramjet combustors, where turbulent Prandtl and Schmidt numbers vary substantially.

Scalar Fluctuation Modeling for High-Speed Aeropropulsive Flows

A Supersonic Combustion Ramjet (scramjet) is, at least in theory, an efficient air-breathing propulsion system for sustained hypersonic flight at Mach numbers above approximately M=5.
Important design issues for such hypersonic propulsion systems, are the lack of ground based facilities capable of testing a full-sized engine at cruise flight conditions and the absence of general scaling laws for the extrapolation of wind tunnel data to flight configurations. Therefore, there is a strong need for the development and validation of CFD tools to support the design process of scramjet-powered vehicles. Specific challenges for the applied CFD solvers include the accurate prediction of skin friction and heat transfer caused by turbulent boundary layers, the mixing and combustion of fuel in compressible turbulent shear layers, and the modelling of chemical nonequilibrium effects, which can be of significant importance for the prediction of engine performance.
Due to the uncertainties associated with the modelling of turbulent compressible and chemically reacting flows that are still associated with current CFD solvers and the limitations of experimental methods to comprehensively characterize the flow properties, a close interaction of CFD and experimental investigations is necessary to further improve the understanding of flow phenomena iinside scramjet engines.
The aims of this thesis are, in this context, to assess the applicability of, to further develop, and to validate the DLR TAU flow solver for the CFD analysis of the complete flow-path of a scramjet vehicle. The basis of this validation and of the identification of critical modelling assumptions is the
recalculation of a series of wind tunnel tests of the HyShot II generic scramjet configuration that were performed in the High Enthalpy Shock Tunnel Gottingen (HEG) at the German Aerospace Center, DLR.
Appropriate models for turbulent hydrogen combustion are implemented in the TAU solver. These include models for the thermodynamic and transport properties of the participating species, appropriate reaction mechanisms and an assumed-PDF model of the turbulence-chemistry iinteractions. The complete modelling strategy is validated using a representative test case
consisting of detailed experimental results for a lifted flame in a co-axial burner configuration.
The TAU code is then applied to determine the free stream conditions in the HEG test section, to simulate the HyShot intake flow field, and for a numerical investigation of the turbulent reacting flow in the combustor. The sensitivity of the numerical results to relevant modelling parameters
such as, for example, the choice of the turbulence model, the Schmidt number assumption and the influence of turbulence-chemistry interactions were assessed to draw conclusions regarding the uncertainty margins of the CFD predictions. Finally, further numerical investigations are performed
to assess the applicability of the pL-scaling law for scramjet combustors.

P. Gerlinger

Papers

Investigation of an Assumed PDF Approach for Finite-Rate Chemistry

Investigation of an assumed PDF approach for finite-rate chemistry