Generalized cylindrical coordinates for characteristic boundary conditions and characteristic interface conditions

The aim of this report is to derive generalized coordinates for the specific case of mapping only the streamwise and radial coordinate of a cylindrical coordinate system, while leaving the azimuthal coordinate unchanged. The characteristic equations and the required matrices for the transformation from conservative to characteristic form are presented for this specific case. All equations and procedures are based on previous work on generalized characteristic boundary conditions (Kim &amp; Lee, 2000) and characteristic interface conditions (Kim &amp; Lee, 2003).<br/

A modification of Amiet's classical trailing edge noise theory for strictly two dimensional flows

The aim of this report is to derive theoretical expressions for the far-field pressure generated by disturbances convecting over a trailing edge. First, a general calculation of thefar-field pressure is discussed. Then the classical theory of Amiet (1976b) is reviewed,listing the most relevant assumptions. Amiet's theory is then revised for two-dimensional flows

RANS Turbulence Model Development using CFD-Driven Machine Learning

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method (Weatheritt and Sandberg, 2016), but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.Comment: Accepted by Journal of Computational Physic

A Comparative Study of Contrasting Machine Learning Frameworks Applied to RANS Modeling of Jets in Crossflow

Classical RANS turbulence models have known deficiencies when applied to jets in crossflow. Identifying the linear Boussinesq stress-strain hypothesis as a major contribution to erroneous prediction, we consider and contrast two machine learning frameworks for turbulence model development. Gene Expression Programming, an evolutionary algorithm that employs a survival of the fittest analogy, and a Deep Neural Network, based on neurological processing, add non-linear terms to the stress-strain relationship. The results are Explicit Algebraic Stress Model-like closures. High fidelity data from an inline jet in crossflow study is used to regress new closures. These models are then tested on a skewed jet to ascertain their predictive efficacy. For both methodologies, a vast improvement over the linear relationship is observed