A Machine Learning Approach for Determining the Turbulent Diffusivity in Film Cooling Flows

Abstract

In film cooling flows, it is important to know the temperature distribution resulting from the interaction between a hot main flow and a cooler jet. However, current Reynolds-averaged Navier-Stokes (RANS) models yield poor temperature predictions. A novel approach for RANS modeling of the turbulent heat flux is proposed, in which the simple gradient diffusion hypothesis (GDH) is assumed and a machine learning algorithm is used to infer an improved turbulent diffusivity field. This approach is implemented using three distinct data sets: two are used to train the model and the third is used for validation. The results show that the proposed method produces significant improvement compared to the common RANS closure, especially in the prediction of film cooling effectiveness.

Enriching MRI mean flow data of inclined jets in crossflow with Large Eddy Simulations

“…Such data will be further analyzed in future work, especially in regards to the turbulent scalar flux. The datasets presented here consist of a high quality and validated set of simulations with parameter variation (in this case, the velocity ratio r) that will be used for data-driven turbulence modeling in film cooling flows, as was done by Milani et al [29]. They can also be made available to any researcher upon request.…”

“…The main feature of jets that separate from the wall right after injection is the sharp drop in the averaged adiabatic effectiveness after injection, as can be seen for all three velocity ratios. RANS simulations employing typical turbulent mixing models fail to predict this behavior (Milani et al [29]). Since the r = 1 jet re-attaches to the wall, its averaged adiabatic effectiveness recovers to much higher levels, and does so over a short streamwise distance.…”

Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot

“…The diffusivity α t = ν t Pr t is modeled as eddy viscosity over turbulent Prandtl number Pr t . In this study, instead of using a turbulent viscosity by constant turbulent Prandtl number assumption, the machine-learning framework, outlined in the previous section, is used to infer the thermal diffusivity as a function of velocity gradients and temperature α t = α t (T, S i j , Ω i j ), much like an existing study for jets in crossflow [12].…”

“…The models φ mod are found by constructing independent invariants from ∂ T ∂ x j , S i j and Ω i j . The full list used in this study closely mirrors the work of Milani et al [12] and is given as…”

“…One group has successfully extracted functional forms for intermittency transport, in order to model bypass transition [10,11]. For heat-transfer problems, similar to that addressed in this paper, random forest regression has been applied to model the turbulent thermal diffusivity, for a gradient-diffusion model in the scalar transport of temperature [12].…”