The trailing-edge slot is a canonical representation of the pressure-side bleed flow encountered in high pressure turbines. The purpose of the slot is to inject fluid at a relatively cooler temperature to protect the wall surface against the working fluid which has a higher temperature.  Predicting the flow downstream of the slot exit is still a challenge with both RANS and URANS, with a significant overprediction in the non-dimensional wall temperature, i.e., the adiabatic wall-effectiveness. This overprediction in both RANS/URANS is attributable to the incorrect momentum mixing prediction influenced by the vortex shedding present. In case of RANS the modelling error is rooted in not properly accounting for the shedding scales while in URANS the closures account for the shedding scales twice: once by resolving the shedding and twice with the model for all the scales. Several approaches have been attempted to improve this prediction, ranging from tuning of the RANS model coefficients and developing explicit algebraic models for the Reynolds stress closure, to using machine learning for linear as well as non-linear model development.

 

We present an alternative to the existing modelling methods, which models only the scales that contribute to turbulence while resolving the scales that do not, i.e. scales considered as contributing to deterministic unsteadiness. In case of flows that exhibit vortex shedding, the scales associated with vortex shedding are resolved while the remaining scales, i.e., the stochastic scales are modelled. The model for the stochastic scales is obtained through a data-driven machine-learning algorithm, which produces a bespoke turbulence closure model from a high-fidelity dataset. This involves first processing the high-fidelity dataset to extract the contribution of the stochastic scales, which is then utilised to generate the turbulence closure through a symbolic regression algorithm: Gene-Expression Programming. The  algorithm produces a tangible equation for the stochastic quantity which can be implemented as is into the URANS solver to conduct unsteady calculations.

 

In this paper, the work of Lav et al. \[TurboExpo 2019\] is extended by taking the best closure (blowing ratio of 1.26) for the Reynolds stresses obtained *a priori* and implementing it in a compressible URANS solver to perform calculations *a posteriori*. In the first stage, the energy equation is solved utilising the standard gradient diffusion hypothesis for the heat-flux closure. In the next stage, the heat-flux closure is also modified similar to the anisotropy tensor by developing a machine-learnt model for the stochatic heat-flux component. Subsequently, calculations are performed using the machine-learnt closures for the heat-flux and the anisotropy together. All calculations are performed on the blowing ratio of 1.26 case to realise improvements. Finally, the generalisability of the best developed closures is evaluated by testing them on additional blowing ratios of 0.86 and 1.07 in a bid to obtain one set of closures each for the heat-flux and the anisotropy. High-resolution LES of the three blowing ratios are utilised for the sake of model development as well providing a benchmark to compare the results from the machine-learnt models.


Unsteady Simulations of a Trailing-Edge Slot Using Machine-Learnt Turbulence Stress and Heat-Flux Closures

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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