The Significance of Quantifying Uncertainties in Turbomachinery CFD

The increased use of CFD for turbomachinery design is an outcome of the increasing accuracy thanks to high computational resources. Although the benefits of such computations are strong, the approximations and errors derived from CFD could significantly affect the prediction of crucial parameters such as flow temperature and heat transfer. This article will present the challenges related to uncertainties in turbomachinery CFD, based on “Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines” [1]

The exact definition of boundary conditions presents one of the biggest challenges in CFD and turbomachinery given the high accuracy needed to determine the distributions of the non-uniform conditions to which turbomachinery components are subjected [2].

An additional limitation related to CFD is known as geometric uncertainty. It should be noted that, in a geometric model, a lot of details are neglected for simplicity and speed or because they are unknown, which leads to differences between the real model and the simulated one. However, even if all the details are included along with secondary air systems, they could be affected by manufacturing of the components. A study [3] quantified the change of the stage efficiency due to manufacturing errors in the rotor end-wall and to different interaction between the purge flow and the main flow.

Moreover, grid dependence analysis is a fundamental task of every numerical simulation and must be considered as such. In fact, grid spacing effects can be responsible for the poor prediction of both flow structures (i.e. von Karman Vortex Street, shock intensity and position, secondary flows…) and integral parameters such as stagnation losses. For those reasons, the effects of computational grid on the obtained results must be accounted for, when performing high-fidelity computational fluid dynamics.

Another uncertainty arises due to the improper selection between steady and unsteady simulations. For instance, when it comes to losses prediction, Pullan [4] demonstrated that a steady simulation generates 10 % less losses compared with the unsteady one. Another classical error caused by a steady simulation is the analysis of the redistribution for a hot spot in the rotor row [5].

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Along with the use of accurate boundary conditions to analyze turbomachinery flows, the simulation of component interaction is equally important. For example, an accurate methodology for the exchange of turbulence information across the interfaces is essential, especially concerning the evaluation of the turbulent length scale.

Finally, attention must be paid to the simulation of cooling devices since design is affected by geometrical uncertainty, numerical accuracy, fluid/solid interaction and boundary conditions variability [6]. It could be argued that the numerical simulation of a cooled, transonic high-pressure vane is one of the most challenging topics in CFD. Geometric uncertainty is so high that a 10 % variation of cooling hole diameter would generate an increase of 40 K in the local metal temperature of the vane [7].

Most of the described problems are related to the stochastic uncertainty, which is a function of the knowledge problem physics and the complexity of the algorithm. Then, numerical accuracy can rise with an improved knowledge of the physics and with the computational resources, while uncertainty quantification should be a strong support in the analysis and design of turbomachinery.

References:

[1] F. Montomoli et al., Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines, SpringerBriefs in Applied Sciences and Technology, DOI 10.1007/978-3-319-14681-2_2
[2] Salvadori, S., Montomoli, F., Martelli, F., Chana, K. S., Qureshi, I., & Povey, T. (2012). Analysis on the effect of a nonuniform inlet profile on heat transfer and fluid flow in turbine stages. Journal of Turbomachinery, 134(1), 011012-1-14. doi:10.1115/1.4003233.
[3] Adami, P., Martelli, F., & Cecchi, S. (2007). Analysis of the shroud leakage flow and mainflow interactions in high-pressure turbines using an unsteady computational fluid dynamics approach. Proceedings of the IMechE Part A: Journal of Power and Energy, 21. doi:10.1243/09576509JPE466.
[4] Pullan, G. (2006). Secondary flows and loss caused by blade row interaction in a turbine stage. ASME Journal of Turbomachinery, 128(3), 484–491.
[5] Butler, T. L., Sharma, O. P., Joslyn, H. D., & Dring, R. P. (1989). Redistribution of an inlet temperature distortion in an axial flow turbine stage. AIAA Journal of Propulsion and Power, 5, 64–71.
[6] Montomoli, F., Massini, M., & Salvadori, S. (2011). Geometrical uncertainty in turbomachinery: Tip gap and fillet radius. Elsevier Computers and Fluids, 46(1), 362–368. doi:10.1016/j.compfluid.2010.11.031.
[7] Bunker, R. S. (2009). The effects of manufacturing tolerances on gas turbine cooling. ASME Journal of Turbomachinery, 131, 041018-1-11. doi:10.1115/1.3072494.

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