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Research Papers

Unsteady Adjoint of Pressure Loss for a Fundamental Transonic Turbine Vane

[+] Author and Article Information
Chaitanya Talnikar

Aerospace Computational Design Laboratory,
Department of Aerospace and Astronautics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: talnikar@mit.edu

Qiqi Wang

Aerospace Computational Design Laboratory,
Department of Aerospace and Astronautics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: qiqi@mit.edu

Gregory M. Laskowski

Engineering Technologies,
GE Aviation,
Lynn, MA 01910
e-mail: laskowski@ge.com

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 29, 2016; final manuscript received September 9, 2016; published online November 8, 2016. Editor: Kenneth Hall.

J. Turbomach 139(3), 031001 (Nov 08, 2016) (10 pages) Paper No: TURBO-16-1217; doi: 10.1115/1.4034800 History: Received August 29, 2016; Revised September 09, 2016

High-fidelity simulations, e.g., large eddy simulation (LES), are often needed for accurately predicting pressure losses due to wake mixing and boundary layer development in turbomachinery applications. An unsteady adjoint of high-fidelity simulations is useful for design optimization in such aerodynamic applications. In this paper, we present unsteady adjoint solutions using a large eddy simulation model for an inlet guide vane from von Karman Institute (VKI) using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backward in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unsteady compressible Navier–Stokes adjoint equations indicates that adding artificial viscosity to the adjoint equations can dissipate the adjoint energy while potentially maintaining the accuracy of the adjoint sensitivities. Analyzing the growth term of the adjoint energy provides a metric for identifying the regions in the flow where the adjoint term is diverging. Results for the vane obtained from simulations performed on the Titan supercomputer are demonstrated.

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References

Figures

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Fig. 1

Turbine vane geometry

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Fig. 2

Contour plot of shear stress on the surface of the vane. Nondimensionalized with respect to flow velocity Mach 0.9. Reynolds number 1 × 106, turbulent intensity 1%.

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Fig. 3

Stagnation pressure on a vertical spanwise cross section 10 mm downstream of the trailing edge of the vane. Nondimensionalized with respect to inlet stagnation pressure.

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Fig. 4

Instantaneous and time-averaged stagnation pressure loss coefficient for the vane. X-axis denotes the time normalized by the time it takes for the flow to pass from the inlet to outlet.

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Fig. 5

Turbine vane computational domain

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Fig. 6

A visualization of the density adjoint field from halfway through a short time 3D unsteady adjoint simulation

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Fig. 7

Growth of energy norm of adjoint fields for different simulations. Y-axis shows energy norm of a dimensional conservative adjoint field.

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Fig. 8

Contour plot of divergence indicator σ1 for the turbine vane, normalized by inverse of a single flow through time

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Fig. 9

Growth of energy norm of adjoint for various scaling factors. X-axis is time normalized by a single flow through time.

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Fig. 10

Error in adjoint sensitivity for various scaling factors

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Fig. 11

Density adjoint solution at t = 0

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