This paper describes the implementation of a set of nonreflecting boundary conditions of increasing approximation quality for time-accurate and time-linearized 3D RANS solvers in the time and frequency domain. The implementations are based on the computation of eigenfunctions, either analytically or numerically, of the linearized Euler or Navier-Stokes equations for increasingly complex background flows. This results in a hierarchy of nonreflecting boundary conditions based on 1D characteristics, 2D circumferential mode decomposition, and 3D circumferential and radial mode decomposition, including viscous effects in the latter, for the frequency domain solver. By applying a Fourier transform in time at the boundaries the frequency domain implementations can be employed in the time domain solver as well. The limitations of each approximation are discussed and it is shown that increasing the precision of the boundary treatment the nonreflecting property of the boundary conditions is preserved for more complex flows without incurring an excessive increase in computing time. Results of a flutter analysis of a low pressure turbine blade obtained by time and frequency domain simulations are validated against each other and against reference results obtained with a 3D Euler frequency domain solver. The comparison of the results for different boundary conditions reveals the importance of using high quality boundary conditions.

The TP400 intermediate pressure compressor (see Figure 1) is characterized by its extremely wide aerodynamic operating range with strong requirements concerning efficiency and surge margin. Both goals could have been achieved by the proper introduction of variable stator vanes. However, the resulting weight penalty due to the necessary control and actuator system is not accepted — thus this conventional design is rejected and a sophisticated Casing Treatment developed by MTU is introduced. While the underlying multipoint design process is in general expensive and complex the chosen Casing Treatment design (enhanced axial skewed slots [17]) requires the introduction of time accurate 3D CFD simulations in the standard design chain. This ambitious goal leads to the demand for enhanced 3D aerodynamic design tool capabilities like accurate flow prediction in fully turbulent and transitional flow regimes due to different operating conditions as well as the resolution of different geometry features outside the main flow path. In the present paper the effect of different numerical resolution of the “real” geometry as well as the “real” behavior of the flow e.g. steady simulation versus time accurate simulations is discussed. The differences are analyzed and compared to rig-measurements.

Both linear and nonlinear frequency domain methods have been applied successfully to the investigation of time-periodic phenomena in turbomachinery. Linear methods allow to perform flutter analysis of turbomachinery blade rows very efficiently. Nonlinear frequency domain method can be applied to flutter analysis as well. If a pseudo-time solution algorithm is employed as a solver the nonlinear frequency domain method takes advantage of the stabilizing effect of the nonlinear coupling of the harmonics. Additionally, it allows studying the influence of nonlinear effects on the flutter stability. A linear GMRes based method and a harmonic balance method using a pseudo-time solution approach are compared with respect to computational efficiency when applied to the flutter analysis of blades of a stationary gas turbine and a low pressure turbine of a jet engine. It is shown that both methods have their merits and limitation depending on the type of problem at hand.

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This is the first part of a series of three papers on the simulation of turbulence and transition effects in a multistage low pressure turbine. In this first part, the extension, verification and validation of a Harmonic Balance (HB) method recently proposed by the authors to fully include established turbulence and transition models in the method is presented. As an alternating frequency/time-domain type method the implemented HB solver has the advantage of being able to utilize models (e.g. boundary conditions or residual functions) formulated in either the frequency- or time-domain. On the one hand this allows highly accurate nonreflecting boundary conditions formulated in the frequency-domain to be used along entry, exit or interface boundaries, and on the other hand complex nonlinear terms formulated in the time-domain to be used to describe nonlinear effects. Nevertheless, the wish to minimize the number of harmonics used to describe a given time-periodic unsteady flow, coupled with the often highly nonlinear nature of turbulence and transition models makes the full inclusion of such models in the HB method challenging. In this work the integration of Menter’s SST two-equation k–ω turbulence model along with Menter and Langtry’s two-equation γ–Reθ transition model in the context of a general framework for transport equations in the CFD solver TRACE is described in detail. Following the basic verification of the underlying transport equation framework, the implemented models are used to compute the well known high lift, low pressure turbine airfoil T106C and results are compared with the available experimental data as well as results from more conventional time-domain simulations. Alongside the basic validation of the models this testcase is furthermore used to investigate the importance of including higher harmonics, as opposed to only the zeroth harmonic, of the turbulence and transition models for the accurate prediction of the time-mean flow.