Nina Wolfrum

Nonreflecting Boundary Conditions for Aeroelastic Analysis in Time and Frequency Domain 3D RANS Solvers

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.Copyright

CFD Simulations of the TP400 IPC With Enhanced Casing Treatment in Off-Design Operating 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.Copyright

On the Simulation of Unsteady Turbulence and Transition Effects in a Multistage Low Pressure Turbine: Part I — Verification and Validation

This is the first part of a series of three papers on the simulation of turbulence and transition effects in a multistage low npressure turbine. In this first part, the extension, verification nand validation of a Harmonic Balance (HB) method recently proposed by the authors to fully include established turbulence and ntransition models in the method is presented. As an alternating frequency/time-domain type method the implemented HB nsolver 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 nhighly 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. nIn this work the integration of Menter’s SST two-equation nk − w turbulence model along with Menter and Langtry’s two-equation gamma − ReTheta 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.

A Numerical Model for Casing Treatment Applications in Axial Flow Compressors

A numerical model has been developed to reproduce the effects of complex casing treatments (CT) in steady RANS simulations of multistage compressors. While some CTs, such as circumferential grooves, can be described by a rotation surface and can thus easily be included in conventional steady simulations, the CFD analysis of other casing treatments like axial slot or recessed vanes, currently requires a time-resolving analysis of the interaction between such structures and rotating parts. At present unsteady simulations are still too time consuming to be used in the early phase of a compressor design. In the presented study a numerical model was developed for casing treatment applications, to introduce the unsteady effects caused by such casing treatments into steady CFD-simulations. With the help of the model, non-axisymmetric elements can be eliminated from the geometry allowing a steady simulation to be used. The flow acceleration and redirection caused by these geometrical elements is replaced with adequate source terms introduced into the three-dimensional Navier-Stokes equations. These source terms, derived from a consecutive time- and circumferential averaging of the three-dimensional unsteady Reynolds-averaged Navier-Stokes-equations, arise from the momentum and energy equations. Using these additional terms, the CT-model simulates both the pressure forces that the walls of the real casing treatment exert on the flow, and the effects of the mean blockage induced by the omitted geometry. Furthermore, the deterministic stresses, caused by a circumferentially inhomogeneous flow within the CT-structure, are modeled. The source terms consist of geometrical data that can be derived directly from the real geometry of the casing treatment as well as physical quantities of the time-averaged flow in the real casing treatment. The latter terms can be obtained from a reference unsteady simulation. In the presented case one unsteady simulation was sufficient to set up the model for a complete speed line. The model was implemented into the three-dimensional Navier-Stokes-code TRACE [5][12]. By using steady instead of unsteady CFD simulations, the time required for a speedline computation was reduced by a factor of 10. At the same time, the numerical results of the CT-model showed good alignment with the reference data. The model was evaluated for several different styles of compressors. In this paper various results are presented, including speedlines as well as radial inflow- and outflow-profiles.© 2013 ASME