Virtually all turbomachinery flows involve turbulent phenomena, including transition from laminar to turbulent states.Thus, the adequate representation of transition and turbulence is crucial for the predictive accuracy of the computational method used in the turbomachinery design process.

Secondary flows in turbine stator computed with SSG/LRR-w DRSM.

.

Rig250 speed line, comparison of fully turbulent and transitional computation

.

Rig250 intermittency on blade profiles

.

The full or even partial resolution of turbulent structures by Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES), respectively, - see (Link, Numerical Test Rig) – is currently outside of the realm of industrial applications for Reynolds numbers typically found in turbomachinery aerodynamics. Hence, the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations forms the backbone for the numerical simulation of flows of industrial relevance. However, modelling assumptions of some kind have to be made, where transition and turbulence are addressed separately. While turbulence modelling is based on statistics, transition modelling heavily relies on empirical correlations.

Turbulence Modelling

Flows in multistage turbomachinery are inherently unsteady. However, while unsteady simulations are of ever-increasing importance, steady RANS computations will remain the workhorse of industrial CFD in the near future. Solving the RANS equations, a closure is needed for the Reynolds stresses. A variety of RANS methods exist, ranging from simple algebraic models up to Differential Reynolds Stress Models (DRSM). To date, however, transport-equation Eddy-Viscosity Models (EVM) remain the backbone of turbulent viscous computations in the industrial design process. These models, however, have difficulties predicting e.g. pressure-induced separation and recirculation, secondary flows, shock-induced separation and shock/boundary-layer interaction.

Several approaches for turbulence representation are followed up in TRACE:

The inclusion of turbomachinery-specific extensions to two-equation EVM forms the backbone of the turbulence modelling effort. Starting from the standard Wilcox 1988 k-ω model, the approach improves the prediction of viscous effects by successively implementing a fix for spurious production of turbulent energy as well as measures to account for the effects of compressibility and rotation, respectively. This enhanced model is used successfully as the standard turbulence representation in TRACE for both compressor and turbine flow computations. Other models implemented include the Menter SST k-ω model in several variants as well as the one-equation model of Spalart and Allmaras (1992).

An improved modelling quality is realized in Explicit Algebraic Reynolds Stress Models (EARSM). EARSM are a class of non-linear EVM derived by a systematic approximation to Reynolds Stress Transport Models. This approach can be regarded as a generalized (non-linear) two-parameter model, which retains the predictive benefits of the second-moment closure methodology, while numerical advantages of the Boussinesq-viscosity concept are conserved. In TRACE, the EARSM of Wallin and Johannson (2000) is implemented.

The anisotropic nature of turbulence can also be accounted for by solving the transport equations for the six Reynolds stresses instead of the turbulent kinetic energy only (DRSM). Effects such as system rotation, stream line curvature and secondary flows, which are usually encountered in turbomachinery flows, are accounted for by an anisotropy resolving turbulence model and, therefore, the quality of prediction can be improved. Performance and stability, however, pose a challenge for the implementation. Differential Reynolds stress models of different complexity are available in TRACE. There is the SSG/LRR-ω model, which was developed at DLR Braunschweig, and a variant of Jakirlic and Hanjalic’s model. The former features great robustness in the application to complex configurations but is a high Reynolds model without concrete modelling of wall effects. The latter, on the other hand, is a full near-wall model which includes wall effects through functions of the anisotropy tensor invariants. After the basic implementation and validation of these models, now the focus is on secondary flow effects in turbomachinery flows such as 3D corner separations and vortices. Appropriately capturing these is crucial towards the prediction of off-design conditions.

With increasing computer power, unsteady computations will be of increasing importance to supplement the standard steady runs typically performed in the industrial design. Owing to the deficiencies of unsteady RANS, hybrid RANS-LES methods have drawn significant attention over the past decade. Such approaches attempt to overcome well-known deficiencies of RANS models regarding the prediction of separated flow by treating such regions in an LES-type manner, while at the same time retaining their undisputed performance for attached boundary layers. TRACE features the Detached-Eddy Simulation (DES) approach in different variants. Furthermore, the SAS-SST model (Scale-Adaptive Simulation) by Menter (2007) is currently under investigation.

Transition Modelling

Even though the flow in a turbomachine is turbulent most of the time, it is very important to accurately predict where transition from laminar to turbulent flow takes place. The state of a boundary layer - laminar, transitional or turbulent - has a great impact on its properties, such as frictional losses or heat transfer in the fluid. Depending on the geometry of the component and the flow conditions, this transition process can happen in different places and follow different patterns or modes.

TRACE can use two different models to predict transition: An algebraic model (Multimode model), which uses integral values of the boundary layer to predict the different transition modes and a local, transport-equation-based model (ɣ-ReӨ model) which uses local values of the flow. The models are coupled to the source mechanisms of the turbulence model and thus allow transport of turbulent quantities even in areas where flow is predicted to be laminar. Extensions for the ɣ-ReӨ model in combination with two-equation-models are continuously developed by our university partner (Institute of Turbomachinery and Fluid Dynamics, Hannover). These extend the model with prediction capability of transition due to cross flow effects, on end walls or due to wakes of upstream blade rows.

Kontakt

Dr.-Ing. Edmund Kügeler Institute of Propulsion Technology Numerische Methoden Köln Tel.: +49 2203 601-3248