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During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

Exploitation of stator–stator interaction phenomena can increase overall efficiency in axial turbomachines. The first part of this paper sets out to present results of steady and unsteady flow experiments obtained in a new three stage cold flow low pressure turbine. Observation and understanding of boundary layer development and transition phenomena on the vanes dependent on relative stator position will be the focal point. In addition to this, stator position influence on profile loss, turbine efficiency and the development of secondary flow are examined. The experiments were carried out in the closed circuit test bed of the Institute of Aeronautical Propulsion at Stuttgart University. Annulus geometry and blading design of the research turbine were taken from the low pressure turbine of a modern commercial jet engine. The three stage test rig had identical blade counts for all stators or rotors respectively, whilst the circumferential position of each stator row could be individually adjusted. The second and third stators were optimised with respect to the radial alignment of the vanes. Surface mounted hot film gauges on the vanes and hot film probes were employed to assess the unsteady interaction phenomena. For steady measurements, pneumatic five hole probes and multiple kielhead pressure and temperature probes were used. For both the second and third stator, circumferential position was varied in eight steps over one pitch. Whereas the design point forms the basis of this detailed investigation, some attention was also paid to variations in Reynolds number and wheel speed. The results, such as quasi wall shear stress, stochastic and periodic fluctuations, total pressure etc., are presented in the form of chordwise ensemble-averaged distributions and contour plots and should be compared with the corresponding numerical studies presented in the second part of this paper.

The paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments on a three-stage low-pressure turbine. The investigation emphasizes the study of unsteady flow interaction. A time-accurate, Reynolds-averaged Navier-Stokes solver is applied for the computations. Turbulence is modelled using the Spalart-Allmaras one-equation turbulence model. The influence of modern transition models on the unsteady flow predictions is investigated. Integration of the governing equations in time is performed with a four-stage Runge-Kutta scheme, which is accelerated by a two-grid method in the viscous boundary layer around the blades. At the inlet and outlet, non-reflecting boundary conditions are used. The quasi-three-dimensional calculations are conducted on a stream surface around mid-span, allowing a varying stream tube thickness. A three-stage, low-pressure turbine rig of a modern commercial jet engine is used for a study of the unsteady flow interaction. The numerical method is able to capture important unsteady effects found in the experiments, i.e. unsteady transition as well as the bladerow interaction. In particular, the flowfield with respect to time-averaged and unsteady quantities such as surface pressure, vorticity and turbulence intensity is compared with the experiments conducted in the cold airflow test rig.

The paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments of a three stage low pressure turbine. The investigation emphasize the study of unsteady flow interaction. A time accurate Reynolds averaged Navier-Stokes solver is applied for the computations. Turbulence is modeled using the Spalart-Allmaras one equation turbulence model and the influence of modern transition models on the unsteady flow predictions is investigated. The integration of the governing equations in time is performed with a four stage Runge-Kutta scheme, which is accelerated by a two grid method in the viscous boundary layer around the blades. At the inlet and outlet non-reflecting boundary conditions are used. The quasi 3D calculations are conducted on a stream surface around midspan allowing a varying stream tube thickness. In order to study the unsteady flow interaction a three stage low pressure turbine rig of a modern commercial jet engine is built up. Besides the design point, the Reynolds number, the wheel speed and the pressure ratio are varied in the tests. The numerical method is able to capture important unsteady effects found in the experiments, i.e. unsteady transition as well as the blade row interaction. In particular, the flow field with respect to time averaged and unsteady quantities such as surface pressure, entropy and skin friction is compared with the experiments conducted in the cold air flow test rig.