AEROELASTICITY IN AXIAL FLOW TURBOMACHINES

Transcription

1 von Karman Institute for Fluid Dynamics Lecture Series Programme AEROELASTICITY IN AXIAL FLOW TURBOMACHINES May 3-7, 1999 Rhode-Saint- Genèse Belgium CASE STUDIES IN TURBOMACHINERY AEROELASTICITY USING AN INTEGRATED 3D NON-LINEAR METHOD M. Vahdati, A. Sayma & M. Imregun Mechanical Engineering Department Imperial College, London SW7 2BX, UK

2 CASE STUDIES IN TURBOMACHINERY AEROELASTICITY USING AN INTEGRATED 3D NON-LINEAR METHOD M. Vahdati, A. Sayma & M. Imregun Mechanical Engineering Department Imperial College, London SW7 2BX, UK 1. Introduction. The lecture will be presented by Dr. Imregun, who acknowledges his two co-authors, Drs. Vahdati & Sayma. The lecture will first describe an integrated non-linear time domain model. Two case studies, fan forced response and flutter stability of a bird-damaged fan assembly, will then be discussed in some detail. Further information can be found in: Sayma, A. I., Vahdati, M. & Imregun, M. Fan Forced response predictions due to inlet distortions and excitation from inlet guide vanes at high deflection 4 th National Turbine Engine HCF Conference, Monterey, Feb 1999 Ferrari, E., Vahdati, M. & Imregun, M. Flutter Stability analysis of a bird-damaged fan assembly 3 rd European Conference on Turbomachinery, IMechE, London, 2-5 March 1999 Sbardella, L, Sayma, A. I. & Imregun, M. Semi-unstructured mesh generator for flow calculations in axial turbomachinery blading 8 th Int. Conf on Unsteady Aerodynamics and Aeroelasticity of Turbomachines, Stockhom, September 1997 Integrated non-linear time-domain approach. As shown in Figs AE-2 & AE-3, an integrated, non-linear time domain approach will be used in the case studies. The main aeroelasticity code, AU3D, is based on unstructured meshes and the aerodynamic part is an edge-based upwind solver. Both time-accurate non-linear and linearized unsteady flow models are available. The flow is discretized described using general grids of 3D elements such as tetrahedra, bricks and wedges, a feature that offers great flexibility for modelling complex shapes. The time stepping is done in an implicit fashion and hence very large CFL numbers can be used without creating numerical instabilities in the solution algorithm. The code can be run in viscous mode via Reynolds-averaged Navier-Stokes equations with Baldwin-Barth, Spalart-Allmaras or q-zeta turbulence models. It can also be run in inviscid mode, in which case the viscous losses are approximated using a distributed loss model. The system of equations is advanced in time using a second-order, point implicit time integration technique. A point relaxation procedure with Jacobi iterations is used for steady flows. Solution acceleration techniques, such as residual smoothing and local

3 time stepping, are also employed. For unsteady flow computations, a dual time stepping procedure is used where external Newton iterations are employed to ensure time accuracy. Within each Newton iteration, the point Jacobi relaxation and its associated acceleration techniques are used to drive the solution to convergence. Integrated solution. The flow model is coupled to the structure using a linear modal model where the mode shapes and frequencies are obtained using a standard FE analysis. It is inherently assumed that the structural behaviour is linear and that the amplitude is small compared to the blade s chord. The modeshapes are interpolated onto the fluid mesh and hence velocities and displacements can be calculated without interpolation during the coupled motion. The equations are advanced in time using the Newmark-β method, which is unconditionally stable. The information are exchanged between the fluid and structure every time step at the blade's surface via pressure/displacement boundary conditions. At every time step, the flow mesh is moved according to the structural motion using spring analogy which prevent sever mesh distortions. Optimum meshing. In recent years, the rapid development of numerical methods and the availability of powerful computers led to the emergence of various systems for the prediction of complex turbomachinery flows. Most such methods use structured grids. On the other hand, unstructured grids received a great deal of research and development effort for external compressible flows. It is only in recent years that unstructured tetrahedral grids found their way into turbomachinery applications. While unstructured grid methods provide flexibility for discretising complex geometries, they have the drawback of requiring larger computer storage and more CPU effort than their structured counterparts. Due to the relatively simple shape of turbomachinery blades, structured grids are considered by many researchers as the most suitable discretization route. With increasing computer power and fast developments in numerical models, it is now possible to include various complex turbomachinery features such as over tip gap leakage, cooling holes in turbine blades, snubbered fan blades, fan assemblies with intake ducts, struts and various other structural elements. Due to the complexity of such geometries, the natural way forward is to use unstructured grids. Although tetrahedral grids, the choice of which appears obvious, are relatively easy to generate for inviscid flow calculations and away from the walls for viscous flow calculations, the situation becomes more complicated in boundary layers, where large aspect ratio cells are required for computational efficiency. Such considerations led to the development of hybrid grid models where hexahedral or prismatic cells can be used in the boundary layers and tetrahedral and prismatic cells can be used to fill the domain away from the walls. The very fact that tetrahedral unstructured meshes do not exhibit any preferred direction is what makes them ideal for discretizing arbitrarily complex configurations. In fact most of the unstructured mesh generation techniques rely on this property. However, when a configuration with a preferred direction, such as a turbomachinery blade, is to be discretized, and different resolutions are desired in the various directions, unstructured generation techniques are known to experience great difficulties in meeting such requirements. Turbomachinery blades require high resolution near their leading and trailing edges and radial spacing can be relatively coarse.

4 When using an isotropic unstructured mesh, the high leading and trailing edge resolution requirements also result in a high radial resolution in these areas, a feature greatly increases the number of grid points. Such a degree of radial resolution is superfluous since the radial gradients are known to be relatively small for turbomachinery blade flows. Similar difficulties occur in the boundary layer regions near a wall for high-reynolds number viscous flows, where the normal gradients are several orders of magnitude grater than the stream-wise gradients. The considerations above lead to the use of semi-structured meshes for turbomacinery blades. A novel approach for discretizing turbomachinery blades will be introduced by using a combination of structured and unstructured meshes, the former in the radial direction and the latter in the axial and tangential directions. The basic idea relies on the fact that blade-like structures are not strongly three dimensional since the radial variation is usually small. It is therefore possible to start with a structured and bodyfitted two-dimensional O-grid around a given aerofoil section in order to resolve the boundary layer. This core mesh is then extended in an unstructured fashion up to the far-field boundaries, the triangulation being performed using an advancing front technique. Once this two-dimensional grid is generated, it is projected to the remaining radial sections via quasi-conformal mapping techniques. When all such radial sections are formed, a three-dimensional prismatic grid is obtained by simply connecting the corresponding points of different layers. In this way, hexahedral elements are generated in the viscous region and triangular prisms in the rest of the solution domain. An example is given in Fig. AE Case Study 1: Fan FR due to inlet distortions and excitation from IGVs Overall summary. This case study presents the forced response analysis of a fan using the above-described integrated aeroelasticity tool. Three whole bladerows, consisting of 11 struts, 33 variable inlet guide vanes (VIGVs) and 26 rotor blades, were modelled in full for most of the cases studied. The aim of the work is to predict the combined effects of inlet distortion and stator wakes on the response of the rotor blades. VIGV angles between 0 and 50 degrees were considered. For each angle, the response predictions were obtained for two types of inlet flow conditions: no distortion and distortion due to a gauze arrangement placed upstream. The unsteady flow calculations were conducted using a time-accurate non-linear viscous representation together with blade motion. Such an undertaking required about 4.2 million grid points to include all three bladerows in a complete stage calculation. To reduce the computational effort, a number of smaller bladerow computations were conducted by considering the stator and rotor domains separately: the outflow solution of the stator domain was used as an in flow boundary condition to the rotor domain. The results indicated that bladerow computations were likely to underpredict the response levels because of rotor-stator interactions. The clean intake predictions showed good agreement against available measured data. Around the vicinity of the 7 nodal diameter assembly mode, a response increase of about 10% of was predicted for the gauze distortion cases. Also, an inspection of the unsteady forcing revealed that the gauze distortion would create a number of low engine order harmonics. Modelling and steady-flow analysis. The stator domain was first modelled using the existing cyclic symmetry. A semi-unstructured mesh was generated for a representative sector of 3 VIGVs and 1 strut. An unstructured triangular mesh was generated for a typical blade-to-blade plane but a structured mesh of rectangular elements was used in

5 the boundary layer. The resulting 2D mixed-element mesh was mapped to specified radial planes along the length of the blade. These layers were then connected in a structured manner to produce hexahedral cells in the boundary layer and triangular prisms elsewhere. Once a mesh was generated for a single blade passage, the sector mesh containing three VIGVs and one strut was obtained by matching periodic boundaries. Such a semi-structured discretization produces a near-optimum distribution of the mesh points and allows full assembly analyses to be undertaken with available computing power. Four different IGV angles were considered and most of the results will be presented for a IGV angle of 20 degrees. The overall geometry and the discretization of a typical sector are shown in Fig. AE-7. The steady-state Mach number contours for two sections near the hub and the tip are shown in Fig. AE-8. It can be seen that, due to the much larger size of the strut, the strut wake is stronger near hub. The steady-state solution for the rotor blade is also shown in Fig. AE-8. Unsteady flow analysis for the clean intake. Using a structured mesh, a straight long intake was added to the sector mesh in order to model the clean intake case for which there are no low-engine harmonics. The aeroelasticity analysis considers both the stator and rotor domains in one calculation. At the sliding plane between the two domains, specialised boundary conditions are used to exchange information in a conservative fashion. Because of the non-matching blade numbers, all three bladerows are modelled in full (Fig. AE-9). One further feature of the analysis is the inclusion of the flexibility of the rotor blade so that actual vibration response predictions can be made. The required natural frequencies and mode shapes were obtained using a standard FE formulation, the mode of interest being depicted in Fig. AE-10. During the unsteady computations, the fluid mesh is moved at each time step according to the structural motion using a spring analogy algorithm. Fig. AE-11 shows the instantaneous unsteady pressure contours near the tip section for the 0 degree VIGV angle case. As can be seen, the rotor blade's leading edge bow shock hits the VIGV trailing edge and such an interaction affects the VIGV domain flow field significantly. This feature, which requires the propagation of the rotor flow information back to the stator domain, cannot be captured by combining individual bladerow computations. An underprediction of the unsteady forcing on the rotor blade becomes likely in such a situation and hence the structural response will also be underpredicted. Combined bladerow computations were also performed for the 50 degree VIGV closure angle and a very similar trend was observed again. The measured and predicted rotor blade vibration amplitudes are compared in Fig. AE-12. Response predictions with inlet distortion. The actual inlet flow distortion is due to several geometric factors, including the turning of the flow around upstream obstructions. When testing development engines, gauzes are used to simulate such effects. The flow distortion pattern, obtained from actual measurements downstream of unevenly spaced gauzes, was imposed as an inflow boundary condition, upstream of the struts. Two sets of distortion patterns, corresponding to two different gauze arrangements, were used in the resonant forced response calculations. The total pressure variation for both sets is in Fig. AE-13. Fig. AE-14 shows the entropy contours at the tip section for both sets of gauze distortion patterns as well as those for the clean intake. The flow solution at the stator outflow was imposed as an inflow boundary condition onto the rotor blade domain in order to compute the actual

6 vibration levels in the vicinity of the 7 nodal diameter assembly mode. This resonance is of particular interest as it corresponds to an aliasing between 33 VIGVs and 26 rotor blades. Overall increases of 8% and 15% were noted for the first and second distortion patterns respectively. A spatial Fourier transform of the axial velocity along a circle of the stator outflow is shown in Fig. AE-15. It is seen that the clean intake case has the blade passing engine orders while the inlet distortion created by the gauzes gives rise to several other engine-orders. 3. Case Study 2: Bird-damaged fan assembly Overall summary. Bird strike is a major consideration when designing fans for civil aero engines. In addition to bird impact tests and structural optimisation, it is now possible to investigate the aeroelastic behaviour of fan assemblies after actual or predicted damage due to ingested birds. It is found that such investigations require the use of whole assembly models, as the cyclic symmetry is lost by one or more blades undergoing plastic deformation under the effect of the bird impact. Here, it was assumed that two consecutive blades had suffered unequal amount of bird damage, the so-called heavy- and medium-damaged blades. A viscous steady state solution of the bird-damaged assembly was computed first. The results indicated the formation of a strong wake from the heavy-damaged blade onto the downstream medium-damaged blade. It was also found that the mass flow had reduced considerably due to the blockage effect of the damaged region. Viscous unsteady flow calculations with and without blade motion were performed for the whole assembly and the results indicated the possibility of rotating stall, due to flow separation behind the heavy-damaged blade. The findings are in good agreement with available experimental data as both predictions and observations indicated a torsional instability for the medium damaged blade. Background. The need for a flutter stability analysis of a bird-damaged fan assembly is outlined in Figs AE-17 and AE-18. The possibility of severe bird damage is a significant consideration in fan blade design as the engine is expected to remain functional for some time after the event. Such a requirement involves the assessment of its flutter stability, in addition to the study of other factors such as blade strength, tip clearance, etc. Given the practical difficulties of experimentally determining the flutter stability for a large number of possible damage configurations, a proven computational route becomes very attractive. It is usual for two or more blades to be damaged. As shown in Fig. AE-18, the design requirement is to relate the amount of damage suffered by, say two damaged the blades, to a safe stability margin. The experimental determination of a design chart is not possible and hence a reliable numerical simulation is highly desirable. However, As shown in Fig. AE-20, a significant number of difficulties exist for such a numerical calculation. Computations. Because of the loss of symmetry, the calculation can only be conducted with a full assembly mesh, a zoom view of which is given in Fig. AE-21. There are two damaged blades, upstream heavy damage (HD) blade and downstream medium damage (MD) blade. A side view and a rotor blade tip view are shown in Fig. AE-22.

7 The axial mass flow at the fan outlet is shown in Fig. AE-23. It is easily seen that there is significant blockage, corresponding to a mass flow drop of about 8%, due to the damaged blades. It is debatable whether such a case has a true steady-state solution. In any case, the Mach number and density contours near the tip section of the damaged blades are shown in Fig. AE-24. From these pictures it can be noted that there is no shock on the HD blade's suction surface, and that the flow is completely separated. A strong recirculation area, that will be referred to as `wake', is released from the leading edge of the HD blade and hits the medium-damaged blade. Important viscous effects take place in the wake and the flow appears to be truly unsteady. Significant reverse flow can be observed from the velocity vectors of Fig. AE-25. Another consequence of the wake and of the flow blockage is the change in the suction surface shock position, especially around the damage area (Fig. AE-25 ). Where the flow incidence is locally increased, the shock gets stronger and vice-versa. The mistuned whole-assembly mode shapes were computed using a finite element program. With such a geometry, there is no cyclic symmetry and the disc flexibility has to be taken into account. Considerable structural mistuning, caused by the bird strike, changes significantly the mode shapes patterns. The nodal lines have preferred orientations since they either tend to go through or to be orthogonal to the damaged blades (Fig. AE-26). However, some modes resemble closely the single blade modes and can be interpreted as the 1T modes of the HD and MD blades respectively (modes 53 and 54 in Fig. AE-27). On the other hand, modes 55 and 56 can be considered as the orthogonal 1T modes of the rest of the blades. As can be seen from Fig. AE-27, all 1T modes are stable, except that corresponding to the MD blade. It may be concluded that the torsional vibration of the MD blade is unstable, probably due to the upstream excitation produced by the HD blade. Finally, contour plots of negative axial velocity are shown at four time instants during the flutter computation with moving grids (fig. AE-28). These plots indicate significant re-circulating and reversed flow, which seems to be to re-attaching. Such a phenomenon is indicative of rotating stall, a feature that is closely related to the viscous nature of the flow and may also be affected by the blade vibration.