VALIDATION OF UNSTRUCTURED CFD MODELLING APPLIED TO THE C3X TURBINE INCLUDING CONJUGATE HEAT

TRANSFER

F. Mendonça** - J. Clement - D. Palfreyman - A. Peck

CD-adapco, 200 Shepherds Bush Road, Hammersmith, London, UK, W6 7NL fred.mendonca@uk.cd-adapco.com (**for correspondence)

ABSTRACT This paper supports a concerted effort towards validating an unstructured finite volume

methodology for combined flow, thermal and stress analysis of turbine blades. In this part, CFD and conjugate heat transfer solutions are compared against measured surface pressure and heat transfer profiles on the C3X turbine. Sensitivities of the prediction to inlet turbulence levels and laminar-to-turbulent boundary layer transition are also presented.

The general framework of the paper describes an integrated system incorporating three

important analysis components with respect to CAE analysis of turbine blade: CAD geometry handling and repair; surface and volume mesh generation for arbitrarily complex three-dimensional geometries; multi-domain and multi-physics modeling. Such a framework offers possibilities to achieving substantial productivity gains. Therefore, validation of the modeling techniques used is implicit to building confidence and trust in the use of the integrated system.

INTRODUCTION Difficulties continue to be experienced in performing computational analyses (CAE) on real turbine blades. The challenges are clearly stated, and objectives listed, by many turbine manufacturers both independently and collaboratively (see AITEB-2 project, 2005-2009). Recent reports, e.g. Davison et. al. 2008, explore developments in areas of integrated geometry handling, multi-domain meshing and multi-disciplinary analysis. The application of an integrated software framework first to import and repair CAD, then automatically to generate surface and volume meshes, and finally to perform a combined fluid, thermal and stress analyses, can go some way to easing these difficulties. A general goal therefore is to present an integrated simulation environment; in particular, the possibilities to handle non-simplified turbine blade geometries, then to perform conjugate-heat transfer using a single mesh, automatically generated, continuous mesh through the fluid paths (external and internal cooling passages) and blade solid. The ability do this implies very obvious productivity gains. We exemplify this here in the context of the Siemens Tornado turbine blade. The first section in this paper describes in general terms the "Framework" for integration. The second section of this paper then demonstrates the application of this framework, including more specific details of grid, modeling parameters and boundary conditions. A necessary next step is to validate the underlying physical models against well-known test cases. We have chosen here to report computations on the NASA C3X cooled turbine vane (Hylton 1983) on which several previous computational studies have been performed (e.g. Canelli 2004, Luo 2006). For this case, we also illustrate the sensitivity of results to inlet turbulence profiles and laminar-to-turbulent transition modeling using the Malan (2009) implementation of the correlation-based γ–Reθ model of Menter-Langtry (2004). Previous literature citations that use this transition model omit to publish two vital experimental correlations; Malan published validated correlations for both.

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GENERAL FRAMEWORK for INTEGRATED THERMAL, FLOW and STRESS ANALYSIS In geometric terms, production turbine blade designs are arbitrarily complex. Details in and around the hub, shroud, squealer, tip clearances, internal cooling passages containing ribs and pedestals, and transpiration/film cooling holes continues to pose a major challenge in respect of geometry definition, manipulation and meshing. For practical reasons, many simplifications with respect to geometry and boundary conditions between the flow and thermal parts are sought. These typically lead to separate analyses being performed on the external and internal flow paths, blade metal and surface heat transfer. It creates the need to iterate many times between the separate analyses, updating boundary conditions up to a point where the interdependency between them converges. Often, simplifications to geometries are so extreme that experimental correlations are needed so as to force validity of simplified modelling. By contrast, any possibility to work with actual geometries and to combine flow and thermal analysis in one model reduces the dependence on correlations, and significantly optimises the workflow. Existing workflows are based on commercial CAD repair tools, then separately on internal and commercial tetrahedral meshing and solver combinations. Future workflows are aimed at integrating geometry, meshers, flow-solvers and post-processing (Dawes 2006, 2008). We can reasonably argue that a faithful geometric representation of arbitrarily complex blades and adherences to well established well understood best practices for modelling, provides a reasonable framework to realise major productivity gains in flow, thermal and stress simulations.

Geometry handling and meshing process Such a framework is exemplified here on a shrouded production blade geometry, see Figure 1, which originates from the Tornado engine, a 5-7MW power-generation unit from Siemens (formerly Ruston Gas Turbines).

Figure 1: CAD representation of the shrouded-blade Figure 2: Transparency showing internal detail The blade contains a curvilinear internal cooling path exiting at the shroud, Figure 2. A combination of surface wrapping and surface re-meshing techniques are used to repair flaws in CAD surface representations such as overlapping surface and voids. At the same time, feature detail such as film cooling holes and high curvature can be retained. Volume meshing uses an automated methodology that still affords the user important controls. The controls include specification of refinement zones (typically to capture the film cooling holes) and specification of boundary-layer extrusion thickness, near-wall cell height to control y+, and growth rate. The automation complies with contiguous

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meshing constraints between fluid and solid domains, suitable for conjugate heat transfer and finite volume stress analysis to be performed. First, a subsurface of user-defined thickness is grown normal to the triangulated re-meshed surface into the fluid and/or solid volumes. The rest of the volume is then filled with tetrahedra using an advancing front technique, and the tetrahedra are then "dualised" (agglomerated) into abritrary-shaped polyhedra. The resulting polygonal shapes on the sublayer surface are finally extruded back to the original geometry in layers controlled by a user-specified expansion factor to satisfy y+ constraints. Though it is outside the scope of this paper, the workflow presented is not limited to steady-state flow/thermal analysis. It can be extended to transience in order to assess the thermal response of the system to changes in load condition, between idle, take-off and cruise, consequently providing an insight into low-cycle fatigue issues. The integrated framework (CD-adapco 2008) is consistent with generating and solving on several million cells, with up to half that number being placed typically in the solid part to preserve a high level of accuracy for the thermal and finite-volume stress prediction. The methodology is fully parallelisable and scalable. Figure 3 depicts the re-meshed triangulated surface in the region of the blade root, faithfully representing the original CAD imported tessellation shown in Figure 1.

Figure 3: Surface triangulation Figure 4: Conformal Polyhedral Mesh showing

primary gas path in grey, blade in blue and cooling path in brown.

The volume mesh on both fluid and solid sides is generated using arbitrary polyhedra. A polyhedral cell comprises 12-16 faces typically. Polyhedra offer significant advantages over traditional mesh types. They are automatically generated. They exhibit less numerical diffusion than tetrahedra because of the greater likelihood of face alignment to the flow. Gradient computations are more accurate due to the greater number of cell-face neighbours. Therefore, cell counts are typically a third of the equivalent tetrahedral meshes for similar fineness of resolution. Consequently, polyhedral meshes converge faster and are more accurate than tetrahedral meshes (see Peric 2004). On the fluid side, the re-meshed triangulated surface is first inflated to a user-controlled distance equivalent the boundary layer thickness. Surface inflation contains sufficient intelligence to account for close-proximity surface and inside edges, where the extrusion-layer is automatically squeezed as

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surfaces approach each other. The remaining volume is meshed with polyhedra that are generated from dualization of an automatically generated tetrahedral-based mesh. The near-wall cell height can be chosen to satisfy the y+<1 constraint everywhere. Boundary-layer extrusions can applied to both internal and external fluid domains and also the solid if required. The mesh is conformal across all three regions. Through this conformality, no interpolation or mapping is required between fluid and solid domains. A schematic of the final mesh topology produced in this way is illustrated in Figure 4.

Flow, Conjugate Heat Transfer and Stress methodology Standard segregated pressure-based (SIMPLE) or coupled algorithms (with and without pre-conditioning) may be to solve for fully or mildly compressible systems across the Mach number range. The enthalpy transport equation is solved continuously from the fluid through to the solid domains. At the interface, the thermal diffusion coefficient connecting the centres of adjacent fluid and solid cells is calculated from a harmonic average of their separate cell heat-transfer functions: these are the solid conductivity divided by the wall distance in the solid part, and fluid heat transfer coefficient calculated from a y+ independent wall-treatment on the flow-side. The latter is effectively equal to the fluid molecular conductivity divided by the near-wall cell height, since the near-wall cell is almost always in the laminar sub-layer when best-near-wall resolution practices are followed. In rotating machinery, the flow domain is solved in a rotating reference frame. Periodic cyclic boundary conditions are applied to the boundaries in the rotation-direction. For the upstream and downstream boundaries, both fixed-mass-flow/pressure or stagnation/static pressure boundary condition combinations are possible. Cooling mass flow rates are known or derived from measurements, and imposed as a fixed mass boundary condition at the inlet to the internal cooling passages. Turbulence is modelled using standard eddy-viscosity based models. Explicit modelling of boundary-layer transition is possible through the use of a correlation-based transition model. The finite volume stress analysis approach used in the integrate framework comes from that described by Demirdžić, 1995. Diffusion based transport equations are used to solve the mechanical and thermal stresses in the solid. Displacements are directly calculated but are assumed to be small enough not to affect the flow – therefore the grid is not moved. A variety of boundary conditions can be applied, ranging from fixed to traction, zero-normal displacement, applied pressure or applied force. For this demonstration, figures 5 and 6 illustrate the continuous temperature distributions in the external and internal flow paths and on the external metal surface.

Figure 5: External, internal and blade temperatures Figure 6: Metal surface temperatures

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Figure 7 and 8, for illustration purposes only, show the displacement and stress fields, based on constraining the surface-normal movement along linear contact patches at the root. The additional cost for solving the stress equations is less than 10% of those for the flow.

Figure 7: Solid displacement

Figure 8: Solid Stress

 

 

CONJUGATE HEAT TRANSFER on the NASA C3X TURBINE (Hylton 1983, Case 1) The C3X experiment comprises three linear cascade vanes cooled internally by 10 circular parallel holes running through from hub to shroud. Measurements were taken on the centre vane. Several tests were performed. Case 1, against which the present methodology is validated, was operated at a Reynolds number based on chord of 2.0 million, with an inlet total pressure and temperature of 3.217bar and 783K, the exit Mach number being measured as 0.9. The internal holes were supplied independently with different mass flows for which unfortunately the inlet temperatures were not recorded in Hylton’s original measurements. For the purposes of this validation, the inlet temperatures for each of the holes are taken from Luo (2006). Figure 9 and the accompanying table summarise the vane dimensions and cooling holes inlet temperatures.

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Hole No. Diameter (cm) Tin (K) 1 0.63 393.3 2 0.63 393.1 3 0.63 375.2 4 0.63 381.0 5 0.63 359.2 6 0.63 419.1 7 0.63 373.0 8 0.31 371.6 9 0.31 426.9 10 0.198 451.4 Figure 9: C3X vane geometry and cooling hole arrangement and inlet temperature

Figure 10: Mesh, domain, and near wall resolutions

Model settings The results from two meshes types, a topologically block-structured hexahedral and polyhedral, were compared. In both cases, since the vane geometry is a linearly extrusion, 20 equally spaced mesh layers were used in the 7.62cm between the hub and shroud, consistent with previous studies (Luo, 2006). All results herein are reported for the mid-span section where the flow is nominally two-dimensional and unaffected by end-wall effects. y+ values were found to be less than 1 everywhere over the vane surface for both meshes. The inlet and outlet to the domain were placed 14cm upstream and downstream of the vane leading and trailing edges, respectively. Figure 10 illustrates the meshes and near wall resolution. Both hexahedral and polyhedral meshes contain just over 1million cells (~800k in the external flow, ~150k in the solid and ~10k in each hole). Two turbulence models were assessed. The first is a standard two-equation model, k-ω-SST, with implicit low-Re near-wall attributes but with no special laminar-to-turbulent transition features. The second contains a correlation-based modification, referred to as the γ-Reθ model from Menter-

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Langtry (2004). A transport equation for intermittency, γ, tracks the likelihood of the flow to be locally laminar (value 0.0) or turbulent (value 1.0) whereas the transport equation for the transition Reynolds number, Reθ, uses experiment correlations to feed back to the γ-equation source terms when transition is adjudged to occur. Malan (2009), has published the two experimental correlations usually missing in the standard references to the model. Malan’s calibrations are performed on many standard transition test cases, including the ECROFTAC T3-series, and are extensively validated on single and multi-element aerofoils, turbine blades and more challenging three-dimensional geometries including a Formula-1 rear wing. The inlet turbulence intensity was set to 8.3% as recorded in the experiment. The inlet turbulence length scale (inlet turbulence viscosity ratio) was not measured; therefore this validation exercise takes the opportunity to test the modeling sensitivities to inlet turbulence length scale. The working fluid was given ideal gas properties with a temperature dependent specific heat capacity, and viscosity varying according to Sutherlands Law. The vane metal density and specific heat capacity were set to 7200kg/m3 and 587.15 J/kg.K respectively, with conductivity set to a linear function of temperature.

Results The hexahedral mesh pressure coefficient over the pressure and suction surfaces compared favorably with the measurements, and was insensitive to inlet turbulence length scales. The pressure profile was equally insensitive to the use, or not, of the transition model. Figure 11 below shows the pressure and suction side profiles from the non-transition model.

Figure 11: Pressure and Suction surface pressure profiles, hex mesh, C3X Case 1 Conversely, prediction of wall heat transfer coefficient was found to be strongly dependent on both the use/non-use of the transition modeling and, only with the transition model, to inlet turbulence length scale (or turbulent viscosity ratio, TVR). Figure 12 compares the non-transition/transition model heat-transfer predictions on the hexahedral mesh. The transition model has the effect of suppressing the over-penetration of turbulence within the boundary layer; the effect at the leading edge is to reduce the heat transfer at the stagnation point. The levels here still continue to be higher than the measured values, but we shall see later that the heat transfer at stagnation is closely related to the upstream turbulence intensity.

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The transition model clearly delays the onset of boundary-layer transition on the suction surface until around 40% of chord, consequently reducing the wall heat-transfer in line with the measurements. The predictive trend follows the measured trend in the form of increasing heat transfer subsequent to transition, except that the transition length is predicted to be too short. In principle, the model correlation flength (see Malan 2009) may be tuned to improve this predictive trend. On the pressure surface, the heat-transfer levels are lowered consistent with the reduced levels at the stagnation point. The wiggles close to the trailing edge on both suction and pressure surface are a manifestation of the effect of the internal blade cooling holes. Figure 12: Normalised wall heat-transfer: no-transition (top), transition (bottom) Figure 13 shows the sensitivity of the transition model predictions to the inlet turbulence viscosity ratio on the polyhedral. The main differences are obseved in the shift of overall levels of wall heat-transfer below 50% , becoming relatively insensitive above 50% TVR. Two points arise. The first relates to the importance of upstream turbulence measurements as a requirement to perform well qualified CFD validation studies. In this case, we have been able only

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to demonstrate that there is sensitivity of the heat-transfer solutions to the levels of incoming turbulence, and thereby draw notice to its importance of this feature.

10% Figure 13: Transition model normalised heat-transfer sensivity to inlet turbulent viscosity ratio, TVR: from 10% (top), 40%, 70% to 100% (bottom).

40%

70% 100%

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The second point relates to modelling, namely the effect that the dissipation terms in the turbulence model have on damping the turbulence levels between the inlet of the calculation domain, where they are prescribed, and adjacent to the blade where they directly affect the aerodynamics and heat transfer. Malan (2009), in his implementation of the γ-Reθ model, has added a user control to suppress the upstream damping, thereby retaining the levels of turbulence set at the inlet. Differences between the heat-transfer transition-based predictions on the hexahedral mesh (Fig 12, bottom) and polyhedral mesh (Fig 13, bottom) are indicative of only minor mesh dependency still inherent in these solutions. Figure 14: Mach Number: polyhedral mesh (left) hexahedral mesh (right) Figure 15: Pressure: polyhedral mesh (left) hexahedral mesh (right)

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Figure 16: Mid-span blade temperatures: polyhedral mesh (bottom) hexahedral mesh (top) Finally, Figures 14-16 show the comparisons in Mach number, pressure and blade temperatures between the hexahedral and polyhedral meshes. Differences are barely perceptable except for a marginally sharper wake structure seen in the Mach number contours on the hexahedral mesh, attributable to the block-structured clustering of cells behing the blade where the effects on heat-transfer are negligible.

CONCLUSIONS A framework for handling arbitrarily complex turbine blade geometries has been presented. It uses automated features for geometry handling and CAD repair, multi-domain meshing and advanced physical modeling. The modeling methodology has been validated against experimental measurements of surface pressures and wall heat transfer on the NASA C3X turbine vane, Case 1. Sensitivities to modeling parameters have been assessed. These modeling uncertainties arise because of incomplete experimental data. Careful adjustment of inlet turbulence parameters and judicious use of advanced modeling techniques, in particular transition modeling, has been shown to improve the predictions with respect to the measurements. Solutions have been shown to be insensitive to mesh type as long as basic best practices are followed. These experiences contribute to a better understanding of conjugate heat-transfer modeling of turbine blades, and when embedded in an automated framework for geometry handing and fluid-solid continuous meshing, offers substantial benefits and productivity gains to the overall modeling process. It has not been possible to validate any predictions of the displacement or stress fields in the C3X case. Validation data is sparse, and any means to acquiring qualified data for this purpose is encouraged.

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