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Research Papers

Use of an Immersed Mesh for High Resolution Modeling of Film Cooling Flows

[+] Author and Article Information
B. Lad

e-mail: bharat.lad@eng.ox.ac.uk

L. He

e-mail: li.he@eng.ox.ac.uk
Osney Thermofluids Laboratory
Department of Engineering Science
Oxford University
Southwell Building, Osney Mead
Oxford, OX2 0ES, United Kingdom

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 13, 2011; final manuscript received August 9, 2011; published online October 30, 2012. Editor: David Wisler.

J. Turbomach 135(1), 011022 (Oct 30, 2012) (9 pages) Paper No: TURBO-11-1134; doi: 10.1115/1.4006398 History: Received July 13, 2011; Revised August 09, 2011

The development of a high pressure turbine requires the accurate prediction of flow within and around film cooling holes. However, the length scales inherent to film cooling flows produce a large disparity against those of the mainstream flow; hence they cannot be resolved by a mesh generated for an aerodynamics analysis. Furthermore, the process of meshing cooling holes is not only time consuming but cumbersome; thus making the parametric study of film cooling effectiveness for a given blade geometry, using hole geometry and distribution, very difficult in a design environment. In this paper an immersed mesh block (IMB) approach is proposed which allows the refined mesh of a cooling hole to be immersed into the coarser mesh of a nozzle guide vane (NGV) and solved simultaneously while maintaining mass conservation. By employing two-way coupling, the flow physics in and around cooling holes is able to interact with the mainstream; hence the length scales of both types of flow are appropriately resolved. A generic cooling hole design can then be mapped to a given aerofoil geometry multiple times to achieve an appropriate distribution of cooling holes. The results show that for a realistic transonic blade, a configuration consisting of up to 200 cooling holes can be efficiently and accurately calculated—while retaining the original aerodynamic mesh but with a much enhanced resolution for the film cooling.

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Figures

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Fig. 1

NGV mesh suitable for an aerodynamics analysis

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Fig. 2

NGV mesh with hypothetical cooling hole distribution

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Fig. 3

Coarse mesh for a generic cooling hole

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Fig. 4

Concept of the IMB methodology. (a) Cooling hole mesh with suitable mesh density. (b) IMB inserted into NGV mesh to allow for simultaneous solution of film cooling and NGV flow.

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Fig. 5

Immersed mesh block

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Fig. 6

Implemented Runge–Kutta algorithm

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Fig. 7

2D representation of a base node within an IMB hexahedral

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Fig. 8

Calculation of the net flux entering/exiting an IMB. (a) IMB and base mesh schematic. (b) Simplification of boundaries surrounding cooling hole. (c) Representation of the IMB and base mesh net flux.

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Fig. 9

Rotation of IMB about cooling hole center to achieve the desired injection angle

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Fig. 10

Placement of an IMB onto an NGV surface

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Fig. 11

Mapping of IMB to aerofoil surface. (a) Initial placement of IMB. (b) Translation of nodal columns to aerofoil surface. (c) Rotation of each column about wall node.

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Fig. 12

Mapped IMB on aerofoil surface

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Fig. 13

Seven cooling hole IMBs on a flat plate: (a) axial view and (b) 3D view

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Fig. 14

IMB temperature distribution, line indicates extent of IMB

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Fig. 15

Film cooling effectiveness and convergence history plots for the flat plate test case: (a) streamwise film cooling effectiveness distribution and (b) convergence history of the IMB and base mesh solution

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Fig. 16

IMB and directly meshed cooling hole geometries—side views. (a) IMB and base mesh. (b) Directly meshed cooling holes.

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Fig. 17

IMB and directly meshed cooling hole geometries—3D views. (a) IMB and base mesh. (b) Directly meshed cooling holes.

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Fig. 18

Comparison of IMB results to a directly meshed solution: (a) static temperature distribution of directly meshed cooling holes on a curved surface and (b) static temperature distribution of a curved surface with 24 cooling holes in an IMB

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Fig. 19

Approximately 200 cooling holes in eight IMBs meshed to NGV: (a) front view and (b) plan view

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Fig. 20

IMB temperature profiles on NGV: (a) temperature profile of approximately 150 cooling holes on NGV and (b) temperature profile of approximately 200 cooling holes on NGV

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