Toward a High Order Throughflow - Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses
[en] Capturing a level of modeling of the flow inside a multi-stage turbomachine, such as unsteadiness for example, can be done at different degrees of details, either by capturing all deterministic features of the flow with a pure unsteady method or by settling for an approximated solution at a lower computational cost. The harmonic methods stand in this second category.
Amongst them the "Nonlinear Harmonic Method'' from He revealed the most efficient. This method consists of solving the fully nonlinear 3D steady problem and a linearized perturbation system in the frequency domain. As it has been shown by the authors that the circumferential variations exhibit a harmonic behavior, it is proposed here to adapt this method to the throughflow model, where the main nonlinear system would be the common throughflow equations and the auxiliary system would give access to the circumferential stresses.
As the numerical local explicit impermeability conditions are unsupported by Fourier series, the adaptation of this technique to the throughflow model passes through a reformulation of the blade effect by a smooth force field as in the "Immersed Boundary Method'' from Peskin.
A simple example of an inviscid flow around a cylinder will illustrate the preceding developments, bringing back the mean effect of the circumferential non uniformities into the meridional flow.
Disciplines :
Aerospace & aeronautics engineering Mathematics Space science, astronomy & astrophysics
Author, co-author :
Thomas, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Turbomachines et propulsion aérospatiale
Léonard, Olivier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Turbomachines et propulsion aérospatiale
Language :
English
Title :
Toward a High Order Throughflow - Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses
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Bibliography
Adamczyk J.J. Model Equation for Simulating Flows in Multistage Turbomachinery. 1984, NASA-TM-86869.
He L. Ning W. Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines. AIAA J. 1998, 36:2005-2012. AIAJAH, 0001-1452, 10.2514/2.328.
Chen T. Vasanthakumar P. He L. Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach. J. Propul. Power 2001, 17:651-658. JPPOEL, 0748-4658, 10.2514/2.5792.
Stridh M. Eriksson L.E. Modeling Unsteady Flow Effects in a 3D Transonic Compressor. ASME 2005, and Paper No. GT2005-68149.
Vilmin S. Lorrain S. Hirsch C. Swoboda S. Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Nonlinear Harmonic Method. ASME 2006, and Paper No. GT2006-90210.
Simon J.-F. Thomas J.P. Léonard O. On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations. ASME J. Turbomach. 2009, 131(3):031019. JOTUEI, 0889-504X, 10.1115/1.2992514.
Thomas J.P. Simon J.F. Léonard O. Investigating Circumferential Non-Uniformities in Throughflow Calculations Using a Harmonic Reconstruction. ASME 2008, and Paper No. GT2008-50328.
Thomas J.P. Léonard O. Towards a High Order Throughflow. Part I: Investigating the Effectiveness of a Harmonic Reconstruction for 3D Flows. ASME 2010, and Paper No. GT2010-22841.
Hall K.C. Thomas J.P. Clark W.S. Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique. AIAA J. 2002, 40:879-886. AIAJAH, 0001-1452, 10.2514/2.1754.
McMullen M. Jameson A. Alonso J. Demonstration of Nonlinear Frequency Domain Methods. AIAA J. 2006, 44:1428-1435. AIAJAH, 0001-1452, 10.2514/1.15127.
Goldstein D. Handler R. Sirovich L. Modeling a No-Slip Flow Boundary With an External Force Field. J. Comput. Phys. 1993, 105:354-366. JCTPAH, 0021-9991, 10.1006/jcph.1993.1081.
Khadra K. Angot P. Parneix S. Caltagirone J.-P. Fictitious Domain Approach for Numerical Modelling of Navier-Stokes Equations. Int. J. Numer. Methods Fluids 2000, 34:651-684. IJNFDW, 0271-2091, 10.1002/1097-0363(20001230)34:8<651::AID-FLD61>3.0.CO;2-D.
Mohd-Yusof J. Development of Immersed Boundary Methods for Complex Geometries. CTR Annual Research Briefs 1998, 325-336. Center for Turbulence Research, NASA Ames/Stanford University.
Liu Q. Vasilyev O.V. A Brinkman Penalization Method for Compressible Flows in Complex Geometries. J. Comput. Phys. 2007, 227:946-966. JCTPAH, 0021-9991, 10.1016/j.jcp.2007.07.037.
Chiavassa G. Donat R. A Penalization Technique for the Efficient Computation of Compressible Fluid Flow With Obstacles. Hyperbolic Problems: Theory, Numerics, Applications 2008, 89-100. 10.1007/978-3-540-75712-2_7, and , Springer Berlin, Heidelberg.
Keistler P.G. An Immersed Boundary Method for Supersonic Flow. Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit 2008, AIAA Paper No. 2008-529.
Adamczyk J.J. Mulac R.A. Celestina M.L. A Model for Closing the Inviscid Form of the Averaged-Passage Equation System. ASME J. Turbomach. 1986, 108:180-186. JOTUEI, 0889-504X, 10.1115/1.3262035.
Mittal R. Iaccarino G. Immersed Boundary Methods. Annu. Rev. Fluid Mech. 2005, 37:239-261. ARVFA3, 0066-4189, 10.1146/annurev.fluid.37.061903.175743.
Billson M. Erilsson L.E. Davidson L. Acoustic Terms for the Linearized Euler Equations in Conservative Form. AIAA J. 2005, 43:752-759. AIAJAH, 0001-1452, 10.2514/1.12858.
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