Nghiên cứu lý thuyết bài toán tương tác FSI ứng dụng vào mô phỏng bài toán tuabin gió và tuabin động cơ phản lực hai luồng

Mu 1a MU BèA LUN VN Cể IN CH NH VNG Kh 210 x 297 mm B GIO DC V O TO TRNG I HC BCH KHOA H NI LU HNG QUN LU HNG QUN MY V THIT B THY KH NGHIấN CU Lí THUYT BI TON TNG TC FSI NG DNG VO Mễ PHNG BI TON TUABIN GIể V TUABIN NG C PHN LC HAI LUNG LUN VN THC S KHOA HC K thut mỏy v thit b thy khớ KHO 2009 H Ni 03 Nm 2011 Mu 1b MU TRANG PH BèA LUN VN B GIO DC V O TO TRNG I HC BCH KHOA H NI LU HNG QUN NGHIấN CU Lí THUYT BI TON TNG TC FSI NG DNG VO Mễ PHNG BI TON TUABIN GIể V TUABIN NG C PHN LC HAI LUNG Chuyờn ngnh : K thut mỏy v thit b thy khớ LUN VN THC S KHOA HC K thut mỏy v thit b thy khớ NGI HNG DN KHOA HC : TS NGUYN PH KHNH H Ni 03 Nm 2011 MC LC Danh mc cỏc kớ hiu, cỏc ch vit tt Danh mc cỏc hỡnh v, th GII THIU TNG QUAN TI PHN I: C S Lí THUYT NGHIấN CU TNG TC FSI 12 Chng I TNH TON NG LC HC CHT LNG CFD 12 1.1 Nhng khỏi nim c bn v cỏc phng trỡnh bo ton ca cht lu 1.1.1 L i gii thiu 12 1.1.2 C ỏc nh lut bo ton c bn 13 1.2 G ii thiu v phng phỏp s 19 1.2.1 P hng phỏp tip cn ng lc hc dũng cht lu 19 1.2.2 C FD l gỡ 20 1.2.3 K h nng v hn ch ca phng phỏp s 21 1.2.4 C ỏc thnh phn ca phng phỏp s 22 1.2.5 C ỏc phng phỏp ri rc húa 26 Chng II TNH TON KT CU BNG PHNG PHP PTHH(FEM) 28 2.1 K hỏi nim 28 2.2 L ch s phỏt trin 28 2.3 N i dung 29 2.3.1 X p x bng phn t hu hn 29 2.3.2 nh ngha hỡnh hc cỏc phn t hu hn 30 2.3.3 C ỏc dng phn t 31 2.3.4 P hn t quy chiu, phn t thc 32 2.3.5 L c, chuyn v, bin dng, ng sut 35 2.3.6 N guyờn lý cc tiu húa th nng ton phn 37 2.3.7 T rỡnh t phõn tớch bi toỏn theo phng phỏp PTHH 37 2.3.8 S tớnh toỏn bng phng phỏp PTHH 39 2.4 ng dng 41 Chng III TNH TON TNG TC FSI 42 3.1 C ỏc khỏi nim c bn ca tng tỏc FSI 42 3.1.1 G ii thiu 42 3.1.2 P hõn loi tng tỏc FSI 43 3.1.3 C ỏc ng dng in hỡnh 45 3.2 P hng phỏp s tớnh toỏn tng tỏc FSI 46 3.2.1 L a chn phng phỏp s 46 3.2.2 C ỏc phng trỡnh kt hp (coupling) 48 3.2.3 S thut gii 50 3.2.4 P hng phỏp truyn ti b mt tng tỏc cht lu - kt cu 51 PHN II: NG DNG TNH TON FSI VI Mễ HèNH TUABIN GIể V TUABIN NG C MY BAY 56 Chng IV GII THIU CHUNG V CODE TNH TON ANSYS WORKBENCH V ANSYS FLUENT 56 4.1 T ng quan v mụi trng ANSYS WORKBENCH 57 4.1.1 G ii thiu chung ANSYS WORKBENCH 57 4.1.2 K h nng ca phn mm ANSYS WORKBENCH 57 4.1.3 T ng quan v cỏc cụng c gúi phn mm ANSYS WORKBENCH 57 4.2 G ii thiu chung v phn mm ANSYS Fluent 59 4.2.1 K h nng ca ANSYS Fluent 59 4.2.2 c im ca quỏ trỡnh mụ phng s bng CFD 60 4.3 T rung tõm Phỏt trin v ng dng Phn mm Cụng nghip DASI 60 Chng V Mễ PHNG TNG TC FSI CNH TUABIN GIể 62 5.1 t 62 5.2 N ghiờn cu c tớnh khớ ng tuabin giú 64 5.2.1 L a chn mụ hỡnh s 64 5.2.2 M ụ hỡnh hỡnh hc v li 66 5.2.3 iu kin biờn 68 5.2.4 K t qu mụ phng v ỏnh giỏ 70 5.3 N ghiờn cu c tớnh kt cu cỏnh tuabin (FSI) 75 5.3.1 P hng phỏp s 75 5.3.2 M ụ hỡnh hỡnh hc v li 77 5.3.3 iu kin biờn 79 5.3.4 K t qu mụ phng v ỏnh giỏ 80 Chng VI Mễ PHNG TNG TC FSI TUABIN CAO P NG C GE90 82 6.1 t 82 6.2 P hng phỏp s 83 6.2.1 T ớnh toỏn CFD 83 6.2.2 T ớnh toỏn kt cu 83 6.3 M ụ hỡnh hỡnh hc v li 83 6.3.1 M ụ hỡnh hỡnh hc 83 6.3.2 M ụ hỡnh li 86 6.4 P hng phỏp mụ phng v iu kin biờn 89 6.4.1 T ớnh toỏn CFD 89 6.4.2 T ớnh toỏn tng tỏc FSI 92 6.5 K t qu mụ phng 92 6.5.1 K t qu mụ phng CFD 92 6.5.2 K t qu mụ phng tng tỏc FSI 95 KT LUN CHUNG V HNG NGHIấN CU 98 DANH MC TI LIU THAM KHO 100 Danh mc cỏc kớ hiu v ch vit tt M : S Mach m : Khi lng v : Vn tc : nht ng hc Re : S Reynold Fr : S Froude St : S Strouhal CM : Control Mass CV : Control Volume PTVPTP: Phng trỡnh vi phõn tng phn a : H s dũng chy dc theo trc-h s thu hp dũng chy a : H s dũng chy theo phng tip tuyn A , Aw , Ad : Tit din dũng chy cỏc v trớ xa vụ cựng phớa trc,phớa sau v ti rotor c : Chiu di dõy cung ca phõn t cỏnh CT : H s lc theo phng dc trc tỏc dng lờn cỏnh rotor Cx : H s lc lờn phõn t cỏnh theo phng dc trc C y : H s lc lờn phõn t cỏnh theo phng tip tuyn N : S cỏnh qut ca rotor pd+ , pd : p sut tnh ca dũng chy trc v sau rotor U ,U w ,U d : Vn tc dũng chy ti cỏc v trớ xa vụ cựng phớa trc,phớa sau v ti rotor P: Cụng sut nh mc : Khi lng riờng ca khụng khớ W : Vn tc tng i ca dũng chy vi phõn t cỏnh x : T s bỏn kớnh (r/R) : Vn tc gúc ca rotor cỏnh qut : T s tc u mỳt cỏnh : Hiu sut rotor cỏnh qut : Gúc tn : Gúc ti : Gúc t cỏnh CFD (Computational Fluid Dynamics): ng lc hc cht lu CSD (Computational Structure Dynamics): ng lc hc kt cu FEM(Finite Elements Method): Phng phỏp phn t hu hn (PPPTHH) FSI (Fluid Structure Interaction) : Tng tỏc cht lu kt cu AC (Axial chord): Chiu di ca dõy cung chiu lờn phng dc trc HPT ( High Pressure Turbine): Turbin cao ỏp RPM (Rounds Per Minute): Vũng trờn phỳt PPH (Pounds Per Hour): Pound trờn gi SFC (Specific Fuel Consumption): Sut tiờu hao nhiờn liu TO (Take-off): S ct cỏnh PSI (Pound Per Inch): Pound trờn inch bỡnh phng gamm header will be provided by the publisher 11 contraction air intake windows xxxXX end plate propeller test section diffusor air outlet 500 Cv Tuu z [ mm ] 400 300 200 100 0 0.2 0.4 0.6 0.8 Cv , Tu [ - ] Fig Schematic side view of the boundary layer wind tunnel at the IAG, wind tunnel model in the test section with view in flow direction and velocity and turbulence profile The deformation of the membrane was measured contactlessly with two laser triangulators at two points By turning of the model the deformation could be measured on two circular cuts at a time By changing the radial position of the transducers several circular cuts could be recorded 3.2 Structure mechanical model As material for the membrane a rubber sheet was selected, whose material properties have been determined at the IAG: thickness t = 0.2 mm, linearized modulus of elasticity E M em = MPa, transverse extension number M em = 0.2 and density M em = 1100 kg/m3 For the Copyright line will be provided by the publisher 12 Wind loads on lightweight structures: Wind loads on lightweight structures outside rim of the membrane a silicone tube with an outer diameter of d Rim,out = 1.8 mm and a modulus of elasticity of ERim,out = 4.3 MPa was used For the anchoring wires a kite string (e.g Dyneema SK 60) with d Anchor = 0.3 mm, EAnchor = 2260 MPa, Anchor = 0.2 and Anchor =1340 kg/m3 was used Due to their high stiffness (compared to the membrane) the deformations of the mast and the supports could be neglected The material parameters used for the structural elements are described in detail in [7] Before being able to simulate the fluid-structure interaction, the geometric shape of the unloaded membrane has to be found in a numerical form finding process, where geometric nonlinear structural behavior has to be assumed (see [28]) The form finding process starts with a displacement of the singular center point, so that a height of the membrane of h z = 8.5 cm and a total height of the membrane roof of Hz = 16.8 cm with respect to the supports of the columns is achieved Furthermore, the prestress in the membrane is described with a prescribed ratio of tangential/radial prestresses with increasing radial stresses towards the center point of the membrane The prestresses in the outside rims and anchoring wires are chosen accordingly, which results in: FM em,rad FM em,tang FRim,out FAnchor = 8.50 N/m = 2.98 N/m = 0.80 N = 0.50 N 3.3 Fluid dynamical model For the CFD simulation a k- model [24] is used Based on a measured turbulence degree T u = 0.05 the turbulent kinetic energy at the inflow boundary can be computed to k(z) = T u2 U (z)2 (7) In accordance to experimental measurements the velocity field U (z) at the inlet of the simulation domain was described by an exponential wind profile The dissipation rate at the inlet is given by (z) = k(z)3/2 lc (z) (8) Following [25] the characteristic length scale lc is chosen to lc (z) = z C03 with C0 = 0.427 and = 0.4 (9) Using density and viscosity of air ( = 1.14 kg/m3 and = 18.24 ã 106 kg/(m s)) the Reynolds number referring to the height of the membrane hz is obtained to Re = 65 875 and Re = 87 125 for the reference velocities Uref = 12.3 m/s and 16.2 m/s, respectively The geometric description of the structural model is the starting point for the definition of a CFD model The computational domain is discretized by a block-structured finite volume grid into 228 800 control cells Fig shows a part of this discretization The projection of the grid to the membrane surface is plotted in Fig Copyright line will be provided by the publisher gamm header will be provided by the publisher 13 Fig Part of the block-structured finite volume grid Fig CFD interface discretization (3072 quadrilaterals) As we only consider the stationary fluid-structure interaction, only the gray part of the algorithm plotted in Fig is relevant for this example Further investigations using a fully dynamic interaction and a large-eddy simulation approach for the CFD computation are described in [8] Comparison of wind tunnel and simulation results 4.1 Deformation of the structure Fig shows the deformed wind tunnel model and Fig 10 the corresponding deformed numerical model Simulation and experiment are in good qualitive agreement To investigate Copyright line will be provided by the publisher 14 Wind loads on lightweight structures: Wind loads on lightweight structures Fig Deformed wind tunnel model Fig 10 Deformed structural model during simulation the system behavior of wind tunnel and numerical model in more detail the following three different cases are examined The upper row in Fig 11 shows measured displacements of the wind tunnel model and below the corresponding results of simulation starting from an inflow velocity Uref and a given prestress FAnchor (Fig 11, left) In a first step the prestress is doubled yielding a reduction of the structural deformation (Fig 11, center) In a second step the configuration is changed again by increasing the inflow velocity The system reacts by an increase of deformation (Fig 11, right) In all three cases good correspondence of wind tunnel experiments and numerical simulation can be observed For a more detailed comparison the deformed structures are shown in cutlines in Fig 12 (in flow direction and vertical to the flow direction) Good agreement can be observed again even when small differences in the absolute displacement values are obtained Concerning the high complexity of the model and, e.g., the inaccuracies in the definition of prestresses in the wind tunnel model, the agreement of the simulation and experiment is highly satisfactory Copyright line will be provided by the publisher gamm header will be provided by the publisher 15 Fig 11 System response 4.2 Windloads Fig 13 shows the horizontal load components in the cables for the three cases of comparison Forces are plotted over the circumferential angle degree corresponds to the luvward part and 180 degrees to the leeward part Qualitatively, again good agreement can be observed, although there are quantitative differences in the prestresses at individual columns This discrepancy is due to the simplifications which had to be made for the experiment as well as for the numerical approach Further investigations are necessary to clarify the exact source of these discrepancies Conclusions and future work The most significant result of the presented investigation is the good agreement of experiment and simulation, being dependent on the exactness of the definition of the corresponding models A very significant advantage of numerical simulation is the possibility of coupling it to CAD models and automatic mesh generation and thus being able to modify shape and parameters of the structure, easily On the other hand, modification of a wind tunnel model is in general time consuming and expensive Furthermore, in a physical experiment only pointwise or integral quantities can be measured, whereas numerical simulation gives a very detailed spatial solution of the quantities of interest Yet, the very high requirements on computational effort for a numerical simulation of fluid-structure interaction is still very demanding and today only possible in academic research projects Furthermore, when stepping to dynamic wind-structure interaction in a highly turbulent atmospheric boundary layer even more computational power would be necessary Considering this situation, the wind tunnel experiment could investigate a complete configuration with different prestresses over a time span Copyright line will be provided by the publisher 16 Wind loads on lightweight structures: Wind loads on lightweight structures 0.32 N 84 Pa: numerical simulation 0.32 N 84 Pa: wind tunnel test 0.65 N 84 Pa: numerical simulation 0.65 N 84 Pa: wind tunnel test 0.65N 150 Pa: numerical simulation 0.65N 150 Pa: wind tunnel test 150 -300 z [mm] V -200 100 50 -100 x [mm] 100 200 300 100 200 300 z [mm] 150 100 50 -300 -200 -100 y [mm] Fig 12 Comparison of deformed systems corresponding to a storm of 36 h on the original structure Future increase of computer power and additional developments in computational mechanics let yet expect that in only few years even complex practical problems of wind-structure interaction can be numerically simulated These computations will be a highly welcome alternative to expensive and rather inflexible experiments in wind tunnels One important final experience of our investigations should be mentioned The definition of the right model of reality is much more difficult for a fluid-structure problem than for classical single field problems Even seemingly small modifications of load conditions, of the shape of the membrane or the inflow conditions can lead to very significant differences in the systems answer The necessity of a very detailed model description can be seen in the numerical simulation as well as in the wind tunnel experiment and underlines that multi-field problems need still a lot of research in computational and experimental mechanics Acknowledgements The authors would like to thank the Bayerische Forschungsstiftung for funding this work in the Competence Network for Technical, Scientific High Performance Computing in Bavaria (KONWIHR) Furthermore the support ofOFiSTiK AG, especially of Dr Bellmann and Dr Katz, is acknowledged Copyright line will be provided by the publisher gamm header will be provided by the publisher 2.5 17 Experiment experiment num Simulation numerical simulation F [N ] 1.5 0.5 Fv=0.32N V=12.3m/s Fv=0.65N V=12.3m/s Fv=0.65n V=16.2m/s 45 90 135 horizontale Richtung der Abspannung horizontal direction of anchor [][ ] 180 Fig 13 Comparison of cable forces References [1] K Zilch , Ein anschauliches Lastkonzept făur Hochhăauser in băoigem Wind, Habilitationsschrift, Technische Hochschule Darmstadt (1983) [2] P Droll, R Sieber, A Cozzani and M Schăafer, Numerical investigation of the performance of a deep space antenna under environmental loads, Bauingenieur, January, pp 712 (2002) [3] http://www.enm.bris.ac.uk/anm/tacoma/tacoma.html [4] K J Bathe, H Zhang, Finite element developments for general fluid flows with structural interactions, International Journal for Numerical Methods in Engineering , vol 60, pp 213232 (2004) [5] W A Wall, Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen, Dissertation, Institut făur Baustatik, Universităat Stuttgart (1999) [6] A Halfmann, E Rank, M Glăuck, M Breuer, F Durst, J Bellmann and C Katz, Computational Engineering for Wind-Exposed Thin-Walled Structures, Lecture Notes in Computational Science and Engineering, vol 21, pp 6370, Springer, Berlin, Heidelberg, New York (2002) Copyright line will be provided by the publisher 18 Wind loads on lightweight structures: Wind loads on lightweight structures [7] A Halfmann, Ein geometrisches Modell zur numerischen Simulation der FluidStruktur-Interaktion windbelasteter, leichter Flăachentragwerke, Dissertation, Lehrstuhl făur Bauinformatik, Technische Universităat Măunchen (2002) [8] M Glăuck, Ein Beitrag zur numerischen Simulation von Fluid-Struktur-Interaktionen Grundlagenuntersuchungen und Anwendung auf Membrantragwerke, Dissertation, Technische Fakultăat, Universităat Erlangen-Năurnberg (2002) [9] I Demirdzic and M Peric, Space Conservation Law in Finite Volume Calculations of Fluid Flow, International Journal for Numerical Methods in Fluids, vol 8, pp 1037 1050 (1988) [10] C Bartels, M Breuer, K Wechsler and F Durst, CFDApplications on ParallelVector Computers: Computations of Stirred Vessel Flows, Computers & Fluids, vol 31, no 1, pp 6997, Elsevier Science Ltd, Oxford (2001) [11] F Durst and M Schăafer, A Parallel BlockStructured Multigrid Method for the Prediction of Incompressible Flows, International Journal for Numerical Methods in Fluids, vol 22, pp 549565 (1996) [12] C Katz and J Bellmann, ASEHandbuch, SOFiSTiK AG (19881995) [13] K C Park and C A Felippa, Partitioned Analysis of Coupled Systems, in Computational Methods for Transient Analysis (Eds Belytschko, T & Hughes, T.J.R.), pp 157 219 (1983) [14] C Farhat and M Lesoinne, On the Accuracy, Stability, and Performance of the Solution of Three-Dimensional Nonlinear Transient Aeroelastic Problems by Partitioned Procedures, AIAA-96-1388-CP, pp 629641 (1995) [15] A C Frank, Organisationsprinzipien zur Integration von geometrischer Modellierung, numerischer Simulation und Visualisierung, Dissertation, Lehrstuhl făur Ingenieuranwendungen in der Informatik, Numerische Programmierung, Fakultăat făur Informatik, Technische Universităat Măunchen (2000) [16] M Glăuck, M Breuer, F Durst, A Halfmann and E Rank, Computation of Fluid Structure Interaction on Lightweight Structures, International Journal of Wind Engineering and Industrial Aerodynamics, vol 89, no 1415, pp 13511368 (2001) [17] M Glăuck, M Breuer, F Durst, A Halfmann and E Rank, Computation of Wind Induced Vibrations of Flexible Shells and Membranous Structures, Journal of Fluids and Structures, vol 17, pp 739765 (2003) [18] M Lesoinne and C Farhat, Improved Staggered Algorithms for the Serial and Parallel Solutions of Three-Dimensional Nonlinear Transient Aeroelastic Problems, Proceedings of 4th World Congress on Computational Mechanics, Buenos Aires, pp 483485 (1998) [19] W A Wall, D P Mok and E Ramm, Partitioned Analysis Approach for the Transient, Coupled Response of Viscous Fluids and Flexible Structures, Proceedings of European Conference on Computational Mechanics, Măunchen (1999) Copyright line will be provided by the publisher gamm header will be provided by the publisher 19 [20] D P Mok, Partitionierte Lăosungsansăatze in der Strukturdynamik und der Fluid StrukturInteraktion, Dissertation, Institut făur Baustatik der Universităat Stuttgart (2001) [21] R Ahrem, M G Hackenberg, P Post, R Redler and J Roggenbuck, MpCCI Mesh based parallel Code Coupling Interface, Institute for Algorithms and Scientific Computing (SCAI), GMD, http://www.mpcci.org/ (2000) [22] E Rank, M Răucker and M Schweingruber, Automatische Generierung von FiniteElement-Netzen, Bauingenieur, vol 69, pp 373379 (1994) [23] C Fahrhat, M Lesoinne and P LeTallec, Load and Motion Transfer Algorithms of Fluid/Structure Interaction Problems with Non-Matching Discrete Interfaces: Momentum and Energy Conservation, optimal Discretization and Application to Aeroelasticity, Computational Methods in Applied Mechanics and Engineering, vol 157, pp 95114 (1998) [24] B E Launder and D B Spalding, The numerical computation of turbulent flows, Computer methods in Applied Mechanical Engineering, vol 3, pp 269289 (1974) [25] J R Garratt, The atmospheric boundary layer, Cambridge University Press, Cambridge, pp 71 ff (1992) [26] S Wagner, D Bergmann and U Kaiser, Kraftmessungen an einem Membranschirm im Original unter Windeinfluss, Bericht, Institut făur Aerodynamik und Gasdynamik, Universităat Stuttgart (2001) [27] U Kaiser, Windwirkung auf schwach vorgespannte Membranstrukturen am Beispiel eines 30m - Membranschirmes, Dissertation, Fakultăat Luft- und Raumfahrttechnik, Universităat Stuttgart (2002) [28] J Bellmann, Membrantragwerke und Seifenhaut - Unterschiede in der Formfindung, Bauingenieur, March, pp 118123 (1998) Copyright line will be provided by the publisher 756 2008,20(6):756-761 COMBINATION OF CFD AND CSD PACKAGES FOR FLUID-STRUCTURE INTERACTION* WANG Yi-wei Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China, E-mail: wang_y_wei@yahoo.com.cn LIN Yong-wen China Academy of Space Technology, Beijing 100094, China (Received October 9, 2007, Revised January 3, 2008) Abstract: In this article the UDF script file in the Fluent software was rewritten as the connecting file for the Fluent and the ANSYS/ABAQUS in order that the joined file can be used to aero-elastic computations In this way the fluid field is computed by solving the Navier-Stokes equations and the structure movement is integrated by the dynamics directly An analysis of the computed results shows that this coupled method designed for simulating aero-elastic systems is workable and can be used for the other fluid-structure interaction problems Key words: CFD/CSD, fluid-structure interaction, aero-elasticity fluttering Introduction  Aero/hydro-elasticity problems arise in structures in air flows or water flows [1,2] Such problems would be serious when the structure is thin, the stiffness is low and mutually coupled vibration is induced, which might cause structure damage The aero-vehicle structure design looks for the light weight and it makes the fluttering problem more serious In the coupling system, the fluid and the solid obey their own equations [3] Only the movement and stresses must be matched at their interfaces at any time It is a very tough job for the airplane designer to derive and solve the equations which take the fluid part and the solid part as a whole In order to solve the fluid-solid coupling problem, people used to assume tremendous simplifications, i.e., to assume the interface position is fixed, fluid is inviscous, etc [4] In recent decades, perfect commercial codes for fluid mechanics and solid mechanics are available which can solve very complicate engineering problems The progress in CAD code development  Biography: WANG Yi-wei(1983-), Male, Master offers unified standard data form which is accepted by both fluid mechanics and solid mechanics In such case, people can run the CFD and CSD code simultaneously and exchange numerical data on the interfaces in order to understand the coupling effect [5] Fluid-Structure Interaction [6] (often referred to as FSI), is where fluid flow exerts pressure on a solid structure causing it to deform such that it perturbs the initial fluid flow Aeroelastic analysis is one special kind of FSI problems, of which the interaction only performs on the interface of the fluid and structure, and there is remarkable relative motion In aeroelastic instability, fluttering, which requires the most attention, usually results in catastrophic disaster to structures One of the difficulties of the study on this phenomenon lies in its multi-patterns In traditional methods, assumptions and approximations are usually applied Now, however, due to the development of large-scale computers and the application of mature commercial software, it is possible to apply fewer or even no assumptions, which has been attempted in this work with the help of mature commercial software In this article, a loosely-coupled Computational Aeroelastic Simulation (CAS) method is conducted, [7,8] that is, the flow and the structure equations are 757 treated separately, using synchronization procedure in space and time More details of the method are described in the following sections Applications 3.1 3-D elastic flag swings in the wind 3.1.1 Problem description This example presents a coupling simulation between ABAQUS and Fluent[10,11] The elastic flag hangs on the top part of the channels The angle between the normal of the flag and the normal of inlet is 20o The velocity of the wind is m/s The scale of elastic flag is specified in Fig.2 Fig.2 Shape of flag 3.1.2 Solutions The mesh of Fluent is generated by ICEM and it is unstructured, which are illustrated in Figs.3 and Fig.1 Process flow diagram Solution methods This loosely-coupled CAS method contains four main modules, and their functions are respectively (1) to simulate the flow and obtain the pressure distribution on the surface of the solid portion by using the Fluent, (2) to read the pressure file, then output the journal file of ANSYS by using the UDF, (3) to run the ANSYS/ABAQUS to analyze the deformation of the solid, and then output the displacement at the nodes on the solid portion, and (4) to regenerate the mesh of the fluid portion following the displacement of solid nodes by using the moving-mesh function of Fluent, and then go back to module A flow diagram of the solution method is illustrated in Fig.1[9] Fig.3 Mesh of flag used by Fluent Fig.4 Boundary of fluid zone In the Fluent portion [12,13] the flag surface is specified as an adiabatic, moving, no-slip wall and the location of the nodes of flag surface is calculated by ABAQUS, and then updated by the Fluent dynamic mesh UDF The front surface of channels is set as the velocity-inlet Boundary Condition (BC), the back 758 surface is set as the pressure-outlet BC, and the other surfaces of channels are set as walls The situation is unsteady, and a segregated-implicit solver is used, with the 0.001s per time step are obtained from the results of Fluent The material property is constant, isotropic, and linear, Youngs modulus is u 106 N/m2, Poisson's ratio is 0.45, and the density is 3000 kg/m3 The time step size is set as 0.001s, the same as that of the fluid portion 3.1.3 Results The whole simulation process uses 0.38 s, the z and y coordinates of node (  0.030 0.005 0.000) changing with the time, are recorded (as shown in Figs.6 and 7) The torsion mode of flag is excited The largest flag deformation is shown in Fig.8 Fig.5 Flag mesh of ABAQUS Fig.8 Largest deformation of flag 3-D wing deformation in a subsonic flow 4.1 Problem description This example [15, 16] involves the sweep-back wing shown in the Fig.9, the length of wing span is 1.5 m, the root chord length is 1m and the tip chord length is 0.6 m The wing has a leading-edge sweep angle of 40o with the NACA0012 sections All the degrees of freedom of the root nodes are constrained Fig.6 Curve for z coordinates Fig.7 Curve for y coordinates In the ABAQUS portion [14], all degrees of the upside of elastic flag are constrained The nodes of surface mesh of ABAQUS have the same location as that of Fluent, as shown in Fig.5, and the element types are C3D8R The ABAQUS solver is specified as explicit dynamic analysis, with geometry nonlinear switch opened Every analysis step restarts from the result of pre-step Surface node concentrated forces Fig.9 Shape of the wing 4.2 Solutions In this example, the unstructured mesh generated by ICEM is used, surrounded by a semi-cylinder boundary, and the grid near the wing is refined There are about 150 thousand tetrahedral cells of the whole mesh and 1572 solid nodes on the wing surface, which are illustrated in Fig.10 759 to check the frequency components of the CL and CD data, and the frequency-amplitude obtained is shown in Figs.14 and 15 Fig.10 Mesh of the boundaries on the wing surface and symmetry In the fluid portion [12,13], the wing surface is specified as an adiabatic, moving, no-slip wall, and the velocities of the nodes are obtained from the result of ANSYS The surface with the root of the wing is set as a symmetric one, and other outer surfaces surrounding the grid are set as the pressure far-field The Mach number of the far field is 0.6, and the angle of attack is 10o The unsteady, segregated-implicit solver is chosen as the numerical method, with a time step size of 0.002 s The mesh for ANSYS is the same as the surface mesh of the wing in the fluid portion [14], using the shell 63 elements, so there is no problem about interpolating The solver of the solid portion is specified as a transient dynamic analysis using the full method The material property is constant, isotropic, linear, Youngs modulus is 12 GN/m2, Poissons ratio is 0.3, the density is 3000 kg/m3 and the thickness is 0.05 m The time step size is set as 0.002 s, the same as that for the fluid portion 4.3 Results With the time increasing, the wing vibrates in an approximate period, changing the flow, meanwhile, the lift and drag curves of the wing change, as shown in Figs.11 and 12 4.4 Result analysis It can be seen that the lift and drag data are made up with several periodic elements of different frequencies, which are on the basis of wings nature frequencies For the purpose of confirming the result, a modal analysis is taken by the use of ANSYS, the result of which is shown in Table The foregoing six modes are illustrated in Fig.13 Considering that the lift coefficient (CL) and drag coefficient (CD) data reflect the holistic deformation of the wing, the Fast Fourier Transform (FFT) is taken Fig.11 Flow streamlines and contours 760 Table Results of modal analysis Mode Frequency Mode Frequency 16.930 189.88 72.999 191.92 82.515 256.84 87.951 268.47 162.74 10 278.36 Fig.12 CL and CD curves Fig.14 Curve for frequency-amplitude of CL Fig.15 Curve for frequency-amplitude of CD Fig.16 Partial enlargement of Fig.15 From the last figure, it can be seen that the peak frequencies correspond with the first order natural frequency, the octave of that, the second and the third order natural frequency Figure 15 is zoomed in as Fig.16 Fig.13 Mode shapes 761 The frequencies of those small peaks correspond with the fifth and sixth natural frequencies, but there is no peak corresponding with the fourth natural frequency, because the shape of the fourth order mode has little influence on the variety of the CL and CD data, which is shown in Fig.13 [6] [7] Conclusion This article provides an effective new idea to solve aeroelastic problem, in which the tools Fluent and ABAQUS/ANSYS employed are both effective and widely used CFD/CSD commercial software The results obtained also indicates that this coupling method is very accurate and logical, which can be used in engineering applications Furthermore, this method is a general way that can also be employed to solve other kinds of fluid-structure interaction problems [8] [9] [10] [11] References [1] [2] [3] [4] [5] DOWELL E H., CURTISS H C and SCANLANET R H et al A modern course in aeroelasticity[M] Alphen aan den Rijn, The Netherlands: Sijthoff and Noordhoff International Publisher,1978 ZWAAN R J., PRANANTA B B Fluid/structure interaction in numerical aeroelastic simulation[J] International Journal of Non-Linear Mechanics, 2002, 37: 987-1002 QUARTERONI A., VALLI A Numerical approximation of partial differential equations[M] New York, USA: Springer-Verlag, 1998 LI Sheng-yuan., QIU Ji-bao A treating method for coupling boundaries with large movement in fluid-solid interaction dynamics[J] Journal of Astronautics, 2001, 22(1): 1-8(in Chinese) XU Min, AN Xiao-min and CHEN Shi-lu CFD/ CSD [12] 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supersonic panel flutter at elevated temperatures[J] Computers and Structures, 2006, 84(24-25): 1619-1628 ANDERSON J D Computational fluid dynamics: The basics with applications[M] New York, USA: McGraw-Hill, 1995 PATANKAR S V Numerical heat transfer and fluid flow[M] New York,USA: McGraw-Hill, 1980 WANG Xu-cheng Finite element method[M] Beijing: Tsinghua University Press, 2003 (in Chinese) HENSHAW M J de C., BADCOCK K J and VIO G A et al Non-linear aeroelastic prediction for aircraft applications[J] Progress in Aerospace Sciences, 2007, 43(4-6): 65-137 RAO V M., BEHAL A and MARZOCCA P et al Adaptive aeroelastic vibration suppression of a supersonic airfoil with flap[J] Aerospace Science and Technology, 2006, 10(4): 309-315 ... DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI LƯU HỒNG QUÂN NGHIÊN CỨU LÝ THUYẾT BÀI TOÁN TƯƠNG TÁC FSI ỨNG DỤNG VÀO MÔ PHỎNG BÀI TOÁN TUABIN GIÓ VÀ TUABIN ĐỘNG CƠ PHẢN LỰC HAI. .. tính toán tương tác FSI ứng dụng sở lý thuyết vào tính toán hai toán thực tế Ngoài để tài mở hướng nghiên cứu mới… - Ý nghĩa thực tiễn: Hai ứng dụng tính toán mô tương tác FSI cho cánh tuabin gió. .. hai phần sáu chương chính: Phần 1: Cơ sở lý thuyết - Tính toán động lực học chất lưu CFD - Tính toán kết cấu - Tính toán tương tác FSI Phần 2: Ứng dụng tính toán FSI cho hai toán tuabin gió TUABIN