Acta mathematica scientia, Series B >
NEW METHOD FOR IMPROVED CALCULATIONS OF UNSTEADY COMPLEX FLOWS IN LARGE ARTERIES
Received date: 2011-09-16
Online published: 2011-11-20
Using an improved computational fluid dynamics (CFD) method developed for highly unsteady three-dimensional flows, numerical simulations for oscillating flow cy-cles and detailed unsteady simulations of the flow and forces on the aortic vessels at the iliac bifurcation, for both healthy and diseased patients, are analyzed. Improvements in computational efficiency and acceleration in convergence are achieved by calculating both an unsteady pressure gradient which is due to fluid acceleration and a good global pressure field correction based on mass flow for the pressure Poisson equation. Applications of the enhanced method to oscillatory flow in curved pipes yield an order of magnitude increase in speed and efficiency, thus allowing the study of more complex flow problems such as flow through the mammalian abdominal aorta at the iliac arteries bifurcation.
To analyze the large forces which can exist on stent graft of patients with abdominal aor-tic aneurysm (AAA) disease, a complete derivation of the force equations is presented. The accelerated numerical algorithm and the force equations derived are used to calculate flow and forces for two individuals whose geometry is obtained from CT data and whose respective blood pressure measurements are obtained experimentally. Although the use of endovascular stent grafts in diseased patients can alter vessel geometries, the physical characteristics of stents are still very different when compared to native blood vessels of healthy subjects. The geometry for the AAA stent graph patient studied in this investi-gation induced flows that resulted in large forces that are primarily caused by the blood pressure. These forces are also directly related to the flow cross-sectional area and the an-gle of the iliac arteries relative to the main descending aorta. Furthermore, the fluid flow is significantly disturbed in the diseased patient with large flow recirculation and stagnant regions which are not present for healthy subjects.
Key words： numerical computations; fluid dynamics; stent graphs; blood pressure; flow pressure
A. Cheer , Harry A. Dwyer , T. Kim . NEW METHOD FOR IMPROVED CALCULATIONS OF UNSTEADY COMPLEX FLOWS IN LARGE ARTERIES[J]. Acta mathematica scientia, Series B, 2011 , 31(6) : 2247 -2264 . DOI: 10.1016/S0252-9602(11)60397-4
[1] Dean W R. Note on the motion of a fluid in a curve pipe. Phil Mag, 1927, 4: 208
[2] Pedley T J. The Fluid Mechanics of Large Blood Vessels. Cambridge University Press, 1980
[3] Berger S A, Talbot L, Yao L S. Flow in curved piper. Ann Rev Fluid Mech, 1983, 15: 461
[4] Chung J H, Hyun J M. Heat transfer from a fully-developed pulsating flow in a curved pipe. Int J Heat Mass Transfer, 1994, 37(1): 43–52
[5] Hamakiotes C C, Berber S A. Periodic flows through curved tubes. J Fluid Mech, 1990, 210: 353–370
[6] Karaholois G T, Panagopoulous A. Oscillatory flow in a curved annular pipe. Physics of Fluids A-Fluid Dynamics, 1989, 1(7): 11-4-1111
[7] Riley N. Unsteady fully-developed flow in a curved pipe. J Eng Math, 1998, 34(1/2): 131–141
[8] Sumida M, Sudou K, Wada H. Pulasting Flow in a curved pipe-secondary flow. JSME International Journal Series II - Fluids Engineering Heat Transfer Power Combustion Thermophysical Properties, 1989, 32(4): 523–531
[9] Yam C, Dwyer H A. Unsteady flow in a curved pipe//Fluid Dynamics in Biology, Contemporary Mathe-matic 141. American Mathematical Society, 1993: 543–564
[10] Nelsenador M, Cheer A, Dwyer H, Rutaganira T. Unsteady three-dimensional flow in curved distensible tubes//Safofuka N, ed. Computational Fluid Dynamics. Springer, 2000: 227–232
[11] Chuter T, Risburg B, Hopkinson B, et al. Clinical experience with a bifurcated graft system-development and early experience. Cardiovas Surg, 1996, 4: 706–712
[12] Walsh P W, Chin-Quee S C, Moore J E Jr. Flow changes in the aorta associated with the deployment of a AAA stent graft. Med Engr Phys, 2003, 25: 299–307
[13] Liffman K, Lawrence-Brown M, et al. Analytical modeling and numerical simulation of forces in an endoluminal graft. J EndoVascular Therapy, 2001, 8: 358–371
[14] Saloner D. Private communication from Univ of California, San Francisco, 2004
[15] Kim T, Dwyer H A, et al. Analysis of the unsteady flow & forces in an AAA endovascular stent//Safofuka N, ed. Computational Fluid Dynamics. Springer, 2008: 189–194
[16] Womersley J R. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Phys, 1955, 127: 553–563
[17] Dandy D S, Dwyer H A. A sphere in shear flow at finite reynolds numbers: effect of shear on particle lift, drag and heat transfer. J Fluid Mech, 1990, 216: 381–410
[18] Pyret R, Taylor T D. Computational Methods for Fluid Flow. Springer-Verlag, 1983
[19] Shahcheraghi N, Dwyer H A, Cheer A, et al. Unsteady and three-dimensional simulation of the blood flow in the human aortic arch. J Biom Eng, 2002, 124: 378–387
[20] Wigton L B, Yu N J, Young D P. GMRES Acceleration of Computational Fluid Dynamics Codes. AIAA Computational Fluid Dynamics Meeting, Cinn, Ohio, 1985: 67–74
[21] Dwyer H A, Cheer A, Rutaganira T, Shahcheraghi N. Calculation of unsteady flows in curved pipes. J Fluids Eng, 2001, 123: 869–877
[22] Schlichting H. Boundary Layer Theory. Sixth ed. McGraw-Hill Book Company, 1968
[23] Dias N V, et al. Intra-aneurysm sac pressure measurements after endovascular aneurysm repair: Differences between shrinking, unchanged, and expanding aneurysms with and without leaks. J Vascular Surgery, 2004, 39(6): 1229–1235
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