The onset condition of flow separation in diverging tee junctions was investigated numerically. Flow separation and recirculation at the proximal region of a bypass graft can contribute to early phase graft failure in aortocoronary bypass (ACB) surgery. Rounding the inlet edge of the branch reduces the likelihood of flow separation and recirculation. The recirculating zone at the upstream end of the branch is fully eliminated when a threshold value of mass flow rate ratio is reached. The corresponding flow characteristics obtained from diverging tees with a diameter ratio ≤0.2 and a radius of curvature ≤ 0.25 for a Reynolds number ≤ 1817 indicate that an increasing flow rate ratio induces an exponential decrease in the recirculation length. An increase in the diameter ratio and Reynolds number increases both the onset condition of the flow separation and the recirculation length at the upstream end of the branch. However, a decrease in the diameter ratio reduces the onset condition of separation more effectively than a decrease in the radius of curvature at the junction.

References

1.
Chiu
,
J.-J.
, and
Chien
,
S.
,
2011
, “
Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives
,”
Physiol Rev.
,
91
(
1
), pp.
327
387
.
2.
Davies
,
P. F.
,
2009
, “
Hemodynamic Shear Stress and the Endothelium in Cardiovascular Pathophysiology
,”
Nat. Clin. Pract. Cardiovasc. Med.
,
6
(
1
), pp.
16
26
.
3.
Warboys
,
C. M.
,
de Luca
,
A.
,
Amini
,
N.
,
Luong
,
L.
,
Duckles
,
H.
,
Hsiao
,
S.
,
White
,
A.
,
Biswas
,
S.
,
Khamis
,
R.
,
Chong
,
C. K.
,
Cheung
,
W. M.
,
Sherwin
,
S. J.
,
Bennett
,
M. R.
,
Gil
,
J.
,
Mason
,
J. C.
,
Haskard
,
D. O.
, and
Evans
,
P. C.
,
2014
, “
Disturbed Flow Promotes Endothelial Senescence Via a p53-Dependent Pathway
,”
Arterioscler. Thromb. Vasc. Biol.
,
34
(
5
), pp.
985
995
.
4.
Frolova
,
E. G.
,
Pluskota
,
E.
,
Krukovets
,
I.
,
Burke
,
T.
,
Drumm
,
C.
,
Smith
,
J. D.
,
Blech
,
L.
,
Febbraio
,
M.
,
Bornstein
,
P.
,
Plow
,
E. F.
, and
Stenina
,
O. I.
,
2010
, “
Thrombospondin-4 Regulates Vascular Inflammation and Atherogenesis
,”
Circ. Res.
,
107
(
11
), pp.
1313
1325
.
5.
Steucke
,
K. E.
,
Tracy
,
P. V.
,
Hald
,
E. S.
,
Hall
,
J. L.
, and
Alford
,
P. W.
,
2015
, “
Vascular Smooth Muscle Cell Functional Contractility Depends on Extracellular Mechanical Properties
,”
J. Biomech.
,
48
(
12
), pp.
3044
3051
.
6.
Lantz
,
J.
, and
Karlsson
,
M.
,
2012
, “
Large Eddy Simulation of LDL Surface Concentration in a Subject Specific Human Aorta
,”
J. Biomech.
,
45
(
3
), pp.
537
542
.
7.
Hunt
,
B. J.
,
Poston
,
L.
,
Schachter
,
M.
, and
Halliday
,
A.
,
2002
,
An Introduction to Vascular Biology
,
Cambridge University Press
,
New York
, pp.
55
56
.
8.
Dolan
,
J. M.
,
Kolega
,
J.
, and
Meng
,
H.
,
2013
, “
High Wall Shear Stress and Spatial Gradients in Vascular Pathology: A Review
,”
Ann. Biomed Eng.
,
41
(
7
), pp.
1411
1427
.
9.
Hsiai
,
T. K.
,
Cho
,
S. K.
,
Wong
,
P. K.
,
Ing
,
M.
,
Salazar
,
A.
,
Sevanian
,
A.
,
Navab
,
M.
,
Demer
,
L. L.
, and
Ho
,
C. M.
,
2003
, “
Monocyte Recruitment to Endothelial Cells in Response to Oscillatory Shear Stress
,”
FASEB J.
,
17
(
12
), pp.
1648
1657
.
10.
Hwang
,
J.
,
Saha
,
A.
,
Boo
,
Y. C.
,
Sorescu
,
G. P.
,
McNally
,
J. S.
,
Holland
,
S. M.
,
Dikalov
,
S.
,
Giddens
,
D. P.
,
Griendling
,
K. K.
,
Harrison
,
D. G.
, and
Jo
,
H.
,
2003
, “
Oscillatory Shear Stress Stimulates Endothelial Production of O2—From p47phox-Dependent NAD(P)H Oxidases, Leading to Monocyte Adhesion
,”
J. Biol. Chem.
,
278
(
47
), pp.
47291
47298
.
11.
van Thienen
,
J. V.
,
Fledderus
,
J. O.
,
Dekker
,
R. J.
,
Rohlena
,
J.
,
van Ijzendoorn
,
G. A.
,
Kootstra
,
N. A.
,
Pannekoek
,
H.
, and
Horrevoets
,
A. J.
,
2006
, “
Shear Stress Sustains Atheroprotective Endothelial KLF2 Expression More Potently Than Statins Through mRNA Stabilization
,”
Cardiovasc. Res.
,
72
(
2
), pp.
231
240
.
12.
Loufrani
,
L.
, and
Henrion
,
D.
,
2008
, “
Role of the Cytoskeleton in Flow (Shear Stress)-Induced Dilation and Remodeling in Resistance Arteries
,”
Med. Biol. Eng. Comput.
,
46
(
5
), pp.
451
460
.
13.
Jadlowiec
,
C.
, and
Dardik
,
A.
,
2013
, “
Shear Stress and Endothelial Cell Retention in Critical Lower Limb Ischemia
,”
Inflammatory Response in Cardiovascular Surgery
,
E. A.
Gabriel
, and
S. A.
Gabriel
, eds.,
Springer
,
London
, pp.
107
116
.
14.
Hess
,
C. N.
,
Lopes
,
R. D.
,
Gibson
,
C. M.
,
Hager
,
R.
,
Wojdyla
,
D. M.
,
Englum
,
B. R.
,
Mack
,
M. J.
,
Califf
,
R. M.
,
Kouchoukos
,
N. T.
,
Peterson
,
E. D.
, and
Alexander
,
J. H.
,
2014
, “
Saphenous Vein Graft Failure After Coronary Artery Bypass Surgery: Insights From Prevent IV
,”
Circulation
,
130
(
17
), pp.
1445
1451
.
15.
Thielmann
,
M.
,
Massoudy
,
P.
,
Jaeger
,
B. R.
,
Neuhäuser
,
M.
,
Marggraf
,
G.
,
Sack
,
S.
,
Erbel
,
R.
, and
Jakob
,
H.
,
2006
, “
Emergency Re-Revascularization With Percutaneous Coronary Intervention, Reoperation, or Conservative Treatment in Patients With Acute Perioperative Graft Failure Following Coronary Artery Bypass Surgery
,”
Eur. J. Cardiothorac. Surg.
,
30
(
1
), pp.
117
125
.
16.
Canos
,
D. A.
,
Mintz
,
G. S.
,
Rock
,
B. Y.
,
Escolar
,
E.
,
Gevorkian
,
N.
,
Pichard
,
A. D.
,
Satler
,
L. F.
,
Kent
,
K. M.
, and
Weissman
,
N. J.
,
2004
, “
Early Saphenous Vein Graft Failure: A Predictor of Poor Outcomes After Percutaneous Coronary Intervention
,”
J. Am. Coll. Cardiol.
,
43
(
5
), p.
A76
.
17.
Qiao
,
A.
, and
Liu
,
Y.
,
2006
, “
Influence of Graft-Host Diameter Ratio on the Hemodynamics of CABG
,”
Biomed Mater. Eng.
,
16
(
3
), pp.
189
201
.http://content.iospress.com/articles/bio-medical-materials-and-engineering/bme401
18.
Sui
,
Y.
,
Ma
,
B.
,
Chu
,
B.
, and
Qiao
,
A.
,
2009
, “
Optimization of Anastomotic Configuration in CABG Surgery
,”
Commun. Numer. Methods Eng.
,
25
(
11
), pp.
1097
1106
.
19.
Ghista
,
D. N.
, and
Kabinejadian
,
F.
,
2013
, “
Coronary Artery Bypass Grafting Hemodynamics and Anastomosis Design: A Biomedical Engineering Review
,”
Biomed. Eng. OnLine
,
12
(
1
), p.
129
.
20.
Campeau
,
L.
,
Crochet
,
D.
,
Lespérance
,
J.
,
Bourassa
,
M. G.
, and
Grondin
,
C. M.
,
1975
, “
Postoperative Changes in Aortocoronary Saphenous Vein Grafts Revisited: Angiographic Studies at Two Weeks and at One Year in Two Series of Consecutive Patients
,”
Circulation
,
52
(
3
), pp.
369
377
.
21.
Rennels
,
D. C.
, and
Hudson
,
H. M.
,
2012
,
Pipe Flow—A Practical and Comprehensive Guide
,
Wiley-Blackwell
,
Hoboken, NJ
.
22.
Costa
,
N. P.
,
Maia
,
R.
,
Proença
,
M. F.
, and
Pinho
,
F. T.
,
2006
, “
Edge Effects on the Flow Characteristics in a 90 Deg Tee Junction
,”
ASME J. Fluids Eng.
,
128
(
6
), p.
1204
.
23.
Hamilton
,
J. B.
,
1929
, “
Suppression of Pipe Intake Losses by Various Degrees of Rounding
,” University of Washington Engineering Experiment Station, Seattle, WA, Bulletin No. 51.
24.
Bullen
,
P. R.
,
Cheeseman
,
D. J.
, and
Hussain
,
L. A.
,
1988
, “
The Effects of Inlet Sharpness on the Pipe Contraction Pressure Loss Coefficient
,”
Int. J. Heat Fluid Flow
,
9
(
4
), pp.
431
433
.
25.
Tanaka
,
G.
,
Yamaguchi
,
R.
,
Liu
,
H.
, and
Hayase
,
T.
,
2016
, “
Fluid Vibration Induced by High-Shear-Rate Flow in a T-Junction
,”
ASME J. Fluids Eng.
,
138
(
8
), p.
081103
.
26.
Neofytou
,
P.
,
Housiadas
,
C.
,
Tsangaris
,
S. G.
,
Stubos
,
A. K.
, and
Fotiadis
,
D. I.
,
2014
, “
Newtonian and Power-Law Fluid Flow in a T-Junction of Rectangular Ducts
,”
Theor. Comput. Fluid Dyn.
,
28
(
2
), pp.
233
256
.
27.
Tomor
,
A.
, and
Kristóf
,
G.
,
2016
, “
Hydraulic Loss of Finite Length Dividing Junctions
,”
ASME J. Fluids Eng.
,
139
(
3
), p.
031104
.
28.
Sawada
,
R.
,
Kaneko
,
T.
, and
Sano
,
M.
,
2015
, “
Pressure Loss and Fluid Flow Characteristics of Square Duct Flow With T-Junction
,”
Trans. JSME
,
81
(
828
), p.
15-00100
.
29.
Karino
,
T.
,
Kwong
,
H. H.
, and
Goldsmith
,
H. L.
,
1979
, “
Particle Flow Behaviour in Models of Branching Vessels: I. Vortices in 90° T-Junctions
,”
Biorheology
,
16
(
3
), pp.
231
248
.
30.
Vogel
,
G.
,
1928
, “
Investigation of the Loss in Right—Angled Pipe Branches
,”
Hydro Inst. Technol. Hoschule–Munchen
,
1
, pp. 61–64.
31.
Iwanami, S., Suu, T., and Kato, H.,
1969
, “
Study on Flow Characteristics in Right-Angled Pipe Fittings
,”
Bull. Jpn. Soc. Mech. Eng.
,
12
(53), pp. 1041–1050.
32.
Gardel
,
A.
,
1957
, “
Pressure Drops in Flows Through T-Shaped Fittings
,”
Bull. Technique De La Suisse Romande
,
9
, pp.
143
148
.
33.
Ito
,
H.
, and
Imai
,
K.
,
1973
, “
Energy Losses at 90° Pipe Junctions
,”
J. Hydraulics Div.
,
99
(
9
), pp.
1353
1368
.http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0020090
34.
He
,
X.
, and
Ku
,
D. N.
,
1995
, “
Flow in T-Bifurcations: Effect of the Sharpness of the Flow Divider
,”
Biorheology
,
32
(
4
), pp.
447
458
.
35.
Paal
,
G.
,
Pinho
,
F.
, and
Maia
,
R.
,
2006
, “
The Effect of Corner Radius on the Energy Loss in 90° T-Junction Turbulent Flows
,”
The 13th International Conference on Modelling Fluid Flow
(
CMFF
), Budapest, Hungary, Sept. 6–9, pp.
470
477
.https://www.researchgate.net/publication/242157868_THE_EFFECT_OF_CORNER_RADIUS_ON_THE_ENERGY_LOSS_IN_90_T-_JUNCTION_TURBULENT_FLOWS
36.
Gijsen
,
F. J. H.
,
van de Vosse
,
F. N.
, and
Janssen
,
J. D.
,
1999
, “
The Influence of the Non-Newtonian Properties of Blood on the Flow in Large Arteries: Steady Flow in a Carotid Bifurcation Model
,”
J. Biomech.
,
32
(
6
), pp.
601
608
.
37.
Foo
,
K.
,
Myose
,
R.
, and
Hoffmann
,
K. A.
,
2015
, “
Shear-Thinning Properties of Blood in Large Arteries
,”
AIAA
Paper No. 2015-2914.
38.
Johnston
,
B. M.
,
Johnston
,
P. R.
,
Corney
,
S.
, and
Kilpatrick
,
D.
,
2004
, “
Non-Newtonian Blood Flow in Human Right Coronary Arteries: Steady State Simulations
,”
J. Biomech.
,
37
(
5
), pp.
709
720
.
39.
Morales
,
H. G.
,
Larrabide
,
I.
,
Geers
,
A. J.
,
Aguilar
,
M. L.
, and
Frangi
,
A. F.
,
2013
, “
Newtonian and Non-Newtonian Blood Flow in Coiled Cerebral Aneurysms
,”
J. Biomech.
,
46
(
13
), pp.
2158
2164
.
40.
DeRubertis
,
B. G.
,
Alktaifi
,
A.
,
Finn
,
J. P.
,
Farley
,
S.
,
Saleh
,
R. S.
,
Moore
,
W. S.
, and
Lawrence
,
P. F.
,
2011
, “
RR7. Anatomic Assessment of the Aortic Arch: Relationship Between Arch Anatomy and Age
,”
J. Vasc. Surg.
,
53
(
6
), p.
95S
.
41.
Ramchandani
,
M.
, and
Bedeir
,
K.
,
2011
, “
Vascular Connector Devices Increase the Availability of Minimally Invasive Cardiac Surgery to Ischemic Heart Patients
,”
HSR Proc. Intensive Care Cardiovasc. Anesth.
,
3
(
4
), pp.
239
243
.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3563438/
42.
Izutani
,
H.
,
Yoshitatsu
,
M.
,
Kawamoto
,
J.
, and
Katayama
,
K.
,
2005
, “
A Case of Ostial Stenosis With the PAS-Port Proximal Anastomosis System in Off-Pump Coronary Artery Bypass Grafting
,”
Interact Cardiovasc. Thorac. Surg.
,
4
(
4
), pp.
341
343
.
43.
Liepsch
,
D.
,
Moravec
,
S.
,
Rastogi
,
A. K.
, and
Vlachos
,
N. S.
,
1982
, “
Measurement and Calculations of Laminar Flow in a Ninety Degree Bifurcation
,”
J. Biomech.
,
15
(
7
), pp.
473
485
.
44.
Biswas
,
D.
,
Casey
,
D. M.
,
Crowder
,
D. C.
,
Steinman
,
D. A.
,
Yun
,
Y. H.
, and
Loth
,
F.
,
2016
, “
Characterization of Transition to Turbulence for Blood in a Straight Pipe Under Steady Flow Conditions
,”
J. Biomech.
,
138
(
7
), p.
071001
.
45.
Roach
,
M. R.
,
Scott
,
S.
, and
Ferguson
,
G. G.
,
1972
, “
The Hemodynamic Importance of the Geometry of Bifurcations in the Circle of Willis (Glass Model Studies)
,”
Stroke
,
3
(
3
), pp.
255
267
.
46.
Sierra-Espinosa
,
F. Z.
,
Bates
,
C. J.
, and
O’Doherty
,
T.
,
2000
, “
Turbulent Flow in a 90° Pipe Junction. Part 1: Decay of Fluctuation Upstream of the Flow Bifurcation
,”
Comput. Fluids
,
29
(
2
), pp.
197
213
.
47.
Sierra-Espinosa
,
F. Z.
,
Bates
,
C. J.
, and
O’Doherty
,
T.
,
2000
, “
Turbulent Flow in a 90° Pipe Junction. Part 2: Reverse Flow at the Branch Exit
,”
Comput. Fluids
,
29
(
2
), pp.
215
233
.
48.
Khandelwal
,
V.
,
Dhiman
,
A.
, and
Baranyi
,
L.
,
2015
, “
Laminar Flow of Non-Newtonian Shear-Thinning Fluids in a T-Channel
,”
Comput. Fluids
,
108
, pp.
79
91
.
You do not currently have access to this content.