This paper proposes using topology optimization to design fixed-geometry fluid diodes that allow easy passage of fluid flowing in one direction while inhibiting flow in the reverse direction. Fixed-geometry diodes do not use movable mechanical parts or deformations, but rather utilize inertial forces of the fluid to achieve this flow behavior. Diode performance is measured by diodicity, defined as the ratio of pressure drop of reverse flow and forward flow, or equivalently the ratio of dissipation of reverse and forward flow. Diodicity can then be maximized by minimizing forward dissipation while maximizing reverse dissipation. While significant research has been conducted in topology optimization of fluids for minimizing dissipation, maximizing dissipation introduces challenges in the form of small, mesh dependent flow channels and that artificial flow in solid region becomes (numerically) desirable. These challenges are circumvented herein using projection methods for controlling the minimum length scale of channels and by introducing an additional penalty term on flow through intermediate porosities. Several solutions are presented, one of which is fabricated by 3D printing and experimentally tested to demonstrate the diodelike behavior.

References

References
1.
Sochol
,
R. D.
,
Glick
,
C. C.
,
Lee
,
K. Y.
,
Brubaker
,
T.
,
Lu
,
A.
,
Wah
,
M.
,
Gao
,
S.
,
Hicks
,
E.
,
Wolf
,
K. T.
,
Iwai
,
K.
,
Lee
,
L. P.
, and
Lin
,
L.
,
2013
, “
Single-Layer “domino” Diodes Via Optofluidic Lithography for Ultra-Low Reynolds Number Applications
,”
2013 IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS)
, IEEE, pp.
153
156
.
2.
Tesla
,
N.
,
1920
, Valvular Conduit, Feb. 3, U.S. Patent No. 1,329,559.
3.
Thompson
,
S.
,
Ma
,
H.
, and
Wilson
,
C.
,
2011
, “
Investigation of a Flat-Plate Oscillating Heat Pipe With Tesla-Type Check Valves
,”
Exp. Therm. Fluid Sci.
,
35
(
7
), pp.
1265
1273
.10.1016/j.expthermflusci.2011.04.014
4.
Forster
,
F. K.
,
Bardell
,
R. L.
,
Afromowitz
,
M. A.
,
Sharma
,
N. R.
, and
Blanchard
,
A.
,
1995
, “
Design, Fabrication and Testing of Fixed-Valve Micro-Pumps
,” The
ASME
Fluid Engineering Division, Vol.
234
, pp.
39
44
.http://faculty.washington.edu/forster/forsterpubs/forster95.pdf
5.
Morganti
,
E.
, and
Pignatel
,
G.
,
2005
, “
Microfluidics for the Treatment of the Hydrocephalus
,”
Proceedings of International Conference on Sensing Technology
, Palmerston North.
6.
Stemme
,
E.
, and
Stemme
,
G.
,
1993
, “
A Valveless Diffuser/Nozzle-Based Fluid Pump
,”
Sens. Actuators, A
,
39
(
2
), pp.
159
167
.10.1016/0924-4247(93)80213-Z
7.
Andersson
,
H.
,
van der Wijngaart
,
W.
,
Nilsson
,
P.
,
Enoksson
,
P.
, and
Stemme
,
G.
,
2001
, “
A Valve-Less Diffuser Micropump for Microfluidic Analytical Systems
,”
Sens. Actuators, B
,
72
(
3
), pp.
259
265
.10.1016/S0925-4005(00)00644-4
8.
Olsson
,
A.
,
Enoksson
,
P.
,
Stemme
,
G.
, and
Stemme
,
E.
,
1997
, “
Micromachined Flat-Walled Valveless Diffuser Pumps
,”
J. Microelectromech. Syst.
,
6
(
2
), pp.
161
166
.10.1109/84.585794
9.
Bardell
,
R. L.
,
2000
, “
The Diodicity Mechanism of Tesla-Type No-Moving-Parts Valves
,” Ph.D. thesis, University of Washington, Seattle.
10.
Gamboa
,
A. R.
,
Morris
,
C. J.
, and
Forster
,
F. K.
,
2005
, “
Improvements in Fixed-Valve Micropump Performance Through Shape Optimization of Valves
,”
ASME J. Fluids Eng.
,
127
(
2
), pp.
339
347
.10.1115/1.1891151
11.
Clabuk
,
H.
, and
Modi
,
V.
,
1992
, “
Optimum Plane Diffusers in Laminar Flow
,”
J. Fluid Mech.
,
237
, pp.
373
393
.10.1017/S0022112092003458
12.
Madsen
,
J.
,
Olhoff
,
N.
, and
Condra
,
T.
,
2000
, “
Optimization of Straight, Two-Dimensional Diffusers by Wall Contouring and Guide Vane Insertion
,”
Proceedings of the 3rd World Congress of Structural and Multidisciplinary Optimization, WCSMO-3
, May 17–21, 1999, State University of New York at Buffalo, Buffalo.
13.
Liu
,
Z.
,
Deng
,
Y.
,
Lin
,
S.
, and
Xuan
,
M.
,
2012
, “
Optimization of Micro Venturi Diode in Steady Flow at Low Reynolds Number
,”
Eng. Optim.
,
44
(
11
), pp.
1389
1404
.10.1080/0305215X.2011.652100
14.
Borrvall
,
T.
, and
Petersson
,
J.
,
2003
, “
Topology Optimization of Fluids in Stokes Flow
,”
Int. J. Numer. Methods Fluids
,
41
(
1
), pp.
77
107
.10.1002/fld.426
15.
Guest
,
J. K.
, and
Prévost
,
J. H.
,
2006
, “
Topology Optimization of Creeping Fluid Flows Using a Darcy–Stokes Finite Element
,”
Int. J. Numer. Methods Eng.
,
66
(
3
), pp.
461
484
.10.1002/nme.1560
16.
Wiker
,
N.
,
Klarbring
,
A.
, and
Borrvall
,
T.
,
2007
, “
Topology Optimization of Regions of Darcy and Stokes Flow
,”
Int. J. Numer. Methods Eng.
,
69
(
7
), pp.
1374
1404
.10.1002/nme.1811
17.
Challis
,
V. J.
, and
Guest
,
J. K.
,
2009
, “
Level Set Topology Optimization of Fluids in Stokes Flow
,”
Int. J. Numer. Methods Eng.
,
79
(
10
), pp.
1284
1308
.10.1002/nme.2616
18.
Evgrafov
,
A.
,
2006
, “
Topology Optimization of Slightly Compressible Fluids
,”
ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech.
,
86
(
1
), pp.
46
62
.10.1002/zamm.200410223
19.
Gersborg-Hansen
,
A.
,
Sigmund
,
O.
, and
Haber
,
R. B.
,
2005
, “
Topology Optimization of Channel Flow Problems
,”
Struct. Multidiscip. Optim.
,
30
(
3
), pp.
181
192
.10.1007/s00158-004-0508-7
20.
Olesen
,
L. H.
,
Okkels
,
F.
, and
Bruus
,
H.
,
2006
, “
A High-Level Programming-Language Implementation of Topology Optimization Applied to Steady-State Navier–Stokes Flow
,”
Int. J. Numer. Methods Eng.
,
65
(
7
), pp.
975
1001
.10.1002/nme.1468
21.
Duan
,
X.-B.
,
Ma
,
Y.-C.
, and
Zhang
,
R.
,
2008
, “
Shape-Topology Optimization for Navier–Stokes Problem Using Variational Level Set Method
,”
J. Comput. Appl. Math.
,
222
(
2
), pp.
487
499
.10.1016/j.cam.2007.11.016
22.
Zhou
,
S.
, and
Li
,
Q.
,
2008
, “
A Variational Level Set Method for the Topology Optimization of Steady-State Navier–Stokes Flow
,”
J. Comput. Phys.
,
227
(
24
), pp.
10178
10195
.10.1016/j.jcp.2008.08.022
23.
Kreissl
,
S.
, and
Maute
,
K.
,
2012
, “
Levelset Based Fluid Topology Optimization Using the Extended Finite Element Method
,”
Struct. Multidiscip. Optim.
,
46
(
3
), pp.
311
326
.10.1007/s00158-012-0782-8
24.
Pingen
,
G.
,
2008
, “
Optimal Design for Fluidic Systems: Topology and Shape Optimization With the Lattice Boltzmann Method
,” Ph.D. thesis, University of Colorado, Boulder.
25.
Pingen
,
G.
,
Evgrafov
,
A.
, and
Maute
,
K.
,
2008
, “
A Parallel Schur Complement Solver for the Solution of the Adjoint Steady-State Lattice Boltzmann Equations: Application to Design Optimisation
,”
Int. J. Comput. Fluid Dyn.
,
22
(
7
), pp.
457
464
.10.1080/10618560802238267
26.
Elman
,
H.
,
Silvester
,
D.
, and
Wathen
,
A.
,
2014
,
Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics
,
Oxford University
.
27.
Kreissl
,
S.
, and
Maute
,
K.
,
2012
, “
Levelset Based Fluid Topology Optimization Using the Extended Finite Element Method
,”
Struct. Multidiscip. Optim.
,
46
(
3
), pp.
311
326
.10.1007/s00158-012-0782-8
28.
Sigmund
,
O.
, and
Petersson
,
J.
,
1998
, “
Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima
,”
Struct. Optim.
,
16
(
1
), pp.
68
75
.10.1007/BF01214002
29.
Guest
,
J. K.
,
Prévost
,
J.
, and
Belytschko
,
T.
,
2004
, “
Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions
,”
Int. J. Numer. Methods Eng.
,
61
(
2
), pp.
238
254
.10.1002/nme.1064
30.
Sigmund
,
O.
,
2007
, “
Morphology-Based Black and White Filters for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
33
(
4–5
), pp.
401
424
.10.1007/s00158-006-0087-x
31.
Guest
,
J. K.
,
2009
, “
Topology Optimization With Multiple Phase Projection
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
1
), pp.
123
135
.10.1016/j.cma.2009.09.023
32.
Sigmund
,
O.
,
1997
, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
J. Struct. Mech.
,
25
(
4
), pp.
493
524
.
33.
Guest
,
J. K.
,
Asadpoure
,
A.
, and
Ha
,
S.-H.
,
2011
, “
Eliminating Beta-Continuation From Heaviside Projection and Density Filter Algorithms
,”
Struct. Multidiscip. Optim.
,
44
, pp.
443
453
.10.1007/s00158-011-0676-1
34.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
, pp.
359
373
.10.1002/nme.1620240207
35.
Sigmund
,
O.
,
2009
, “
Manufacturing Tolerant Topology Optimization
,”
Acta Mech. Sin.
,
25
(
2
), pp.
227
239
.10.1007/s10409-009-0240-z
36.
Guest
,
J. K.
, and
Igusa
,
T.
,
2008
, “
Structural Optimization Under Uncertain Loads and Nodal Locations
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
1
), pp.
116
124
.10.1016/j.cma.2008.04.009
37.
Asadpoure
,
A.
,
Tootkaboni
,
M.
, and
Guest
,
J. K.
,
2011
, “
Robust Topology Optimization of Structures With Uncertainties in Stiffness–Application to Truss Structures
,”
Comput. Struct.
,
89
(
11
), pp.
1131
1141
.10.1016/j.compstruc.2010.11.004
38.
Schevenels
,
M.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2011
, “
Robust Topology Optimization Accounting for Spatially Varying Manufacturing Errors
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
49
), pp.
3613
3627
.10.1016/j.cma.2011.08.006
39.
Wang
,
F.
,
Jensen
,
J. S.
, and
Sigmund
,
O.
,
2011
, “
Robust Topology Optimization of Photonic Crystal Waveguides With Tailored Dispersion Properties
,”
J. Opt. Soc. Am. B
,
28
(
3
), pp.
387
397
.10.1364/JOSAB.28.000387
You do not currently have access to this content.