Conference PaperPDF Available

# Transitional and Turbulent Flow Modeling in a Tesla Valve

Authors:
• Kohler Co.

## Abstract and Figures

A Tesla valve is a fluidic dioide that may be used in a variety of mini/micro channel applications for passive flow rectification and/or control. The valve’s effectiveness is quantified by the diodicity, which is primarily governed by the incoming flow speed, its design and direction-dependent minor losses throughout its structure during forward and reverse flows. It has been previously shown that the Reynolds number at the valve inlet is not representative of the entire flow regime throughout the Tesla structure. Therefore, pure-laminar solving methods are not necessarily accurate. Local flow instabilities exist and exhibit both transitional and turbulent characteristics. Therefore, the current investigation seeks to identify a suitable RANS-based flow modeling approach to predict Tesla valve diodicity via three-dimensional (3D) computational fluid dynamics (CFD) for inlet Reynolds numbers up to Re = 2,000. Using ANSYS FLUENT (v. 14), a variety of models were employed, including: the Realizable k-ε, k-kL-ω and SST k-ω models. All numerical simulations were validated against available experimental data obtained from an identically-shaped Tesla valve structure. It was found that the k-ε model drastically under-predicts experimental data for the entire range of Reynolds numbers investigated and cannot accurately model the Tesla valve flow. The k-kL-ω and SST k-ω models approach the experimentally-measured diodicity better than regular 2D CFD. The k-kL-ω demonstrates exceptional agreement with experimental data for Reynolds numbers up to approximately 1,500. However, both the k-kL-ω and k-ω SST models over-predict experimental data for Re = 2,000.
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Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposition
IMECE2013
November 15-21, 2013, San Diego, California, USA
IMECE2013-65526
TRANSITIONAL AND TURBULENT FLOW MODELING IN A TESLA VALVE
Scott M. Thompson, Tausif Jamal, Basil J. Paudel, D. Keith Walters
Department of Mechanical Engineering
Mississippi State University
Mississippi State, Mississippi U.S.A.
ABSTRACT
A Tesla valve is a fluidic dioide that may be used in a
variety of mini/micro channel applications for passive flow
rectification and/or control. The valve’s effectiveness is
quantified by the diodicity, which is primarily governed by the
incoming flow speed, its design and direction-dependent minor
losses throughout its structure during forward and reverse
flows. It has been previously shown that the Reynolds number
at the valve inlet is not representative of the entire flow regime
throughout the Tesla structure. Therefore, pure-laminar solving
methods are not necessarily accurate. Local flow instabilities
exist and exhibit both transitional and turbulent characteristics.
Therefore, the current investigation seeks to identify a suitable
RANS-based flow modeling approach to predict Tesla valve
diodicity via three-dimensional (3D) computational fluid
dynamics (CFD) for inlet Reynolds numbers up to Re = 2,000.
Using ANSYS FLUENT (v. 14), a variety of models were
employed, including: the Realizable k-ε, k-kL-ω and SST k-ω
models. All numerical simulations were validated against
available experimental data obtained from an identically-
shaped Tesla valve structure. It was found that the k-ε model
drastically under-predicts experimental data for the entire range
of Reynolds numbers investigated and cannot accurately model
the Tesla valve flow. The k-kL-ω and SST k-ω models
approach the experimentally-measured diodicity better than
regular 2D CFD. The k-kL-ω demonstrates exceptional
agreement with experimental data for Reynolds numbers up to
approximately 1,500. However, both the k-kL-ω and k-ω SST
models over-predict experimental data for Re = 2,000.
NOMENCLATURE
D diameter, m
Di diodicity
P static pressure, Pa
Re Reynolds number
u mean velocity magnitude, m/s
volumetric flow rate, m3/s
Greek symbols
μ dynamic viscosity, Pa-s
ρ density, kg/m3
Subscripts
f forward
H hydraulic
i Tesla valve inlet
r reverse
INTRODUCTION
The Tesla valve [1] is a ‘no-moving-parts’ check valve
(NMPV) which is currently used in a variety of micro/mini
fluidic applications [2]. It functions as a fluidic diode by
passively promoting one flow direction over another via its
unique design. As shown in Fig. 1, when fluid (typically in
liquid phase) flows in the ‘reverse’ direction, minor pressure
losses retard fluid motion primarily by: sudden expansion, flow
splitting and mini-jet impingement. In the ‘forward’ flow
direction, the total minor pressure loss is smaller since the flow
is less prone to splitting as a result of the design features.
Fig. 1. A miniature Tesla valve with reverse and forward
flow directions.
The Tesla valve diodicity, Di, is the ratio of pressure
differences across the valve in the reverse, , and forward
direction, , for a given flow rate, i.e.:
 

where a diodicity greater than one indicates flow promotion in
the forward direction, with higher values indicating a more
effective Tesla valve.
Forster et al. [2] first proposed utilizing the Tesla valve for
micro-fluidic applications as a no-moving-parts pump. An
experimental investigation was undertaken to characterize an
initial prototype, which was etched onto silicon substrate and
had a width of 0.1 mm. The design of this particular Tesla
valve, referred to as the T45-R, is depicted in Fig. 1.
Experimental results demonstrated that the T45-R Tesla valve’s
diodicity increased almost linearly with flow rate. A diodicity
of 1.14 was achieved for a flow rate of approximately 500
μL/min. The entire investigation was for low Reynolds number
(Re < 300).
Other works have focused on the optimal design of the
Tesla valve for steady-state, low Reynolds number flow. Using
two-dimensional (2D) CFD via ANSYS CFX v4.2, Bardell
investigated the optimal design of a Tesla valve [3].
Experimental investigation of the Tesla valve diodicity was also
conducted. The viscous flow and jet impingement at the Tesla
valve outlet were visualized and quantified in detail. Using 2D
CFD via ANSYS FLOTRAN 6.0, Truong and Nguyen studied
the optimal Tesla valve design for Reynolds numbers up to
1,000 [4]. The design of the T45-R valve, first introduced by
Forster et al. [2], was used as a reference point. Their 2D CFD
simulations over-predicted diodicity relative to the
experimental data of Forster et al.
Zhang et al. investigated the effect of Tesla valve aspect
ratio on diodicity using 3D CFD [5]. The T45-R valve was
used as a reference point and numerical simulations were
performed using ANSYS FLUENT® 6.2. The Reynolds
number was varied to values as high as 2,000. The details of
the numerical investigation are not fully provided (i.e. laminar
or turbulent models). Their results indicate that a Tesla valve
with square cross-section provides for optimal diodicity for
relatively low Reynolds number (ReD < 500). A greater-than-
unity, rectangular channel aspect ratio is advantageous for
higher Reynolds numbers.
Gamboa et al. [6] used 2D CFD to optimize the Tesla valve
geometry and conducted experiments to compare numerically-
predicted diodicities with experimental results. ANSYS
FLOTRAN v. 6.1 was used to calculate the velocity and
pressure difference across the Tesla valve and a subroutine was
utilized for automated, dimensionless optimization of the Tesla
valve shape. Approximately 7,000 10,000 total elements
were used for the Tesla valve and laminar flow was assumed.
The Reynolds number was varied up to 2,000. An optimized
valve shape was shown to possess features different from the
T45-R valve. This optimized valvehere dubbed the GMF
(Gamboa, Morris and Forster) Tesla valvealong with the 2D
domain used for the numerical simulation, is shown in Fig. 2.
The GMF Tesla valve was found to yield a 25% higher
diodicity, on average, relative to the T45-R valve.
Fig. 2. Two-dimensional domain for the numerical
simulation conducted on a GMF Tesla valve [6].
As a means to corroborate numerical results and determine
the diodicity of a single GMF Tesla valve, a separate
experimental investigation was conducted [6]. Two GMF Tesla
valves were etched onto plastic along with a cylindrical plenum
(or pumping chamber), with a diameter of 10 mm and depth of
0.75 mm. The plenum behaved as a pump via an attached
piezoelectric actuator on its non-wetted side and was located
between the valves. Each Tesla valve had a depth similar to the
plenum and possessed a width of 0.3 mm. This valve/plenum
system is shown in Fig. 3. Its purpose was for electronics
cooling at the chip-scale. Note the presence of the two
cylindrical (inlet or outlet) ports beside each Tesla valve. These
ports had a diameter of 2.5 mm and allowed for the entrance or
exit of the working fluid (water). Fluid was inputted to the
system via a syringe pump and the opposite port was open to
atmosphere [6]. Pressure drop was measured via a pressure
transducer and/or a water column. The pressure drop across a
single Tesla valve was approximated as the total pressure drop
of the valve/plenum system (from inlet port to outlet port)
divided by two.
Fig. 3. Schematic of Tesla valve/plenum prototype used
for experimental measurement [6].
It was found that the 2D CFD results overestimated the
experimentally-measured diodicity across a single Tesla valve
[6]. For ReD = 2000, the relative percent error was
approximately 20 %. The disagreement between CFD and
experimental results was attributed to the loss-mechanisms in
the Tesla valve being primarily due to out-of-plane vorticity,
which 2D modeling is incapable of capturing.
Using 3D CFD and ANSYS FLUENT® 14, Thompson et
al. [7] numerically investigated the GMF valve aligned in-series
to create a Multi-Staged Tesla Valve (MSTV). The number of
Tesla valves, valve-to-valve distance and Reynolds number
were varied to determine their effect on overall MSTV
diodicity. For low Reynolds number (i.e. Re < 300) it was
found that utilizing Tesla valves in-series provides for a
significant increase in diodicity. Also, the MSTV diodicity
increases with more Tesla valves and when the valve-to-valve
distance is minimized. It was demonstrated that the Reynolds
number at the inlet of the Tesla valve, ReD,i, is not indicative of
the flow regime throughout the entire valve, i.e. the condition
ReD,i < 2300 is not an accurate criterion for complete laminar
conditions throughout the valve. For a single GMF valve, it
was found that transitional flow behavior existed for ReD,I ~
500. In the same study, it was shown that 3D CFD more
accurately matches the experimental results of Forster et al. [2]
than the 2D CFD results presented by Truong and Nguyen [4].
Unlike previous Tesla valve CFD investigations, the
current study employs turbulence models with 3D CFD to
determine if improved accuracy in numerically-predicted Tesla
valve diodicty can be obtained. Currently, experimental
measurements of Tesla valve diodicity for relatively high
Reynolds number (Re > 500) are limited to the work of
Gamboa et al. [6]. Hence, all effort was made to replicate the
experimental setup and procedure for accurate numerical
simulation. A well-resolved meshing scheme was employed
and parallel supercomputing was utilized. This study also
provides an initial evaluation of the strengths and weaknesses
of various turbulence models in their application for predicting
high-speed flow through and across a Tesla valve. The
Realizable k-ε, k-kL-ω and Shear Stress Transport (SST) k-ω
models were employed and compared to the available 2D,
laminar CFD results and experimental data.
PROBLEM SETUP
Using 3D CFD, the effect of Reynolds number on the diodicity
of a GMF Tesla valve [6] was investigated. The Reynolds
number at the Tesla valve inlet, defined by:
 

was varied between 500, 1000, 1500 and 2000. The
experimental setup (including flow conditions and exact
prototype dimensions), as shown in Fig. 3, was replicated for
the current numerical simulations. An isometric view of the
valve/plenum domain is shown in Fig. 4. Note that the lengths
of the inlet/outlet ports were extended to allow for flow
development prior to Tesla valve entrance. Similar to the
experimental procedure of Gamboa et al. [6], the diodicity for a
single Tesla valve was found by first determining the pressure
difference across the valve-plenum system and then dividing it
by two for the forward and reverse flow directions. Note that
for the inlet/outlet ports, the flow is normal into (or out of) the
page. Forward flow occurs from left to right, with the left port
acting as an inlet and right port acting as an outlet.
Fig. 4 Numerical domain consisting of center plenum, two
GMF Tesla valves and extended ports.
The geometry shown in Fig. 4 was created using ANSYS
GAMBIT® v2.4. A multi-block structured grid was created
using a first cell height such that the wall y+ values were close
to 1. A pressure based finite volume double precision 3-D
commercial flow solver (ANSYS FLUENT® v14.0) was used
for the simulations.
Solutions were obtained for single-phase, incompressible
turbulent flow with constant fluid properties, governed by the
Reynolds-averaged Navier-Stokes (RANS) equations:

 
 





 
where and are the Reynolds-averaged velocity and
pressure, and
is the kinematic Reynolds stress tensor.
Initially, test cases were run using a steady-state solver.
However, converged results could not be obtained due to flow
instabilities, so all simulations were run using the unsteady
solver. Results presented here are from the unsteady
simulations. A second-order, three-point backward difference
scheme was used for discretization of the unsteady term. Global
time stepping was used with a time-step size chosen such that
the maximum Courant-Friedrichs-Lewy (CFL) number in the
domain was approximately equal to one.
Pressure and velocity were coupled with the SIMPLE
algorithm [8]. All convective terms were discretized using a
second-order upwind (linear reconstruction) scheme with slope
limiting [9]. All spatial gradients were computed using a least
square cell-based method. A cell-based collocated variable
arrangement was used with momentum weighted interpolation
for computation of the pressure and mass flux at cell faces [10].
All diffusion terms were discretized using second-order central
differencing. Convergence at each time step was determined
based on a reduction of residuals by at least three orders of
magnitude. To achieve this the simulations used 20 solution
iterations per time step.
Velocity components based on the Reynolds number were
specified at the inlet port to match the experiments. It is
important to note that the hydraulic diameter of the Tesla valve
inlet was used and not the diameter of the port. Atmospheric
pressure (pressure outlet boundary condition) was specified at
the outlet port. The no slip boundary condition was specified at
all other walls.
Three different turbulence models used were used to close
the RANS equations: Realizable k-ε realizable model [11],
Menter’s Shear Stress Transport (SST) model [12], and Walters
and Cokljat’s three-equation transition-sensitive model (k-kL-
ω) [13]. The k-kL-ω model is based on the standard k-ω
framework and solves an extra laminar kinetic energy transport
equation, which represents the low frequency velocity
fluctuations in the pre-transitional boundary layer. A turbulence
intensity of 2% and turbulent-to-laminar viscosity ratio of 10
was specified at the inlet and the values of k (Turbulent Kinetic
Energy), (Turbulent Dissipation Rate) and/or ω (Specific
Dissipation Rate) were calculated using the dimensionless inlet
conditions.
To investigate solution sensitivity to mesh size, the
diodicity was found at ReD,i = 3,000 for all three models
investigated for three different grids at approximately: 2.0
million, 3.3 million or 5.6 million cells. The results of this
mesh-independence study are provided in Fig. 5. Based on
these results, a grid consisting of 3.3 million cells was utilized
for all simulations.
Fig. 5 Diodicity vs. number of cells for various CFD models
utilized at ReD,I = 3,000.
RESULTS & DISCUSSION
For the results in this section, quantitative values including
diodicity are computed based on the time-averaged flowfield,
while velocity and total pressure contours are shown based on
the instantaneous flowfield. The predicted diodicity results for
the various simulations, along with the approximate
experimental and 2D CFD data from Gamboa et al. [6], are
shown in Fig. 6.
Fig. 6. Diodicity vs. inlet Reynolds number for various CFD
solvers utilized.
It may be seen from Fig. 6 that all models predict a
distinctively different diodicity for any given Reynolds number.
All models also predict a diodicity that increases with Reynolds
number. Especially for the high Reynolds number range (i.e.
ReD,i > 1500), most models over-predict the experimental data.
However, with the exception of the k-ε model, the employed
turbulence models provide for a significant improvement in
matching the experimentally measured diodicities compared
with the previously documented 2-D simulatons. The k-ε
model, unlike all other models, under-predicts the
experimentally-measured diodicity for all Reynolds numbers.
The k-kL-ω transition model appears to be the most accurate,
especially for ReD,i < 1500. The SST k-ω model, relative to the
k-kL-ω model, predicts higher diodicities and has a similar
growth trend. At ReD,i = 500, in which the flow through the
Tesla valve exhibits transitional characteristics, the SST k-ω
and k-kL-ω models provide identical results.
The percent relative error of each model (relative to
experimental data) is shown for all investigated Reynolds
numbers in Table 1. The discrepancy between the diodicities
predicted via 3D turbulent solvers and the experimental data
can be explained by either instrumental error or real-world
losses which are not being simulated via CFD.
0
0.5
1
1.5
2
2.5
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Di
Number of Cells (in Millions)
k-ε
SST k-ω
k-kL-ω
1
1.2
1.4
1.6
1.8
2
500 1000 1500 2000
Di
Re
Experimental [6]
2D CFD (Laminar) [6]
k-ε
SST k-ω
k-kL-ω
Table 1. Percent error of each model’s predicted diodicity
relative to available experimental
Percent Relative Error
Re
2D CFD [6]
k-ε
SST k-ω
k-kL-ω
500
7%
19%
2%
0%
1000
11%
18%
7%
0%
1500
17%
14%
14%
6%
2000
17%
12%
23%
14%
Figures 7 - 9 show the contours of the instantaneous
velocity magnitude through the Tesla valve/plenum system for
ReD,i = 1000 in the forward direction and Figs. 10-12 show
contours for the reverse direction. The subtle differences in the
various models in predicted fluid motion through the Tesla
valves and into the plenum can easily be visualized. The
diodicity mechanism is very apparent in Figs. 10-12 in which
high Reynolds number jet impingement exists at the Tesla valve
outlet.
Fig. 7. Contours of velocity magnitude (m/s) for forward
flow direction for k-ε model (ReD,i = 1,000).
Fig. 8. Contours of velocity magnitude (m/s) for forward
flow direction for SST k-ω model (ReD,i = 1,000).
Fig. 9. Contours of velocity magnitude (m/s) for forward
flow direction for k-kL-ω model (ReD,i = 1,000)
Fig. 10. Contours of velocity magnitude (m/s) for reverse
flow direction for k-ε model (ReD,i = 1,000).
Fig. 11. Contours of velocity magnitude (m/s) for reverse
flow direction for SST k-ω model (ReD,i = 1,000).
Fig. 12. Contours of velocity magnitude (m/s) for reverse
flow direction for k-kL-ω model (ReD,i = 1,000).
From the velocity contours, it may be seen that relatively
high speeds are realized for waterup to 2.5 m/s (for
ReD,i=1,000). Maximum speeds are higher for reverse flow
direction due to flow development, specifically jetting that
occurs in the separation regions. In general, all models predict
similar maximum velocity magnitudes in the forward direction;
however, the k-ε model provides a notably different maximum
velocity in the reverse flow relative to other turbulent models.
For the visualization of the velocity magnitude, it is apparent
that the k-kL-ω model demonstrates more large scale
unsteadiness in the fluid jet in the plenum structure. Nearly
stagnant fluid is observed in the plenum and ports.
Figures 13 - 15 provide the contours of the total pressure
through the Tesla valve for ReD,i = 1000 in the forward direction
and Figs. 16 - 18 provide the reverse direction. The subtle
differences in the various models can easily be visualized with
respect to pressure.
Fig. 13. Contours of total pressure (Pa) for forward flow
direction for k-ε model (ReD,i = 1,000).
Fig. 14. Contours of total pressure (Pa) for forward flow
direction for SST k-ω model (ReD,i = 1,000).
Fig. 15. Contours of total pressure (Pa) for forward flow
direction for k-kL-ω model (ReD,i = 1,000)
Fig. 16. Contours of total pressure (Pa) for reverse flow
direction for k-ε model (ReD,i = 1,000).
Fig. 17. Contours of total pressure (Pa) for reverse flow
direction for SST k-ω model (ReD,i = 1,000).
Fig. 18. Contours of total pressure (Pa) for reverse flow
direction for k-kL-ω model (ReD,i = 1,000).
From Figs. 16-18, it may be seen that the reverse flow
pressure drop is higher than the forward flow pressure drop for
all models. This illustrates the functionality of the Tesla valves
in providing the check-valve effect. Negative pressure exists
in the exit port for either forward or reverse flow. The minor
pressure losses associated with the flow-splitting, flow-
merging, sudden-expansion and sudden-contraction are
apparent in the Tesla valve vicinity.
CONCLUSIONS
Using three-dimensional (3D) CFD, the diodicity across a
Tesla valve for high Reynolds number was estimated and
compared with available experimental data. Three
transitional/turbulent models in ANSYS FLUENT v. 14 were
utilized and compared, including the: k-ε model, k-kL-ω model,
and SST k-ω model. The main conclusions are as follows:
1) The Reynolds number, evaluated using the Tesla valve
inlet hydraulic diameter, is not the best criterion for
estimating the flow regime. Transitional/turbulent
flow characteristics were observed for ReD,i = 1,000.
2) For ReD > 500, 3D CFD with turbulence modeling via
the k-kL-ω model or SST k-ω model provides more
accurate fluid simulation in a Tesla valve relative to
standard (laminar) 2D CFD.
3) For Reynolds numbers up to 1,500, the k-kL-ω model
performs the best providing only a 6% maximum
percent relative error with available experimental data.
For Reynolds number up to 1,000, the model is
superior, with 0% percent relative error.
4) Both the k-kL-ω model and SST k-ω model over-
estimated the available experimental data for ReD =
2,000.
5) The k-ε model drastically under-predicted the Tesla
valve diodicity for all Reynolds numbers investigated.
In summary, the 3D CFD with turbulence modeling can
accurately model the fluid mechanics in a Tesla valve for
relatively high Reynolds numbers. Based on the available
experimental data, it is recommended that the k-kL-ω model be
utilized for flow simulation in a Tesla valve up to ReD,i 1,500.
Discrepancy between the experimental and numerical data at
ReD,I = 2,000 may be attributed to real-world pressure
losses/effects or experimental nuances not being modeled via
the CFD.
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... The conduit, according to Tesla's claim, can function as a uidic diode. It has inspired many inventions and studies of channels with asymmetric geometry to be used as ow control devices [1,4,5,10,38,40,45,54,55,59,60,67,97,114,116,124,128,140,168,169,171,183]. They fall under a class of "Tesla-type" channels. ...
... For computing Reynolds numbers for pipe ows, it is customary to set as the average ow speed and to use the diameter (or a corresponding dimension for non-circular conduits) as the length scale. Saving a deeper discussion of these quantities for Section VII, the parameters in our experiments yield Re = / ∼ 10 2 − 10 4 , as reported on the upper axis of Fig. 2.3 10,124,169,183]. For low Re, ow reversibility has been con rmed by experimental visualization [158], and future work should verify the symmetric resistance expected in this regime. ...
... The case of steady pressure/ ow-rate considered in previous studies on Tesla-like channels provides a point of comparison to our results [4, 10,38,54,55,59,100,114,124,168,169,171,183]. Experiments and simulations have reported weaker diodicity for corresponding conditions [10,55,56,59,88,100,148], e.g. ...
Preprint
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network topology, connectivity, internal boundaries and other geometrical aspects affect the global flow state is a challenging problem that depends on complex fluid properties characterized by different length and time scales. The study of flow in micro-scale networks focuses on low Reynolds numbers where small volumes of fluids move at slow speeds. The flow physics at these scales is governed by the Stokes equation, which is linear. This linearity property allows for relatively simple theoretical and computational solutions that greatly aid in the understanding, modeling and designing of micro-scale networks. At larger scales and faster flow rates, macrofluidic networks are also important but the flow physics is quite different. The underlying Navier-Stokes equation is nonlinear, theoretical results are few, simulations are challenging, and the mapping between geometry and desired flow objectives are all much more complex. The phenomenology for such high-Reynolds-number or inertially-dominated flows is well documented and well-studied: Flows are retarded in thin boundary layers near solid surfaces; such flows are sensitive to geometry and tend to separate from surfaces; and vortices, wakes, jets and unsteadiness abound. The counter-intuitive nature of inertial flows is exemplified by the breakdown of reversibility. This dissertation explores two general ways of how rectified flows emerge in macrofluidic networks as a consequence of irreversibility and unsteady effects: When branches or channels of a network have asymmetric internal geometry and the second when a network contains loops.
... The simplicity of the operation of this valve makes it applicable in various industries at both macro and microscales. It has been used as micropumps in micro-electromechanical systems (MEMS) devices [3], electronics cooling at the chip-scale [4], flow control device in oil recoveries [5], and pulsating heat pipes to enhance their heat transfer capability [6]. ...
... Several researchers have calculated diodicity and studied the flow phenomena in Tesla valves [4,[7][8][9][10][11][12][13][14][15]. In these studies, the performance of the valves mostly has been assessed using numerical simulations [11,16,17] and validated using point pressure measurements. ...
Article
The Tesla-diode valve, with no moving parts, allows restricted flow in one direction. It has many potential applications in different industrial situations. Despite the application of the valve and the importance of the effect of flow phenomena on the Tesla valve's performance, very few studies have experimentally investigated the motion of flow within the Tesla valve. This study aims to contribute to this growing area of research on the performance of Tesla valves by demonstrating the flow phenomena and the flow conditions needed to be used in numerical studies. In this work, the effect of direction of the flow and Reynolds number on the flow phenomena generated in a Tesla-diode valve is studied. Particle shadowgraph velocimetry (PSV) is utilized to investigate and visualize the velocity field. The results of this study confirm some of the phenomena that has been observed using numerical simulations. It also highlights the flow phenomena leading to an increase in the diodicity by an increase in the number of Tesla loops in the valve. An important observation often ignored in numerical simulation is the presence of unsteady behavior and vortex shedding for higher Reynolds number flows.
... This work presents systematic experimental characterizations of Nikola Tesla's fluidic valve or diode across a wide range of both steady and unsteady flow conditions. The case of steady pressure/ flow-rate considered in previous studies on Tesla-like channels provides a point of comparison to our results 13,[16][17][18][21][22][23][24]31,34,35,13 . No earlier work reports on the abrupt rise in diodicity, which likely reflects the singular values or narrow ranges in Re explored. ...
Article
Full-text available
Microfluidics has enabled a revolution in the manipulation of small volumes of fluids. Controlling flows at larger scales and faster rates, or macrofluidics , has broad applications but involves the unique complexities of inertial flow physics. We show how such effects are exploited in a device proposed by Nikola Tesla that acts as a diode or valve whose asymmetric internal geometry leads to direction-dependent fluidic resistance. Systematic tests for steady forcing conditions reveal that diodicity turns on abruptly at Reynolds number $${\rm{Re}}\approx 200$$ Re ≈ 200 and is accompanied by nonlinear pressure-flux scaling and flow instabilities, suggesting a laminar-to-turbulent transition that is triggered at unusually low $${\rm{Re}}$$ Re . To assess performance for unsteady forcing, we devise a circuit that functions as an AC-to-DC converter, rectifier, or pump in which diodes transform imposed oscillations into directed flow. Our results confirm Tesla’s conjecture that diodic performance is boosted for pulsatile flows. The connections between diodicity, early turbulence and pulsatility uncovered here can inform applications in fluidic mixing and pumping.
... This work presents systematic experimental characterizations of Nikola Tesla's fluidic valve or diode across a wide range of both steady and unsteady flow conditions. The case of steady pressure/ flow-rate considered in previous studies on Tesla-like channels provides a point of comparison to our results 13,[16][17][18][21][22][23][24]31,34,35,13 . No earlier work reports on the abrupt rise in diodicity, which likely reflects the singular values or narrow ranges in Re explored. ...
Preprint
Full-text available
Microfluidics has enabled a revolution in the manipulation of small volumes of fluids. Controlling flows at larger scales and faster rates, or \textit{macrofluidics}, has broad applications but involves the unique complexities of inertial flow physics. We show how such effects are exploited in a device proposed by Nikola Tesla that acts as a diode or valve whose asymmetric internal geometry leads to direction-dependent fluidic resistance. Systematic tests for steady forcing conditions reveal that diodicity turns on abruptly at Reynolds number $\textrm{Re} \approx 200$ and is accompanied by nonlinear pressure-flux scaling and flow instabilities, suggesting a laminar-to-turbulent transition that is triggered at unusually low $\textrm{Re}$. To assess performance for unsteady forcing, we devise a circuit that functions as an AC-to-DC converter, rectifier or pump in which diodes transform imposed oscillations into directed flow. Our results confirm Tesla's conjecture that diodic performance is boosted for pulsatile flows. The connections between diodicity, early turbulence and pulsatility uncovered here can inform applications in fluidic mixing and pumping.
Article
The microchannel cooling technology is an effective method to solve heat dissipation problems caused by high heat flux devices. In this study, microchannel heat sinks imitating Tesla valve (MCTV), mounted with sector bump (MCSB) and diamond bump (MCDB) were designed. Compared to the straight microchannel with the same heat transfer area, the heat transfer and flow characteristics (Nu, f and performance evaluation criterion PEC) of three innovative microchannel heat sinks were investigated numerically. The results show that Nu of MCTV, MCSB and MCDB are increased by 102.3%, 111.2% and 94.8% while f of these structures is increased to 3.21 times, 3.14 times and 2.81 times with Re of 800, respectively. The PEC of three novel microchannels were bigger than that of the straight microchannel. It can be attributed to the flow separation and convergence caused by the innovative structure, which resulting in the periodic interruption and redevelopment of the thermal boundary layer to promote momentum and energy exchange of fluid inside and outside the boundary layer. Due to the largest PEC, the effects of geometric parameters on the thermal performances of MCSB were further analyzed. It shows that the Nu of MCSB increases with the increase of sector bump angle θ and the decrease of arc radius r. The Tmax of MCSB is below 70 °C with r of 1.4 mm and θ of 15° when Re ≥ 700, which is suitable for heat dissipation application of electronic devices.
Article
The operating temperature can significantly influence the performance, cycle life, and safety of Li-ion batteries used in electric vehicles. One of the critical factors is to assess the temperature distribution within the battery pack when operated under extreme conditions and choosing an appropriate cooling method. Concerning this, a liquid cooling plate comprising Tesla valve configuration with high recognition in microfluidic applications is proposed to provide a safer temperature range for pouch type Li-ion batteries. A multi-stage Tesla valve with forward and reverse flow configuration is designed and analysed to improve a conventional rectangular channel's intrinsic temperature gradient issues for turbulent flow conditions. Moreover, the influence of various parameters such as channel number, the distance between two consecutive valves, coolant temperature, and heat flux applied on the cold plate's top and bottom surfaces are numerically investigated for varying Reynold's number using COMSOL Multiphysics software. An enhancement in heat transfer with the reverse flow in multi-stage Tesla valve is seen, mainly caused by flow bifurcation and mixing mechanisms, at the cost of pressure drop. A cold plate with 4 channels and valve to valve distance of 8.82 mm exhibits the most effective cooling performance.
Preprint
Full-text available
Reasoning by analogy is powerful in physics for students and researchers alike, a case in point being electronics and hydraulics as analogous studies of electric currents and fluid flows. Around 100 years ago, Nikola Tesla proposed a flow control device intended to operate similarly to an electronic diode, allowing fluid to pass easily in one direction but providing high resistance in reverse. Here we use experimental tests of Tesla's diode to illustrate principles of the electronic-hydraulic analogy. We design and construct a differential pressure chamber (akin to a battery) that is used to measure flow rate (current) and thus resistance of a given pipe or channel (circuit element). Our results prove the validity of Tesla's device, whose anisotropic resistance derives from its asymmetric internal geometry interacting with high-inertia flows, as quantified by the Reynolds number (here, Re ~ 1e3). Through the design and testing of new fluidic diodes, we explore the limitations of the analogy and the challenges of shape optimization in fluid mechanics. We also provide materials that may be incorporated into lesson plans for fluid dynamics courses, laboratory modules and further research projects.
Article
Full-text available
Reasoning by analogy is powerful in physics for students and researchers alike, a case in point being electronics and hydraulics as analogous studies of electric currents and fluid flows. Around 100 years ago, Nikola Tesla proposed a flow control device intended to operate similarly to an electronic diode, allowing fluid to pass easily in one direction but providing high resistance in reverse. Here, we use experimental tests of Tesla's diode to illustrate principles of the electronic-hydraulic analogy. We design and construct a differential pressure chamber (akin to a battery) that is used to measure flow rate (current) and thus resistance of a given pipe or channel (circuit element). Our results prove the validity of Tesla's device, whose anisotropic resistance derives from its asymmetric internal geometry interacting with high-inertia flows, as quantified by the Reynolds number (here, Re ∼ 10 3). Through the design and testing of new fluidic diodes, we explore the limitations of the analogy and the challenges of shape optimization in fluid mechanics. We also provide materials that may be incorporated into lesson plans for fluid dynamics courses, laboratory modules, and further research projects.
Article
Full-text available
The fixed-geometry valve micropump is a seemingly simple device in which the interac-tion between mechanical, electrical, and fluidic components produces a maximum output near resonance. This type of pump offers advantages such as scalability, durability, and ease of fabrication in a variety of materials. Our past work focused on the development of a linear dynamic model for pump design based on maximizing resonance, while little has been done to improve valve shape. Here we present a method for optimizing valve shape using two-dimensional computational fluid dynamics in conjunction with an opti-mization procedure. A Tesla-type valve was optimized using a set of six independent, non-dimensional geometric design variables. The result was a 25% higher ratio of re-verse to forward flow resistance (diodicity) averaged over the Reynolds number range 0 Re 2000 compared to calculated values for an empirically designed, commonly used Tesla-type valve shape. The optimized shape was realized with no increase in for-ward flow resistance. A linear dynamic model, modified to include a number of effects that limit pump performance such as cavitation, was used to design pumps based on the new valve. Prototype plastic pumps were fabricated and tested. Steady-flow tests verified the predicted improvement in diodicity. More importantly, the modest increase in diodic-ity resulted in measured block-load pressure and no-load flow three times higher com-pared to an identical pump with non-optimized valves. The large performance increase observed demonstrated the importance of valve shape optimization in the overall design process for fixed-valve micropumps.
Article
Full-text available
A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.
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Presents introductory skills needed for prediction of heat transfer and fluid flow, using the numerical method based on physical considerations. The author begins by discussing physical phenomena and moves to the concept and practice of the numerical solution. The book concludes with special topics and possible applications of the method.
Conference Paper
The Tesla valve is a passive-type check valve used for flow control/rectification in a variety of micro/mini-channel systems. Previous studies have focused on its optimal design and effectiveness (i.e. diodicity) for the low-Reynolds number regime (Re < 500). Using three-dimensional (3D) CFD, multiple, identically-shaped Tesla valves arranged in-series, i.e.: a Tesla “tree” or multi-staged Tesla valve (MSTV), were investigated. Fully-developed flow at the inlet and complete-laminar conditions throughout the entire valve structure were imposed on all numerical simulations. The number of Tesla valves, valve-to-valve distance and Reynolds number were varied to determine their effect on MSTV diodicity. The individual Tesla valves within each MSTV possessed pre-optimized design parameters as reported from the literature. Results clearly indicate that the MSTV can provide for a significantly higher diodicity than a single Tesla valve and that this MSTV diodicity increases with Reynolds number. Minimizing the distance between adjacent Tesla valves can significantly increase the MSTV diodicity and, for very low Reynolds number (Re < 50), the MSTV diodicity is near-independent of valve-to-valve distance and number of valves used. In general, more Tesla valves are required to maximize the MSTV diodicity as the Reynolds number increases. The current investigation also demonstrates that 3D numerical simulations more accurately predict the diodicity of a single Tesla valve over a wider range of Reynolds numbers.
Conference Paper
A three-dimensional (3-D) parametric model of Tesla-type valves is proposed. A geometrical relationship is derived for optimization study, and based on the model, performance investigations in terms of diodicity and pressure-flow rate characteristics of the valve are numerically carried out with same hydraulic diameter and different aspect ratios (of the model cross-sectional dimensions) ranging from 0.5 to 4. The 3-D computational simulations show that, for the same hydraulic diameter, the unity aspect ratio gives higher diodicity at Reynolds number less than 500 and higher will be achieved with bigger aspect ratio when the Reynolds number is above 500. Investigations of pressure-flow rate characteristics of the Tesla valve show that Tesla valve with high aspect ratio gives more flow control ability.
Article
A finite numerical method is presented for the solution of the two-dimensional incompressible, steady Navier-Stokes equations in general curvilinear coordinates. This method is applied to the turbulent flows over airfoils with and without trailing edge separation. The two-equation model is utilized to describe the turbulent flow process. Body-fitted coordinates are generated for the computation. Instead of the staggered grid, an ordinary grid system is employed for the computation and a specific scheme is developed to suppress the pressure oscillations. The results of calculations are compared with the available experimental data.
Article
An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretran-sitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in compari-son with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.
Design, fabrication and testing of fixed-valve micro-pumps
• F K Forster
• R L Bardell
• M A Afromowitz
• N R Sharma
• A Blanchard
Forster, F. K., Bardell, R. L., Afromowitz, M. A., Sharma, N. R., Blanchard, A., 1995, "Design, fabrication and testing of fixed-valve micro-pumps," Proceedings of the ASME Fluids Engineering Division, San Francisco, CA, U.S.A., 234, pp. 39-44.