Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition
IMECE2011
November 11-17, 2011, Denver, Colorado, USA
IMECE2011-65262
A NUMERICAL STUDY TO PREDICT THE EFFECTS OF STRUCTURED ROUGHNESS
ELEMENTS ON PRESSURE DROP AND HEAT TRANSFER ENHANCEMENT IN MINICHANNELS
AND MICROCHANNELS
V. V. Dharaiya
Rochester Institute of Technology
Rochester, NY, USA
[email protected]
ABSTRACT
Better understanding of laminar flow at microscale level is
gaining importance with recent interest in microfluidics
devices. The surface roughness has been acknowledged to
affect the laminar flow, and this feature is the focus of the
current work to evaluate its potential in heat transfer
enhancement. A numerical model is developed to analyze the
thermal and hydrodynamic characteristics of minichannels and
microchannels in presence of roughness elements. Structured
roughness elements following a sinusoidal pattern are generated
on two opposed rectangular channel walls with a variable gap.
A detailed study is performed to check the effects of roughness
height, roughness pitch, and channel separation on pressure
drop and heat transfer coefficient in the presence of structured
roughness elements. As expected, the structured roughness
elements on channel walls result in an increase in pressure drop
and heat transfer enhancement as compared to smooth channels
due to the combined effects of area enhancement and flow
modification. This is due to the fact that the roughness element
as a small obstruction in the flow passage of narrow channels
which introduces flow modifications in the flow and increases
the energy transport. The improvement in global heat transfer
enhancement is observed in rough channels due to velocity
fluctuations. At the same time, it also causes pressure drop to
increase as compared to smooth channels. The fully developed
friction factor and Nusselt number results obtained from CFD
simulations for smooth and rough channels are compared with
the experimental data carried out in the same laboratory. The
current numerical scheme is validated with the experimental
data and can be used for design and estimation of transport
processes in the presence of different roughness features.
INTRODUCTION
Microchannel heat sinks are of more interest to researchers
due to its ability to generate very high rates of heat transfer.
The advantage of microchannel heat sinks arises from their
small passage size and high surface area to volume ratio which
makes it possible to achieve enhancement in heat transfer with
relatively low cooling fluid flow rate [1]. An extensive
literature review shows the difference in transport behavior in
S. G. Kandlikar
Rochester Institute of Technology
Rochester, NY, USA
[email protected]
microchannels as compared to conventional sized channels.
Moreover, at microscale, channels might have surface
roughness heights present due to fabrication on walls
comparable to channel dimensions. In spite of having wide
experimental data for pressure drop in literature, the flow
behavior in still under a lot of discussion and remains an open
problem [2].
Previous Experimental Work:
Nikuradse [3] conducted an extensive experimental study
with water in circular pipes to predict the effect of surface
roughness on pressure drop for laminar and turbulent regions,
varying Re from 600 to 106. Kandlikar [4] performed critical
review on Nikuradse's [3] experimental data to understand the
mechanisms that affect fluid-wall interactions in rough
channels. For narrow channels, experimental data sometimes
misleads as they are strongly influenced by a number of
competing effects such as surface roughness, flow
modifications and varying experimental uncertainties.
Nikuradse [3] used sand grains deposition to generate
roughness structures on inner channel walls with diameters
from 2.42 cm to 9.92 cm. The results predicted that surface
roughness on channel walls do not have any significance on
pressure drop in laminar flow regime.
Kandlikar [4] concluded that the overall uncertainty
associated to measure pressure drop was estimated between 3 to
5% in turbulent region whereas it was expected to be
significantly higher in laminar region. The errors associated
were mainly due to large inaccuracies in manometers used to
measure pressure drop in laminar region and surface geometry
measurements. Kandlikar [4] showed that measurements of
channel dimensions, reading accurate flow parameters, and
recognizing experimental uncertainties were the major
problems of researches to obtain accurate experimental data in
late 80's and 90's.
Wu and Little [5, 6] performed experiments on etched
channels with hydraulic diameters varying from 45 to 150
microns and found an early transition from laminar to turbulent
regime in microminiature J-T refrigerators. Their results were
tested for hydrogen, neon and argon as refrigerants and
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predicted higher friction factor values compared to
conventional theory. In 2005, Kandlikar et al. [2] presented
experimental data for water and air as fluids in rectangular
channels of Dh varying from 325 µm to 1819 µm. The pressure
drop showed a significant difference compared to conventional
channels and also predicted early transition to turbulence.
Weilin et al. [7] carried out experiments on trapezoidal
silicon microchannels to investigate flow characteristics of
water with Dh ranging from 51 to 169 µm. Experimental result
predicted higher pressure gradient and friction factor values as
compared to conventional laminar flow theory which may be
due to effect of surface roughness of microchannels. More
recently, Gamrat et al. [8] presented experimental and
numerical study to predict the influence of roughness on
laminar flow in microchannels. The authors noted that
Poiseuille number increases with relative roughness and is
independent of Reynolds number in laminar regime (Re<2000).
Brackbill [9], Brackbill and Kandlikar [10-12] have
generated a considerable experimental data to investigate the
effects of surface roughness on pressure drop. Structured sawtooth roughness was fabricated on channel walls with relative
roughness ranging from 0 to 24%. The results predicted early
transition to turbulence and showed the use of constricted flow
parameters that would cause the data to collapse on to
conventional theory line for laminar flow regime.
Previous Numerical Work:
Hu et al. [13] developed a numerical model to simulate
rectangular prism rough elements on the surfaces and showed
significant effects of roughness height, spacing and channel
height on velocity distribution and pressure drop. Croce et al.
[14, 15] investigated the effects of roughness elements on heat
transfer and pressure drop in microchannels through a finite
element CFD code. They modeled roughness elements as a set
of random peak heights and different peak arrangements along
the ideal smooth surface. Their results predicted a significant
increase in Poiseuille number as a function of Reynolds
number. Moreover, a remarkable effect of surface roughness on
pressure drop was observed as compared to a weaker one on the
Nusselt number.
Rawool et al. [16] presented a three-dimensional simulation
of flow through serpentine microchannels with roughness
elements in the form of obstructions generated along the
channel walls. They found that the obstruction geometry plays
a vital role in predicting friction factor in microchannels. The
effect of friction factor in case of rectangular and triangular
obstructions was more and the value decreased for trapezoidal
roughness element. The numerical results concluded that
roughness pitch as an important design parameter and the value
of pressure drop decreases with increase in roughness pitch.
Kleinstreuer and Koo [17, 18] proposed a new approach to
capture relative surface roughness in terms of a porous medium
layer (PML) model. They evaluated the microfluidics variable,
i.e. roughness layer thickness and porosity, uncertainties in
measuring hydraulic diameters, and inlet Reynolds number as a
function of PML characteristics. Stoesser and Nikora [19]
numerically investigated the turbulent open-channel flow over
2D square roughness for two roughness regimes using Large
Eddy Simulation (LES). They signified the effects of roughness
height, roughness pitch, and roughness width as the relative
contributions on pressure drag and viscous friction.
Previous Experimental Data Used for Current Numerical
Model Validation:
In order to study the effects of surface roughness on fluid
flow and friction factor in microchannels, an extensive
experimental data set was generated by Wagner and Kandlikar
[20]. Structured sinusoidal roughness elements were fabricated
on opposed rectangular channel walls to predict the effect of
roughness pitch and height on pressure drop along the channel
length. The author observed that as the hydraulic diameter
decreases, the experimental friction factor increases and
becomes more pronounce for tall and closely spaced roughness
elements.
In current work, same experimental data set was utilized for
comparison and validation of proposed numerical model to
predict the effects of surface roughness on pressure drop in
microchannels. The dataset used for numerical scheme were
obtained from data generated in previous work [20]. The test
species used for experimentation were measured under laser
confocal microscope to locate roughness height and roughness
pitch accurately. LabView software was used for measuring the
flow rate and pressure at inlet, outlet and along the length of
microchannel. The data was further processed and values of
friction factors were calculated for given set of test matrix.
NOMENCLATURE
a
Height of rectangular microchannel, (m)
b
Width of rectangular microchannel, (m)
L
Length of rectangular microchannel, (m)
Dh
Hydraulic diameter, (m)
ṁ
Mass flow rate (kg/s)
V
Velocity (m/s)
Cross-sectional area of microchannel, (m2)
P
Perimeter of microchannel (m)
f
Friction factor
k
Thermal conductivity of fluid (W/m-K)
µ
Dynamic viscosity (N-s/m2)
Re
Reynolds number
Roughness Parameters
Fp
Floor profile line
Ra
Average roughness (µm)
Rp
Maximum peak height (µm)
FdRa Distance from Fp to average (µm)
RR
Relative roughness
Sm
Mean spacing of irregularities
Subscripts
w
wall
f
fluid
fd
fully developed
avg
average
x
local
m
mean
cf
Constricted flow parameter
expt
Experiment based calculation
num
Numerical based calculation
2
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Greek
α
λ
ε
Aspect ratio (a/b)
Roughness pitch (µm)
Roughness height (µm)
OBJECTIVE
At microscale level, fluid flow and heat transfer are known
to deviate as compared to conventional theories in laminar as
well as turbulent regimes. Moreover, it is also difficult to
analyze the effects of surface roughness on channel walls in
microchannels because uncertainties remain such as the shape
of the rough microstructures and also due to the inhomogeneities of their distribution. The main objective of the
proposed numerical model is to develop a better understanding
of the roughness effects by generating structured sinusoidal
roughness elements on opposed rectangular channel walls.
Initially, the numerical model was developed to characterize
flow in smooth rectangular microchannels using CFD software
code, FLUENT. The results for fully developed region were
analyzed for smooth channels and validated with the
experimental data [20] and conventional theory [21].
Thereafter, numerical simulations were performed for two
different roughness geometries and the results obtained for
friction factor were compared with previous experimental data.
Constricted flow parameters were used to solve the numerical
cases with surface roughness elements.
THEORETICAL FORMULATION
Kandlikar et al. [2] characterized the effects of surface
roughness on pressure drop in single phase fluid flow. Based on
their experimental results, the relation between critical
Reynolds number versus relative roughness (ε/Dh,cf) and
friction factor versus constricted flow hydraulic diameter Dh,cf
was observed. Kandlikar et al. [1] proposed that critical
Reynolds number decreases with increase in relative roughness.
Based on the enhancement of roughness effects on transport
behavior in minichannels and microchannels, a new modified
Moody diagram was developed using the constricted flow
parameters over the entire range of Reynolds number. The new
Moody diagram shows the representation of early transition
from laminar regime to turbulent at micro level, as observed by
many researchers.
In representing the roughness effects on microscale,
Kandlikar et al. [2] proposed a new set of roughness
parameters. Figure 1 shows the new set of parameters. Rp is the
maximum height from the mean line along the profile. Next, S m
is defined as the mean separation of profile irregularities, which
correspond to the pitch of roughness elements in this work.
Lastly, FdRa is the distance of the floor profile (F p) which lies
below the mean line. These values are established to replace the
assumption that a surface needs only be defined by the average
roughness, Ra. The roughness height , is the sum of FdRa and
Rp. These parameters detail the surface profile in a more indepth fashion compared to Ra.
The derivation of the constricted parameters is useful in
accurately calculating friction factor in high roughness channels
[11]. The current work is based on the constricted parameter
scheme of Kandlikar et al. [2] and Brackbill and Kandlikar [1012]. In the case of smooth microchannels, a channel has a
cross-section of height a, and width b. Whereas, for roughness
on two opposite sides of a rectangular microchannel, the
parameter acf represents the constricted channel height. Figure 2
shows a generic representation of the constricted geometric
parameters.
Figure 1: Schematic diagram of roughness parameters [2]
In order to re-calculate the constricted parameters, acf and
cross-sectional channel area Acf can be defined as follows:
(1)
and
(2, 3)
Figure 2: Generic constricted parameters
Constricted perimeter for rough channels was obtained by
substituting acf instead of channel separation a used for smooth
channels;
and
(4, 5)
Similarly, the definitions of hydraulic diameter and constricted
hydraulic diameter were defined as:
and
(6, 7)
Theoretical friction factors are calculated using the constricted
parameters. For laminar flows in rectangular channels, the
theoretical friction factor is predicted by Kakac et al. [21], by
Eq. (8). In smooth channels, friction factor was obtained by
substituting conventional aspect ratio as defined in Eq. (9).
Whereas, in case of microchannels with surface roughness on
channel walls, Eq. (10) is used to define constricted aspect ratio
as shown below:
0.9564 4−0.2537 5
(8)
and
(9, 10)
Relative roughness is defined as the ratio of roughness height to
hydraulic diameter of a channel. Eq. (11) and Eq. (12) defines
the relative roughness for smooth and rough channels
respectively.
and
(11, 12)
Reynolds number and constricted Reynolds number can be
calculated as follows:
and
(13)
(14, 15)
The theoretical pressure drop can be calculated using Eq. (16)
which is used for validating the current numerical model for
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predicting effects of fluid flow in smooth rectangular channels.
Using the constricted flow parameters, Eq. (17) can be used to
find the friction factor for channels with surface roughness on
channel walls. The pressure drop data obtained from numerical
simulations for rough microchannels will be compared with Eq.
(17). This comparison will validate the usage of current
numerical code to accurately predict the effects of structured
roughness elements on fluid flow in minichannels and
microchannels.
and
(16, 17)
Moreover, in case of surface roughness generated on all the
four sides of a rectangular microchannel, all the above
equations should be modified by using constricted channel
width as bcf, instead of b.
MODEL DESCRIPTION
Initially, the fluid flow effects in smooth rectangular
microchannels with varying aspect ratios from 0.007 to 0.06
were investigated using commercial CFD software tool,
FLUENT. The obtained results were supposed to be compared
with conventional theory and prior experimental data to provide
validation of the current numerical scheme. Later on, the
numerical scheme was extended to predict the flow
characteristics with structured surface roughness elements on
channel walls using constricted flow parameters.
Case I: Smooth Channels
Figure 3 shows a schematic of a microchannel with
channel height (a), channel width (b) and channel length (L).
The channel width and length of microchannel were kept as
very large as compared to channel height to test the numerical
simulations for extremely low aspect ratios. The width and
length of the channel were kept as 12.7 mm and 114.3 mm
respectively for all the cases of smooth and rough channels.
The dimensions were determined based on the experimental
test matrix, so as to provide comparison of numerical model
with experimental pressure drop results. Flow direction was
kept as shown in figure 3.
All the cases were numerically simulated using CFD
software, FLUENT. GAMBIT was used as pre-solver software
for designing geometric models, grid generation and boundary
definition. Water enters the rectangular microchannels with a
fully developed velocity profile. The first step in CFD
Figure 3: Schematic of smooth rectangular channel
geometry
modeling was to compare smooth channel geometries with
conventional theory and prior experimental data. Hence, the
experimental tested flow rates were selected and the same were
used for inlet flow rates for numerical simulation.
For numerical investigation of smooth microchannels, the
geometries were created for four different channel separations
of 100 µm, 400 µm, 550 µm, and 750 µm. The pre-solver
software GAMBIT was used for performing mesh generation
and defining inlet and outlet boundaries. Figure 4 shows a
schematic of meshed geometry for rectangular microchannel
with channel height as 400 µm, channel width as 12.7 mm, and
channel length as 114.3 mm. Waters enters the rectangular
channel from left face as shown in figure 4.
Flow Direction
Figure 4: Meshed geometry for smooth rectangular channel
having channel height (a=400 µm), channel width (b=12.7
mm), and channel length (L=114.3 mm)
All the smooth rectangular geometries were created with
varying aspect ratios from 0.007 to 0.06 in similar way.
Tet/Hybrid T-grid scheme were used for generating mesh for
all the geometries. The mesh spacing was kept as low as
possible to ensure accurate predictability depending upon each
generated model. There were approximately 3 million grid
elements in each rectangular geometry and the processing time
for the simulation was noted to be around 14-16 hours (Intel
Core 2 Duo processor). Grid independence test were carried out
for all the geometries to ensure best mesh spacing for numerical
model.
Further, all the mesh geometries were imported in
numerical simulation CFD software, FLUENT. Reynolds was
kept low for all the cases in order to confirm laminar flow
through rectangular microchannels. Pressure-based solver was
used to achieve steady state analysis. The SIMPLE (SemiImplicit Method for Pressure-Linked Equations) algorithm was
used for introducing pressure into the continuity equation. The
inlet temperature was kept as room temperature for all the cases
as used for experimental data as well. The flow equations were
solved with a first-order upwind scheme. The convergence
criterion for velocities, continuity and energy equation in each
numerical model were kept as E-6.
Case II: Rough Channels
The numerical model used to predict the pressure drop for
smooth rectangular microchannels is extended to rough
channels using constricted flow parameters. In order to
investigate structured roughness effects on pressure drop,
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sinusoidal roughness elements on opposed rectangular channel
walls were generated as shown in Figure 5. Two roughness
geometries as shown in figure 6, were selected from
experimental test matrix to validate numerical model. In both
the roughness profiles, the only varying parameter was
roughness pitch.
Table 1 shows the channel geometries used for validating
proposed numerical model. There were four smooth channel
geometries and two geometries with surface roughness on
opposed rectangular channel walls. The values for constricted
flow parameters were used to calculate pressure drop in rough
microchannels. As seen in Table 1, the usage of constricted
parameters makes significant difference in values of aspect
ratio and hydraulic diameters for channels with roughness
elements. The controlling parameters that were used to define
channel width and channel length for all the cases in Table 1
were kept as 12.7 mm and approximately 114.3 mm
respectively.
Table 1: Test matrix used for CFD model validation
Case I: Smooth Channels
a
(µm)
Re
100
define roughness elements were roughness height and
roughness pitch. Figure 7 represents roughness geometry with
channel separation of 550 µm, roughness height of 50 µm, and
roughness pitch of 250 µm. For creating a geometric model in
b
a Inlet
Flow direction
Figure 7: Schematic of rough microchannel having channel
separation=550µm, roughness pitch=250µm, and roughness
height=50µm
% Errorexpt-
ftheory
fexpt [20]
fnum
784
0.0303
0.0232
0.0238
2.58
400
800
0.0288
0.0331
0.0336
1.51
550
784
0.0289
0.0330
0.03325
0.76
750
785
0.0283
0.0299
0.0304
1.67
num
Figure 5: General Schematic of rough microchannels used
for numerical simulation
Figure 8: Meshed geometry of rough microchannel having
channel separation=550µm, roughness pitch=250µm, and
roughness height=50µm
pre-solver GAMBIT, a single roughness element of 250 µm
pitch was duplicated 457 times to match the channel length of
114.25 mm. All the 457 segments were unified to create a
single volume with roughness elements on opposite walls as
depicted in Figure 7. The inlet was given on the left face and
the flow direction was kept as shown in Figure 7. Figure 8
shows the section of meshed geometry of the model created in
Figure 7. Tet/Hybrid T-grid meshing was used and
conformance of mesh spacing was done employing a grid
Table 2: Test matrix used for numerical simulation of
rough channels with varying roughness height, roughness
pitch, and channel separation
a (µm)
550
550
550
Figure 6: Profiles of structured sinusoidal roughness
elements generated on opposite channel walls
550
550
550
As discussed earlier, two roughness geometries were used
to validate the proposed numerical scheme. Figure 7 represents
the outline and solid model of roughness geometry with
structured sinusoidal elements generated on opposed channel
walls of width (b) 12.7 mm. The two major parameters used to
250
550
750
5
λ (µm)
ε (µm)
Varying roughness height, ε
250
20
250
50
250
100
Varying roughness pitch, λ
50
150
50
250
50
400
Varying channel separation, a
250
50
250
50
250
50
λ/ε
12.5
5
2.5
3
5
8
5
5
5
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independence plot. Table 1 summarizes the detailed geometry
parameters used for generating smooth and rough rectangular
microchannels for validating current numerical model with
available experimental data.
In a similar way, all the other roughness geometries were
generated as shown in Table 2 to predict the effects of
roughness pitch, roughness height, and channel separation on
heat transfer. Tet/Hybrid T-grid scheme of mesh generation and
lowest possible mesh spacing was used for all roughness
geometries. For each analysis, it was reported that any further
reduction in mesh spacing does not affect the pressure profiles
at varying cross-sections. This confirms the grid independency
for accurately predicting numerically simulated results.
RESULTS AND DISCUSIONS
The different models were generated and meshed using
pre-solves software, GAMBIT. Further, the meshed geometries
were numerically simulated with prescribed boundary
conditions using a CFD software tool, FLUENT. The pressure
data along the length of microchannel was extracted from the
converged simulated models. Later on, the pressure drop was
calculated and once the pressure drop achieves linearity along
the length of a channel, a fully developed region was meant to
be achieved. Also, hydrodynamic entrance lengths were
calculated for each case and made sure that the values for fully
developed pressure drop were obtained at a length greater than
Lh. The fully developed friction factors were then calculated
from the numerical simulated pressure drop data. All the cases
were solved with a Reynolds number in a range of laminar flow
for microchannels.
Four smooth geometries and two rough geometries were
selected from experimental data of Rebecca [20] to compare
and validate the current numerical model. The comparison can
rate the accuracy of numerical model to predict the effects of
fluid flow in microchannels with and without roughness
elements. In case of rough channels, the numerical cases were
solved on the basis of constricted flow parameters and the
resultant numerical fully developed laminar friction factor (ffd,cf,
num) were compared with the experimental friction factor (ffd, cf,
expt) for validating current numerical model.
CFD Model Validation:
Case I: Smooth Channels
Table 3 shows the results for smooth rectangular
microchannels tested for channel separation of 100 µm, 400
µm, 550 µm, and 750 µm. For each case, pressure drop data
along the length of a microchannel obtained from FLUENT
simulations were in well agreement with the measured
experimental pressure drop data. This shows the conformity of
the numerical model to accurately predict the fully developed
friction factor in microchannels. Equation (16) was used to
calculate the numerical friction factor values for smooth
channels, where pressure drop value was obtained from
FLUENT. Boundary conditions and geometric parameters were
maintained exactly the same as experimental data [20] to show
better comparison. Hence, the Reynolds number for each
smooth channel was varied as seen in Table 3.
As discussed in literature, the fluid flow characteristic
seems to deviate for microscale and macroscale channels.
Therefore, the numerical results were also compared with
friction factor values obtained using conventional theory (using
Eq. 8) for smooth channels. The values of fully developed
friction factor were higher as compared to conventional theory
approach except for a case having extremely low aspect ratio of
0.0078. The numerical data for smooth channels was in good
agreement with experimental data by Rebecca [20]. For smooth
narrow rectangular channels, the percentage deviation of
numerical model with experimental data was less than 2.58%.
Table 3: Comparison of fully developed laminar friction
factor for smooth channels
a
(µm)
100
400
550
750
Re
Case I: Smooth Channels
fexpt
ftheory
fnum
% Errorexpt-
[20]
784
800
784
785
0.0303
0.0288
0.0289
0.0283
0.0232
0.0331
0.0330
0.0299
num
0.0238
0.0336
0.03325
0.0304
2.58
1.51
0.76
1.67
Case II: Rough Channels
The roughness geometries were numerically simulated using
the same numerical scheme with constricted flow parameters.
Table 4 shows the Reynolds number used for each simulation
which was utilized from experimental data set. Two roughness
cases with varying roughness pitch as 150 µm and 250 µm
were simulated. Equation (17) was used to calculate fully
developed laminar friction factor values for both experimental
and numerical cases. The numerically simulated results show
good agreement with the experimental data as seen in Table 4.
The percentage errors calculated were approximately 3%. This
shows that a numerical model is always a good tool to predict
the fluid flow characteristics in microchannels.
Table 4: Comparison of fully developed laminar friction
factor for rough channels using constricted flow parameters
Case II: Rough Channels
a
(µm)
α
550
550
550
550
0.043
0.043
0.043
0.043
αcf
0.035
0.035
0.035
0.035
λ
(µm)
Re
250
250
150
150
80
190
85
190
fcf,
fcf,
expt
num
0.39
8
0.15
7
0.34
5
0.15
8
0.406
0.162
0.342
0.168
%
Error
exptnum
2.01
3.12
0.72
6.33
Data Analysis for Rough Channels:
As seen earlier, the accuracy of this numerical model to
evaluate the pressure drop was found to be in good agreement
with the previous experimental results. Thereafter, the current
numerical model was extended to predict the effects of various
roughness parameters such as roughness height, roughness
pitch and channel separation on heat transfer. All the geometric
parameters were calculated using constricted flow theory for
rough channels. The physical properties involved in these
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analysis, such as density and dynamic viscosity, were
determined from the properties of water at STP conditions. Rest
of the parameters such as average velocity, friction factor and
heat transfer were calculated using the velocity field and
average temperature difference between the wall and fluid
obtained from numerical simulations.
Figure 9 below shows the temperature variation of wall
and fluid along the length of channel for one of the roughness
geometry having channel separation as 550 µm, roughness
pitch as 250 µm, and roughness height as 50 µm. The figure
shows that the heat transfer coefficient was very high at the
entrance region and progressively becomes constant, i.e. when
fully developed laminar flow was achieved. Based on the
temperature difference (ΔT) in figure, heat transfer coefficient
can be estimated which was used to calculate fully developed
Nusselt number. As seen from the figure, the average wall
temperature profile seems to have a larger bandwidth compared
to mean bulk temperature along the length of a microchannel.
Figure 9 also shows the zoomed view of same temperature
profile for roughness geometry for the first 10 mm length of
channel. It can be seen that the wall temperature varies on the
basis of roughness profile along the channel. Also, the analysis
in a single roughness element shows that the temperature at the
extreme bottom node of the roughness element has the highest
temperature whereas the extreme top node has the lowest
temperature. This is due to the fact that the extreme top node
comes in direct contact with the mean fluid temperature and it
has more tendencies to dissipate heat to the fluid domain.
Figure 9: Temperature variation for the roughness
geometry having a = 550 µm, λ = 250 µm, and ε = 50 µm
the fluid following the path of sinusoidal roughness pattern.
Figure 10 shows the schematic of roughness profiles for a
geometry having channel separation as 550 µm, roughness
pitch as 250 µm, and roughness height as 50 µm. Figure 10 also
shows the corresponding variation of wall temperature along
the length of microchannel for same geometry.
Figure 10: Wall temperature variations along the length of
the channel for roughness geometry
Initially, in order to calculate the average wall temperature,
several node points were computed along a single roughness
element. Thereafter, the mean of all the different nodes was
calculated to estimate average wall temperature. Also, as
defined in earlier, the wall temperature was measured a
distance of an average maximum profile peak height (Rpm) to
estimate average wall temperature based on theory. Both the
values of average wall temperature tend to lie over each other
with a maximum deviation of 0.03%.
Therefore, to simplify the calculations, the average wall
temperature was measured at the main profile mean line as
shown in Figure 10. The data points computed for wall
temperature in Figure 10 were in a fully developed laminar
region and therefore it corresponding average wall temperature
follows a linear increasing trend as expected. In a similar way,
the heat transfer coefficients for all the roughness geometries
were estimated based on the wall temperature computed at a
distance of averaged maximum profile peak height (Rpm).
Figure 11 shows the flow direction of water along the
length of the microchannel having a width of 12.7 mm. Figure
The sinusoidal roughness elements provides flow
modifications which increases heat transfer compared to
smooth channels at the expense of increase in pressure head.
Moreover, the temperature variation for sinusoidal roughness
geometries was observed in both directions, along the length as
well as the width of the channels. Therefore, it becomes
important to properly analyze the average wall temperature for
roughness geometries to estimate correct heat transfer from the
system.
As discussed above, the wall temperature varies along the
length of the microchannel due to flow modifications caused by
Figure 11: Geometric representation of flow over the
roughness geometry
7
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Figure 12: Wall temperature variation along the width of
the rough channel (a = 550 µm, λ = 250 µm, and ε = 50 µm)
12 represents single roughness element of the same geometry.
In case of roughness geometries, constant heat flux
H2boundary condition was applied on the two opposite channel
walls having surface roughness. The maximum temperature
was observed at the corners and minimum at the center line
subjected under H2 boundary condition as seen in Figure 12.
Figure 11 shows the temperature variation along the width of
rough microchannel at 90 mm axial distance (along the width
highlighted with orange color line in Figure 11). Several nodes
were taken across the width and temperature of all the nodes
was used to calculate the average wall temperature along the
width of the microchannel for different roughness geometries.
Effects of Roughness Parameters on Heat Transfer:
In this current work, roughness elements were configured
as structured sinusoidal pattern along the channel walls. Using
structured roughness features on surfaces will provide better
understanding of different roughness parameters such as
roughness height, roughness pitch, and channel separation on
pressure drop and heat transfer in minichannels and
microchannels.
Effects of Roughness Height:
In narrow channels, structured sinusoidal roughness
elements act as small obstructions in the flow which provides
mixing of fluid and aids in heat removal from the system.
Figure 13 show the temperature profiles along the axial length
of a microchannel for three different roughness geometries with
varying roughness height. The temperature profiles are shown
for the first 25 mm length of microchannel as the flow becomes
fully developed within that length and it follows linear trend
thereafter. As seen in the figures, the channel separation and
roughness pitch were kept as 550 µm and 250 µm respectively
for all the three cases. The roughness height was varied from 20
µm to 100 µm. This study helps to signify the effects of
roughness height on transport processes in microchannels.
Also, the temperature variation was plotted by computing
the wall temperatures at different locations on roughness
element such as tip, base and average roughness peak height.
The heat transfer coefficient and fully developed laminar
Nusselt number were estimated by considering the temperature
profile at the main profile mean line as discussed earlier. It was
observed from the figure that the wall temperature at the base
of roughness element was maximum whereas it was the lowest
at the tip of the roughness element. Moreover, the temperature
profile at a distance of average roughness peak height (Rpm) lies
between the maximum roughness peak height and floor profile
mean line.
In all the cases, constant heat flux H2 boundary condition
was applied on the two opposite roughness walls which was
calculated based on the constricted flow parameters. As seen
from three plots in Figure 13, in a fully developed laminar flow
region, the temperature difference between the wall and fluid
tends to increase with increase in roughness height. This
corresponds to the decrease in the heat transfer coefficient with
increment in the roughness height from 20 µm to 100 µm.
These results were observed due to the fact that the roughness
height grows taller keeping the channel separation and
roughness pitch constant. Basically, the majority of the fluid
flows through the gap between the roughness peaks created on
opposite channel walls. The function of the roughness element
was to enhance the mixing of the fluid flowing through the
channel. As the roughness element height increases, its
functionality decreases.
Table 5 shows the effect of roughness height on the fully
developed Nusselt number for rough microchannels. The
constricted Nusselt number was calculated based on constant
heat flux on two rough surfaces. The heat transfer coefficient
decreases with the corresponding increase in the structured
roughness height. This was due to the decrease in the
magnitude of the effective hydraulic diameter which was
calculated using the constricted flow parameters as seen in the
table below.
Effects of Roughness Pitch:
To study the effects of roughness pitch on fluid flow and
heat transfer properties, three geometries were selected with
varying pitch as 150 µm, 250 µm, and 400 µm respectively.
Also, all the other geometric dimensions such as channel
separation and roughness height were kept constant. Figure 14
shows the temperature profile for roughness geometries with
varying pitch from 150 µm to 400 µm. The effect of roughness
pitch on fluid behavior seems to have very less influence of
transport phenomena for selected roughness geometries.
Table 5 shows the results of fully developed Nusselt
number with varying roughness pitch. The values of fully
developed Nusselt number were decreasing with increase in
magnitude of roughness pitch but the variation was very less.
These results were observed due to the fact that the effective
hydraulic diameter remains the same for all the cases as the
channel separation and roughness height were kept constant.
Effects of Channel Separation:
In order to perform numerical simulation to evaluate the
effects of channel separation on heat transfer, the other two
roughness parameters such as roughness pitch and roughness
height were kept constant as 250 µm and 50 µm respectively.
8
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The channel separation was varied from 250 µm to 750 µm.
Figure 15 shows the temperature profile for the first 25 mm
length of microchannel as the flow becomes fully developed
and follows constant slope thereafter.
The values of temperature difference between the wall and
fluid in a fully developed region increased with increase in
channel separation as expected. Table 5 showed the effects of
channel separation on fully developed Nusselt number for
rough microchannels. The heat transfer enhancement decreases
with corresponding increase in channel separation assuming the
roughness height and roughness pitch as constant.
The observed results were due to the fact that the
roughness parameters were kept constant to study the effects of
channel separation. Therefore, the tendency of the roughness
elements to affect the fluid flow behavior diminishes with
increase in channel separation.
CONCLUSIONS
The numerical model was developed to predict the effects
of fluid flow characteristics in smooth channels and channels
with surface roughness. Smooth rectangular geometries were
tested for hydraulic diameters varying from 0.0078 to 0.06.
Fully developed laminar friction factors were calculated from
the pressure drop values obtained from numerical simulated
cases. The numerical model was validated with experimental
data and the percentage deviation was less than 2.58% for
smooth rectangular microchannels. Also, the fully developed
friction factor values were found higher as compared to
conventional theory. The constricted flow parameters were
further used to simulate cases with structured sinusoidal surface
roughness elements on channel walls. The numerical simulation
for two roughness geometries (λ = 150 µm and 250 µm)
Figure 13: Temperature variation along the length of channel for roughness geometry to predict the effects of roughness
height on heat transfer
Figure 14: Temperature variation along the length of channel for roughness geometry to predict the effects of roughness
pitch on heat transfer
Figure 15: Temperature variation along the length of channel for roughness geometry to predict the effects of channel
separation on heat transfer
9
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Table 5: Rough Channels: NuH2,fd for fully developed laminar flow with varying roughness height, roughness pitch, and
channel separation
a (μm )
λ (μm)
ε (μm)
b (mm)
Dh (μm)
Dh, cf (μm)
NuH2, fd
NuH2, fd, cf
Effects of Roughness Height, ε
550
550
550
250
250
250
20
50
100
12.7
12.7
12.7
550
550
550
150
250
400
50
50
50
12.7
12.7
12.7
250
550
750
250
250
250
50
50
50
12.7
12.7
12.7
1054.3
1054.3
1054.3
980.6
869.2
681.2
19.332
8.039
7.678
17.981
6.628
4.961
7.979
8.039
7.378
6.578
6.628
6.082
14.871
8.039
6.163
8.993
6.628
5.381
Effects of Roughness Pitch, λ
1054.3
1054.3
1054.3
869.2
869.2
869.2
Effects of Channel Separation, a
490.4
1054.3
1416.4
296.5
869.2
1236.7
showed very good agreement with experiments as well.
Significant enhancement of heat transfer of approximately
250% is found in one of the roughness geometry with channel
separation as 550 µm, roughness pitch as 250 µm, and
roughness height as 20 µm. Moreover, looking at the velocity
vectors for different rough geometries, continuous streamlines
were observed with no presence of vortices formation beneath
the roughness elements. This was due to the fact that roughness
were generated as smooth structured sinusoidal rather than
having sharp corners in roughness elements which can
significantly increase the potential of high heat transfer but at
the expense of pressure head. The enhancement observed in
the current work was purely due to flow modifications and area
enrichment in presence of roughness elements. Therefore,
roughness can be used as an important feature in designing and
operation of micro-systems as it promises to show significant
heat transfer enhancement as compared to smooth channels.
In this work, a hydrodynamic and thermal analysis model
was developed for microchannels with structured sinusoidal
roughness elements to check the effects of roughness elements
on pressure drop and heat transfer. The current numerical
model was validated with experimental data and can be used to
accurately predict the effects of surface roughness elements on
pressure drop and heat transfer in minichannels and
microchannels.
[4]
ACKNOWLEDGMENTS
The current work was carried out in Thermal Analysis,
Microfluidics, and Fuel cell Lab (TAµFL) at Rochester
Institute of Technology, Rochester, NY, USA. This material is
based upon work supported by the National Science Foundation
under Award No. CBET-0829038. Any opinion, findings, and
conclusions or recommendation expressed in this material are
those of the authors and do not necessarily reflect the views of
the National Science Foundation.
[14]
REFERENCES
[18]
[1]
[2]
[3]
Kandlikar, S. G., Garimella, S., Li, D., Colin, S., and King, M. R., 2006,
"Heat Transfer and Fluid Flow in Minichannels and Microchannels," 1st
ed., Elsevier, New York.
Kandlikar, S. G., Schmitt, D. J., Carrano, A. L., and Taylor, J. B., 2005,
"Characterization of surface roughness effects on pressure drop in singlephase flow in minichanels," Physics of Fluids 10, Vol. 17, DOI 100606.
Nikuradse, J., 1950, "Laws of flow in roughness pipes," Technical
Memorandum No. 1292, US National Advisory Committee for
Aeronautics, Washington, DC.
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[15]
[16]
[17]
[19]
[20]
[21]
10
Kandlikar, S. G., 2005, "Roughness effects at microscale – reassessing
Nikuradse's experiments on liquid flow in rough tubes," Bulletin of the
Polish Academy of Sciences, Vol. 53, No. 4, pp. 343-349.
Wu, P., and Little, W. A., 1983, "Measurement of friction factors for the
flow of gases in very fine channels used for Microminiature JouleThomson Refrigerators," Cryogenics, Vol. 23, pp. 273-277.
Wu, P., and Little, W. A., 1984, "Measurement of heat transfer
characteristics in the fine channel heat
exchangers used for
Microminiature Refrigerators," Cryogenics, Vol. 24, pp. 415-420.
Weilin, Q., Mala, G. M., and Li, D., 2000, "Pressure-driven water flows
in trapezoidal silicon microchannels," International Journal of Heat and
Mass Transfer 43, pp. 353-364.
Gamrat, G., Favre-Marinet, M., Person, S. L., Baviere, R., and Ayela, F.,
2008, "An experimental study and modelling of roughness effects on
laminar flow in microchannels," J. Fluid Mech., Vol. 594, pp. 399-423.
Brackbill, T. P., 2008, "Experimental Investigation on the effects of
surface roughness on microscale fluid flow," M. S. thesis, Rochester
Institute of Technology, Rochester, NY.
Brackbill, T. P., and Kandlikar, S. G., 2006, "Effect of triangular
roughness elements on pressure drop and laminar-turbulent transition in
microchannels and minichannels," Proceedings of the International
Conference on Nanochannels, Microchannels, and Minichannels,
ICNMM2006-96062.
Brackbill, T. P., and Kandlikar, S. G., 2007, "Effects of sawtooth
roughness on pressure drop and turbulent transition in microchannels,"
Heat Transfer Engineering, Vol. 28, No. 8-9, pp. 662-669.
Brackbill, T. P., and Kandlikar, S. G., 2007, "Effects of low uniform
relative roughness on single-phase friction factor in microchannels and
minichannels," Proceedings of the International Conference on
Nanochannels, Microchannels, and Minichannels, ICNMM2007-30031.
Hu, Y., Werner, C., and Li, D., 2003, "Influence of three-dimensional
roughness on pressure-driven flow through microchannels," Journal of
Fluid Engineering, Vol. 125, pp. 871-879.
Croce, G., and D'Agaro, P., 2005, "Numerical Simulation of roughness
effect on microchannel heat transfer and pressure drop in laminar flow," J.
Phys. D: Appl. Phys., Vol. 38, pp. 1518-1530.
Croce. G., D'Agaro, P., and Nonino, C., 2007, "Three-dimensional
roughness effect on microchannel heat transfer and pressure drop," Int. J.
of Heat and Mass Transfer, Vol. 50, pp.5249-5259.
Rawool, A. S., Mitra, S. K., Kandlikar, S. G., 2006, "Numerical
simulation of flow through microchannels with designed roughness,"
Microfluidics Nanofluidics Vol. 2, pp. 215-221.
Koo, J., and Kleinstreuer, C., 2003, "Liquid flow in microchannels:
experimental observations and computational analyses of microfluidics
effects," J. Micromech. Microeng. 13, pp. 568-579.
Kleinstreuer, C., and Koo, J., 2004 "Computational analysis of wall
roughness effects for liquid flow in micro-conduits," Journal of Fluids
Engineering, Vol. 126, pp. 1-9.
Stoesser, T., and Nikora, V. I., 2008, "Flow structure over square bars at
intermediate submergence: Large eddy simulation study of bar spacing
effect," Acta Geophysica, Vol. 56, pp. 876-893.
Wagner, R. N., and Kandlikar, S. G., 2011, "Effects of structured
roughness on fluid flow at the microscale level," Submitted to
International Journal of Heat and Fluid Flow.
Kakac, S., Shah, R. K., and Aung, W., 1987, Handbook of Single-phase
Convective Heat Transfer, John Wiley and Sons, New York.
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