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Hydrodynamics of laminar flow through dimpled pipes

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An understanding of uid ow through pipes and ducts is a
fundamental requisite for the design and optimization of uid–ow
systems. In particular, the relationship between ow rate and pressure
variation is critical and is among the most studied problems in uid
mechanics. Great efforts have been made to optimize uid systems
and these optimization efforts generally involve the maximization of
uid ow and/or the minimization of pressure loss. Pressure variations
within piping systems are a result of so–called “friction pressure
losses” and “minor pressure losses”. Friction pressure losses refer to
pressure drop caused by friction between the uid and the bounding
wall. Minor losses, on the other hand, are associated with pressure drop
that occurs when the ow passes through some obstacles in the piping
system, such as a bend, a valve, an orice plate, a change in diameter,
or other. It should be noted that “minor” losses are often signicant
components of pressure loss within a system. There is a design
balance between minimization of pressure loss and maximization
of ow that is often sought by a uid engineer. Reasonable efforts
to reduce pressure losses yet increase ow rates are of signicant
value for both the scientic and the engineering elds. In this regard,
the present study aims at assessing the impact of dimpling on pipe
walls to improve the optimal piping performance. That is, dimpled
surfaces have been shown to increase hydrodynamic performance (for
instance, dimpled surfaces reduce drag). Often these improvements
are related to ow over external bodies and the dimples modify the
boundary layer to reduce ow separation. For internal ows (i.e., ow
through pipes/tubes/ducts), on the contrary, separation is not germane
however the dimples still impact the ow. In fact, it has been noticed
that dimpling can affect the heat/mass transfer processes between the
uid and the wall1 and it often leads to an increase in the thermal or
mass transport behavior.
The history of similar studies is rich and includes fully developed
friction in coiled pipes2 as well as the impact of dimples on external
ow over at surfaces.3 Generally, it was found that the presence
of dimples increases both the rate of heat transfer as well as the
frictional pressure losses. These ndings are conrmed in multiple
independent studies4–10 and are evident for a wide range of geometries
and Reynolds numbers.8 These ndings are also relevant for
combined force/natural convection internal ows,11 for ows that
are transitional12 and for ows within narrow channels.13 With the
impact of dimples on the ow and heat transfer characteristics well
established, some works have also turned to design optimization14–21
and to the localized inuences of the dimples on the ow patterns
(both adjacent to and nearby the dimples). The ultimate goal of these
studies is to nd a strategy to optimize both the size and the density
of dimples, to dene their distribution on the tube/duct wall, and to
characterize the hydrodynamic performance of dimpled tubes/ducts
compared to undimpled ones.22–29 Here, a systematic study of the
pressure/ow relationship is made using numerical simulation. The
study encompasses a wide range of dimple shapes. Comparisons of
pressure/ow results with pre–existing solutions are made in order to
establish the veracity of the solutions.
The model
For the present investigation, a circular tube with uniform
dimpling is considered. The dimpling may be fabricated by a number
of manufacturing processes but it is envisioned as uniform both
along the length of the duct as well as around the tube perimeter. The
dimples are semicircles with radius R that are formed on the tube/
duct wall. Dimples are arranged uniformly around the perimeter of
the duct and are not staggered in the ow direction. For the thus–
described situation, the ow behavior in a short segment of duct will
be repeated along the duct length. Consequently, ow periodicity can
be enforced, i.e., the ow patterns through one row of dimples can be
repeated through subsequent rows. The solutions are obtained using
computational uid dynamics wherein the uid region is subdivided
into a multitude of small elements over which conservation equations
of mass and momentum are solved. The results presented here
correspond to a laminar ow with Reynolds numbers of approximately
1150 (halfway to the onset of transitional ow and turbulence). The
qualitative behavior and interpretation of the results is the same for
other Reynolds numbers, provided the ow is laminar. The relevant
equations are the steady state, incompressible laminar Navier Stokes
MOJ Civil Eng. 2018;4(3):150154. 150
©2018 Abraham. This is an open access article distributed under the terms of the Creative Commons Attribution License, which
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Hydrodynamics of laminar ow through dimpled
Volume 4 Issue 3 - 2018
John Abraham, Ryan Maki
School of Engineering, University of St. Thomas, USA
Correspondence: John Abraham, School of Engineering,
University of St. Thomas, 2115 Summit Ave, St. Paul, MN 55105–
1079, USA, Tel 6129-6321-69, Email
Received: June 07, 2018 | Published: June 15, 2018
Laminar ow through a dimpled pipe has been investigated with a focus to determine the
relationship between hydrodynamic resistance and dimple geometry. Using a periodic
solution domain, in–line dimples were simulated with diameters that varied from 0.125mm
to 2mm (with a pipe diameter of 6 mm). It was found that for small dimples, the ow does
not enter into the dimple to forming a coherent recirculation zone. On the contrary, as
the dimple diameter increases, a recirculation zone forms and moves in the downstream
direction for increasing dimple size. The ow patterns within the dimple are connected to
changes of hydrodynamic resistance. For dimples whose sizes are small enough to prevent
recirculation, the ow resistance is constant with dimple size. Once the dimples become
sufciently large to allow recirculation, there is an inverse relationship between ow rate
and pressure drop. These ndings allow optimization of hydrodynamic performance when
a balance between pressure drop, ow rate, and wall mass transfer is required.
Keywords: dimple geometry, pipe, recirculation, ow resistance, pressure drop, ow
rate, wall mass
MOJ Civil Engineering
Research Article Open Access
Hydrodynamics of laminar ow through dimpled pipes 151
©2018 Abraham et al.
Citation: Abraham J, Maki R. Hydrodynamics of laminar ow through dimpled pipes. MOJ Civil Eng. 2018;4(3):150154. DOI: 10.15406/mojce.2018.04.00113
equations, including both conservation of mass and momentum. They
are given below:
1, 2, 3 1, 2 , 3
i ji i
u ij
x xx x
=−+ = =
∂∂ ∂
 
 
 
In these equations, the symbols
are the uid density and
dynamic viscosity, respectively while the ui terms are the velocities
in Cartesian tensor notation, and term p represents the uid pressure.
The tube diameter is 6 mm and its length is 6 mm. The inlet and
outlet of the tube are connected by periodic conditions wherein a pre–
dened pressure drop across the pipe segment is specied to be 1Pa.
The periodicity enforces a matching of the velocity prole at the inlet
and outlet. The uid used in the simulation was water, with a density
and kinematic viscosity of 998kg/m3 and 8.9 x 10–7m2/s, respectively.
The uid–ow equations are solved using ANSYS CFX v18.0 which
is a nite volume based solution algorithm. The rst calculation was
performed for the no–dimple case. In this case, in fact, exact solutions
for fully developed laminar ow exist and allow a validation check
on the numerical results. The analytical solution, with the applied
pressure drop along the pipe of 1Pa, gives a mass ow rate of 5.9g/s.
The numerical results, on the other hand, give a mass ow rate of
5.8g/s, in excellent agreement.
Once the ow rate through a straight, non–dimpled tube is
validated, attention is turned to the dimpled cases. Figure 1 has been
prepared to illustrate the distribution of dimples around the pipe
circumference. It can be noticed that eight dimples are positioned
around the pipe circumference, equidistant from each other. The
diameter of the dimples, indicated in Figure 1 by an annotation, is
changed from 0.125mm to 2mm for different simulations. For the
largest diameters, the dimples are sufciently large to merge together
and form a toroidal shape around the pipe. The follow–on gure
(Figure 2) shows an oblique view of the pipe with dimples. It can
be noticed that the dimples are placed midway between the inlet
and outlet surfaces of the periodic segment. Once the dimensions
and boundary conditions are explained, attention is turned to the
computational mesh. Above–described mesh was subject to a mesh–
independence test wherein the number of elements was increased and
the calculations were repeated. For instance, for simulations involving
a 2mm dimple, the initial mesh encompassed 282,541 elements while
the rened mesh totaled 1,497,549 elements. Results obtained from
the two meshes were compared to ascertain whether there was an
appreciable difference. By way of example, mesh independent tests
for dimples of 1 mm diameter dimples showed that the calculated
ow rates differed by less than 0.3%. A similar test for 2mm diameter
dimples revealed that initial mesh and rened mesh results differed
by only ~1%. These results demonstrated that the initial mesh was
suitable to provide results of high accuracy
More details regarding the computational mesh are provided in two
further images which are shown in Figure 3. The two images focus
on the mesh in a straight pipe and in a dimpled pipe near a dimple,
respectively, so that the mesh deployment can easily be seen. It is
seen that for both geometries, a rectangular–element mesh is deployed
along the walls while tetrahedral elements are used within the core of
the ow space. When a dimple is present, the wall–elements follow
the dimple shape and within the dimple space itself, the elements are
ner than at other locations.
Figure 1 Illustration of the deployment of dimples around the pipe perimeter.
Figure 2 Oblique view showing the positioning on the dimples on the pipe
Figure 3 Distribution of elements for a straight (top image) and dimpled pipe
(bottom image).
Hydrodynamics of laminar ow through dimpled pipes 152
©2018 Abraham et al.
Citation: Abraham J, Maki R. Hydrodynamics of laminar ow through dimpled pipes. MOJ Civil Eng. 2018;4(3):150154. DOI: 10.15406/mojce.2018.04.00113
Results and discussion
The presentation of results will rst focus on quantitative results
and then turn toward qualitative ow patterns and their inuence on
the results. The primary issue to be addressed is the impact of dimples
on the hydrodynamic efciency of the pipe. Thus, for a predened
pressure drop, a comparison of ow rates through the various dimpled
pipes will be made. The effect of dimple size on mass ow rate is
provided in Figure 4, where dimple sizes vary from 0.125mm to a
maximum of 2mm. It is found that very small dimples (0.125mm)
result in a lower ow rate. As dimple sizes increase slightly, there is
a more or less constant mass ow rate until the size of the dimples
reaches ~1.0mm. Then, the ow begins to decrease again with dimple
size. In order to explore the behavior of Figure 4, vectors of local
uid velocity are provided (Figure 5) (Figure 6). These vectors are
arranged for sequentially increasing dimple sizes. It is seen that for
smaller dimples, there is no coherent central eddy conned within
the dimple, i.e., the dimple volume is not large enough to support a
coherent eddy. To the contrary, for larger dimples (~1mm), a coherent
eddy begins to form within the dimple (Figure 5). As the dimple size
increases further, the recirculation patterns within the dimple become
more coherent and they move downstream (Figure 6). For instance,
for the largest dimple shown in Figure 6 (2mm), the center of the
recirculation zone is clearly downstream of the dimple center. The
off–center location is associated with a stronger uid impact on the
downstream face of the dimple and a larger stagnation pressure there.
It is believed that the formation, strengthening, and movement of this
recirculating ow are associated with the mass ow rate behavior
displayed in Figure 4.
Figure 4 Effect of dimple size on mass ow rate.
It should be noted that for dimple sizes of 1mm and larger, the
images show a portion of a second dimple intruding into the image.
The protrusion is the semitransparent dimple walls that have become
large enough to enter into the image. A deeper exploration of the
hydrodynamics is provided by evaluating the pressure within the
tube. Figure 7 shows the pressure along a plane that bisects the
tube; the gure corresponds to a dimple size of 2mm. Flow moves
from left to right in the image. It is seen that there is a large pressure
(stagnation location) at the downstream face of the dimple. This
location corresponds to the impact of ow against the downstream
dimple surface.
A corresponding image is shown in Figure 8. There, streamlines
are illustrated and they are colored according to local pressure
variations along the streamline. The gure has two parts: the bottom
image closely focuses on ow patterns in one of the dimples. The
recirculation zone can be easily identied: it is clear that it is not
centrally located within the dimple, but is rather situated downstream.
Also, the pressure within the uid in the downstream portion of the
dimple exceeds that in the upstream portion leading to the added
hydrodynamic resistance. The observations obtained from Figure 4–8
provide some guidance for the design of uid conveyance systems.
It is seen that relatively large and constant ow rates can be obtained
(for a predened pressure decrease) provided that the dimples are
small enough to prevent coherent eddy formation. For instance, it
is possible to use dimple–walled pipes to promote mixing and mass
transfer in a uid dynamic application thus limiting the consequence
of added pressure losses. Alternatively, for situations where increased
pressure losses are desired, for instance in ow control applications,
the dimple design should be large enough to allow the formation of
the coherent recirculation region within the dimple. The quantitative
results are specic to the parameters considered in the present
calculations (Reynolds number, tube diameter, number of dimples
deployed around the perimeter, etc.) However, the behavior of
coherent recirculation within the dimple and its effect on ow rate can
be generalized to other situations where these parameters differ from
those presented here.
Figure 5 Changes in ow patterns with increasing dimple size (dimple sizes
from 0.375 to 1.0 mm).
Hydrodynamics of laminar ow through dimpled pipes 153
©2018 Abraham et al.
Citation: Abraham J, Maki R. Hydrodynamics of laminar ow through dimpled pipes. MOJ Civil Eng. 2018;4(3):150154. DOI: 10.15406/mojce.2018.04.00113
Figure 6 Changes in ow patterns with increasing dimple size (dimple sizes
up to 2.0 mm).
Figure 7 Pressure variation within tube and dimples, 2mm dimple size.
Figure 8 Pressure along streamlines, 2mm dimple size.
Concluding remarks
In this study, a three–dimensional numerical simulation of
laminar ow in a dimpled pipe has been performed. The simulations
accounted for dimple sizes that range from 0 mm (a smooth pipe)
2mm. It was found that the no–dimple calculations agreed very well
with established laminar ow expectations. It was also found that the
presence of dimples always decreased the ow compared to the smooth
wall situation; however, the size of the dimple played a signicant
role in the ow. For very small dimples, there was a relatively large
effect on the ow. On the contrary, for intermediate sized dimples,
a more–or–less stable ow rate was calculated. As dimple size
continued to increase, a new ow regime was established and a
coherent recirculation formed within the dimple. The recirculation
became more coherent as the dimple size increased and also moved
downstream. The strengthening and location of the recirculation zone
resulted in additional pressure losses for the ow and consequently in
a decrease of ow rate.
Conict of interest
The author declares there is no conict of interest.
Hydrodynamics of laminar ow through dimpled pipes 154
©2018 Abraham et al.
Citation: Abraham J, Maki R. Hydrodynamics of laminar ow through dimpled pipes. MOJ Civil Eng. 2018;4(3):150154. DOI: 10.15406/mojce.2018.04.00113
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... Hence, heat transfer can improve as compared to a smooth pipe. Abraham and Maki [15] conducted hydrodynamics of laminar flow in pipes using dimples. They simulated varied dimple diameters between 0.125 and 2 mm inside tube diameter of 6 mm. ...
This paper presents the findings from a research study using computational fluid dynamics (CFD) on the impact of different diameter Ball Tabulators Inserts (BTI) on the three-dimensional flow pattern and heat transfer characteristics within a circular tube. This analysis was carried under uniform heat flux conditions with different BTI diameters (1, 2, 3, 4, 5, 6, 7, and 8 mm). Fluid flow, pressure drop, dynamic pressure, velocity components, thermo-hydraulic, turbulent kinetic energy, and turbulent viscosity were analysed qualitatively and quantitatively. The performance evaluation results revealed that the characteristics of flow behaviour and the velocity field contours variations are closely associated with the BTI configurations. Also, the computational results indicated that the change in fluid flow velocity near the pipe wall and around the BTI is important parameters for the heat transfer enhancement as compared to that obtained without BTI under the same conditions. Moreover, using BTI presented a distinguished influence on the rate of heat transfer. Additionally, vortex flow through means of this kind of BTI is an important parameter in the enhancement of heat transfer. The use of BTI can enhance the rate of heat transfer performance by more than 46%. Furthermore, the maximum value for the PEF is found to be more than 1.03.
... Unlimited researches were conducted to characterize the hydrodynamic performance of dimpled tubes compared to the ones without dimples [10][11][12][13]. Abraham and Maki [14] conducted a numerical simulation of laminar flow in a dimpled pipe to determine the relationship between hydrodynamic resistance and dimple geometry. The simulations considered for dimple sizes that range from 0 mm (a smooth pipe) to 2 mm. ...
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Flow properties and performances are analyzed in an annulus-diffusing channel with divergent dimpled tube DDT. 3-D Computational Fluid Dynamics CFD has been achieved to study the flow characteristics. The standard k-e turbulence model is employed in the numerical simulations. The main goal of the study is to present details of flow field characteristics and velocity distribution enhancement of the flow in an annulus-diffusing channel fitted with DDT. The effects of three different area ratios ARs (2, 2.5 and 3) on the flow performance have been discussed. The velocity structure in terms of radial velocities and pressure structures is studied by using commercial software ANSYS. Area ratios (ARs) and Reynolds number (Re) 62393 are achieved as governing parameters. The results show that the velocity and pressure performance is strongly affected by the insertions of dimples. The velocity values decrease and the pressure drop increases with an increasing area ratio through the diffusing channel. Therefore, increasing area ratio AR increases model performance.
... Another approach to enhance the heat transfer characteristics involving artificial roughness technique by providing dimple/protrusion is well known. The heat transfer characteristics are affected by the arrangement of dimples i.e. inline or staggered alignment [9,10], the effect of dimple depth [10], types of dimples [9,11,12], dimple diameter [13,14] and channel height [15]. Shin et al. [15] have measured the heat transfer coefficient in a channel with one side dimpled surface. ...
In this work, heat transfer behaviour of γ-Al2O3/water nanofluid in turbulent flow condition in a dimple plate heat exchanger is investigated. The effects of flow rates of hot and cold fluids for different concentrations (0.1, 0.2 and 0.3%w/w) of suspended nanoparticles on the heat characteristics and effect of enhancement by the addition of nanoparticles to base fluid are also examined. The comparison of the heat transfer behavior of nanofluid with that of the base fluid (water) resulted in heat transfer augmentation with an increase in the concentration of the nanoparticle. The γ-Al2O3/water nanofluid possesses better heat transfer performance than the base fluid at higher nanoparticle concentrations. The studies on pressure drop are also investigated to determine the friction factor of the fluid in the Reynolds number range. Nusselt number correlations are developed for the working fluids for evaluation of heat transfer coefficient.
The pressure drops and flow characteristics in a diffuser fitted with a semi-dimpled tube are numerically studied. Air is selected as a working fluid and its physical properties are modelled using pressure and velocity distribution. The study reveals that every semi-dimple acts as a vortex generator. They provide the flow with intensive vortices between the dimpled surface and the diffuser wall. Therefore, they cause an enhancement in the pressure drop inside the diffuser. The performance of the dimples consisting of sphere type dimples with 5 mm in diameter. Three “Reynolds number” operated in the range of 25000 ˂Re˂ 50000 that is based on the hydraulic diameter of the diffuser Dh. The variation in Reynolds number is examined to further investigations of the pressure drop and flow characteristics of the diffuser. The numerical simulations are conducted using incompressible steady-state Reynolds Averaged Navier Stokes equations and the turbulence model “RNG k-e is utilized in the current study. The flow characteristics of the diffuser with semi-dimpled tube are analysed and compared in terms of pressure contour, velocity profile, and velocity vectors, at the operating range of Reynolds numbers. The results are discussed to point out the flow structure mechanisms. It is found that equipping the diffuser with a semi-dimpled tube leads to an increase in the recirculation and vortices inside and near the dimples area. Therefore, they have a considerable influence on the flow field. For the diffuser equipped with a semi-dimpled tube, it is noted that the flow characteristics depend on the Reynolds number. The pressure drop in the flow direction becomes lower with increasing Reynolds number. The findings indicate that for the semi-dimples, increasing Reynolds number increases the velocity distribution significantly due to better mixing of the air.
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This simulation study has been designed to study and scale the head losses (hf) through internal flow passages with different five cross-section areas: these are circular, elliptical, rectangular, square and triangular cross-sectional passages. Those equivalent hydraulic diameters (Dh) were modelled for each shape to be used in head loss calculations and analysis using the Darcy-Weisbach equation. These equations formed the main structure of the mathematical model of this study to enable the building of the subsequent computerized model using MATLAB® software. Five major parameters were considered for head losses investigation and scaling for each pipe shape, these are the pipe length (L), the hydraulic diameters (Dh), friction coefficient (f), volumetric flow rate or discharge (Q) and mass flow rate (dm/dt). The results showed that head losses of non-circular pipes have relatively higher head losses than that of circular pipes, also the scaling head losses were strongly affected by the pipe geometry and shape, the flow characteristics and fluid properties. Furthermore, the head losses have been severely inversely affected by low pipe hydraulic diameter (Dh 0.10 m) and then be likely to be the same at higher pipe diameter (Dh ≥ 0.25 m) for all pipe shapes. Also, the most recommended pipe shapes for lower head losses next to the circular pipe are elliptical and square, while the less recommended are triangular and rectangular shapes respectively.
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There are many modalities that may be used to enhance heat transfer performance. One of these modes, the embossing of channel walls with dimples and/or protrusions, is a technique which has the advantage of simplicity of fabrication. The assessment of the quality of a geometry-based heat transfer enhancement technique frequently involves the change in pressure drop that accompanies the geometric modification. This realization provides the motivation for the investigation reported here. The focus of this work is the identification of the existence of various sub-regimes within the laminar-flow regime. The investigation was implemented by numerical simulation supplemented by a three-dimensional model of periodic fully developed flow. The selected channel-height Reynolds number range extended from 200 to 800. Within this range, three sub-regime laminar flows were identified: friction-dominated flow, inertial-loss-dominated flow, and the transition between these flows. Another focus of the results was the presentation of patterns of fluid flow and their impacts on the variation of the pressure drop with Reynolds number.
The fully-developed mixed turbulent convective heat transfer characteristics in dimpled tubes of parabolic trough receiver are numerically studied at a certain Reynolds number of 2×10⁴ and different Grashof numbers ranged from 0 to 3.2×10¹⁰ to produce substantial surface heat transfer augmentations with relatively small pressure drop penalties. The Boussinesq approximation is applied, in which variations in fluid properties other than density are ignored. The Realizable k-ε two-equation turbulence model with enhancement wall treatment is adopted. The influences of outer wall heat flux distributions and dimple depth on flow resistance and heat transfer rate are illustrated and analyzed. The results indicate that the average friction factor and Nusselt number in dimpled receiver tubes under non-uniform heat flux (NUHF) are larger than those under uniform heat flux (UHF). In most cases, the comprehensive performance of dimpled receiver tube under NUHF is also better than that under UHF. The deep dimples (d/Di=0.875) are far superior to the shallow dimples (d/Di=0.125) at a same Grashof number.
Enhanced surfaces have larger heat transfer surface area and offer increased turbulence level hence allowing higher heat exchange performance. In this study, numerical simulations are conducted to simulate geometric design optimization of enhanced tubes for optimal thermal–hydraulic performance. The simulations are validated with experimental data. Two and three dimensional steady incompressible turbulent flow in dimpled enhanced tube is numerically studied using realizable k–ε method. The pressure–velocity coupling is solved by Semi-Implicit Method for Pressure Linked Equations Consistent (SIMPLEC) algorithm. Results show that dimples on tube surface present high heat transfer performance. Compared to staggered configuration, the in-line dimples arrangement provided better overall heat exchange characteristics. The geometric parameters like dimple shape, depth, pitch and starts are found to have significant effects on overall heat exchange performance while the dimple diameter has insignificant effect on thermal performance.
Thermal-hydraulic performance of an enhanced tube was evaluated using experimental and numerical simulation techniques in a pipe-in-pipe heat exchanger. Steady state single phase (liquid-to-liquid) experiments were performed to determine Nusselt number and friction factor. Experiments with water as working fluid were carried out in the Reynolds number range of (500 < Re < 8000), while for water/glycol solution based experiments the Reynolds number range was kept at (150 < Re < 2000). A non-dimensional performance evaluation criterion (PEC) was used to assess the thermal-hydraulic performance of heat transfer enhancement achieved with the enhanced tube. Based on the experimental data, Nusselt number and friction factor estimation correlations were proposed for the enhanced tube.
The effect of the dimple shape and orientation on the heat transfer coefficient of a vertical fin surface was determined both numerically and experimentally. The investigation focused on the laminar channel flow between fins, with a Re=500 and 1000. Numerical simulations were performed using a commercial computational fluid dynamics code to analyze optimum configurations, and then an experimental investigation was conducted on flat and dimpled surfaces for comparison purposes. Numerical results indicated that oval dimples with their "long" axis oriented perpendicular to the direction of the flow offered the best thermal improvement, hence the overall Nusselt number increased up to 10.6% for the dimpled surface. Experimental work confirmed these results with a wall-averaged temperature reduction of up to 3.7 K, which depended on the heat load and the Reynolds number. Pressure losses due to the dimple patterning were also briefly explored numerically in this work.
The convective cooling heat transfer in mini-channels with dimples, cylindrical grooves and low fins is numerically studied by using the field synergy principle. We solve the synergy angle distribution to examine the mechanisms of the heat transfer enhancement in the enhanced surfaces. The parameter PEC as the evaluation coefficient is employed to study the comprehensive performance of the enhanced surfaces. The results show that the dimple surface presents the highest performance of heat transfer enhancement. The geometry size effects of dimple are studied over a Reynolds number range of 2700–6100, and the most favorable dimple geometric structures are optimized by using the performance evaluation plot of enhanced heat transfer techniques.
Measurements of detailed Nusselt number (Nu) distributions and pressure drop coefficients (f) for four hexagonal ducts with smooth and dimpled walls are performed to comparatively examine the thermal performances of three sets of dimpled walls with concave-concave, convex-convex and concave-convex configurations at Reynolds numbers (Re) in the range of 900-30,000. A set of selected experimental data illustrates the influences of dimple configuration and Re on the detailed Nu distributions, the area-averaged Nu over developed flow region (Nu-bar) and the pressure drop coefficients. Relative enhancements of Nu and f from the smooth-walled references (Nu{sub } and f{sub }) along with the thermal performance factor () defined as (Nu-bar/Nu{sub })/(f/f{sub })¹³ are examined. Nu-bar and f correlations are individually obtained for each tested hexagonal duct using Re as the controlling parameter. (author)
Flow structural characteristics over dimple surfaces located on one wall of a rectangular channel with three different dimple depths (δ∕D=0.1, 0.2, and 0.3) are studied experimentally. Reynolds number based on channel height ReH ranges from 2100 to 20 000, and the ratio of channel height to dimple print diameter H∕D is 1.0. Presented are instantaneous flow visualization images, spectra of longitudinal velocity fluctuations, vortex pair frequency information, and time-averaged surveys and profiles of different quantities. Regardless of dimple depth, primary vortex pairs are periodically ejected from the central parts of each dimple and exist in conjunction with edge vortex pairs present near the spanwise edges of staggered dimples. As dimple depth increases, larger deficits of total pressure and streamwise velocity are present, along with higher magnitudes of time-averaged streamwise vorticity, vortex circulation, and longitudinal Reynolds normal stress. Bigger and stronger vortices with increased turbulence transport capabilities are thus produced by deeper dimples. Ensemble-averaged power spectral density profiles show that primary vortex pair ejection frequencies range from 7 to 9 Hz, and edge vortex pair oscillation frequencies range from 5 to 7 Hz, with similar distributions as the Reynolds number varies, regardless of dimple depth.
Instantaneous, dynamic and time-averaged characteristics of the vortex structures which are shed from the dimples placed on one wall of a channel are described. The dimpled test surface contains 13 staggered rows of dimples in the streamwise direction, where each dimple has a print diameter of 5.08 cm, and a ratio of depth to print diameter of 0.2. Considered are Reynolds numbers (based on channel height) ReH from 600 to 11 000, and ratios of channel height to dimple print diameter H/D of 0.25, 0.50, and 1.00. For all three H/D, a primary vortex pair is periodically shed from the central portion of each dimple, including a large upwash region. This shedding occurs periodically and continuously, and is followed by inflow advection into the dimple cavity. The frequency of these events appears to scale on time-averaged bulk velocity and dimple print diameter, which gives nondimensional frequencies of 2.2-3.0 for all three H/D values considered. As H/D decreases, (i) the strength of the primary vortex pair increases, and (ii) two additional secondary vortex pairs (which form near the spanwise edges of each dimple) become significantly stronger, larger in cross section, and more apparent in flow visualization images and in surveys of time-averaged, streamwise vorticity. The locations of these primary and secondary vortex pairs near the dimpled surface coincide closely with locations where normalized Reynolds normal stress is augmented. This evidences an important connection between the vortices, Reynolds normal stress, and mixing. The large-scale unsteadiness associated with this mixing is then more pronounced, and encompasses larger portions of the vortex structure (and thus extends over larger volumes) as H/D increases from 0.25 to 1.0.
Heat transfer, friction factor and thermal enhancement factor characteristics of a double pipe heat exchanger fitted with square-cut twisted tapes (STT) and plain twisted tapes (PTT) are investigated experimentally using the water as working fluid. The tapes (STT and PTT) have three twist ratios (y = 2.0, 4.4 and 6.0) and the Reynolds number ranges from 2000 to 12000. The experimental results reveal that heat transfer rate, friction factor and thermal enhancement factor in the tube equipped with STT are significantly higher than those fitted with PTT. The additional disturbance and secondary flow in the vicinity of the tube wall generated by STT are higher compared to that induced by the PTT is referred as the reason for better performance. Over the range considered, the Nusselt number, friction factor and thermal enhancement factor in a tube with STT are respectively, 1.03 to 1.14, 1.05 to 1.25 and 1.02 to 1.06 times of those in tube with PTT. An empirical correlation is also formulated to match with experimental data of Nusselt number and friction factor for STT and PTT.