Manipulation of turbulent flow for drag reduction and heat transfer enhancement 5

However, as a result of the more rapid rise ofthe friction factor than Nusselt number, the performance factors very soonreach their asymptotic limit and even start to decrease at larger

Chapter 5

In this chapter, heat transfer characteristics and flow structures overprotrusions in a turbulent channel flow are systematically investigated byDES numerically The thermal-hydrodynamic performances are also closelyexamined, including Nussselt number, friction and performance factor, andthe effect of changing the height ratio Additionally, the distribution

of friction factors and Nusselt number are studied with the objective

of providing the connectivity, if any, between them and the flow/vortexpatterns over the protrusion

In this chapter, fluid flows inside a channel with length L, width W and height 2H in the x, z and y direction, respectively (Figure 5.1) For all the

cases discussed here, only the lower wall consists of protrusions, while the

1Part of this chapter has been published as Chen et al (2012b)

upper wall is always flat The protrusion’s print diameter is a constant at

D = 5H, and its height h varies from 5%D to 25%D.

X Y

Z

2H

L W

D

h

Figure 5.1: Channel with protrusions

The spherical protrusion with smooth rounded edge (see Figure 5.2)considered in the present chapter is the inverse of the dimple case fromChapter 4 The geometry of protrusion can be described by the followingheight functions:

D=2XEd2XI

r

h

Figure 5.2: Sectional drawing of a single protrusion

R, h, d and r are, respectively, the protrusion’s radius of curvature in

inner region, height, nominal diameter and rounded edge’s radius Otherparameters are given by the following equations:

For the cases in which there are N protrusions on the channel floor,

the composite height function is given by the summation of the individualheight functions:

where Y = 0 indicates the center plane of the channel, and Y = −H

indicates the flat portion of the channel floor where the protrusions reside

The dimpled surface in Chapter 4, which is used to compare withprotrusions, has the same dimension with the protrusions except that thedimpled portion is below the flat plate instead of above the flat plate forthe protrusion

In this chapter, eight protrusions are closely placed in a staggered pattern

on the lower wall of the channel to study the interaction between boring protrusions, and the upper wall is smooth and flat (see Figure 5.1)

neigh-As such, a channel with length L = 10 √

3, width W = 10 and half channel height H = 1 is taken as the main/working computational domain The

grid resolution of current study is 160× 128 × 96, so the grid size is fairly

similar to that of mesh 3 in Table 2.3 albeit slightly better resolution forthe protrusion features In this section, heat transfer and flow structure

over protrusions with different height ratios (h/D = 5%, 10%,15%, 20%,

25%) are presented and discussed

The normalized average friction ratio C f /C f 0, Nusselt number ratio

with various height ratios are shown in Figure 5.3 and compared with

those obtained for dimpled surface taken from Chapter 4 It is observed

from Figure 5.3(a) that protrusions with larger height ratio (h/D) produce

higher heat transfer rate and friction It can be also seen that the friction

ratio C f /C f 0 increases much more rapidly than the Nusselt number ratio

to the acceleration of main flow with reduced flow cross-sectional area andthe flow instability induced by vortices As shown in Figure 5.3(c), with

the increase of height ratio, the performance factors (Ga/Ga0 and Gv/Gv0)also show an initial increase However, as a result of the more rapid rise ofthe friction factor than Nusselt number, the performance factors very soonreach their asymptotic limit and even start to decrease at larger height

application of dimple or protrusion for enhanced heat transfer The present

finding suggests that the optimum depth/height ratio (h/D) to achieve the

(d) performance factors for dimples

Figure 5.3: Effect of h/D on Nusselt number, friction coefficient and performance factors: h/D stands for height ratio for protrusion, while it

stands for depth ratio for dimple

highest volume goodness factor (Gv/Gv0) are around 15%–20% for both

the protrusions and dimples arrangement Higher volume goodness factorherein means that implementing protrusions reduces the volume of heatexchanger, although the area goodness factors are comparable which meansthe surface area of the heat exchanger is still similar

The distributions of local average friction factor C f (comprising the

components of time averaged skin friction Sm and form drag F m) and

Nusselt number on protrusions with different height ratios are presentedand discussed in this section

5.2.2.1 Skin friction

The normalized skin friction Sm/Sm0 distribution on protrusions is sented in Figure 5.4 It is shown that two local highest skin friction (redregion) are located at the upstream portion of protrusion while the lowestskin friction (blue region) is found around the downstream centerline ofprotrusion It can be observed that the skin friction on protrusions withlarger height is generally larger than that on protrusions with lower height.The distribution of skin friction factor significantly depends on the height

pre-ratio of protrusion h/D In particular, two local highest skin friction

positions are located fairly symmetrically about the streamwise centerline

of protrusion when height ratio is low (h/D ≤ 10%) Conversely for

h/D ≥ 15%, the value of skin friction distributes asymmetrically about

the streamwise of protrusions, especially for the local highest skin friction

at the upstream portion As such, the local highest skin friction as found

on one side (which can be on the left or right side, depending on the initialinput conditions, see §5.2.2.4) is higher than the other side of upstream

portion of protrusion when h/D ≥ 15%.

The normalized form drag F m/Sm0 distribution on protrusions is sented in Figure 5.5 It is shown that the single highest form drag (redregion) is located at the upstream portion of protrusion while the lowestform drag (blue region) is found around the downstream centerline ofprotrusion It can be observed that the form drag on protrusions with larger

(e) 25%

Figure 5.4: Normalized friction Sm/Sm0 at different height ratios h/D

height is generally higher than that on the protrusions with lower height.

It can be also found that the form drag distributes fairly symmetricallyabout the streamwise centerline of protrusion when height ratio is low

(h/D ≤ 10%) Conversely for h/D ≥ 15%, the form drag distributes

asymmetrically about the streamwise centerline of protrusions However,the asymmetry of form drag distribution is less obvious than that forfriction drag Being so, the highest form drag is found at a position slightlyoffset from the upstream centerline of protrusions (arbitrary offset, either

on the left or right side, see §5.2.2.4).

To further investigate the influence of protrusions on the heat transfer, thenormalized Nusselt number distribution on protrusions is presented in Fig-ure 5.6 It is shown that the highest Nusselt number (red region) is located

at the upstream portion of protrusion while the lowest Nusselt number(blue region) is found around the downstream centerline of protrusion Itcan be observed that the Nusselt number for the protrusions with largerheight is generally higher than that on the counterpart with lower height

It can be also found that Nusselt number distributes fairly symmetricallyabout the streamwise centerline of protrusion when the height ratio is low

(h/D ≤ 10%), and there exists two local highest Nusselt number located

on the two sides of centerline of protrusions Otherwise (h/D ≥ 15%), the

Nusselt number distributes asymmetrically about the streamwise centerline

of protrusions Being so, the highest Nusselt number is found on one singleside (either on the left or right side, see §5.2.2.4) of upstream portion of

(e) 25%

Figure 5.5: Normalized friction F m/Sm0 at different height ratios h/D

the protrusion In addition, the location of the highest Nusselt numbergenerally coincides with the location of both the highest skin friction andform drag.

(e) 25%

Figure 5.6: Normalized Nusselt number Nu/Nu0 at different height ratios

h/D

5.2.2.4 Effect of initial conditions for protrusions with h/D =

20%

It is noticed that the highest skin friction, form drag and Nusselt numberare located on one side of protrusions if the height is sufficiently large

(h/D ≥ 15%), hence leading to asymmetric distribution To further

verify this finding and to ascertain what affects the location of the highesthydrodynamic and thermal factors, more computational runs were carried

out for the flow and heat transfer over protrusion at h/D = 20% with

different initial conditions imposed The results obtained are shown inFigure 5.7

The initial condition is set as follows:

So the random perturbation component ε N (0, 1) determines the

initial condition, which does affect the final result It is found that the localhighest skin friction, form drag and Nusselt number may be found at eitherside of protrusions subject to the initial conditions The distributions ofhydrodynamic and thermal factors for the original run (shown in earliersections) and the subsequent run are generally opposite Additionally,extra runs caried out which are not shown here indicate that the highestlocalized factors are found at arbitrary side of centerline; these locations areessentially mirror images of each other on the respective side These implythat the asymmetrical location of the highest Nusselt number generallyonly depends on the initial condition because all the other parameters arekept the same for these runs

What we have observed can be broadly classified as bifurcation nomenon, which is inactive or insignificant when protrusion is low andbecomes active or important when the protrusion is high Furthermore,the locations of the highest skin friction, form drag and Nusselt numberare found on the same side of the protrusions, thus implying the strongconnectivity between them To understand better the possible mechanismsfor such asymmetric distribution of hydrodynamic and thermal factors, thevarious quantities on streamlines, vortex structures and velocity contoursare studied and discussed in the next section

Figure 5.7: Normalized skin friction Sm/Sm0, form drag F m/F m0 and

Nusselt number Nu/Nu0 at h/D = 20%

5.2.3 Flow structure

In order to explore the underlying mechanisms for the asymmetric bution of hydrodynamic and thermal factors over protrusions with largeheight ratio, the associated flow structures are studied in some greaterdetails For simplicity but without loss of generality, only the cases with

distri-height ratio h/D = 10% and 20% are compared and shown.

In this section, the mean flow field (streamlines) based on time averagedvelocity field are investigated The streamlines in the vicinity of the

protrusions (y+ = 1.5) for the cases with height ratio h/D = 10% and

20% are compared in Figure 5.8 The fluid bifurcates at the upstream edge

of protrusions, and then flows through the valleys between protrusions.Thereafter, fluid starts to recirculate, forming vortex structure behindprotrusions However, these vortex features are symmetric when the heightratio is low, but asymmetric when the height ratio is large The asymmetricflow and vortex pattern in deep dimples, which was also observed by Kornev

et al (2010), was believed to enhance heat transfer more than symmetricflow in shallow dimple This may be a cause of higher heat transfer rate

on higher protrusions other than blockage effects as introduced by Hwang

et al (2008)

According to the Taylor’s hypothesis, the evolution of flow patternalong the mean flow direction can present the temporal evolution of fluidflow In order to examine what happens to the vortical flow over the

Figure 5.8: Streamlines on y+ = 1.5 at different height ratios h/D

protrusions, 3-dimensional streamlines are shown in Figure 5.9 For aclearer presentation of the 3D streamlines, the streamlines are colored by

vertical position Y In order to show the whole evolution cycle of fluid

flow over protrusions, Figures 5.9(a) and (b) depict the behavior of thefluid before these vortices are generated; on the other hand, Figures 5.9(c)and (d) show the behaviors of fluid after these vortices are generated.Specifically, Figures 5.9(a) and (b) are streamlines traced backwards fromthe series of markers between the last two row protrusions; on the otherhand, Figures 5.9(c) and (d) are streamlines traced forwards from the series

of markers between the first two row of protrusions Similar to planar 2Dstreamlines above, it is also found in Figure 5.9 that the fluid bifurcates

at the upstream edge of protrusions, and then recirculates and is lifted

up, hence forming the vortex structure However, the patterns of thestreamlines differ for protrusions with different height ratios both beforeand after the vortices are generated

Before the vortices are generated, the fluid sweeps down to the valley

between the neighboring protrusions from the center plane of channel (Y =

0) The number of the coming flow groups before vortices are generated over

the low protrusions is four, but the counterpart over the high protrusions

is two This may be due to the symmetric and asymmetric flows over thelow and high protrusions: for symmetric flow pattern over low protrusions,two groups of flow can merge into one flow group inside the valley betweenprotrusions; for asymmetric/inclined flow, only one group of incoming flowcan enter the valley between protrusions However, the angle of sweep ofthe flow over protrusions with larger height ratio is much larger than thatover the low protrusions, hence resulting in a stronger mixing between thefluid in the center region and near-wall region This partially explains thehigher Nusselt number observed for the higher protrusions

After the vortices are generated: (i) for low protrusions (h/D =

10%), the vortices are relatively less intense and symmetric, so they aretransported through the valley of next row of protrusions; (ii) for high

protrusions (h/D = 20%), the vortices are more intense and asymmetric,

so they flow directly downstream and then impinge on one side of the nextrow of protrusions As a result of the different behavior of vortices abovethe protrusions at different height ratios, the Nusselt number distribution

is symmetric for low protrusion geometry (h/D = 10%) while asymmetric for high protrusion geometry(h/D = 20%) Furthermore, the positions of the highest Nusselt number for the high protrusion (h/D = 20%) coincide

with the impingement between vortex and protrusion wall There is moreintense mixing between the center region of channel and near-wall region,and stronger vortices which impinge the downstream protrusions have led

to higher Nusselt number for protrusions with larger height ratio

It is also worthwhile to further investigate the impingement and

1 2

(b) before vortex generation at h/D =

Z Y: -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(d) after vortex generation ath/D = 20%

Figure 5.9: 3-D streamlines at different height ratios h/D, the dashed line

refers to the streamline tracing markers, the fluid flows from left bottomcorner to right top corner

culation regions, respectively, in the upstream and downstream portions ofprotrusions For simplicity but without loss of generality, only streamlines

for the cases with height ratio h/D = 10% and 20% are compared in Figure

5.10 It is found that there is recirculation behind the protrusion around

the centerline (Z = 5) It can also be observed that the recirculation for higher protrusion (h/D = 20%) is stronger than that for lower protrusion (h/D = 10%) On the upstream portion of protrusion, the streamlines

follows the surface profile of the protrusion on the wind-ward side and overthe top and then join the freestream In addition, the higher protrusiontends to trigger more intense mixing between the center region of channeland near-wall region than the lower protrusion does In general, the intense