EFFECTS OF ROTATION ON FLOW IN A RIB-ROUGHENED CHAN-

NEL: LES STUDY

D. Borello1, F. Rispoli1, A. Salvagni1, and K. Hanjalic2

1Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Italy 2Delft University of Technology, the Netherlands, and Novosibirsk State University, Russia

domenico.borello@uniroma1.it

Abstract.

We report on large-eddy simulations of fully-

developed flow in a duct of a rectangular cross-

section in which square-sectioned, equally-spaced

ribs, oriented perpendicular to the flow direction,

were mounted on one of the walls. The duct was sub-

jected to clock-wise (stabilizing) and anti-clock-wise

(destabilizing) rotation. We analyzed the effects of

stabilizing and destabilizing rotation on the flow, its

vortical structures and turbulence statistics by com-

paring results with non-rotating case.

1 Introduction

The quest for increasing gas-turbine cycle effi-

ciency by rising the turbine inlet temperature poses

ever new challenges to the design of blade cooling

system (e.g. Saravanamuttoo et al., 2001). Among

various methods, the internal cooling enhanced by

turbulence promoters (pins, ribs, grooves) inside the

blades has proved to be both convenient and effi-

cient. A number of studies of flow and heat transfer

in passages with turbulence promoters can be found

in the literature, but less is known about the effect

of rotation on the flow, vortical and turbulence

structures and heat transfer in such configurations.

Among various options for passive enhancement

of heat transfer, rib-roughened channels and ducts

appear especially popular because of their generic

and simple configuration and straightforward repro-

ducibility both experimentally and computationally.

Several experimental and computational studies ap-

peared recently in the literature dealing with flow

and heats transfer in ribbed ducts of a similar con-

figurations. Tafti (2005) reported on LES of flow

and heat transfer in a non-rotating rectangular duct

with the opposing walls roughened with square-

sectioned ribs at Re=20.000. The focus of the analy-

sis was the role and effect of different subgrid-scale

(sgs) models in predicting the flow and heat trans-

fer. He concluded that dynamic Smagorinsky sgs re-

turns better predictions (here compared with

MILES), and that a 1283 discretisation (about 2.1M

cells) is sufficient for obtaining wall-resolved LES.

Abdel-Wahab and Tafti (2004) performed LES of

flow and heat transfer in the same ribbed duct sub-

jected to rotation. Different rotational numbers (up

to 0.67) were studied. These authors observed that

turbulence and heat transfer was augmented in the

trailing side (destabilizing), whereas the opposite

effect was detected in the leading side (stabilizing)

region. The origin of the heat transfer enhancement

and depression was traced in the influence of the

Coriolis force on the various components of the

Reynolds stress tensor through the production term

related to rotation. It is recalled that the rotational

“production” term in the Re-stress equation is trace-

less, thus it has a redistributive character and it does

not appear in the turbulent kinetic energy nor scale-

providing (scalar) equations. For this reason, the

first-moment (linear eddy viscosity) URANS mod-

els are not appropriate for solving flows with sys-

tem rotation. As for the velocity field Abdel-Wahab

and Tafti (2005) reported that in the rotating cases,

in the trailing (destabilizing) region the recircula-

tion bubble is weakly shrunk, and after a threshold

value it is not reduced at all. On the opposite, on the

leading (stabilizing) region the length of the recircu-

lation region increases with the angular velocity

eventually extending over the most of the region be-

tween the two successive ribs. Another effect of the

Coriolis force is the generation of secondary, coun-

ter-rotating flow cells in the duct cross section af-

fecting the shear layer and consequently the heat

transfer on the smooth walls.

Recently Coletti et al. (2011) reported on exper-

imental investigation of the influence of rotation on

the flow over a rib-roughened wall in a duct of a

rectangular cross-section at the bulk Reynolds num-

ber of 1.5 x 104. Ten square-sectioned, equally

spaced ribs aligned with the rotation axis were

mounted on one of the walls. In addition to the non-

rotating situation, both the clock-wise (stabilizing)

and anti-clockwise (destabilizing) rotation were

considered at the rotation number of 0.3, using the

PIV technique. The measurements were reported for

only for the vertical mid-plane.

This paper reports on large-eddy-simulations of

the Coletti et al. (2011) flows, aimed at providing

additional information that were not measured or

are inaccessible to the experiments. We attempt to

gain some new insights into the effect of stabilizing

and destabilizing rotation with focus on the region

over the ribs.

2 Flow and computational details

Coletti et al. (2011) observed that the flow be-

comes periodic after the 6th rib. We focussed thus on

solving the fully-developed periodic flow at

Re=15,000 mimicking the experiment, and used for

verification the PIV data obtained between 6th and 7th

rib. The solution domain was thus xyz=

100.951.05, where the dimensions are expressed in

hydraulic diameters Dh. The rib height h is equal to

1/10 of Dh. The computational domain is meshed us-

ing an unstructured hexahedral orthogonal grid. The

grid was refined in the region y<2h, where the wake

of the rib is relevant. Three grids were considered:

3.5, 5.8 and 8.8106 (M) cells. The finest grid was

created from the intermediate one by increasing the

refinement in the wake region and the number of grid

points in the spanwise direction (Fig.1).

The LES of the case with clockwise (stabilizing)

rotation showed satisfactory results with the interme-

diate grid, while the other two cases require a finer

meshing. In fact, the non-rotating flow showed to be

most grid-sensitive and satisfactory predictions were

obtained only when using the finest grid. The coun-

ter-clockwise case on the intermediate grid showed a

fair comparison with the experiments, though still not

fully satisfactory. For a fair comparison, the case

with counter-clockwise rotation is currently being

recomputed on the finest grid. The results here re-

ported refers to the intermediate grid (5.8 M) for the

two rotating cases and to the fine grid (8.8M) for the

non-rotating flow.

The grid refinement close to the wall allows to

achieve the wall-nearest y+ value (of the first row of

cells) always smaller than 0.5 (the height of the first

cells row was 0.002 compared with the hydraulic di-

ameter, being roughly 2% of the rib height).

The quality of the grid discretisation is illustrated

in Fig. 2. The first subfigure 2a shows the ratio of the

characteristic LES (sgs) length scale =(xyz)1/3

and the Kolmogorov length scale 3 1/4( / ) in the

mid-span plane for the 5.8 M grid. The scale was

computed using the dissipation rateobtained from a

RANS computation with the k--f model (not dis-

cussed here). The scale ratio is never greater than 10

and it is smaller than 5 in most of the relevant region.

Moreover, the power spectra in Fig 2.b at 6 different

points in the mid-plane show that the resolved grid

scales are well beyond the inertial (-5/3) sub-range.

Finally, the grid spacing for the 8.8 M cells, normal-

ised with the rib height, is depicted in Fig.2.c. The

grid density is very high around the ribs, where x/h

andy/h are always lower than 510-3. In the rest of

the domain the ratio never exceeds 1.510-2. These

values demonstrate that the used discretization is al-

ways finer than the one used by Tafti (2005) for the

LES of non-rotating rib-roughened grid at

Re=20,000. The grid discretization used for the 5.8

M grid (not shown here), shows near-wall spacing

similar with that used by Tafti (2005).

Periodic boundary conditions are set at the inlet

and outlet cross-sections. On the solid walls no-slip

conditions are imposed. The non-dimensional time

step was set equal to 10-4, to maintain the CFL num-

ber always lower than 0.3.

The subgrid-scale (sgs) motion was modelled us-

ing the dynamic Smagorinsky approach. No correc-

tion was included in the sgs model to account for the

rotational effects.

The governing equations, non-dimensionalized by

the hydraulic diameter Dh, the bulk flow velocity and

standard air properties, were solved by the well-

validated in-house unstructured finite-volume com-

putational code T-FlowS from TU Delft (Ničeno and

Hanjalić, 2004), now advanced in Sapienza Universi-

tà di Roma. The code has been used successfully for

LES computations of a variety of flows and heat

transfer (e.g. Delibra et al. 2010, Borello et al. 2013).

A second-order accurate CDS scheme is used for

the discretization of the convection and diffusion

terms. The time integration was carried out using also

a second-order scheme. The velocity and pressure

were coupled using the SIMPLE scheme. The linear-

ized algebraic system of the discretized equations

was solved using the Preconditioned BiCG solver.

The threshold for the global mass balance residu-

al was set to 10-6, while for the momentum and con-

tinuity equations it was 10-7. Simulations were per-

formed on the ENEA-Cresco3 and on CINECA-

Eurora supercomputers using up to 64 cores.

About 40 wall clock hours are required for per-

forming 1 flow-through-time (FTT). After an initial

development interval (equal to 2 FTT), the simula-

tions were averaged over 25 FTT for the clockwise-

rotating case and 15 FTT for the other cases.

3 Results and Discussion

3.1 Time-averaged results

The blockage effect of the rib causes the flow to

accelerate and subsequently to expand after the ob-

stacle. In the centre of the duct the flow is nearly

two-dimensional in the bulk, but with several vortical

systems clearly identifiable: a leading edge vortex at

the rib-wall junction, a large recirculation region be-

hind the rib with a small counter-rotating vortex at

the base of the rib, a recirculation region on the rib

tip, and a recovering boundary layer after reattach-

ment. All these structures are captured in all the LES

computations, Fig.3, in agreement with Abdel-

Wahab and Tafti (2004).

Table 1 compares the recirculation lengths for

the three cases considered, obtained by the present

LES, the experiments of Coletti et al. (2011) and the

LES of Abdel-Wahab and Tafti (2004) at Re=20,000

and Ro=0.18.

Table 1 – Length of the recirculation bubble Bubble length Stab. Non-rot Destab.

Exp 5.65 3.85 3.45

LES 5.60 3.90 3.50

Abdel-Wahab and Tafti ~7.00 4.0 3.6

A broader picture of the velocity field is given in

Fig 3, showing the time-averaged streamlines and

coloured mean velocity field in the vertical mid-

plane. To expose the effect of rotation in the rib-wall-

adjacent area, only a fraction of the cross-section is

shown for y/h<3.0. The LES and PIV plots show fair

agreement for all the configurations considered. As

seen, system rotation strongly affects the flow as a

whole, but the major effect appears in the recircula-

tion regions behind the rib. Presumably, this is in part

due to the direct effect of the bulk Coriolis force in

the momentum equation on the separated shear layer

that would be sensed also in laminar flow, but also by

the indirect contribution of the fluctuating Coriolis

force to the production/redistribution terms in the

Reynolds stress equation. The latter affects the level

of different component of the turbulent stress tensor.

In the destabilizing case the shear layer is pushed up-

stream towards the wall thus contributing to an early

reattachment (Fig. 3.b). The opposite occurs for the

stabilizing rotation (Fig.3c), where the recirculation

bubble is stretched and the recirculation length ex-

tends over more than 60% of the surface between the

two successive ribs. This structure modification will

have a strong effect on heat transfer, as a larger

amount of fluid trapped in the recirculating region

will get heated and lose the capacity to remove heat

from the adjacent wall.

Remarkably, rotation seems to have little effect

on the small bubble in front of the rib, though the

stabilizing rotation shows visibly earlier separation

than in the destabilizing case.

Figure 4 shows a comparison of the LES-

computed mean velocity profiles with the experi-

mental data of Coletti et al. (2011). The latter are

available only for the region close to the ribbed wall.

For an overall impression, Fig. 4 shows also a sketch

of the whole flow configuration with typical flow

patterns and main vortical systems. The agreement

between the computed and measured profiles at five

streamwise locations for all three cases considered

can be regarded as satisfactory. In fact the stabilizing

and the non-rotating cases were reproduced very well

and the destabilizing case reasonably well. The stabi-

lized rotation makes the profiles less turbulent and

the opposite occurs for the destabilizing rotations.

The LES returns very satisfying results especially in

predicting the recirculating boundary layer in the first

measurement sections and the successive develop-

ment downstream from the reattachment point.

Secondary motions pertinent to flows in square-

sectioned ducts play a significant role in removing

fluid (and heat) from the walls. The effects of the

side walls are depicted in Figs 5 and 6, showing the

axial velocity profiles over the whole flow in three

stream-wise vertical cross-sections placed at the

channel mid-plane (z/Dh=0.0), close to one of the

side walls (z/Dh=0.45, the wall being at z/Dh=0.475)

and in a plane in between (z/Dh=0.3) for the non-

rotating flow and for the destabilizing rotation. Three

streamwise locations were considered: at the down-

stream edge of the rib (x/h=0), at the end of the recir-

culation bubble (x/h=4), and in the boundary layer

recovering region (x/h=8).

A common feature of both cases is that, when

moving away from the near rib region (i.e. y/h>0.3),

the velocity profile remains more or less the same at

all streamwise locations considered.

In the non-rotating case (Fig.5) the influence of

the secondary motion is clearly evident. Close to the

lower wall the secondary motions induced by the rib

transport fluid towards the smooth walls. Then, at

z/Dh=0.3 where the influence of smooth wall is weak,

the streamwise velocity is higher compared with the

velocity at z/Dh=0.0. For the same reason, for y/h>0.5

the velocity at z/Dh=0.3 is lower than at the center-

line. Closer to the smooth wall (z/Dh=0.45), the

streamwise velocity is dumped by the lateral bounda-

ry layers.

In the destabilizing case (Fig.6), the increase in

the turbulence level is evident. The boundary layer is

thinner and the velocity distribution much more uni-

form across the channel height. Also in this case, at

y/h=0.3 the velocity is greater than at the centerline.

To illustrate the flow pattern close to the ribs and

in the region in between, the velocity and streamline

distribution in two planes parallel to the lower wall,

(y/h=0.05 and 0.5) are shown in Fig. 7.

Close to the wall (y/h=0.05), the destabilizing ro-

tation results in shrinking of the recirculation bubble,

while the stabilizing rotation produced an opposite

effect, i.e. the bubble elongation. Furthermore, in the

non-rotating case, the recirculation bubble has a

‘bow’ shape reaching the minimum extension close

to the smooth walls (i.e. for maximum and minimum

z values) and increasing when moving toward the

mid-span. On the opposite, in the rotating cases the

presence of secondary flows makes the recirculation

bubble more uniform. The small eddy formed below

the recirculation bubble is also subjected to shrinking

(or extension) when destabilizing (or stabilizing) ro-

tation is imposed. Similar features are noticed in the

plane at the rib mid-height (y/h=0.5).

Fig. 8 show mean velocity field in a flow-normal

cross-section, here at x/h= 4.5. In the non-rotating

flow, Fig.8a shows very regular two structures divid-

ed vertically, whereas the destabilizing Coriolis force

greatly distorts, but strengthens this motion (Fig 8.b

and 8.c) relative to the axial velocity. It is worth not-

ing that in the destabilizing case, the two vortical

structures placed close the two smooth walls are sim-

ilar to the two eddies that are noticed in a rotating

square duct (Fig.8.d). In this simplified case, the vor-

tical structures are also present close to the trailing

surface too, though of a simpler topology (see also

Abdel-Wahab and Tafti, 2004).

Some example of the second-moment statistics

for the non-rotating and destabilizing rotating flows

are shown in Figs 9 and 10. In general the LES re-

sults show a similar qualitative trends as the experi-

ments, though agreement is not fully satisfactory, es-

pecially further downstream at the location x/h=8.

Admittedly, more sampling is needed for gathering

statistics, but the discrepancy could be attributed to

the insufficiently long solution domain (only one pe-

riod); we are currently running the same cases in a

twice longer solution domain encompassing the

length of two rib periods. Nevertheless, an indication

of the strong flow three-dimensionality and of the ef-

fects of the side wall can be envisaged from profiles

shown in the vertical mid-plane and two laterally

displaced planes, all parallel to the flow direction (at

z/Dh=0.0, 0.3 and 0.45). Likewise, the turbulence en-

hancement due to destabilizing rotation is clearly vis-

ible in both figures. Needless to say that the stabiliz-

ing rotation dampens all turbulent stress components

(not shown here).

3.2 Flow unsteadiness

Some illustrations of the instantaneous velocity

and streamlines are given by selected snapshots of

the whole solution domain in Fig.11. In the non-

rotating case the high velocity appears in the core of

the flow (at about y/h=4), where periodic peaks ap-

pear roughly midway between the ribs. Multiple

spanwise vortical rolls appear behind the rib, with

their width exceeding the rib height and thus con-

tracting the flow cross-section. It is symptomatic that

the above mentioned velocity peaks appear roughly

at the positions of the maximum roll thicknesses.

This very unsteady flow is rich on turbulent activity,

but the streamlines remain confined without deliver-

ing fluid into the outer main flow. Similar pattern is

evident also in the clockwise rotation, but here the

rolls are much smaller, less vigorous and less turbu-

lent. The external flow shows smooth and almost un-

deformed streamlines, testifying of the rotation stabi-

lizing effect. High velocity flow is moved toward the

upper wall under the influence of the Coriolis force.

In contrast, in the anti-clockwise rotation case, a vig-

orous turbulence is visible not only close to the

ribbed wall but also in the bulk flow, indicating at a

stronger mixing and momentum (and supposedly also

heat) exchange. The streamlines indicate that fluid is

removed from the wall-adjacent regions towards the

core. Here, the Coriolis force pushes the core of high

velocity to deflect towards the ribbed wall. Similar

effects have been detected in planes close to the lat-

eral (side) wall (not shown here)

4 Conclusions

LES of flow in a rectangular-sectioned ribbed

duct, subjected to stabilizing and destabilizing system

rotation, have been conducted aimed at gaining a fur-

ther insight into the effects of rotation on flow, vorti-

cal and turbulence structures. The simulations were

verified against the PIV measurements in a character-

istic plane. The analysis shows that the destabilizing

(anti-clockwise) rotation enhances turbulence pro-

duction along the ribbed wall, enhances the lateral

mixing and strengthens the secondary motion, which

all enhance momentum (and, presumably, also heat)

transfer. In contrast, the stabilizing Coriolis force

make the whole flow less turbulent, the effects being

especially noticeable in the vicinity of the bottom

ribbed wall (pressure-side). These effects are ex-

pected to profoundly influence heat transfer, the topic

currently studied.

Secondary motions pertinent to flows in rectan-

gular-sectioned ducts play a significant role in re-

moving fluid (and heat) from the walls. Rotation (as

well as ribs and flow separation) modify their struc-

tures. In the non-rotating flow, two very regular

structures appear, being clearly divided vertically. In

contrast, the destabilizing Coriolis force greatly dis-

torts, but strengthens this motion relative to the axial

velocity.

As in turbine blades ribs are placed usually on

both sides of the interior cavities, both rotation cases

are relevant for the practical design of gas-turbine

blade cooling.

References

Abdel-Wahab, S. and Tafti, D. K. 2004, Large eddy

simulation of flow and heat transfer in a 90° ribbed

duct with rotation – Effect of Coriolis forces, Turbo-

Expo 2014, June 14-17, Wien, Austria.

Borello, D., Salvagni, A., Rispoli, F. and Hanjalic, K.

(2013) LES of the flow in a rib-roughened duct,

DLES 9, 3-5 April, 2013, Dresden, Germany

Coletti, F., Maurer, T., Arts, T. & Di Sante, A.

(2011), Flow field investigation in rotating rib-

roughened channel by means of particle image veloc-

imetry, Exp. Fluids, 54(9), n.1589.

Delibra, G., Borello, D., Hanjalic, K. and Rispoli, F.

(2010), Les of flow and heat transfer in a channel

with a staggered cylindrical pin matrix, Direct and

Large-Eddy Simulation VII, Springer.

Tafti, D. K. (2005), Evaluated the role of subgrid

stress modelling in a ribbed duct for the internal cool-

ing of turbine blades, Int. J. Heat and Fluid Flow,

Vol. 26, pp. 92-104.

Niceno, B. and Hanjalic, K. (2004), Unstructured

large-eddy and conjugate heat transfer simulations of

wall-bounded flows, in Modeling and Simulation of

Turbulent Heat Transfer, WIT Press. 3573.

Saravanamuttoo, H.I.H., Rogers G.F.C. and Cohen,

H., 2001, Gas Turbine Theory, 5th Edition, Prentice

Hall.

a) b)

Fig. 1: Grid discretisation - details of the cross planes: a) 5.8 Million cells; b) 8.8 Million cells

Fig. 2: Assessment of the quality of the LES predictions: left – ratio in the mid plane center – energy spectra;

right variation of the grid spacing (for the finer grid).

Non-rotating

Destabilizing rotation

Stabilizing rotation

Fig. 3: Comparison of LES and PIV streamines and velocity field (colour-bar) in the central vertical plane: left non-

rotating; center stabilizing; right: destabilizing. Remark: non-rotating configuration has finer grid (8.8M cells)

Fig. 4: Top left: sketch of the flow configuration (from Coletti et al. 2011). Mean streamwise velocity profiles at x/h

LES

=0, 2, 4, 6 and 8: Symbols: experiments (PIV, Coletti et al. 2011); lines: present LES.

Fig. 5: Non-rotating case. Mean streamwise velocity profiles at x/h =0, 4 and 8: Symbols: experiments (PIV, Coletti et

al. 2011); lines: LES.

Fig. 6: Destabilizing case. Mean streamwise velocity profiles at x/h =0, 4 and 8: Symbols: experiments (PIV, Coletti et

al. 2011); lines: LES.

Non-rotating

Destabilizing rotation

Stabilizing rotation

Fig. 7: Velocity and streamlines in two planes parallel to the lower (rib-roughened) wall: top y/h=0.05; bottom: y/h=0.5

a

b

c.

d.

Fig. 8 Mean velocity in the the y-z plane at x/h=4.5: a-no rotation, b-clockwise, c-anti-clockwise; d:

rotating square duct (different velocity scale)

Ω=0

Ω>0

Ω=0

Ω>0

Fig. 9: The streamwise (top) and wall-normal (bottom) turbulence intensity component for the non-rotating (Ω=0) and

destabilizing rotating case (Ω>0). Symbols: Experiments (Coletti et al, 2011). Lines: simulations. Chain line: z/D=0,

full line: z/D=0.3, dotted line: z/D=0.45

Ω=0

Ω>0

Fig. 10: Turbulent shear stress component uv for the non-rotating (Ω=0) and destabilizing rotating case (Ω>0). Sym-

bols: Experiments (Coiletti et al, 2011). Lines: simulations. Chain line: z/D=0, full line: z/D=0.3, dotted line: z/D=0.45

Fig. 11: Instantaneous streamlines and velocity profiles at mid-plane for the three configurations: left –non-rotating;

centre – clock-wise; right – anti-clockwise

a

b

c

Fig. 12 Instantaneous velocity field in the y-z plane at x/h=4.5: a-no rotation, b-

clockwise, c-anti-clockwise