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Direct numerical simulation of flow in stenotic channel to understand theeffect of stenotic morphology on turbulenceKiran Bhaganagar a

a Department of Mechanical Engineering, University of Texas, San Antonio, Texas, USA

First published on: 09 December 2009

To cite this Article Bhaganagar, Kiran(2009) 'Direct numerical simulation of flow in stenotic channel to understand theeffect of stenotic morphology on turbulence', Journal of Turbulence, Volume 10, Art. No. N 41,, First published on: 09December 2009 (iFirst)To link to this Article: DOI: 10.1080/14685240903468796URL: http://dx.doi.org/10.1080/14685240903468796

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Journal of TurbulenceVol. 10, No. 41, 2009, 1–16

Direct numerical simulation of flow in stenotic channel to understandthe effect of stenotic morphology on turbulence

Kiran Bhaganagar∗

Department of Mechanical Engineering University of Texas, San Antonio, Texas, USA

(Received 6 March 2009; final version received 17 October 2009)

A fundamental fluid dynamics study has been performed in order to understand the effectof shape of blockage in a stenotic channel on turbulence flow characteristics using directnumerical simulation (DNS) as a tool. DNS has been performed for four canonical typeswith identical degree of blockage (stenosis) but with varied morphological forms. Theresults revealed large-scale and small-scale features of the flow represented by the rootmean square (rms) of velocity and vorticity statistics are type-dependent. The turbulentstructures exhibited characteristic structures and mechanics very specific to the typeof blockage. The analysis indicates that for given degree of stenosis, the turbulencecharacteristics are significantly dependent on the morphology of the blockage, andhence to quantify turbulence flow characteristics in stenosed channel, the stenosis shapeis an important metric that needs to be considered. The results of this study are directlyrelevant to the flow dynamics in diseased stenotic coronary artery, in the context ofthe importance of stenotic morphology in addition to the height of the stenosis as animportant indicator for the prediction of the flow dynamics in diseased coronary artery.

Keywords: roughness; direct numerical simulation; turbulent boundary layers

1. Introduction

Turbulent flow in a stenosed channel has been studied as a fundamental fluid dynamicsproblem as well as in various applications of fluids in environmental and bio-engineeringapplications. In literature, the stenosed (obstructed/blocked) channel has been representedas the flow over rough wall in a channel/pipe. The underlying idea is that the geometricalobstruction (such as surface roughness) or blockage results in the modification of theflow dynamics, which is of great interest to fundamental fluid dynamician as well as tobiomedical or environmental engineer for prediction of the flow properties/physics dueto the obstruction/blockage. To understand the effects of surface roughness on turbulentflow in a channel, significant experimental and numerical investigations under idealizedlaboratory setting have been performed by various groups [1, 5, 6, 10, 16, 18, 30]. It is wellaccepted that the inner layer of the turbulent boundary layer is significantly altered due tosurface roughness. This results in modification of first-order statistics of velocity, vorticityand pressure fluctuations in inner layer due to rough walls. The depth of the roughnesssublayer and wall-normal extent of influence of roughness has been characterized in termsof the roughness height (k) [15, 30]. One of the important off-shoot of these studiesis that in addition to the geometrical height of the surface roughness, its shape has a

Email: kiran.bhaganagar@utsa.edu

ISSN: 1468-5248 online onlyC© 2009 Taylor & Francis

DOI: 10.1080/14685240903468796http://www.informaworld.com

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2 K. Bhaganagar

profound influence on the nature of the flow physics. However, it is not clear which ofthe flow characteristics or features are significantly altered and which of these features areindependent of the shape.

An interesting application in which understanding the flow distal to the blockage isof critical importance is the flow in a diseased coronary artery. During the course ofthe coronary artery disease plaques form on the artery walls, the disease is initiated bydeposition of fatty material in the coronary artery resulting in the accumulation of streaksof plaques on the artery walls. These plaques result in a localized blockage or stenosis ofthe artery. The height of this blockage is generally referred to as the degree of stenosis.The degree of stenosis is an important indicator of the severity of stenosis. As of now, thesignificance of the morphological features of the blockage on the severity of the stenosis,though of obvious importance, is still not clear. From a fluid dynamics perspective, the flowin a normal artery is laminar in nature. Genesis of turbulence occurs when the stenosis isatleast 20% of the half height of the channel [9, 20, 25, 26]. It is known that flow undergoesa transition from laminar to a turbulence state in regions distal to the stenosis and turbulenceis the characteristic flow dynamic feature in the diseased coronary artery [12, 14, 22, 24, 26,32]. The real coronary flow dynamics in diseased stenotic artery poses several challengesin that the flow is pulsative [29], the geometry is pipe flow with loss of symmetry [21, 29,35], presence of geometrical bifurcations and vessel compliance [4].

In coronary hemodynamics, one of the important issue that remains unclear is therelationship between the flow characteristics and the geometrical parameters that definethe severity of the stenosis [31]. Under laminar flow assumptions, Stroud et al. [33] havedemonstrated that for idealized test cases with identical degree of stenosis, axisymmetric,and nonaxisymmetric lesions exhibited significantly different flow fields and wall sheardistributions. Their recent analysis under turbulent flow conditions have also demonstratedsensitivity of flow parameters to geometrical features of the stenosis [34]. Their study haslead to profound interpretation suggesting the importance of plaque morphology ratherthan a degree of stenosis criterion to characterize the flow. It is becoming clear that degreeof stenosis or the height of the blockage is not a true representation of the characteristicsof turbulence, and suggests a need to explore the dependence of the flow features onthe morphological features of the blockage. It is still not clear which of the turbulencecharacteristics are dependent on the plaque morphology.

This research is targeted toward an important goal: Under idealized conditions of chan-nel geometry and turbulent conditions, the effect of the shape of the blockage on turbulencecharacteristics will be explored. If the shape of the blockage has a significant effect onthe flow dynamics under these ideal conditions, it is very likely that with the presence offlow pulsativity, vessel compliance, the effects would, nonetheless, be more significant, thussuggesting the need for direct numerical simulations (DNS) with realistic morphologiesrather than the simple morphologies being currently used in the community to quantifythe severity of the disease. Hence, this fundamental fluid dynamic study will serve thefollowing two important purposes: (1) address a core fluid-dynamic question on the effectof shape of the blockage in a stenosed channel with turbulent flow conditions, (2) whetherthe need to perform expensive and complicated DNS to understand coronary flow dynam-ics is justified. The study focuses on four different types of blockages, namely, protruding,ascending, descending, and diffused. The motivation of selecting these particular blockagesis the outcome of the recent work of the author (see [3]). This research is justified as thepurpose is not to predict the complicated flow dynamics in a diseased coronary artery, butrather to justify the need for including the shape of the blockage in predicting the turbulencecharacteristics distal to the stenosis. Further, using the channel geometry is justified for this

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Journal of Turbulence 3

Figure 1. Sketch of the four types of blockage configurations introduced in the channel: type 1 –peak valley, type 2 – ascending, type 3 – descending, and type 4 – diffuse.

purpose: study conducted by [36, 37] associated with transitional pipe flow has revealedturbulent structures very similar to that observed in turbulent channel flow studies of Liuet al. [17] at low Reynolds number. Further, a recent study of Monty et al. [23] has revealedinteresting similarities in the nature of large-scale dynamical features in turbulent pipe andchannel flows, which is of direct relevance in this present study.

DNS is the most accurate method to simulate turbulence exactly by resolving allthe scales accurately. With the current advances in computational resources, and withnovel numerical methods such as immersed boundary methods (IBM) [38], it is becomingfeasible to use DNS to simulate complex geometries such as surfaces with arbitrary three-dimensional roughness and other complex geometries [13]. DNS of the channel flow forvarious types of roughness elements have been successfully performed for 3-D “egg-cartonroughness” [5, 6, 16]; 2-D and 3-D roughness [2, 27, 28] and for riblets [19], to namea few.

The present paper addresses a fundamental fluid dynamic issue: which of the turbulencecharacteristics are altered due to differences in blockage-morphology for a fixed height ofthe blockage in a stenotic channel. An extremely accurate, high-order DNS is performed forflow in a stenotic channel with four different types of canonical roughness (Figure 1). Werefer to type 1 as blockage with peak-valley pattern, type 2 as blockage with ascending orincreasing slope pattern, type 3 as blockage with descending or decreasing slope pattern, andtype 4 comprised those blockage with constant slope or diffuse in extent. We are interestedto determine, under turbulent flow conditions which of the turbulence characteristics andmechanisms are morphology-dependent, and which are not? This study will provide furtherunderstanding of turbulence characteristics in a stenosed channel from a morphologicalperspective.

The paper is organized as follows. Section (2) discusses the details of the numericalmethodology. The results are presented in section (3), and the discussion is presented insection (4).

2. Numerical methodology

DNS is the most accurate way to simulate a turbulent flow, as the flow field is solved directlyfrom the exact Navier–Stokes equations without any form of averaging or modeling ofturbulence quantities (closure parameters).

Direct numerical flow solver has been developed to simulate turbulent flow in a chan-nel with rough walls using an IBM. The blockage in the channel has been introducedas prescribed surface roughness on the lower wall of the channel. The governing fluidflow equations are the three-dimensional incompressible Navier–Stokes equations. The

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4 K. Bhaganagar

flow equations are calculated on the regular geometry of a periodic channel. The Navier–Stokes equations are expressed in vertical velocity and vertical vorticity formulation [7].The blockage is prescribed within the channel as a function of the streamwise (x) andspanwise (z) variables at a specified virtual surface. A no-slip condition is imposed at thisvirtual boundary via a body force term. For purposes of defining the body force, a first-ordertemporal discretization of the Navier–Stokes equations is employed:

un+1 − un

�t+ un · ∇un = −∇pn + ν∇2un + fn, (1)

where fn = (fx , fy , fz)n is the body force, u = (u, v, w) the velocity vector, p the pressure,ν the kinematic viscosity, �t the time-step increment, and the superscripts n and n + 1respectively indicate the current and next time level. On the immersed boundary σ (x, z),the velocity is zero, such that

un+1 = (0, 0, 0) (2)

and the body force is approximated as

fn = V − un

�t+ un · ∇un + ∇pn − ν∇2un, (3)

where V = (0, 0, 0). The time-dependent body force has been applied at a set of two points,the one just below the immersed boundary and the one just above. (When the boundarycoincides with the grid, the body force is applied at the boundary and at a point below.)This method gives flexibility in choosing the immersed boundary not found in some othermethods, since there is no need to line up the boundary with a grid. Fourier series areused in the streamwise and spanwise directions. In the wall-normal direction a fourth-ordercompact finite-difference scheme is used.

The spatial discretization consists of 256 streamwise Fourier modes, 257 wall-normalcompact finite-difference grid points of fourth-order accuracy and 256 spanwise Fouriermodes. In the wall-normal direction, nonuniform mesh was used. The grid spacing variedfrom 0.94 wall units (based on uτ at the rough wall) adjacent to the virtual no-slip surfaceto 6.5 at the centerline. In the horizontal directions �x+ and �z+ was approximately15 and 8 wall units respectively. The code has been thoroughly validated for flow in aturbulent channel with rough walls consisting of “egg-carton” roughness elements. Referto Bhaganagar et al. [5] for validation results.

3. Turbulence flow characteristics

The height and the width of the channel were chosen to be 4 mm each. The length of thechannel (x) was selected as 24 mm, such that the blockage is prescribed midway (x = 6 –18 mm). Roughness (or the blockage) is prescribed on the lower wall of the channel. The fourtypes of blockages are shown in Figure 1. Turbulent initial conditions (consisting of smooth-wall simulations for identical Reynolds number) were imposed for the entire computationaldomain and the simulations were performed for a long time (40 nondimensional timeunits) till converged statistics were obtained. Simulations were performed on a parallelsupercomputer consisting of 34 nodes with a total simulation time for each case of roughly

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Journal of Turbulence 5

U/uτ(upper)

y/δ

0 10-1

-0.5

0

0.5

1

type1type2type3type4

Figure 2. Mean velocity profiles scaled by uτ plotted against wall-normal distance scaled by thechannel half-height (δ) for types 1–4.

two–three days. The simulations have been performed for the four types with identicaldegrees of stenosis of 25% (h/δ = 0.25) at Re = 3000. This corresponds to h+ of 36 wallunits. Where h is the height of the roughness (or the blockage), δ is the channel half-height,Reynolds number is based on mean velocity and δ.

Turbulent statistics including mean velocity, root mean square (rms) velocity and vor-ticity fluctuations and turbulent kinetic energy (TKE) budget were evaluated. The turbulentvelocity and vorticity structures in the x–y and y–z planes were analyzed to understand thedifferences in flow features between the blockage shapes.

3.1. Mean velocity

Figure 2 shows the mean velocity profiles for all four types. The mean velocity scaled bywall-shear velocity uτ is plotted against the wall-normal distance scaled by the channelhalf-height. The mean velocity has been computed by averaging over time as well as thestreamwise and spanwise directions. For all the types, due to the presence of the roughnesson the lower wall of the channel, the symmetry between the upper- and lower-walls is nolonger present, resulting in shift of location of maximum mean velocity (centerline velocity)from the center of the channel ( y

δ= 0) toward the upper half of the channel. This shift is

about the same for all the types. Closer to the lower-rough wall, differences between thefour types is apparent. Away from the rough wall, the mean profiles are indistinguishable.This leads to a conclusion that the region in the vicinity of the roughness plaque is directlyaffected by the plaque morphology. The maximum mean velocity, and it location appearto be dependent only on the height of the plaque (degree of stenosis) and independent ofother morphological features.

3.2. Root mean square velocity fluctuations

The higher order statistics are examined next. Of particular interest are the turbulentintensities for velocity and vorticity, since the behavior of the former allows us to infer howroughness affects the largest scales of motion, while that of the latter indicates how it alters

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6 K. Bhaganagar

urms/uτ(upper)

y/δ

0 2-1

-0.5

0

0.5

1

type1type2type3type4

Figure 3. Rms of u (streamwise) velocity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

the small-scale features. Figure 3 shows the rms of u (streamwise) velocity fluctuationsscaled by uτ , for all the four types plotted against wall-normal distance scaled by channelhalf-height. In the lower half of the channel, the profiles are distinctly type-dependent.The effect of plaque morphology on rms of u fluctuations is quite significant compared tothe mean velocity. Types 2 and 3 exhibit larger peak value compared to types 1 and 4. Thelocation of this peak velocity is roughly the same for all the types other than type 2, whichis moved further away from the wall. The influence of the roughness is not present on theupper wall of the channel, thus supporting our assumption of a channel with lower-roughwall and upper-smooth wall, and that the effects of the roughness are not experiencedon flow near the opposite wall. Figures 4 and 5 show the rms of v (wall-normal) and w

(spanwise) velocity fluctuations scaled by uτ respectively plotted against the wall-normaldistance scaled by the channel half-height. Similar to the rms of u velocity fluctuations,the shape of the stenosis also has a significant effect on the rms of v velocity fluctuations.The peak v fluctuations for types 1 and 3 are enhanced compared to types 2 and 4. Similarly,the magnitude of the peak w fluctuation is type-dependent. All the four types exhibit similartrends in terms of profile but show differences in the location and magnitude of peak values.From the rms of velocity fluctuations, it can be concluded that for identical height of theroughness (degree of stenosis/blockage), the large scale features of the flow are stronglytype-dependent.

3.3. Rms vorticity fluctuations

The behavior of the small scales can be revealed by the rms vorticity fluctuations. InFigures 6, 7, and 8, rms of streamwise (ωx), wall-normal (ωy) and spanwise (ωz) vorticityfluctuations components are normalized by uτ and they are plotted in terms of wall-normaldistance scaled by channel half-height. The profiles of rms of streamwise and wall-normalvorticity for all the four types are very similar suggesting that they are independent of theroughness types. On the other hand, the profiles of rms of ωz are distinctly type-dependentin the lower half of the channel. Type 1 exhibits strong peak value, this is followed by type3, type 2 and type 4 respectively. From the rms of vorticity fluctuations it can concludedthat rms of ωx and ωy are dependent only on the plaque height. Whereas, rms of ωz shows

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Journal of Turbulence 7

vrms /uτ

y/δ

0 1 2 3-1

-0.5

0

0.5

1

type 1type 2type 3type 4

Figure 4. Rms of v (wall-normal) velocity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

a dependence on other morphological factors of the blockage (roughness) in addition to itsheight.

3.4. Turbulent kinetic energy budget

To obtain a better understanding of the nature of the mechanisms involved, the TKE budget isinvestigated for the four types. The TKE budget consists of the four important mechanismsinvolved, namely, turbulence production (P), transport due to viscous effects (D), transportdue to turbulence fluctuations (T) and the balance is the turbulence dissipation. Figures 9(a),(b), (c), (d) shows the TKE budget for types 1, 2, 3, 4 respectively. All the four types show a

wrms/uτ(upper)

y/δ

0 2 4 6-1

-0.5

0

0.5

1

type 1type 2type 3type 4

Figure 5. Rms of w (spanwise) velocity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

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8 K. Bhaganagar

ωx

y/δ

0 0.2 0.4 0.6-1

-0.5

0

0.5

1

type 1type 2type 3type 4

Figure 6. Rms of ωx (streamwise) vorticity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

similar trend with regards to turbulence production (P). The peak value on the rough side ismore or less similar to that on the smooth-side. The extent to which production is dominantfor types 1, 2, and 3 is y

δis 0.4, and for type 4 is 0.2. Types 2, 3, and 4 exhibit more or less

production of similar peak magnitudes. On comparing the transport of TKE due to turbulentfluctuations, type 1 shows they are significantly enhanced and modified. Near the wall, thetransport is directed toward the wall, further from the wall, the transport is directed awayfrom the wall. A similar trend is observed for the other types. On comparing the transportof energy due to viscous forces it is seen that this transport is smaller fraction compared toturbulent transport. The TKE budget shows that the four types exhibit a similar trend butthe magnitude, direction, and extent of these mechanisms are strongly type-dependent.

ωy

y/δ

0 0.2 0.4 0.6-1

-0.5

0

0.5

1

type1type2type3type4

Figure 7. Rms of ωy (wall-normal) vorticity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

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Journal of Turbulence 9

ωz

y/δ

0 0.2 0.4 0.6-1

-0.5

0

0.5

1

type 1type 2type 3type 4

Figure 8. Rms of ωz (spanwise) vorticity fluctuations scaled by uτ plotted against wall-normaldistance scaled by channel half-height (δ) for types 1–4.

3.5. Turbulent flow structures

Next, the turbulent structures are analyzed by examining u, v, w velocity fluctuations inx–y and y–z planes at an instantaneous time.

For type 1, Figure 10(a) (top figure) shows the u velocity contours in the x–y planeof the channel at z = 2.0 mm. In the wall region surrounding the plaque, shear layers

y/δ-0.75 -0.5 -0.25 0 0.25 0.5 0.75

-0.2

0

PTV

y/δ-0.75 -0.5 -0.25 0 0.25 0.5 0.75

-0.2

0

PTV

y/δ

y/δ

-0.75 -0.5 -0.25 0 0.25 0.5 0.75

-0.2

0

PTV

y/δ-0.5 0 0.5

-0.2

0

0.2

PTV

Figure 9. Profiles of terms in the turbulent kinetic energy (TKE) budget scaled by uτ plotted againstwall-normal distance for (a) type 1, (b) type 2, (c) type 3 (d) type 4 (P: production of TKE, T: turbulenttransport of TKE, V: viscous transport of TKE).

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10 K. Bhaganagar

x (mm)

y(m

m)

5 150

1

2

3

86431

-1-3-4-6-8

z (mm)

y(m

m)

0

1

2

3

z (mm)

y(m

m)

0

1

2

3

Figure 10. For type 1 case (a) contours of fluctuating component of u velocity in x–y plane atz = 2.0 mm (b) contours of fluctuating component of u velocity in y–z plane at x corresponding tothe peak location (c) fluctuating component of v–w velocity vectors in y–z plane.

are formed due to the surrounding higher speed fluid impacting the low-momentum fluid.As a portion of the low-momentum fluid lifts in an ejection, an intense, lifted shear layerforms along the upstream face of the ejection around x = 15 mm. The high streamwisemomentum required for the lift-up is being produced by the severe near-wall mean velocitygradients. Near the peak location of the roughness, the roll-up of the near-wall shear layerlift-up is the characteristic feature present. The presence of shear-layer type instability dueto stenosed flow has been reported before by [22] for semicircular stenosis. Next, the flowis examined in the y–z plane. Figures 10(b) and (c) (lower left and right figures) show the u

contours, and v–w velocity vectors in the y–z plane respectively. In regions above the peak,large scale negative patterns of u are observed, which corresponds to vortex-type structureas seen in Figure 10(c). The region of dynamically intense activity extends to more thanhalf the channel height. In the valley region of the roughness, large-scale positive patternsof u are observed. From the v–w velocity vectors, the flow in this region is toward the wall,resulting in the formation of a recirculation zone.

For type 2, Figure 11(a) (top figure) shows the u velocity contours in x–y plane atz = 2.0 mm. In the ascending portion of the roughness (x = 6–11 mm), structures withpositive u are observed. Downstream of the pinnacle of the ascending slope (x = 11 mm),the large-scale structures breakdown resulting in the formation of smaller scales positiveand negative structures. This feature is in contrast to well-defined shear layer observed in

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Journal of Turbulence 11

x(mm)

y(m

m)

5 10 15 200

1

2

3

4852

-1-4-7-9-12-15-18

z (mm)1 2 30

1

2

3

4

z (mm)1 2 30

1

2

3

4

y(m

m)

y(m

m)

Figure 11. For type 2 case (a) contours of fluctuating component of u velocity in x–y plane at x =2.0 mm (b) contours of fluctuating component of u velocity in y–z plane (c) fluctuating comonent ofv–w velocity vectors in y–z plane.

type 1. Figures 11(b) and (c) (lower left and right figures) show the u contours and v–w

velocity vectors in the y–z plane at x = 11 mm respectively. As seen from u contours,large-scale mushroom shaped pattern is the characteristic feature present. On analysis ofv–w velocity vector field, the three-dimensional nature of this mushroom-shaped vortex isrevealed. On analysis of the flow patterns at other locations corresponding to x = 14, 15, 18mm, similar patterns have been observed (figures have not been shown). Thus suggestingthat the mushroom shaped pattern is the characteristic feature in the y–z plane for type 2.

For type 3, Figure 12(a) (top figure) shows the contours of u velocity in the x–y

plane at z = 2.0 mm. High-magnitude positive velocity fluctuations resulting in significantvelocity gradients are the dominant features present. On analyzing the u contours (lowerleft figure) and v–w velocity vectors (lower right figure), three dimensional large-scalevortex corresponding to the high-magnitude positive contours in x–y plane is observed.

For type 4, Figure 13(a) (top figure) shows contours of u velocity in the x–y planeat z = 2.0 mm. The structures are more diffused in nature and are confined to a regionclose to the roughness. A flattened shear layer is formed as the high-speed fluid presses

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12 K. Bhaganagar

x (mm)

y(m

m)

5 10 15 200

1

2

31410740

-3-6-9-13-16

z (mm)

y(m

m)

1 2 30

1

2

3

z (mm)

y(m

m)

1 2 30

1

2

3

Figure 12. For type 3 case (a) contours of fluctuating component of u velocity in x–y plane at z =2.0 mm (b) contours of fluctuating component of u velocity in y–z plane, (c) fluctuating componentof v–w velocity vectors in y–z plane.

against the wall, creating locally high wall-shear stress. The flattened near-wall shear layersare not dynamically significant, since they produce local vorticity concentration at thewall, rather than in the flow-field. Large-scale structures evident for other three types arenot observed, on the contrary the structures are confined to region in the vicinity of theblockage. Figures 13(b) and (c) (lower left and lower right figures) show the u contoursand v–w velocity vectors in the y–z plane. High-magnitude positive u contours are seen inthe near-wall region, and the v–w velocity vectors reveal flow patterns with flow directedaway from the wall. As observed in the x–y planes, the structures are modified in regionvery close to the roughness. Thus suggesting that due to lack of strong gradients or sharpcorners in blockage, the flow modifications are confined to regions close to the blockage,and the flow in the regions away from the wall is not significantly affected.

4. Discussion

An accurate characterization of turbulent flow is of significant importance in our betterunderstanding of flow dynamics in stenotic channel. In this regard, an important aspect thatis still unclear is the significance of blockage morphology in altering the flow dynamics in a

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Journal of Turbulence 13

x (mm)

y(m

m)

0 5 10 15 200

1

2

3

4

8642

-1-3-5-7-10-12

z (mm)

y(m

m)

1 2 30

1

2

3

4

z (mm)

y(m

m)

1 2 30

1

2

3

4

Figure 13. For type 4 case (a) contours of fluctuating component of u velocity in x–y plane at z =2.0 mm (b) contours of fluctuating component of u velocity in y–z plane, (c) fluctuating componentof v–w velocity vectors in y–z plane.

stenotic channel. Toward this direction, we address a fundamental issue – are the turbulencecharacteristics dependent on shape of the blockage for a given height of the stenosis? Thiswill have important outcome in the future of the prediction of flow dynamics in a diseasedcoronary artery. As, to date, it is a common practice to approximate the geometry of theplaque formed on the walls of the artery as an idealized protrusion, where the stenosis isjust characterized by its height, and this has been the measure to represent the extent offlow alterations due to the presence of plaque in an artery. The present study has clearlyrevealed that turbulence generated due to the stenosis is strongly dependent on the shapeof this stenosis. An important conclusion is that stenosis shape is also an important metricthat needs to be considered to quantify the flow dynamics in a diseased coronary artery.

An extremely accurate, high-order DNS is performed to simulate turbulent flow in astenotic channel with identical degree of stenosis ( h

δ) but with four different shapes (refered

to as types) of blockages (roughness). The four types are peak valley (type 1), ascending(type 2), descending (type 3) and diffuse (type 4).

Detailed analysis has been performed to evaluate the difference in turbulence statisticsand the flow structures between these four types. Only close to the rough-surface differences

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14 K. Bhaganagar

in the mean velocity is revealed. Away from the wall, the mean velocity is not effected bythe shape of the stenosis. Next, the rms of the velocity fluctuations have revealed significanteffect of the shape of the stenosis on both rms of u and v velocity fluctuations. The TKEbudget has revealed the magnitude, direction, and extent of the transport mechanisms arestrongly type-dependent.

The turbulent structures exhibit characteristic structures and mechanisms very specificto the types. Type 1 (peak valley) results in strong near-wall velocity gradients with roll-up of shear layer near the peak locations and with recirculating region near the valleylocations. The flow physics is similar to that observed by [22]. For this type, the peakturbulence production and peak rms of ωz are higher compared to the other three types.Type 2 and type 3 with prominent sloping geometry exhibit high peak rms of u fluctuationscompared to the other types. Type 2 (ascending) cannot sustain strong near-wall shear layersresulting in breakdown of these structures to smaller scales. A dominant large-scale regionof negative u in the y–z plane is formed. Type 3 (descending) generates strong near-wallvelocity gradients, which corresponds to a large-scale vortex like structure. Type 4 ( diffuse)results in alterations of the flow which are confined to regions close to the wall, exhibitflattened near-wall shear layers which are not dynamically significant as demonstrated bythe turbulence production, rms of u and ωz fluctuation profiles.

The results indicate that turbulence flow characteristics in stenotic channel are governedby accurate morphology for given degree of stenosis. This study is primarily offered as acontribution to rough-wall flow dynamics with a possible extension to the study of flowin stenosed coronary artery. The flow features for type 1 are similar to that observed by[22] distal to the stenosis, thus giving further confidence that the underlying large-scaleturbulent flow features distal to the blockage have been realized. In future, it is a worthyeffort to invest in expensive numerical computation to simulate over realistic geometriesfor accurate flow prediction.

AcknowledgmentsThe author would like to acknowledge the medical imaging group Dr. Ozer and Dr. ShoenhagenM.D. for their valuable input to this study. The author would like to acknowledge Dr. Hygriv Rao,Cardiologist, CARE-GROUP, Hyderabad, India for his valuable input on this problem. The authorwould like to acknowlege support from NSF instrumentation grant to conduct the simulations.

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