12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

HIGH-FIDELITY COMPUTATIONAL STUDY OF ROUGHNESS EFFECTS
ON HIGH PRESSURE TURBINE PERFORMANCE AND HEAT TRANSFER

Thomas O. Jelly
School of Engineering
University of Leicester
LE1 7RH, United Kingdom
tj119@leicester.ac.uk

Massimiliano Nardini
Department of Mechanical Engineering
University of Melbourne
Victoria 3010, Australia
mnardini@unimelb.edu.au

Marco Rosenzweig
Department of Mechanical Engineering
University of Melbourne
Victoria 3010, Australia
marco.rosenzweig@unimelb.edu.au

John Leggett
Department of Mechanical Engineering
University of Melbourne
Victoria 3010, Australia
jake.leggett@unimelb.edu.au

Ivan Marusic
Department of Mechanical Engineering
University of Melbourne
Victoria 3010, Australia
imarusic@unimelb.edu.au

Richard D. Sandberg
Department of Mechanical Engineering
University of Melbourne
Victoria 3010, Australia
richard.sandberg@unimelb.edu.au

ABSTRACT

high Reynolds and Mach numbers featuring strong pressure
gradients and surface curvature. Furthermore, although empirical models have been proposed to account for roughness
effects (Stripf et al., 2008), predictive models that faithfully
reproduce blade boundary-layer dynamics and the associatedloss mechanisms in engine-relevant operating conditions remain elusive.
Whilst computational fluid dynamics (CFD) is a key design tool in gas turbine (GT) development, its potential is far
from being fully realised due to challenges in simulation andmodelling of aero-thermal performance in realistic environments (Sandberg & Michelassi, 2022). In practice, design
iterations are accomplished by modelling all scales of turbulence with the well-known Reynolds Averaged Navier-Stokes(RANS) and Unsteady RANS (URANS) equations. While fastand robust, RANS and URANS can suffer from accuracy issues in the presence of complex mixing processes (Michelassi
et al., 1998; Pichler et al., 2016) or blade surface roughness effects (Joo et al., 2016). Considering that just a 2% error in thepredicted metal temperature is estimated to halve the effective
blade life (Han et al., 2012), detailed analysis of roughness effects in HPT flows is necessary not only to gain deeper insightof the fundamental flow physics, but also to more accurately
predict pressure losses and heat transfer.
High-fidelity simulations, including both Direct Numerical Simulation and Large-Eddy Simulation (LES), have beenshown to be very accurate in simulating flow past smooth HPTvanes (Bhaskaran & Lele, 2010; Jee et al., 2016; Zhao & Sandberg, 2020). On the other hand, high-fidelity simulations offlow past rough HPT vanes remain very limited. To date,most past work has focussed on roughness effects in low pressure turbines (Hammer et al., 2018) or non-equilbrium flat-

A series of high-resolved Large-Eddy Simulations (LES)of the LS89 high-pressure turbine (HPT) vane with systematically varied levels of blade surface roughness have been performed. Three roughness amplitudes have been investigated,namely, ks /c = {1.0, 2.0, 3.0} × 10−3 , where ks is an equivalent value of Nikuradse’s sandgrain roughness for a nearGaussian height distribution, and c is the axial blade chord.
A reference smooth-blade simulation at matched flow conditions was also conducted for comparison. All simulations havebeen performed at a chord Reynolds number of 0.59×106 andMach number of 0.9, based on the exit conditions of the reference smooth vane, and with synthetic inflow turbulence tomimic incoming disturbances from an upstream combustion
chamber. The data presented here highlight the strong aerothermal effect that blade surface roughness has not only uponboundary-layer transition mechanisms on the blade suctionside but also on wall shear stress and wall heat flux, as well as
the levels of turbulence kinetic energy and total pressure loss
in the wake.

INTRODUCTION
Blade surface roughness ranks amongst the most criticalfactors affecting high pressure turbine (HPT) aero-thermal performance and is especially relevant in the case of in-service
degradation (Bons, 2010) and additively manufactured components (McClain et al., 2021). Whilst it is well-known thatblade surface roughness can increase heat transfer and pressure losses well above aerodynamically smooth levels (Bons,
2002), the detailed underlying mechanisms remain far fromfully understood — particularly in realistic environments at

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
plate boundary-layers (Vadlamani et al., 2018), at significantly
lower Reynolds number. As a result, several questions regarding the fundamental mechanisms that govern the aero-thermal
performance of HPTs remain open.
The present study complements this past work by studying surface roughness effects upon the aero-thermal performance of the LS89 HPT vane using a high-fidelity computational approach for the very first time. Particular attention isdrawn towards how systematically varying the levels of surface
roughness affects the dynamics of laminar-turbulence transition on the blade suction side and its associated impact uponwall shear stress and wall heat flux, as well as the levels of turbulence kinetic energy and total pressure losses in the wake of
the HPT blade.

(a)

(b)

COMPUTATIONAL METHODOLOGY
Large-Eddy Simulations (LES) were performed using
an in-house multi-block structured curvilinear compressible
Navier-Stokes solver called HiPSTAR (Sandberg et al., 2015)that uses higher-order numerical methods optimised for performance on the world’s fastest supercomputers. For the cases
reported herein, simulations were undertaken using a minimum of 576 Nvidia V100 GPUs of the Summit supercomputer at Oak Ridge National Laboratory. Spatial discretisationis achieved using fourth-order wavenumber-optimised compact finite differences. An ultra-low storage frequency optimised fourth-order explicit Runge-Kutta method is used fortime advancement. The subgrid-scale contribution is provided
by the WALE model (Nicoud & Ducros, 1999) with a standard coefficient of Cw = 0.325. The present study employs
the same overset mesh configuration devised by Zhao & Sandberg (2021), which consists of an O-type grid wrapped aroundthe HPT blade embedded into a background H-type grid. A
schematic of the overset grid configuration is shown in Figure 1a. Whilst HiPSTAR has been used extensively to perform LES of HPT flows (Pichler et al., 2017; Zhao & Sandberg, 2020, 2021), these past studies have focussed on smooth
blade geometries that were explicitly resolved using bodyfitted grids. In the present study, the roughened blade geometries are represented using a second-order accurate boundary
data immersion method (BDIM) (Schlanderer et al., 2017).
The blade surface roughness under consideration here isirregular, three-dimensional and near-Gaussian. According toBons (2002), near-Gaussian roughness on turbine blades develops as a result of metal erosion mechanisms, whereas nonGaussian roughness develops due to thermal barrier coating
spallation or pitting. The Gaussian height distribution used in
the present study was synthesised using an algorithm devisedin past work by Jelly & Busse (2018, 2019), which generates
irregular roughness with doubly periodic boundary conditions
by taking weighted linear combinations of Gaussian random
number matrices using a moving average process. So far,three roughness amplitudes have been investigated, namely,
ks /c = {1.0, 2.0, 3.0} × 10−3 , where ks is an equivalent valueof Nikuradse’s sandgrain roughness and c is the axial blade
chord. Here, ks is related to the r.m.s. roughness height, krms ,through the scaling factor C ≡ ks /krms = 5.0. Close-up viewsof the trailing edge (TE) surface roughness for each value of
ks /c are shown in Figure 2. According to Bons (2010), theeffects of blade surface roughness become admissible above
ks /c ≈ 1 × 10−4 . Hence, the roughness under investigation
here is anticipated to have an appreciable aero-thermal effect.
In the LES, the BDIM algorithm is used to apply noslip isothermal boundary conditions on the roughened blade

Figure 1. (a) Schematic of the overset mesh setup showing
the curvilinear O-type grid around blade embedded into thebackground Cartesian H-type grid. For clarity, only every 64th
and 8th grid point is shown in the streamwise and pitchwise direction, respectively. Pitchwise periodic boundaries are highlighted as solid blue lines () and the inlet and outlet planes
are highlighted as solid red lines (). (b) Zoomed-in view ofthe blade trailing edge, illustrating the pitchwise extent of theroughness layer (shaded green area), where the discrete threedimensional point cloud of the roughened HPT blade (×) is
immersed in a constant mesh spacing region. The mean blade
coordinates are shown as the black dashed line (). For clarity, only every 6th and 3rd grid point is shown in the streamwise
and pitchwise direction, respectively.

surface. A discrete representation of the three-dimensional
blade geometry is immersed in a “roughness layer” that extends above and below the roughness mean plane, which coincides with the coordinates of the smooth HPT vane. The
roughness layer was resolved using a minimum of 140 grid
points which were spaced equally in the blade-normal direction. Above the roughness layer the blade-normal grid spacing
is gradually increased, reaching a maximum value at the outeredge of the embedded O-type grid. A schematic of the roughness layer in the TE region is shown in Figure 1b.
For each roughness amplitude, an LES was performed at
at a chord Reynolds number of Re = 0.59 × 106 and Mach
number of Ma = 0.9, based on the exit conditions of the reference smooth vane. The width of the computational domain
in the spanwise direction was set equal to 40% of the axial
blade chord, which is wide enough to ensure that the turbu-

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
& Sandberg (2020). For the rough blades, the spanwisethen-time-averaged grid spacings were evaluated at the meanroughness height, which coincides with the coordinates ofthe smooth HPT blade, and were found to be ∆s+ . 1.0,
∆n+ . 1.0 and ∆z+ . 10.0 for all cases considered here.
To verify the accuracy of the BDIM algorithm in simulating flow past a smooth HPT vane, results from Pichler
et al. (2017) and Zhao & Sandberg (2020) that used bodyfitted computational grids and similar inlet turbulence intensities and integral length-scales were reproduced. The bladesurface static pressure coefficient, C p , and blade surface skinfriction coefficient, C f , are compared in Figure 3 — goodlevels of agreement are observed between the body-fitted andBDIM data.

(a)

(b)

(a)

(c)

(b)

Figure 2. Close-up view of blade surface roughness on the
HPT trailing edge (TE) for (a) small ks /c = 1.0 × 10−3 ;(b) intermediatek /c = 2.0 × 10−3
and (c) large
 s−3
ks /c = 3.0 × 10
amplitude cases.

lence structures decorrelate to satisfactorily low levels. A compressible version of the Klein et al. (2003) digital filter method
was used to synthesise isotropic inlet turbulence with an intensity of Tu /U iq= 8% and an integral length scale of Lx /c = 8%,
02

02

02

where Tu ≡ u +v3 +w , and U i is the axial velocity at the
inlet. A non-reflective zonal characteristic boundary condition(Sandberg & Sandham, 2006) was enforced at the outlet, andRiemann invariant boundary conditions were used at the inlet.
Periodic boundaries were imposed in the pitchwise (y) direction and the spanwise (z) directions.
In terms of the mesh dimensions, the background H-type
grid for the smooth case was comprised of Nx × Ny × Nz =1470 × 716 × 384 points, where Nx , Ny , Nz are the number ofpoints in the axial, pitchwise and spanwise directions, respectively, whereas, for the rough cases, it had Nx × Ny × Nz =1470 × 716 × 576 points. For the smooth case, the embedded O-type grid was comprised of (N1 × N2 × N3 ) =(6796 × 254 × 384) points, whilst for the ks /c = 0.001 caseit had (N1 × N2 × N3 ) = (6796 × 254 × 576) points, and, forthe remaining ks /c = 0.002 and ks /c = 0.003 cases, it had(N1 × N2 × N3 ) = (6796 × 358 × 576) points. The grid spacings in the tangential, wall-normal, and spanwise directions
normalised with the local viscous length scale δν = ν/uτ
+
+
+
are
p denoted as ∆s , ∆n , and ∆z , respectively. Here uτ =
τw /ρ is the wall friction velocity with the wall shear stressτw and density ρ. The spanwise-then-time-averaged grid spacings on the surface of the smooth blade were found to be∆s+ . 7, ∆n+ . 0.5 and ∆z+ . 12, which is slightly
finer than the mesh resolution reported in past work by Zhao

Figure 3. Validation against previous body-fitted HPT simulations performed by Pichler et al. (2017) and Zhao & Sand). (a) Blade surface
berg (2020) and current BDIM data (static pressure coefficient, C p , plotted against axial position
normalised by axial chord length, x/c. (b) Skin-friction coefficient, C f , plotted against the the blade surface length, s, wheres > 0 and s < 0 correspond to the SS and PS, respectively.

RESULTS
Two typical snapshots of the simulated flow-field areshown in Figure 4, which compares contours of instantaneous
spanwise velocity (ur ) normalised by the axial time-averaged
inlet velocity (ux ) on the axial-pitchwise (x-y) plane for thesmooth HPT blade (Figure 4a) and the intermediate roughness

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(a)
To further elucidate how the levels of surface roughness
affects the blade boundary-layer development along the SS
surface, the wall heat flux (WHF) and wall shear stress (WSS)
were examined. The former quantity is defined here as

q=

µ
∂T
Pr (γ − 1) M 2 ∂ n(1)where Pr is the Prandtl number, γ is the heat capacity ratio,
and M is the Mach number and ∂ T /∂ n is surface temperature
gradient with respect to surface-normal direction. The WSS
vector (in Cartesian coordinates) is defined here as~τw = µ

(b)

∂Vt1
∂V
~t1 + t2~t2
∂n
∂n


(2)

where ∂Vt1 /∂ n and ∂Vt2 /∂ n are the wall-normal derivative ofthe tangential velocity with respect to ~t1 and ~t2 , respectively.
Here, attention is directed towards the wall-normal derivativeof the tangential velocity
with respect to~t1 , which can be written as ∂Vt1 /∂ n = ∇~V T ·~t1 ·~n, where ~n is the surface normal
vector and where ~t1 is the tangential direction lying in the x-yplane with ~t1 ·~i ≥ 0, where ~i is the unit streamwise vector.
Contours of µ∂Vt1 /∂ n, and q on the SS surface of thesmooth and roughened HPT blades are compared in Figure 5.
The instantaneous data show that surface roughness introduces
instabilities in the boundary layer along the whole span of theblade, which are not present on the smooth blade. These instabilities trigger an early transition to turbulence and the breakdown to turbulence occurs quicker, i.e., the transition point
moves towards the LE, as the level of blade surface roughness
increases. To be specific, whilst the transition onset appears to
be confined to the final 15% of the SS surface for the smoothand ks /c = 0.001 cases, the boundary-layer is almost entirely
turbulent along the entire length of the HPT vane for both the
ks /c = 0.002 and ks /c = 0.003 cases. This observation is consistent with previous findings of Zhang & Ligrani (2006), who
also noted a rapid breakdown to turbulence on the SS surface of roughened HPT blade with ks /c = 1.6 × 10−3 . Consequently, a markedly different transition mechanism occurs
on the intermediate and large amplitude roughness blades considered here compared to the smooth-blade bypass transition
discussed in past work by Zhao & Sandberg (2020). The factthat blade surface roughness can trigger such a rapid breakdown to turbulence implies that significant changes will also
occur in the wake of HPT blade.
Figure 6a shows the effect of blade surface roughness on
pitchwise profiles of turbulence kinetic energy (TKE) at 20%
axial chord downstream of the TE. TKE is defined here as

Figure 4. Contours of instantaneous spanwise velocity (uz )normalised by the axial time-averaged inlet velocity (ux ) at
mid-span (Lr /c = 0.2) on the axial-pitchwise (x-y) plane (a)smooth HPT blade and (b) HPT blade with intermediate amplitude roughness (ks /c = 0.002). Inset panel shows closeup view of boundary-layer transition of the blade suction side.
Note that the computational domain has been copied twice inthe pitchwise (y) direction.

case (Figure 4b) at mid-span (z/c = 0.2). Looking from leftto-right, a rich array of complex flow physics can be observed
throughout the HPT cascade. These include: distortion andextension of freestream turbulence around the HPT leadingedge (LE) due to a curvature-driven favourable pressure gradient, pronounced vortex stretching in the HPT passage andboundary-layer transition on the blade suction-side (SS), as
well as highly turbulent vortex shedding in the TE region that
produces a wake with a broadband distribution of scales. The
impact of blade surface roughness can be seen in the inset panels on Figure 4, which show close-up views of the SS blade
boundary-layer in the TE region of the HPT blade. Comparing the boundary-layer development over the rough TE (Figure4b) against that of the smooth (Figure 4a), it is clear that theflow over the rough surface not only undergoes an earlier transition to turbulence, but also contains finer-scale eddies whose
size is commensurate with the topographical features of theunderlying roughness distribution.

1
k = u0i u0i2(3)

where u0i is the turbulent velocity component. Whereas the
TKE profiles of the smooth and small-amplitude roughness
cases are practically indistinguishable from one another, thetwo remaining cases show some notable differences. For instance, relative to the smooth HPT blade, the peak TKE value
increases by 8% and 32% for the intermediate- and largeamplitude roughness, respectively. The increase in the peak
TKE value is accompanied by a widening of the profiles in thepitchwise direction as the blade surface roughness becomes412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

(a)

(b)

Figure 5. Spatial distribution of (a) instantaneous wall shear stress, µ∂Vt1 /∂ n, and (b) instantaneous wall heat flux, q, on the suction
side of the smooth and roughened HPT blades.

CONCLUSIONS

larger. This increase in the fluctuations might be attributed toa higher turbulent kinetic energy production in the rough-wallboundary layer, which is advected downstream as the shear
layer separated from the TE.
Pitchwise profiles of the kinematic wake loss, defined
here asΩ (y) =

pt1,mix − pt2 (y)pt1,mix − p2,mix

The effects of blade surface roughness upon HPT performance and heat transfer has been studied using highlyresolved LES at an exit Reynolds and Mach number of
590,000 and 0.9, respectively. Three roughness amplitudes
have been investigated, namely, ks /c = {1.0, 2.0, 3.0} × 10−3
(figure 2), where ks is an equivalent value of Nikuradse’s sandgrain roughness for an irregular near-Gaussian roughness topography. The rough HPT geometries were represented using a boundary-data immersion method (BDIM) in conjunction with a two-block overset mesh configuration (figure 1),
which was validated against existing simulation data that used
body-fitted smooth HPT geometries (figure 3).
Whilst it is well-known that blade surface roughness cansignificantly affect aero-thermal performance, relatively to
aerodynamically smooth blades, several questions regarding
the fundamental mechanisms that govern pressure losses andheat transfer remain open. The results presented here highlight the strong impact that blade surface roughness has uponlaminar-turbulence transition on the suction surface (figure 4),
which, in turn, affects the wall shear stress and wall heat flux
(figure 5), as well as the levels turbulence kinetic energy andtotal pressure losses in the wake (figure 6). Ongoing work
is focussing on associating particular physical mechanisms tochanges in aero-thermal performance, such as mean viscous
dissipation and turbulent wall heat flux.

(4)

where pt1,mix and p2,mix are the mixed out stagnation pressure
at the inlet and the mixed out static pressure at the outlet, respectively, and pt2 (y) is the stagnation pressure, are plotted
20%Cax downstream of the blade TE for each roughness amplitude are plotted in figure 6b. The kinematic wake loss increases as the non-dimensional roughness amplitude, ks /c, increases. Relative to the smooth HPT vane, the peak value ofthe kinematic wake loss increases by almost 70% — underlying the significant impact that small-scale surface roughness
have upon loss generation. Again, the increase in is apparent
at peak value locations and is accompanied by increases in thewidth of the profiles as roughness size becomes larger. Thisis largely due to increased thickening of the boundary layers
along the airfoil surfaces as increases. As noted by Ligrani(2012), possible explanations for the broader wakes with increased roughness size in Figure 6 could be (i) augmentationsof mixing and turbulent transport in the boundary layers whichdevelop along the roughened airfoils and / or (ii) increased turbulent diffusion in the transverse direction within the wake as
it advects downstream. A detailed interrogation of (i) and (ii)
is in progress.

ACKNOWLEDGMENTS
The presented data were obtained using resources of the
Oak Ridge Leadership Computing Facility at the Oak Ridge

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
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(b)

Figure 6. Pitchwise profiles of (a) turbulence kinetic energy(k) and (b) kinematic wake loss (Ω). Both profiles are shown
20% axial chord downstream of the blade TE.
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