Optimal Riblets Applied to Gas Turbine Compressor Blades Studied via Direct Numerical Simulation (GT2024–122305)

More efficient gas turbines (GTs) would reduce fuel usage and additionally increase the viability of costlier, more sustainably sourced fuels. In GTs, the high-pressure compressor (HPC) must operate at a wide range of strongly off-design conditions, for example, across the flight envelope when used for aero-propulsion, and in power generation during fast start-up and rapid changes of load when a GT is called upon to absorb the intermittency of renewable energy sources. The current study investigates the application of streamwise micro-grooves termed “riblets,” a well-known surface texture targeting drag reduction, to an HPC blade at both on- and off-design incidences. Whereas a previous numerical study [1] investigated riblets with a fixed geometry over the entire chord, the present work investigates “locally optimal” riblet surfaces based on the local viscous scale with the aim of maximizing the performance benefit.

Riblets are a well-known passive surface treatment to reduce viscous drag in fully turbulent flows. The riblets serve to restrict the fluctuating cross-flow component in the vicinity of the wall, which reduces the momentum transfer close to the surface and in turn reduces the shear stress [2]. Most investigations to date have been of riblets as applied to flat surfaces in simple flow configurations, for example, in a channel. For a range of riblet geometries, a comprehensive experimental investigation [2] found that a riblet spacing of $s+≈17$ (where the “+” denotes scaling with viscous wall unit $ν/uτ$⁠, where $ν$ is the kinematic viscosity, and $uτ$ the friction velocity), which, for many industrially relevant flows translates to 10s of micrometers in the laboratory, will maximize the reduction in shear stress for a zero-pressure gradient (ZPG) boundary layer flow.

There are comparatively few studies of the action of riblets under a transitioning boundary layer, such as that existing over an HPC blade. A notable study [3] found riblets tend to constrain the growth of turbulent spots in a nominally laminar, ZPG boundary layer by reducing the spot spreading angle by 14%. A very recent numerical study [4] investigated the action of riblets subject to an adverse pressure gradient (APG) transitional flow in the context of a low-pressure turbine. It was found that a riblet spacing of $s+=17$ maximized the profile loss reduction, agreeing with the optimal drag-reducing range for riblet spacing for ZPG turbulent boundary layers. In addition, considering skin friction and the maximum turbulent kinetic energy variation, it was suggested that riblets tend to hasten transition for flows subject to an APG. Riblets were also found to prolong the transition length, delaying turbulent boundary layer development.

The potential for drag reduction on an airfoil geometry by riblets has been studied numerically and experimentally. An early experimental study [5] found a drag reduction of more than 10% for a compressor cascade (NACA65) when sawtooth riblets were applied only to the pressure side. A much smaller benefit was found when the riblets were placed on both the pressure and suction sides of the airfoil. However, subsequent experimental campaigns have found that a larger benefit follows from the riblets on the suction side of the airfoil. Experiments conducted on a NACA 0012 airfoil [6] targeted the effect of riblets for angles of attack of 6 deg, with their measurements indicating that the larger contribution to the drag reduction results from the airfoil upper (or suction) surface. The skin-friction reduction was found to be up to 16% for 6 degrees of incidence, significantly higher compared to flat plate flows, indicating an increased effectiveness of riblets in APGs. The experiments of Ref. [7] suggested skin-friction drag reduction in the range of 5–8% is achievable on 2D airfoils at low incidence with optimized riblets. This study also found a trend of increasing viscous drag reduction with airfoil incidence (initially), with the increased drag reduction contributed by the airfoil suction surface, again pointing to the increased effectiveness of riblets in APG flows. The study of Ref. [8], targeting ideal triangular riblets with a trapezoidal groove, also found a larger profile loss reduction by applying riblets to the suction side and, however, noted an additional smaller benefit by applying them to both the pressure and suction sides. A very recent experimental study [9] targeting a novel, and potentially more cost-effective, manufacturing technique for micro-riblets for use in the harsh operating environment of aero-engines signals ongoing academic and industrial interest in the use of riblets.

Despite the progress made to date, accurate prediction of the aerothermal behavior in the presence of riblets at realistic GT conditions remains a formidable challenge, due to the complex flow physics and the small scales and micro-topology of the riblet geometry. To date, the majority of research on riblets applied to turbomachinery components and their effect on performance has been carried out by costly physical tests. Moreover, physical testing often can only provide integral parameters of components (e.g., the pressure coefficient [8]), rather than providing sufficient detail to dissect the action of the riblets on the airfoil’s performance.

Within the literature, wall-resolved large-eddy simulation (LES) has been used to study riblets on an airfoil [10]. This study considered triangular riblets applied to the suction side of a low-speed airfoil (Eppler E374), starting at streamwise location $x/C=0.3$ where $C$ is the chord length. The riblets were found to be most effective at suppressing the Reynolds stress and wall friction at the location where the pressure gradient is the greatest. However the large size of the riblets (⁠$0.002C$⁠, presumably due to resolution constraints), and a lower Reynolds number (⁠$2×105$⁠) also commonly studied experimentally, meant that the riblets ultimately increased the pressure drag over a reference smooth wall case. Another study [11] used LES to assess the effect of a mild APG, common to applications where riblets might be used (e.g. airfoils) on scalloped riblet performance. Only a very small drag reduction under mild APG was found when compared to ZPG conditions. Given reports in the experimental literature that riblet drag reduction can double in the mild APG common to airfoils at moderate angles of attack, the authors suggested their simulations to be evidence for the notion that the drag-reducing property of riblets is enhanced only under moderate to strong APG. A recent numerical effort [12], also considering the NACA65 profile, used LES and unsteady Reynolds-averaged Navier–Stokes (URANS) analyses to investigate “shark-inspired” curved riblets applied to the suction side of a compressor blade, although it should be noted that the grid resolution for this study was quite low. The riblets were placed only at the leading edge (chord extent [9.1%, 36.3%]). Due to the cost associated with using a mesh able to resolve the riblets, they were placed across only 4% of the spanwise domain. The total pressure loss of the cascade was reduced by a maximum of 20.5% at an incidence angle of 2 deg, for design parameters $s+=7.5$ (spanwise spacing of riblets) and $h+=15$ (height of riblets). The authors noted that cascade performance is much more sensitive to the relative change of $s+$ rather than $h+$⁠. Compared with the smooth cascade, the shear stress near the riblets was significantly reduced, and downstream flow separation was delayed. However, at the maximum incidence angle of 6 deg, the pressure loss of the compressor cascade could be reduced by only 8.1%. Another recent LES [13] of the flows around NACA 0015, NACA 0012, and Eppler 387 airfoils at different angles of attack modeled the action of the riblets by use of a slip length boundary condition. The authors found that not only frictional but also form drag was reduced in the presence of riblets, since they reduce the displacement thickness of the boundary layer, reducing the equivalent thickness of the body.

The present numerical investigation seeks to scale the riblet geometry such that it can best target skin-friction reduction for the local flow condition and is inspired by the experimental campaign of Ref. [8]. They found an additional benefit by adapting the riblet geometry to the local flow conditions along the blade surface. Due to limitations in the riblet production technology, a continuous change of the geometry along the surface was not feasible and the authors compromised by segmenting the surface with a constant riblet geometry optimized to the local flow conditions on the suction side for each chord section, targeting an optimal riblet separation of $s+=17$⁠. Since the local viscous scale increases down the chord as the Reynolds number increases, the riblets were made wider toward the trailing edge. Note in that study the authors attempted (given manufacturing accuracy this was not strictly possible) to scale the height of the riblets with the same factor as the spacing, such that the nominal slope of the micro-riblets would be maintained along the chord.

The present work extends a recent study [1] which investigated the effect of fixed triangular or “sawtooth” riblets on HPC blades subject to inflow turbulence via direct numerical simulation (DNS) at engine-relevant conditions. In that study, being the first DNS of fully resolved riblets over an HPC, a riblet spacing of $≈$17 viscous wall-units was targeted at mid-chord, informed by a previous comprehensive experimental investigation on a flat plate [2]. Two riblet geometries (60-deg and 90-deg tip angle) at on- and off-design inflow incidence angles were considered. The present work seeks to uncover whether an additional benefit can be realized by locally scaling the riblet spacing $s$ or the riblet height $h$ to be approximately fixed in terms of viscous units along the blade’s chord. Where the experimental campaign of Ref. [8] used segments of different-sized riblets along the chord, the present numerical campaign permits a smoothly changing riblet height or spacing.

As in Ref. [1], the action of the riblets will be examined at on-design as well as off-design (both positive and negative) incidence, to ultimately understand the impact of the riblet microstructure on the overall loss bucket of the HPC. The majority of research on riblets has been performed on simpler, canonical configurations, such as flat plates and streamwise-periodic channels. Research of riblets applied to turbomachinery components and their effect on performance has generally been carried out by costly physical tests that could not easily reveal detailed physical mechanisms. The present study allows the assessment of detailed fundamental physical mechanisms associated with the effects of riblets in boundary layers exposed to curvature, pressure gradients and external perturbations in the form of freestream turbulence, as relevant to turbomachinery flows.

The viscous scaling from the fixed riblet cases [1] is shown in Fig. 1(a). This diminishing scale in viscous units is suspected to be partly responsible for the fact that $ΔCf$ (skin-friction reduction relative to the reference smooth-blade case) diminishes down the chord if the riblets are fixed in physical units, pointing to riblets being less effective toward the trailing edge. Therefore a geometric scaling of the riblet is proposed (Fig. 1(b)), to counteract the diminishing scale of the riblets in viscous units. This factor is in effect the inverse of that shown in Fig. 1(a), noting that it is smoothed and simplified, especially at the leading edge flow, and needs to match up at the trailing edge with the scaling on the pressure side of the blade. In the present work, the riblet spacing $s$ and the riblet height $h$ are scaled independently in two separate campaigns.

The literature suggests that the spanwise spacing $s$ is more important for the drag-reducing function of streamwise-aligned riblets than the height $h$⁠. The present riblet simulations vary only $s$ or $h$⁠, seeking to understand which geometrical feature of the riblets is most critical to their performance given the flow conditions and curvature on an HPC. Therefore, we begin by designing a riblet surface where the riblet spacing $s$ varies smoothly along the chord, which is possible with our present numerical approach (in contrast to the discrete strips of differently sized riblets in Ref. [8]). For this case where riblet spacing $s$ is scaled, the riblets are slightly yawed along the chord as the riblets are “stretched” in the spanwise direction. However this yaw angle is very small: on the suction side, from the point of minimal $s$ (where the scaling factor in Fig. 1(b) is at a minimum) at $x/C≈0.1$ to the trailing edge, the riblet yaw angle is $≈$0.07 deg. On the pressure side, where the slope of the scaling factor in Fig. 1(b) is slightly shallower, the riblet yaw angle is $≈$ 0.05 deg.

The spanwise extent, normalized by true chord, is $Lz=0.1$⁠. A narrow span was specified to control simulation costs; however, a preliminary smooth-airfoil study showed that quantities such as skin friction (⁠$Cf$⁠) and Reynolds number (⁠$Reτ=δuτ/ν$⁠, for boundary layer thickness $δ$⁠, friction velocity $uτ$ and kinematic viscosity $ν$⁠) development as well as airfoil loading (⁠$Cp$⁠) are virtually indistinguishable when comparing between the present $Lz=0.1$ span and a wider $Lz=0.2$ span. Therefore, we conclude the narrower $Lz=0.1$ is sufficient. The computational domain is periodic in the pitchwise and spanwise directions. Therefore, there is the complication of enforcing periodicity in the span with riblets that are changing width (and consequently, number, across the span). This was resolved by the addition of a smooth 10% buffer region either side of the “core” 0.1$C$ region, and a min/max search outside of this core region was used to ensure riblets were not bisected on either end (see Fig. 2). Note that the 10% buffer regions are excluded from the ensuing on-blade data analysis of the skin friction $Cf$ for example. The same datum (mean riblet surface height) is used for the smooth-blade case. There is an increased grid count due to 2 more points being added in the (boundary data immersion method [BDIM]) inner O-grid (under the BDIM surface) for reasons of numerical stability. Additionally, more grid points were required in the span due to the increased width to accommodate the buffer regions. For the varying $h$ case, the same scaling is applied as for the varying $s$ case, hypothesizing that they may be less effective. The spacing $s$ is fixed over the entire chord with an integer riblet count, akin to the previous fixed riblet cases. Hence the periodic boundary condition in the spanwise direction is obeyed and no buffer regions are required.

Figure 3 shows the riblet geometry at three locations along the suction side for both the present optimal riblet cases. As in the previous study [1], these nominally triangular riblet geometries have rounded tips and valleys, which is more representative of achievable profiles given manufacturing limitations at the micro-scale, as well as in-service wear of initially sharp tips. Since either the spacing $s$ or the height $h$ is solely changing, the slope of the riblet geometry is not constant along the chord. For the varying $s$ case (Fig. 3(a)), the effective tip angle ranges from $≈$50.1 deg at the leading edge to a much larger $≈$91.8 deg at the trailing edge, where the riblet is visibly shallower (note at the mid-chord, where the scaling factor applied is 1, the effective riblet tip angle is simply 60 deg as for the previous fixed riblet cases). For the varying $h$ case (Fig. 3(b)), the effective tip angle ranges from $≈$70.4 deg at the leading edge to $≈$35.6 deg at the trailing edge where the riblets are much sharper as shown in the cross section.

The baseline HPC geometry (NACA 6510) and flow conditions are based on the laboratory experiment of Ref. [8] (inlet Mach number $Main=0.5$⁠, and the Reynolds number based on true chord $C$ is Re = 700,000; note the inlet Reynolds number was $Rein=106$ in the experimental campaign). Thus simulations are carried out at engine-relevant conditions. Isotropic turbulence with a turbulence intensity of 4% (based on inflow velocity) and length scale 3% (based on true chord $C$⁠) is prescribed at the inlet using a compressible version of the digital filter technique [14]. The nominal inflow incidence angle is 60 deg; the same positive and negative incidence inflow angles will be considered as in Ref. [1]. Based on the loss bucket (computed with Reynolds-averaged Navier–Stokes (RANS) analyses) and the airfoil loadings, two additional cases were selected for the production DNS studies: a positive incidence inflow angle of 63 deg, and a negative incidence inflow angle of 54 deg. Both of these reflect loadings and incidence swings that can be found in typical compressor airfoils. The present numerical simulations are carried out using the in-house solver HiPSTAR, a high-performance solver for compressible flow. HiPSTAR solves the compressible Navier–Stokes equations on curvilinear structured grids, employing a fourth-order accurate finite difference scheme to compute the spatial derivatives, and a five-step, fourth-order accurate, low-storage Runge–Kutta method for time integration [15]. HiPSTAR has been well validated for HPC simulations [16]. Precursor simulations are used to establish the bulk flow conditions for the nominal inflow and selected positive and negative incidence cases. These coarse-grain LES were undertaken to deduce the correct back pressure and establish the bulk flow conditions, which required an iterative approach. The resulting fluid fields were subsequently interpolated onto a much finer grid for the production simulations for which results are reported herein. These production simulations were undertaken as DNS, that is, fully resolving all scales and with no subgrid-scale modeling.

The airfoil geometry, in both the smooth and riblet cases, is represented using a novel three-dimensional immersed boundary method, here referred to as the 3D BDIM [17]. The present implementation, especially with respect to data collection at the BDIM surface, is discussed in Nardini et al. [18]. The advantage of the BDIM lies in the possibility to simulate complex three-dimensional surfaces without the need for computational grids that conform to the geometry of the solid boundary. This means that high computational efficiency can be retained with the use of Cartesian grids. In the present case where two riblet geometries are investigated, it also means that a very similar in-plane fluid mesh can be used, that is, grid generation for each new micro-geometry is avoided. Further advantages of the BDIM approach over other immersed boundary layer techniques are that it represents flow variables on the surface with second-order accuracy, and that it does not incur a significant time-step penalty as forcing methods do. The latter is particularly important for high Reynolds number configurations which require very large computational grids and already are hampered by small time-steps needed to ensure numerical stability when time-explicit solvers are used.

The fluid domain is discretized using a three-block mesh setup as shown in Fig. 4. It is composed of an H-type grid for the background flow (Block $1$⁠), with $Nx×Ny×Nz$ grid points, and two O-grids wrapped around the airfoil: an outer grid (Block 2), to capture the boundary layers forming over the airfoil, and an inner grid (Block 3). Grid details are given in Table 1. The grid counts for the two O-grids are described by $Nt×Nn×Nz$⁠, where the subscript $t$ denotes the blade tangential direction and $n$ the wall-normal direction. Whilst the use of an H-grid and a single O-grid is typical in airfoil simulations undertaken with HiPSTAR, the main purpose of the innermost O-grid (Block 3) is to permit higher local spanwise resolution (i.e., into the page on Fig. 4) of the riblets, which are located in a thin region close to the blade surface around the airfoil (shown by the innermost line for the O-grid in Fig. 4). This present riblet micro-geometry is highly resolved via the same computational approach based on the BDIM as in Ref. [1]. We note the true micro-scale of the riblets: if the present HPC had the same physical chord length as that in the experimental study of Lietmeyer et al. [8], the riblets for the varying $h$ case would be spaced $≈56μm$ in the spanwise direction. The grid size is therefore driven by the requirement to resolve the riblets: approximately half of all grid points are located in this thin region represented by Block 3 at the airfoil surface. The three grids are connected by means of overlapping regions using an overset method [19]. The total fluid grid size is $≈4.2×109$ for the varying $s$ riblet case, and $≈3.9×109$ for the varying $h$ riblet case (the previously conducted smooth cases have a grid of $≈1.4×109$ fluid points in comparison, due to a much smaller spanwise grid count). For the reference smooth-blade cases, the grid spacing at the blade surface is $Δt+≲12$ and $Δn+≲1.0$ using a normalization based on the local viscous length scale. The spanwise resolution is $Δz+≲5.0$ for the smooth-blade cases, yet $Δz+≲0.5$ for the riblet cases, due to the large $Nz$ employed to resolve the riblets within Block 3. Note that although the riblet geometry is changing, the spanwise resolution is fixed for both present optimal riblet geometries.

Integral boundary layer quantities are shown along the suction side for the nominal inflow incidence case in Fig. 8. The boundary layer (Fig. 8(a)), is slightly thicker for the present optimal riblet cases compared to the reference smooth case over the entire suction-side chord. The difference in the boundary layer is more significant at a positive inflow incidence angle as shown in Fig. 9: whereas the boundary layer (Fig. 9(a)) is thinner for both previous fixed riblet cases, it is clearly thicker for the present optimal riblet cases, particularly at the trailing edge. A significantly higher level of blockage (displacement thickness, Fig. 9(b)) is evident at the trailing edge for the varying $s$ case. According to the loss analysis approach based on boundary layer quantities by Denton [20], losses will tend to increase if the boundary layer is thicker at the trailing edge of the suction surface. The results in Fig. 9 therefore suggest increased losses for the present optimal boundary layer case at positive inflow incidence, as was found from integrating the pressure wake loss profiles of Fig. 7.

Riblet height $h$ and spanwise spacing $s$ is plotted as a fraction of the local boundary layer thickness $δ$ in Fig. 10 for the nominal, negative and positive inflow incidences. For all cases, the riblets become significantly smaller toward the trailing edge as a fraction of $δ$⁠. The decrease in $h/δ$ is somewhat less rapid toward the trailling edge (TE) for the varying $h$ case (Figs. 10(a), 10(c), and 10(e)), and conversely, $s/δ$ decreases less toward the TE for the varying $s$ case (Figs. 10(b), 10(d), and 10(f)), although we note that the riblet scaling for the optimal riblet cases was derived from the viscous scaling at the blade surface (since the optimal spacing of riblets has been expressed in terms of viscous units in the literature) and not in terms of boundary layer thickness. At the leading edge (LE), the spanwise spacing of the riblets for the optimal varying $s$ case is significantly smaller, especially at positive incidence (Fig. 10(f)). This may explain the very different behavior of the flow for this case, that is, the significantly increased loss seen in Table 2.

In Fig. 5, the local wall shear stress was plotted for all cases normalized by the reference dynamic pressure at the inlet. Due to the appreciable differences in the boundary layer thickness for the positive incidence case (Fig. 9), in Fig. 11, we replot the suction-side skin friction normalized by the local dynamic pressure at the boundary layer edge to verify if the apparent reduction in skin friction shown in Fig. 5 holds. The present locally optimal riblet surfaces appear to still give the largest reduction in skin friction with respect to the reference smooth wall case given this local scaling. Figure 11 also shows an inset of the TE region. The skin friction going below 0 indicates a separating flow: all positive inflow incidence cases appear to separate near or just before the TE. The present optimal cases seem more prone to separation at an earlier $x/C$ compared to the fixed riblets and the smooth reference case.

To understand how $PR$ behaves over the entire chord and beyond the near wake, Fig. 12(a) plots the streamwise running integral of the entropy generation due to turbulence production $PR$ at positive incidence. Additionally the same for the total entropy generation rate $Gs$ is plotted in Fig. 12(b). The overall trend of $Gs$ is similar to that of $PR$⁠, justifying the focus on this single term for the present cases. The additional entropy generation for the varying $s$ case appears to start from the LE and then increases further over that of the reference smooth-blade case within the wake.

A significant increase in $PR$ at the LE is seen for the present optimal riblet cases in Fig. 12(b). Therefore, Fig. 13 plots contours of $PR$ for the reference smooth case, the fixed 60-deg riblet case and for both present optimal riblet surfaces near the LE. For both optimal riblet cases (Figs. 13(c) and 13(d)), significantly different structures are evident in the LE region: the high-$PR$ region at the LE is a different shape, and moreover, the high-$PR$ region is much thicker over the suction side for both the varying $h$ and varying $s$ cases. These contours are suggestive of a complex interaction with LE structures at positive incidence, leading to a much larger value of $PR$⁠, that is, loss generation, from the LE for these cases, which then translates into a much higher integrated value of $PR$ (Table 3). This is further interrogated in Sec. 4.

Since $PR$ continues to increase after the TE in Fig. 12(a), Fig. 14 plots contours of $PR$ near the TE for the reference smooth case, the fixed 60-deg riblet case and for the present optimal, varying $s$⁠. The contours show less intense generation of entropy by turbulence production $PR$ for the fixed 60-deg riblet case compared to the smooth case, which aligns with the reduction in losses found in Table 2. On the other hand, the contours of $PR$ are more intense for the present optimal, varying $s$ riblet surface, for which a 20% increase in loss was found. Figure 14 highlights $PR$ in the trailing edge region.

The present high-fidelity numerical study investigates locally optimal riblets with a view to effecting a larger skin-friction reduction than fixed-geometry riblets, which were the topic of a previous study [1] and which tend to become very small in terms of viscous units toward the TE. We considered riblet surfaces where either the height $h$⁠, or the spanwise spacing $s$⁠, is smoothly scaled to target $h+≈10$ or $s+≈17$ in local viscous units. These “locally optimal” riblet surfaces do indeed reduce the skin friction on the surface of the HPC blade at both design and off-design inflow incidences and are generally at least as effective as the previous fixed-geometry riblet cases in doing so. Yet the present varying geometry riblet cases tend to result in increased pressure wake loss. In particular, at positive incidence, where the varying $s$ riblets reduced the skin friction reduction more than the fixed riblets, the wake loss was found to increase by a significant 20% with respect to the reference smooth-blade case. The boundary layers for both present varying riblet cases were found to be significantly thicker on the suction side, suggesting increased blockage.

Additionally, increased entropy generation by turbulence production is evident over the entire chord as well as within the wake and was found to be consistent with the pressure wake loss calculated. The fact that entropy generation was increased from the LE (as seen in the running integral of $PR$ in Fig. 12(a)), despite the decrease in skin friction with respect to the smooth blade case, suggests the importance of this region for setting the ensuing boundary layer flow state and in turn the performance of the HPC. Figure 13 clearly shows a complex flow structure in the LE region, with a much thicker region of very high $PR$ close to the blade’s surface for the present optimal riblet cases, borne out in the running integral shown in Fig. 12. The magnitude of velocity $|u|$ is shown in Fig. 15 for both the reference smooth blade case as well as for the present varying $s$ riblet surface which showed the largest increase in pressure loss and entropy. A separation bubble is evident on the suction side at the LE, which has markedly increased in size for the varying $s$ riblet case. This suggests a complex flow interaction at the LE which results in an increased loss. We note however, that the fixed riblet cases, which are not so different in height (Figs. 10(a), 10(c), and 10(e)) compared to the present optimal riblet cases, do not provoke such a large change in the flow physics near the separation bubble. Yet, the riblet spacing $s$ (Figs. 10(b), 10(d), and 10(f)) is much smaller for the varying $s$ case than for all the other riblet surfaces, especially for the positive incidence case. This smaller spanwise spacing of the riblets may have provoked the significant change in flow physics at the LE for the varying $s$ case as positive incidence. In addition, the contours of $PR$ shown for the TE (Fig. 14) show that, despite reductions in skin friction at the blade’s surface, additional losses (in this case, $PR$⁠), may be generated away from the surface of the blade. We note integrals of the viscous force over the blade’s surface confirm significant reductions of up to 25% with respect to the smooth blade reference cases, in agreement with the skin friction curves shown in Figs. 5 and 9. Yet, the viscous force for the HPC is typically two orders of magnitude smaller than the pressure force; therefore, only larger changes to boundary layer development induced by the riblets (i.e. changes in transition location and mode) are likely to result in significant changes to the blockage and therefore loss statistics. Figure 15 also shows contours of the pressure field; a larger low-pressure region is evident for the varying $s$ riblet case on the suction side (Fig. 15(d)).

Therefore, we conclude that riblets applied to an HPC blade can be effective at reducing the skin friction, but that this may not be the only effect at play. In particular, small geometric changes to the riblets in the LE region were seen to result in significant changes to the development of the flow over the suction side of the blade. In particular, the interaction of the riblets with the suction-side separation bubble at the LE for the positive inflow incidence has the potential to negatively impact loss statistics. The present riblet cases considered riblets wrapped around the entire HPC blade for reasons of simplicity, and concerns about increased losses resulting from a sudden appearance of riblets at some location along a smooth blade. A recent work [22] used an LE ramp to effectively minimize the additional spurt in the turbulent kinetic energy and the associated losses incurred due to an abrupt surface change when using a riblet surface. In the future, it may be prudent to consider a riblet surface with a smooth LE, to avoid possible deleterious effects to loss statistics at positive incidence in particular.

We are grateful for the permission of GE Aerospace to publish the results from this study. Support from the Australian Research Council is acknowledged. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$h$ =

Riblet height

$p$ =

Static pressure

$s$ =

Riblet spanwise spacing

$pT$ =

Total pressure

$Cp$ =

Pressure coefficient

$Cf$ =

Skin-friction coefficient

$Gs$ =

Entropy generation rate

$PR$ =

Entropy generation by turbulence production

$Ω(y)$ =

Kinetic wake loss profile

$ω$ =

Pressure loss coefficient

1, 2 =

inlet, outlet plane

APG =

Adverse pressure gradient

DNS =

Direct numerical simulation

HPC =

High-pressure compressor

LE =

Leading edge

LES =

Large-eddy simulation

TE =

Trailing edge