Influence of Complex Surface Structures on the Aerodynamic Loss Behaviour of Blades

Abstract

Operating airfoils under mechanical stress in combination with oxidation and corrosion, abrasion wear, and subsequent regeneration results in complex surface structures that influence the performance of aircraft engines. For predicting this impact on performance the authors propose a reduced order model capable of assessing the effect of surface roughness as a basis for making decisions before or during the regeneration process. The accuracy of this model is increased by using improved roughness sensitive transition and turbulence models created for Reynolds-Averaged Navier–Stokes simulations. Experimental studies are carried out to determine the local and integral effect of complex surface structures on blades and on a flat plate. Direct numerical simulations are also performed to study the effect of complex surface structures on a turbulent boundary layer and contribute to improving the accuracy of prediction, which is achieved by using re-calibrating models and taking into account the effect of skewness and anisotropy of complex surface structures on turbine blade losses.

1 Introduction

During operation, an aircraft engine experiences many different operating conditions that can lead to deterioration. Among them is an increase of surface roughness, consisting of highly complex surface structures. Depending on the location in the engine and the regeneration process, the surfaces show isotropic (stochastically irregular) and anisotropic (oriented) structures. With a confocal laser microscope, the surface of a blade can be optically measured and converted into a height map. For the Computational Fluid Dynamics (CFD) simulation, the calculation of the equivalent sand-grain roughness k_s of the optically measured height map has been considered appropriate. The equivalent sand-grain roughness k_s was first introduced by Nikuradse (1933) and Schlichting (1936), who studied the influence of surface roughness on the flow at different Reynolds numbers and established a relation with the aerodynamic drag. Each technical roughness can be assigned an equivalent sand-grain roughness based on the aerodynamic drag. In an overview, Bons (2010) summarises the most common correlations for the conversion of a technical roughness into the equivalent sand-grain roughness, e.g. the Shape and Density parameter Λ_s of Sigal and Danberg (1990), which specifies the shape and density of roughness elements on the surface. Significant research on this topic has also been carried out within this project of the Collaborative Research Centre 871 (CRC 871). For instance, Hohenstein and Seume (2013) and Gilge et al. (2019a) propose the use of the Shape and Density parameter Λ_s in combination with the approach of Bons (2005):

$$\text{log}\left(\frac{{k}_{\text{s}}}{k}\right)=-0.43\text{log}\left({\Lambda }_{\text{s}}\right)+0.82.$$

(1)

Bons (2005) and Hohenstein and Seume (2013) have shown that the absolute roughness height R_z as a scaling factor k in Eq. 1 is suitable in order to be able to map the influence of complex surfaces in CFD. The use of this approach is also in accordance with the results for polished surfaces (Goodhand et al. 2016).

Initially, the local and integral effect of complex surface structures on turbine blades was studied by Hohenstein et al. (2013b) who measured the surfaces of 9 turbine blades of the second rotor stage of a worn high-pressure turbine (HPT) in the dismantled state. The flight region, in which the turbine blades had completed around 24,000 h and 9,000 cycles, is specified with moderate environmental conditions of Europe and North America. Primarily anisotropic structures were found on the first rotor stage. Some of the roughness structures are applied on an aerodynamically scaled turbine blade and investigated in the cascade wind tunnel of the Institute of Turbomachinery and Fluid Dynamics (TFD). By using total pressure probes, particle image velocimetry (PIV), and an innovative laser ablation process, the effect of locally applied real complex surface structures and their combinations on the wake was measured. Gilge and Mulleners (2016) showed that the local pressure gradient has a significant effect on the roughness-induced loss mechanisms. Additionally, Neuhaus et al. (2016) found a shift of slightly anisotropic turbulence for the wake of a smooth blade to isotropic turbulence in the wake of rough blades. In conjunction with an increase in turbulent kinetic energy, this correlates with higher profile losses. Hohenstein et al. (2013b) also compared the experimental results to Reynolds-averaged Navier–Stokes (RANS) simulations, which predicted significant different total pressure losses. Subsequently, a compressor cascade was designed for the cascade wind tunnel and investigated with regard to complex surface structures within this project of the CRC 871. Gilge et al. (2018) show that a roughness on the suction side affects the entire wake and leads to friction losses up to 7.1%. A roughness on the pressure side affects mainly the shear region on the pressure side leading to friction losses up to 2.3%. In general, the roughness’s effect depends strongly on the location and is not completely superimposable, which is consistent with the study of the turbine cascade. To analyse the local flow effects, a boundary-layer water tunnel was installed during the project. In an experimental study, Kurth et al. (2018) show that the anisotropy of surface structures has a significant effect on the boundary-layer flow. This effect is not included in the k_s-correlation of Bons (2005) (see Eq. 1). Similar results to Kurth et al. (2018) can be found in Lorenz et al. (2013) and Ahrens et al. (2021).

Based on the results of this project within the CRC 871, a reduced order model for the quantitative prediction of the effect of surface roughness during operation and after regeneration for the regeneration process is developed. Here, the reduced order model is based on RANS simulations. This type of CFD simulation is mainly used for the aerodynamic design of turbomachinery with lower time requirements compared to the regeneration process. Due to the time averaging, RANS simulations require models that approximate the turbulent viscosity µ_t. As the reduced order model is based on RANS simulations, the accuracy of the RANS models must be high and able to capture the effects of surface roughness. Thus, the objective is to provide a RANS-based turbulence and transition model combination that improves the prediction of the effect of complex surface structures. Two approaches must be pursued: standardizing the roughness’s characterization and improving the modelling of the influence of complex surface structures. From these approaches, the question arises: Can an improved prediction of the roughness effect be achieved by a change of the modelling, i.e. RANS model, or by changing the k_s correlation? Before answering this question, the next section presents the significance of surface roughness in turbomachinery.

2 Roughness Effect in Multistage Modules

2.1 High-Pressure Compressor

Gilge et al. (2019a, b) used a confocal laser microscope to measure optically the surfaces of worn rotor blades of a ten-stage high-pressure compressor (HPC) in the dismantled state. The blades measured were rotor blades of a front, middle, and rear stage, which had completed 20,000 cycles in geographic regions with mainly low environmental impact (Wensky et al. 2010). On the pressure side, more homogeneous isotropic structures are found and the roughness height decreases along the blades and across the stages. The isotropic structures are caused by impacts and erosion or deposition. On the suction side, the roughness height also decreases across the stages, but the surface structures vary. At the leading edge, anisotropic structures occur, which become more isotropic along the blade (see Fig. 1). The authors explain the anisotropic structures with oil leakages sticking flow particles to the surface. Seehausen et al. (2020) built a model of a typically rough HPC blading. Figure 1 shows the roughness height k_s across the stages divided into the suction and pressure side. The surfaces of Gilge et al. (2019a), measured optically, serve as supporting points.

Fig. 1

Roughness distribution across the stages of the HPC after 20,000 cycles in service and examples of measured surfaces Gilge et al. (2019a, b). The figure is adopted from Goeing et al. (2020b)

In a CFD study, the effect of the real complex surface structures measured and interpolated for the HPC blading on the module performance was investigated. The mesh of the ten-stage HPC of the V2500 engine consists of approx. 26 million cells and was provided by Reitz et al. (2018). The numerical model of the compressor contains the cavities of the front stages, as well as the bleed air extractions. In addition, the snubber in the first blade row is taken into account as it has a significant influence on the flow and the blockage of the compressor. The radial tip-gaps of the rotor rows are set to 1% of the respective duct height. The CFD simulations were carried out with the non-commercial flow solver TRACE 9.1 (Franke et al. 2005; Nürnberger 2004; Kugeler et al. 2008) provided by the German Aerospace Center (DLR). Based on the finite volume method, the Favre-averaged Navier Stokes equations are solved on block-structured meshes. The discretization of the convective flows is carried out with the second-order backward difference scheme according to Roe (1981). The diffusive flows are solved with a second-order central difference method. The HPC is calculated fully turbulent and takes into account the equivalent sand-grain roughness k_s via the wall function. This means that the viscous sublayer of the boundary layer is not directly solved. The wall function is based on the wall shear stress velocity u_τ, which describes a turbulent velocity scale at the wall. If a roughness is assigned to the wall, the logarithmic boundary-layer profile is calculated as a function of the dimensionless equivalent sand-grain roughness ${k}_{s}^{+}\left({=}\frac{{u}_{\tau }{k}_{s}}{\nu}\right)$ according to:

$$\frac{U}{{u}_{\tau }}{=u}^{+}=\frac{1}{\kappa }\text{ln}\left({y}^{+}\right)+\frac{1}{\kappa }\text{ln}\left(\frac{1}{{k}_{s}^{+}}\right)+8.4$$

(2)

Seehausen et al. (2020) created a compressor map, which allows to asses the effect of surface roughness on the module performance (see Fig. 2). The generation of a compressor map requires several CFD simulations with gradually increased or decreased static pressure at the HPC outlet. Here, throttle lines for the operating points ‘cruise’ and ‘take-off’ were created with about 15 CFD simulations each. The black squares represent smooth operating points, while green dots show the fully rough map. The fully rough map is shifted towards lower mass flows with a reduction of 5.73% in mass flow $\dot{m}_{\text{corr}}$ at ‘take-off’ and 4% in mass flow $\dot{m}_{\text{corr}}$ at ‘cruise’. Additionally, the map narrows between the reduced surge and choke margins, leading to a reduction of 4% (12.3%) in total pressure ratio π_tt, and a reduction by 2.36% (2.68%) in polytropic efficiency η_poly at ‘take-off’ (‘cruise’). Consequently, increased surface roughness leads to an increase in the specific fuel consumption. Reitz et al. (2018) investigated the effect of a macro-scale geometry change through doubled tip-gaps on the performance of the HPC. To reduce computational resources, Reitz et al. (2018) used a method to scale performance maps based on scaling factors Li et al. (2011). The operating points scaled for doubled tip-gaps are represented by the magenta coloured crosses. The effect of surface roughness on the performance reduction is about 1% greater than the effect of doubled tip-gaps. The effect of doubled tip-gaps on the pressure ratio is quite small due to the boundary conditions set in the numerical setup, i.e. total pressure at the inlet and static pressure at the outlet. Goeing et al. (2020a) extended the investigation of Seehausen et al. (2020) by four different sets of rough HPC blades and vanes of a fully rough HPC. Subsequently, a map of scaling factors is obtained to represent the roughness effect of different states on compressor maps. Using this map reduces the computational effort and it is sufficient to import the smooth compressor map into the performance analysis of project D6 “Interaction of combined module variances and influence on the overall system behaviour” within this CRC 871. The results of this study are also used in Goeing et al. (2020b) to asses the effect of combined module variances.

Fig. 2

Compressor maps with different deterioration modes. Inspired by Seehausen et al. (2020)

Seehausen et al. (2020) further analyse the loss-sources in a multistage HPC with respect to surface roughness. A stage roughness variation with surface roughness uniformly distributed over the blade’s suction side of single stages is performed. The simulations show that the first stage has the biggest effect on the compressor performance at both operation conditions, ‘take-off’ and ‘cruise’. Additionally, it is shown that the stage losses are not superimposable. Seehausen et al. (2020) conclude that surface roughness changes the stage-by-stage matching resulting in bigger overall performance in front stages than in rear stages. These results also confirm that predicting the local roughness effect accurately is necessary when evaluating the module performance.

2.2 High-Pressure Turbine

In this project of the CRC 871, the authors also studied the effect of surface roughness on the performance of a high-pressure turbine (HPT). In order to demonstrate the process of blade regeneration, a system demonstrator was set up in project S “System Demonstrator” within this CRC 871. A part of the regeneration process is the performance evaluation in the virtual layer of the system demonstrator. To include the effect of surface roughness on the module performance, a reduced order model was required. The description of the reduced order model for the virtual regeneration process of a V2500 HPT blade can be found in Goeing et al. (2022). Based on scaling factors obtained by RANS simulations of the V2500 HPT with different modes of deterioration, a neural network was trained. Subsequently, project D6 “Interaction of combined module variances and influence on the overall system behaviour” within this CRC 871 used this neural network to predict the module performance for the performance simulation of the engine. Figure 3 shows the HPT setup for the RANS simulations consisting of 8M cells, which required about 84 CPUh for a converged solution. It was found that the roughness effect is not as dominant in an HPT as for the HPC with significantly more stages.

Fig. 3

HPT geometry with blade under consideration highlighted in red and blade geometry with exemplary measured roughness structures. The figure is adopted from Goeing et al. (2022)

Nevertheless, modern blade profiles aim for large laminar boundary layers that lead to low heat transfers and low heat loads. This is accompanied by low aerodynamic losses for laminar boundary layers. In general, surface roughness leads to an opposite effect by introducing disturbances that destabilize the boundary layer. Hohenstein (2014) investigated the effect of locally applied surface structures on the boundary layer and the profile losses. The results show that roughness structures can lead to a shift of the location of transition, a change of the transition mode, and a reduction of the suction peak. These results are in accordance with the results of Stripf (2007). Stripf (2007) studied the effect of surface roughness on the transition with respect to the heat transfer. Although a different concept is used to evaluate surface structures (in this case a discrete element method), the importance of accurately predicting the roughness’s effect on the laminar-transitional boundary layer is shown.

3 Modelling the Roughness Effect

3.1 Fundamentals

Solving the RANS equations requires models which approximate the turbulent eddy viscosity µ_t. The turbulence model attempts to predict the production and the decay of turbulence, e.g. turbulent kinetic energy k. In this work, the focus is on the k-ω turbulence model by Wilcox (1988) and the SST turbulence model by Menter (1994). Both models are based on two transport equations: one for the turbulent kinetic energy k and one for the specific dissipation rate ω. Outside the boundary layer, a cross-diffusion term is added to the SST model formulation resulting in the k-$\epsilon$ formulation. This eliminates the sensitivity to the free stream turbulence of the conventional k-ω formulation. Besides this difference, the SST model considers the Bradshaw assumption that, when calculating the eddy viscosity µ_t, the shear stress τ_ij is proportional to the turbulent kinetic energy k. This limits the turbulence production in regions where the conventional formulation overestimates the eddy viscosity. In case of laminar shear-layers, transition models are used for the correct prediction of transition and the modes of transition. To account for the different modes of transition, different approaches for modelling the transition evolved in the past decades (Suzen et al. 2002; Menter et al. 2006, 2015; Kožulović 2007; Stripf et al. 2008; Langtry and Menter 2009). The transition model controls the production of turbulent kinetic energy of the turbulence model and, thus, most of the transition models are designed to trigger the turbulence model instead of predicting the physical effect in detail (Langtry and Menter 2009). In contrast, a few concepts of laminar kinetic energy (LKE) models exist, which present a more physically-based approach for transition modelling (Walters and Leylek 2004; Walters and Cokljat 2008). However, the use of LKE models is still limited to academic test cases. In this work, the γ-Re_θ transition model of Menter et al. (2006) is used. This transition model is based on local variables of each cell without the need for any boundary layer integration and no requirement on the geometry or meshing. The model solves two additional transport equations, i.e. one for the intermittency γ and one for the momentum-thickness Reynolds-number Re_θ. Based on these two transport variables, experimental correlations are used to predict the correct point of transition. In its original formulation, the model is not able to consider a rough-wall boundary condition. Due to the difficulty to combine different transition modes, Menter et al. (2006), Langtry and Menter (2009) concentrated on first order effects, i.e. natural, bypass transition, and separation-induced transition. Extensions for secondary flow effects, such as injection-induced transition or crossflow-induced transition, are proposed by Herbst et al. (2014) and Müller and Herbst (2014). Boyle and Senyitko (2003), Hohenstein et al. (2013b), Gilge et al. (2017) show that extensions for other second order effects, such as surface roughness, are needed. Dassler (2013) added a third transport equation to the transition model formulation of Langtry and Menter (2009) for modelling the effect of surface roughness. Wilcox (1988) adjusts the dissipation rate ω at the wall depending on the non-dimensional sand-grain roughness k ⁺_s to incorporate second-order flow effects in turbulent boundary layers. This method, however, is not suitable for surface structures such as riblets (exemplary for a strongly anisotropic surface structure) due to their drag-decreasing effects. To realize this effect, Koepplin et al. (2017) applied a damping function to the destruction term of the dissipation rate ω. The sections below describe the process of assessing the original modelling of the roughness effect for turbulent and laminar boundary layers. They also answer the above question: Can an improved prediction of the roughness effect be achieved by a change of the modelling, i.e. RANS model, or by changing the k_s correlation? Below, we will first concentrate on a turbulent boundary layer with DNS and then on a laminar boundary layer with experiments. Changes to the modelling approach are made in the non-commercial flow solver TRACE 9.1 of the DLR (Franke et al. 2005; Nürnberger 2004; Kugeler et al. 2008).

3.2 Turbulent Boundary Layer

From a modelling point of view, a decrease of the specific dissipation ω results in an increase of the eddy viscosity µ_T and turbulent kinetic energy k. Thus, higher turbulent fluctuations and viscous losses occur. Wilcox (1988) shows that the modification of the specific dissipation ω at the wall can accurately predict the velocity profile affected by a rough surface. These results could be verified for complex isotropic surface structures by using the immersed boundary method (IBM) for direct numerical simulations (DNS) (Kurth et al. 2021, 2022). In comparison with body-fitted approaches, the IBM allows regular meshes that are independent of the immersed body and can be easily transferred to other surfaces without need for major human interaction. The DNS-IBM approach provided in foam-extend-4.0 is used to asses the prediction accuracy of the roughness effect in turbulent boundary layers. The IB-method used can be found in Senturk et al. (2019). The DNS is based on a cell-centred finite volume discretization with a PISO algorithm for the solution of the incompressible flow equations. For the second-order accurate time and space discretization, Gauss linear scheme and backward temporal discretization are chosen from the incompressible solver icoFoam. To analyse the local flow effect, a channel setup is used. At channel’s top, which corresponds to the boundary layer thickness δ, symmetric conditions are imposed. A periodicity is imposed at the lateral boundaries to limit the flow domain and to allow spatial averaging for better flow statistics. The roughness is immersed in the bottom wall with no-slip condition. A linear blending function to blend 10% of the roughness patch on the borders is used to ensure periodicity of the roughness. Specifying the friction velocity Reynolds number

$$\text{Re}_{\tau }=\frac{{u}_{\tau }\cdot \delta }{\nu},$$

(3)

by a constant momentum body force in the momentum equations allows comparing different surface structures at same aerodynamic conditions. Additional settings can be found in Kurth et al. (2022). Next to the DNS-IBM channel setup, a double infinite channel sized two times the boundary-layer thickness in lateral direction and three times in flow direction is built for the RANS computation with approx. 4M cells. In contrast to the DNS-IBM channel setup, the roughness is not physically visible, but rather represented by a wall boundary condition. For different roughness structures, the RANS simulations with a rough-wall boundary condition are performed enforcing the same friction velocity Reynolds number as in the DNS-IBM setup. Subsequently, the velocity profiles are extracted. As depicted in Fig. 4, it is possible to find a k_s value resulting in the velocity profile of the DNS-IBM approach. In a sensitivity study, Kurth et al. (2022) shows that the skewness of a surface has a significant impact on the local effect of roughness. The skewness Ssk of the roughness is a parameter used to quantify, whether a roughness consists primarily of hills (Ssk > 0) or valleys (Ssk < 0) (see DIN EN ISO 25178). Based on the effect of the skewness on the velocity deficit in the DNS-IBM approach, the k_s correlation (see Eq. 1) can be extended by:

$$\frac{{k}_{s,\text{SD},Ssk}}{{k}_{s,\text{SD}}}=0.0266 \cdot Ss{k}^{2}+0.1426\cdot Ssk+0.7977.$$

(4)

Fig. 4

Comparison of velocity profile between DNS and RANS, with roughness height in DNS represented by a dashed vertical line

In addition to complex isotropic surface structures, anisotropic surface structures occur during operation or regeneration. Within this project, Ahrens et al. (2021) investigated the effect of synthetic anisotropic structures superimposed with real complex surface structures on the flow losses. A sinusoidal function with a period s⁺ = 252.5 and an amplitude of z⁺ = 6 is used for anisotropic surface structures. The dimensions for these anisotropic surface structures are found on worn compressor blades (Gilge et al. 2019a). It was found that the flow losses increase with higher relative flow angles, but have a non-linear relationship with the orientation of the anisotropic structures. Additionally, the anisotropic structures show a dominant effect over the isotropic roughness effect above a certain relative flow angle. For building new models, the database has to be extended, as only one parameter combination has been investigated so far. Nevertheless, this database is useful for validating new models.

3.3 Laminar Boundary Layer

Alldieck et al. (2020) studied the effect of rough-wall boundary conditions on the RANS-based transition prediction. As could be derived from the full set of equations of the γ-Re_θ transition model, it is not only the transition model responding to a rough-wall boundary condition in laminar boundary layers, but also the turbulence model. A modification of the specific dissipation rate ω by the turbulence model for rough walls must have an effect via the increased eddy viscosity ratio on the roughness-induced transition prediction due to an increased production of γ. This means that the turbulence model can have an accelerating effect on the transition for rough-wall boundary condition. Alldieck et al. (2020) shows that the robustness of the eddy viscosity ratio against surface roughness in the SST model gives low sensitivity to the transition onset prediction of the γ-Re_θ model. This behaviour is advantageous compared to the k-ω model, where the modelled roughness effect strongly depends on the turbulent length scale (Dassler 2013; Bode et al. 2014). Unfortunately, the SST model in its original formulation is not able to account for rough-wall boundary conditions, since the eddy-viscosity limiter ensuring the Bradshaw assumption disables the rough-wall boundary condition of the k-ω formulation (Hellsten and Laine 1997). By introducing an additional limiter which deactivates the Bradshaw assumption in specific regions, such as in the sublayer and roughness layer, Hellsten and Laine (1997) solved this problem. Here, the limiter is implemented in the source code of TRACE 9.1. The model is activated with the command all immediate ChangeTurbulenceSettings—model MenterSST2003 –HellstenRoughness ON. Dassler (2013) developed an extension for the γ-Re_θ transition model to consider the rough-wall boundary condition in the transition model. The command to activate the roughness model is given in the TRACE User Guide (2019).

The roughness modification of the γ-Re_θ transition model by Dassler (2013) is based on the experiments of Feindt (1956) in an annular wind tunnel. Dassler (2013) introduced a third transport equation for the non-dimensional value A_r

$$\frac{D(\rho {A}_{r})}{Dt}=\frac{\partial }{\partial {x}_{j}}\left[{\sigma }_{{A}_{r}}\left(\mu +{\mu }_{T}\right)\frac{\partial {A}_{r}}{\partial {x}_{j}}\right]$$

(5)

allowing the roughness effect to convect and diffuse into the flow field. Similar to the incorporation of a rough-wall boundary condition in the ω-equation of the turbulence model, the value of A_r is correlated with the local non-dimensional sand-grain roughness k⁺

$${A}_{r,W}=8\cdot {k}_{s}^{+}$$

(6)

at the wall. The transported value A_r adds sensitivity to the momentum thickness Reynolds number $\widetilde{Re}$_θt via the variable Arg_r. A reduction of the transport value $\widetilde{Re}$_θt results in a shift of the transition to an upstream position. Since the model formulation is initially calibrated in conjunction with the k-ω model, a re-calibration is required before applying it with the SST model. The re-calibration process shows that amplifying the function of Arg_r over A_r by a factor of 5 is required, because the SST model damps the roughness effect compared to the k-ω model. These results are presented in Fig. 5. Here, the transition onset Reynolds number Re_xt is plotted as a function of the surface roughness height Re_ks for different pressure gradients. The transition onset Re_xt is defined at the minimum of the friction coefficient c_f. This point agrees with the definition of Feindt (1956). The experimentally measured points of Feindt (1956) are represented by the black circles. The re-calibrated model is tested for different roughness heights and gives a good approximation of the experimentally determined data.

Fig. 5

Transition onset location Re_xt depending on the critical roughness Reynolds-number Re_ks for different pressure gradients

4 Experimental Results and Validation

4.1 Boundary-Layer Water Tunnel

The boundary-layer water tunnel of TFD is used to study the effect of isotropic and anisotropic surface structures on laminar-transitional boundary layers. In this work, the data serve as validation data for complex isotropic surface structures, but also for the development of new models with respect to anisotropic surface structures. Publications by Kurth et al. (2018, 2022) include a description of the water tunnel and present recent work on the effect of surface structures on the local flow. In the present investigation, a flat plate is placed in the measurement section of the water tunnel, and a laminar boundary layer develops on this plate. In accordance with the experiments of Feindt (1956), optically scanned sandpapers with different grain sizes are selected to study the effect on local flow of surface roughness. Each sandpaper is measured at 10 different positions. Subsequently, the roughness correlation of Kurth et al. (2022) is applied to obtain the equivalent sand-grain roughness for each of the samples. The Shape and Density parameter is calculated using the roughness parameter Sz. The equivalent sand-grain roughness of the optically measured sandpapers is in a good agreement with the roughness used by Feindt (1956) (see Table 1). In contrast, the samples for the sandpaper P150 show a sand-grain roughness that is too high.

Table 1 Comparison of equivalent sand-grain roughness k_s of scanned sandpaper with 95% confidence interval

Due to the lower kinematic viscosity of water compared with air, the structures must be scaled. The aerodynamic scaling is obtained by using the RANS simulations of the experiment by Feindt (1956) (Alldieck et al. 2020). A 3D polyjet printer is used for the additive manufacturing of scaled surface structures that have a size of 180 mm × 80 mm (L × W) and approx. 5 mm in height. The roughness structures investigated by Feindt (1956) show high positive skewness values due to the use of sandpapers. According to DIN EN ISO 25178, the roughness height is negative when the point is facing the material from the reference surface. The reference surface of sandpaper is defined by the lowest point of the surface, while the reference surface of complex surface structures of blade profiles can conveniently be assumed to be the mean profile of the measured roughness. Hohenstein (2014) shows that most of the surfaces of worn blades have a skewness of around 0, negative skewness values being slightly more common. The 3D printed surfaces show a skewness of approx. 0.5–1. However, we consider the skewness with the correlation of Kurth et al. (2022) and, thus, are able to predict the roughness effect on the boundary layer.

The isotropic roughness structures P60 and P240 are superimposed with a sinusoidal function with different periods s and amplitudes t to study the effect of anisotropy. A synthetically created surface is chosen for a better isolation of the individual effects on the flow. The ranges of the anisotropic roughness parameters are shown in Table 2. A new parameter Sq_r is introduced to specify the ratio of the anisotropy with respect to the isotropic surface. The parameter is defined as follows:

$$\text{Sq}_{\text{r}}=\frac{S{q}_{\text{filt}} }{Sq}$$

(7)

based on the root mean square roughness height of the filtered and non-filtered surface. The 3D topography is first subjected to a Fourier transform. Then, the spatial frequency with the highest amplitude is filtered. An anisotropy is said to exist when the filtered surface has a significantly lower root-mean-square roughness height than the non-filtered surface. In case of an isotropic surface the ratio of Sq is approx. 1.

Table 2 Parameter ranges for the anisotropic surface structures investigated in the boundary-layer water tunnel

The 3D-printed isotropic and anisotropic surface structures are placed in the flat plate. The flow over the rough surfaces is measured using the stereo PIV. A set of 3000 image pairs is recorded with a frequency of 10 Hz. A shift of approx. 10 px/image and an interrogation window size of 32 × 32 pixel results in an uncertainty of 0.196 pixel for the evaluation process representing a 95% confidence interval (Westerweel 1997; Raffel et al. 2018). Figure 6 shows an extract of the results. The lateral flow velocity normalized by the free stream velocity is plotted over a period s for different relative flow angles α. The flow is deflected by the wind-wetted flanks of the anisotropic structures. This flow deflection is convected within the boundary layer. A relative flow angle of 60% results in a flow deflection of up to 20%. Kurth et al. (2018) obtain similar results and shows that anisotropy of surface structures can result in a significant flow deviation depending on the parameters of the anisotropy. Based on the experimental setup, a turbulent boundary layer can be assumed. With that, the results are in accordance with the measurements of the 3D-printed surface structures in a laminar boundary layer.

Fig. 6

Contour plot of the lateral velocity induced by the anisotropy of the surface structure normalized with the free stream velocity for Sq_r = 0.52

Hohenstein and Seume (2013) show that the equivalent sand-grain roughness k_s can capture the induced drag due to anisotropy. For incorporating the effect of anisotropic surface structures in the RANS models, the roughness correlation of Eq. 8 is extended. By comparing the velocity profiles at specific positions, an equivalent sand-grain roughness is found, which captures the drag increasing effect of the anisotropy. In a first approach, the following correlation is derived for the range of laminar boundary layers:

$$\frac{{k}_{s,\text{SD},Ssk,A}}{{k}_{s,\text{SD},Ssk}}=-0.06\cdot \left(\text{Sq}_{\text{r}}-1\right)\cdot \left(\text{tanh}\left(0.8987\cdot \pi \cdot \frac{\alpha }{45}-\pi \right)+6.276\right)+1.$$

(8)

It will be of interest for future studies, to see, whether the correlation also applies to turbulent boundary layers. Moreover, if there are additional parameters that are important for the correlation.

4.2 Cascade Wind Tunnel

The cascade wind tunnel of the TFD was used extensively within this project as it is easily accessible and versatile. In this section, we validate the integral prediction using results of the influence of complex surface structures on the aerodynamics of turbine blades. Please refer to Gilge et al. (2018) for results on the compressor blade investigations. The turbine blade geometry used is designed within an optimization algorithm based on the aerodynamics of a blade from an HPT’s second stage (Hohenstein et al. 2013a). The optically measured surface roughness of worn and regenerated blades serves as a data base. Initially, Hohenstein (2014) selected some of the optically measured surfaces to be attached on the turbine blade. The surface structures are aerodynamically scaled and applied on metal strip with 4 mm length in flow direction. A laser ablation process was used for the application. The metal strip is placed in a groove of the blade at different relative chord length positions, i.e. 0, 20, 50, and 85%. The blade of interest is divided in two parts within the cascade. This eliminates external effects by referring to the smooth neighbour blade. A double wedge probe is used to measure the flow quantities in the wake. The integral total pressure loss is calculated based on the wake measurements. Figure 7 shows the relative total pressure loss with respect to a smooth blade for different roughness configurations. The bar plot compares the experiment with the RANS prediction by the old and the new model. Table 3 shows the specifications of the different configurations.

Fig. 7

Relative total pressure loss coefficient with 95% confidence interval for the experiment of different complex surface structures applied on the turbine blade. Old model: SST without extension of Hellsten and Laine (1997), original γ-Re_θ, and k_s correlation according to Eq. 1. New model: SST with extension of Hellsten and Laine (1997), re-calibrated γ-Re_θ, and k_s correlation according to Eq. 8

Table 3 Specifications of the roughness configurations applied on the turbine blade

The RANS prediction of the integral effect of complex surface structures shows more accurate results for the new model in the laminar boundary layer than the old model (M1b1 and M2b1). Even though the equivalent sand-grain roughness decreases by using the correlation of Eq. 4, the re-calibrated γ-Re_θ roughness model is able to satisfy the mean experimental results. The improved model reduces the deviation from 0.3 to 0.016% of the measured value for M1b1 and from 0.183 to 0.11% for M2b1. In the turbulent boundary layer, the mean of the experimental results is not that consistent (M4b1 and M4b2). An increase in total pressure loss is expected with increasing surface roughness, as shown by the RANS prediction. This leads to a slight increase in the deviation from 1.08 to 1.27% of the measured value for M4b1, but a decrease in the deviation from 0.828 to 0.737% of the measured value for M4b2. In the experiments, roughness applied at 50% chord showed a suppression of the laminar separation bubble (Hohenstein 2014). The re-calibrated transition model is not able to predict this behaviour (M3b1 and M3b2). One reason for this phenomenon could be the locally changed blade geometry due to the roughness patch glued in the blade groove. However, the new approach significantly increases the prediction accuracy of the mean losses. Nevertheless, the interaction of surface roughness and the suppression of a laminar separation bubble needs further investigations.

5 Conclusions

Aircraft engine performance is influenced by complex surface structures that occur during operation. The authors propose a reduced order model capable of assessing the effect of surface roughness on the performance as a basis for the decision making in the regeneration process. The reduced order model is based on an improved RANS approach for which detailed numerical and experimental studies have been carried out on different test benches.

The modelling deficit for complex surface structures is reduced by considering the skewness of a surface structure when calculating the equivalent sand-grain roughness. The transition model is re-calibrated for a better prediction of a roughness-induced transition. This results in an improved prediction of the effect of complex surface structures on the integral flow parameters. It is found that the conventional rough-wall boundary condition in most of the CFD solvers is applicable when modelling the effects of isotropic complex surface structures.

However, experimental studies show that anisotropic surface structures can lead to a significant flow deflection. The roughness correlation can predict the drag increasing effect in the flow direction due to anisotropy, but not the flow deflection effect. Thus, the authors further strive to improve the model by imposing volume forces to model the flow deflection.