Momentum Thickness Research Articles

Artificial intelligence control of flow separation from a curved ramp

This work aims to control flow separation from a two-dimensional curved ramp. The Reynolds number examined is Reθ = 5700 based on the momentum thickness of the turbulent boundary layer right before the ramp. Three steady jets, blowing tangentially along the ramp from three spanwise slits, are deployed at the most likely flow separation position, upstream and downstream of this position, respectively. Three different control modes are investigated, i.e., a single jet, multiple jets, and genetic algorithm-optimized blowing rates of three jets. The single jet placed at the time-averaged flow separation position is found to be most effective and efficient in eliminating flow separation among the first and second control modes. However, it is the third control mode that may not only eliminate the separation bubble completely but also cut down the energy consumption, by up to 30%, compared to the single jet blowing at the flow separation position. The flow physics underlying the control modes is also discussed.

Point-enhanced convolutional neural network: A novel deep learning method for transonic wall-bounded flows

Low order models can be used to accelerate engineering design processes. Ideally, these surrogates should meet the conflicting requirements of large design space coverage, high accuracy and fast evaluation. Within the context of aerospace applications at transonic conditions, this can be challenging due to the associated non-linearity of the flow regime. Different methods have been investigated in the past to predict the flow-field around shapes such as airfoils or cylinders. However, they usually have reduced spatial resolution, limiting the prediction capabilities within the boundary layer which is of interest for transonic wall-bounded flows. This work proposes a novel Point-Enhanced Convolutional Neural Network (PCNN) method that combines the advantages of the well-established PointNet and convolutional neural network approaches. The PCNN model has relatively low memory requirements in the training process, preserves the spatial correlation in the domain and has the same resolution as a traditional computational method. The architecture is used for the flow-field prediction of civil aero-engine nacelles in which it is demonstrated that the flow features of peak isentropic Mach number (Mis), pre-shock isentropic Mach number and shock location (X/Lnac) are captured within ΔMis = 0.02, ΔMis=0.04, ΔX/Lnac=0.007, respectively. The PCNN model successfully predicts the integral parameters of the boundary layer, in which the incompressible displacement thickness, momentum thickness and shape factor are typically within 5% of the CFD. Overall, the PCNN method is demonstrated for transonic wall-bounded flows for a range of flow physics that include shock waves and shock-induced separation.

Performance of Rough-Ribbed Low-Pressure Turbine Blades Under Varying Loading and Operating Conditions

Abstract In this research, we pursue the efficacy of riblets in reducing blade profile loss of Low-Pressure Turbine (LPT) blades under various design and off-design conditions. We adopt a strategy in which surface roughness is employed in the transitional regime to minimize the separation bubble-related losses and flush mounted riblets downstream to mitigate the boundary layer losses due to an increase in the turbulent wetted area. Several high-fidelity scale resolving simulations are carried out to test the efficacy of this ‘rough-ribbed’ LPT blade for loadings ranging from low-lift (LL), high-lift (HL) and ultra-high-lift (UHL) conditions. Furthermore, two exit Reynolds numbers - 83,000 and 166,000 pertaining to engine-relevant design and off-design conditions, respectively, are considered. The streamwise evolution of skin friction coefficient, boundary layer integral parameters, instantaneous flow features and second-order statistics are analyzed to determine the design and off-design performance of riblets. The results demonstrate the efficacy of scallop-shaped riblets in reducing the profile loss and the blockage due to boundary layers with loading and Reynolds number. This resulted in a net skin-friction reduction of 3.4% for LL and 8% for UHL loading at cruise and a corresponding reduction in the trailing edge momentum thickness from 10% to 15%. Furthermore, the study highlights the necessity to optimize the riblet ramp to achieve skin friction reduction under off-design conditions.

Growth characteristics of the mean shear layer in pipe bends with and without a guide vane

The growth characteristics of two identical pipe bends with and without a guide vane are investigated by means of large eddy simulation. The two pipe bends, with a radius of curvature slightly above the separation threshold, are subjected to two fully developed upstream flow conditions, with a corresponding Reynolds number of 11 700 and 24 000. A precursor computation method is employed to provide the fully developed turbulence inflow conditions for all cases. The growth of the mean shear layer in this work is characterized by the local momentum thickness, which measures the extent of momentum deficit confined under the mean shear layer. For both pipe bends, the initial growth of momentum thickness is observed in the first quarter of the bend. The onset location is almost independent of the Reynolds numbers. However, a clear Reynolds number dependence is observed in the onset magnitude, which strongly defines the growth rate thereafter. By examining the mean momentum balance in the bend section, the results show that rather than the adverse pressure gradient, the overall growth characteristics of the mean shear layer, which include the onset location and the growth rate, are better described by the balance between the centrifugal force and the radial pressure gradient. This balance manifests itself as a change in the swirling intensity of the secondary flow. The presence of guide vane significantly suppresses the swirling intensity in the bend section, leading to a noticeable reduction in the overall momentum thickness growth and the production of turbulence in the flow downstream of the bend. Further inspection also indicates that the initial mechanism leading to the suppression of separation at the inner bend is linked to the increasing dominance of the small vortices at the near-wall vicinity relative to the local adverse pressure gradient. Certain aspects pertaining to the turbulent statistics are also discussed.

Optimal disturbances in round submerged jets

In this paper, optimal growth analysis of spatial disturbances in round submerged jets is performed. Optimal energy growth is studied for various Reynolds numbers Re and frequencies ω. Different velocity profiles proposed by Michalke [“Survey on jet instability theory,” Prog. Aerosp. Sci. 21, 159–199 (1984)] are investigated by varying the shear layer momentum thickness δ, while the jet radius R is considered fixed (as characteristic length). In the case of stationary disturbances, there are no amplified eigenmodes, so eventually the energy of such disturbances decays downstream. Such disturbances are characterized by optimal energy growth as a function of streamwise coordinate z. At certain location downstream zmax this value reaches its maximum Gmax and then decays, although not monotonically, unlike the result of the temporary setting [Jimenez-Gonzalez et al., “Modal and non-modal evolution of perturbations for parallel round jets,” Phys. Fluids 27, 044105 (2015); Jimenez-Gonzalez and Brancher, “Transient energy growth of optimal streaks in parallel round jets,” Phys. Fluids 29, 114101 (2017)]. The well-known scaling Gmax∝Re2 and zmax∝Re is confirmed for stationary disturbances. Conversely, for nonstationary disturbances there is a range of frequencies in which an amplified mode is present. In this case, optimal perturbations far downstream consist only of the amplified mode. The main effect of non-modality here is “the energy pumping” of the amplified mode, so the disturbances are characterized by the “energy ratio” G/Em, i.e., the ratio of the energy of an arbitrary perturbation to the energy of the amplified mode. The influence of the shear layer momentum thickness on optimal disturbances is studied; increasing the shear layer momentum thickness of the base flow “smears” the area occupied by the optimal disturbance, although it does not dramatically affect energy gain values, slightly decreasing maximum energy as shear layer momentum thickness increases. Spatial oscillations in the energy of stationary optimal disturbances in jet flows are discovered. The spectrum structure examination shows that the frequency of these oscillations corresponds to the frequencies of the two least damped discrete eigenmodes.

Transitional flow in a two-stage low-pressure axial turbine under different clocking of blades

Different modes of transitional flows are numerically analyzed in a two-stage low-pressure axial turbine, while being exposed to various clocking of second stator blades and results are presented in this paper. The numerical method utilizes coupled approach of SST k-ω turbulence andγ−Re˜θt transitional models. Kinematic of the wake flow in the blades passage and flow topology are presented and discussed. Different types of transitional flows including “separation induced transition” (i.e., “laminar separation bubble”), “reverse transition” and “bypass transition” are distinguished. Results of surface distribution of pressure and skin friction coefficients, turbulence intensity, intermittency and also transition momentum thickness Reynolds number are presented for the worst and optimum clocking cases, in detail. Results show that the onset points of separation induced transition and bypass transition move upstream by 6.64% and 5.47% in the optimum clocking in comparison to the worst case, respectively. In the optimum clocking the separation bubble length decreases by 1.57% and the onset point of the reverse transition moves downstream by 1.2%. All these beneficial effects happen basically as a result of impinging the first stage wake flow on the leading edge of the second stator blade suction side, which in turn, causes transition from laminar to turbulent to occur within the boundary layer.

Boundary-Layer Transition-Onset Variation Under Wide Range of Mach Numbers and Wall Temperature Ratios

Linear stability analysis is carried out for the boundary layer under a wide range of Mach numbers (4<Mae<16) and wall temperature ratios (0.1<Tw/Taw<1.0), and for the first time, the characteristics of the third mode are analyzed under different Mae and Tw/Taw. It is found that the unstable third mode appears at Mae=10 with an adiabatic wall, and its growth rate first increases and then decreases with increasing Mae. As the wall becomes colder, the unstable third mode is enhanced and appears at lower Mae. The transition-onset variations are investigated by the eN method. As Mae reaches 14, the third mode begins to promote the transition. The transition-onset Reynolds number of the third mode can be reduced by 11.4% compared to that of the second mode at Mae=16. The transition-onset momentum thickness Reynolds number Reθt varies significantly under different Mae and Tw/Taw. At 4<Mae<10, Reθt is around 800–2000 and increases with increasing Tw/Taw significantly. At 10<Mae<16, Reθt rises to 2000–3800 and is less sensitive to the change of Tw/Taw. Therefore, it is necessary to consider the effects of Mae and Tw/Taw on Reθt in transition prediction modeling for hypersonic boundary layers.

Görtler-number-based scaling of boundary-layer transition on rotating cones in axial inflow

This paper reports on the efficacy of the Görtler number in scaling the laminar-turbulent boundary-layer transition on rotating cones facing axial inflow. Depending on the half-cone angle $\psi$ and axial flow strength, the competing centrifugal and cross-flow instabilities dominate the transition. Traditionally, the flow is evaluated by using two parameters: the local meridional Reynolds number $Re_l$ comparing the inertial versus viscous effects and the local rotational speed ratio $S$ accounting for the boundary-layer skew. We focus on the centrifugal effects, and evaluate the flow fields and reported transition points using Görtler number based on the azimuthal momentum thickness of the similarity solution and local cone radius. The results show that Görtler number alone dominates the late stages of transition (maximum amplification and turbulence onset phases) for a wide range of investigated $S$ and half-cone angle ( $15^{\circ } \leq \psi \leq 50^{\circ }$ ), although the early stage (critical phase) seems to be not determined by the Görtler number alone on the broader cones ( $\psi =30^{\circ }$ and $50^{\circ }$ ) where the primary cross-flow instability dominates the flow. Overall, this indicates that the centrifugal effects play an important role in the boundary-layer transition on rotating cones in axial inflow.

Local correlations for predicting the transition process in separated flows tuned with a large experimental database

This work provides new correlations based on local variables for characterizing the transition process developing in the case of separated flows. The goal is to improve the capability of correlation-based transition models through the use of local variables. This may indeed simplify the implementation of the correlations into modern numerical codes, especially dealing with parallel computation and unstructured meshes. A large experimental database considering about 90 different flow conditions has been used to tune the present correlations. The database accounts for the variation of the flow Reynolds number, the free-stream turbulence intensity and the adverse pressure gradient affecting the boundary layer developing over a flat plate. The parameter variation induces the formation of both short and long laminar separation bubbles. The vorticity Reynolds number, based on the second invariant of the vorticity tensor, has been used as the main local variable for the activation of the transition process. Since it is proportional to the momentum thickness Reynolds number at the separation position, the vorticity Reynolds number (local) can be used in place of its counterpart based on the momentum thickness (integral), which is the variable usually adopted for activation of transition. Then, correlations providing a critical threshold for the vorticity Reynolds number promoting transition are tuned, for both short and long bubbles. These may be used into transition models to directly provide the location where the turbulence production needs to be activated. The proposed correlations have been validated using a second database not adopted for tuning and finally tested with data concerning a separated flow case in a low-pressure turbine cascade.

Local flow topology of a polymer-laden turbulent boundary layer

Fine-scale flow motions are measured in a Newtonian and polymer drag-reduced turbulent boundary layer (TBL) at a common momentum thickness Reynolds number $Re_{\theta }$ of 2300. Relative to the Newtonian TBL, the polymer-laden flow has a 33 % lower skin-friction coefficient. Three-dimensional (3-D) particle tracking velocimetry is used to measure the components of the velocity gradient tensor (VGT), rate of deformation tensor (RDT) and rate of rotation tensor (RRT). The invariants in these tensors are then used to distinguish the different types of fine-scale flow motions – a method called the $\varDelta$ -criterion. Joint probability density functions (j.p.d.f.s) of the VGT invariants, $Q$ and $R$ , for the Newtonian TBL produce the familiar tear-drop pattern, commonly seen in direct numerical simulations of Newtonian turbulence. Relative to the Newtonian TBL, the polymer-laden flow has significantly attenuated values of $R$ , implying an overall reduction in fluid stretching. The invariants in the RDT, $Q_D$ and $R_D$ , imply that straining motions of the polymeric flow are more two dimensional compared with the Newtonian flow. Moreover, j.p.d.f.s of $Q_D$ and the invariant in the RRT $Q_W$ , suggest that the flow consists of fewer biaxial extensional events and more shear-dominated flow. Few, if any, experimental investigations have measured the 3-D structure of fine-scale motions in a Newtonian and polymer drag-reduced TBL using the $\varDelta$ -criterion. We provide the first experimental evidence that supports the notion that an attenuation of fluid stretching, particularly biaxial straining motions, is central to the mechanism of polymer drag reduction.

Thermal radiative and Hall current effects on magneto-natural convective flow of dusty fluid: Numerical Runge–Kutta–Fehlberg technique

This research article intends to examine the consequences of Hall impact on the natural convection of magnetohydrodynamic (MHD) fluid flowing and the thermal characteristics of the fluid flow which containing dusty particles via a vertical stretchable sheet. Slip velocity and convective boundary conditions are taken into consideration in this research article. The flow is mathematically described by partial differential equations. The governing equations are renovated into a group of nonlinear differential equations with the use of similarity conversations, which are then resolved numerically by applying Runge–Kutta–Fehlberg. The behavior of these physical factors on the rapidity and temperature profiles of the dust and fluid phases are exposed graphically in this article. Furthermore, frictional force and heat transfer are also examined and discussed. According to the investigation, the existence of suspended particles in the fluid lead to increment in momentum and thermal boundary layer thickness. The temperature of the fluid seems can be controlled by the significant parameter, such as it seem to be increase due to the magnetic, radiation, and Hall parameters, while it is seen to have decreased due to the slip thermal parameter. While the radiation accelerates up the fluid velocity, the magnetic parameter is excellent at slowing it down. The fluid phase’s temperature and velocity profiles are almost usually higher than those of the dust phase. The outcomes contribute to a better understanding of the two-phase theory’s fluid flow phenomenon.

Insight of mixed convectional heat transport in molybdenum disulfide-water nanofluid flow on moving vertical permeable plate with homogeneous-heterogeneous reactions

This analysis is framed to take care of the high heat transfer demand from various application prospects and in this context nanofluid may be in consideration because nanofluids are well-known liquids with higher heat transfer capabilities. Here, a mixed convection flow of Molybdenum disulfide-water (MoS2-H2O) nanofluid on a moving vertical plate is examined when there are chemical reactions. Nanofluid problem is investigated using Tiwari and Das model, and numerically solved by “bvp4c” method. For the considered effects in the study, overshoots in temperature profile of nanofluid are observed. Momentum and thermal layer thicknesses become thinner with suction and thicker with blowing. Temperature overshoot is higher for blowing cases. Enhanced homogeneous–heterogeneous reactions lead to rise of the concentration boundary layer’s thickness. Also, magnitude of surface-drag force decays and cooling rate enhances with MoS2-H2O nanofluid mixed convection. For weaker suction and for blowing, cooling of nanofluid is faster with larger volume fraction of nanoparticles, but contrast results are obtained for greater suction. Importantly, compared to the homogeneous reaction, the heterogeneous reaction exhibits more impactful influences on flow and heat-mass transport characters.

An extension of Thwaites’ method for turbulent boundary layers

Thwaites (Aeronaut. Q., vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

LDV measurements of boundary layer velocity profiles on flat plates with different surface roughnesses

The dynamics acting upon thin flat plates submerged in a fluid are chiefly governed by the delicate boundary layer enveloping their surfaces. Through a series of experiments, we investigated the impact of surface roughness elements on the boundary layer adjacent to a flat plate across a range of Reynolds numbers. The experiments were performed in the Chungnam National University-Cavitation Tunnel (CNU-CT). Three flat plates, each characterized by distinct surface roughness heights denoted by k, were subjected to scrutiny. One boasted a pristine smoothness, while the others bore the deliberate roughness of sandpaper, each with its own unique texture. With precision instrumentation, including Laser Doppler Velocimetry (LDV), we meticulously documented the axial velocity profile and the RMS (Root Mean Square) velocity at strategic points along the flat plates. Through these measurements, we unveiled the boundary layer's thickness, δ, and momentum thickness, θ, elucidating their variations under differing free-stream velocities. As our exploration deepened, the relationship between the local Reynolds number, Rnx, and the non-dimensional velocity profiles, u+ − y+, became apparent. A systematic shift along the log-law line ensued, with both u+ and y + increasing in tandem with the rise in Rnx. Yet, our inquiry did not conclude with observation alone. Employing empirical rigor, we quantified the drag forces acting upon flat plates of varying roughness heights, deriving them from the measured momentum thickness across a range of local Reynolds numbers, Rnx.

Analytical and Numerical Solutions for Heat, Mass and Entropy Generation of Fourth Grade Nanofluid Flow Over A Vertical Plate

The focus of this research is to investigate magnetohydrodynamic flow, entropy generation, heat and mass transfer analysis for fourth grade nanofluid over a vertical plate in a porous medium subject to slip and convective boundary conditions. Lie group invariant similarity variable is used to transform the partial differential equations (PDEs) governing the problem to system of coupled nonlinear ordinary differential equations (ODEs). The resulting dimensionless ODEs are solved using Homotopy Perturbation Method (HPM). HPM results are validated with the numerical solutions via shooting method alongside the six order Runge-Kutta integration technique. The results revealed effects of new embedded governing flow parameters on velocity, temperature, entropy generation and concentration profiles.Furthermore, the impact of new embedded flow parameters on skin friction coefficient, Nusselt number and Sherwood number at the plate surface are investigated and the results are shown in tabular forms. The results indicate that suction on the plate can be used to control momentum, thermal and solutal boundary layer thickness. This research discovered that magnetic parameter, Eckert number, Biotsolutal number and Hartmann number can be respectively used to adjust fluid flow’s velocity, temperature, concentration and entropy generation. This research also detected that the force driving the fourth grade nanofluid flow called buoyancy driven force can be accelerated or decelerated by adjusting angle of magnetic field inclination. The present investigation has applications in industries and engineering, such as petroleum industries, chemical industries and metallurgy sciences

Deformation and aerobreakup of RP-2 droplets from hypersonic shock waves

The shock-induced atomization and burning of liquid fuel droplets are paramount for hypersonic propulsion and detonation-based combustion systems. The present work experimentally explores the atomization and aerobreakup of liquid RP-2 droplets in a hypersonic shock tube. The shock tube is operated with normal shocks propagating between Mach 5–10 interacting with RP-2 droplets with diameters between 200 and 300 µm. The droplet deformation and breakup dynamics are characterized by ultra-high-speed 5 MHz shadowgraph imaging diagnostics. For all hypersonic shock-droplet interactions, the droplets first undergo structural deformations with subsequent breakup occurring from a shear-stripping mechanism along the periphery of the droplet. The structural changes and droplet deformation rate are found to be self-similar among all cases, and the rate of deformation collapsed to a unified non-dimensional timescale. The complete breakup time of the fuel droplets were analyzed, and theoretical scaling arguments were used to quantify the effects of the Mach number, Weber number, and Ohnesorge number. The experimental data is then used to develop a modified boundary layer stripping model to estimate the breakup time of liquid drops. The model leverages the concept of displacement and momentum thickness to provide a numerical solution to estimate droplet breakup times when exposed to a high-speed gas stream. The model is compared to the experimental RP-2 data and water data available in the literature. The model predicts the breakup time for a range of droplet sizes between 200 and 2000 µm within a reasonable accuracy. The results can be used to optimize liquid fuel injection for hypersonic and detonation-based combustion systems.

Local correlation, compressibility, and crossflow corrections of γ-Reθ transition model for high-speed flows

Based on the original γ-Reθ transition model framework, in this work, an improved local correlation-based transition closure model is developed for high-speed flows. The local correlation between the vorticity Reynolds number and the momentum thickness Reynolds number obtained by compressible boundary-layer self-similar solutions, local compressibility correction including the pressure gradient parameter and momentum thickness Reynolds number, and local crossflow correlation are applied to improve the original γ-Reθ model for hypersonic transition predictions. The function Fonset1 used to control the transition onset and several relevant model parameters are also modified to make the improved model suitable for high-speed flow. The improved transition model is validated through several basic test cases under a wide range of flow conditions, including high-speed flat plates, sharp cones, double ramp, Hypersonic International Flight Research Experimentation, and complex hypersonic configuration X-33 vehicles. The numerical results show that the transition onset locations and the changes of heat transfer rate predicted by the present improved transition model are reasonably consistent with experimental results. The proposed model predicts the high-speed boundary layer transition behaviors induced by streamwise and crossflow instabilities with reasonable precision.

Response of a Turbulent Boundary Layer to an Imposed Synthetic Large-Scale Structure

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to an active flow control actuator was experimentally investigated. The experimental TBL had a sufficiently low momentum thickness Reynolds number, such that there were no energetic organized large-scale structures in the outer region, as evidenced from measurements of the premultiplied wavenumber–frequency spectra. The periodically pulsed plasma actuator, placed inside the outer region of TBL, introduced a synthetic large-scale structure, and the boundary-layer response to this synthetic structure downstream of the actuator at select wall-normal and streamwise locations was investigated. The turbulence amplitude modulating effect of the synthetic large-scale structure, within the inner and log-linear regions of the boundary layer, was isolated and analyzed using a phase-locked analysis. The dynamic interaction of the synthetic large-scale structure and smaller-scale turbulent motions was quantified using a modulation coefficient, and a strong positive correlation within the inner and log regions of the boundary layer was measured. The streamwise development of the synthetic large-scale structure and its modulating effect on the near-wall turbulence across several streamwise locations are described. Profiles of the phase speed at these streamwise locations were extracted and were found to be constant within the log region, further confirming a strong coupling between the near-wall fluctuations in turbulence intensity and the synthetic large-scale motions introduced in the outer region. Overall, the turbulence amplitude modulation effect induced by the synthetic large-scale structure was found to be dynamically similar to the large-scale modulation measured in canonical TBLs at higher Reynolds numbers.

Unsteady Hiemenz Flow of Cu-SiO2 Hybrid Nanofluid with Heat Generation/Absorption

The use of hybrid nanofluid as an alternate heat transfer fluid has shown great potential, and ongoing research to improve its thermal conductivity is important. This study focuses on the impact of heat generation/ absorption on the unsteady Hiemenz flow of aqueous hybrid nanofluid containing copper and silica nanoparticles. Mathematical equations for the hybrid nanofluid model are derived using suitable similarity transformations and solved numerically using bvp4c codes in Matlab software. The results indicate that increased heat generation/absorption leads to an increase in both momentum and thermal boundary layer thickness. The effects of suction and nanoparticle concentration are also analysed and presented graphically. Additionally, a stability analysis is also performed, which discloses that the first solution produced is stable, however, the second solution is not. The findings of this study provide valuable insights into the behaviour of hybrid nanofluid in unsteady flow and can aid in the development of more efficient heat transfer fluids for various engineering applications.

Effects of Riblet Dimensions on the Transitional Boundary Layers Over High-Lift Turbine Blades

Abstract Substantial research exists in the literature on reducing the profile loss of transitional boundary layers over low-pressure turbine (LPT) blades via different mechanisms such as freestream turbulence, upstream wakes, and surface roughness. These mechanisms have proven to be beneficial in mitigating the separation bubble-related losses in ultra-high-lift blade designs, despite an increase in the loss due to increased turbulent wetted area (TWA). In this work, we adopt a strategy of employing surface roughness in the transitional regime to minimize the separation bubble-related losses and flush-mounted riblets downstream to further mitigate the skin-friction drag and boundary layer losses due to an increase in the TWA. Several high-fidelity scale-resolving simulations are performed on this “rough-ribbed blade surface” to discern the effect of varying the riblet spacing (s+) and height (h+). The streamwise evolution of skin-friction coefficient, boundary layer integral parameters, and shape factor are compared and contrasted among riblets of different dimensions. The instantaneous flow features and second-order statistics such as the Reynolds stress, turbulent kinetic energy, and its production are analyzed for different test cases to determine the impact of riblets on these quantities. When compared to the roughness alone configuration, the scalloped shape riblets with s+ = 17 and h+ = 22 reduced the net skin-friction drag by 7.3% and the trailing edge momentum thickness by 14.5%, thereby demonstrating the efficacy of riblets in reducing the mixing losses under adverse pressure gradients. Through an analysis of flow blockage introduced by the application of riblets, the deleterious effects of increasing the riblet height along with the necessity of optimizing the riblet ramp are highlighted.