Separation-induced Transition Research Articles

Insights into the transition of separation bubble over a rough surface at varying angles of attack

The evolution of a separated boundary layer on the rough surface in the vicinity of a leading edge of a model airfoil is documented at varying angles of attack. Particle image velocimetry and hotwire data are analyzed to elucidate the flow feature, depicting the manifestation of the shear layer, its rollup, growth of perturbations, spectral response, and intermittency. For a hydrodynamically smooth surface, a laminar separation bubble often appears near the leading edge, where the shear layer becomes inviscidly unstable. Wall roughness amplifies the near-wall perturbations, resulting in earlier transition and reattachment. This leads to a reduction in bubble length and laminar shear layer length compared to the smooth surface at the corresponding angle of attack. Notably, despite the amplification of selective frequency, the inviscid instability is bypassed on the rough surface for varying angles of attack. Moreover, the linear stability analysis proves inadequate in predicting the most amplified frequency and the growth of disturbances. Furthermore, the universal intermittency curve formulated for the bypass transition is valid for the separation-induced transition, illustrating the significance of viscous effect.

Separation-induced transition on a T106A blade under low and elevated free stream turbulence

The separation-induced transition on the suction surface of a T106A low pressure turbine blade is a complex phenomenon with implications for aerodynamic performance. In this numerical investigation, we explore an adverse pressure gradient-dominated flow subjected to varying levels of free stream excitation, as the underlying separation-induced transition is a critical factor in assessing blade profile loss. By comprehensively analyzing the effects of free stream turbulence (FST) on the transition process, we delve into the various mechanisms which govern the instabilities underlying bypass transition by studying the instantaneous enstrophy field. This involves solving the two-dimensional (2D) compressible Navier–Stokes equation through a series of numerical simulations, comparing a baseline flow to cases where FST with varying turbulent intensity (Tu=4% and 7%) is imposed at the inflow. Consistent with previous studies, the introduction of FST is observed to delay flow separation and trigger early transition. We explore the different stages of bypass transition, from the initial growth of disturbances (described by linear stability theory) to the emergence of unsteady separation bubbles that merge into turbulent spots (due to nonlinear interactions), by examining the vorticity dynamics. Utilizing the compressible enstrophy transport equation for the flow in a T106A blade passage, we highlight the various routes of bypass transition resulting from different levels of FST, emphasizing the relative contributions from baroclinicity, compressibility, and viscous terms.

Relaminarization of jet impingement on a flat plate using separation-induced transition correction turbulence modeling preliminarily applied in archeological applications

The focus of the study was the validation of transition flow model which works with jet impingement applications. Reynolds averaged Navier Stokes (RANS) techniques, including a variation of transition options, such as γ−GEKO−k−ω, γ−SST−k−ω, transition SST and transition k−kl−ω, were employed to simulate the turbulent flow fields. ANSYS-Fluent 2022R2 was the tool used in the study and a constant surface heat flux on a flat plate was chosen for the test case. The flow characteristics and averaged Nusselt number prediction were investigated and compared with measurement data. The results show that the collapse of turbulence performed the flow became lamina-like in the transition region, 1 < r/D < 3, while the shape of velocity distribution within that region was parabolic profiles near a target wall. That means the relaminarization mechanism was captured by the transition SST model. Moreover, the thermal results demonstrated that the highest values of the Nusselt number prediction were located near the stagnation point and decreased monotonically within the wall jet regions. The predicted results from γ−SSTk−ω and transition SST models provided strong agreement with experimental data. Secondary peaks of the Nusselt number in the radial direction were also depicted by transition SST models, and these second peaks were still aligned on the ratio (1 ≤ r/D ≤ 3) which was not impacted by jet diameter variation. This range will be used in the next step of developing a prototype of a dehumidifying unit for use in archeological applications.

A data-driven analysis of short and long laminar separation bubbles

This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.

Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

Compressibility effects on the flow past a T106A low-pressure turbine cascade

The present numerical investigation delves into the intricate interplay between Mach number (Ms), flow characteristics, and vorticity dynamics within a T106A low-pressure turbine (LPT) blade passage. The two-dimensional (2D) compressible Navier–Stokes equations are solved using a high-accuracy, dispersion relation preserving methodology, which is validated against benchmark direct numerical simulations. Four Ms ranging from 0.15 to 0.30 are computed in order to display the intricate response of compressibility on the separation-induced transition process. The emergence and evolution of unsteady separation bubbles along the suction surface of the T106A blade are explored, revealing a growing trend with Ms. The time-averaged boundary layer parameters evaluated along the suction surface display a delayed separation with a smaller streamwise extent with increasing Ms. However, an overall increase in the blade profile loss and a decrease in turbulent mixing are observed with increasing Ms, suggesting a detrimental effect on LPT performance. Applying the compressible enstrophy transport equation (CETE) to the flow in a T106A blade passage reveals that while a linear relationship exists between Ms and certain CETE budget terms, other terms have a nuanced dependency, which paves the way for future investigations into the role of compressibility on enstrophy dynamics.

Investigation on transition characteristics of laminar separation bubble on a hydrofoil

The phenomenon of water–jet pump stall can be ascribed to the development of blade boundary layer separation with the transition process playing a significant role in this separation. The hydrofoil is usually used as a simplified model of the water–jet pump impeller blade, and its flow field characteristics have important reference values for analyzing the impeller flow. Based on the transition model and the dynamic mode decomposition method, this article presents the results of a study that was carried out on the stall characteristics of the NACA0009 blunt trailing edge hydrofoil. The transition characteristics of hydrofoil surfaces at different angles of attack (AoA)and Chord-based Reynolds numbers (ReL) are obtained. The hydrofoil boundary layer transition is dominated by natural transition as the AoA is less than 4°, while the transition is dominated by leading-edge separation-induced transition as the AoA is greater than 4°. The investigation yields the dynamic properties of the LSB (Laminar Separation Bubble) as the AoA is varied. The phenomenon known as the deep stall is distinguished by the movement of the stall vortex toward the upstream direction near the trailing-edge region, where it merges with the LSB in the leading-edge region. This phenomenon leads to oscillations in the lift and drag coefficients. The relationship between the LSB and the trailing-edge stall vortex is established using DMD (Dynamic Mode Decomposition) methods. As the phenomenon of the deep stall occurs, it can be observed that the modal energy of the leading-edge LSB is comparatively higher than the modal energy of the trailing-edge stall vortex, inducing the dominant role of the LSB and the movement toward the trailing-edge region and, consequently, the phenomenon of trailing-edge vortex shedding in the hydrofoil. The findings of this study could be guidance for the design of fluid machinery blades.

The effect of leading-edge shape on separation-induced transition on the suction surface of a controlled-diffusion airfoil

To investigate the effect of leading-edge shape on separation-induced transition on suction surface, a large eddy simulation is performed on two compressor controlled-diffusion airfoils: a conventional one with an elliptical leading edge and an optimized one with a curvature-continuous design based on the B-spline description. The Reynolds number based on inflow velocity and chord length is 4.5×105. The critical angle of attack +4°, over which the aerodynamic loss rises sharply, is chosen for simulation. Two transitions are observed on the suction surface, one near the leading edge and the other at 40% chord length. The primary difference between the two airfoils lies in the leading-edge transition, which also leads to the distinction of fluctuating velocity amplitude and energy loss in the subsequent development of boundary layer flow. In order to provide an insight into the transition mechanism, the frequency spectrum analysis is conducted, and the results indicate that the amplification of disturbances during transition is dominated by Kelvin–Helmholtz instability. The mechanisms of energy transport and dissipation are analyzed, and the influence of leading-edge curvature on the initial state of boundary layer flow is elucidated from a dynamic perspective. The results show that continuous and large curvature distributions are more conducive to suppressing the formation of leading-edge separation bubble and delaying the onset of transition.

Wall-distance free transition model based on the laminar kinetic energy

The next fluid dynamics solvers will be based on innovative numerical schemes and models to increase the fidelity and decrease the computational cost. The higher accuracy and geometrical flexibility guaranteed by discontinuous Galerkin spatial discretization methods in solving Reynolds-Averaged Navier–Stokes equations could represent an appealing solution in comparison with finite volume solvers for real-life simulations. In this context, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models and the costs of high-fidelity approaches, e.g., Direct Numerical Simulations and Large Eddy Simulations, for the efficient design of many industrial applications, e.g., aerospace, turbomachinery, maritime, automotive, and cooling applications. Among the transition models proposed in the literature, the local and phenomenological formulation seems to guarantee better robustness, fidelity, and easiness of implementation in all the solvers. All the transition models are based also on the wall-distance, to define some local terms or parameters and model the transition phenomenon. The calculation of the wall-distance can be critical in the discontinuous Galerkin framework for the high-order representation of the boundaries, which can become very expensive and high-memory consuming. To alleviate this problem, a wall-distance free version of a transition model based on the laminar kinetic energy is proposed and implemented in a high-order discontinuous Galerkin solver, and the robustness and fidelity are assessed by computing flows with bypass and separation-induced transition and different Reynolds number, turbulent intensity, and pressure gradient on flat plates. The wall-distance free formulation proves robustness and fidelity in all the cases, in comparison with the original formulation and an ad hoc modified formulation for the separation-induced transition cases.

Validation of SST-SCM correlation-based transition model by the simulation of wall-bounded flows

A modified correlation-based transition model coupled with SST turbulence model(k−ω−γ−R˜eθt) is proposed in this work. For better verification of intermittency, the constraint definition strictly based on local variables is cited to ensure physical solution. In order to obtain more details of laminar and transition boundary layer for separation-induced transition, a local correction method based on streamline curvature modification (SCM) has been developed to extend model ability in predicting adverse-pressure-gradient flows. The mean strain rate involved with mean rotation rate and shear rate is modified according to wall-bounded condition with rotation and non-rotation features to preserve the anisotropic characteristics encountered in large range flows. Furthermore, separation-induced intermittency is corrected by considering the effect of average strain rate to prevent outliers in local intermittency whenever the laminar boundary layer separates. Considering that results of test cases simulation with different empirical correlations vary huge from each other, all cases are matched with its suitable empirical correlations to ensure the stability and accuracy calculated by proposed model. Transitional flat-plate cases are calculated to validate the basic ability for near-wall flow simulation.Massive separated flow over two-dimensional circular cylinder has been studied to verify the predicted accuracy for non-equilibrium flows. Flow over multi-element airfoil 30P30N and the simulation of vortex system over three-dimensional Low Pressure Turbine(LPT) cascade T106A are given to examine the predictions of Reynolds shear stress profiles and pressure distribution with flow disturbance; reasonable results show a good match between experimental data and calculation by proposed model.

Algebraic modifications of the [formula omitted] and Spalart–Allmaras turbulence models to predict bypass and separation-induced transition

Many reliable and robust turbulence models are nowadays available for the Reynolds-Averaged Navier–Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not suited to correctly described flows with low to moderate Reynolds numbers, which are characterized by strong transitional phenomena. Therefore, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models for the efficient design of many industrial applications. The only ways to describe transition are Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and transition models, where the computational cost of DNS and LES is still too high for their routine use in industry. A modified version of the k-ω̃ and Spalart–Allmaras turbulence models is here proposed to predict transition due to the bypass and separation-induced modes. The modifications are based on the γk-ω̃ and the SA-BCM models and avoid complex formulations of transport equations ad-hoc defined for transition. Both the transition models are correlation-based algebraic models that rely only on local flow information and an intermittency function, which damps the turbulent production according to some transition onset requirements. The proposed transition models are implemented in a high-order discontinuous Galerkin (dG) solver and validated on benchmark cases from the ERCOFTAC suite to the Eppler 387 airfoil, with different transition mode, freestream Reynolds number and turbulent intensity, and pressure gradient.

Aerodisk Effect on Hypersonic Boundary Layer Transition and Heat Transfer of HIFiRE-5 Vehicle

The substantial aerodynamic drag and severe aerothermal loads, which are closely related to boundary layer transition, challenge the design of hypersonic vehicles and could be relieved by active methods aimed at drag and heat flux reduction, such as aerodisk. However, the research of aerodisk effects on transitional flows is still not abundant. Based on the improved k-ω-γ transition model, this study investigates the influence of the aerodisk with various lengths on hypersonic boundary layer transition and surface heat flux distribution over HIFiRE-5 configuration under various angles of attack. Certain meaningful analysis and results are obtained: (i) The existence of aerodisk is found to directly trigger separation-induced transition, moving the transition onset near the centerline upstream and widening the transition region; (ii) The maximum wall heat flux could be effectively reduced by aerodisk up to 52.1% and the maximum surface pressure can even be reduced up to 80.4%. The transition shapes are identical, while the variety of growth rates of intermittency are non-monotonous with the increase in aerodisk length. The dilation of region with high heat flux boundary layer is regarded as an inevitable compromise to reducing maximum heat flux and maximum surface pressure. (iii) With the angle of attack rising, first, the transition is postponed and subsequently advanced on the windward surface, which is in contrast to the continuously extending transition region on the leeward surface. This numerical study aims to explore the effects of aerodisk on hypersonic boundary layer transition, enrich the study of hypersonic flow field characteristics and active thermal protection system considering realistic boundary layer transition, and provide references for the excogitation and utilization of hypersonic vehicle aerodisk.

Predicting transition with wall-distance-free SST k-[formula omitted] model

Unlike the correlation-based γ–Reθ transition model, an exceptionally simplified approach is applied to extend the wall-distance-free (WDF) model toward transition predictions. An anisotropic stress-intensity parameter as a function of eddy-to-laminar viscosity ratio is introduced, preserving the “flow-structure-adaptive” characteristic. The prospective parameter is included with the constitutive relation for the eddy-viscosity. The proposed formulation is intrinsically plausible, having a dramatic influence on the prediction of bypass, separation-induced and natural transitions. The newly devised transitional WDF (TWDF) model is further modified to compute separation-induced transition over a low-Reynolds number (LRN) airfoil. The curiosity toward airfoil performance at an LRN has been executed with growing attention to marine autonomous systems. An extra viscous-production term Pklim is added to the turbulent kinetic energy (k) equation to ascertain proper development of k at the viscous sublayer region. Reliance on this Pklim is likely to be suitable for forecasting separation-induced transition over an LRN airfoil. Results illustrate that the TWDF model sustains decent agreement with the four-equation γ–Reθ transition model.

Parametrical study on separation-induced transition and vortex dynamics of a reversed pitching airfoil

The pitching airfoils, applied to the vertical axis turbines and propellers, are critical to extract more energy from the environment. At retreating side, when the airfoil blunt leading edge becomes the trailing edge, the transition and vortex dynamics are quite different from that at advancing side. The goal of the present work is to investigate the transition and vortex evolution over the reversed pitching airfoil, with main focus on the parametrical effect, including the mean pitching angle and pitching amplitude, reduced frequency and Reynolds number. The main results show that the flow structure on the reversed airfoil is more complex compared with that over the forward airfoil due to the earlier flow separation near the sharp leading edge. Then, the transition on the reversed airfoil firstly occurs within the separated shear layer near the sharp leading edge, and then the flow reattaches, leading to the generation of the leading-edge vortex. Near the blunt trailing edge, the second transition appears on two sides, resulting in the asymmetrical boundary layer as the incidence increases continuously. This event is totally different from that on the forward airfoil, shown by the transition always moving from the trailing edge to the leading edge. The flow unsteadiness of the reversed airfoil is mainly induced by the separated shear layer and leading-edge vortex, which is greatly affected by different parameters. Besides, the trajectory of some specific vortices also depends on the working conditions significantly. It is believed that this work can deepen the understandings of underlying flow physics of the reversed airfoils.

Flow transition on the suction surface of a controlled-diffusion compressor blade using a large-eddy simulation

Separation-induced transition is discussed here on a suction surface of a controlled-diffusion compressor blade using a large eddy simulation, where the Reynolds number based on the chord is 210 000. The filtered, incompressible Navier–Stokes and energy equations in the covariant form are solved with second-order spatial and temporal accuracy, where the subgrid stress tensor and temperature flux are assessed by a dynamic model. Flow features are resolved with appreciable accuracy, exhibiting a separation bubble on the suction surface in the vicinity of mid-chord. Excitation of the shear layer is evident with the evolution of Kelvin–Helmholtz (K–H) rolls, depicting amplification of the selective frequency in the first half of the bubble, where the normalized shedding frequency based on the momentum thickness at the point of separation becomes 0.011. The secondary instability appears in the second half of the bubble, which is attributed to the spanwise deformation of K–H rolls. This leads to significant growth of perturbations in the braid region, resulting in breakdown near reattachment. In brief, outer shear layer activities are initiated via inviscid instability, while the near-wall region might be susceptible to the viscous effect in the second half with increasing levels of velocity fluctuations, production, and wall-normal turbulent heat flux. The validity of the universal intermittency curve also bears evidence of a significant viscous effect. The instantaneous temperature contours closely follow the vorticity field, illustrating a strong correlation between species and momentum transport.

Capturing transition and non-transition flows with a new shear stress transport model

A new Shear Stress Transport (SST) k-ω model is devised to integrate salient features of both the non-transitional SST k-ω model and correlation-based γ-Reθ transition model. An exceptionally simplified approach is applied to extend the New SST (NSST) model capabilities toward transition/non-transition predictions. Bradshaw’s stress-intensity factor Rb=-uv¯/k can be parameterized with the wall-distance dependent Reynolds numberRey=ky/v; however, as the Rey is replaced by a “flow-structure-adaptive” parameterRμ=vT/v, the resulting Rb is capable of capturing various transition phenomena naturally. The prospective stress-intensity parameter Rb=Rb(Rey,Rμ) is incorporated in the constitutive relations for eddy-viscosity vT and production termPk. The proposed formulation is intrinsically plausible, having a dramatic impact on the prediction of bypass, separation-induced and natural transitions together with non-transitional flows. An extra viscous-production term Pklim is added with the k-equation to ensure proper generation of k at the viscous sublayer when computing separation-induced transition over a Low-Reynolds Number (LRN) airfoil. Results demonstrate that the NSST k-ω model maintains an excellent consistency with both SST k-ω and γ-Reθ models.

Capturing transition around low-Reynolds number hydrofoil with zero-equation transition model

Compared with the local correlation-based shear stress transport (SST) γ−Reθ transition model (where SST k−ω transport equations are coupled with intermittency γ and transitional momentum-thickness Reynolds number Reθ transport equations), relatively simple and convenient modifications are applied to the parent SST k−ω model for computing natural and separation-induced transitions over the hydrofoil at a low-Reynolds number (LRN). The curiosity toward hydrofoil performance at an LRN has been enhanced by increasing attention to autonomous marine systems, deserving numerical simulations for transitional flow using computational fluid dynamics. With the newly devised transitional SST (T-SST) model, the viscous sublayer blending function F2 is slightly modified, and a stress-intensity parameter as a function of eddy-to-laminar viscosity ratio RT is introduced; intended formulations are plausible and have significant impacts on the transition prediction. Owing to the inherent potential for predicting bypass transition, two anisotropic versions of the v¯2−f(V2F) turbulence model are selected to evaluate their competencies in capturing separation-induced and natural transitions. Results demonstrate that natural transition prediction is more challenging than separation-induced transition for the V2F model. Nonetheless, the T-SST model performs consistently well in replicating both transitional phenomena.

Validation of the gamma text{-Re }_{theta } Transition Model for Airfoils Operating in the Very Low Reynolds Number Regime

Micro Aerial Vehicles (MAVs) are state of the art in the aerospace industry and are involved in many operations. The reduced dimensions of these vehicles generate very low Reynolds number conditions in which separation-induced transition typically occurs. The extremely large computational cost of scale resolving simulations, which are capable of capturing laminar to turbulent transition, is prohibitive for most engineering and design applications. Therefore, it becomes very interesting to couple transition models with conventional Reynolds Averaged Navier–Stokes (RANS) simulations to allow the prediction of transition to turbulence at a reduced computational cost. This paper performs an investigation of the application of the gamma text{-Re }_{theta } transition model analysing different empirical correlations available in literature and studying the influence of the relevant model parameters using the commercial Computational Fluid Dynamics (CFD) code STAR-CCM+. The flow around the Eppler 387, Selig/Donovan 7003 and Ishii airfoils has been studied for different Reynolds numbers and angles of attack comparing the drag and lift forces and separation bubble characteristics with experimental and numerical results reported in literature.

Numerical investigations on unsteady vortical flows and separation-induced transition over a cycloidal rotor at low Reynolds number

The unsteady vortical flows and separation-induced transition over a 2-bladed cycloidal rotor are investigated numerically at two advance coefficients, with special emphasis on the influence of two different turbulence models, namely the original SST k-ω model and SST γ-Reθt transition model. Firstly, the applicability of the transition model in predicting the transitional flows over a single airfoil at different incidences is evaluated, and the main results show a good agreement with the experiments, in terms of the mean pressure coefficients and transition locations. Then, the global performance and detailed internal flow structures of the cycloidal rotor are also used to compare with the existing numerical and experimental data. The primary results show that increasing the advanced coefficient can’t change the transition location of the performance of the single blade, but the magnitudes of these variables (vertical force, propulsive force and power coefficients). Then, combining the forces (lift and drag) acting on two blades, the blade loadings and the detailed near-wall flows, the difference of the vertical force and propulsive force of the rotating system and single blade are clarified clearly for two turbulence models. Finally, at advancing side, the transition and its evolution on a single blade is elaborated. It shows that the SST γ-Reθt transition model is superior in predicting the overall performance, but is highly subjected to the disturbances, characterized by the large-scale vortex structures and massive flow separation, compared with SST k-ω model. Simultaneously, it has the capability to capture the transition process, from growing waves of the laminar boundary layer induced by the roll-up vortices to the fully generation of the separation bubble. It believes that this work can deepen the understandings of underlying flow physics inside the cycloidal rotor at low Reynolds number.

Assessment and improvement of k-ω-γ model for separation-induced transition prediction

The purpose of this work is to improve the k-ω-γ transition model for separation-induced transition prediction. The fundamental cause of the excessively small separation bubble predicted by k-ω-γ model is scrutinized from the perspective of model construction. On the basis, three rectifications are conducted to improve the k-ω-γ model for separation-induced transition. Firstly, a damping function is established via comparing the molecular diffusion timescale with the rapid pressure-strain timescale. The damping function is applied to prevent the effective length scale from incorrect distribution near the leading edge of the separation bubble. Secondly, the pressure gradient parameter λζ, is proposed as an indicator for local susceptibility to the separation instability. Additionally, λζ,-based separation intermittency γsep is constructed to accelerate the substantial growth of turbulent kinetic energy after flow separation. The improved model appropriate for both low- and high-speed flow has been calibrated against a variety of diverse and challenging experiments, including the subsonic T3L plate, Aerospatial A airfoil, transonic NLR-7301 airfoil and deformed hypersonic inflatable aerodynamic decelerator aeroshell. The improved model is strictly based on local variables and Galilean invariance. Besides, the proposed improvement for k-ω-γ model can be fairly convenient to incorporate into other existing intermittency-based transition models.