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An Actuator Line Method (ALM) based on integral velocity sampling is developed for application to ducted fans. In this work, the lifting surface is replaced by momentum source terms in the unsteady Reynolds-averaged Navier-Stokes equations. The source terms are computed at discrete locations along the blade’s span before being spread on the mesh using a nonisotropic Gaussian kernel allowing the source terms distribution to mimic the geometrical attributes of the blade at that location. The determination of the local effective freestream vector, a common difficulty of ALM approaches, is done with an integral velocity sampling that accounts for the blade’s local induced velocity. Including the projection function in the computation of the effective freestream velocity vector makes the formulation more general and removes the ambiguity surrounding the determination of the local velocity. The method is first validated against experimental data from Caradonna & Tung [1] for the open rotor case, and the influence of the nonisotropic Gaussian kernel parameters on the solution is then presented. The appropriateness of the method when applied to ducted geometries is validated against experimental data from wind tunnel testing of a ducted fan and against blade-resolved CFD. The results obtained for the ducted geometry show that the ALM is able to account for the presence of the duct, but that the effective expansion ratio of the duct in the ALM simulations is smaller than its blade-resolved equivalent.

In this work, the homogeneous approach, frequently used to simulate cavitation in hydraulic machinery, is used to compute unsteady cavitating flows for two simplified geometries. After a quick review of the literature and a rigorous presentation of the proposed methodology, the detailed computed physics of sheet and cloud cavitation are compared with experimental observations and with theory. Results suggest that the assumption of a homogeneous medium is not suitable to predict the fine physics of attached cavitation and thus to predict its precise unsteady characteristics. However, the inhomogeneous approach, in which a momentum equation is solved for both phases under a volume of fluid (VOF) approach, is shown to be more promising. Although it is numerically less stable, such an approach allows the effective body to be modified by the presence of vapor in contrast with the homogeneous approach. The resulting flow topology around the vapor cavity is found to better agree with the experimental observations, and thus the inhomogeneous approach offers the potential to better predict the unsteady characteristics of attached cavitation.

A numerical and experimental comparison of a fully-passive oscillating-foil turbine operating in different confinement levels is conducted to assert how well CFD-based FSI simulations can predict the performances of the turbine. It is found the present 3D URANS simulations match reasonably well the experimental observations, especially in terms of pitch angles and power extraction. Indeed, the results confirm that confinement increases the extracted power and the efficiency of the fully-passive blade. At low confinement level, the main flow features are shown to be well captured by the simulations. At large confinement levels, some issues with lateral walls interactions are discussed as possible explanation for the observed discrepancies.

In the planning of hydrokinetic turbine array deployment and for the performance prediction of its constituent turbines, the use of simplified turbine models is essential to alleviate the computational costs. The Effective Performance Turbine Model (EPTM) introduced in 2018 is a promising tool for that purpose, allowing array analysis and optimization. Its performance predictions scale with a local flow velocity characterization, which ensures to take into account inherently blockage effects and mean, local flow conditions. However, the characteristics of the local flow within an array also include different types of perturbation such as shear, large-scale temporal fluctuations, and turbulence. To ensure that the model is still reliable in those conditions, this paper presents a validation of the EPTM through the analysis of a large-scale tandem turbine configuration. In fact, three unsteady-Reynolds-averaged-Navier–Stokes simulations of a cross-flow turbine tandem configuration with a longitudinal spacing of six diameters have been conducted in this study, in addition to a simulation of a single turbine with turbulent ambient conditions. This set of simulations allows us to study independently the different types of perturbations associated with array deployment. Whereas the slow-varying large-scale upstream velocity fluctuations do not seem to affect significantly the turbine operation, the upstream non-uniform velocity distribution affects appreciably the extracted power. We find also that the value of the effective power coefficient associated with the EPTM needs to be adapted to the array simulation. Compared to the case of a single turbine in a uniform flow with a low turbulence level, we show that a smaller effective power coefficient value must be used in array simulations. An important result is that the different types of perturbations are found to yield similar effective performance coefficients, which suggests that the same set of values can be used thro

End-wall effects for high aspect ratio (AR) turbulent duct flows under moderate spanwise rotation are investigated using Reynolds-Averaged Navier–Stokes (RANS) calculations with a Reynolds stress turbulence closure model. It is shown that despite an important uniformisation of the mean streamwise flow compared to the non-rotating case, the channel flow solution (AR ¼ 1) is not recovered in practical high AR ducts used in experiments. The unavoidable end-wall generated secondary flow causes transverse advection which is capable of altering the mean velocity profile, even for AR as high as 22. In addition, for Re ¼ 40,000 and Ro ¼ 0.22, persistent longitudinal roll cells are found in the RANS solutions. The results suggest that their interaction with the secondary flow may challenge the prospect of formally reaching a steady, streamwise invariant regime in actual rotating duct experiments.

This study focuses on the interaction between the water free surface, the riverbed, and some Darrieus-type hydrokinetic turbines deployed in river flows. As turbines offer a resistance to the flow, they affect the upcoming velocity, which in turn affects their performance. The proximity of the neighboring deformable free surface or rigid bed may also influence their power extraction. In this context, 2D and 3D URANS simulations of a cross-flow (H-Darrieus type) turbine are conducted with free-surface modeling and adapted boundary conditions allowing the capture of the interactions between the turbine and the resource. Different water depth immersions are considered in order to study local proximity effects. It is found, neglecting riverbed friction, that shallow immersion is detrimental to power extraction whereas bed proximity associated with deep immersion is favorable. This observation does not hold when considering a more realistic river with a velocity profile throughout the depth. Direction of rotation in high proximity cases also plays a role. Although the literature suggests a slight increase in power extraction with the Froude number, we find that when interaction with the resource is taken into account, the power extraction is rather independent of the Froude number for deep immersion or slightly decreasing for shallow immersion. Nonetheless, all the variations in power extraction reported in this study remain small compared to the ones associated with blockage effects. Finally, the shallow immersion case simulated in 3D behaves similarly to that simulated in 2D. Switching the orientation of the rotation axis from horizontal to vertical, despite changing the local interaction with the free surface, does not affect significantly the performance of the turbine.

and Figures The impact of the blade support structures (the struts) on the performance of vertical-axis turbines at a high Reynolds number is investigated here. Numerical simulations of a single-blade turbine with different strut configurations are carried out and the results are compared to a reference hypothetical turbine without strut. The results show that the struts are less detrimental to the turbine efficiency if they are located at the tips of the turbine blade, rather than at other intermediate positions along the blade span. Moreover, for struts located at the blade tips, it is shown that using rounded junctions between the struts and the blade can lead to a significant increase in the turbine efficiency. Indeed, the best turbine configuration presented in this paper has an efficiency that is more than 20% larger than that of the reference turbine without strut. This important increase in the turbine efficiency can partly be attributed to the fact that the tip struts with rounded junctions act as efficient winglets, leading to a significant decrease in the induced drag on the turbine blade. The results presented show that well-designed blade support structures can be very beneficial to the performance of vertical-axis turbines.

This study focuses on the interaction between the water free surface, the riverbed, and some Darrieus-type hydrokinetic turbines deployed in river flows. As turbines offer a resistance to the flow, they affect the upcoming velocity, which in turn affects their performance. The proximity of the neighboring deformable free surface or rigid bed may also influence their power extraction. In this context, 2D and 3D URANS simulations of a cross-flow (H-Darrieus type) turbine are conducted with free-surface modeling and adapted boundary conditions allowing the capture of the interactions between the turbine and the resource. Different water depth immersions are considered in order to study local proximity effects. It is found, neglecting riverbed friction, that shallow immersion is detrimental to power extraction whereas bed proximity associated with deep immersion is favorable. This observation does not hold when considering a more realistic river with a velocity profile throughout the depth. Direction of rotation in high proximity cases also plays a role. Although the literature suggests a slight increase in power extraction with the Froude number, we find that when interaction with the resource is taken into account, the power extraction is rather independent of the Froude number for deep immersion or slightly decreasing for shallow immersion. Nonetheless, all the variations in power extraction reported in this study remain small compared to the ones associated with blockage effects. Finally, the shallow immersion case simulated in 3D behaves similarly to that simulated in 2D. Switching the orientation of the rotation axis from horizontal to vertical, despite changing the local interaction with the free surface, does not affect significantly the performance of the turbine.

In the planning of hydrokinetic turbine array deployment and for the performance prediction of its constituent turbines, the use of simplified turbine models is essential to alleviate the computational costs. The Effective Performance Turbine Model (EPTM) introduced in 2018 is a promising tool for that purpose, allowing array analysis and optimization. Its performance predictions scale with a local flow velocity characterization, which ensures to take into account inherently blockage effects and mean, local flow conditions. However, the characteristics of the local flow within an array also include different types of perturbation such as shear, large-scale temporal fluctuations, and turbulence. To ensure that the model is still reliable in those conditions, this paper presents a validation of the EPTM through the analysis of a large-scale tandem turbine configuration. In fact, three unsteady-Reynolds-averaged-Navier–Stokes simulations of a cross-flow turbine tandem configuration with a longitudinal spacing of six diameters have been conducted in this study, in addition to a simulation of a single turbine with turbulent ambient conditions. This set of simulations allows us to study independently the different types of perturbations associated with array deployment. Whereas the slow-varying large-scale upstream velocity fluctuations do not seem to affect significantly the turbine operation, the upstream non-uniform velocity distribution affects appreciably the extracted power. We find also that the value of the effective power coefficient associated with the EPTM needs to be adapted to the array simulation. Compared to the case of a single turbine in a uniform flow with a low turbulence level, we show that a smaller effective power coefficient value must be used in array simulations. An important result is that the different types of perturbations are found to yield similar effective performance coefficients, which suggests that the same set of values can be used thro

A self-propelled flexible flapping wing 2D numerical model undergoing a combined pitching and heaving motion ispresented. Since such freely moving foil experiences zero net thrust, a definition of efficiency for this kind of problemis proposed and discussed against other formulations found in the literature. It is also shown that the deviation motionof wings such as that found in natural flyers is likely a consequence of the fluid-structure dynamics of the wings.The passive deviation motion observed in numerical simulations is either a consequence of a feathering mechanismreferred to as rigid feathering or of the inertial displacement caused by the wing deformation. The effects of flexibilityon the performance of the wing are also presented. It is found that flexibility may significantly enhance the efficiencyin pressure-driven deformation cases. The rigid feathering mechanism is found to have an effect similar to that of thefeathering caused by wing flexibility on the performances of pressure-driven deformation cases.

This paper presents a numerical investigation of the effects of chordwise flexibility on flapping wings at low Reynoldsnumber. The numerical simulations are performed with a partitioned fluid-structure interaction algorithm using artifi-cial compressibility stabilization. The choice of the structural dimensionless parameters is based on scaling argumentsand is compared against parameters used by other authors. The different regimes, namely inertia-driven and pressure-driven wing deformations are presented along with their effects on the topology of the flow and on the performanceof a heaving and pitching flapping wing in propulsion regime. It is found that pressure-driven deformations can sig-nificantly increase the thrust efficiency if a suitable amount of flexibility is used. Significant thrust increases are alsoobserved in zero pitching amplitude cases. The effects of the second and third deformation modes on the perfor-mances of pressure-driven deformation cases are discussed. On the other hand, inertia-driven deformations generallydeteriorate aerodynamic performances of flapping wings unless the behavior of the wing deformation is modified bythe presence of sustainable superharmonics in a way that produces slight improvements. It is also shown that wingflexibility can act as an efficient passive pitching mechanism that allows fair thrust and better efficiency to be achievedwhen compared to a rigid pitching-heaving wing.

A self-propelled flexible flapping wing 2D numerical model undergoing a combined pitching and heaving motion ispresented. Since such freely moving foil experiences zero net thrust, a definition of efficiency for this kind of problemis proposed and discussed against other formulations found in the literature. It is also shown that the deviation motionof wings such as that found in natural flyers is likely a consequence of the fluid-structure dynamics of the wings.The passive deviation motion observed in numerical simulations is either a consequence of a feathering mechanismreferred to as rigid feathering or of the inertial displacement caused by the wing deformation. The effects of flexibilityon the performance of the wing are also presented. It is found that flexibility may significantly enhance the efficiencyin pressure-driven deformation cases. The rigid feathering mechanism is found to have an effect similar to that of thefeathering caused by wing flexibility on the performances of pressure-driven deformation cases.

This paper presents a numerical investigation of the effects of chordwise flexibility on flapping wings at low Reynoldsnumber. The numerical simulations are performed with a partitioned fluid-structure interaction algorithm using artifi-cial compressibility stabilization. The choice of the structural dimensionless parameters is based on scaling argumentsand is compared against parameters used by other authors. The different regimes, namely inertia-driven and pressure-driven wing deformations are presented along with their effects on the topology of the flow and on the performanceof a heaving and pitching flapping wing in propulsion regime. It is found that pressure-driven deformations can sig-nificantly increase the thrust efficiency if a suitable amount of flexibility is used. Significant thrust increases are alsoobserved in zero pitching amplitude cases. The effects of the second and third deformation modes on the perfor-mances of pressure-driven deformation cases are discussed. On the other hand, inertia-driven deformations generallydeteriorate aerodynamic performances of flapping wings unless the behavior of the wing deformation is modified bythe presence of sustainable superharmonics in a way that produces slight improvements. It is also shown that wingflexibility can act as an efficient passive pitching mechanism that allows fair thrust and better efficiency to be achievedwhen compared to a rigid pitching-heaving wing.

Incompressible, viscous flows in the spherical gap between a rotating inner-sphere and a stationary outer-shell, Spherical Couette Flows (SCF), are studied via direct numerical simulations. The investigation covers both "small-gap" and "large-gap" geometries, and is concerned primarily with the first occurrence of transition in those flows. Strong emphasis is put on the physical understanding of the basic flows and their transition mechanisms. An alias-free spectral method, based on divergence-free vector expansions for the 3-D velocity field in spherical coordinates, is developed. The vector expansions are constructed with Chebyshev polynomials in the radial direction and Vector Spherical Harmonics for the two angular directions. Accuracy and spectral convergence of the resulting initial-value code are thoroughly tested. Three-dimensional transitional flows in both narrow-gaps and large-gaps as well as axisymmetric transitions in moderate-gaps are simulated. For small-gap SCF's, this study shows that the formation of Taylor-vortices at transition is a deterministic process and not the result of the instability of initial perturbations. The formation process involves the sub-critical appearance of a saddle-stagnation point within the meridional circulation cell in each hemisphere. A minimum length-scale ratio is shown necessary, and for a given inner-sphere radius, this leads to a theoretical prediction of the largest gap-width in which Taylor-vortices may form. This investigation confirms that the first transition in large-gap SCF's is caused by a 3-D instability of a linear nature. It is found that the process is characterized by very small growth-rates of the disturbance and by the absence of a "jump" in the friction torque. The supercritical flow is a complex-structured, laminar, time-periodic flow that exhibits traveling azimuthal-waves. The physical mechanism responsible for the large-gap transition is shown to be related to a shear instability of the "radial

Incompressible, viscous flows in the spherical gap between a rotating inner-sphere and a stationary outer-shell, Spherical Couette Flows (SCF), are studied via direct numerical simulations. The investigation covers both "small-gap" and "large-gap" geometries, and is concerned primarily with the first occurrence of transition in those flows. Strong emphasis is put on the physical understanding of the basic flows and their transition mechanisms. An alias-free spectral method, based on divergence-free vector expansions for the 3-D velocity field in spherical coordinates, is developed. The vector expansions are constructed with Chebyshev polynomials in the radial direction and Vector Spherical Harmonics for the two angular directions. Accuracy and spectral convergence of the resulting initial-value code are thoroughly tested. Three-dimensional transitional flows in both narrow-gaps and large-gaps as well as axisymmetric transitions in moderate-gaps are simulated. For small-gap SCF's, this study shows that the formation of Taylor-vortices at transition is a deterministic process and not the result of the instability of initial perturbations. The formation process involves the sub-critical appearance of a saddle-stagnation point within the meridional circulation cell in each hemisphere. A minimum length-scale ratio is shown necessary, and for a given inner-sphere radius, this leads to a theoretical prediction of the largest gap-width in which Taylor-vortices may form. This investigation confirms that the first transition in large-gap SCF's is caused by a 3-D instability of a linear nature. It is found that the process is characterized by very small growth-rates of the disturbance and by the absence of a "jump" in the friction torque. The supercritical flow is a complex-structured, laminar, time-periodic flow that exhibits traveling azimuthal-waves. The physical mechanism responsible for the large-gap transition is shown to be related to a shear instability of the "radial

Incompressible, viscous flows in the spherical gap between a rotating inner-sphere and a stationary outer-shell, Spherical Couette Flows (SCF), are studied via direct numerical simulations. The investigation covers both "small-gap" and "large-gap" geometries, and is concerned primarily with the first occurrence of transition in those flows. Strong emphasis is put on the physical understanding of the basic flows and their transition mechanisms. An alias-free spectral method, based on divergence-free vector expansions for the 3-D velocity field in spherical coordinates, is developed. The vector expansions are constructed with Chebyshev polynomials in the radial direction and Vector Spherical Harmonics for the two angular directions. Accuracy and spectral convergence of the resulting initial-value code are thoroughly tested. Three-dimensional transitional flows in both narrow-gaps and large-gaps as well as axisymmetric transitions in moderate-gaps are simulated. For small-gap SCF's, this study shows that the formation of Taylor-vortices at transition is a deterministic process and not the result of the instability of initial perturbations. The formation process involves the sub-critical appearance of a saddle-stagnation point within the meridional circulation cell in each hemisphere. A minimum length-scale ratio is shown necessary, and for a given inner-sphere radius, this leads to a theoretical prediction of the largest gap-width in which Taylor-vortices may form. This investigation confirms that the first transition in large-gap SCF's is caused by a 3-D instability of a linear nature. It is found that the process is characterized by very small growth-rates of the disturbance and by the absence of a "jump" in the friction torque. The supercritical flow is a complex-structured, laminar, time-periodic flow that exhibits traveling azimuthal-waves. The physical mechanism responsible for the large-gap transition is shown to be related to a shear instability of the "radial