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Two (static and dynamic) fundamental models of the flow over airfoils in the reverse flow region of a helicopter in forward flight are investigated experimentally and computationally at Reynolds numbers of O(10 5). The first model examines the time-averaged and unsteady flow resulting from a two-dimensional NACA 0012 airfoil held at a static angle of attack. Computational tools successfully predict the presence of three unsteady wake regimes and time-averaged airloads measured experimentally at the University of Maryland (UMD). A second model is investigated by pitching a two-dimensional NACA 0012 airfoil through deep dynamic stall in reverse flow. Both experimental and computational results reveal flow separation at the sharp leading edge for shallow angles of attack, leading to the early formation of a reverse flow dynamic stall vortex. Subsequent flow features in the pitching cycle (i.e., a trailing edge vortex and a secondary dynamic stall vortex) are also captured by the numerical simulation, although the timing and strength of some of these features do not align completely with experiment. This work gives fundamental insight into the aerodynamic behavior of airfoils in reverse flow, improves understanding of the complex nature of the reverse flow region, and demonstrates a promising new computational tool for simulating this unique flow regime. Nomenclature A wing planform area, m 2 AR blade aspect ratio, b 2 /S a ∞ free-stream speed of sound, m/s b blade span length, m C p pressure coefficient, (p − p ∞)/q ∞ c blade chord length, m c d drag coefficient, D/(q ∞ A) c l lift coefficient, L/(q ∞ A) c m pitching moment coefficient, M/(q ∞ Ac) D diameter of the circular cylinder, m d projected diameter of the airfoil, m f shedding frequency, Hz k reduced frequency, ωc/2U ∞ M ∞ free-stream Mach number, U ∞ /a ∞ q ∞ free-stream dynamic pressure, 1/2ρ ∞ U 2 ∞ R rotor radius, m Re Reynolds number, U ∞ c/ν ∞ S planform area, m 2 St d

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... At this reverse angle, the flow that impinges on the trailing edge exceeds the reverse stall angle of the blade, which makes this leeward dynamic stall a reverse dynamic stall. 51 The windward dynamic stalls simulated in this work are found to have reasonable magnitudes, in the sense that their behaviors were similarly observed in other works previously. For instance, the work by Lind and Jones 52 experimentally investigated the effects of dynamic stall on a pitching NACA0012 airfoil and found that the C L magnitude reaches a value of 1:5 (in contrast to a typical static C L of 1:25). ...

... With regard to the reverse dynamic stalls in the leeward quadrant, the experimental study by Hodara et al. 51 demonstrated that a reverse dynamic stall on an NACA0012 airfoil can cause C L to reach a value of 2:5, which is higher compared to that of the windward quadrant (as demonstrated in this study). Nonetheless, there are some variations between this study and those from the literature-such as the blade motion, Re numbers, reduced frequencies, and airfoil geometries-that lead to the minor differences in the C L values as compared above between these studies. ...

... On the other hand, dynamic C D in Fig. 9(e) varies strongly and is sometimes below or above the static C D . Compared with the works in the literature, C L and C D in the accelerated phase in this work are similar to those featured in the work by McCroskey 17 and Celik et al. 42 The magnitudes of the coefficients altered by the dynamic stall also have similar magnitudes to those in the experimental works by Hodara et al., 51 Lind and Jones 52 and Rival and Tropea. 49 The dynamic stalls in this cycle boost its dynamic C t values by 166% and 549% larger than the static C t values in the upwind and leeward quadrants, respectively. ...

Darrieus turbines face difficulty to self-start, especially in environments with fluctuating inflows that cause them to deviate repeatedly from their designed operating parameters. To elucidate the self-starting process in this study, a three-bladed Darrieus rotor was simulated numerically with vector diagrams to facilitate visualizations on the rotor behaviors. Based on segments of the average rotor torque coefficients (Cτ), the self-starting process consisted of linear and accelerated phases, with the first two segments in the linear phase and the next two segments in the accelerated phase. The simulation showed that the self-starting process was largely influenced by dynamic stalls. The rotor experienced difficulty to self-start in the first segment as it encountered a region of “dead band” with a negative mean cyclical caused by a reverse dynamic stall. This dynamic stall and its corresponding dead band disappeared in the second segment, which initiated the transition into the accelerated phase. In the third segment, forward dynamic stalls that formed boosted the generation and accelerated the angular speed of the rotor toward its peak. Finally, without any dynamic stalls formed in the fourth segment due to reduced values of the inflow angles on the blades, they reduced drastically until the rotor reached its steady phase. Outcomes from this work demonstrate that understanding the effects of unsteady aerodynamics is vital to improving the self-starting process. Potential design improvements on the rotor that address this aspect include static and dynamic pitching, blade flaps, intracyclical control, and flow controls using blowing and suction mechanisms.

... Evidence of reverse flow dynamic stall was first observed as a low pressure wave passing over blade-mounted pressure sensors in the reverse flow region of a full-scale UH-60 A test at high advance ratios [120]; similar results were obtained through later computations [121]. Following this finding, a series of more canonical experiments were undertaken to better understand the details of these flow physics and the effect of sharp versus blunt trailing edge geometries [17,[122][123][124][125]. A NACA 0012 blade section mounted in reverse flow and undergoing sinusoidal pitching in a constant freestream was found to undergo dynamic stall initiated by flow separation from the sharp aerodynamic leading edge (unlike traditional dynamic stall, where separation is delayed to high angles of attack). ...

... Hodara et al. [125] provide a comparison of experimental and numerical data on reverse flow dynamic stall and outline five stages of this process. The stages are described below and the resulting lift curve is shown in Fig. 15. ...

... Stages I-V of reverse flow deep dynamic stall are labeled; dash line: angle of attack; solid line: lift coefficient. From[125]. ...

... It is known that the sharp aerodynamic leading edge of a NACA 0012 causes early flow separation and the formation of several vortex structures during reverse flow dynamic stall. 13 However, the influence of these structures on the unsteady airloads and the sensitivity of the evolution of reverse flow dynamic stall to flow and pitching parameters is unknown. The current work aims to provide insight on the flow physics of reverse flow dynamic stall to develop a physics-based analytical model that can be compared with classical dynamic stall models. ...

... The discussion is carried out for a case with −α 0,rev = 8.9 • , α 1 = 9.9 • , Re = 3.3 × 10 5 , and k = 0.160, similar to the conditions presented in prior work. 13 Figure 3 shows the kinematics for this case and Figure 8 shows selected phases to illustrate key events in the flow morphology of reverse flow dynamic stall. In all cases considered in the present work, reverse flow dynamic stall behaves generally similar to classical deep dynamic stall. ...

... A more detailed description of the flow morphology for a similar pitching case has been given in prior work. 13 Insight can also be gained by examining Figure 9 which shows the phase-averaged pressure distributions in reverse flow (top) and a nominally similar case in forward flow (bottom). Figure 9(a) shows the suction side of the airfoil and Figure 9(b) shows the pressure side. ...

Wind tunnel experiments were performed on a sinusoidally oscillating NACA 0012 blade section in reverse flow. Time-resolved particle image velocimetry and unsteady surface pressure measurements were used to characterize the evolution of reverse flow dynamic stall and its sensitivity to pitch and flow parameters. The effects of a sharp aerodynamic leading edge on the fundamental flow physics of reverse flow dynamic stall are explored in depth. Reynolds number was varied up to Re = 5 × 105, reduced frequency was varied up to k = 0.511, mean pitch angle was varied up to 15∘, and two pitch amplitudes of 5∘ and 10∘ were studied. It was found that reverse flow dynamic stall of the NACA 0012 airfoil is weakly sensitive to the Reynolds numbers tested due to flow separation at the sharp aerodynamic leading edge. Reduced frequency strongly affects the onset and persistence of dynamic stall vortices. The type of dynamic stall observed (i.e., number of vortex structures) increases with a decrease in reduced frequency and increase in maximum pitch angle. The characterization and parameter sensitivity of reverse flow dynamic stall given in the present work will enable the development of a physics-based analytical model of this unsteady aerodynamic phenomenon.

... Lind et al. experimentally studied the unsteady aerodynamic loads [1], Reynolds number effects [2], vortex shedding [3], and time-averaged aerodynamic forces [4]. On the numerical side, the reverse flow past NACA0012 was simulated by Unsteady Reynolds-averaged Navier-Stokes (URANS) equations or hybrid RANS-LES (large-eddy simulation) methods [5]. The errors by URANS were as high as 126% at a high AoA, then the hybrid method was the first choice when simulating the reverse flow. ...

... he Mach number is 0.26 and the Reynolds number based on the chord (C) is Re=1.1×10 5 . The AoA is 30°and is associated with a massive separation. ...

The improved delayed detached-eddy simulation (IDDES) method is used to simulate the reverse flows past an NACA0012 airfoil at medium (10°) and large (30°) angles of attack. The numerical results of the baseline configuration are compared with the available measurements. The effects of the undulating leading edge with four different amplitudes are compared and analyzed at angle of attack of 10°. Based on these analyses, the amplitude of A/C=0.04 yields the best performance. Compared with the uncontrolled case, the performances of the undulating leading edge are greatly improved with reducing of the aerodynamic fluctuations. Furthermore, the mechanisms of performance are explored by comparing the local flow structures near the undulations.

... Reverse flow over conventional blade sections was found to separate at low angles of attack, leading to deep dynamic stall in which the number of shed vortices depends on pitching kinematics [5] . This flow was well predicted by numerical simulations [7] . The reverse flow dynamic stall vortex (RFDSV) is an unsteady flow feature that is believed to be a dominant source of unsteady airloads in the reverse flow region. ...

... The RFDSV has been studied experimentally by Hiremath et al. using phase-averaged PIV on a sub-scale rotor operating at advance ratios up to µ = 1.0, but with a relatively low maximum advancing tip Mach number of 0.08 [8] . The present work builds on the authors' prior two-dimensional experimental and computational efforts [7] by investigating the reverse flow region of a Mach-scale rotor operating at advance ratios up to µ = 0.9 with a maximum advancing tip Mach number of 0.45. Previous unsteady surface pressure measurements have provided evidence of RFDSV convection on the same sub-scale model rotor used in the present work [9] , as well as on a full-scale slowed UH-60A rotor [10] . ...

A 1.7 m-diameter Mach-scaled slowed rotor was tested at advance ratios up to µ = 0.9 and three shaft tilt angles of −4, 0 , and 4 deg. Two-component time-resolved particle image velocimetry was used to characterize the flow field around a blade element in the reverse flow region, nominally positioned at ψ = 270 deg and y/R = 0.4. Four dominant flow structures were observed: the reverse flow starting vortex, the blunt trailing edge wake sheet, the reverse flow dynamic stall vortex, and the tip vortex. As advance ratio increases, the duration of reduced time that the blade element spends in the reverse flow region also increases. This affects the strength, trajectory, and predicted vortex-induced pitching moment of the reverse flow dynamic stall vortex. Shaft tilt angle also has a strong effect on the evolution of the reverse flow dynamic stall vortex with forward shaft tilt resulting in dramatically increased strength and size. The results of this characterization and sensitivity study are aimed at informing the development of unsteady reverse flow models for use in comprehensive rotorcraft codes.

... A methodology that couples the unsteady Reynolds-averaged Navier-Stokes (URANS) equations with a subgrid-scale turbulence closure for large eddy simulations (LES) has been developed and validated using both structured and unstructured solvers. The development of the model, including details on the turbulence closure modelling, validation of the approach on a wide range of canonical problems, and demonstration 6 D. T. Prosser and M. J. Smith with experimental correlation on complex configurations can be found in Kim & Menon (1999), Sánchez-Rocha & Menon (2009, 2011), Lynch & Smith (2011), Smith, Liggett & Koukol (2011), Shenoy, Smith & Park (2014, Hodara & Smith (2015), and Hodara et al. (2016). As the focus of the paper is not on the hybrid methodology development, but rather its application for studying fluid physics, a short review of the methodology is provided here for the reader who may wish to replicate the computational assessment. ...

... The prior evaluations with traditional URANS models have proved less successful, particularly in the prediction of side of side force (Theron et al. 2005(Theron et al. , 2006Cicolani et al. 2009). Similar findings have been reported across a broad spectrum of configurations (with smooth curves and sharp corners) at moderate and high Reynolds numbers where separation and reattachment is present, including airfoils and wings at high and reverse angles of attack Hodara et al. 2016) and rotor-fuselage interactions (Shenoy et al. 2014), for example. These latter simulations were performed with both URANS and HRLES using the same grids and otherwise the same numerical parameters, verifying the inability of the URANS turbulence methods to correctly capture the leeward-side physics of all of these configurations. ...

Three-dimensional bluff body aerodynamics are pertinent across a broad range of engineering disciplines. In three-dimensional bluff body flows, shear layer behaviour has a primary influence on the surface pressure distributions and, therefore, the integrated forces and moments. There currently exists a significant gap in understanding of the flow around canonical three-dimensional bluff bodies such as rectangular prisms and short circular cylinders. High-fidelity numerical experiments using a hybrid turbulence closure that resolves large eddies in separated wakes close this gap and provide new insights into the unsteady behaviour of these bodies. A time-averaging technique that captures the mean shear layer behaviours in these unsteady turbulent flows is developed, and empirical characterizations are developed for important quantities, including the shear layer reattachment distance, the separation bubble pressure, the maximum reattachment pressure, and the stagnation point location. Many of these quantities are found to exhibit a universal behaviour that varies only with the incidence angle and face shape (flat or curved) when an appropriate normalization is applied.

... The computational tools used in prior work were able to capture the fundamental physics of reverse flow dynamic stall, including the formation and convection of a primary dynamic stall vortex, trailing edge vortex, and secondary dynamic stall vortex with a slight over-prediction in the phasing by the numerical simulation (Ref. 11). Lind and Jones further examined the flow physics of reverse flow dynamic stall and found that its evolution is insensitive to Reynolds number for 1.65 × 10 5 ≤ Re ≤ 5 × 10 5 due to flow However, reduced frequency and pitch angles affect the number, strength, and trajectory of vortex structures that form. ...

... The insight on the flow physics gained in this work can be compared with the findings for reverse flow dynamic stall observed with sinusoidal pitching (Refs. 5,11). Collectively, these works will aid in the development of a physics-based analytical model of reverse flow dynamic stall that can be implemented in comprehensive rotorcraft codes to improve performance predictions of high advance ratio rotors. ...

The reverse flow region of a high advance ratio rotor is modeled using a linearly pitching semi-infinite NACA 0012 blade section in a constant reverse flow freestream. A coupled experimental-numerical approach is used to investigate the instantaneous and ensemble-averaged unsteady aerodynamics. Two pitch cases were considered: 0° ≤ αrev ≤ 20° (i.e., high pitch) and 5° ≤ αrev ≤ 15° (i.e., low pitch). Transient flow phenomena were characterized experimentally using time-resolved particle image velocimetry and unsteady pressure measurements. In the high pitch case, the measured velocity field was dominated by a periodic primary dynamic stall vortex, a trailing edge vortex, and several weak secondary vortices. All three flow structures were present in the Hybrid Reynolds-Averaged Navier Stokes Large Eddy Simulation (tHRLES), while only the primary dynamic stall vortex and trailing edge vortex were present in Unsteady Reynolds-Averaged Navier Stokes (URANS) solver. For the low pitch case, the experimentally measured velocity field was instead characterized by a series of weak vortices that rapidly along the chord; these aperiodic vortices were present in the tHRLES simulation but absent from URANS simulation. The experimental and numerical results suggest that initial pitch angle and pitch rate are driving forces in the character of a NACA 0012 undergoing linear pitching in a constant reverse flow freestream. The comparisons between experimental and numerical flow fields and integrated unsteady airloads show promise in the ability of the Hybrid Reynolds-Averaged Navier Stokes Large Eddy Simulation (tHRLES) code to accurately capture the nonlinear transients observed experimentally.

... 37), which has been specifically designed for modeling statically and dynamically separated flows (Refs. [38][39][40]. GTsim employs a finite volume (cell-centered) formulation with fourth-order spatial and second-order (backward differentiation formula) temporal discretization schemes in a block-structured approach to ensure high accuracy. GTsim has been validated with experimental data and correlated with extant comparable solvers for a full suite of canonical flows (Ref. ...

Rotary-wing vehicles, in particular smaller, lighter unmanned and urban air vehicles in urban and shipboard settings, will operate in low-speed flight conditions that are dominated by strong transient aerodynamics. Understanding the physics of these transient aerodynamics, specifically large amplitude transverse gusts and the resulting vehicle response, is crucial to the successful development and certification of safe air vehicles that operate in these environments. A high-fidelity computational study, including validation with experiments, explores sharp-edged or step transverse gusts where the gust velocity induces nonlinear behavior caused by flow separation. The behavior of the maximum lift and leading edge vortex behavior with the gust ratio is presented. Gust responses are observed to depart from Küssner's theory when the leading edge vortex first forms as a distinct feature and breaks away from the wing, resulting in flow nonlinearities. Traditional linear indicial admittance techniques are shown to no longer be valid to predict gust responses when the gust velocity approaches the vehicle flight speed.

... Aerodynamic designs of the future need to combat and thrive in time-varying, unsteady environments. These conditions commonly arise because of the kinematic motion of the flyers themselves (Hodara et al. 2016;Liu et al. 2020) or alternatively, due to the unsteady nature of the atmospheric boundary layer (Watkins et al. 2010;White et al. 2012). Such rapidly changing conditions are a special concern for micro aerial vehicles (MAVs) because of the high ratio between the velocity of the flow disturbance and their comparatively low flight speed (Watkins et al. 2006;Andreu-Angulo et al. 2020). ...

The impulse theory used to calculate the force from a vorticity distribution in two-dimensional, incompressible flow, is re-cast with the aim of approximating, to a first order, the forces generated by a specific flow feature, such as a free vortex passing by an object. To achieve this, the force acting on the body is split up into several core contributions. The first component arises from the time variation of the body’s boundary layer. The second is generated by the advection of any free vorticity located in the flowfield by the object’s boundary layer vorticity. The final force contribution is due to new vorticity being shed. To test the theory, it is applied to two multi-body flowfields consisting of a circular cylinder and a flat plate wing at incidence in close proximity. Force balance measurements and planar particle image velocimetry data are simultaneously obtained at Reynolds numbers of $$10\,000$$ 10 000 and $$20\,000$$ 20 000 . The forces acting on the cylinder are successfully recovered from the vorticity data using the derived formulation, verifying its accuracy. Subsequently, the proposed force formulation is used to create force heat maps that demonstrate how the location of a leading edge vortex affects its force contribution around a pitching NACA-0021 wing translating at a Reynolds number of $$10\, 000$$ 10 000 .

... Aerodynamic designs of the future need to combat and thrive in time-varying, unsteady environments. These conditions commonly arise because of the kinematic motion of the flyers themselves [17,22] or alternatively, due to the unsteady nature of the atmospheric boundary layer [35,37]. Such rapidly changing conditions are a special concern for micro aerial vehicles (MAVs) because of the high ratio between the velocity of the flow disturbance and their comparatively low flight speed [34,3]. ...

The impulse theory used to calculate the force from a vorticity distribution in two-dimensional, incompressible flow, is re-cast with the aim of approximating, to a first order, the forces generated by a specific flow feature, such as a free vortex passing by an object. To achieve this, the force acting on the body is split up into several core contributions. The first component arises from the time variation of the body's boundary layer. The second is generated by the advection of any free vorticity located in the flowfield by the object's boundary layer vorticity. The final force contribution is due to new vorticity being shed. To test the theory, it is applied to two multi-body flowfields consisting of a circular cylinder and a flat plate wing at incidence in close proximity. Force balance measurements and planar particle image velocimetry data are simultaneously obtained at Reynolds numbers of 10 000 and 20 000. The forces acting on the cylinder are successfully recovered from the vorticity data using the derived formulation, verifying its accuracy. Subsequently, the proposed force formulation is used to create force heat maps that demonstrate how the location of a leading edge vortex affects its force contribution around a pitching NACA-0021 wing translating at a Reynolds number of 10 000.

... However, the unsteady loads for the coaxial rotor are at least one order of magnitude larger than those of a single isolated rotor under the same conditions [2,3]. There are multiple reasons for high vibratory loads, including the interaction between the upper and lower rotors [2,4,5] and flow separation in the reverse region [5][6][7]. Reverse flow occurs when a fluid travels from the geometric trailing edge of an airfoil to the geometric leading edge. The resulting flow field is generally characterized by a negative lift, early onset of flow separation, and periodic vortex shedding, which is believed to contribute to the unsteady aerodynamic loads experienced by a rotor blade [6]. ...

As a practical rounded trailing edge airfoil for coaxial rotors, DBLN-526 is a fore and aft symmetrical airfoil with two steps on its lower side. This airfoil has been used at the inboard section of the coaxial rotor system. As there are always two eddies behind the airfoil because of its rounded trailing edge, the interaction between the separation and transition should be considered. Thus, the unsteady Reynolds-averaged Navier-Stokes- (RANS-) based γ − Re ¯ θ t model was used to analyze the unsteady transition and separation features. Three different rounded trailing-edge airfoils were compared with DBLN-526. Power spectrum density analysis and Δ Cl calculations demonstrated that the lift coefficient fluctuation of DBLN-526 was smaller than that of other rounded airfoils with different angles. Further investigation indicated that the locations of transition for DBLN-526 can be fixed at a wide range of angles by the unique design on its lower side. Because of this settled transition location, the size of separation is decreased, and the position of separation is settled as well, which leads to a lower lift coefficient fluctuation. The turbulent kinetic energy after the transition was higher, which injected a lot of energy into the boundary layer, and the separation zone near the transition position was relatively smaller. This study provides an indication for controlling separation and reducing unsteady fluctuations for rounded trailing edge airfoils.

... The numerical simulations were done with an in-house developed high fidelity computational solver, GTSim [9], which was specifically designed for modeling statically and dynamically separated flows for simulating steady and unsteady flows [10,11,16]. GTsim employs a finite volume (cell-centered) formulation with fourth-order spatial and second-order (Backward Differentiation Formula) temporal discretization schemes in a block structured approach to ensure high accuracy. ...

Operations of vehicles, in particular smaller, lighter un-manned and urban air vehicles in urban environments, will have missions that are dominated by strong transient aerodynamics. Understanding the physics of these transient aerodynamics, specifically large amplitude transverse gusts and the resulting vehicle response, is crucial to the successful development and certification of safe air vehicles that operate in these environments. This paper expands understanding of the physics of nonlinear transverse gusts with flow separation with a state-of-the art computational fluid dynamics solver. Behavior of the maximum lift and leading edge vortex magnitude and direction are correlated with gust ratio and with gust width with and without separated flows. Gust responses are observed to depart from Küssner theory when the leading edge vortex first forms as a distinct feature and breaks away from the wing, resulting in flow nonlinearities. NOMENCLATURE b, c wing half-span and chord, resp., m C L wing lift coefficient, C L = L/qc GR Gust Ratio, GR = W /U i, j, k grid coordinates in the X,Y, Z directions, resp., m q dynamic pressure, m/s 2 s/c leading edge distance into gust, nondimensional-ized by the wing chord U towed wing velocity, m/s W gust velocity from the wall jet, m/s X,Y, Z stream, span, normal coordinate system, resp., m z nearest normal distance to the wing, m ν kinematic viscosity, m 2 /s ω y spanwise vorticity, 1/s

... Pitching airfoil studies allow researchers to simplify the problem into its most basic form and as a result, detailed studies have been conducted on a variety of aspects related to dynamic stall. This includes in depth analysis of turbulent transition [4], reversed flow [5,6], laminar separation bubbles [7,8], compressibility effects [9], and passive/active flow control [10][11][12][13][14]. ...

View Video Presentation: https://doi.org/10.2514/6.2022-2414.vid This paper describes a combined experimental and computational effort to characterize the cycle-to-cycle variations previously observed in oscillating airfoil experiments. It is common in the dynamic stall community to assume that the variation in loads between pitch cycles is primarily due to random turbulent fluctuations, which in turn justifies the assumption that the loads can be accurately represented using simple phase averages. However this work, which numerically and experimentally models an oscillating modified VR-12 airfoil at two different conditions, shows that various aspects ranging from model setup to the inherent fluid dynamics may lead to significant furcation in the loads. These clusters of loads are poorly represented by simple phase averaging techniques and require special consideration. To the best of the authors' knowledge, this work is the first study to successfully capture furcation using CFD and excellent agreement is observed overall for cluster averaged quantities. Furthermore, this work also presents several lessons learned concerning best practices for the dynamic stall community towards improving future correlations between CFD and experimental data and the quality of future dynamic stall datasets in general.

... These simulations provide a baseline of how accurate CFD can be given unlimited resources for physics exploration, and they act as the basis of correlation with less refined meshing. Some physics can still be explored with fewer grid points, augmented with large eddy simulation (LES) equations and sized to capture the salient length scales in the wake, when there are trusted experimental data available, and configurations are restricted to components rather than vehicles or systems [5,6]. Further reductions in mesh size that are conducive to routine engineering use can lead to larger errors, as observed in validation exercises, that may not be acceptable. ...

The cost of Reynolds-Averaged Navier-Stokes simulations can be restrictive to implement in aeromechanics design and analysis of vertical lift configurations given the cost to resolve the flow on a mesh sufficient to provide accurate aerodynamic and structural loads. Dual-solver hybrid methods have been developed that resolve the configuration and the near field with the Reynolds-Averaged Navier-Stokes solvers, while the wake is resolved with vorticity-preserving methods that are more cost-effective. These dual-solver approaches can be integrated into an organisation’s workflow to bridge the gap between lower-fidelity methods and the expensive Reynolds-Averaged Navier-Stokes when there are complex physics present. This paper provides an overview of different dual-solver hybrid methods, coupling approaches, and future efforts to expand their capabilities in the areas of novel configurations and operations in constrained and turbulent environments.

... highly dynamic loading on any immersed object or structure, whilst at the same time, the increased Introduction complexity makes them considerably more difficult to understand and model. As such, wind or water turbines can suffer from fatigue failure due to dynamic loading created by fluctuating incoming velocities and may even need to be turned off to avoid damage in especially gusty conditions, when the most energy could otherwise be created [35]. Similarly to the unsteady dynamics observed around turbines, transient flow also affects full scale aircraft. ...

The time varying nature of many real flows has a strong effect on the resulting force experienced by aerodynamic bodies, where the transient force response can readily exceed the steady-state equivalent. This therefore poses a significant threat to small drones as well as larger aircraft that can be subjected to highly unsteady flow fields. Sensing the flow and using predictive modelling to mitigate the unsteady forces shows potential, yet requires a detailed knowledge of the aerodynamic principles at play. This work is a fundamental study into the underlying mechanisms involved in low Reynolds number unsteady aerodynamics to help facilitate future low order models (LOMs). Specifically, the focus is on the development of the unsteady force, by exploring the origin and evolution of boundary layer vorticity as well as the impact of free vorticity located in the flow. Four sets of experiments are conducted in the towing tank facilities at the University of Cambridge using a rotating and translating circular cylinder as well as a flat plate. To capture the fluid dynamic response, force balance and planar particle image velocimetry (PIV) measurements are acquired in combination, at Reynolds numbers between 4000 and 20000. It is found that whilst the potential flow `added mass' vortex sheet distribution around a stationary object immersed in an accelerating freestream is correct in shape, it ascribes the vortex sheet to the wrong origin. Instead, the vortex sheet is found to develop as a result of external vorticity that is created at the interface between the moving freestream and the quiescent surrounding. Moreover, the evolution of the boundary layer vortex sheet is investigated around a translating and rotating cylinder. The vortex sheet contributions due to kinematics and free vorticity are experimentally recovered. It is further proposed that the vortex sheet contribution due to free vorticity can be decomposed into a local and far-field component. Examining the vortex sheet strength at the unsteady separation point, which has been used in literature explicitly or implicitly to predict unsteady separation, shows that it is strongly affected by the instantaneous velocity, rotation rate and far-field vorticity. Accounting for these contributions collapses the strength of the vortex sheet at the unsteady separation point for the kinematics studied, even as the flow field evolves. In future this may provide avenues with which to predict unsteady separation. Furthermore, the rate at which vorticity sheds from the surface of an object is linked to the boundary layer vortex sheet components. When the unsteady separation point is known, this makes it possible to predict the vorticity shedding rate only from the motion kinematics and the boundary layer vortex sheet. To minimise computational effort for LOMs, only the most dominant flow physics are ideally modelled. To help determine which flow features therefore need to be incorporated in an LOM, a methodology to approximate the force due to an individual flow structure is proposed. A study of a cylinder encountering a sharp-edged transverse gust explores the force caused by external vorticity located within the gust shear layers. The rigid shear layer assumption inherent in Küssner's model is found to overestimate the related non-circulatory gust force. However, the discrepancy remains small compared to the total force.

... Today, very high-fidelity CFD simulations of pitching airfoils have become very popular to investigate specific characteristics of dynamic stall. For example, Hodara et al.[72] demonstrated the clear benefits of a hybrid RANS/LES approach (here HRLES ...

High-fidelity CFD simulations of helicopter rotors are carried out to investigate the dynamic stall flow phenomenon. The simulations are based on two experimental test cases, namely a model rotor with high cyclic pitch control operated at DLR Göttingen, and a highly-loaded, high-speed turn flight of the Bluecopter demonstrator. URANS and DDES simulations are carried out using the flow solver FLOWer coupled with CAMRAD II.
A validation of the numerical methods is conducted based on the experimental model-rotor case, which shows that the onset of dynamic stall and the associated load overshoots agree well in overall. An unprecedented comparison of instantaneous PIV and CFD results reveals that after stall onset, only the DDES captures the chaotic nature of separated flow and exhibits small-scale vortical structures that correlate nicely with the measurement. However, the DDES suffers from the numerical artifact of modeled-stress depletion leading to grid-induced separation. Therefore, several improvements to the so-called boundary-layer shielding are investigated for both dynamic stall cases and found to eliminate the issue. Also, a shear-layer-adaptive filter width is successfully applied to the LES mode of the DDES that promotes a more realistic development of flow instabilities in separated shear layers.
Concerning the turn flight simulation of the Bluecopter, the computed main rotor control angles agree very well with the flight-test measurements. A comparison of the pitch-link loads shows a good correlation regarding the overall trends and a significant improvement over a lower-order analysis. However, the pitch-link-load amplitudes are still underpredicted. Furthermore, the flow field is found to be highly unsteady and complex throughout a large portion of the azimuth, exhibiting strong separation and multiple dynamic stall events that are partly triggered by blade-vortex interaction.

... Marchand et al. [36] observed that the occurrence of lift discontinuity is at 0° for the hydrofoil in reverse flow, as a consequence of the leading edge separation bubble and asymmetrical boundary layers, which can't be detected by the original RANS turbulence model. With the consideration of dynamic stall in reverse flow, the distinctive vortex structures are reverse flow dynamic stall vortices (RFDSVs) and the dynamic stall has a close correlation with the Reynolds number, pitching frequency, mean pitch angle and pitch amplitude [37], yaw angle [38] and foil shape [39]. Due to the massive flow separation and vortex shedding, the reverse flow can lead to the unsteady loading, vibration and fatigue. ...

... The same study also investigated the effect of the yaw angle [15] and reduced frequency [16]. Hodara et al. [17] applied the Reynolds-averaged Navier-Stokes and large eddy simulation (RANS-LES) hybrid method to simulate the pitching motions past the NACA0012 airfoil in the reverse state. Their experimental and computational results revealed that the flow separation at the sharp leading edge could lead to the early formation of a dynamic stall vortex (DSV). ...

The delayed detached-eddy simulation with adaptive coefficient (DDES-AC) and original DDES method are applied to simulate the dynamic stall of the reverse flow past a finite-span wing with NACA0012 airfoil. The numerical results match the measurements well. DDES-AC performs better than the original DDES, especially for the second dynamic stall.

... Marchand et al. [36] observed that the occurrence of lift discontinuity is at 0 • for the hydrofoil in reverse flow, as a consequence of the leading edge separation bubble and asymmetrical boundary layers, which cannot be detected by the original RANS turbulence model. With the consideration of dynamic stall in reverse flow, the distinctive vortex structures are reverse flow dynamic stall vortices (RFDSVs) and the dynamic stall has a close correlation with the Reynolds number, pitching frequency, mean pitch angle and pitch amplitude [37], yaw angle [38] and foil shape [39]. Due to the massive flow separation and vortex shedding, the reverse flow can lead to the unsteady loading, vibration and fatigue. ...

The laminar-turbulence transition phenomenon widely exists on the surface of many energy equipment, which is deserved to be studied because of the complex mechanics and some induced undesirable consequences. The goal of present work is to investigate the transitional flows around the forward and reversed hydrofoils at different incidences using the SST γ-Re˜θt transition model, with special emphasis on the dynamics of the transition. The effect of inflow turbulence condition is considered initially. Then, the difference between the original SST k-ω model and SST γ-Re˜θt transition model is analyzed, in terms of the near-wall velocity profiles and flow morphology. Afterwards, the change of the transition with the incidence for the reversed hydrofoil is clarified in detail. The primary results show that the flow separation near the sharp leading edge where the reverse dynamic vortex (RDV) appears makes the contribution to the transition. The size of RDV is much larger than laminar separation bubble (LSB) over the forward hydrofoil and it forms near the leading edge earlier. Moreover, the transition locations are mapped both for the forward and reversed hydrofoils. Finally, the effect of Reynolds number on the transition process for the reversed hydrofoil is presented. It is believed that this work can deep the understandings of the transition, especially for the reversed hydrofoils.

... Aerodynamics studies the behavior of the airflow around a patched body and associated force coefficients acting on the body's surface (Anderson et al., 2015;Tewari, 2016;Hodara et al., 2016). An aircraft is said to be aerodynamically performing if the lift-to-drag (L/D) ratio is relatively high for a particular Angle Of Attack (AOA). ...

Steady airflow over the wing of an aircraft in-flight is critical to achieving maximum aerodynamic performance. However, commercial flight routes are most times characterized by fluctuations in the airflow properties. The unsteadiness in the air velocity vectors and mass flow directly affects the aerodynamic efficiency (AE) of the aircraft during flight and could lead to air accidents. The correlations between the variation in the airflow properties and the aerodynamic coefficients of a fixed-wing aircraft are not yet fully established. Therefore, this paper makes use of computational fluid dynamics code to study the link between these functions. Herein, a realistic wing model of the BOEING 737 aircraft was used for the investigation. Simulations were carried out at a Mach number of 0.84, with the nonzonal Hybrid RANS-LES method. The fluctuations in the airflow properties were modeled using the vortex fluctuation algorithm (vortex method) in Fluent software. The number vortex,N formed in the flow field were varied in the range of 100 to 300. Findings from the numerical study revealed that the wing achieved an optimal AE of 95.1% for the steady case scenario. However, the wing’s AE was significantly reduced by 30% when the streamlined velocity was perturbed by the fluctuating velocity component. Also, a further decrease in the wing performance was observed with an increase in the divergence of the airflow velocity vectors which experienced a stalling effect after an 80 s flow period forN=300. Moreover, a static increase in the density of the airflow from 1.255 kg/m3 (15°C) to 1.455 kg/m3 (-10°C) contributed to approximately a 20% reduction in the lift and moment coefficients forN=300.

... The same study also investigated the effect of the yaw angle [15] and reduced frequency [16]. Hodara et al. [17] applied the Reynolds-averaged Navier-Stokes and large eddy simulation (RANS-LES) hybrid method to simulate the pitching motions past the NACA0012 airfoil in the reverse state. Their experimental and computational results revealed that the flow separation at the sharp leading edge could lead to the early formation of a dynamic stall vortex (DSV). ...

The delayed detached-eddy simulation with adaptive coefficient (DDES-AC) method is used to simulate the baseline and leading-edge undulation control of dynamic stall for the reverse flow past a finite-span wing with NACA0012 airfoil. The numerical results of the baseline configuration are compared with available measurements. DDES and DDES-AC perform differently when predicting the primary and secondary dynamic stalls. Overall, DDES-AC performs better owing to the decrease of grey area between the strong shear layer and the fully three-dimensional separated flow. Moreover, the effects of the undulating leading-edge on the forces, lift gradients, and instantaneous flow structures are explored. Compared with the uncontrolled case, the lift gradient in the primary dynamic stall is reduced from 18.4 to 8.5, and the secondary dynamic stall disappears. Therefore, periodic unsteady air-loads are also reduced. Additionally, the control mechanism of the wavy leading edge (WLE) is also investigated by comparison with the straight leading edge (SLE). No sudden breakdown of strong vortices is the main cause for WLE control.

... The variant characteristics of the flow variables in the flow field can be used to describe a virtual flight environment with disturbances in the airflow (Mitch et al., 2010;Kornev et al., 2010). Aerodynamics studies the behavior of the airflow around a patched body and associated force coefficients acting on the body's surface (Anderson et al., 2015;Tewari, 2016;Hodara et al., 2016). An aircraft is said to be aerodynamically performing if the lift-to-drag (L/D) ratio is relatively high for a particular Angle Of Attack (AOA). ...

Aerodynamics is the study of motion of air, particularly as interaction with a solid object, such as an airplane wing. It is a sub-field of fluid dynamics and gas dynamics, and many aspects of aerodynamics theory are common to these fields. The term aerodynamics is often used synonymous with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational in nature.

... Reverse flow over dynamically pitching conventional blade sections was found to separate at low angles of attack, leading to deep dynamic stall in which the number of shed vortices depends on pitching kinematics (Lind and Jones 2016a). This flow was well predicted by numerical simulations (Hodara et al. 2015). ...

One challenge that plagues the high-speed operation of rotorcraft is the inherent increase in size of the reverse flow region on the retreating side of the rotor disk. The present work experimentally investigated a portion of the reverse flow region on a 1.7- m-diameter sub-scale slowed rotor at advance ratios up to \(\mu =0.9\) and three shaft tilt angles \({\alpha _{\text {s}}=-\ 4^\circ ,\,0^\circ ,\,4^\circ }\). Two-component time-resolved particle image velocimetry was used to characterize the flow field around a blade element in the reverse flow region, nominally positioned at \(\psi =270^\circ \) and \({y/R=0.4}\). Four dominant flow structures were observed: the reverse flow entrance vortex, the blunt trailing edge wake sheet, the reverse flow dynamic stall vortex, and the tip vortex. Analyses are focused on the reverse flow dynamic stall vortex due to its influence on unsteady airloads, and similarities to that of a leading edge vortex over a rotating or surging wing at high angle of attack. The number of semi-chords traveled by the blade element through the reverse flow region directly affects the strength, trajectory, and estimated vortex-induced pitching moment of the reverse flow dynamic stall vortex. Shaft tilt angle also has a strong effect on the evolution of the vortex, with forward shaft tilt resulting in dramatically increased strength and size. The results of this characterization and sensitivity study serve as a reference for evaluation of numerical simulations and aid in the development of low-order aerodynamic models of the reverse flow region and resulting force histories. Collectively, these tools will be used to better predict airloads, wake interactions, and vibrations of rotors operating at high advance ratios.

... It is prohibitively expensive to run experiments, and lower fidelity numerical analysis is not sufficient to capture the details of dynamic stall [7] so computational fluid dynamics (CFD) or computational fluid dynamics-computational structural dynamics (CFD-CSD) analyses must be used. To capture the intricate details necessary to advance current understanding of the dynamic stall event, computations must be run on very fine grids using small time steps augmented with Newton subiterations, as demonstrated by prior research [8][9][10][11]. These analyses indicate that the time steps and subiterations needed for a full three-dimensional finite rotating wing is prohibitively expensive for engineering analyses. ...

High-speed rotorcraft experience a region of reversed flow over the retreating blade at high advance ratios. This reverse flow region results in multiple unfavorable effects, including negative lift, increased drag, and a large pitching moment impulse. The effect of the sweep angle on a rotor blade in reverse flow was explored, and it was demonstrated that the introduction of a trailing edge reflex camber could mitigate the adverse effects seen in this regime. A cantilevered, finite-span NACA 63-218 blade was examined at a Reynolds number [Formula: see text] both with and without a 10° trailing edge reflex camber. Three blades were tested: one with 20° forward sweep, one with 20° backward sweep, and one with no sweep. The experiments consisted of load measurements across a range of angles of attack, as well as volumetric flowfield measurements using stereoscopic particle image velocimetry on the two swept models at 10° angle of attack in reverse flow. The flowfields exhibited a highly three-dimensional separation bubble that existed on the blades in both backward and forward sweep conditions. Cambering of the trailing edge led to almost complete flow attachment on the backward swept model and a significant reduction in separation over the forward swept model. Cambering also led to a large reduction in drag in the entire reverse flow regime in both swept and unswept conditions. A large reduction in pitching moment and a smaller reduction in negative lift were also observed at moderate angles of attack.

An inherent aerodynamic limitation of high-advance-ratio high-speed helicopters is reverse flow on the retreating blades, which can be a source of several unsteady effects, like vortex formation, that reduce rotor performance. The current study is the first detailed comparison of a rotor with a conventional, sharp trailing-edge NACA 0012 airfoil section with one equipped with a blunt-edge elliptical airfoil section. The aim was to detect and quantify vortex formation in reverse flow using planar particle image velocimetry on a subscale, low-Reynolds-number rotor rig in a water tank. The investigated blade azimuth angles ranged from 240 to 300 deg for advance ratios between 0.40 and 1.00 at pitch angles from 13 to 25 deg. Four main vortex structures were detected. At the aerodynamic leading edge, a strong interference of the tip vortex with the reverse-flow dynamic stall vortex was identified when blade flapping was restricted. Dynamic stall vortices advect closer to the blade surface for the blunt elliptical airfoil, thus reducing the wake area in reverse flow. Blade pitch kinematics govern the reverse-flow entrance-vortex strength and coherency. A coherent vortex street or wake sheet forms at the aerodynamic trailing edge of either airfoil. Overall, the vortex structures that form on the ellipse are more coherent than those on the NACA 0012. The current study highlights the significance of airfoil geometry, specifically the trailing-edge curvature, of an airfoil on the resulting vortex structures in reverse flow, strongly affecting the rotor performance at high advance ratios.

This paper describes a combined experimental and computational effort to characterize the cycle-to-cycle variations previously observed in oscillating airfoil experiments. It is common in the dynamic stall community to assume that the variation in loads between pitch cycles is primarily due to turbulent fluctuations, which in turn justifies the assumption that the loads can be accurately represented using simple phase averages. However this work, which numerically and experimentally models an oscillating modified VR-12 airfoil at two different conditions, shows that various aspects ranging from model setup to inherent fluid dynamics may lead to furcation in the loads that can have first-order impacts on the flow. These clusters of loads are poorly represented by simple phase averaging techniques and require special consideration. This study successfully captures dynamic stall furcation using computational fluid dynamics (CFD) and shows good agreement for cluster-averaged quantities when compared with experimental data. Furthermore, this work also presents several lessons learned concerning best practices for the dynamic stall community toward improving future correlations between CFD and experimental data and the quality of future dynamic stall datasets in general.

Aeromechanic and aeroacoustic simulation of helicopters and other rotorcraft have made tremendous progress over the last years, especially at the upper end of the fidelity spectrum. Advances in high performance computing have enabled the detailed aerodynamic simulation of complete rotorcraft configurations under trimmed flight conditions. This book presents recent results created at the author's working group, as well as giving an overview of other relevant international developments in the field.
Methods of varying complexity, accuracy and reliability are covered, discussing their respective strengths and weaknesses. Emphasis is on high fidelity computational fluid dynamics (CFD) coupled to structure dynamic simulation on the rotor blades, including the flight mechanical trim in free flight. Detailed analysis of local flow features assists in the profound understanding of complex phenomena, facilitating further progress. Aeroacoustic postprocessing of aerodynamic data gives insight into major noise mechanisms and can identify potential improvements.
With this information the responsible rotorcraft aeromechnics engineer can competently select and apply the appropriate tools for the problem given, taking into account boundary conditions like accuracy requirements and resource constraints. Accordingly, reliable simulations support rotorcraft development throughout the entire design process.

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.

View Video Presentation: https://doi.org/10.2514/6.2022-1537.vid An inherent aerodynamic limitation of high advance ratio, high-speed helicopters is the reverse flow region on the retreating blades being the source of several unsteady effects that can reduce rotor performance. To better understand rotor blade efficiency in reverse flow, a novel elliptical airfoil was compared to conventional NACA0012 blades using a sub-scale, low Reynolds number rotor rig in a water tank. Planar particle image velocimetry was used to obtain vorticity and velocity fields in and at the boundaries of the reverse flow region. The investigated azimuth angles ranged from 230° to 300° for advance ratios between 0.40 and 1.00 at pitch angles from 13° to 25°. The results revealed a strong interference of the tip vortex with the reverse flow dynamic stall vortex at the aerodynamic leading edge when blade flapping was restricted, resulting in a lower vertical position of the tip vortex. The dynamic stall vortices advect closer to the blade surface for the blunt elliptical airfoil, thus reducing the wake area in reverse flow. Unlike in previous studies, the reverse flow entrance vortex forms a dispersed flow structure instead of a coherent vortex. A blunt trailing edge vortex street sheds for high advance ratios close to 1.00 for the elliptical airfoil and the NACA0012 at 13° pitch. For higher pitch angles the NACA0012 sheds a dispersed wake sheet. This study reveals the significance of the trailing edge curvature on the resulting vortex structures in the reverse flow region, highly affecting the rotor performance at high advance ratios.

View Video Presentation: https://doi.org/10.2514/6.2022-0475.vid High speed rotorcraft experience a region of reversed flow over the retreating blade at high advance ratios. This reverse flow region results in multiple unfavorable effects, including negative lift, increased drag, and a large pitching moment impulse. The effect of sweep on a rotor blade in reverse flow was explored, and it was demonstrated that the introduction of a trailing edge reflex camber could mitigate the adverse effects seen in this regime. A cantilevered, finite span NACA 63-218 blade was examined at a Reynolds number Rec = 2.38*10^5 both with and without a 10° trailing edge reflex camber. The blades were tested at 20° forward sweep, 20° backward sweep, and at no sweep conditions. Experiments consisted of static load measurements across a range of angles of attack, as well as stereoscopic particle image velocimetry (SPIV) on the swept models at 10° angle of attack in reverse flow. SPIV showed that a highly three-dimensional separation bubble existed on the baseline blade at both backward and forward sweep conditions. Cambering led to almost complete flow attachment on the backward sweep model and a significant reduction on the forward sweep model. Cambering also led to a large reduction in drag in the entire reverse flow regime at both swept and upswept conditions. A large reduction in pitching moment and a smaller reduction in negative lift were also observed at moderate angles of attack

In high-speed rotorcraft applications, large sections of a blade undergo reverse flow due to a high advance ratio. Flow separation at the sharp aerodynamic leading edge during reverse flow leads to negative lift, pitching moment, and drag penalties. The kinematics of a rotor blade leads to a dynamic stall in reverse flow, which further accentuates the problem by causing unsteady loading. The present experimental study shows that these problems can be mitigated by passively morphing the camber near the trailing edge of the blade. A finite-span cantilevered NACA 63-218 blade was examined at a chord-based Reynolds number of 3.75×105 with and without trailing-edge morphing. The morphing was implemented by deflecting the last quarter-chord near the trailing edge by 5, 10, or 15 deg. Experiments included global measurements of the forces and moments using a load cell as well as detailed flow measurements using stereoscopic particle image velocimetry. A couple of scenarios were explored: static pitch and dynamic pitch at different pitch amplitudes and frequencies. Cambering of the blade near its trailing edge led to a significant reduction in the size of the separation region over the model, and of the wake. For the static pitch case, it led to a large reduction in drag and pitching moment and a minor reduction in negative lift. For the dynamic pitch cases, the hysteresis loop was significantly reduced, leading to a large reduction in unsteady loading.

Minijet is one of the most promising active methods for the enhancement of jet mixing. The injection of minijets into a turbulent jet before the jet exit may have multiple impacts on the jet mixing structure. This work aims to understand the jet flow structure controlled by multiple unsteady minijets, especially the effect of the minijet phases on the jet mixing enhancement. Large eddy simulation was conducted for a round, turbulent jet, disturbed with six unsteady minijets, with a view to reveal the flow structures for various control modes and enhance the jet mixing. The Reynolds number is 8000 based on the jet exit diameter and jet centerline velocity at the jet exit. A space/time-dependent boundary condition at jet exit is deployed to generate a statistically stable turbulent jet flow field within an acceptable short computational time.

Three different aerodynamic models are used to analyze a modern lift-offset coaxial helicopter in high-speed cruise. The first and simplest method, dynamic inflow, is used along with Computational Structural Dynamics (CSD) to determine the trimmed flight conditions at speeds up to 250 kt. Two higher order models, the Viscous Vortex Particle Method (VVPM) and Computational Fluid Dynamics (CFD) are then used to evaluate the same trimmed condition at a speed of 230 kt. VVPM is capable of capturing the rotor to rotor interference from first-principles at a significantly lower cost than CFD. The high resolution CFD solution revealed significant deviations in the airloads from the values obtained with the first two methods.

One of the primary challenges in the study of gust encounters lies in isolating, defining, and parametrizing a specific problem in a highly unsteady, three-dimensional, and multiscale flow. Recent efforts have decomposed the complex gusty environment typical of atmospheric turbulence and wakes into three canonical gust types: transverse gusts, vortex gusts, and streamwise gusts. By applying analytical, experimental, and numerical methods, a comprehensive picture of the flow fields and force histories typical of gust encounters has been achieved, shedding light on how the defining parameters in the problem affect unsteady forcing. The focus of the current work is on vortex formation and lift production on rigid two-dimensional wings. Despite these simplifications, analytical and low-order modeling of gust encounters resulting in massively separated flows remains a challenge, largely because the force response of the wing is highly sensitive to the growth and motion of vorticity in the flow. It also remains to be seen how well canonical gusts represent real-world gust encounters, and whether there is some region of the parameter space where linear superposition of these inherently nonlinear flows results in a reasonable approximation of the true problem. This article provides an overview of a limited selection of recent and classic work on large-amplitude gust encounters to motivate a discussion of current challenges in parametrizing and modeling these flows, as well as thoughts on working toward a long-term goal of mitigating gust responses.

Dynamic stall has been studied for more than fifty years; in the last decade significant advances have been accomplished in the understanding, prediction, modeling and control of dynamic stall on rotors. In September 2019, an Army Research Office-funded workshop was held at the Georgia Institute of Technology to evaluate the state of the art and future directions in the understanding and control of dynamic stall found on rotors, specifically for vertical lift vehicles. Approximately forty attendees drawn from top experts in the field to graduate students convened to discuss experimental, computational, theoretical, and control research in the field over a two-day period. This paper provides a summary of the findings from this workshop, including a synopsis of best practices for experiments and first-principles-based computational prediction of rotor dynamic stall. Experimental data sets are discussed, as well the direction of research for empirical (non-first-principles) modeling and control of dynamic stall.

The origin of the noncirculatory force arising during a cylinder sharp-edged gust encounter is investigated experimentally at a Reynolds number of 6000. Planar particle image velocimetry and force balance measurements are employed simultaneously to assess the response of a translating cylinder encountering nominal gust ratios of 0.5, 1, and 1.5. Although the vortex sheet distribution, which represents the boundary-layer vorticity, agrees with that calculated following Küssner’s potential flow approach for a sharp-edged transverse gust, it was found that the sheet can also be determined from the vorticity distribution in the shear layers forming the gust edges. Furthermore, it is found that the noncirculatory force calculated using Küssner’s model is an overestimate because the implicit assumption of rigid gust shear layers leads to an unphysical additional momentum change as a body of volume enters the gust regime. A volume correction is therefore proposed. In addition, it is found that the gust shear layer width and deformation have a noticeable effect on the unsteady noncirculatory force development, which reduces the applicability of Küssner’s method for large gust ratios and objects with considerable volume.

The definition of a vortex is a topic of much discussion in fluid mechanics . The common intuitive features of a vortex are a pressure minimum, closed or spiraling streamlines, and iso-surfaces of constant vorticity. [Jeong & Hussain] have proposed a definition of a vortex as a pressure minimum in the absence of unsteady straining and viscous effects. According to [Majumdar] , decreasing μ and increasing the fluid velocity, disintegrate the fluid parcel moving along U. into smaller parcels moving in arbitrary directions with random velocities. This is where the vortices are generated.

The multiscale development of dynamic stall was studied using a scale-based modal analysis technique. Time-resolved velocity field data around an airfoil during dynamic stall were used for this analysis, with experimental conditions corresponding to Rec=9.2×105 and k=0.05. Intrinsic mode functions were determined by a multivariate, multidimensional empirical mode decomposition method, which ensures mode alignment between velocity components and modal dependency on the full spatiotemporal flowfield. Individual intrinsic mode functions were linked to physically significant phenomena in the flowfield, including the formation of vortical structures due to the Kelvin–Helmholtz instability, interactions between shear-layer vortices leading to vortex pairing, and ultimately shear-layer roll-up and the formation of the dynamic stall vortex. In addition to qualitatively describing these flow structures and interactions, their characteristic length and time scales within the intrinsic mode functions were quantified. These quantitative measures were found to be consistent with time and length scales reported in the literature on experimental investigations of canonical fluid dynamic processes.

The leading-edge vortex (LEV) is a powerful unsteady flow structure that can result in significant unsteady loads on lifting blades and wings. Using force, surface pressure and flow field measurements, this work represents an experimental campaign to characterize LEV behaviour in sinusoidally surging flows with widely varying amplitudes and frequencies. Additional tests were conducted in reverse flow surge, with kinematics similar to the tangential velocity profile seen by a blade element in recent high-advance-ratio rotor experiments. General results demonstrate the variability of LEV convection properties with reduced frequency, which greatly affected the average lift-to-drag ratio in a cycle. Analysis of surface pressure measurements suggests that LEV convection speed is a function only of the local instantaneous flow velocity. In the rotor-comparison tests, LEVs formed in reverse flow surge were found to convect more quickly than the corresponding reverse flow LEVs that form on a high-advance-ratio rotor, demonstrating that rotary motion has a stabilizing effect on LEVs. The reverse flow surging LEVs were also found to be of comparable strength to those observed on the high-advance-ratio rotor, leading to the conclusion that a surging-wing simplification might provide a suitable basis for low-order models of much more complex three-dimensional flows.

A new hybrid analysis framework that addresses some of the major shortcomings of prior hybrid solvers is being developed through an academic-industry partnership between the Georgia Institute of Technology and Continuum Dynamics, Inc. In this effort, one of the hybrid solvers, comprising of a Computational Fluid Dynamics - Computational Structural Dynamics (CFD-CSD) solver coupled with a wake-panel module, is assessed. The hybrid
solver’s ability to replicate the accuracy of the more expensive CFD-CSD approach and its ability to capture the physics of the system are described. The criteria that have been evaluated include integrated aerodynamic performance quantities, structural loads and moments, and near-body wakes. If the best practices extracted from this analysis are applied, the OVERFLOW+CHARM analysis with a reduced off-body mesh (contiguous mesh approach) is able to predict forward-flight rotor behavior that is as accurate as a full OVERFLOW simulation at 45%-50% of the cost. This accuracy has been assessed on both the high-speed and high-thrust flight conditions, and has been quantitatively verified for aerodynamic, structural, and hub variables of interest at a number of radial blade
stations for a frequency range of 0 – 16/rev.

The numerical prediction of transition from laminar to turbulent flow has proven to be an arduous challenge for computational fluid dynamics, with few approaches providing routine accurate results within the cost confines of engineering applications. The recently proposed y-Reθ transition model shows promise for predicting attached and mildly separated boundary layers in the transitional regime, but its accuracy diminishes for massively separated flows. In this effort, a new turbulence closure is proposed that combines the strengths of the local dynamic kinetic energy model and the widely adopted y-Reθ transition model using an additive hybrid filtering approach. This method has the potential for accurately capturing massively separated boundary layers in the transitional Reynolds number range at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, NACA 63-415 wing, and circular cylinder in crossflow. The new closure captures the physics associated with a separated wake (circular cylinder) across a range of Reynolds numbers from 10 to 2 million (2 × 10⁶) and performed significantly better in capturing performance and flowfield features of engineering interest than existing turbulence models. The transitional hybrid approach is numerically robust and requires less than 2% extra computational work per iteration as compared with the baseline Langtry.Menter transition model.

Rotating blades at high advance ratios can experience reverse flow, where the freestream flow is directed from the sharp trailing edge of the blade to the blunt leading edge. Better understanding of this flow regime can help advance the design of high-speed rotorcraft. In this work, it is hypothesized that the sharp trailing edge of a reverse flow blade develops an attached vortex in a similar manner to a sharp-edged delta wing. Lift, drag and pitching moment data for a static yawed blade in reverse flow are acquired using a load cell and the lift measurements are compared to predictions made with an adaptation of the Polhamus model. Surface tuft flow visualization confirms the presence of an attached span-wise vortex on the blade. Surface flow behavior is used to explain the behavior of observed aerodynamic loads, and correlations are made to previous results found in the literature.

Direct force measurements and qualitative flow visualization were used to compare flow field evolution versus lift and drag for a nominally two-dimensional rigid flat plate executing smoothed linear pitch ramp manoeuvres in a water tunnel. Non-dimensional pitch rate was varied from 0.01 to 0.5, incidence angle from 0 to 90°, and pitch pivot point from the leading to the trailing edge. For low pitch rates, the main unsteady effect is delay of stall beyond the steady incidence angle. Shifting the time base to account for different pivot points leads to collapse of both lift/drag history and flow field history. For higher rates, a leading edge vortex forms; its history also depends on pitch pivot point, but linear shift in time base is not successful in collapsing lift/drag history. Instead, a phenomenological algebraic relation, valid at the higher pitch rates, accounts for lift and drag for different rates and pivot points, through at least 45° incidence angle.

Flow over a circular cylinder at Reynolds number 3900 is studied numerically using the technique of large eddy simulation. The computations are carried out with a high-order accurate numerical method based on B-splines and compared with previous upwind-biased and central finite-difference simulations and with the existing experimental data. In the very near wake, all three simulations are in agreement with each other. Farther downstream, the results of the B-spline computations are in better agreement with the hot-wire experiment of Ong and Wallace [Exp. Fluids 20, 441–453 (1996)] than those obtained in the finite-difference simulations. In particular, the power spectra of velocity fluctuations are in excellent agreement with the experimental data. The impact of numerical resolution on the shear layer transition is investigated.

Modifications are proposed of two recently developed hybrid CFD strategies, Delayed Detached Eddy Simulation (DDES) and DDES with Improved wall-modeling capability (IDDES). The modifications are aimed at fine-tuning of these approaches to the k-ω SST background RANS model. The first one includes recalibrated empirical constants in the shielding function of the SA-based DDES model which are shown to be suboptimal (not providing the needed level of elimination of the Model Stress Depletion (MSD)) for the SST-based DDES model. For the SST-IDDES variant, in addition to that, a simplification of the original SA–based formulation is proposed, which does not cause any visible degradation of the model performance. Both modifications are extensively tested on a range of attached and separated flows (developed channel, backward-facing step, periodic hills, wall-mounted hump, and hydrofoil with trailing edge separation).

The paper is an attempt to provide a comprehensive description of the state-of-the-art in the area of Detached-Eddy Simulation (DES) of massively separated turbulent flows. DES is a new approach to treatment of turbulence aimed at the prediction of separated flows at unlimited Reynolds numbers and at a manageable cost in engineering. It soundly combines fine-tuned Reynolds-Averaged Navier-Stokes (RANS) technology in the attached boundary layers and the power of Large-Eddy Simulation (LES) in the separated regions. It is essentially a three-dimensional unsteady approach using a single turbulence model, which functions as a subgrid-scale model in the regions where the grid density is fine enough for an LES, and as a RANS model in regions where it is not. SGS function or LES mode prevails where the grid spacing in all directions is much smaller than the thickness of the turbulent shear layer. The model senses the grid density and adjusts itself to a lower level of mixing, relative to RANS mode and, as a result, unlocks the large scale instabilities of the flow and lets the energy cascade extend to length scales close to the grid spacing. In other regions (primarily attached boundary layers), the model is in RANS mode. The approach is non-zonal, i.e., there is a single velocity and model field, and no issue of smoothness between regions. The computing-cost outcome is favorable enough that challenging separated flows at high Reynolds numbers can be treated quite successfully on the latest personal computers. We present a motivation for and detailed formulation of the DES approach based on both its original version employing the one-equation Spalart-Allmaras (S-A) turbulence model, and a new one, using the k-w Shear Stress Transport model of Menter (M-SST). Numerical issues in DES are also addressed in terms of both accuracy and efficiency. The credibility of the approach is supported by a set of numerical examples of its application: NACA 0012 airfoil at high (up to 90°) angles of attack, circular cylinder with, laminar and turbulent separation, backward-facing step, triangular cylinder in a plane channel, raised airport runway, and a model of the landing gear truck. The DES predictions are compared with experimental data and with RANS solutions. © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Particle image velocimetry (PIV) measurements are made in a highly turbulent swirling flow. In this flow, we observe a coexistence of turbulent fluctuations and an unsteady swirling motion. The proper orthogonal decomposition (POD) is used to separate these two contributions to the total energy. POD is combined with two new vortex identification functions, Γ1 and Γ2. These functions identify the locations of the centre and boundary of the vortex on the basis of the velocity field. The POD computed for the measured velocity fields shows that two spatial modes are responsible for most of the fluctuations observed in the vicinity of the location of the mean vortex centre. These two modes are also responsible for the large-scale coherence of the fluctuations. The POD computed from the Γ2 scalar field shows that the displacement and deformation of the large-scale vortex are correlated to these modes. We suggest the use of such a method to separate pseudo-fluctuations due to the unsteady nature of the large-scale vortices from fluctuations due to small-scale turbulence.

Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 103 ≤ Rec ≤ 210 × 103, and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

This document describes the current formulation of the SST turbulence models, as well as a number of model enhancements. The model enhancements cover a modified near wall treatment of the equations, which allows for a more flexible grid generation process and a zonal DES formulation, which reduces the problem of grid induced separation for industrial flow simulations. Results for a complete aircraft configuration with and without engine nacelles will be shown.

Germano(Theor Comput Fluid Dyn 17:225–331, 2004) proposed a hybrid-filter approach, which additively combines an LES-like filter operator (F) and a RANS-like statistical operator (E) using a blending function k: H = kF + (1 − k)E. Using turbulent channel flow as an example, we first conducted a priori tests in order to gain some insights into this hybrid-filter
approach, and then performed full simulations to further assess the approach in actual simulations. For a priori tests, two
separate simulations, RANS (E) and LES (F), were performed using the same grid in order to construct a hybrid-filtered field (H). It was shown that the extra terms arising out of the hybrid-filtered Navier–Stokes (HFNS) equations provided additional
energy transfer from the RANS region to the LES region, thus alleviating the need for the ad hoc forcing term that has been
used by some investigators. The complexity of the governing equations necessitated several modifications in order to render
it suitable for a full numerical simulation. Despite some issues associated with the numerical implementation, good results
were obtained for the mean velocity and skin friction coefficient. The mean velocity profile did not have an overshoot in
the logarithmic region for most blending functions, confirming that proper energy transfer from the RANS to the LES region
was a key to successful hybrid models. It is shown that Germano’s hybrid-filter approach is a viable and mathematically more
appealing approach to simulate high Reynolds number turbulent flows.
KeywordsNumerical simulation-Large-eddy simulation-Hybrid approach-Turbulent flow-Channel flow

In this work, the compressible governing equations for the hybrid Reynolds-averaged/large-eddy simulations are formally derived by applying a hybrid filter to the Navier–Stokes equations. This filter is constructed by linearly combining the Reynolds-average (RANS) and large-eddy simulation (LES) operators with a continuous blending function. The derived hybrid equations include additional terms that represent the interactions between RANS and LES formulations. The relevance of these terms is investigated in flat-plate turbulent boundary layer simulations and indicate that these additional terms play a fundamental role in compensating for the turbulence that is neither modeled nor resolved in the transition region between RANS and LES. Results also show that when the additional terms are included, the calculations are not very sensitive to the blending function implemented in the hybrid filter. In the contrary, when these terms are neglected and a step function is implemented in the hybrid filter, nonphysical discontinuities are predicted in the flow statistics.

We give the "philosophy", fairly complete instructions, a sketch and examples of creating Detached-Eddy Simulation (DES) grids from simple to elaborate, with a priority on external flows. Although DES is not a zonal method, flow regions with widely different gridding requirements emerge, and should be accommodated as far as possible if a good use of grid points is to be made. This is not unique to DES. We brush on the time-step choice, on simple pitfalls, and on tools to estimate whether a simulation is well resolved.

The vortex shedding characteristics of three airfoils held at static angles of attack through 360 deg are presented with a focus on reverse flow (150 ≤ α ≤ 180 deg). Wind tunnel testing was performed on one airfoil with a sharp trailing edge (NACA 0012) and two airfoils featuring a blunt trailing edge (ellipse and DBLN-526). Time-resolved particle image velocimetry and smoke flow visualization were used to identify three reverse flow wake regimes: slender body vortex shedding, turbulent, and deep stall vortex shedding. The slender body regime is present for low angles of attack and low Reynolds numbers. In the turbulent regime, separation occurs in reverse flow at the sharp aerodynamic leading edge of a NACA 0012, whereas flow separation occurs further down the chord of airfoils with a blunt geometric trailing edge. The deep stall vortex shedding frequency was measured using unsteady force balance measurements. The Strouhal number Std (based on the projected diameter d of the airfoils) was found to be 0.145-0.161 for 45 ≤ α ≤ 135 deg, which is well below the value of Std = 0.19 for a corresponding cylinder. The results of the work presented here provide fundamental insight for rotor applications where flow separation and vortex shedding due to reverse flow can lead to unsteady loading, vibrations, and fatigue. Copyright © 2015 by A. Lind. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Two-dimensional wind-tunnel experiments have been conducted on three airfoils held at static angles of attack through 360 deg at a Reynolds number of Re = 1.1 × 105 to evaluate the influence of trailing-edge shape on timeaveraged force and flowfield measurements. The present study focuses on airfoil performance in reverse flow to advance the understanding of this flow regime for high-speed helicopter applications. It is shown that the drag of a NACA 0012 airfoil in reverse flow is more than twice as large compared to forward flow due to early flow separation, similar to a flat plate. Two blunt trailing-edge airfoils are considered in this work: an elliptical airfoil and the DBLN-526. Both airfoils exhibit a rapid increase in lift at low angles of attack in both forward and reverse flows. The drag of the elliptical airfoil in reverse flow is significantly lower than the NACA 0012 for 5 < αrev < 17 deg. Lift was calculated via a circulation box method applied to time-averaged flowfield measurements and compared to force measurements. The findings presented here give fundamental insight into the selection of airfoils for the inboard section of a rotor blade for optimal performance in both forward and reverse flows.

This paper describes and analyzes the measurements from a full-scale, slowed revolutions per minute (rpm), UH-60A rotor tested at the National Full-Scale Aerodynamics Complex 40- by 80-ft wind tunnel up to an advance ratio of 1.0. A comprehensive set of measurements that includes performance, blade loads, hub loads, and pressures/airloads makes this data set unique. The measurements reveal new and rich aeromechanical phenomena that are unique to this exotic regime. These include reverse chord dynamic stall, retreating side impulse in torsion load, large inboard-outboard elastic twist differential, diminishing rotor forces and yet a dramatic buildup of blade loads, and high blade loads and yet benign levels of vibratory hub loads. The objective of this research is the fundamental understanding of these unique aeromechanical phenomena. The intent is to provide useful knowledge for the design of high-speed, high-efficiency, slowed rpm rotors of the future and a database for validation of advanced analyses.

To investigate aerodynamic behaviors of two dimensional wings at the extreme angle of attack the traditional lift and drag force measurements were carried out during one revolution angle of attack by using the dynamic balance in the wind tunnel, and their flow visualizations were also performed. Five different wings were used to measure basically lift and drag coefficients and their polar plots, and their comparisons were also made. It was found that most wings have a second peak in the lift profile even after the stall angle with comparable magnitude to the first peak. At more than 90 degrees of angle of attack, the trailing edge vortex became main vortex to lead the wake structure. Especially, near the 140 degrees angle there appeared drag jumps for most wings. It was interesting feature that the polar plot of the flat wing has an profile very close to an elliptic curve. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Experimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range to with mean of and amplitude of . The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients () are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.

Current rotorcraft research to increase flight speed or to alleviate adverse physical phenomena expand the Mach/angle-of-attack envelope in which the rotor blades operate. For example, rotor blades will experience large areas over the rotor disk where reverse-flow effects cannot be neglected during the design and analysis of an efficient rotor at high advance ratios. A cost-effective alternative to extensive experimental analyses is the use of computational fluid dynamics codes to quantify the behavior of airfoils at high and reverse angles of attack, as well as to add to the knowledge of the behavior of airfoils when they are immersed in these flows. Numerical experiments have been performed with correlation to experimental databases that examine the ability of computational fluid dynamics to accurately model airfoil characteristics at these angles of attack. It is observed that the use of recently developed hybrid Reynolds-averaged Navier-Stokes and large-eddy simulation turbulence methods result in a significant improvement in the ability of computational fluid dynamics to predict the characteristics of airfoils in these angle-of-attack regimes. Modeling of the airfoil trailing edge is more sensitive when reverse-flow angles of attack are considered.

Electrochemical techniques have been used to measure the velocity gradients at the surface of a cylinder for Reynolds numbers from 5 × 103 to 105. This is a companion study to that already reported by Dimopoulos & Hanratty (1968) for a Reynolds number range of 60–360. The use of a specially designed sandwich electrode enabled the direction of the velocity gradient as well as its magnitude to be measured. Of particular interest is the region of definite length after separation where the velocity gradient is negative, followed by an ill-defined region where the flow moves in the positive direction. Still farther downstream the direction of flow changes with time in an irregular fashion. The measured velocity gradients prior to separation are described satisfactorily by boundary-layer theory. The presence of a splitter plate in the rear of the cylinder eliminates periodic fluctuations in the wake and has a significant effect on the boundary layer prior to separation.

This paper presents a range of guidelines that the authors have come to formulate during research work related to Detached-Eddy Simulation (DES). In the course of this work, DES has been implemented, calibrated and tested for three different linear and non-linear eddy viscosity turbulence models (EVM) of varying degrees of complexity, thorough literature researches were conducted and the authors participated in two European research projects involving DES. The key steps along the path to implementation of DES in existing Reynolds-Averaged Navier–Stokes (RANS) solvers are outlined, and open questions regarding the DES technique are identified.ZusammenfassungIm Rahmen von Forschungsarbeiten zum Thema Detached-Eddy Simulation (DES) haben die Autoren eine Reihe von Richtlinien erarbeitet, die in dieser Veröffentlichung dargestellt werden. In diesem Zusammenhang wurde die DES für drei unterschiedliche lineare und nicht-lineare Wirbelviskositäts-Turbulenzmodelle von variierender Komplexität implementiert, kalibriert und getestet. Darüberhinaus sind umfangreiche Literaturrecherchen durchgeführt worden, und die Autoren haben im Rahmen zweier europäischer Forschungsvorhaben zum Thema DES mitgearbeitet. Die entscheidenden Schritte zur Implementierung der DES-Methode in einen vorhandenen Löser auf der Basis der Reynolds-gemittelten Navier–Stokes (RANS) Gleichungen werden aufgezeigt und offene Fragen im Zusammenhang der DES identifiziert.

Hot-wire measurements were conducted in the very near wake (x/d10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re
d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. In order to improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction were investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low speed and high speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart-Allmaras-type models to state-of-the-art seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

Aircraft aerodynamics have been predicted using computational fluid dynamics for a number of years. While viscous flow computations for cruise conditions have become commonplace, the non-linear effects that take place at high angles of attack are much more difficult to predict. A variety of difficulties arise when performing these computations, including challenges in properly modeling turbulence and transition for vortical and massively separated flows, the need to use appropriate numerical algorithms if flow asymmetry is possible, and the difficulties in creating grids that allow for accurate simulation of the flowfield. These issues are addressed and recommendations are made for further improvements in high angle of attack flow prediction. Current predictive capabilities for high angle of attack flows are reviewed, and solutions based on hybrid turbulence models are presented.

Thesis (Ph. D.)--Stanford University, 1995. Includes bibliographical references (leaves 227-239). Photocopy. s

Dynamic stall and its consequences which are important to aircraft design and operation are discussed. A certain degree of unsteadyness always accompanies the flow over streamlined bodies at high angle of attack, however, the stall of lifting surface undergoing unsteady motion is more complex than static stall. Dynamic stall remains a major unsolved problem with a variety of applications in aeronautics, hydrodynamics and wind engineering.

Improvement of Cross-Flow Aerodynamic Predictions for Forward Flight at All Advance Ratios

- J Hodara
- M J Smith

Hodara, J., and Smith, M. J., "Improvement of Cross-Flow Aerodynamic Predictions for Forward Flight at All Advance Ratios," ERF
2014-104, 40th European Rotorcraft Forum, Southampton, UK, September 2-5, 2014.

Computation of Unsteady Turbulent Airfoil Flows with an Aeroelastic AUSM+ Implicit Solver

- D Darracq
- S Champagneux

Darracq, D., Champagneux, S., and Corjon, A., "Computation of
Unsteady Turbulent Airfoil Flows with an Aeroelastic AUSM+ Implicit
Solver," AIAA 1998-2411, 16th AIAA Applied Aerodynamics Conference, Albuquerque, NM, June 15-18, 2012.

Detailed Investigation of Detached-Eddy Simulation for the Flow Past a Circular Cylinder at Re = 3900

- R Zhao
- J Liu

Zhao, R, Liu, J., and Yan, C., "Detailed Investigation of Detached-Eddy Simulation for the Flow Past a Circular Cylinder at Re = 3900,"
NNFM 117, Progress in Hybrid RANS-LES Modelling, Springer-Verlag,
Berlin, 2012, pp. 401-412.

The Forces and Pressures over an NACA 0015 Airfoil through 180 Degrees Angle of Attack

- A Pope

Pope, A., "The Forces and Pressures over an NACA 0015 Airfoil
through 180 Degrees Angle of Attack," Georgia Institute of Technology,
1947.