Article

Aerodynamics of Airfoils at High and Reverse Angles of Attack

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Abstract

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.

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... Airfoil grid sizing criteria were based on attached and separated flow results from grid studies on NACA0012 and SC1095 profiles using OVERFLOW with the two turbulence methods [23]. These grids had between 811 and 971 nodes around the circumference of the airfoil to achieve integrated force and moment results that were nominally converged within 2-4% of their asymptotic values for separated flows. ...
... A configuration without including the wind tunnel test section (to reduce computational costs) was evaluated using an O-grid topology to replicate the blunt trailing edge VR7 airfoil. An O-grid topology was chosen on the basis of the study performed by Smith et al. [23] where the importance of its modeling in the stalled regime was quantified. ...
... The angle of attack at which the maximum lift ðc 'max Þ occurs is often not well predicted with CFD methods [23,25]. It is not understood if this poor estimate is a function of the turbulence or transition model, or if it is due to the numerical options applied during the simulation, such as time step. ...
Article
Airfoils and wings undergoing static and dynamic stall still elude accurate simulation by computational methods. While significant emphasis has been placed on the quantification of grid dependence, as well as influence of the turbulence method, many elements defining temporal convergence remain ad hoc. To address this, convergence and accuracy for two different turbulence methods were examined for both static and dynamic stall. New approaches to define numerical convergence that include an assessment of the physical accuracy have been developed and evaluated via a blind analysis at other stall conditions. A key finding is the need to ensure that the combination of time step and subiterations achieves a true second order accurate solution. It was also observed that accurate prediction of separation was controlled primarily by the turbulent transport terms, while the mean flow equations influenced reattachment. Temporal convergence of dynamic stall can be quantitatively assessed by an approach developed in this effort.
... A structured grid modeled the wings under consideration. This mesh was generated by Smith et al. [3,22] for analyzing the behavior of wings at high and reverse angles of attack. This previous article includes grid refinement studies for angles of attack ranging from 0 • to 180 • . ...
... The mesh was generated with an O-grid topology, for the purpose of capturing the finite trailing edge. It is important to maintain a high fidelity at the trailing edge in order to study the effect of yaw in reverse flow, as demonstrated in Smith et al. [3,22] . ...
... The streamwise points were distributed equally over the upper and lower surfaces of the airfoil. The initial cell spacing at the wall was chosen to ensure that y + < 1 at the Reynolds number considered in this study (see Table 1) and that 35-50 normal cells resolve the boundary layer [22,23] . The grid extent from the airfoil to the outer boundary was progressively increased until convergence of the integrated forces and moments was obtained. ...
Conference Paper
Full-text available
The aerodynamics of rotorcraft in forward flight, particularly at high advance ratios, are highly complex. Of particular interest is the impact of crossflow on forward flight performance that occurs over large portions of the rotor disk. Results from high fidelity numerical experiments on an infinite yawed wing, previously validated with experimental data for a wide range of Mach numbers, angles of attack and yaw angles, are analyzed for use in airfoil tables (C81 tables) for rotorcraft comprehensive codes. Investigation of the errors introduced by interpolation of airfoil tables and application of the Betz crossflow and independence principles in various flight regimes has been completed, including further understanding of the physics driving the behavior of the integrated airfoil performance. The analysis has also been extended to reverse flow conditions, which become significant at high advance ratios. Empirical corrections have been developed that improve the lift, drag and pitching moment predictions of the crossflow model. Copyright © (2014) by the Royal Aeronautical Society. All rights reserved.
... The hybrid approach couples URANS in the near-wall regions with largeeddy simulation (LES) in the wake, permitting large eddies in the separated wake to be resolved without requiring an excessively fine grid. This hybrid turbulence approach has been validated for unsteady bluff body configurations [20,24,25] . ...
... Grids were created for the bluff body geometries using best practices established for similar configurations with the hybrid URANS/LES approach [20,24,25] . The boundary layer region of the grids used prismatic elements aligned with the wall-normal direction; at least 35 cells in the normal direction with a nondimensional wall spacing (y + ) of less than 1.0. ...
... The boundary layer region of the grids used prismatic elements aligned with the wall-normal direction; at least 35 cells in the normal direction with a nondimensional wall spacing (y + ) of less than 1.0. This boundary layer spacing is necessary to correctly capture separation and reattachment on surfaces at high angles normal to the flow [20,24,29] . ...
Conference Paper
Full-text available
Fundamental three-dimensional aerodynamic phenomena have been investigated for small-aspect-ratio rectangular prisms and circular cylinders, canonical bluff body geometries representative of typical helicopter sling loads. A detailed identification and quantification of the unsteady aerodynamic phenomena at differing orientation angles associated with instabilities has been undertaken. The numerical experiments indicate that shear layer reattachment is the primary factor in determining the mean forces and moments of the bluff bodies. Many characteristics of the shear layer behavior are similar for the three-dimensional bluff bodies and, in some cases, similar to two-dimensional behavior extant in the literature. Differences in the canonical shape and aspect ratios occur and are quantified with varying reattachment distances as the orientation changes. Strouhal numbers vary in the range from 0.15-0.3 and exhibited a highly three- dimensional, multimodal nature at the Reynolds numbers investigated. These findings are significant for the development of reduced-order aerodynamic modeling of sling loads. Copyright © (2014) by the Royal Aeronautical Society. All rights reserved.
... 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. ...
... Grids have been created for the bluff body geometries using best practices established for similar configurations during validation of the HRLES turbulence closure (Lynch & Smith 2011;Smith et al. 2011;Shenoy et al. 2013). The grids are unstructured and overset, with hexahedral boundary layer cells aligned with the wall-normal direction. ...
... Here, u * is the friction velocity, u * = √ τ w /ρ, and τ w is the shear stress at the wall. It has been previously demonstrated that a y + value and number of normal-growth-layer cells similar to those applied here are important to capture separation and reattachment on surfaces at high angles of incidence (Lynch & Smith 2011;Smith et al. 2011;Liggett & Smith 2012). Figure 3 shows representative views of the grid spacing on the surface. ...
Article
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.
... Finally, Smith et al. (2011) presented a numerical study of two foils: a NACA 0012 and a SC1095 in reverse-flow configuration. This study was conducted in the context of rotor craft development, as at high advance ratio a portion of the blade experiences a reverse flow. ...
... For higher angles of attack, C L increases more rapidly and tends to the same maximum value as for the smooth hydrofoil, also observed around 10˚angle of attack. The lift curve obtained with roughness addition is very similar to that published by Yates (1980) from experiments of Smith on a reversed NACA 0012 (Smith et al. (2011)). The overall lift level is thus not as low as it might have been expected for a foil used in the wrong direction, but it is counter balanced by a higher drag level. ...
... The discussion of numerical results focusses on the different estimations of the lift coefficient from the fully turbulent model (SST) and from the transition model (SST-TM). The drag is not accurately predicted by the present computations because 3D effects are significant on the drag in the experiment, and resolving the drag would require to accurately model the boundary layer separation around the rounded trailing edge which would necessitate a more refined mesh and/or more advanced models like LES and DES as stated by Smith et al. (2011). Figure 10 shows the average lift coefficient computed with the fully turbulent (SST) and transition (SST-TM) models, compared to experimental results with roughened and smooth surfaces. ...
Article
This work presents an experimental investigation of a hydrofoil in reversed flow configuration in the context of marine current turbine development. Experiments consist in hydrodynamic force measurements and PIV flow observations on a NACA 0015 hydrofoil, at Reynolds number. The hydrofoil in reversed flow produces a higher lift than in the classical forward flow for very low angles of attack and proved to be relatively efficient for an angle of attack lower than 10°, despite a much higher drag than the same foil in direct flow. Moreover, the lift coefficient shows a discontinuity with an hysteresis effect when the angle of attack is varied up and down around zero-degree. It is shown that the sharp leading edge generates an early Leading Edge Separation Bubble on one side (suction side) even for vanishing angles of attack. This separation bubble triggers the transition to turbulence of the boundary layer on the suction side while the pressure side boundary layer remains laminar. As a consequence, separation on the rounded trailing edge occurs farther downstream on the (turbulent) suction side compared to the (laminar) pressure side. The Leading Edge Separation Bubble and the inherent up-down asymmetry in the boundary layer regime are responsible for the lift singularity.
... Finally, Smith et al. [10] presented a numerical study of two foils: a NACA 0012 and a SC1095 in reverse-flow configuration. This study was conducted in the context of rotor craft development, as at high advance ratio a portion of the blade experiences a reverse flow. ...
... For higher angles of attack, C L increases more rapidly and tends to the same maximum value as for the smooth hydrofoil, also observed around 10°angle of attack. The lift curve obtained with roughness addition is very similar to that published by Yates [25] from experiments of Smith on a reversed NACA 0012 [10]. ...
... The discussion of numerical results focuses on the different estimations of the lift coefficient from the fully turbulent model (SST) and from the transition model (SST-TM). The drag is not accurately predicted by the present computations because 3D effects are significant on the drag in the experiment, and resolving the drag would require to accurately model the boundary layer separation around the rounded trailing edge which would necessitate a more refined mesh and/or more advanced models like LES and DES as stated by Smith et al. [10]. Fig. 10 shows the average lift coefficient computed with the fully turbulent (SST) and transition (SST-TM) models, compared to experimental results with roughened and smooth surfaces. ...
... The grid spacing at the wall corresponds to y < 1 with approximately 50 points resolving the boundary layer. This mesh was generated using guidelines provided for similar cases [61]. The physical time step is Δt × u ∞ × c −1 0.01, with 10 subiterations to reduce the L ∞ norm of the residuals by at least two orders of magnitude between each iteration. ...
... As the Reynolds number is further increased, both URANS models begin to fail, reaching mean drag coefficients of approximately 1.6 at Re D 10 4 . This inability to predict massively separated boundary layers is a known issue of URANS models [61], because the low-pressure region is significantly overpredicted at the back of the cylinder, resulting in excessive drag predictions. The force predicted by the SST model decreases below the γ-Re θ t level, because its fully turbulent boundary layer remains attached over a longer portion of the cylinder. ...
Article
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.
... Computational predictions of static and dynamic stall have improved over the past decade due to the increased speed and accessibility of computational hardware, in concert with the development of improved transition and turbulence methods. Researchers, including Smith et al., [12][13][14] Sanchez-Rocha, 15,16 Gleize et al., 17 and Szydlowski and Costes 18 have studied stall and post-stall characteristics of static airfoils with unsteady Reynolds Averaged Navier-Stokes (URANS) computational fluid dynamics (CFD). They have examined the influence of grid dependence, spatial algorithms, and temporal integration, as well as turbulence modeling effects. ...
... The Menter k −ω SST model has been observed to provide the most consistent results among a number of studies 13,19 in stalled conditions with less grid dependence than other models, such as the Spalart-Allmaras model. The hybridization of the models with detached eddy or large eddy simulation algorithms permits the simulation to capture more of the unsteady physics, such as the vortex shedding. ...
Conference Paper
A solver has been developed within the OpenFoam framework to compute large amplitude motion of two-dimensional rigid configurations. The results obtained with this code were successfully validated on rigid airfoils at static and dynamic conditions, as well as correlated with experimental data and numerical solutions from similar unsteady solvers. The results demonstrated that while current computational methods are able to predict the self-sustained oscillations characterizing a pitch-dominated stall flutter, including energy transfer, improvements are needed. The influence of grid, temporal integration, turbulence modeling, and flow equations is examined for the stall flflutterstarting solution of dynamic stall.
... Smith (Ref. 6) used a larger width of 2 × c while roughly maintaining the same node resolution (31 nodes per chord) to resolve the flow past a NACA 0012 wing at Re c = 1 × 10 6 with angles of attack ranging from 0 • to 180 • . While all three authors obtained excellent results for massively separated boundary layers, it was decided to select the finest grid dimensions and resolution used by Smith to ensure that the complex wake physics would be properly captured. ...
... These conclusions are not surprising, since URANS closures are well known for their poor prediction of massively separated flows (Refs. 6,25). For this reason, Harris postulates that URANS analysis "can not -at the present time -be recommended for use beyond an advance ratio of 0.35 to 0.40" (Ref. ...
Conference Paper
Two fundamental models of the flow (static and dynamic) over airfoils in the reverse How region of a helicopter in forward flight are investigated experimentally and computationally at Reynolds numbers of O(105). 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 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 (trailing edge vortex, 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 of the aerodynamic behavior of airfoils in reverse flow towards a better understanding of the complex nature of the reverse flow region as well as promising new computational tools to be used in the simulation of this unique flow regime.
... They have independently (Refs. 16,17) obtained similar static solutions and have demonstrated that a reverse flow airfoil can be categorized into three distinct behaviors as angle of attack increases. Dynamically (with stall), the airfoil has five stages in the reverse flow cycle. ...
... Most researchers (Refs. 29-31) have used a width of 1 × c to simulate the flow past a semi-infinite wing in post-stall conditions, while Smith (Ref.16) used a larger width of 2 × c. ...
Conference Paper
A low-Reynolds number rectilinear analog of the retreating-blade problem is considered by computationally and experimentally studying a NACA0012 blade in spanwise oscilla-tion in a free stream. Three-dimensional hybrid RANS-LES simulations with spanwise periodic boundary conditions and experimental flow visualization support the description of experimental direct force measurements for a wide range reduced frequencies and advance ratios, including fully reversed flow conditions. A fixed incidence of 6 degrees is taken as a nominally attached-flow case, and agrees reasonably well with Isaacs' theory. A fixed incidence of 20 degrees is taken as a fully-separated case, and departs markedly from invis-cid theory, and even more so from quasi-steady approximation. Experimental-computational comparison shows a computational overprediction of lift relative to experimental results, at moderate advance ratios. Agreement in fully reversed flow is, however, quite good.
... At a Reynolds number value of Re c = 1.23 ⇥ 10 6 , both balance measurements and pressure integration gave a maximum lift coefficient of 0.8 occurring at 10 AoA. As noticed by Smith et al. [2011], lift force and pitching moment are not null at 180 , meaning 0 reversed. Pope [1947] attributes this to tare and interference effects. ...
... Finally, Smith et al. [2011] have presented a numerical study of two foils: a NACA 0012 and a SC1095 in reverse-flow configuration. This study was conducted under the framework of rotor craft development, as at high advance ratio a portion of the blade experiences reversed flow. ...
Thesis
Dans un contexte de développement des énergies renouvelables, les énergies marines suscitent un grand intérêt. Parmi elles, les courants de marée paraissent constituer une ressource intéressante du fait de la densité de l'eau de mer et de la possibilité de prévoir les oscillations de marée à un endroit donné. Pour une turbine à axe vertical et en accord avec le partenaire industriel, les contraintes à l'échelle de la section de pale incluent la bidirectionnalité de l'écoulement, l'état de surface ainsi que la turbulence amont. La première partie du travail présentée ici s'est donc attachée à étudier deux solutions permettant de répondre à la bidirectionnalité de l'écoulement à l'échelle d'une section de pale. Un profil bidirectionnel spécifique a ainsi été comparé à un NACA 0015 en écoulement directe et inversé. La seconde partie s'est attachée à caractériser l'effet de la rugosité de surface et de la turbulence amont sur les propriétés d'un profil unidirectionnel spécifiquement développé pour les turbines à axe horizontal. Les deux sujets ont été abordés sur des profils académiques 2D, au travers d'une approche expérimentale originale et d'étude numériques. Des calculs tout turbulents et avec prise en compte de la transition ont été comparés à des mesures d'effort par balance, couplés à des observations de l'écoulement par PIV. Le foil bidirectionnel ainsi que le foil NACA en écoulement direct et inversé ont montrés des comportements singuliers qui pénalisent leurs performances dans l'optique d'une utilisation en tant que section de pale. A partir d'une valeur seuil, la hauteur de la rugosité de surface a montré engendrer un changement profond de la nature de l'écoulement autour du foil unidirectionnel. Finalement, il a été observé que la turbulence amont modifiait modérément les propriétés de ce type de foils, mais de façon moins significative à l'échelle de la pale.
... The flat C p profile at r=R D 0:47 indicates separation, and the fact that the separation occurs at the leading edge suggests that it is a laminar separation, followed by reattachment. This location has previously been identified as a region of transition from laminar to turbulent flow, 45 contrary to the fully turbulent assumption made in the present methodology and in Sørensen et al. 6 Although the advanced hybrid RANS/LES approach has been demonstrated to predict flow separation in a turbulent flow much more accurately than RANS methods, 26,46,47 the significant turbulent kinetic energy near the leading edge generated from the fully turbulent flow assumption prevents the stall from occurring. The inability to stabilize the simulation at the prescribed thrust also confirms the presence of transition, as the fully turbulent assumption would not be physically correct. ...
Article
Overset computational fluid dynamics (CFD) methods are the most sophisticated methods currently available to predict the unsteady motion of wind turbine blades without the need for additional simplifications or restrictions on the turbine operational conditions. An unstructured implementation of the governing equations of motion permits rapid modeling of the salient components, such as nacelles, towers and other localized obstructions of interest. A time-accurate incompressible formulation accelerates the convergence of the solution, in addition to eliminating the need for low-Mach number preconditioning, which can be problematic and computationally expensive for time-accurate simulations. The use of a hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence method is observed to improve the prediction and extent of separation, as well as integrated performance variables for stalled rotors under fully turbulent conditions. Copyright (c) 2012 John Wiley & Sons, Ltd.
... It is also important to realize that aerodynamic data is generally relatively uncertain at high angles of attack due to tunnel effects while computed polars are laden with inaccuracies due to modelling limitations. Nevertheless, a comprehensive study of modeling airfoils at high angles of attack including a satisfactory comparison with experimental data was presented by Smith et al. [26]. Further, aeroelastic characteristic of a 2-D section is not necessarily representative for a whole blade. ...
Article
The present study investigated physical phenomena related to stall-induced vibrations potentially existing on wind turbine blades at standstill conditions. The study considered two-dimensional airfoil sections while it omitted three-dimensional effects. In the study, a new engineering-type computational model for the aeroelastic response of an elastically mounted airfoil was used to investigate the influence of temporal lag in the aerodynamic response on the aeroelastic stability in deep stall. The study indicated that even a relatively low lag significantly increases the damping of the model. A comparison between the results from a model with lag imposed on all force components with the results from a model with lag imposed exclusively on the lift showed only marginal difference between the damping in the two cases. A parameter study involving positions of the elastic hinge point and the center of gravity indicated that the stability is relatively independent of these parameters. Another parameter study involving spring constants showed that the stability of each mode is dependent only on the spring constant acting in the direction of the leading motion of the mode. An investigation of the influence of the added mass terms showed that only the pitch-rate and flapwise-acceleration terms have any influence on the stability. An investigation of three different profiles showed that the stability is heavily dependent on the aerodynamic characteristics of the profiles—mainly on the lift. It was also shown that only the edgewise mode is unstable in deep stall. Moreover, independent of the amount of temporal lag in the aerodynamic response of the model, the inflow-angle region in the vicinity of 180° remains unstable in the edgewise mode. Therefore, this inflow-angle region may create stability problems in real life. The other type of vibrations potentially present at standstill conditions is vortex-induced, being outside the scope of the present study. Copyright
... The effect of diminishing was observed to be the elimination of the secondary peak [7], a result also seen in the data of Wenzinger and Harris [2]. In addition, recent computational fluid dynamics studies have not shown the clear presence of the secondary peak, even for airfoil data [8]. ...
... In this work, HRLES data validated for turbulent bluff body flows including dynamic cases (Refs. 17,[21][22][23][24][25][26] have been employed to generate the quasi-steady data set. The details of the solver, grids, and conditions for the computation of quasi-steady aerodynamic coefficients for 3D rectangular prism and cylinder geometries have been presented previously (Refs. ...
Article
A novel reduced-order model for the simulation of bluff bodies in unsteady, arbitrary motion has been developed. The model is physics-based, meaning that it is derived from known fundamental aerodynamic phenomena of bluff bodies instead of response fitting of experimental data. This physics-based approach is essential to ensure that the model is applicable to new, untested configurations. We describe the development of a physics-based model, including detailed explanations of the fundamental aerodynamic phenomena and how they are modeled in simulation. The reduced-order model is evaluated by application to rotorcraft-tethered loads and validated against much more expensive high-fidelity computational fluid dynamics simulations and flight tests. Excellent correlation in the predictions of aerodynamic forces and moments, as well as the dynamic response, is observed, while the computational cost has been reduced by several orders of magnitude relative to high-fidelity computational-fluid-dynamics-based simulations. Additionally, the important role that unsteady aerodynamics play in bluff body dynamics and instability is demonstrated.
... 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. In addition, the results were very sensitive with the grid quality at the leading edge [6]. ...
Article
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.
... Seeking a means to alleviate the downward-acting lift generated in the reverse flow region of a conventional helicopter rotor, Ewans and Krauss evaluated the timeaveraged aerodynamic performance of double-ended airfoils in an effort maintain a positive lift distribution across the entire rotor disk [30]. More recently, Smith et al. conducted a computational study on yawed and reverse flows over three airfoils with a sharp geometric trailing edge that have been widely used on rotorcraft (NACA 0012, NACA 0015, and SC 1095) [31]. In reverse flow, the sharp geometric trailing edge serves as the aerodynamic leading edge and a discrete separation point for flow over the suction side of the airfoil. ...
Article
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.
... With the range of angle of attack significant for rotorcraft analysis, the typical trends in lift, drag and moment coefficient are examined from attached flow to deep stall, with the typical trends for each presented in Figure 1.6. These trends are highlighted by Bielawa [21], with correlation to previous experimental [34,105] and numerical studies [87,126]. ...
Thesis
Full-text available
Propeller flutter can manifest in a variety of ways. This includes classical bending-torsion flutter, stall flutter and whirl flutter. Classical bending-torsion flutter for propeller blades is driven by the coupling, and excitement, of selected modes of motion. Such flutter problems are often a result of structural coupling and in the linear aerodynamic regime. As a result, low-fidelity, fast calculations can be used to determine boundaries and mitigate the effects via changes in the structural design. Whirl flutter is the most complex and involves the coupling of the aircraft wing modes of motion to the gyroscopic and aerodynamic effects of the propeller. This phenomenon can be highly non-linear due to both the structure and flow-field, and any mitigation involves sophisticated modelling efforts with respect to the airframe. Propeller stall flutter is less complex in terms of the structure, however, involves the highly non-linear aerodynamics associated with detached flow. This phenomena, like classical flutter, is driven by the propeller design and conditions, but due to its nature, the stall flutter boundary significantly reduces the overall flutter boundary of a propeller. Hence, the understanding of this limitation must be known to ensure safe operation. The development of modern propeller blades utilising high sweep/taper with thin aerofoil sections can result in a change in the flutter boundary. In addition to this, propellers are coming back into focus due to the development of electrically driven Vertical Take-off/Landing (eVTOL) vehicles and, due to the nature of such a vehicle design, the propellers are being pushed into significantly different operating conditions. This motivation, coupled with the increased computational power available in the modern era, requires the need to reassess what is required to understand the stall flutter boundary associated with a modern, in-service, propeller blade. To this end, a numerical investigation using Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) was conducted on the Commander propeller blade of Dowty Propellers. This blade was selected from the list of experimentally investigated blades due to the availability of geometry, structural data and applicability in real life applications. A validation procedure was conducted to assess the effects of the computational setup. This included the effects of turbulence, structural modelling and implementation, with a validated process found whilst using Scale-Adaptive-Simulation (SAS) with interpolated structural modes. An attempt was made to extract aerodynamic damping data of the stall flutter phenomenon via the development of a method from the aeroelastic simulations. Such values give an indication of the stability, with links made to typical two-dimensional modelling. The thesis ends on the parametric study of the validated Commander Simulation. This was conducted in order to gain greater detail on the effects of key structural and aerodynamic parameters on the blade stall flutter response. The key outcome from this investigation is the need for scale-resolving methods in propeller stall flutter investigations. This study utilises a hybrid RANS/LES model to capture the key detached flow content. This detached flow content results in significant pressure fluctuations, not observed in traditional statistical models, which drive the aeroelastic deformations. In addition, the requirement for a well validated structural model is highlighted including the setup of the structural solver for which an interpolated modal response method is used. It is also found from this investigation that there is a need for a modern experimental test case focusing on propeller stall flutter. The last comprehensive study was conducted in the 1980’s and, with improvements in experimental techniques, greater understanding and data can now be extracted. This new data can be used to validate modern CFD efforts. The novelty of this work lies within the derivation of a method for the extraction of the aerodynamic damping data from three-dimensional simulations. This had previously not be done before and the extracted results correlated with equivalent two-dimensional aerodynamic damping data. Additionally, the development and application of three-dimensional Navier-Stokes based CFD, with a coupled structural model, had not been conducted on propeller stall flutter.
... The fundamental two-dimensional characteristics of airfoils in reverse flow has been studied more recently experimentally and computationally, although these studies only focused on airfoils with a sharp geometric trailing edge. 17,18 The present work is an expansion of previous studies conducted by the authors on airfoils held at static angles of attack through 360 deg for low Reynolds numbers, up to Re = 1.65 × 10 5 . 2, 19 One aim of this research effort is to characterize the influence of trailing edge shape on airfoil performance. ...
Conference Paper
This work is aimed at providing an improved understanding of the impact of the radial Reynolds number distribution that exists in the reverse flow region of a helicopter operating at high advance ratios. Time-averaged sectional airloads and flow fields were measured experimentally for four airfoils in forward and reverse flow at Reynolds numbers between 330,000 and 1,000,000. Two airfoils with a sharp geometric trailing edge (NACA 0012 and NACA 0024) and two airfoils with a blunt geometric trailing edge (a 24% thick elliptical airfoil, and a 26% thick cambered ellipse airfoil) were tested. This work shows that the airloads for a NACA 0012 in reverse flow (a "thin" airfoil with a sharp aerodynamic leading edge) are insensitive to Reynolds number due to early flow separation. The airloads of thicker airfoils are found to be more sensitive to Reynolds number. In reverse flow, a NACA~0024 airfoil exhibits a decrease in the magnitude of the airloads with increasing Reynolds number for -3 to 15 deg. The lift curve of an elliptical airfoil becomes more linear with increasing Reynolds number. The character of the lift curve for the cambered ellipse airfoil in both forward and reverse flow changes drastically for Re greater than 330,000. This includes a large shift in the zero-lift angle of attack. These results give insight to the design of high-speed helicopter rotor blades by examining the sensitivity of airloads to the range of Reynolds numbers encountered in the reverse flow region.
... In reverse flow, the airfoil effectively acts like a bluff body in an unsteady free-stream. In typical sharp TE airfoils, reverse flow generates excessive vortex shedding at the LE, and is accompanied by increased drag [168][169][170][171]. ...
Thesis
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Coaxial rotor helicopters are a candidate for the next generation of rotorcraft due to their ability to achieve high speeds without compromising hover performance. Coaxial rotors are designed to offload the retreating side of the rotor in high speed flight to delay the effects of reverse flow and blade stall which limit the speed of conventional single main rotor helicopters. The proximity of the two rotors induces periodic blade passage effect loads and unsteady rotor wake interactions absent in single rotor configurations. Coaxial rotors employ stiff composite hingeless blades to prevent the possibility of blade strike. At high speeds, the coaxial rotor operates at reduced RPM to avoid the drag penalty on the advancing blade tip. This combination of rotor lift distribution, periodic blade passage effect, unsteady rotor wake interaction, combined with stiff hingeless blades and reduced rotor RPM implies that a coaxial rotor system requires a specialized aeromechanical analysis. The goal of this dissertation is to develop a comprehensive aeromechanical analysis capable of modeling the aeroelasticity of stiff hingeless counter-rotating blades and the complex rotor-wake interactions present in a coaxial rotor system. The rotor wake is modeled with the Viscous Vortex Particle method, a grid free approach for calculating vortex interactions over long distances. The spanwise blade loading in attached flow is obtained from a computational fluid dynamics based rational function approximation unsteady aerodynamic model. The ONERA dynamic stall model is extended to capture three dimensional effects due to flow separation. The combination of the viscous vortex particle method with reduced order models for spanwise loading captures the unsteady coaxial rotor loads with computational efficiency. Trim procedures are developed to determine control inputs for a coaxial rotor to maintain equilibrium in hover and forward flight. In forward flight, two different trim conditions are considered: trim with propulsor off, and trim at level attitude. The two trim conditions have a significant impact on the vibratory hub loads, rotor inflow distribution and the aeroelastic stability. A unique aspect of the coaxial rotor is that its stability in both hover and forward flight are governed by equations with periodic coefficients. Therefore, a periodic aeroelastic stability analysis based on Floquet theory is applied. A new graphical method is developed to identify coupling between the blade modes of the two rotors. The aeromechanical formulation is applied to a rotor resembling the Sikorsky X2TD coaxial helicopter. In hover, the rotor experiences 8/rev blade passage loads due to oscillations in the blade bound circulation induced inflow. Increasing the collective pitch increases the coupling between the flap and lag modes of the blade. The aerodynamic interactions lead to an inter-rotor coupling of the first flap modes. In forward flight, the effects of trim condition, advance ratio, lift offset, and separated wake on the hub loads, inflow distribution and aeroelastic stability are examined. The results indicate that the aeroelastic stability of the lag mode is reduced in forward flight at a level attitude compared to hover. This study provides an improved physical understanding of the aeroelastic interactions in coaxial rotors. The work presented in this dissertation has the potential to facilitate design and development of future high-speed coaxial rotorcraft.
... In this design, air is modulated to flow in through a duct in the blade and out through a slot along the blunt geometric trailing edge to inject momentum into the boundary layer and delay flow separation. More recently, experimental and compu- tational studies have been performed to examine the two-dimensional characteristics of airfoils in reverse flow, although these studies only focused on airfoils with a sharp geometric trailing edge [8,25,26]. The computational studies have shown promising agreement with experimental results, and emphasize the importance of the trailing- edge shape on the flow-separation characteristics in reverse flow. ...
Article
The retreating blade of a high-advance-ratio rotor encounters a wide range of Reynolds numbers when passing through the reverse flow region. The present work was aimed at providing an improved understanding of Reynolds number effects in both forward and reverse flow. Time-averaged sectional airloads and surface oil flow visualizations were obtained experimentally for four airfoil cross sections at Reynolds numbers between 3.3×105 and 1.0×106. Two airfoils with a sharp geometric trailing edge (a NACA 0012 and a NACA 0024) and two airfoils with a blunt geometric trailing edge (a 24% thick elliptical airfoil and a 26% thick cambered ellipse airfoil) were tested. This work shows that the airloads for a NACA 0012 in reverse flow are insensitive to Reynolds number due to early flow separation, because it acts as a “thin” airfoil due to the sharp aerodynamic leading edge. The airloads of thicker airfoils were found to be more sensitive to Reynolds number. In reverse flow, the NACA 0024 exhibits a decrease in the magnitude of the airloads with increasing Reynolds number for −3≤−αrev≤15 deg. The lift curve of an elliptical airfoil becomes more linear with increasing Reynolds number. The character of the lift curve for the cambered ellipse airfoil changes drastically for Re≥3.3×105 in both forward and reverse flow. These results provide insight for the design of high-speed helicopter rotor blades by examining the sensitivity of airloads to the range of Reynolds numbers encountered in the reverse flow region.
... Vortex methods such as prescribed wake models [9] can capture some unsteady effects , but like BEM methods, lack the ability to handle 3-D effects. As a result, both typically underpredict torque, even when they incorporate a 3-D correction [10]. Designs based on such simulations can result in structures that succumb to fatigue sooner that expected [11] [12]. ...
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This paper describes an innovative, efficient actuating blade model to capture the unsteady motion of a rotating system within Computational Fluid Dynamics (CFD) methods, with application to wind turbine blades. Each blade planform is modeled via a cloud of sources that move independently during the simulation to provide rotation of the blade as well as optional motion such as blade flexibility (aeroelasticity) and active controls (flaps, morphing, adaptive shapes). The model can be implemented into structured or unstructured methods that span the gamut from full potential to Large Eddy Simulations (LES), and it does not require the use of overset grids. A key feature of this model is the development of a highly efficient parallelized kd-tree algorithm to determine the interactions between actuator sources and grid nodes. Computational evaluation of the method successfully demonstrates its capability to predict root and tip vortex location and strength compared to an overset Navier–Stokes methodology on an identical background grid, and further improvements in the solution are shown by the use of grid adaptation.
... The unsteady aerodynamics of wings and airfoils fixed at high angles of attack and in reverse flow has also been investigated, but in less depth than time-averaged aerodynamics. Work has been conducted experimentally (Yen, 2011;Lind and Jones, 2015) and by numerical simulation (Pellegrino and Meskell, 2013;Akoury et al., 2009;Smith et al., 2011). ...
Article
The present work is aimed at understanding the sources, magnitude, and frequency of unsteady airloads acting on airfoils at high angles of attack and in reverse flow in order to improve the design of rotor blades for high-speed helicopters and wind turbines. Four rotor blade airfoils were tested at angles of attack through 180° and at three Reynolds numbers, up to one million. The unsteady airloads acting on each airfoil were calculated by integrating time-resolved pressure measurements acquired along the midspan of the airfoil. Unsteady velocity fields for a NACA 0012 were calculated from time-resolved particle image velocimetry measurements. For all airfoils, the unsteady airloads were found to be large in magnitude near stall, when an unstable shear layer induces unsteady flow on the suction side of the airfoil. At post-stall angles of attack, the unsteady airloads generally decreased as a region of separated flow builds over the suction side. As the angle of attack was increased further, the airloads become periodic and the flow entered the deep stall vortex shedding regime. At high angles of attack (30°. ≤. α. ≤. 150. °), the unsteady airloads were greatest for airfoils with a blunt aerodynamic trailing edge due to unsteady induced flow from trailing edge vortices. Aerodynamic hysteresis was shown to cause large unsteady airloads as the static angle of attack is decreased near stall. The unsteady airloads of a NACA 0012 in reverse flow were observed to be insensitive to Reynolds number due to flow separation at the sharp leading edge of this relatively thin airfoil.
... Rotor blade elements in the reverse flow region are subjected to a time-varying freestream, blade pitching, and significant amount of spanwise flow (i.e., crossflow) (Ref. 6). Collectively, these effects create a complex flow environment that can be characterized by vortex formation and convection (similar to classical dynamic stall), bluff body vortex shedding, and large unsteady airloads. ...
Conference Paper
A solver has been developed within the OpenFoam framework to compute large ampli-tude motion of two-dimensional rigid conffigurations. The results obtained with this code were successfully validated on rigid airfoils at static and dynamic conditions, as well as cor-related with experimental data and numerical solutions from similar unsteady solvers. The results demonstrate that current computational methods are, within the constraints im-posed by spatial grids, temporal integration and turbulence modeling, capable of capturing the self-sustained oscillations characterizing stall utter event with reasonable accuracy, including the mechanisms of energy transfer. Copyright © 2012 by Sacha Yabili, Marilyn J. Smith and Grigorios Dimitriadis.
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This paper describes an innovative, efficient actuating blade model to capture the unsteady motion of a rotating system within Computational Fluid Dynamics (CFD) methods, with application to wind turbine blades. Each blade planform is modeled via a cloud of sources that move independently during the simulation to provide rotation of the blade as well as optional motion such as blade flexibility (aeroelasticity) and active controls (flaps, morphing, adaptive shapes). The model can be implemented into structured or unstructured methods that span the gamut from full potential to large eddy simulations (LES), and it does not require the use of overset grids. A key feature of this model is the development of a highly efficient parallelized kd-tree algorithm to determine the interactions between actuator sources and grid nodes. Computational evaluation of the method successfully demonstrates its capability to predict root and tip vortex location and strength compared to an overset Navier-Stokes methodology on an identical background grid, and further improvements in the solution are shown by the use of grid adaptation.
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Active trailing-edge flaps are a method of aerodynamic control under extensive research to reduce the detrimental effects of dynamic stall. Physical phenomena are poorly understood in the context of active flaps including vorticity and acoustics, separation, and transition. In addition, discrete trailing-edge flaps create a cavity-like flow within the airfoil-flap gap that can complicate these phenomena. This work has explored the physical response of a static airfoil with a discrete noncontoured oscillating flap over a range of freestream parameters. The effects of attached and separated flows, flap oscillation scheduling, airfoil-flap gap size, and freestream speed have all been investigated. Time-accurate predictions were performed using a hybrid Reynolds-averaged Navier-Stokes/large eddy simulation turbulence model. Trailing-edge stall suppression and an increase between aerodynamic response and deflection input were observed as the flap oscillation frequency increased. The lag between response and input also increased approximately linearly with airfoil-flap gap size. Results indicated the transition was unaffected by the flap oscillations. During the frequency content of flow the unsteadiness was consistent with separated flow driven by the flap. Discrete noncontoured flaps are not recommended; if they are required, the size of the gap should be minimized to maintain performance and reduce lag.
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Turbulence and transition modeling still accounts for most of the uncertainties in numerical modeling of complex flows associated with rotorcraft vehicles and components. Computational fluid dynamics (CFD) methods typically cannot capture complex physics with traditional Reynolds-averaged Navier-Stokes (RANS)-based models since majority of physics are transient and occur at different scales. Over the past decade, a resurgence in research related to turbulence modeling has resulted in new large eddy simulation (LES)-based turbulence techniques that have improved computations that involve separated flows. The accuracy of a hybrid RANS-LES technique, first shown to improve turbulent predictions on rotors in the DARPA Quiet Helicopter program, have been increased via locally varying coefficients.
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Research indicates that active control concepts have promise in mitigating numerous adverse phenomena associated with the aeromechanics of lifting surfaces. These techniques are being applied to delay stall of fixed wing aircraft, as well as to eliminate or mitigate vibratory loads, blade-vortex interaction, and dynamic stall of the flow about rotorcraft and wind turbine blades. These phenomena are nonlinear and unsteady for dynamic systems, which add yet another layer of complexity on the physics of the flow. While a plethora of different active control techniques is being explored, the use of trailing edge flaps appears to be one of the more viable and cost-effective concepts. Static multi-element airfoils and wings have been analyzed computationally, but little exists on the ability to model these when the airfoil and flap are dynamic. The costs associated with modeling the gap between the airfoil and flap have led to approximations where the flap is modeled only as a morphed tip of the airfoil (no gap). Using a hybrid Reynolds-Averaged Navier-Stokes/Large-Eddy-Simulation turbulence technique, an oscillating flapped airfoil has been studied to determine the influence of modeling the gap on the performance and acoustic signature of the airfoil. Results are compared with the experimental data to confirm the validity of the computational approach. Both attached and separated (dynamic stall) oscillating flows are examined. The physics within the gap are found to be important for the airfoil performance when stall is encountered, as well as when acoustic signatures are required.
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Computational uid dynamics (CFD) is used to resolve the unsteady Navier Stokes equations for prediction of aerodynamic forces and moments acting on dynamic helicopter sling loads. The six-degree-of-freedom (6-DOF) rigid-body equations are tightly coupled with CFD to simulate body motion, and a model of the cables is developed to provide constraint forces and moments. This work presents the methodology and results of the coupled simulations with validation against experimental data. In addition, integration schemes for the 6-DOF equations are evaluated, and the effect of feature-based grid adapta- tion is investigated. Results of the simulations demonstrate good correlation with available experimental data and also show that the cable model assumptions are important in the dynamic behavior of the sling load.
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Through computational fluid dynamics simulations and wind tunnel tests, this study examines a NACA 63-218 airfoil in reverse flow at Rec = 375,000 and demonstrates reduction in reverse flow drag through the introduction of reflex camber. Of the three contributors to drag—ram pressure on the upper surface near the trailing edge, suction on the lower surface near the trailing edge, and bluff body separation at the rounded nose—reflex camber (where the camber line near the trailing edge of the airfoil is deflected upward) influences the first two, reducing exposure to ram drag on the upper surface while rotating the suction on the lower surface away from the direction of drag. Particle image velocimetry and surface pressure measurements were utilized in experiment to directly compare with the results obtained through simulation. As expected, the flow was dominated by separation over the sharp trailing edge, where at moderate angles of attack (α<190°), a separation bubble was observed; the use of reflex camber reduced the extent of this separation. The simulations (unsteady Reynolds-averaged Navier–Stokes with and without the Spalart–Allmaras turbulence model) captured the reduction in separation at the trailing-edge well, as there was good agreement between the velocity fields when compared to experiments. This yielded maximum drag reductions near 60% for a 10° reflex camber, compared to reductions near 50% in experiments. Even greater percentage reductions in drag (up to 70%) were observed with a larger 15° reflex angle (not tested experimentally) for nose-up pitch angles greater than 5° in reverse flow. With simulations at a higher Reynolds number (1.5 million) showing very similar drag reductions, using reflex camber over inboard blade sections appears to have significant promise for alleviating reverse flow drag on edgewise rotors at high advance ratio.
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Dual-solver hybrid methodologies that couple fluid solvers in different regions of the flowfield have been developed to accelerate convergence with minimal compromises in accuracy. A new dual-solver hybrid analysis framework that addresses some of the major shortcomings of prior dual-solver hybrid methodologies has been developed through an academic–industry partnership. In this effort, one of the hybrid solvers, comprising of a computational fluid dynamics–computational structural dynamics (CFD-CSD) solver coupled with a Lagrangian 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 rotor system are presented. 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 analysis with a reduced off-body CFD mesh is able to predict forward-flight rotor behavior that is within 4% of a full CFD simulation with up to 70% cost savings. This accuracy has been assessed on both 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.
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A novel, physics-based reduced-order model for the simulation of tethered loads and other dynamic bluff bodies in six-degree-of-freedom motion has been developed. The reduced-order aerodynamic model is founded on physical insights and supporting data from quasi-steady computational fluid dynamics simulations, experiments, or flight tests. The reduced-order model incorporates quasi-steady aerodynamics, unsteady vortex shedding phenomena, and unsteady aerodynamic effects of body motion. The reduced-order model accurately reproduces dynamics predicted by computational fluid dynamics simulations, while computational cost is reduced by more than five orders of magnitude. The methodology can readily be applied or extended to any bluff body geometry beyond those demonstrated in this work. Guidance is provided for the relatively minor modifications to include rotor downwash, atmospheric turbulence, and wind tunnel walls. Copyright© 2014 by the American Helicopter Society International, Inc. All rights reserved.
Conference Paper
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.
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A NACA 0012 airfoil is oscillated in streamwise direction in a constant freestream and at a fixed incidence angle such that reverse flow occurs cyclically. Force measurements reveal that lift is close to unsteady theory while advancing into the freestream, if the angle of attack permits attached flow. Lift is augmented at large angles of attack, where the flow is separated under steady conditions, and does not become appreciatively negative in flow reversal for either attached or separated flow, contrary to one unsteady theory but supported by another. Dye flow visualization reveals a coherent vortical structure upstream of the leading edge before flow reversal, which is believed to attenuate negative lift.
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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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Three helicopter airfoils were selected to investigate an approach to characterize dynamic stall phenomena using unsteady pressure and phase-locked flow-field measurements. The entire process was designed to ensure low cost and time efficiency in performing many measurements over many airfoils. To achieve these requirements, many sections of the blade were manufactured using rapid prototyping, and pressure measurements for all airfoils were gathered through two remotely located electronic scanning pressure modules. A modern pressure correction method estimated the time accurate surface pressures, and the total uncertainty of the pressure measurements was determined. The pressure measurements agreed well with past surface mounted pressure transducer studies that showed strong dependence on surface location and flow conditions. By combining the pressure and flow-field results, differences in stall were observed between the three airfoils, and flow features responsible for these changes were identified. The result of this work suggest that this approach offers a means of rapidly acquiring information about specific airfoils with a level of detail sufficient for understanding the complex processes experienced by these airfoils.
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The present work evaluates the potential of a hybrid RANS-LES method to predict the unsteady flow over airfoils in static and oscillating motion. The method implemented (hereafter termed HRLES) blends the k − omega SST RANS model with a localized dynamic ksgs one-equation LES model (LDKM). The unsteady 2D and 3D flow over a NACA 0015 airfoil is computed to evaluate the model performance. The aerodynamic characteristics of the static configuration are in reasonable agreement with experimental results. For the oscillating case, three conditions are simulated: attached flow, mild stall and deep stall. Two-dimensional simulations are conducted for the three dynamic stall conditions, and only the deep stall case is simulated in 3D so far. Overall, the unsteady loads for the attached and mild stall cases show good agreement with experiments. For the mild and the deep stall cases, the HRLES is able to predict flow separation and vortex shedding during the downstroke. In general, these results demonstrate the potential of hybrid methods to correctly simulate complex high Reynolds number flows encountered in aerodynamic applications.
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The efficient prediction of helicopter rotor performance, vibratory loads, and aeroelastic properties still relies heavily on the use of comprehensive analysis codes. These comprehensive codes utilize look-up tables to provide two-dimensional aerodynamic characteristics. Typically these tables are comprised of a combination of wind tunnel data, empirical data, and numerical analyses. The potential to rely more heavily on numerical computations based on computational fluid dynamics simulations has become more of a reality with the advent of faster computers and more sophisticated physical models. The ability of five different computational fluid dynamics codes, applied independently, to predict the lift, drag and pitching moments of rotor airfoils is examined for the SC1095 airfoil, which is utilized in the UH-60A main rotor. Extensive comparisons with the results of ten wind tunnel tests are performed. These computational fluid dynamics computations are within experimental data limits for predicting many of the aerodynamic performance characteristics.
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Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct thems it is found helpful to introduce “parameter vectors” which notably simplify the structure of the conservation laws.
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In this work, the mathematical implications of merging two different turbulence modeling approaches are addressed by deriving the exact hybrid RANS/LES Navier-Stokes equations. These equations are derived by introducing an additive-filter, which linearly combines the RANS and LES operators with a blending function. The equations derived predict additional hybrid terms, which represent the interactions between RANS and LES formulations. Theoretically, the prediction of the hybrid terms demonstrates that the hybridization of the two approaches cannot be accomplished only by the turbulence model equations, as it is claimed in current hybrid RANS/LES models. The importance of the exact hybrid RANS/LES equations is demonstrated by conducting numerical calculations on a turbulent flat-plate boundary layer. Results indicate that the hybrid terms help to maintain an equilibrated model transition when the hybrid formulation switches from RANS to LES. Results also indicate, that when the hybrid terms are not included, the accuracy of the calculations strongly relies on the blending function implemented in the additive-filter. On the other hand, if the exact equations are resolved, results are only weakly affected by the characteristics of the blending function. Unfortunately, for practical applications the hybrid terms cannot be exactly computed. Consequently, a reconstruction procedure is proposed to approximate these terms. Results show, that the model proposed is able to mimic the exact hybrid terms, enhancing the accuracy of current hybrid RANS/LES approaches. In a second effort, the Two Level Simulation (TLS) approach is proposed as a near-wall model for LES. Here, TLS is first extended to compressible flows by deriving the small-scale equations required by the model. The full compressible TLS formulation and the hybrid TLS/LES approach is validated simulating the flow over a flat-plate turbulent boundary layer. Overall, results are found in reasonable agreement with experimental data and LES calculations. Ph.D. Committee Chair: Menon, Suresh; Committee Member: Cvitanović, Predrag; Committee Member: Sankar, Lakshmi N.; Committee Member: Smith, Marilyn J.; Committee Member: Yeung, Pui-Kuen
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Wind tunnel tests were conducted to determine the drag of two-dimensional wing sections operating in a near-vertical flow condition. Various leading- and trialing-edge configurations, including plain flaps of 25, 30, and 35% chord were tested at angles of attack from -75 to -105 deg. Reynolds numbers examined ranged from approximately 0.6 x 10 to the 6th power to 1.4 x 10 to the 6th power. The data were obtained using a wind tunnel force and moment balance system and arrays of chordwise pressure orifices. The results showed that significant reductions in drag, beyond what would be expected by virtue of the decreased frontal area, were obtainable with geometries that delayed flow separation. Rapid changes in drag with angle of attack were noted for many configurations. The results, however, were fairly insensitive to Reynolds number variations. Drag values computed from the pressure data generally agreed with the force data within 2%.
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The efficient prediction of helicopter rotor performance, vibratory loads, and aeroelastic properties still relies heavily on the use of comprehensive analysis codes by the rotorcraft industry. These comprehensive codes utilize look-up tables to provide two-dimensional aerodynamic characteristics. Typically these tables are comprised of a combination of wind tunnel data, empirical data and numerical analyses. The potential to rely more heavily on numerical computations based on Computational Fluid Dynamics (CFD) simulations has become more of a reality with the advent of faster computers and more sophisticated physical models. The ability of five different CFD codes applied independently to predict the lift, drag and pitching moments of rotor airfoils is examined for the SC1095 airfoil, which is utilized in the UH-60A main rotor. Extensive comparisons with the results of ten wind tunnel tests are performed. These CFD computations are found to be as good as experimental data in predicting many of the aerodynamic performance characteristics. Four turbulence models were examined (Baldwin-Lomax, Spalart-Allmaras, Menter SST, and k-omega).
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This paper discusses how the techniques of computational fluid dynamics (CFD) are being more widely applied in the helicopter industry, and describes how the techniques currently in use at Bell Helicopter Textron have been applied in the aerodynamic design of the Model 400 and 400A helicopters. The design and analysis of main rotor blade airfoils is discussed, and comparisons of experimental data with analytical results are presented. The generation of semiempirical airfoil data tables and their central role in the prediction of hover and forward flight performance is described. The limitations of current technology in predicting aerodynamic loading and overall rotorcraft performance are discussed, and the expected future applications of CFD to overcome some of these limitations are presented.
Article
Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroa-coustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex con-figurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Al-though the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the ex-perimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in un-resolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging.
Conference Paper
The vortex shedding caused by compressible subsonic flow along a wall cavity has been investigated using a Large-Eddy Simulation (LES)-based turbulence modeling technique that is embedded within a legacy Reynolds-Averaged Navier-Stokes (RANS) solver to assess the improvement in the prediction of the flow field and acoustic of cavity flows beyond the application of classic RANS turbulence models. Numerical simulations applying two-equation Kinetic-Energy Simulation (KES), sub-grid scale hybrid-RANS LES (HRLES-sgs), and Menter k - w shear-stress transport (SST) turbulence methods have been carried out and compared with experiment and LES results. Important frequencies of the flow are determined, illustrating the abilities of advanced turbulence modeling to improve these predictions when compared to RANS models. Evaluation of the influence of the grid, time step and simulation period shows the sensitivity of the predictions to these parameters.
Article
The vortex shedding generated by compressible subsonic flow interacting with a wall cavity has been investigated using large-eddy-simulation-based turbulence techniques embedded within a legacy Reynolds-averaged Navier-Stokes solver. Cavity simulations using hybrid turbulence approaches seek the accuracy of large-eddy simulation by providing filtering and modeling of subgrid-scale turbulence with the cost of traditional Reynolds-averaged Navier-Stokes. Simulations applying differing techniques of hybridization of the Menter k-omega shear stress transport Reynolds-averaged Navier-Stokes approach include detached eddy simulation (DES-SST), blended subgrid-scale turbulence models (GT-HRLES), and a self-adjusting large-eddy-simulation very-large-eddy-simulation technique (KES) provide an understanding of differing hybrid approaches. Cavity flow results from Reynolds-averaged Navier-Stokes and hybrid simulations are compared with experiment and large-eddy simulation predictions. Evaluation of important flow characteristics illustrates the abilities of these advanced turbulence modeling techniques compared with traditional Reynolds-averaged Navier-Stokes models. Examination of the influence of the grid, time step, and simulation period demonstrates the sensitivity of the aerodynamic and aeroacoustic predictions to these parameters. In particular the subgrid-scale blended model, GT-HRLES, shows significant improvement in the ability to capture the acoustic signatures and flowfield features on a Reynolds-averaged Navier-Stokes or very-large-eddy-simulation grid compared with the other models.
Article
Turbulent flows are characterized by a very wide range of scales in both time and space. Most of the kinetic energy of a turbulent flow is stored in the large-scale structures of the flow. In contrast, kinetic energy is dissipated as heat at the smallest scales. Although the much more computationally intensive large eddy simulations (LES) and direct numerical simulations (DNS) are performed in research environments, simulations that resolve the Reynolds-averaged Navier-Stokes (RANS) equations are still required for rapid engineering results. The hybrid RANS-LES method (HR-LES) was evaluated with a circular cylinder at a Mach number of 0.2 and a diameter-based Reynolds number of 3900 at standard sea-level conditions on three different grid systems. Strouhal number is calculated from the frequency spectrum of the fluctuating lift. Separation location is given in degrees over the circumference of the cylinder from the leading-edge stagnation point to the point where skin friction along the cylinder centerline drops to zero.
Article
The author compares the state of knowledge of helicopter characteristics during the heyday of early helicopter activity - the 1940's and 50's - to what is known today. He begins with the rotor inflow and wake, and then discusses the application areas of hover performance, forward flight performance, blade loads, aeroelasticity, stability and control, and, finally, noise.
Article
A collection of computational fluid dynamics tools and techniques are being developed and tested for application to stage separation and abort simulation for next-generation launch vehicles. In this work, an overset grid Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of a belly-to-belly wing-body configuration. Steady cases show excellent agreement between Navier-Stokes results, Cartesian grid Euler solutions, and wind tunnel data at Mach 3. Good agreement has been obtained between Navier-Stokes, Euler, and wind tunnel results at Mach 6. An analysis of a dynamic separation at Mach 3 demonstrates that unsteady aerodynamic effects are not important for this scenario. Results provide an illustration of the relative applicability of Euler and Navier-Stokes methods to these types of problems.
Article
The aerodynamic characteristics of the NACA 0012 airfoil section have been obtained at angles of attack from 0 deg to 180 deg. Data were obtained at a Reynolds number of 1.8 x 10(exp 6) with the airfoil surfaces smooth and with roughness applied at the leading and trailing edges and at a Reynolds number of 0.5 x 10(exp 6) with the airfoil surfaces smooth. The tests were conducted in the Langley low-turbulence pressure tunnel at Mach numbers no greater than 0.15. After the stall with the rounded edge of the airfoil foremost, a second lift-coefficient peak was obtained at an angle of attack of about 45 deg; initial and second lift-coefficient peaks were also obtained with the sharp edge of the airfoil foremost. The application of roughness and a reduction of the Reynolds number had only small effects on the lift coefficients obtained at angles of attack between 25 deg and 125 deg. A discontinuous variation of lift coefficient with angle of attack was obtained near an angle of attack of 180 deg at the lower test Reynolds number with the airfoil surfaces smooth. At a Reynolds number of 1.8 x 10(exp 6), the drag coefficient at an angle of attack of 1800 was about twice that for an angle of attack of 0 deg. The drag coefficients obtained at an angle of attack of 90 deg at a Reynolds number of 1.8 x 10(exp 6) were 2.08 and 2.02 with the airfoil surfaces in a smooth and in a rough condition, respectively; the drag coefficient obtained at an angle of attack of 90 deg and a Reynolds number of 0.5 x 10(exp 6) with the airfoil surfaces smooth was 1.95. These values compare favorably with the drag coefficient of about 2.0 obtained from the literature for a flat plate of infinite aspect ratio inclined normal to the flow.
Article
Tests were made in a two-dimensional insert at the University of Maryland's Glenn L. Martin subsonic wind tunnel to examine the effects of simulated ballistic damage on the aerodynamic characteristics of a UH-60A Black Hawk helicopter main rotor blade section. Tests were conducted on the undamaged blade section, and on the same section with simulated ballistic damage comprising a circular hole with a surrounding portion of the skin removed, exposing the internal honeycomb structure. The structural lift, drag and pitching moment were measured at small increments in angle of attack up through stall at Reynolds numbers of 100 and 2xl06. In addition, tests were conducted over a full 360-degree range in angle of attack for a Reynolds number of 106. The measurements were complemented by mini-tuft flow visualization on the upper wing section, particularly near the hole.... Rotor blades, Aerodynamics, Wind tunnel test, Ballistic damage
Article
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain "Property U." Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct them, it is found helpful to introduce "parameter vectors" which notably simplify the structure of the conservation laws.
Article
A computational fluid dynamics (CFD) based methodology that greatly automates the generation of two-dimensional airfoil performance tables has been developed. The method employs a new software code, which controls a two-dimensional Reynolds-averaged Navier-Stokes flow solver. The generated data can be stored in C81 airfoil performance tables for use within comprehensive rotorcraft analysis codes. This paper reports on the development of a general automation method applied to the ARC2D flow solver, but it would be straightforward to add support for other solvers. The method is shown to perform well for its proposed purpose through the largely “hands-off“ generation of C81 tables. Computations for the SC1095 airfoil section are presented and compared with experimental and existing C81 data. Time requirements for C81 table generation are also discussed.
Article
Blade element momentum (BEM) methods are still the most common methods used for predicting the aerodynamic loads during the aeroelastic design of wind turbine blades. However, their accuracy is limited by the availability of reliable aerofoil data. Owing to the 3D nature of the flow over wind turbine blades, the aerofoil characteristics will vary considerably from the 2D aerofoil characteristics, especially at the inboard sections of the blades. Detailed surface pressure measurements on the blade surfaces may be used to derive more realistic aerofoil data. However, in doing so, knowledge of the angle of attack distributions is required. This study presents a method in which a free wake vortex model is used to derive such distributions for the NREL Phase VI wind turbine under different operating conditions. The derived free wake geometry solutions are plotted together with the corresponding wake circulation distribution. These plots provide better insight into how circulation formed at the blades is eventually diffused into the wake. The free wake model is described and its numerical behaviour is examined. Copyright © 2006 John Wiley &Sons, Ltd.
Article
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.
Article
An investigation was conducted in the Langely 6 by 28 inch transonic tunnel to determine the two dimensional aerodynamic characteristics of three helicopter rotor airfoils at Reynolds numbers from typical model scale to full scale at Mach numbers from about 0.35 to 0.90. The model scale Reynolds numbers ranged from about 700,00 to 1,500,000 and the full scale Reynolds numbers ranged from about 3,000,000 to 6,600,000. The airfoils tested were the NACA 0012 (0 deg Tab), the SC 1095 R8, and the SC 1095. Both the SC 1095 and the SC 1095 R8 airfoils had trailing edge tabs. The results of this investigation indicate that Reynolds number effects can be significant on the maximum normal force coefficient and all drag related parameters; namely, drag at zero normal force, maximum normal force drag ratio, and drag divergence Mach number. The increments in these parameters at a given Mach number owing to the model scale to full scale Reynolds number change are different for each of the airfoils.
Article
Two airfoils are used on the main rotor blade of the UH-60A helicopter, the SC1095 and the SC1094 R8. Measurements of the section lift, drag, and pitching moment have been obtained in ten wind tunnel tests for the SC1095 airfoil, and in five of these tests, measurements have also been obtained for the SC1094 R8. The ten wind tunnel tests are characterized and described in the present study. A number of fundamental parameters measured in these tests are compared and an assessment is made of the adequacy of the test data for use in look-up tables required by lifting-line calculation methods.
Article
Many current comprehensive rotorcraft analyses employ lifting-line methods that require main rotor blade airfoil data, typically obtained from wind tunnel tests. In order to effectively evaluate these lifting-line methods, it is of the utmost importance to ensure that the airfoil section data are free of inaccuracies. A critical assessment of the SC1095 and SC1094R8 airfoil data used on the UH-60 main rotor blade was performed for that reason. Nine sources of wind tunnel data were examined, all of which contain SC1095 data and four of which also contain SC1094R8 data. Findings indicate that the most accurate data were generated in 1982 at the 11-Foot Wind Tunnel Facility at NASA Ames Research Center and in 1985 at the 6-inch by 22-inch transonic wind tunnel facility at Ohio State University. It has not been determined if data from these two sources are sufficiently accurate for their use in comprehensive rotorcraft analytical models of the UH-60. It is recommended that new airfoil tables be created for both airfoils using the existing data. Additional wind tunnel experimentation is also recommended to provide high quality data for correlation with these new airfoil tables.
Article
A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.
Article
In this paper, we have applied a new aerodynamic tool to the study of helicopter airfoil characteristics. We have shown that the computed airloads reproduce completely the experimental behavior of representative airfoils across the transonic regime. In addition, the computational details of the flow fields, the surface pressure distributions, and the viscous-layer characteristics enable us to trace the evolution of the physical changes that occur as m infinity or Re increases. Descriptions of the complicated development of shock waves, shock-induced separation supplement the information that has been obtained heretofore in wind tunnels. In validating our calculations and assessing the accuracy of the results, including extensive grid-refinement studies and comparisons with data from numerous wind tunnels, we have defined the capabilities and limitations of the code ARC2D more precisely. This important aspect of the investigations can complement wind-tunnel tests, by providing flow-field details that are difficult to measure and by extending the range of low parameters beyond the capabilities of existing wind tunnels. The code has now progressed from a purely research stage to almost a production stage, where it can be run by specialists in the helicopter industry.
Article
A comprehensive package of scalable overset grid CFD software is reviewed. The software facilitates accurate simulation of complete aircraft aerodynamics, including viscous effects, unsteadiness, and relative motion between component parts. The software significantly lowers the manpower and computer costs normally associated with such efforts. The software is discussed in terms of current capabilities and planned future enhancements.
Article
The growing application of computational aerodynamics to nonlinear rotorcraft problems is outlined, with particular emphasis on the development of new methods based on the Euler and thin-layer Navier-Stokes equations. Rotor airfoil characteristics can now be calculated accurately over a wide range of transonic flow conditions. However, unsteady 3-D viscous codes remain in the research stage, and a numerical simulation of the complete flow field about a helicopter in forward flight is not now feasible. Nevertheless, impressive progress is being made in preparation for future supercomputers that will enable meaningful calculations to be made for arbitrary rotorcraft configurations.
Article
A large body of experimental results, obtained in more than 40 wind tunnels on a single, well known two-dimensional configuration, was critically examined and correlated. An assessment of some of the possible sources of error was made for each facility, and data which are suspect were identified. It was found that no single experiment provided a complete set of reliable data, although an investigation stands out as superior in many respects. However, from the aggregate of data the representative properties of the NACA 0012 airfoil can be identified with reasonable confidence over wide range of Mach numbers, Reynolds number, and angles of attack. This synthesized information can now be used to assess and validate existing and future wind tunnel results and to evaluate advanced Computational Fluid Dynamics codes.
Article
Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-omega model of Wilcox In the inner region of the boundary layer and switches to the standard k -epsilon model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity. The second model results from a modification to the definition of the eddy-viscosity in the BSL model, which accounts for the effect of the transport of the principal turbulent shear stress. The new model is called the shear-stress transport-model and leads to major improvements in the prediction of adverse pressure gradient flows.
Article
The purpose of this paper is to highlight some recent enhancements that have been made to the Navier-Stokes code OVERFLOW. The enhancements we are concerned with are in three major areas: a multigrid method, for convergence acceleration; a lowMach preconditioning algorithm, for convergence acceleration and solution quality improvement for low Mach number flows; and a matrix dissipation algorithm for solution quality improvement. We will describe these methods and show examples of their efficacy. Introduction The computer code OVERFLOW computes numerical solutions of the compressible Navier-Stokes equations using finite differences in space and implicit timestepping. 1, 2, 3 To handle complex geometries OVERFLOW uses the "chimera" or overset grid approach: 4 grids are generated independently for different zones, with arbitrary overlap permitted. Some zones will get their y Associate Fellow, AIAA z Senior Member, AIAA. Current address: NASA/Langley Research Center. Copyright c f...
The Forces and Pressures over an NACA 0015 Airfoil Through 180 Degrees Angle of Attack
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A Chimera Grid Scheme Advances in Grid Generation
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Aerodynamics of the Helicopter World Speed Record
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15 SC1095 airfoil lift-curve slope magnitude as a function of Mach number
  • Fig
Fig. 15 SC1095 airfoil lift-curve slope magnitude as a function of Mach number.
Fluid-Dynamic Drag, S. Hoerner
  • S Hoerner
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