Trapezoidal Wing Research Articles

Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow

Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3 ≤ Ma ≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. Firstly, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state-of-the-art computational fluid dynamics solvers as cross-validated benchmarks. Indicial functions are calculated for a step change in the angle of attack and for a sharp-edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following an encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories.

Analysis of nonlinear aeroelastic characteristics of a trapezoidal wing in hypersonic flow

Nonlinear aeroelastic behavior of a trapezoidal wing in hypersonic flow is investigated. The aeroelastic governing equations are built by von Karman large deformation theory and the third-order piston theory. The Rayleigh–Ritz approach combined with the affine transformation is formulated and employed to transform the equations of a trapezoidal wing structure, modeled as a cantilevered wing-like plate, into modal coordinates. And then the modal equations are solved by numerical integrations. Several typical cases are studied to validate the capability of the proposed method for linear and nonlinear aeroelastic analysis of trapezoidal cantilever plate in hypersonic flow. The effects of Rayleigh–Ritz mode truncation for various wing-plate geometrical characteristics, i.e., sweep angle of leading edge, taper ratio and span, are examined to determine the appropriate mode number for accurate modeling and fast calculation. Meanwhile, the effects of various geometries of trapezoidal cantilever plates on the flutter stability are investigated. The nonlinear dynamic behaviors of the model with three typical geometries, namely, the rectangular, parallelogram and trapezoidal wing-like plate, are simulated numerically. Furthermore, complex dynamic behaviors are observed and identified via the phase plot, the Poincare map and the largest Lyapunov exponent. The results demonstrate that geometrical parameters of trapezoidal wing have significant effects on the nonlinear aeroelastic behaviors of wing structure. In particular, the evolution processes of chaos exhibit remarkable difference for these three wing configurations.

Flutter analysis of hybrid metal-composite low aspect ratio trapezoidal wings in supersonic flow

An effective 3D supersonic Mach box approach in combination with non-classical hybrid metal-composite plate theory has been used to investigate flutter boundaries of trapezoidal low aspect ratio wings. The wing structure is composed of two main components including aluminum material (in-board section) and laminated composite material (out-board section). A global Ritz method is used with simple polynomials being employed as the trial functions. The most important objective of the present research is to study the effect of composite to metal proportion of hybrid wing structure on flutter boundaries in low supersonic regime. In addition, the effect of some important geometrical parameters such as sweep angle, taper ratio and aspect ratio on flutter boundaries were studied. The results obtained by present approach for special cases like pure metallic wings and results for high supersonic regime based on piston theory show a good agreement with those obtained by other investigators.

Numerical investigation of a finned-tube heat exchanger with novel longitudinal vortex generators

A novel longitudinal vortex generator (LVG), which is comprised of a modified rectangular wing and an accessory trapezoidal wing, was proposed. The performance of finned-tube heat exchanger with a single row of novel combined winglet pairs (NCWPs) was analyzed. Numerical simulation shows that compared with rectangular winglet pair (RWP), the NCWP generates main vortex with larger centric intensity. Furthermore, the accessory vortex has a lower core and flows into the back of tubes compressing wake regions' size behind tubes due to the influence of accessory wing. It can disturb the developing of boundary layers on the bottom fin and enhance effectively the heat transfer of the wake region behind the tube. Therefore, the performance of heat transfer for finned-tube heat exchanger is significantly enhanced by NCWP with a moderate pressure drop penalty. Compared with the heat exchanger without LVGs, the heat transfer for finned-tube heat exchanger with NCWPs is improved by 1.8–24.2%, with a pressure penalty increase of 1.3–29.1%. In addition, theory analysis and numerical simulation well agree with the experiment results, indicating the reliability of the research.

A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law

Growing evidences show that the Symmetrical Conservative Metric Method (SCMM) is essential in preserving freestream conservation and orders of accuracy for high-order finite difference schemes to simulate flows with complex geometries. In this paper, a new family of Hybrid cell-edge and cell-node Dissipative Compact Schemes (HDCSs) has been developed for geometry-complex flows by fulfilling the SCMM as well as by introducing dissipation according to the concept adopted in the construction of the high-order Dissipative Compact Schemes (DCSs). The resolution and dissipation properties of HDCSs are investigated by the Fourier analysis, and the stability property of HDCSs is also investigated by asymptotic stability analysis and amplification factor analysis. HDCSs are validated by computing several benchmark test cases. The vortex convection test case demonstrates that the orders of accuracy of the HDCSs are preserved unless the GCL is satisfied. Although high resolution of HDCSs is observed in the test of acoustic wave scattering of multiple cylinders, the solutions can be contaminated if the GCL is not satisfied. Moreover, the numerical solutions of flow past a high lift trapezoidal wing demonstrate the promising ability of the newly developed HDCSs in solving complex flow problems.

Calibration of a [formula omitted] transition model and its validation in low-speed flows with high-order numerical method

Based on the Reynolds-averaged Navier–Stokes (RANS) equations and structured grid technology, the calibration and validation of γ-Reθ transition model is preformed with fifth-order weighted compact nonlinear scheme (WCNS), and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the γ-Reθ transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity profile in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.

Performance Assessment in a Heat Exchanger Tube with Opposite/Parallel Wing Twisted Tapes

The thermohydraulic performance in a tube containing a modified twisted tape with alternate-axes and wing arrangements is reported. This work aims to investigate the effects of wing arrangements (opposite (O) and parallel (P) wings) at different wing shapes (triangle (Tri), rectangular (Rec), and trapezoidal (Tra) wings) and on the thermohydraulic performance characteristics. The obtained results show that wing twisted tapes with all wing shape arrangements (O-Tri/O-Rec/O-Tra/P-Tri/P-Rec/P-Tra) give superior thermohydraulic performance and heat transfer rate to the typical twisted tape. In addition, the tapes with opposite wing arrangement of O-Tra, O-Rec, and O-Tri give superior thermohydraulic performances to those with parallel wing arrangement of P-Tra, P-Rec, and P-Tri around 2.7%, 3.5%, and 3.2%, respectively.

3D high lift flow computations using HiFUN

A summary of the results obtained using the flow solver HiFUN for the 3D High lift NASA Trapezoidal wing are presented. Hybrid unstructured grids have been used for the computations. Grid converged solution obtained for the clean wing and the wing with support brackets, are compared with experimental data. The ability of the solver to predict critical design parameters associated with the high lift flow, such as α max and $$C_{L_{max}}$$ is demonstrated. The utility of the CFD tools, in predicting change in aerodynamic parameters in response to perturbational changes in the configuration is brought out. The solutions obtained for the high lift configuration from two variants of the Spalart-Almaras turbulence model are compared. Inferences from the study on useful design practices pertaining to the 3D high lift flow simulations are summarized.

Calibration of a γ-Re θ transition model and its application in low-speed flows

The prediction of laminar-turbulent transition in boundary layer is very important for obtaining accurate aerodynamic characteristics with computational fluid dynamic (CFD) tools, because laminar-turbulent transition is directly related to complex flow phenomena in boundary layer and separated flow in space. Unfortunately, the transition effect isnt included in todays major CFD tools because of non-local calculations in transition modeling. In this paper, Menters γ - Re θ transition model is calibrated and incorporated into a Reynolds-Averaged Navier-Stokes (RANS) code - Trisonic Platform (TRIP) developed in China Aerodynamic Research and Development Center (CARDC). Based on the experimental data of flat plate from the literature, the empirical correlations involved in the transition model are modified and calibrated numerically. Numerical simulation for low-speed flow of Trapezoidal Wing (Trap Wing) is performed and compared with the corresponding experimental data. It is indicated that the γ - Re θ transition model can accurately predict the location of separation-induced transition and natural transition in the flow region with moderate pressure gradient. The transition model effectively imporves the simulation accuracy of the boundary layer and aerodynamic characteristics.

NASA Trapezoidal-Wing Simulation Using Stress-, and One- and Two-Equation Turbulence Models

The Wilcox 2006 stress- model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley Research Center code CFL3D, and used to study a variety of two-dimensional and three-dimensional configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent-stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than the experiment, similar to the results of a two-equation model.

NASA Trapezoidal Wing Computations Including Transition and Advanced Turbulence Modeling

Flow about the NASA trapezoidal wing is computed with several turbulence models by using grids from the first high-lift prediction workshop in an effort to advance understanding of computational fluid dynamics modeling for this type of flowfield. Transition is accounted for in many of the computations. In particular, a recently developed four-equation transition model is used and works well overall. Accounting for transition tends to increase lift and decrease moment, which improves agreement with the experiment. Upper surface flap separation is reduced, and agreement with experimental surface pressures and velocity profiles is improved. The predicted shape of wakes from upstream elements is strongly influenced by grid resolution in regions above the main and flap elements. Turbulence model enhancements to account for rotation and curvature have the general effect of increasing lift and improving the resolution of the wing-tip vortex as it convects downstream. However, none of the models improve the prediction of flap surface pressures near the wing tip.

Elements of Underwater Glider Performance and Stability

AbstractUnderwater gliders are winged autonomous underwater vehicles (AUVs) that can be deployed for months at a time and travel thousands of kilometers. As with any vehicle, different applications impose different mission requirements that impact vehicle design. We investigate the relationship between a glider’s geometry and its performance and stability characteristics. Because our aim is to identify general trends rather than perform a detailed design optimization, we consider a generic glider shape: a cylindrical hull with trapezoidal wings. Geometric parameters of interest include the fineness ratio of the hull, the wing position and shape, and the position and size of the vertical stabilizer. We describe the results of parametric studies for steady wings-level flight, both at minimum glide angle and at maximum horizontal speed, as well as for steady turning flight. We describe the variation in required lung capacity and maximum lift-to-drag ratio corresponding to a given vehicle size and speed; we also consider range and endurance, given some initial supply of energy for propulsion. We investigate how the turning performance varies with wing and vertical stabilizer configuration. To support this analysis, we consider the glider as an 8-degree-of-freedom multibody system (a rigid body with a cylindrically actuated internal moving mass) and develop approximate expressions for turning flight in terms of geometry and control parameters. Moving from performance to stability and recognizing that a glider’s motion is well described in terms of small perturbations from wings-level equilibrium, we study stability as an eigenvalue problem for a rigid (actuators-fixed) flight vehicle. We present a number of root locus plots in terms of various geometric parameters that illuminate the design tradeoff between stability and control authority.

Form Factor and Critical Mach Number Estimation for Finite Wings

Empirical methods used in conceptual aircraft design for the calculation of form factor drag and critical Mach number typically have been based on two-dimensional profile considerations alone or, at most, limited wing parameters. This paper compares many of these legacy methods. Motivated by the limited wing features modeled in current approaches, surrogate models for form factor and critical Mach number have been built as functions of airfoil thickness and trapezoidal wing parameters. These surrogate models are regressed from the results of a threedimensional potential flow solution coupled to a profile boundary-layer analysis. The surrogates are physics based, yet their simple functional forms make them applicable for inclusion in aircraft sizing algorithms for rapid conceptual and preliminary design trade studies. The models capture the increasing influence of tip effects and spanwise flow as the aspect ratio is decreased and sweep is increased. A primary finding is the strongly beneficial effects of reduced aspect ratio on the form drag and critical Mach number of thick wings.

A Study of Estimating Structural Weight for Reusable Launch Vehicles

This paper presents a method for estimating the vehicle structural weight in the conceptual design phases of reusable launch vehicles and analyzes the sensitivity of the multi-factors which affect the structural weight. The method is an application of liner regression analytic methods. Based on the analysis about the statistical data of the overall parameters of the vehicles, the estimating formulas of the structural weight for the vehicles are deduced using the method. By defining a sensitivity function and a sensitivity factor with dimensionless, the sensitivity of the estimating formulas to every overall parameter is analyzed. Numerical examples and the sensitivity tests indicate that those estimating formulas are available and practicable, and that wing aspect ratio, trapezoidal wing area, fuselage structural depth, vertical tail area and tail length are the most important factors that greatly affect the structural weight.

Heat transfer enhancement by twisted tapes with alternate-axes and triangular, rectangular and trapezoidal wings

The effects of twisted tapes with alternate-axes and wings on heat transfer, flow friction and thermal performance characteristics in a round tube are investigated. The influence of wing shape including triangle, rectangle and trapezoid is also studied. The experiments are performed using twisted tape with three different wing-chord ratios ( d/ W) of 0.1, 0.2 and 0.3 and constant twist ratio ( y/ W) of 4.0. The alternate-axis is made by arranging each plane of twisted tape to 60 degree difference relative to the adjacent plane. The results show that both heat transfer rate and friction factor associated by all twisted tape are consistently higher than those without twisted tape. Under the similar operating conditions, Nusselt number, friction factor as well as thermal performance factor given by the tape with alternate-axes and trapezoidal wings are higher than those given by the others. It is also found that that Nusselt number, friction factor and thermal performance increase with increasing wing-chord ratio. The maximum thermal performance factor of 1.42 is found with the use of twisted tape with alternate-axes and trapezoidal wings at d/ W = 0.3, where the heat transfer rate and friction factor, respectively increase to 2.84 and 8.02 times of those in the plain tube.

Comparison of Reynolds-Averaged Navier-Stokes Simulations of Multi-Element High-Lift Configurations

Flow computations are performed on three-dimensional high-lift configurations on multiblock structured and unstructured meshes with two turbulence models, Spalart-Allmaras model and Menter's shear stress transport model. Two kinds of three-element trapezoidal wings with full-span flap or part-span flap are computed. The objectives of this paper are to investigate the mesh dependency and the effect of turbulence models and improve the reliability in simulating the flow around high-lift devices

Validation of Computations Around High-Lift Configurations by Structured- and Unstructured-Mesh

In this study, flow computations are performed on two-dimensional and three-dimensional high-lift configurations on multiblock structured and unstructured meshes. The objectives are to assess and improve the reliability in simulating the flow around such devices. First, two-dimensional computations on two-element and three-element airfoils are performed to investigate mesh dependency in detail. For unstructured meshes, this is carried out by using a mesh-refinement approach. The results show that sufficient mesh density away from the wing surface is required for accurate drag prediction because the flow has large circulation and wake. A mesh-refinement approach using entropy increment as the refinement indicator is also applied, and its effectiveness is validated. The method is effective in increasing the mesh points in the region of physical importance, such as wake, and the region where the numerical error is high. Three-dimensional computations on three-element trapezoidal wings with fuselage are also performed, and some modest grid studies are performed with structured meshes. Two configurations with full-span flap and part-span flap are used. Ways to improve the reliability of structured and unstructured meshes are discussed by comparing the results. The prediction of aerodynamic forces is quite reasonable even on the unstructured mesh at moderate settings of slat and flap, despite minor differences in local flow physics. However, it is also shown that the unstructured meshes should be further refined to resolve the wake near trailing edge, wing-tip vortices, and the flow separation at the juncture of the wing and body for more accurate prediction.

1910 FBBMによる翼台形パネル耐フラッタ性向上の積層構成最適化(OS-19B 複合材構造,OS-19 計算力学と最適化)

1910 FBBMによる翼台形パネル耐フラッタ性向上の積層構成最適化(OS-19B 複合材構造,OS-19 計算力学と最適化)

Validation of Computed High-Lift Flows with Significant Wind-Tunnel Effects

The modeling requirements for validating Navier-Stokes computations of a high-lift trapezoidal wing are investigated. This wing has a full-span slat and a full-span flap and has been tested extensively in the NASA Langley 14 x 22-ft Wind Tunnel and the NASA Ames 12-ft Pressure Wind Tunnel. Because of the size of the wing, there are significant facility effects in the data from the 12-ft wind tunnel. Computational models of the test facility of differing fidelity are developed and tested. Results are compared with experimental lift, drag, and surface pressures. In the computations a simplified, inviscid model of the test section performs as well as a high-fidelity, viscous test-section model. Computed results generally compare very well with experimental data at all but the highest angles of attack. A comparison of computational results from both free-air and wind-tunnel simulations at the same lift condition indicates that it is necessary to simulate the wind tunnel to perform validation using the 12-ft wind-tunnel experimental data

Equivalent Skin Analysis of Wing Structures Using Neural Networks

An efficient method of modeling trapezoidal built-up wing structures is developed by coupling. in an indirect way, an Equivalent Plate Analysis (EPA) with Neural Networks (NN). Being assumed to behave like a Mindlin-plate, the wing is solved using the Ritz method with Legendre polynomials employed as the trial functions. This analysis method can be made more efficient by avoiding most of the computational effort spent on calculating contributions to the stiffness and mass matrices from each spar and rib. This is accomplished by replacing the wing inner-structure with an material that combines to the skin and whose properties are simulated by neural networks. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with rec,ard to the EPA in a least-square sense. Neural networks for the material properties are trained in terms of the design variables of the wing structure. Examples show that the present method, which can be called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. The present ESA is very promising to be used at the early stages of wing structure design.