Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier–Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations

Investigation into the Aerodynamics of Swashplateless Rotors Using CFD-CSD Analysis

This study obtains a better understanding of the aerodynamics of integrated trailing edge flap (TEF) based swashplateless rotors. Both two dimensional (2D) and three dimensional (3D) analysis/simulations are performed to understand the behavior of TEF airfoils and integrated TEF based swashplateless rotors. The 2D aerodynamics of TEF airfoils is explored in detail. A semi-empirical approach is developed for modeling drag for TEF airfoils in steady flows based on baseline airfoil drag data alone. Extensive 2D CFD simulations are performed for a wide range of flow conditions in order to better understand various aspects of the aerodynamics of TEF airfoils. The trends in the airloads (lift, drag, pitching moment, hinge moment) for TEF airfoils are obtained. Nonlinear phenomena such as flow separation, shocks and unsteady vortex shedding are investigated, and the flow conditions and trends associated with them are studied. The effect of airfoil properties such as thickness and overhang are studied. Various approaches are used to model the effect of gaps at the leading edge of the flap. An approximate ``gap averaging'' technique is developed, which provides good predictions of steady airloads at almost the same computational cost as a simulation where the gap is not modeled. Direct modeling of the gap is done by using a patched mesh in the gap region. To solve problems (such as poor grid quality/control and poor convergence) that are associated with the patched mesh simulations, an alternate approach using overlapping meshes is used. It is seen that for TEF airfoils, the presence of gaps adversely affects the effectiveness of the flap. The change in airloads is not negligible, especially at the relatively higher flap deflections associated with swashplateless TEF rotors. Finally, uncoupled and coupled computational fluid/structural dynamics (CFD-CSD) simulations of conventional (baseline) and swashplateless TEF rotors is performed in hovering flight. The CFD-CSD code is validated against experiment and good agreement is observed. It is observed that the baseline UH-60 rotor performs better than the swashplateless UH-60 rotor. For an untwisted NACA0012 airfoil based rotor, the performance is similar for the baseline and swashplateless configurations. The effect of gaps on the performance of swashplateless TEF rotors is also investigated. It is seen that the presence of chordwise gaps significantly affects the effectiveness of the TEF to control the rotor. Spanwise gaps also affect the performance of swashplateless rotors but their effect is not as significant

Comparative Analysis of Aerodynamic Characteristics of F16 and F22 Combat Aircraft using Computational Fluid Dynamics

This paper presents the computational investigation of air flow over an aircraft at realistic speeds while demonstrating the importance of extending the existing analysis to the complete airplane and how pivotal it is in improving its in-flight performance. The study is done for F16 and F22 aircraft using ANSYS Fluent (19.2) to obtain pressure distribution, shear stress distribution and temperature variation on the complete surface of the aircraft. Since the front section of the aircraft is prone to direct initial impact of surrounding environment, this portion is also examined. Here, as the speed is doubled from Mach 1 to Mach 2, a rise in the value of all the three variables is noticed for the F16 aircraft, whereas the pressure distribution for F22 aircraft shows strange behaviour for the highest speed (Mach 2). On comparing the results over the whole surface, it is seen that F16 experiences smaller pressure (29% lower for Mach 1 and 30% for Mach 2), temperature (9.5% lower for Mach 1 and 30% for Mach 2) and shear stress relative to F22 and the stress shows a huge change (90% lower for Mach 1 and 83% for Mach 2). Results of the present study imply that the design of the aircraft highly influences its performance as the parameters discussed touch their limits

Unsteady Euler and Navier-Stokes Computations Around Oscillating Delta Wing Including Dynamics

Unsteady flows around rigid or flexible delta wings with and without oscillating leading-edge flaps are considered. These unsteady flow problems are categorized under two classes of problems. In the first class, the wing motion is prescribed a priori and in the second class, the wing motion is obtained as a part of the solution. The formulation of the first class includes either the unsteady Euler or unsteady Navier-Stokes equations for the fluid dynamics and the unsteady linearized Navier-displacement (ND) equations for the grid deformation. The problem of unsteady transonic flow past a bicircular-arc airfoil undergoing prescribed thickening-thinning oscillation is studied using the CFL2D code. This code is used to solve the Navier-Stokes equations using an implicit, flux-difference splitting, finite-volume scheme. For the unsteady supersonic flows around flexible delta wings with prescribed oscillating deformation and rigid delta wings with leading-edge-flap oscillations, the conservative, unsteady Euler and thin-layer Navier-Stokes equations in a moving frame-of-reference, along with the linearized ND equations, have been used. Two main problems are solved to demonstrate the validity of the developed schemes. The first problem is that of a flexible delta wing undergoing a prescribed bending-mode oscillation. In the second problem, a rigid-delta wing with symmetric and anti-symmetric flap oscillations is considered. These applications fall under the first class of problems. For the unsteady flow applications, where the wing motion is not prescribed a priori (second class of problems), either the unsteady Euler or thin-layer Navier-Stokes equations and the rigid-body dynamics equations, in a moving frame of reference, are solved sequentially to obtain the flow behavior and the wing motion. The main application for this class of unsteady flow phenomena, is the wing-rock problem. Using the locally-conical flow assumption, three problems are solved. The first is that of a delta wing undergoing a damped rolling oscillation. The second is that of a delta wing undergoing a limit-cycle, wing-rock motion. In the third problem, suppression of the wing-rock motion is demonstrated using a tuned anti-symmetric oscillation of the leading-edge flap

Aeronautical engineering: A continuing bibliography (supplement 152)

The bibliography lists 338 reports, articles and other documents introduced into the NASA scientific and technical information system in August 1982

Towards Adaptive and Grid-Transparent Adjoint-Based Design Optimization Frameworks

With the growing environmental consciousness, the global perspective in energy production is shifting towards renewable resources. As recently reported by the Office of Energy Efficiency & Renewable Energy at the U.S. Department of Energy, wind-generated electricity is the least expensive form of renewable power and is becoming one of the cheapest forms of electricity from any source. The aeromechanical design of wind turbines is a complex and multidisciplinary task which necessitates a high-fidelity flow solver as well as efficient design optimization tools. With the advances in computer technologies, Computational Fluid Dynamics (CFD) has established its role as a high-fidelity tool for aerodynamic design.In this dissertation, a grid-transparent unstructured two- and three-dimensional compressible Reynolds-Averaged Navier-Stokes (RANS) solver, named UNPAC, is developed. This solver is enhanced with an algebraic transition model that has proven to offer accurate flow separation and reattachment predictions for the transitional flows. For the unsteady time-periodic flows, a harmonic balance (HB) method is incorporated that couples the sub-time level solutions over a single period via a pseudo-spectral operator. Convergence to the steady-state solution is accelerated using a novel reduced-order-model (ROM) approach that can offer significant reductions in the number of iterations as well as CPU times for the explicit solver. The unstructured grid is adapted in both steady and HB cases using an r-adaptive mesh redistribution (AMR) technique that can efficiently cluster nodes around regions of large flow gradients.Additionally, a novel toolbox for sensitivity analysis based on the discrete adjoint method is developed in this work. The Fast automatic Differentiation using Operator-overloading Technique (FDOT) toolbox uses an iterative process to evaluate the sensitivities of the cost function with respect to the entire design space and requires only minimal modifications to the available solver. The FDOT toolbox is coupled with the UNPAC solver to offer fast and accurate gradient information. Ultimately, a wrapper program for the design optimization framework, UNPAC-DOF, has been developed. The nominal and adjoint flow solutions are directly incorporated into a gradient-based design optimization algorithm with the goal of improving designs in terms of minimized drag or maximized efficiency

A coupled discrete adjoint method for optimal design with dynamic non-linear fluid structure interactions

Incorporating high-fidelity analysis methods in multidisciplinary design optimization necessitates efficient sensitivity evaluation, which is particularly important for time-accurate problems. This thesis presents a new discrete adjoint formulation suitable for fully coupled, non-linear, dynamic FSI problems. The solution includes time-dependent adjoint variables that arise from grid motion and chosen time integration methods for both the fluid and structural domains. Implemented as a generic multizone discrete adjoint solver for time-accurate analysis in the open-source multiphysics solver SU2, this provides a flexible framework for a wide range of applications. Design optimization of aerodynamic structures need accurate characterization of the coupled fluid-structure interactions (FSI). Incorporating high-fidelity analysis methods in the multidisciplinary design optimization (MDO) necessitates efficient sensitivity evaluation, which is particularly important for time-accurate problems. Adjoint methods are well established for sensitivity analysis when large number of design variables are needed. The use of discrete adjoint method through algorithmic differentiation enables the evaluation of sensitivities using an approximation of the Jacobian of the coupled problem, thus enabling this approach to be applied for multidisciplinary analysis. This thesis presents a new discrete adjoint formulation suitable for fully coupled, non-linear, dynamic FSI problems. A partitioned approach is considered with finite volume for the fluid and finite elements for the solid domains. The solution includes the time-dependent adjoint variables that arise from the grid motion and chosen time integration methods for both the fluid and structural domains. Implemented as a generic multizone discrete adjoint solver for timeaccurate analysis in the open-source multiphysics solver SU2, this provides a flexible framework for a wide range of applications. The partitioned FSI solver approach has been leveraged to extend the dynamic FSI capabilities to low speed flows through the introduction of a densitybased unsteady incompressible flow solver. The developed methodology and implementation are demonstrated using a range of numerical test cases. Optimal design for steady, coupled FSI problems are firstly presented before moving to the building blocks of dynamic coupled problems using single domain analysis, for both structural and fluid domains in turn. The new unsteady incompressible fluid solver, for both the primal and adjoint analysis, are verified against a range of well-known benchmark test cases, including problems with grid motion. Finally, applications of coupled dynamic problems are presented to verify both the unsteady incompressible solver for FSI as well as the successful verification of the discrete adjoint sensitivities for the transient response of a transonic compliant airfoil for a variety of both aerodynamic and structural objective functions.Open Acces

Transonic flow studies

Major emphasis was on the design of shock free airfoils with applications to general aviation. Unsteady flow, transonic flow, and shock wave formation were examined

Aeronautical engineering: A special bibliography with indexes, supplement 82, April 1977

This bibliography lists 311 reports, articles, and other documents introduced into the NASA scientific and technical information system in March 1977