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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Optimizing Proprotor Blades Using Coupled Aeroacoustic and Aerodynamic Sensitivities

A quieter and aerodynamically more efficient proprotor design requires high-fidelity and well-integrated optimization and analysis tools. To fulfill that requirement, the present paper delivers a methodology based on multidisciplinary, adjoint-based, discrete optimization. SU2-based code development involves the implementation of aeroacoustic analysis, adjoint computations, and integrations into a multidisciplinary rotorcraft optimization suite. Submodules utilized in the optimization are verified with wind tunnel data to demonstrate the accuracy of aerodynamic and aeroacoustic analyses. The developed code is used for NASA's helically twisted proprotor to maximize the aeroacoustic performance of the proprotor while holding thrust constant. The optimization process considers multiple flight conditions (hence, multipoint), which are forward flight and hovering. As an outcome of the analyses, the optimized blade design propagates lower noise as perceived by multiple observers in both flight conditions

R Omur Icke↗
NASA NTRS1997

Numerical Computation of Sensitivities and the Adjoint Approach

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

Lewis, Robert Michael↗
NASA NTRS2011

A Generalized Framework for Constrained Design Optimization of General Supersonic Configurations Using Adjoint Based Sensitivity Derivatives

The Aeronautics Research Mission Directorate (ARMD) sent out an NASA Research Announcement (NRA) for proposals soliciting research and technical development. The proposed research program was aimed at addressing the desired milestones and outcomes of ROA (ROA-2006) Subtopic A.4.1.1 Advanced Computational Methods. The second milestone, SUP.1.06.02 Robust, validated mesh adaptation and error quantification for near field Computational Fluid Dynamics (CFD), was addressed by the proposed research. Additional research utilizing the direct links to geometry through a CAD interface enabled by this work will allow for geometric constraints to be applied and address the final milestone, SUP2.07.06 Constrained low-drag supersonic aerodynamic design capability. The original product of the proposed research program was an integrated system of tools that can be used for the mesh mechanics required for rapid high fidelity analysis and for design of supersonic cruise vehicles. These Euler and Navier-Stokes volume grid manipulation tools were proposed to efficiently use parallel processing. The mesh adaptation provides a systematic approach for achieving demonstrated levels of accuracy in the solutions. NASA chose to fund only the mesh generation/adaptation portion of the proposal. So this report describes the completion of the proposed tasks for mesh creation, manipulation and adaptation as it pertains to sonic boom prediction of supersonic configurations.

Karman, Steve L., Jr.↗
NASA NTRS2019

Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion

Objectives: Reliable evaluation of mass flow rates through permeable boundaries - Estimate and control discretization error- Consider both computational domain outflow and inflow- Applicable to simulating propulsion-system effects, as well as secondary flow paths - Explore feasibility of handling more general outputs at domain boundaries. Design optimization subject to mass-flow-rate constraints - Improve aerodynamic performance and reduce noise due to sonic boom - Control discretization error in design space to improve confidence in final designs.

Nemec, Marian↗
NASA NTRS2015

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

shape optimization↗
NASA NTRS2026

A Modular Conjugate Heat Transfer Optimization Framework for Thermal Management of Electric Aircraft

Conjugate heat transfer (CHT) analysis and optimization is a powerful method for improving thermal management, as it simultaneously resolves the temperature distribution in both fluid and solid domains. This paper presents a modular, discrete adjoint-based CHT optimization capability integrated within the OpenMDAO/MPhys framework. A unique feature of the proposed framework is its flexibility to extend to multidisciplinary optimization, including aero-structural-thermal applications. The fluid domain is modeled using a finite-volume Computational Fluid Dynamics (CFD) solver, and the solid domain with a conduction heat transfer solver. A mixed Neumann-Dirichlet boundary condition is developed to enable full submersion of the solid geometry within the fluid domain, while ensuring consistent temperature and heat flux coupling at the CHT interface. Gradient-based optimization is performed; the gradients are efficiently computed using the discrete adjoint solvers implemented in DAFoam. To demonstrate the method, this paper considers two cases related to electric aircraft thermal management: a U-bend heat exchanger and an actively cooled battery pack. The U-bend case aims to minimize pressure loss while maximizing heat flux by changing the pipe geometry. The optimized design reduces pressure loss by 52.7% and increases total heat flux by 2.3%. In the battery pack case, a 3-by-3 cell configuration is cooled by ambient airflow, with constant heat generation prescribed in the cells. The battery casing shape serves as the design variable, and the objective function is a weighted sum of pressure loss and pack weight, subject to a maximum temperature constraint. The optimized design achieves a 44.6% reduction in pressure loss and a 1.5% reduction in weight, while satisfying the thermal constraint. To ensure the reliability of the optimized designs, this study validates coarse-mesh, steady-state predictions against fine-mesh unsteady simulations, demonstrating consistency within acceptable errors. This work demonstrates the potential of the developed framework to enable rapid, high-fidelity design of thermal management systems for electric aircraft.

heat transfer↗
NASA NTRS1995

Viscous aerodynamic design using the adjoint variable approach

The use of classical optimal control methods, in particular variational methods, to solve the airfoil optimization problem, by deriving a set of adjoint (costate) equations and boundary conditions has already been done for inviscid (potential and Euler flows) and two dimensional, steady state, incompressible flow governed by the Navier-Stokes equations. The interior and boundary terms of the volume integral have been derived (in this work) for the steady Navier-Stokes equations in three dimensions for a viscous, compressible heat conducting fluid. This can be used to derive the adjoint equations and numerical boundary conditions for general classes of problems and hence paves the way for a solution to the aerodynamic optimization problem for compressible viscous flows. The next steps to the realization of that goal are projected as below. The usual square integral pressure functional as an objective function is being replaced by a more realistic drag functional subject to a lift constraint. The feasibility of attempting the more difficult time dependent problem is being investigated. It remains to get the full system of adjoint equations and boundary conditions with the new functional. The state and adjoint equations must be discretized and coded. An appropriate optimization program must be used (steepest descents seems inadequate) and various known airfoil shapes should be recovered in test cases of the computer program.

DeRise, George↗
NASA NTRS2005

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗
NASA NTRS2006

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗
NASA NTRS1997

Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation

A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.

Anderson, W. Kyle↗
NASA NTRS1991

Active control of panel vibrations induced by boundary-layer flow

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Chow, Pao-Liu↗
NASA NTRS2011

Multidisciplinary Modeling Software for Analysis, Design, and Optimization of HRRLS Vehicles

The concept for Highly Reliable Reusable Launch Systems (HRRLS) under the NASA Hypersonics project is a two-stage-to-orbit, horizontal-take-off / horizontal-landing, (HTHL) architecture with an air-breathing first stage. The first stage vehicle is a slender body with an air-breathing propulsion system that is highly integrated with the airframe. The light weight slender body will deflect significantly during flight. This global deflection affects the flow over the vehicle and into the engine and thus the loads and moments on the vehicle. High-fidelity multi-disciplinary analyses that accounts for these fluid-structures-thermal interactions are required to accurately predict the vehicle loads and resultant response. These predictions of vehicle response to multi physics loads, calculated with fluid-structural-thermal interaction, are required in order to optimize the vehicle design over its full operating range. This contract with ResearchSouth addresses one of the primary objectives of the Vehicle Technology Integration (VTI) discipline: the development of high-fidelity multi-disciplinary analysis and optimization methods and tools for HRRLS vehicles. The primary goal of this effort is the development of an integrated software system that can be used for full-vehicle optimization. This goal was accomplished by: 1) integrating the master code, FEMAP, into the multidiscipline software network to direct the coupling to assure accurate fluid-structure-thermal interaction solutions; 2) loosely-coupling the Euler flow solver FEFLO to the available and proven aeroelasticity and large deformation (FEAP) code; 3) providing a coupled Euler-boundary layer capability for rapid viscous flow simulation; 4) developing and implementing improved Euler/RANS algorithms into the FEFLO CFD code to provide accurate shock capturing, skin friction, and heat-transfer predictions for HRRLS vehicles in hypersonic flow, 5) performing a Reynolds-averaged Navier-Stokes computation on an HRRLS configuration; 6) integrating the RANS solver with the FEAP code for coupled fluid-structure-thermal capability; and 7) integrating the existing NASA SRGULL propulsion flow path prediction software with the FEFLO software for quasi-3D propulsion flow path predictions, 8) improving and integrating into the network, an existing adjoint-based design optimization code.

Spradley, Lawrence W.↗
NASA NTRS2016

Inlet Trade Study for a Low-Boom Aircraft Demonstrator

Propulsion integration for low-boom supersonic aircraft requires careful inlet selection, placement, and tailoring to achieve acceptable propulsive and aerodynamic performance, without compromising vehicle sonic boom loudness levels. In this investigation, an inward-turning streamline-traced and axisymmetric spike inlet are designed and independently installed on a conceptual low-boom supersonic demonstrator aircraft. The airframe was pre-shaped to achieve a target ground under-track loudness of 76.4 PLdB at cruise using an adjoint-based design optimization process. Aircraft and inlet performance characteristics were obtained by solution of the steady-state Reynolds-averaged Navier-Stokes equations. Isolated cruise inlet performance including total pressure recovery and distortion were computed and compared against installed inlet performance metrics. Evaluation of vehicle near-field pressure signatures, along with under- and off-track propagated loudness levels is also reported. Results indicate the integrated axisymmetric spike design offers higher inlet pressure recovery, lower fan distortion, and reduced sonic boom. The vehicle with streamline-traced inlet exhibits lower external wave drag, which translates to a higher lift-to-drag ratio and increased range capability.

engine airframe integration↗
NASA NTRS2019

A New Recycling Method to Generate Turbulent Inflow Profiles

The accuracy of the scale-resolving simulations for practical geometries strongly depends on the inflow boundary conditions. Imposing experimentally observed turbulent inflow profiles for the numerical simulations is a major challenge. Existing methods available in the literature assume self-similar behavior, which is not true for most of the experiments. In the present work, we formulate the turbulent inflow profile generation technique as an optimization problem. An adjoint technique is exploited to evaluate the sensitivities of multiple input parameters for the present problem. The present formulation is then tested to generate a laminar boundary layer profile, turbulent boundary layer profile, and turbulent jet profile.

Garai, Anirban↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
NASA NTRSDate not supplied

Sonic Boom Ground Noise Minimization Via the Adjoint Method

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by the sonic boom of a high altitude supersonic body is presented. A Cartesian Euler flow solver is coupled with an atmospheric propagation tool to create a ground-noise analysis capability for supersonic bodies. Adjoint formulations for both the flow solver and propagation tool are also coupled to compute sensitivities of shape variations in the body in a highly efficient manner. A gradient-based optimizer is then introduced to forge a valuable design capability. Output-based mesh adaptation that is driven directly by ground-level noise is employed to increase accuracy and provide error estimation. The design method is demonstrated first on a simple axisymmetric body with few design variables to evaluate the efficacy of the optimization scheme. Guided by the results of this initial case, the problem is then repeated with somewhat different design variables to further demonstrate the capabilities of the design method. Finally, the method is applied to a real-world problem by optimizing control surface deflection settings of a low-boom aircraft to minimize ground noise while maintaining trimmed, level flight.

ARMD↗
NASA NTRSDate not supplied

Fuel-Optimal Trajectory Optimization of Mach 0.745 Transonic Truss-Braced Wing with Variable Camber Continuous Trailing Edge Flap

This paper describes a fuel-optimal trajectory optimization of the Mach 0.745 Transonic Truss-Braced Wing with the variable camber continuous trailing edge flaps (VCCTEF) capable of changing the chordwise pressure distribution and spanwise lift distribution to minimize drag. The trajectory optimization is posed as a minimization of the fuel burn over a fixed cruise range. The trajectory optimization is formulated by the adjoint method which results in a two-point boundary value problem. A numerical shooting method is implemented to solve the minimum-fuel trajectory optimization. The results indicates a fuel burn reduction of 793 lbs or 5.5% for a cruise range of 3000 miles. An approximate trajectory optimization is proposed using a single adjoint variable. This leads to a greatly simplified analytical solution of the adjoint solution. The results of the approximate trajectory optimization are in excellent agreement with those obtained by the shooting method. The approximate trajectory optimization produces a fuel burn reduction of 615 lbs or 4.3%.

Trajectory Optimization↗