10 research outputs found
Sensitivity computations by algorithmic differentiation of a high-Âorder cfd code based on spectral differences
We compute flow sensitivities by differentiating a high-Âorder computational fluid dynamics code. Our fully discrete approach relies on automatic differentiation (AD) of the original source code. We obtain two transformed codes by using the AD tool Tapenade (INRIA), one for each differentiation mode: tangent and adjoint. Both differentiated codes are tested against each other by computing sensitivities in an unsteady test case. The results from both codes agree to within machine accuracy, and compare well with those approximated by finite differences. We compare execution times and discuss the encountered technical difficulties due to 1) the code parallelism and 2) the memory overhead caused by unsteady problems
Toward Adjoint-Based Aeroacoustic Optimization for Propeller and Rotorcraft Applications
The goal of the present project is to build a multidisciplinary, rapid, robust, and accurate computational tool to optimize wing-mounted propeller designs. The full Farassat’s formulation F1A for aeroacoustic analysis is implemented in the open-source software SU2. This extension enables the prediction of far-field noise generated by moving sources. The formulation is verified, for a stationary and rotating sphere in a wind tunnel and for a tiltrotor in forward flight, by comparing the acoustic predictions of SU2 with the predictions computed by NASA’s aeroacoustics code ANOPP2. The algorithmic differentiation capability of SU2 provides discretely consistent, adjoint-based sensitivity analysis for this formulation. The adjoint-based sensitivities are verified through comparison with complex-step sensitivities
Adjoint computations by algorithmic differentiation of a parallel solver for time-dependent PDEs
A computational fluid dynamics code is differentiated using algorithmic
differentiation (AD) in both tangent and adjoint modes. The two novelties of
the present approach are 1) the adjoint code is obtained by letting the AD tool
Tapenade invert the complete layer of message passing interface (MPI)
communications, and 2) the adjoint code integrates time-dependent, non-linear
and dissipative (hence physically irreversible) PDEs with an explicit time
integration loop running for ca. time steps. The approach relies on
using the Adjoinable MPI library to reverse the non-blocking communication
patterns in the original code, and by controlling the memory overhead induced
by the time-stepping loop with binomial checkpointing. A description of the
necessary code modifications is provided along with the validation of the
computed derivatives and a performance comparison of the tangent and adjoint
codes.Comment: Submitted to Journal of Computational Scienc
Index handling and assign optimization for Algorithmic Differentiation reuse index managers
For operator overloading Algorithmic Differentiation tools, the
identification of primal variables and adjoint variables is usually done via
indices. Two common schemes exist for their management and distribution. The
linear approach is easy to implement and supports memory optimization with
respect to copy statements. On the other hand, the reuse approach requires more
implementation effort but results in much smaller adjoint vectors, which are
more suitable for the vector mode of Algorithmic Differentiation. In this
paper, we present both approaches, how to implement them, and discuss their
advantages, disadvantages and properties of the resulting Algorithmic
Differentiation type. In addition, a new management scheme is presented which
supports copy optimizations and the reuse of indices, thus combining the
advantages of the other two. The implementations of all three schemes are
compared on a simple synthetic example and on a real world example using the
computational fluid dynamics solver in SU2.Comment: 20 pages, 14 figures, 4 table
Enhancing the SST Turbulence Model with Symbolic Regression: A Generalizable and Interpretable Data-Driven Approach
Turbulence modeling within the RANS equations' framework is essential in
engineering due to its high efficiency. Field inversion and machine learning
(FIML) techniques have improved RANS models' predictive capabilities for
separated flows. However, FIML-generated models often lack interpretability,
limiting physical understanding and manual improvements based on prior
knowledge. Additionally, these models may struggle with generalization in flow
fields distinct from the training set. This study addresses these issues by
employing symbolic regression (SR) to derive an analytical relationship between
the correction factor of the baseline turbulence model and local flow
variables, enhancing the baseline model's ability to predict separated flow
across diverse test cases. The shear-stress-transport (SST) model undergoes
field inversion on a curved backward-facing step (CBFS) case to obtain the
corrective factor field beta, and SR is used to derive a symbolic map between
local flow features and beata. The SR-derived analytical function is integrated
into the original SST model, resulting in the SST-SR model. The SST-SR model's
generalization capabilities are demonstrated by its successful predictions of
separated flow on various test cases, including 2D-bump cases with varying
heights, periodic hill case where separation is dominated by geometric
features, and the three-dimensional Ahmed-body case. In these tests, the model
accurately predicts flow fields, showing its effectiveness in cases completely
different from the training set. The Ahmed-body case, in particular, highlights
the model's ability to predict the three-dimensional massively separated flows.
When applied to a turbulent boundary layer with Re_L=1.0E7, the SST-SR model
predicts wall friction coefficient and log layer comparably to the original SST
model, maintaining the attached boundary layer prediction performance.Comment: 37 pages, 46 figure
Towards Adjoint-based Broadband Noise Minimization using Stochastic Noise Generation
In this paper, we present an adjoint-based broadband noise minimization framework using stochastic noise generation (SNG). The SNG module is implemented in the open-source multi-physics solver suite SU2 and coupled with the existing Reynolds-averaged Navier-Stokes (RANS) to allow fast assessment of broadband noise sources. In addition, a discrete adjoint solver on the basis of algorithmic differentiation (AD) is developed for the coupled RANS-SNG system to enable efficient evaluation of broadband noise design sensitivities. The adjoint-based RANS-SNG framework developed in this work not only avoids the regularization problem that plagues the adjoint solutions for scale-resolving simulations, but also significantly lowers the computational\ua0cost and leads to a faster turn-around time for the initial design evaluation phase. Current results show that the RANS-SNG method can efficiently provide broadband noise level assessment for various configurations without resorting to computationally prohibitive scale-resolving simulations. Furthermore, current results also show that the AD-based coupled adjoint-RANS-SNG solver is highly accurate. Finally, shape optimizationsperformed on the basis of such coupled-sensitivity are shown to be effective in removing the broadband noise source in the trailing edge of a NACA0012 airfoil profile while maintaining aerodynamic performance imposed as an optimization constraint
Unsteady adjoint computations by algorithmic differentiation of parallel code
International audienceA computational fluid dynamics code relying on a high-order spatial discretization is differentiated using algorithmic differentiation (AD). Two unsteady test cases are considered: a decaying incompressible viscous shear layer and an inviscid compressible flow around a NACA 0012 airfoil. Both tangent and adjoint modes of AD are explored in the viscous case, while only the tangent mode is applied to the inviscid case. The layer of message passing interface (MPI) communications was handled by the AD tool (Tapenade) through the Adjoinable MPI library, with fully automatic inversion of the MPI communications in adjoint mode. A description of the necessary code modifications is provided along with the validation of the computed derivatives and a comparison of the performance of the different codes. The explicit time integration loop of the viscous problem required of the order of 10^6 time steps, which could be inverted in the backward sweep of the adjoint code by means of binomial checkpointing
Development and Applications of Adjoint-Based Aerodynamic and Aeroacoustic Multidisciplinary Optimization for Rotorcraft
Urban Air Mobility (UAM) is one of the most popular proposed solutions for alleviating traffic problems in populated areas. In this context, the proposed types of vehicles mainly consist of rotors and propellers powered by electric motors. However, those rotary-wing components can contribute excessively to noise generation. Therefore, a significant noise concern emerges due to urban air vehicles in or around residential areas. Reducing noise emitted by air vehicles is critically important to improve public acceptance of such vehicles for operations in densely populated areas.
Two main objectives of the present dissertation are: (1) to expand the multidisciplinary optimization to utilize adjoint-based aeroacoustic and aerodynamic sensitivities; (2) to optimize the shape of proprotor blades to improve the overall performance of selected rotorcraft from both aerodynamic and aeroacoustic perspectives.
This dissertation reports on the development and application of an unsteady discrete adjoint solver for aerodynamic and aeroacoustic coupling to obtain an improved design for quieter rotorcraft. The optimization framework developed through this dissertation can be utilized for multiple flight conditions, multiple receivers, and multiple optimization objectives within the same design process. SU2-based code development involves the implementation of aeroacoustic analysis, adjoint computations, and integrations into a multidisciplinary rotorcraft optimization suite. A computational aeroacoustics tool is embedded into the SU2-suite to predict the propagation of the emitted noise from the moving sources with high fidelity. Capabilities of the developed computational aeroacoustics tool are demonstrated for a range of rotor, propeller, and proprotor applications, and they are verified by comparing with wind tunnel data whenever it is available. The aeroacoustic tool also computes sensitivities with respect to the conserved variables and grid coordinates by employing the algorithmic differentiation method. Integration of an acoustic solver into the discrete adjoint solver and related modifications enable the code to compute aeroacoustic sensitivities with respect to the design variables.
Applying the developed optimization framework for a proprotor aims to reduce the noise radiation without sacrificing the required aerodynamic performance value. As an outcome of the optimization during forward-flight and hover, the reshaped blade design emits and propagates lower noise levels as perceived by multiple observers.
The major contributions are: (1) a multidisciplinary optimization framework that presents an optimized rotorcraft design for better aeroacoustics and aerodynamics; (2) a novel adjoint-based formulation for aeroacoustic sensitivities with respect to design variables; (3) single acoustic objective function including multiple flight conditions and multiple microphone positions; (4) implementation of Farassat 1A formulation into opensource software, SU2, to compute noise propagation emitted from moving sources.
In summary, this dissertation provides the results with high fidelity, a well-integrated and rapidly converging optimization tool to improve the rotorcraft\u27s aeroacoustic performance while retaining or improving the aerodynamic performance. Among the conclusions are the following: (1) Computational fluid dynamics analyses (SU2-CFD) can produce accurate results for various rotorcraft applications. (2) The developed aeroacoustic code predicts noise propagation emitted from propellers, rotors, and proprotors with high-fidelity. (3) The acoustic interaction between propeller and wing components can be assessed by employing the aeroacoustic solver. (4) The multidisciplinary optimization framework successively reduces noise level emitted by a proprotor in multiple flight configurations. (5) The optimized design improves emitted noise radiation while satisfying the given aerodynamic constraint(s)
Inclusion of Geometrically Nonlinear Aeroelastic Effects into Gradient-Based Aircraft Optimization
While aircraft have largely featured flexible wings for decades, more
recently, aircraft structures have rapidly become more flexible. The pursuit of
longer ranges and higher efficiency through higher aspect ratio wings, as well
as the introduction of modern, light-weight materials has yielded moderately and
very flexible aircraft configurations. Past accidents, such as the loss of the
Helios High Altitude Long Endurance (HALE) aircraft have highlighted the
limitations of linear analysis methods and demonstrated the peril of neglecting
nonlinear effects when designing such aircraft. In particular, accounting for
geometrical nonlinearities in flutter analyses become necessary in aircraft
optimization, including transport aircraft, or future aircraft may require
costly modifications late in the design process to fulfill certification
requirements. As a result, there is a need to account for geometrical
nonlinearities earlier in the design process and integrate these analyses
directly into the multi-disciplinary design optimization (MDO) problems.
This thesis investigates geometrically nonlinear flutter problems and how these
should be integrated into aircraft MDO problems. First, flutter problems with
and without geometrical nonlinearities are discussed and a unifying
interpretation is presented. Furthermore, methods for interpreting nonlinear
flutter problems are proposed and differences between linear and nonlinear
flutter problem interpretation are discussed. Next, a flutter constraint
formulation which accounts for geometrically nonlinear effects using beam-based
analyses is presented. The resulting constraint uses a
Kreisselmeiser-Steinhauser aggregation function to yield a scalar constraint
from flight envelope flutter damping values. While the constraint enforces
feasibility over the entire flight envelope, how the flight envelope is sampled
largely determines the flutter constraint’s accuracy. To this end, a constrained
Maximin approach, which is applicable for non-hypercube spaces, is used to
sample the flight envelope and obtain a low-discrepancy sample set. The flutter
constraint is then implemented using a beam-based geometrically nonlinear
aeroelastic simulation code, UM/NAST.
As gradient-based optimization methods are used in MDO due to the large number
of design variables in aircraft design problems, the flutter constraint requires
the recovery of flutter damping sensitivities. These are obtained by applying
algorithmic differentiation (AD) to the UM/NAST code base. This enables the
recovery of gradients for any solution type (static, modal, dynamic, and
flutter/stability) with respect to any local design variable available within
UM/NAST. The performance of the gradient prediction is studied and a
hybrid primal-AD scheme is developed to obtain the coupled nonlinear aeroelastic
sensitivities. After verifying the accuracy and performance of the gradient
evaluation, the flutter constraint was implemented in a sample optimization
problem.
Finally, a roadmap for including the beam-based flutter constraint within an
aircraft design problem is presented using analyses of varying fidelity. To this
end, analyses of appropriate fidelity are used depending on the output of
interest. While a shell-based FEM model can recover stress distributions, and is
therefore well-suited for strength constraints, they are ill-suited for
geometrically nonlinear flutter constraints due to their computational cost.
Analyses are presented for a high aspect ratio transport aircraft configuration
to illustrate the proposed approach and highlight the necessity for the
inclusion of a geometrically nonlinear flutter constraint.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163259/1/clupp_1.pd