scholarly journals Continuous Adjoint Approach for the Spalart-Allmaras Model in Aerodynamic Optimization

AIAA Journal ◽  
2012 ◽  
Vol 50 (3) ◽  
pp. 631-646 ◽  
Author(s):  
Alfonso Bueno-Orovio ◽  
Carlos Castro ◽  
Francisco Palacios ◽  
Enrique Zuazua
Keyword(s):  
Aerodynamic Optimization ◽  
Adjoint Approach ◽  
Continuous Adjoint

Continuous adjoint aerodynamic optimization design for multi-stage gas turbine with cooling air

2017 ◽  
Vol 89 (3) ◽  
pp. 444-456
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Gas Turbine ◽  
Optimization Design ◽  
Adjoint Method ◽  
Air Injection ◽  
Aerodynamic Optimization ◽  
Content Type ◽  
Multi Stage ◽  
Surface Code ◽  
Cooling Air ◽  
Continuous Adjoint

Purpose This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method. Design/methodology/approach Continuous adjoint method is combined with the S2 surface code. Findings The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection. Practical implications The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method. Originality/value The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

Aerodynamic Optimization Design of Multi-stage Turbine Using the Continuous Adjoint Method

2015 ◽  
Vol 32 (2) ◽  
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Optimization Design ◽  
Adjoint Method ◽  
Shape Design ◽  
Aerodynamic Optimization ◽  
Aerodynamic Shape ◽  
Adjoint Formulation ◽  
Multi Stage ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint

AbstractThis paper develops a continuous adjoint formulation for the aerodynamic shape design of a turbine in a multi-stage environment based on S

Adjoint Based Aerodynamic Optimization of a Multi-Splitter Turbine Vane Frame

2019 ◽  
Author(s):  
Vincenzo Russo ◽  
Simone Orsenigo ◽  
Lasse Mueller ◽  
Tom Verstraete ◽  
Sergio Lavagnoli
Keyword(s):  
Total Pressure ◽  
Low Pressure ◽  
Design Parameters ◽  
Structural Constraints ◽  
Aerodynamic Optimization ◽  
Pressure Losses ◽  
Turbine Vane ◽  
Gradient Based ◽  
Adjoint Approach ◽  
Multi Body

Abstract This work presents a 2D optimization of a multi-body turbine vane frame (TVF), a particular configuration that can lead to considerable shortening of the aero-engine shaft as well as weight reduction. Traditionally, the turbine vane frame is used to guide the flow from the high pressure (HP) turbine to the low pressure (LP) turbine. Current designs have a mid turbine frame equipped with non lifting bodies that have structural and servicing functions, while multi-body configurations are characterized by the fact that, in order to shorten the duct length, the mid turbine struts are merged with the LP stator vanes, traditionally located downstream. This design architecture consists therefore of a multi-body vane row, where lifting long-chord struts replace some of the low pressure vane airfoils. However, the bulky struts cause significant aerodynamics losses and penalize the aerodynamics of the small vanes. The objective of the present work is to numerically optimize a TVF geometry with multi-body architecture using a gradient based algorithm coupled with the adjoint approach, enabling the use of a rich design space. Steady-state CFD simulations have been used to this end. The aim of this study is to reduce the total pressure losses of the TVF, while imposing several aerodynamic and structural constraints. The parametrization of the TVF geometry represents the airfoil shapes and their relative pitch-wise positions. The outcome of the optimization is to evaluate the potential improvements introduced by the optimized TVF geometry and to quantify the influence of the different design parameters on the total pressure losses.

scholarly journals Derivation of the Adjoint Drift Flux Equations for Multiphase Flow

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 31 ◽  
Author(s):  
Shenan Grossberg ◽  
Daniel S. Jarman ◽  
Gavin R. Tabor
Keyword(s):  
Multiphase Flow ◽  
Objective Function ◽  
Settling Velocity ◽  
Flow Problem ◽  
Adjoint System ◽  
Drift Flux ◽  
Adjoint Approach ◽  
Continuous Adjoint ◽  
First Time ◽  
Mathematical Derivation

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multiphase flow modeled by the commonly used drift flux equations, together with the adjoint boundary conditions necessary to solve a generic multiphase flow problem. The objective function is defined for such a system, and specific examples derived for commonly used settling velocity formulations such as the Takacs and Dahl models. We also discuss the use of these equations for a complete optimisation process.

Study and Verification of Continuous Adjoint System for Aerodynamic Optimization in Turbomachinery Cascades

2013 ◽  
Author(s):  
Pengfei Zhang ◽  
Haitao Li ◽  
Zhenping Feng
Keyword(s):  
Adjoint Method ◽  
Adjoint System ◽  
Inviscid Flow ◽  
Laminar Flows ◽  
Aerodynamic Optimization ◽  
Adjoint Systems ◽  
Inverse Designs ◽  
Turbine Design ◽  
2D And 3D ◽  
Continuous Adjoint

This paper is a further study of the authors’ previous work on the continuous adjoint method based on the variation in grid node coordinates and Jacobi Matrices of the flow fluxes. This method simplifies the derivation and expression of the adjoint system, and reduces the computation cost. In this paper, the differences between the presented and the traditional methods are analyzed in details by comparing the derivation processes and the adjoint systems. In order to demonstrate the reliability and accuracy of the adjoint system deduced by the authors, the presented method is applied to different optimal problems, which include two inverse designs and two shape optimizations in both 2D and 3D cascades. The inverse designs are implemented by giving the isentropic Mach number distributions along the blade wall for 2D inviscid flow and 3D laminar flow. The shape optimizations are implemented with the objective function of the entropy generation in flow passage for 2D and 3D laminar flows. In the 3D optimal case, this method is validated by supersonic turbine design case with and without mass flow rate constraint. The numerical results testify the accuracy of this adjoint method, which includes only the boundary integrals, and furthermore, the universality and portability of this adjoint system for inverse designs and shape optimizations are demonstrated.

Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids

AIAA Journal ◽  
2007 ◽  
Vol 45 (9) ◽  
pp. 2125-2139 ◽  
Author(s):  
Carlos Castro ◽  
Carlos Lozano ◽  
Francisco Palacios ◽  
Enrique Zuazua
Keyword(s):  
Unstructured Grids ◽  
Aerodynamic Design ◽  
Adjoint Approach ◽  
Continuous Adjoint

scholarly journals A complexity-driven framework for waveform tomography with discrete adjoints

2020 ◽  
Vol 223 (2) ◽  
pp. 1247-1264
Author(s):  
Alexandre Szenicer ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Adjoint Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Frequency Scaling ◽  
Seismic Waveform ◽  
Discrete Adjoint ◽  
Continuous Adjoint Method ◽  
Adjoint Approach ◽  
Pseudo Spectral Method ◽  
Continuous Adjoint

Summary We develop a new approach for computing Fréchet sensitivity kernels in full waveform inversion by using the discrete adjoint approach in addition to the widely used continuous adjoint approach for seismic waveform inversion. This method is particularly well suited for the forward solver AxiSEM3D, a combination of the spectral-element method (SEM) and a Fourier pseudo-spectral method, which allows for a sparse azimuthal wavefield parametrization adaptive to wavefield complexity, leading to lower computational costs and better frequency scaling than conventional 3-D solvers. We implement the continuous adjoint method to serve as a benchmark, additionally allowing for simulating off-axis sources in axisymmetric or 3-D models. The kernels generated by both methods are compared to each other, and benchmarked against theoretical predictions based on linearized Born theory, providing an excellent fit to this independent reference solution. Our verification benchmarks show that the discrete adjoint method can produce exact kernels, largely identical to continuous kernels. While using the continuous adjoint method we lose the computational advantage and fall back on a full-3-D frequency scaling, using the discrete adjoint retains the speedup offered by AxiSEM3D. We also discuss the creation of a data-coverage based mesh to run the simulations on during the inversion process, which would allow to exploit the flexibility of the Fourier parametrization and thus the speedup offered by our method.

Continuous adjoint approach to the Spalart–Allmaras turbulence model for incompressible flows

2009 ◽  
Vol 38 (8) ◽  
pp. 1528-1538 ◽  
Author(s):  
A.S. Zymaris ◽  
D.I. Papadimitriou ◽  
K.C. Giannakoglou ◽  
C. Othmer
Keyword(s):  
Turbulence Model ◽  
Incompressible Flows ◽  
Adjoint Approach ◽  
Continuous Adjoint
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