CAD-Based Adjoint Optimization of the Stresses in a Radial Turbine

2017 ◽  
Author(s):  
Tom Verstraete ◽  
Lasse Müller ◽  
Jens-Dominik Müller
Keyword(s):  
Structural Model ◽  
Computational Cost ◽  
Test Case ◽  
Analysis Tool ◽  
Full Potential ◽  
Cad Model ◽  
Stress Concentrations ◽  
Radial Turbine ◽  
Gradient Based ◽  
Von Mises

The design optimization of turbomachinery components has witnessed an increased attention in last decade, and is currently used in many companies in the daily design cycle. The adjoint method proves to have the highest potential in this field, however, has still two major shortcomings before its full potential can be used: 1) the shape is mainly parameterized by its grid and the connection to the CAD model is lost, and 2) the optimization process includes only aerodynamic performance and neglects stress and vibration requirements. Within this paper a methodology is developed to include stress calculations into a gradient-based framework, which requires the differentiation of a stress analysis tool. To allow combining the sensitivities from the structural model with those from the aero performance, the CAD model is used for parameterizing the shape, effectively defining a parametrization that controls both the fluid and solid domain that remain linked to each other without creating voids between both models. The method is tested on a radial turbine test case in which the meridional layout is optimized to reduce the maximum von Mises stresses in the material. The results demonstrate a significant reduction in stress concentrations with a limited computational cost.

Adjoint-Based Multidisciplinary, Multipoint Optimization of a Radial Turbine Considering Aerodynamic and Structural Performances

2019 ◽  
Author(s):  
Lasse Mueller ◽  
Tom Verstraete ◽  
Marc Schwalbach
Keyword(s):  
Mechanical Stresses ◽  
Programming Algorithm ◽  
Navier Stokes ◽  
Analysis Tool ◽  
Element Analysis ◽  
Turbine Efficiency ◽  
Radial Turbine ◽  
Design Variables ◽  
Gradient Based ◽  
Adjoint Approach

Abstract This paper presents a multidisciplinary adjoint-based design optimization of a turbocharger radial turbine for automotive applications. The aim is to improve the total-to-static efficiency of the turbine while keeping mechanical stresses below a predefined limit. The search for the optimal design is accomplished using an efficient Sequential Quadratic Programming algorithm considering additional aerodynamic and manufacturing constraints. The aerodynamic performance of the wheel is evaluated by a Reynolds-Averaged Navier-Stokes solver, whereas the maximum stresses in the material are predicted by a Finite Element Analysis tool. The design gradients required by the optimizer are computed with the adjoint approach which provides sensitivity information largely independent of the number of design variables. The results presented in this paper show the clear need to take into account mechanical stresses during optimization, as they are the most restrictive design limitation. However, the gradient-based optimization algorithm is able to effectively keep the stress levels below the critical value while significantly improving the turbine efficiency in a few design cycles.

scholarly journals Adjoint-Based Multi-Point and Multi-Objective Optimization of a Turbocharger Radial Turbine

2019 ◽  
Vol 4 (2) ◽  
pp. 10 ◽  
Author(s):  
Lasse Mueller ◽  
Tom Verstraete
Keyword(s):  
Computational Cost ◽  
Meridional Flow ◽  
Optimal Designs ◽  
Programming Algorithm ◽  
Turbine Wheel ◽  
Radial Turbine ◽  
Trade Offs ◽  
Order Of Magnitude ◽  
Gradient Based ◽  
The Moment

This paper presents a gradient-based design optimization of a turbocharger radial turbine for automotive applications. The aim is to improve both the total-to-static efficiency and the moment of inertia of the turbine wheel. The search for the optimal designs is accomplished by a high-fidelity adjoint-based optimization framework using a fast sequential quadratic programming algorithm. The proposed method is able to produce improved Pareto-optimal designs, which are trade-offs between the two competing objectives, in only a few iterations. This is realized by redesigning the blade shape and the meridional flow channel for the respective target while satisfying imposed aerodynamic constraints. Furthermore, a comparative study with an evolutionary algorithm suggests that the gradient-based method has found the global Pareto front at a computational cost which is about one order of magnitude lower.

Implicit method for the time marching analysis of flutter

2001 ◽  
Vol 105 (1046) ◽  
pp. 199-214 ◽  
Author(s):  
G. S. L. Goura ◽  
K. J. Badcock ◽  
M. A. Woodgate ◽  
B. E. Richards
Keyword(s):  
Krylov Subspace ◽  
Structural Model ◽  
Computational Cost ◽  
Simulation Method ◽  
Standard Test ◽  
Implicit Method ◽  
Test Case ◽  
Sequencing Errors ◽  
Transfinite Interpolation ◽  
Time Marching

Abstract This paper evaluates a time marching simulation method for flutter which is based on a solution of the Euler equations and a linear modal structural model. Jameson’s pseudo time method is used for the time stepping, allowing sequencing errors to be avoided without incurring additional computational cost. Transfinite interpolation of displacements is used for grid regeneration and a constant volume transformation for inter-grid interpolation. The flow pseudo steady state is calculated using an unfactored implicit method which features a Krylov subspace solution of an approximately linearised system. The spatial discretisation is made using Osher’s approximate Riemann solver with MUSCL interpolation. The method is evaluated against available results for the AGARD 445.6 wing. This wing, which is made of laminated mahogany, was tested at NASA Langley in the 1960s and has been the standard test case for simulation methods ever since. The structural model in the current work was built in NASTRAN using homogeneous plate elements. The comparisons show good agreement for the prediction of flutter boundaries. The solution method allows larger time steps to be taken than other methods.

Extension of an Unsteady Hybrid Navier-Stokes/Vortex-Panel Solver to Wind Turbine Aerodynamic Simulations at Higher Yaw Angles

2014 ◽  
Author(s):  
Kensuke Suzuki ◽  
Sven Schmitz ◽  
Hua Ouyang ◽  
Jean-Jacques Chattot
Keyword(s):  
Wind Turbine ◽  
Computational Cost ◽  
Unsteady Aerodynamics ◽  
Navier Stokes ◽  
Test Case ◽  
Analysis Tool ◽  
Horizontal Axis Wind Turbine ◽  
Work Station ◽  
Lower Estimation ◽  
Free Wake

A new analysis tool, an unsteady Hybrid Navier-Stokes/Vortex model, for a horizontal axis wind turbine (HAWT) has been developed for yawed flow by coupling a prescribed wake Vortex Line Method (VLM) with an unsteady Navier-Stokes solver, and its convergence and computational cost have been studied for 10 and 20 degrees of yaw. In this study, a steady viscous solution of a hybrid method is compared in detail with a full-scale Navier-Stokes simulation as a validation. Furthermore, the unsteady hybrid solver is applied to the NREL Unsteady Aerodynamics Experiment (UAE) Phase VI rotor. A test case under 10 degrees of yaw shows that the global power output agrees well with the NREL experiment, and 10 cycles of computation require less than three days using a work station under a serial CPU simulation. The same simulation performed using a super computer is used as reference, and it is estimated that the equivalent case can be obtained about 8 times faster using the work station with the present method, while keeping the same level of accuracy, than a full-domain Navier-Stokes simulation. To treat high yaw cases, new distorted prescribed vortex sheets are modeled with the VLM code. To see the difference between the base helix and the distorted helicoidal wake, unsteady hybrid VLM/Navier-Stokes solutions are examined for selected azimuth angles, and results are contrasted to a free wake BEM and NREL experimental data. For low yaw angles, the base helix approximation agrees well with the distorted helix, and yield better prediction than a free wake model, whereas for high yaw angles of more than 30 degrees, the present distorted wake gave a lower estimation of rotor torque than the free wake solver.

scholarly journals Gradient-Free and Gradient-Based Optimization of a Radial Turbine

2020 ◽  
Vol 5 (3) ◽  
pp. 14
Author(s):  
Nicolas Lachenmaier ◽  
Daniel Baumgärtner ◽  
Heinz-Peter Schiffer ◽  
Johannes Kech
Keyword(s):  
Internal Combustion Engines ◽  
High Efficiency ◽  
Optimization Techniques ◽  
Projection Algorithm ◽  
Strong Impact ◽  
Cad Model ◽  
Combustion Engines ◽  
Radial Turbine ◽  
Gradient Based ◽  
Fine Tune

A turbocharger’s radial turbine has a strong impact on the fuel consumption and transient response of internal combustion engines. This paper summarizes the efforts to design a new radial turbine aiming at high efficiency and low inertia by applying two different optimization techniques to a parametrized CAD model. The first workflow wraps 3D fluid and solid simulations within a meta-model assisted genetic algorithm to find an efficient turbine subjected to several constraints. In the next step, the chosen turbine is re-parametrized and fed into the second workflow which makes use of a gradient projection algorithm to further fine-tune the design. This requires the computation of gradients with respect to the CAD parametrization, which is done by calculating and combining surface sensitivities and design velocities. Both methods are applied successfully, i.e., the first delivers a well-performing turbine, which, by the second method, is further improved by 0.34% in efficiency.

Nanosecond Photodynamics Simulations of a Cis-Trans Isomerization Are Enabled by Machine Learning

2020 ◽  
Author(s):  
Jingbai Li ◽  
Patrick Reiser ◽  
André Eberhard ◽  
Pascal Friederich ◽  
Steven Lopez
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Excited State ◽  
Adaptive Sampling ◽  
Computational Cost ◽  
Ground Truth ◽  
Absolute Error ◽  
Photochemical Reactions ◽  
Computational Techniques ◽  
Full Potential

<p>Photochemical reactions are being increasingly used to construct complex molecular architectures with mild and straightforward reaction conditions. Computational techniques are increasingly important to understand the reactivities and chemoselectivities of photochemical isomerization reactions because they offer molecular bonding information along the excited-state(s) of photodynamics. These photodynamics simulations are resource-intensive and are typically limited to 1–10 picoseconds and 1,000 trajectories due to high computational cost. Most organic photochemical reactions have excited-state lifetimes exceeding 1 picosecond, which places them outside possible computational studies. Westermeyr <i>et al.</i> demonstrated that a machine learning approach could significantly lengthen photodynamics simulation times for a model system, methylenimmonium cation (CH<sub>2</sub>NH<sub>2</sub><sup>+</sup>).</p><p>We have developed a Python-based code, Python Rapid Artificial Intelligence <i>Ab Initio</i> Molecular Dynamics (PyRAI<sup>2</sup>MD), to accomplish the unprecedented 10 ns <i>cis-trans</i> photodynamics of <i>trans</i>-hexafluoro-2-butene (CF<sub>3</sub>–CH=CH–CF<sub>3</sub>) in 3.5 days. The same simulation would take approximately 58 years with ground-truth multiconfigurational dynamics. We proposed an innovative scheme combining Wigner sampling, geometrical interpolations, and short-time quantum chemical trajectories to effectively sample the initial data, facilitating the adaptive sampling to generate an informative and data-efficient training set with 6,232 data points. Our neural networks achieved chemical accuracy (mean absolute error of 0.032 eV). Our 4,814 trajectories reproduced the S<sub>1</sub> half-life (60.5 fs), the photochemical product ratio (<i>trans</i>: <i>cis</i> = 2.3: 1), and autonomously discovered a pathway towards a carbene. The neural networks have also shown the capability of generalizing the full potential energy surface with chemically incomplete data (<i>trans</i> → <i>cis</i> but not <i>cis</i> → <i>trans</i> pathways) that may offer future automated photochemical reaction discoveries.</p>

Gradient-Based Optimization of a Radial Turbine Volute and a Downstream Bend Using Vertex Morphing

2021 ◽  
Author(s):  
Nicolas Lachenmaier ◽  
Daniel Baumg\xe4rtner ◽  
Heinz-Peter Schiffer ◽  
Johannes Kech
Keyword(s):  
Radial Turbine ◽  
Gradient Based

Comparison of Various Discretization Schemes for Simulation of Large Field Case Reservoirs Using Unstructured Grids

2021 ◽  
Author(s):  
Samier Pierre ◽  
Raguenel Margaux ◽  
Darche Gilles
Keyword(s):  
Large Scale ◽  
Unstructured Grids ◽  
Computational Cost ◽  
Large Field ◽  
Real Field ◽  
Test Case ◽  
Generation Task ◽  
Field Case ◽  
Flux Approximation ◽  
Discretization Schemes

Abstract Solving the equations governing multiphase flow in geological formations involves the generation of a mesh that faithfully represents the structure of the porous medium. This challenging mesh generation task can be greatly simplified by the use of unstructured (tetrahedral) grids that conform to the complex geometric features present in the subsurface. However, running a million-cell simulation problem using an unstructured grid on a real, faulted field case remains a challenge for two main reasons. First, the workflow typically used to construct and run the simulation problems has been developed for structured grids and needs to be adapted to the unstructured case. Second, the use of unstructured grids that do not satisfy the K-orthogonality property may require advanced numerical schemes that preserve the accuracy of the results and reduce potential grid orientation effects. These two challenges are at the center of the present paper. We describe in detail the steps of our workflow to prepare and run a large-scale unstructured simulation of a real field case with faults. We perform the simulation using four different discretization schemes, including the cell-centered Two-Point and Multi-Point Flux Approximation (respectively, TPFA and MPFA) schemes, the cell- and vertex-centered Vertex Approximate Gradient (VAG) scheme, and the cell- and face-centered hybrid Mimetic Finite Difference (MFD) scheme. We compare the results in terms of accuracy, robustness, and computational cost to determine which scheme offers the best compromise for the test case considered here.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

scholarly journals A Computational Model to Assess Poststenting Wall Stresses Dependence on Plaque Structure and Stenosis Severity in Coronary Artery

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zuned Hajiali ◽  
Mahsa Dabagh ◽  
Payman Jalali
Keyword(s):  
Coronary Arteries ◽  
Computational Models ◽  
Strong Dependence ◽  
Internal Stresses ◽  
Shear Stresses ◽  
Stress Concentrations ◽  
Opening Pressure ◽  
Fibrous Cap ◽  
Stent Restenosis ◽  
Von Mises

The current study presents computational models to investigate the poststenting hemodynamic stresses and internal stresses over/within the diseased walls of coronary arteries which are in different states of atherosclerotic plaque. The finite element method is applied to build the axisymmetric models which include the plaque, arterial wall, and stent struts. The study takes into account the mechanical effects of the opening pressure and its association with the plaque severity and the morphology. The wall shear stresses and the von Mises stresses within the stented coronary arteries show their strong dependence on the plaque structure, particularly the fibrous cap thickness. Higher stresses occur in severely stenosed coronaries with a thinner fibrous cap. Large stress concentrations around the stent struts cause injury or damage to the vessel wall which is linked to the mechanism of restenosis. The in-stent restenosis rate is also highly dependent on the opening pressure, to the extent that stenosed artery is expanded, and geometry of the stent struts. The present study demonstrates, for the first time, that the restenosis is to be viewed as a consequence of biomechanical design of a stent repeating unit, the opening pressure, and the severity and morphology of the plaque.

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