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

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.

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.

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.

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

2020 ◽  
Author(s):  
Nicolas Lachenmaier ◽  
Daniel Baumgärtner ◽  
Heinz-Peter Schiffer ◽  
Johannes Kech
Keyword(s):  
Shape Optimization ◽  
Combustion Engine ◽  
Pressure Ratio ◽  
Load Condition ◽  
Adjoint Methods ◽  
Turbine Wheel ◽  
Pressure Drops ◽  
Radial Turbine ◽  
Efficiency Increase ◽  
Gradient Based

Abstract The higher the efficiency of a turbocharger’s radial turbine, the lower is the necessary pressure ratio to deliver a specified power to the compressor. This, in turn, reduces the fuel consumption of the internal combustion engine as a lower pressure upstream of the turbine increases the obtained charge-cycle work. In this paper, two components of a nozzled radial turbine system are redesigned: Both the volute upstream and the 90°-bend downstream of the turbine wheel will be improved. To reduce pressure drops, a gradient-based shape optimization workflow based on adjoint methods is applied. The scheme works in an iterative manner, i.e. after running a primal and an adjoint simulation to gather shape sensitivities, the geometry is deformed and the next iteration is started. A steepest descent approach is used to guide the optimization process. As parametrization strategy the Vertex Morphing Method is used to explore design potential, while maintaining smooth surfaces. Both the volute and the bend are optimized successfully leading to an efficiency increase of the turbine system of up to 3%, depending on the load condition.

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.

Gradient based system-level diagnosis

2007 ◽  
Vol 51 (1-2) ◽  
pp. 43
Author(s):  
Balázs Polgár ◽  
Endre Selényi
Keyword(s):  
System Level ◽  
Gradient Based

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

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