Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

Montanelli, Hadrien; Montagnac, Marc; Gallard, François

doi:10.1115/1.4030016

Cited by 9 publications

(18 citation statements)

References 30 publications

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“…Also, they solved the Reynolds-Averaged Navier-Stokes (RANS) equations and the one-equation transport Spalart-Allmaras turbulence model and computed the gradients assuming that the eddy viscosity and thermal conductivity are constant. Montanelli et al (2015) achieved a total pressure loss reduction below 1% for the nominal case (outlet M ise = 0.927). The question arises whether the LS89 is indeed optimal, and cannot be optimized any further.…”

Section: Introductionmentioning

confidence: 89%

“…The LS89 was originally designed and optimized at the Von Karman Institute for Fluid Dynamics for a subsonic isentropic outlet Mach number of 0.9 by the inverse method (Van den Braembussche et al, 1990), which is an iterative design method based on both potential and Euler type solvers that uses the difference between the calculated velocity distribution and the required one to modify the profile geometry. Montanelli et al (2015) performed both single-point and multi-point optimizations on the LS89 to reduce the total pressure losses by constraining the outlet mass flow, whilst keeping the leading and trailing edge geometries and the profile thicknesses fixed and using the L-BFGS-B algorithm to explore different geometries with a wing parametrization model. Also, they solved the Reynolds-Averaged Navier-Stokes (RANS) equations and the one-equation transport Spalart-Allmaras turbulence model and computed the gradients assuming that the eddy viscosity and thermal conductivity are constant.…”

Section: Introductionmentioning

confidence: 99%

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Optimization Of The Ls89 Axial Turbine Profile Using A Cad And Adjoint Based Approach

Torreguitart

Verstraete

Mueller

2017

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

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The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for CFD validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents the results of a single point CAD-based adjoint CFD optimization of the LS89. The gradients used for the optimization are obtained via a novel approach in which both the CAD kernel and grid generation are differentiated using Algorithmic Differentiation techniques. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced whilst keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The trailing edge thickness and the axial chord length are kept fixed as manufacturing constraints. The flow is governed by the Reynoldsaveraged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Optimization Of The Ls89 Axial Turbine Profile Using A Cad And Adjoint Based Approach

Torreguitart

Verstraete

Mueller

2017

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

View full text Add to dashboard Cite

show abstract

“…The LS89 was originally designed and optimized at the Von Karman Institute for Fluid Dynamics for a subsonic isentropic outlet Mach number of 0.9 by the inverse method [11], which is an iterative design method based on both potential and Euler type solvers that uses the difference between the calculated velocity distribution and the required one to modify the profile geometry. Montanelli et al [12] performed both single-point and multi-point optimizations on the LS89 to reduce the total pressure losses by constraining the outlet mass flow, while keeping the leading edge (LE) and trailing edge (TE) geometries and the profile thicknesses fixed and using the L-BFGS-B algorithm to explore different geometries with a wing parametrization model. This group also solved the Reynolds-Averaged Navier-Stokes (RANS) equations and the one-equation transport Spalart-Allmaras turbulence model and computed the gradients assuming that the eddy viscosity and thermal conductivity are constant.…”

Section: Introductionmentioning

confidence: 99%

Optimization of the LS89 Axial Turbine Profile Using a CAD and Adjoint Based Approach †

Torreguitart

Verstraete

Mueller

2018

IJTPP

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The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for computational fluid dynamics (CFD) validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents a sound methodology to design and optimize the LS89 using computer-aided design (CAD) at design conditions. The novelty of the study resides in the parametrization of design space, which is done at the CAD level, and the detailed analysis of the aerodynamic performance of the optimized design. Higher level constraints are imposed on the shape, such as the trailing edge thickness, the axial chord length, and G2 geometric continuity between the suction side and pressure side at the leading edge. The gradients used for the optimization are obtained by applying algorithmic differentiation to the CAD kernel and grid generator and the discrete adjoint method to the CFD solver. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced while keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The flow is governed by the Reynolds-averaged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case.

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“…Montanelli et al [46] used the adjoint method to perform a multipoint optimization of a turbine cascade in which the total pressure loss was reduced under a mass flow rate constraint, by solving the Reynolds-averaged Navier-Stokes equations. Papadimitriou et al [45] presents a method to compute the Hessian matrix of a functional in both discrete and continous forms, which was tested in an inverse design of a 2D duct.…”

Section: Adjoint Methodsmentioning

confidence: 99%

“…al. [46] performed both single-point and multi-point optimizations on the LS89 to reduce the total pressure losses by constraining the outlet mass flow, whilst keeping the leading and trailing edge geometries and the profile thicknesses fixed. The L-BFGS-B algorithm was used to explore different geometries with a wing parameterization model.…”

Section: Introductionmentioning

confidence: 99%

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

Sanchez Torreguitart

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The present thesis incorporates the CAD model into an adjoint-based optimization loop and uses it for the shape optimization of a 2D transonic turbine blade mid-section (profile). This is demonstrated by performing a single and multipoint optimization of the LS89 turbine, originally designed at the VKI. Substantial aerodynamic improvements are reported for both design point and off-design conditions.The case is deeply analysed from the flow analysis point of view. The present thesis is a step forward in three main aspects. First, the way the CAD model (for turbomachinery applications) is used within the shape optimization loop.To include the CAD model into the optimization loop, the CAD kernel and the grid generator (multiblock structured) are differentiated using the Algorithmic Differentiation (AD) tool ADOL-C. The advantage of including the CAD model in the design system is that assembly or manufacturing constraints can be imposed on the shape, allowing the optimized model or component to be manufactured. Second, a new definition of the parametric effectiveness indicator is proposed, based on the ability of a set of CAD-based design variables to produce a shape change using the adjoint sensitivities. An interesting thing is that parametric effectiveness considers the design variables can be non-orthogonal to each other and it can be applied to any type of constrained or unconstrained problems. If, in the beginning of the optimization, the parametric effectiveness is high, it is expected to reach a final solution with increased performance. Third, a new adaptive shape parameterization strategy is adopted, which is assisted by the above parametric effectiveness indicator in order to explore the design space more efficiently. The parametric effectiveness, which rates the quality of a CAD based parameterization for optimization, is used in a novel multilevel shape refinement procedure to: (1) introduce the minimum amount of design variables required to modify the shape in the direction the adjoint sensitivities dictate; (2) to create the best parameterization to be used during the optimization. By using the proposed methods and tools, not only the optimal geometry is defined by the CAD, which is the industry adopted standard for the design of components, but also, the designer avoids the use of either too few (slow improvements from cycle to cycle) or too many (increase the computational burden) design variables. The proposed methodology results to be an effective strategy to explore rich design spaces, to improve convergence rate, robustness and final solution of the adjoint-based optimization. Aquesta tesi incorpora el model de CAD en un procés iteratiu d'optimització basat en el mètode adjunt i l'utilitza per a l'optimització de la secció d'una turbina transónica 2D (perfil). Això es demostra realitzant una optimització de punt únic i multipunt de la turbina LS89, originalment dissenyada en el VKI. Es reporten millores aerodinàmiques substancials tant per al punt de disseny com per les condicions fora del disseny. El cas s'analitza en profunditat des del punt de vista aerodinàmic. Aquesta tesi representa un avanç en tres aspectes principals. Primer, la forma en què es fa servir el model CAD (per a aplicacions de turbomàquines) dins el procés d'optimització. Per incloure el model CAD en el bucle d'optimització, s'apliquen tècniques de diferenciació algorítmica (l'eina ADOL-C) al kernel del CAD i el generador de la malla (estructurada i multibloc). L'avantatge d'incloure el model CAD en el sistema de disseny és que es poden imposar restriccions de fabricació a la geometria, i això permet que el disseny ja optimitzat es pugui fabricar. En segon lloc, es proposa una nova definició de l'indicador d'efectivitat paramètrica, basat en la capacitat de produir el canvi en la geometria que dicta el mètode adjunt mitjançant l'ús de les variables de disseny que defineixen el model CAD. Cal destacar que l'efectivitat paramètrica considera que les variables de disseny poden ser no ortogonals entre si i es pot aplicar a qualsevol tipus de problemes restringits o no restringits. Si, al començament de l'optimització, l'efectivitat paramètrica és alta, s'espera que l'optimització arribi a una solució final amb major rendiment. En tercer lloc, s'adopta una nova estratègia de parametrització adaptativa, que és assistida per l'indicador d'efectivitat paramètrica anterior per explorar l'espai de disseny de manera més eficient. L'efectivitat paramètrica, que classifica la qualitat d'una parametrització basada en CAD per a l'optimització, s'utilitza en un nou procediment de refinament multinivell per: (1) introduir la quantitat mínima de variables de disseny requerides per modificar la geometria en la direcció que dicten les sensibilitats del mètode adjunt; (2) per crear la millor parametrització que s'utilitzarà durant l'optimització. En utilitzar els mètodes i eines proposats, no només la geometria òptima està definida en el model CAD, que és l'estàndard adoptat per la indústria per al disseny de components, sinó que també el dissenyador evita l'ús de molt poques (millores lentes de cicle a cicle) o massa variables de disseny (augmenten la càrrega computacional). La metodologia proposada resulta ser una estratègia efectiva per explorar espais de disseny enriquits, millora la taxa de convergència, la solidesa i la solució final de l'optimització basada en el mètode adjunt.

show abstract

Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

Cited by 9 publications

References 30 publications

Optimization Of The Ls89 Axial Turbine Profile Using A Cad And Adjoint Based Approach

Optimization Of The Ls89 Axial Turbine Profile Using A Cad And Adjoint Based Approach

Optimization of the LS89 Axial Turbine Profile Using a CAD and Adjoint Based Approach †

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

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