On the handling of turbulence equations in RANS adjoint solvers

Marta, André C.; Shankaran, Sriram

doi:10.1016/j.compfluid.2013.01.012

Cited by 31 publications

(19 citation statements)

References 12 publications

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“…Because a wide body of work concerning adjoint methods reported in the literature is based on the so-called CEVapproximation [19], it is of practical interest to evaluate if the adoption of such approximation may lead to satisfactory results. To this purpose, the adjoint solutions of the Aachen turbine and the APU turbine computed with and without the CEV approximation are presented and discussed.…”

Section: B Assessment Of the Constant Eddy Viscosity Approximationmentioning

confidence: 99%

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Multistage Turbomachinery Design Using the Discrete Adjoint Method Within the Open-Source Software SU2

Vitale

Pini

Colonna

2020

Journal of Propulsion and Power

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This paper documents a fully turbulent discrete adjoint method for three-dimensional multistage turbomachinery design. The method is based on a duality preserving algorithm and is implemented in the open-source computational fluid dynamics tool SU2. The SU2 Reynolds-averaged Navier-Stokes solver is first extended to treat threedimensional steady turbomachinery flow using a conservative formulation of the mixing-plane coupled to nonreflective boundary conditions. The numerical features of the flow solver are automatically inherited by the discrete adjoint solver, ensuring the same convergence rate of the primal solver. The flow solver is then validated against experimental data available for three turbine configurations, namely, a one-and-half axial turbine stage, a transonic radial turbine coupled to a downstream diffuser, and a supersonic mini-organic Rankine cycle radial turbine operating with a fluid made by a heavy molecule. Finally the adjoint-based optimization framework is applied to the concurrent shape optimization of three rows of the axial turbine, demonstrating the advantages deriving from adopting multirow automated design methods in the context of turbomachinery design.

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Section: B Assessment Of the Constant Eddy Viscosity Approximationmentioning

confidence: 99%

“…In this case, the linearization of the mixing-plane interface is an additional challenge. Furthermore, nearly all the studies were restricted to the use of the constant eddy viscosity (CEV) approximation [19] to avoid dealing with the differentiation of the turbulent transport equations.…”

Section: Introductionmentioning

confidence: 99%

Multistage Turbomachinery Design Using the Discrete Adjoint Method Within the Open-Source Software SU2

Vitale

Pini

Colonna

2020

Journal of Propulsion and Power

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“…The adjoint method, for example, is a sensitivity analysis method that has shown promise in high-dimensional turbomachinery optimization. Marta et al (2013) showed that the gradient can be computed at a cost almost independent of the number of variables, for a legacy (RANS) solver. They accurately computed the gradient of functions of interest, including mass flow, pressure ratio and efficiency, with respect to shape parameters, and presented the integration of such tools in an engineering design framework.…”

Section: Figure 29 Optimization Of a Turbulated Passage Using Hles Amentioning

confidence: 99%

Future Directions of High Fidelity CFD for Aerothermal Turbomachinery Analysis and Design

Laskowski¹,

Kopriva²,

Michelassi³

et al. 2016

46th AIAA Fluid Dynamics Conference

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Computational Fluid Dynamics is a powerful tool used on a daily basis by designers and researchers in the advancement of propulsion technology. As hardware and software technology continue to evolve, the impact on propulsion systems has the potential to be disruptive. With continued development of High Performance Computing, Large Eddy Simulation, High-Order unstructured grid algorithms, optimization and uncertainty quantification it is conceivable that a new frontier of simulation based research, analysis and design capability is in the foreseeable future. In order to accelerate this development collaboration between industry, academia and government labs is required. NomenclatureBR = Bypass Ratio c = Chord Length CFD = Computational Fluid Dynamics DNS = Direct Numerical Simulation HLES = Hybrid Large Eddy Simulation HO = High-Order HPC = High Performance Computing HPC = High Pressure Compressor HPT = High Pressure Turbine IDDES = Improved Delayed Detached Eddy Simulation IDDES-T = Improved Delayed Detached Eddy Simulation with Transition LES = Large Eddy Simulation LPC = Low Pressure Compressor LPT = Low Pressure Turbine Ma = Mach Number 1 Principal Engineer high-fidelity CFD, Advanced Design Tools, 2 MDAO = Multi-Disciplinary Analysis and Optimization OPR = Overall Pressure Ratio Pt = Total Pressure RANS = Reynolds Averaged Navier Stokes Equations Re = Reynolds number Ro = Rossby Number S = Slot Height S1B = Stage 1 Blade S2B = Stage 2 Blade S1N = Stage 1 Nozzle S2N = Stage 2 Nozzle SFC = Specific Fuel Consumption St = Strouhal Number TIT = Turbine Inlet Temperature Tt = Total Temperature TVD = Total Variation Diminishing UQ = Uncertainty Quantification URANS = Unsteady Reynolds Averaged Navier Stokes Equations VKI = von Karman Institute WMLES = Wall-Modeled Large Eddy Simulation WRLES = Wall-Resolved Large Eddy Simulation

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“…To further reduce the development cost, the constant eddy viscosity (CEV) assumption is made, that is, the eddy viscosity is independent from changes of the design. The impact of this approximation was analyzed by [55,56] and is assessed in the course of this section for the present application.…”

Section: Adjoint Solver and Gradient Evaluationmentioning

confidence: 99%

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

Mueller

Verstraete

2017

IJTPP

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Abstract:The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD) workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP) algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier-Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.

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On the handling of turbulence equations in RANS adjoint solvers

Cited by 31 publications

References 12 publications

Multistage Turbomachinery Design Using the Discrete Adjoint Method Within the Open-Source Software SU2

Multistage Turbomachinery Design Using the Discrete Adjoint Method Within the Open-Source Software SU2

Future Directions of High Fidelity CFD for Aerothermal Turbomachinery Analysis and Design

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

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