Shape optimization of flow field improving hydrodynamic stability

Nakazawa, Takashi; Azegami, Hideyuki

doi:10.1007/s13160-015-0201-9

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…where ∇ p σ Numerical has been calculated with the numerical version of matrices B p ( q, p), A p (q, p) using Eqs. (19) and (20). The results are shown in Fig.…”

Section: B Analytic Test Casementioning

confidence: 95%

“…The resulting vectors in Eqs. (19) and (20) comprise nonzero elements only in those positions related with the surface mesh nodes of interest and their stencil. The discrete gradients ∇ X σ are recovered by the discrete inner product, •, • , of vectors A p (q, X) and B p ( q, X) with the adjoint base flow and adjoint global mode, respectively,…”

Section: A Numerical Implementation and Methodologymentioning

confidence: 99%

“…(3) Compute the adjoint global modes q + based on the discrete adjoint operator of the Jacobian, A(q, X + 2 d), followed by the matrix B p ( q, X) and the vector A p (q, X), using Eqs. (19) and (20). (9) Calculate the sensitivity to geometrical changes, ∇ X σ , using Eq.…”

Section: A Numerical Implementation and Methodologymentioning

confidence: 99%

“…Heuveline and Strauß [1] pioneered the use of the least stable eigenvalue as the cost function of an optimization process, implementing a sequential quadratic programming (SQP) methodology for the optimization of the flow over a circular cylinder using finite differences in a continuous approach. Nakazawa and Azegami [19] and, later on, Kiriyama et al [2], following a continuous approach, proposed a shape optimization problem based on the evaluation of a shape derivative function from an incompressible Navier-Stokes laminar flow field. The use of a Lagrange multiplier method, in which the cost function is the real part of the least stable eigenvalue, has allowed one to optimize open and enclosed flow field configurations.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

et al. 2020

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We derive a discrete framework for the calculation of eigenvalue sensitivity to geometric deformations. We apply the technique to the steady compressible Navier-Stokes and Reynolds-averaged Navier-Stokes (RANS) flows. The analysis enables one to control (reduce or increase) the amplification rate or frequency associated to the least stable global mode, which is identified using stability analysis. A methodology using a discrete framework is proposed, allowing one to recover the gradients in compressible and turbulent flows. The potential of the resulting shape gradients is evaluated on the well-known circular cylinder flow problem and on a RANS turbulent flow scenario to control the buffet onset on a NACA0012 airfoil. The predicted deformations show excellent performance on the stabilization or excitation, and frequency control, of the global modes and for the two cases tested.

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“…where ∇ p σ Numerical has been calculated with the numerical version of matrices B p ( q, p), A p (q, p) using Eqs. (19) and (20). The results are shown in Fig.…”

Section: B Analytic Test Casementioning

confidence: 95%

Section: A Numerical Implementation and Methodologymentioning

confidence: 99%

Section: A Numerical Implementation and Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

et al. 2020

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“…The critical Reynolds numbers are, respectively, decreasing and increasing. Next, for controlling flow stability more directly, Nakazawa and Azegami [17] reported a pioneering shape optimization method used to stabilize the disturbances. The method is based on linear stability theory.…”

Section: Introductionmentioning

confidence: 99%

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Nakazawa

Nakajima

2019

IIS

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This paper presents optimal design using Adaptive Mesh Refinement (AMR) with shape optimization method. The method suppresses time periodic flows driven only by the non-stationary boundary condition at a sufficiently low Reynolds number using Snapshot Proper Orthogonal Decomposition (Snapshot POD). For shape optimization, the eigenvalue in Snapshot POD is defined as a cost function. The main problems are non-stationary Navier-Stokes problems and eigenvalue problems of POD. An objective functional is described using Lagrange multipliers and finite element method. Two-dimensional cavity flow with a disk-shaped isolated body is adopted. The non-stationary boundary condition is defined on the top boundary and non-slip boundary condition respectively for the side and bottom boundaries and for the disk boundary. For numerical demonstration, the disk boundary is used as the design boundary. Using H 1 gradient method for domain deformation, all triangles over a mesh are deformed as the cost function decreases. To avoid decreasing the numerical accuracy based on squeezing triangles, AMR is applied throughout the shape optimization process to maintain numerical accuracy equal to that of a mesh in the initial domain. The combination of eigenvalues that can best suppress the time periodic flow is investigated.

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Solution of Shape Optimization Problem and Its Application to Product Design

Azegami

2016

Mathematical Analysis of Continuum Mechanics and Industrial Applications

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Shape optimization of flow field improving hydrodynamic stability

Cited by 9 publications

References 22 publications

Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Solution of Shape Optimization Problem and Its Application to Product Design

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