±3-Sigma based design optimization of 3D Finocyl grain

Kamran, Ali; Liang, Gengchiau; Rafique, Amer Farhan; Zeeshan, Qasim

doi:10.1016/j.ast.2012.02.011

Cited by 16 publications

(17 citation statements)

References 22 publications

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“…In moment matching formulation, The g( Z ) is assumed to be a normal distribution function. For example, the popular approaches of applying moment matching method include six sigma method (Sang and Kwon, 2015) as having less than 3.4 failures per million possibilities and three sigma method with a success rate of 93 per cent (Kamran et al , 2013).…”

Section: Uncertainty-based Design Optimization Of Natural-laminar-flow Airfoilmentioning

confidence: 99%

Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles

Zhao

Gao

2019

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Purpose The high probability of the occurrence of separation bubbles or shocks and early transition to turbulence on surfaces of airfoil makes it very difficult to design high-lift and high-speed Natural-Laminar-Flow (NLF) airfoil for high-altitude long-endurance unmanned air vehicles. To resolve this issue, a framework of uncertainty-based design optimization (UBDO) is developed based on an adjusted polynomial chaos expansion (PCE) method. Design/methodology/approach The γ ̄Re-θt transition model combined with the shear stress transport k-ω turbulence model is used to predict the laminar-turbulent transition. The particle swarm optimization algorithm and PCE are integrated to search for the optimal NLF airfoil. Using proposed UBDO framework, the aforementioned problem has been regularized to achieve the optimal airfoil with a tradeoff of aerodynamic performances under fully turbulent and free transition conditions. The tradeoff is to make sure its good performance when early transition to turbulence on surfaces of NLF airfoil happens. Findings The results indicate that UBDO of NLF airfoil considering Mach number and lift coefficient uncertainty under free transition condition shows a significant deterioration when complicated flight conditions lead to early transition to turbulence. Meanwhile, UBDO of NLF airfoil with a tradeoff of performances under both fully turbulent and free transition conditions holds robust and reliable aerodynamic performance under complicated flight conditions. Originality/value In this work, the authors build an effective uncertainty-based design framework based on an adjusted PCE method and apply the framework to design two high-performance NLF airfoils. One of the two NLF airfoils considers Mach number and lift coefficient uncertainty under free transition condition, and the other considers uncertainties both under fully turbulent and free transition conditions. The results show that robust design of NLF airfoil should simultaneously consider Mach number, lift coefficient (angle of attack) and transition location uncertainty.

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Section: Uncertainty-based Design Optimization Of Natural-laminar-flow Airfoilmentioning

confidence: 99%

Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles

Zhao

Gao

2019

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“…(1), in which the surface normal is computed spectrally using Eqs. (3) and (5). Time integration of Eq.…”

Section: Calculation Of Geometric Quantitiesmentioning

confidence: 99%

“…A number of analytical methods have been developed to study simple two-dimensional (2-D) geometries [1][2][3]. For more complex grain shapes or for three-dimensional (3-D) geometries, CAD software has been used to compute the evolving surface [4,5]. A Hamilton-Jacobi problem can also be resolved to compute the time evolution of the burning surface [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Accurate Computation of Grain Burning Coupled with Flow Simulation in Rocket Chamber

Gueyffier¹,

Roux²,

Fabignon³

et al. 2015

Journal of Propulsion and Power

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In this paper, we present a novel numerical approach for predicting the fluid flow in a solid rocket motor chamber with burning propellant grain. We use a high-order technique to track the regressing grain surface. Spectral convergence toward the exact burning surface is achieved thanks to Fourier differentiation. For the computation of the internal chamber fluid flow, we make use of a body-fitted volume mesh deforming with the grain surface. We describe several methods to deform the volume mesh and to keep good mesh element quality without global remeshing. We then couple the surface and volume approaches and integrate them into a complex code for compressible, multispecies, turbulent flow simulations. Thanks to these methods, we are able to exhibit one of the first three-dimensional simulations of the internal flow in a realistic solid rocket motor coupled to complex grain surface regression. In prior work, burning grain surface methods have only been coupled with one-dimensional internal ballistics solvers.

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“…Gaussian curvature at each point of the surface is obtained using the expression The surface normal is computed spectrally using (3) and (5). Markers are transported in a lagrangian manner using equation (1) and using simple forward Euler explicit time stepping.…”

Section: Spectral Methods For Burning Front Surface and Surface Mmentioning

confidence: 99%

“…A number of analytical methods have been developed to study simple 2-D geometries [1][2][3]. For more complex grain shapes or for 3-D geometries, CAD software has been used by some authors [4,5] while others resolve a HamiltonJacobi problem for the time evolution of the burning surface [6][7][8]. The level set method was used in [9,[11][12][13] to predict grain burning.…”

Section: Introductionmentioning

confidence: 99%

High-order computation of burning propellant surface and simulation of fluid flow in solid rocket chamber

Gueyffier

Roux

Fabignon

et al. 2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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In this paper, we present a numerical approach for predicting fluid flows in solid rocket motor (SRM) chambers. We use a novel high-order technique to track the burning grain surface. Spectral convergence toward the exact burning surface is achieved thanks to Fourier differentiation. In addition, we make use of a body-fitted mesh deforming with the burning surface and present a method to avoid manual remeshing. We describe several methods to deform the volume mesh and to keep good mesh element quality during the computation. We then couple the surface and volume approaches. The resulting coupled method is able to handle the formation of geometric singularities on the burning surface while keeping constant surface and volume mesh topology. This geometrical approach is integrated into a complex code for compressible, multi-species, turbulent flow simulations. Applications to the simulation of the internal flow in realistic solid rocket motors with complex grain geometry are then presented.

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±3-Sigma based design optimization of 3D Finocyl grain

Cited by 16 publications

References 22 publications

Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles

Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles

Accurate Computation of Grain Burning Coupled with Flow Simulation in Rocket Chamber

High-order computation of burning propellant surface and simulation of fluid flow in solid rocket chamber

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