Design optimization of rocket nozzles in chemically reacting flows

Yumusak, Mine; Eyi, Sinan

doi:10.1016/j.compfluid.2012.05.002

Cited by 24 publications

(11 citation statements)

References 9 publications

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“…The sensitivity of the flame tip temperature and NOx emissions in hydrogen flames to chemistry model parameters was investigated in [142]. Other implementations of adjoint methods in steady reacting flow solvers can be found in [143][144][145]. In time-dependent problems, Lemke et al [146,147] showed that adjoint equations of one-and two-dimensional compressible reacting flows provide accurate gradient information even with stiff nonlinear reaction rates.…”

Section: Reacting Flowsmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.

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Section: Reacting Flowsmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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“…where a 1 , a 2 , …, a 7 are the coefficients of polynomial equations for different species (38) . For mixtures with K number of species, the specific heat at constant pressure is written as (39) C pm =…”

Section: Thermochemical Modelingmentioning

confidence: 99%

Reacting flow analysis of a cavity-based scramjet combustor using a Jacobian-free Newton–Krylov method

Rouzbar

Eyi

2018

Aeronaut. j.

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The scramjet is a rather a new technology and there are many issues related to their operation, especially when it comes to the combustion processes. Combustion in high-speed flows causes various problems such as flame instability and poor fuel–air mixing efficiency. One of the methods used to overcome these problems is to recess a cavity in the combustor wall where a secondary flow is generated. In this study, a computational fluid dynamics (CFD) code is developed to analyse the reacting flow passing through the cavity-based scramjet combustor. The developed code is based on three-dimensional coupled Navier–Stokes and finite rate chemistry equations. An ethylene-air reduced chemical reaction model is used as a fuel–air combination. The Spalart–Allmaras model is utilised for turbulence closure. The non-dimensional form of the flow and chemical reaction equations are discretised using a finite volume method. The Jacobian-Free Newton–Krylov (JFNK) method is used to solve the coupled system of non-linear equations. The JFNK is a matrix-free solution method which improves the computational cost of Newton’s method. The parameters that affect the performance of the JFNK method are studied in the analysis of a scramjet combustor. The influence of the forcing term on the convergence of the JFNK method is studied in the analysis of scramjet combustor. Different upwind flux vector splitting methods are utilised. Various flux limiter techniques are employed for the calculations of higher order flux vectors. The effects of flux vector splitting and flux limiter methods on the convergence and accuracy of the JFNK method are evaluated. Moreover, the variations of the mixing efficiency with fuel injection angles are studied.

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“…The specific heat of k th species can be calculated as; 4 (12) The specific heat of mixture at constant pressure is estimated using…”

Section: A Thermodynamic Modelmentioning

confidence: 99%

“…The adjoint method has more advantages because the adjoint equation is solved only once to evaluate the sensitivities for all design variables. In some recent studies, the adjoint design optimization method has been used for chemically reacting and hypersonic flows [12][13] . In the present study, both the adjoint and direct differentiation methods are used for sensitivity calculations and their performances are compared under different hypersonic flow conditions.…”

Section: Introductionmentioning

confidence: 99%

Aerothermodynamic Shape Optimization of Hypersonic Blunt Bodies

Yumusak¹,

Eyi

2013

21st AIAA Computational Fluid Dynamics Conference

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The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler and the finite rate chemical reaction equations. These coupled equations are solved by using Newton's method. The analytical method is used to calculate the Jacobian matrix. A gradient based numerical optimization is used. Sensitivities are calculated by using the adjoint and direct differentiation methods. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum pressure drag while keeping the maximum temperature smaller than the baseline value. Bezier curves are used for geometry modification. The performance of the optimization method is demonstrated for different hypersonic flow conditions.

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Design optimization of rocket nozzles in chemically reacting flows

Cited by 24 publications

References 9 publications

Adjoint Methods as Design Tools in Thermoacoustics

Adjoint Methods as Design Tools in Thermoacoustics

Reacting flow analysis of a cavity-based scramjet combustor using a Jacobian-free Newton–Krylov method

Aerothermodynamic Shape Optimization of Hypersonic Blunt Bodies

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