Numerical investigation of sustained planar detonation waves in a periodic domain

Gupta, Prateek; Schwinn, Kyle S.; Lodato, Guido; Slabaugh, Carson D.; Scalo, Carlo

doi:10.2514/6.2018-3240

Cited by 5 publications

(6 citation statements)

References 20 publications

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“…Vector ∂W is composed of 3 + N s entropy waves namely ∂W 1 , ∂W 2 , ∂W 3 , ∂W 5+1 , ⋯, ∂W 5+Ns , propagating at u n = u.n = un x + vn y + wn z and of two acoustic waves ∂W + and ∂W − propagating respectively at u n + c and u n − c. In Eqs. (38)(39)(40), Q = (ρ, u, v, w, P, Y 1 , ⋯, Y Ns ) T has not to be confused with the set of primitive variables used here at FP as explained in paragraph 3.3 where density is replaced by temperature as first variable. Moreover, the transformation matrix (∂Q ∂U) was extended to a multispecies thermally perfect gas compared to the work of Fievet et al [37] considering a monospecies calorically perfect gas.…”

Section: Wave Equationmentioning

confidence: 99%

“…They proved to be very promising for the field of turbulent combustion to capture the main flame structures and the most reacting species in a gas mixture. However, to the author's knowledge, only Gupta et al [39] have done combustion simulation using a strong discontinuous method, here the SD approach, and it was for one-dimensional detonation. Consequently, there is a need to explore the ability of such methods to compute combustion applications when a multispecies gas is considered along with combustion models and stiff reactive source terms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extension of the Spectral Difference method to combustion

Marchal¹,

Deniau²,

Boussuge³

et al. 2021

Preprint

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A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations (NSE) is presented. The classical SD algorithm is shown to be unstable when a multispecies gas where thermodynamic properties depend on temperature and species mass fractions is considered. In that case, a modification of the classical algorithm was successfully employed making it stable. It uses the fact that it is better for the multispecies case to compute primitive variables from conservative variables at solution points and then extrapolate them at flux points rather than extrapolating conservative variables at flux points and reconstruct primitive variables on these points. Characteristic, wall and symmetry boundary conditions for reactive flows in the SD framework are also introduced. They all use the polynomial form of the variables and of the fluxes to impose the correct boundary condition at a boundary flux point. Validation test cases on one-dimensional and two-dimensional laminar flames have been performed using both global chemistry and Analytically Reduced Chemistry (ARC). Results show excellent agreement with the reference combustion code AVBP validating the implementation of this SD method on laminar combustion.

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Section: Wave Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extension of the Spectral Difference method to combustion

Marchal¹,

Deniau²,

Boussuge³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…It gives a scheme order of p + 1. The SD method is becoming quite mature with simulations of wall bounded-turbulent flows 2016), bypass transition (Pinto and Lodato 2019;Lodato et al 2021); shocks and detonations (Gupta et al 2018;Lodato 2019;Tofailli et al 2021) and with moving meshes (Yu et al 2011;Zhang et al 2016).…”

Section: Introductionmentioning

confidence: 99%

“…The recent development of non-reflecting boundary conditions specially adapted to the SD and FR algorithms by Fiévet et al (2020) on tensor-product cells, has opened a way to the simulation of combustion in confined media using these methods. To the author's knowledge, only Gupta et al (2018) and Tofailli et al (2021) have published combustion simulations using the SD approach, and it was only for one-dimensional (1D) detonation. Consequently, there is a need to explore the ability of such methods to compute combustion applications when a multi-species gas is considered along with combustion models and stiff reactive source terms.…”

Section: Introductionmentioning

confidence: 99%

Extension of the Spectral Difference Method to Premixed Laminar and Turbulent Combustion

Marchal

Deniau

Boussuge

et al. 2023

Flow Turbulence Combust

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A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations is presented. The classical SD algorithm is shown to be unstable when a multi-species gas where thermodynamic properties depend on temperature and species mass fractions is considered. It is demonstrated that computing primitive variables from conservative variables at solution points and extrapolating them at flux points, rather than conservative variables, make the SD method stable for such case. In addition, a new methodology, more stable, for computing the diffusive fluxes at an interface is detailed. To allow the simulation of combustion, characteristic and wall boundary conditions for multi-species flows in the SD framework are introduced and the thickened flame turbulent combustion model is adapted to the SD context. Validation test cases from one-dimensional and two-dimensional Flow, Turbulence and Combustion laminar flames to a three-dimensional turbulent flame have been performed showing excellent agreement with each of the reference solutions. To the authors' knowledge, this is the first time that a 3D turbulent flame is simulated using the SD method. The interest of employing a high-order method, such as the SD, in combustion is demonstrated: high values of the polynomial degree improve the quality of the results which advocates for the use of p-refinement when simulating reacting flows.

show abstract

Section: Introductionmentioning

confidence: 99%

Extension of the Spectral Difference method to premixed laminar and turbulent combustion

Marchal

Deniau

Boussuge

et al. 2022

Preprint

View full text Add to dashboard Cite

A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations is presented. The classical SD algorithm is shown to be unstable when a multi-species gas where thermodynamic properties depend on temperature and species mass fractions is considered. It is demonstrated that computing primitive variables from conservative variables at solution points and extrapolating them at flux points, rather than conservative variables, make the SD method stable for such case. In addition, a new methodology, more stable, for computing the diffusive fluxes at an interface is detailed. To allow the simulation of combustion, characteristic and wall boundary conditions for multi-species flows in the SD framework are introduced and the thickened flame turbulent combustion model is adapted to the SD context. Validation test cases from one-dimensional and two-dimensional laminar flames to a three-dimensional turbulent flame have been performed showing excellent agreement with each of the reference solutions. To the authors' knowledge, this is the first time that a 3D turbulent flame is simulated using the SD method. The interest of employing a high-order method, such as the SD, in combustion is demonstrated: high values of the polynomial degree improve the quality of the results which advocates for the use of p-refinement when simulating reacting flows.

show abstract

Numerical investigation of sustained planar detonation waves in a periodic domain

Cited by 5 publications

References 20 publications

Extension of the Spectral Difference method to combustion

Extension of the Spectral Difference method to combustion

Extension of the Spectral Difference Method to Premixed Laminar and Turbulent Combustion

Extension of the Spectral Difference method to premixed laminar and turbulent combustion

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