Direct numerical simulations of a reacting mixing layer with chemical heat release

McMurtry, Patrick; Jou, Wen‐Huei; Metcalfe, Ralph W.; Riley, James J.

doi:10.2514/6.1985-143

Cited by 48 publications

(55 citation statements)

References 5 publications

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“…(8). This is not the case when a backward approximation of ∂ρ ∂t is used to compute the source term of a linear Poisson equation for δ P as proposed earlier [3,6] (see also Subsection 3.3). The other advantage is that the pressure terms remain energy conserving in the high-R e number limit, as discussed in the following subsection.…”

Section: Scheme In Non-conservative Form: Advscmentioning

confidence: 99%

“…(43), is with constant coefficient and can be solved very efficiently. Subsequently, it seems that this approach was used in all the previous studies dealing with low-Mach number flows [1][2][3][4][5][6][7][8]. The approach involving a Poisson equation with variable coefficient as in Subsections 3.1 and 3.2 was preferred in [11][12][13].…”

Section: Scheme With Approximate Poisson Equation: Divsc ρmentioning

confidence: 99%

“…γ M 2 . To derive the low-Mach number equations, one expands the dependent variables as a power series in = γ M 2 , which is a small parameter (see [1,3,6] for details on the derivation of the low-Mach number equations). Substituting these expansions into the compressible Navier-Stokes equations and collecting the lowest order terms in yields ∂ρ ∂t + ∂ρu j ∂ x j = 0 (1)…”

Section: Low-mach Number Approximationmentioning

confidence: 99%

“…At the same time, in flows where the dominating mechanism is free, forced or mixed convection, the acoustical mode of energy carries only a small fraction of the energy present in the fluctuating part of the flow. These observations led several authors [1][2][3][4] to propose a set of low-Mach number equations which do not contain acoustic waves but can still describe the entropy and vorticity modes as well as compressibility due to exothermicity of chemical reactions. A fractional-step method is used most often, the pressure field being obtained by solving a Poisson equation with the time derivative of the density field as part of the source term [3,5] destabilizing part of the algorithm [6].…”

Section: Introductionmentioning

confidence: 99%

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Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

159

149

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Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite-difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non-linear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.

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Section: Scheme In Non-conservative Form: Advscmentioning

confidence: 99%

Section: Scheme With Approximate Poisson Equation: Divsc ρmentioning

confidence: 99%

Section: Low-mach Number Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

159

149

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“…The time integration is performed using the second-order Adams-Bashforth method. The pressure correction scheme is based on the projection method [28]. Further details on the governing equations can be found in Ref.…”

Section: Simulation Detailsmentioning

confidence: 99%

Scalar statistics in variable property turbulent channel flows

2017

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Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ, viscosity μ, and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Re τ ≡ Re τ √ (ρ/ρ w )/(μ/μ w ) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Re τ is the friction Reynolds number based on wall values), and the local Prandtl number Pr = Pr w (μ/μ w )/(λ/λ w ) (Pr w is the molecular Prandtl number based on wall values). Near-wall gradients in Re τ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Re τ variations and only exhibits a Pr -dependent shift.

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A comparative study of high‐order variable‐property segregated algorithms for unsteady low Mach number flows

Knikker

2011

Numerical Methods in Fluids

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SUMMARYIn this paper, five different algorithms are presented for the simulation of low Mach flows with large temperature variations, based on second-order central-difference or fourth-order compact spatial discretization and a pressure projection-type method. A semi-implicit three-step Runge-Kutta/Crank-Nicolson or second-order iterative scheme is used for time integration. The different algorithms solve the coupled set of governing scalar equations in a decoupled segregate manner. In the first algorithm, a temperature equation is solved and density is calculated from the equation of state, while the second algorithm advances the density using the differential form of the equation of state. The third algorithm solves the continuity equation and the fourth algorithm solves both the continuity and enthalpy equation in conservative form. An iterative decoupled algorithm is also proposed, which allows the computation of the fully coupled solution. All five algorithms solve the momentum equation in conservative form and use a constantor variable-coefficient Poisson equation for the pressure. The efficiency of the fourth-order compact scheme and the performances of the decoupling algorithms are demonstrated in three flow problems with large temperature variations: non-Boussinesq natural convection, channel flow instability, flame-vortex interaction.

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Direct numerical simulations of a reacting mixing layer with chemical heat release

Cited by 48 publications

References 5 publications

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Scalar statistics in variable property turbulent channel flows

A comparative study of high‐order variable‐property segregated algorithms for unsteady low Mach number flows

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