Abstract
The paper deals with a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flows in two dimensional geometries, in both cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-ɛ model, where low Reynolds number and compressibility effects are included, and a modified eddy-breack up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit, multi-stage, dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.
Actually at Sistemi Elettronici Tecniche di Controllo, Centro Ricerche FIAT, Strada Torino 50, 10043 Orbassano, Italy
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Abbreviations
- AE:
-
Arrhenius activation energy
- c:
-
concentrations fluctuations parameter
- C:
-
constant
- CFL:
-
Courant number
- D:
-
diffusion vector
- e:
-
specific internal energy
- E:
-
total specific energy
- f:
-
function
- f:
-
unknown vector
- F:
-
flux tensor
- H:
-
total enthalpy
- H:
-
optimization matrix
- Hp :
-
turbulence kinetic energy
- I:
-
identity matrix
- j:
-
index of the spatial discretization
- k:
-
index of the multistage algorithm
- L:
-
length scale of turbulent motions
- m:
-
index of the temporal discretization
- M:
-
Mach number
- n:
-
wall normal
- N:
-
unit outward normal
- NV:
-
updating rate
- p:
-
pressure
- P:
-
production of turbulence kinetic energy
- PF:
-
Arrhenius prefactor
- Pr:
-
Prandtl number
- q:
-
heat flux vector
- Q:
-
work due to turbulence
- R:
-
low Reynolds number term
- Re:
-
Reynolds number
- s:
-
stoichiometric ratio
- S:
-
source vector
- Sc:
-
Schmidt number
- t:
-
time
- T:
-
residual
- tu:
-
turbulence intensity
- v:
-
volume
- V:
-
velocity
- x:
-
axial coordinate
- y:
-
radial coordinate
- Y:
-
mass fraction
- β:
-
perturbation speed
- γ:
-
specific heat ratio
- δ r:
-
characteristic volume dimension
- δ t:
-
time step
- δ Σ:
-
surface area
- Δ H:
-
chemical heat release
- χ:
-
thermal conductivity
- θ:
-
multistage scheme coefficient
- Σ:
-
boundary of the fixed volume
- ϱ:
-
density
- μ:
-
viscosity coefficient
- Γ:
-
diffusion coefficient
- τ:
-
viscous stress tensor
- Ω:
-
artificial viscosity coefficient
- ε:
-
turbulence kinetic energy dissipation rate
- ϕ:
-
Schwab-Zeldovich function
- ϕ:
-
reaction rate
- i:
-
inviscid
- fu:
-
fuel
- l:
-
laminar
- ox:
-
oxidizer
- t:
-
turbulent
- v:
-
viscous
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Boretti, A.A. (1989). An explicit Runge-Kutta method for turbulent reacting flows calculations. In: Dervieux, A., Larrouturou, B. (eds) Numerical Combustion. Lecture Notes in Physics, vol 351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51968-8_84
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DOI: https://doi.org/10.1007/3-540-51968-8_84
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