Luiza Bondar Jan ten Thije Boonkkamp Bob Matheij Combustion associated noise in central heating equipment Department of Mechanical Engineering, Combustion Technology Viktor Kornilov Koen Schreel Philip de Goey 1 3 2 4 FLAME FRONT DYNAMICS
Jan 17, 2016
Luiza Bondar
Jan ten Thije Boonkkamp
Bob Matheij
Combustion associated noise in central heating equipment
Department of Mechanical Engineering, Combustion Technology
Viktor Kornilov
Koen Schreel
Philip de Goey
1 32 4
FLAME FRONT DYNAMICS
Outline
• Combustion noise
• Analytical model
• Extension of the model Numerical techniques
Boundary conditions
Conclusions and future plans
Results and conclusions
Combustion noise
efficient,ultra low NOx,
quietand minimal maintenance”
“Compact,
Combustion noise
Goal of the project
• understand combustion noise
• develop a model that predicts combustion noise
Combustion noise
combustion room
gas flow
Bunsen flames
Combustion noise
http://www.em2c.ecp.frLaboratoire Energétique Moléculaire et Macroscopique, Combustion, E.M2.C
acoustic perturbation
flame
acoustic perturbationacoustic perturbation
t t
G<G0 G>G0
flame surface G(r, z, t)=G0
L
GG S G
t
v
the G-equation
r
z
Combustion noise (flame model)
v
nLS
u
v 012
r
zSv
r
zu
t
zL
z(r,t)
r
z
z(r,0)
u
v
Analytical model
• Poiseuille flow, i.e., 0,12
u
R
rvv
• constant laminar burning velocity SL
physical domain
z(r,ts)
Analytical solution technique
• the nonlinear G-equation was solved analytically using the method of characteristics
• the method of characteristics transforms the G equation in a system of 5 ODEs that depend on an auxiliary variable σ
• the solution of the system gives the expressions in term of elliptic integrals for z(r; σ ) and t(r; σ )
Analytical model
We need σ(r, t) to find z(r, t)
physical domain
);(),( njj
nj rztrz
Analytical model (Results)
• the G-equation only cannot account for the flame stabilisation • a stabilisation process based on the physics of the model was derived to stabilise the flame
• the flame stabilises in finite time
• the nondimensional stabilisation time is ≈1 independently of the value of
• the time needed for a flame to stabilise is directly proportional with and inversely proportional with R • the flame reaches a stationary position that is equal with the steady solution of the G-equation (subject to BC z(δ)=0)
LSv /
LS
• variation of the flame surface area
• variation of the burning velocity due to oscillation of the flame front curvature and flow strain rate
• interaction of the flame with the burner rim
Extension of the model
Extension of the model
nvnv t S
0
0
2 ( )G G
G
n n
n
curvature
stream lines
SL
SL
SL SL
strain rate S
0S0S
SSSS LLL LL 00
Extension of the model
0( ) LH G v G S G
0LS L
G-equation
0( ) LLP G S G hyperbolic term
parabolic term
)( GLt
G
PHL
GS L
SSSS LLL LL 00
parameters of the flame
Extension of the model (Numerical Techniques)
Level set method (initialization t=0)
),( ji yx rbyaxyxG jiji 220 )()(),(
);;();();;;;(1
xyyyxxn
yxn
xyyyxxyxn
nn
GGGPGGHGGGGGLt
GG
Extension of the model (Numerical techniques)
use numerical schemes that deal with steep gradientsENO schemes (Essentially Non Oscillatory)
• avoid the production of numerical oscillations near the steep gradients
• have high accuracy in smooth regions
• computationally cheap in WENO (Weighted ENO) form
• boundary conditions are difficult to implement
Extension of the model (Numerical techniques)
WENO
xixi-1xi-2xi-3 xi+1 xi+2
convex combination with adaptive weights of the
approximations of on the stencils)( ix xf
)( ix xf
01
2
the “smoother” the approximation ofthe larger the weight
)( ix xf
Example
Extension of the model (Boundary conditions)
0-1-2-3 1 2
)( 0xf x
???
“discontinuous” big values
Extension of the model (Boundary conditions)
G(x, y) is the distance from (x, y) to the interface
Extension of the model (Examples)
external flow velocity expansion in the normal direction
Extension of the model (Examples)
shrinking with breaking(normal direction)
collapsing due to the mean curvature
Extension of the model (Examples)
oscillation of a flame front due to velocity perturbations
Extension of the model (Conclusions)
• a high order accuracy numerical scheme was implemented and tested to capture the dynamics of the flame front
(C++ and Numlab )
• a good method to implement the boundary conditions was found
• current research involves applying the method to the Bunsen flame problem
• treat the flame with the “open curve” approach
• input from Lamfla
• analyze and compare the results with the experiments
Extension of the model (Conclusions)