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)