1. 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 1324 FLAME FRONT DYNAMICS

2. Outline Combustion noise Analytical model Extension of the model  Numerical techniques  Boundary conditions  Conclusions and future plans  Results and conclusions

3. Combustion noise efficient, ultra low NOx, quiet and minimal maintenance” “Compact,

4. Combustion noise Goal of the project understand combustion noise develop a model that predicts combustion noise

5. Combustion noise combustion room gas flow Bunsen flames

6. Combustion noise http://www.em2c.ecp.fr Laboratoire Energétique Moléculaire et Macroscopique, Combustion, E.M2.C acoustic perturbation flame acoustic perturbation t t

7. G<G 0 G>G 0 flame surface G(r, z, t)=G 0 the G-equation r z Combustion noise (flame model) u v z(r,t)

8. r z z(r,0) u v Analytical model Poiseuille flow, i.e., constant laminar burning velocity S L physical domain z(r,t s )

9. 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 )

10. Analytical model We need σ(r, t) to find z(r, t) physical domain

11. 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)

12. 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

13. curvature stream lines SLSL SLSL SLSL SLSL strain rate

14. Extension of the model G-equation hyperbolic term parabolic term parameters of the flame

15. Extension of the model (Numerical Techniques) Level set method (initialization t=0)

16. Extension of the model (Numerical techniques) use numerical schemes that deal with steep gradients ENO 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

17. Extension of the model (Numerical techniques) WENO xixi x i-1 x i-2 x i-3 x i+1 x i+2 convex combination with adaptive weights of the approximations of on the stencils 0 1 2 the “smoother” the approximation of the larger the weight Example

18. Extension of the model (Boundary conditions) 0-2-312 ??? “discontinuous” big values

19. Extension of the model (Boundary conditions) G(x, y) is the distance from (x, y) to the interface

20. Extension of the model (Examples) external flow velocity expansion in the normal direction

21. Extension of the model (Examples) shrinking with breaking (normal direction) collapsing due to the mean curvature

22. Extension of the model (Examples) oscillation of a flame front due to velocity perturbations

23. 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

24. treat the flame with the “open curve” approach input from Lamfla analyze and compare the results with the experiments Extension of the model (Conclusions)