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An analogue study for flame flickering

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Abstract

An analogue experiment is proposed to simulate flame flickering comprising a free ascending column fed on its side with a light gas (helium) emerging from a vertical slot in ambient air. The convective motion of the helium jet is considered to represent the motion of burnt gases of buoyant jet flames. The helium jet is accelerated by buoyancy effects and the flow field is similar to that of burnt gases observed for real buoyant flames. The vertical velocity profile of the steady helium jet is measured at different vertical distances. The unsteady helium jet is also studied by measuring the instability frequency as a function of ambient pressure at different injection flow rates, and by analyzing the tomography images of the helium jet. The instability morphology is the same as that observed on real buoyant flames. We conclude that this type of instability can be approximately characterized by the maximum vertical velocityu max, and the distance δ betweenu max in the helium ascending column andu = o in the ambient air. For this type of instability the local vorticity is proportional to\(\frac{{u_{\max } }}{\delta }\) which can be influenced by gravity and ambient pressure. Theoretical prediction of the instability frequency as a function of gravity and ambient pressure has been obtained, and is in good agreement with the experimental results.

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Abbreviations

C 1,C 2 :

constants

F :

instability frequency

F c :

critical frequency

F m :

the most amplified frequency

F (K, ε):

function defined in (11)

g :

gravitational acceleration

g′:

reduced gravity acceleration g(σ0-σ*)/σ*

k :

real wave number of the disturbance

K :

reduced wave numberK=2kδ

K c :

reduced wave number of the critical instability mode

K m :

nondimensional wavenumber of the most amplified mode

L :

vertical characteristic length (in x direction)

P :

ambient pressure

u :

local vertical buoyant velocity (inx direction)

u max :

local maximum vertical velocity

v :

local velocity component iny direction (horizontal)

V 0 :

injection velocity of helium (iny direction)

x :

vertical distance measured from the leading edge of boundary layer

y :

horizontal distance measured from the exit plane of the vertical slot

Z(K, ε):

function defined in equation (11)

δ:

distance betweenu max in the helium ascending column andu = o in the ambient air

ε:

\(\varepsilon = \frac{{\rho _0 - \rho ^* }}{{\rho _0 + \rho ^* }}\)

λ:

wavelength of instability

λ c :

critical wavelength

λ m :

the most amplified wavelength

σ* :

helium density at slot exit

σ0 :

ambient air density

μ* :

helium dynamic viscosity at slot exit

v * :

helium kinematic viscosity at slot exit

ω:

complex number presented in disturbancee i(kx+ωt)

ω i :

imaginary part of ω, representing the amplification rate of disturbance

ω r :

real part of ω, where (ω r /k) represents the group velocity

μ:

reduced complex number of ω, defined\(\Omega = \frac{\omega }{{ku_{max} }}\)

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Authors and Affiliations

  1. Laboratoire d'Aérothermique, CNRS 4 ter Route des Gardes, F-92190, Meudon, France

    T. Yuan & D. Durox

  2. Institut de Mécanique de Grenoble, U.M.R. 101 BP 53X, F-38041, Grenoble, France

    E. Villermaux

Authors
  1. T. Yuan
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  2. D. Durox
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  3. E. Villermaux
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Yuan, T., Durox, D. & Villermaux, E. An analogue study for flame flickering. Experiments in Fluids 17, 337–349 (1994). https://doi.org/10.1007/BF01874414

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