Numerical investigation of symmetry breaking and critical behavior of the acoustic streaming field in high-intensity discharge lamps

Abstract

For energy efficiency and material cost reduction it is preferred to drive highintensity discharge lamps at frequencies of approximately 300 kHz. However, operating lamps at these high frequencies bears the risk of stimulating acoustic resonances inside the arc tube, which can result in low frequency light flicker and even lamp destruction. The acoustic streaming effect has been identified as the link between high frequency resonances and low frequency flicker. A highly coupled 3D multiphysics model has been set up to calculate the acoustic streaming velocity field inside the arc tube of high-intensity discharge lamps. It has been found that the velocity field suffers a phase transition to an asymmetrical state at a critical acoustic streaming force. In certain respects the system behaves similar to a ferromagnet near the Curie point. It is discussed how the model allows to investigate the light flicker phenomenon. Concerning computer resources the procedure is considerably less demanding than a direct approach with a transient model.

Nonlinear behavior in high-intensity discharge lamps

“…Hence, Ψ < 0 indicates that somewhere along the z-axis a downward directed AS force exists that is larger than the upward-directed buoyancy force at the same point. The results of the previous investigation show that symmetry breaking is induced by the downward directed flow with a minimal strength of Ψ ≈ 170 mm/s [11]. In the back coupled model, the flow field does not show symmetry breaking.…”

“…The FE model used to simulate the processes inside the arc tube has been described in detail in a recent publication [11]. Therefore, only an outline of the model is presented.…”

“…In Section 2 it was mentioned that a nonlinear oscillator with a softening spring shows a symmetry breaking bifurcation when the excitation amplitude F exceeds a critical value. We previously reported the detection of a symmetry breaking transition in our simulation results [11]. For this we introduced a control parameter S, which allowed us to continuously interpolate between an AS force equal to zero (S = 0) and a fully activated AS force (S = 1).…”

“…The AS force in the lower centrical part of the arc tube points into the opposite direction as the buoyancy force. In [11] an order parameter Ψ := min z∈D u z (0, 0, z)…”

“…In order to limit memory capacity and computing time, he developed a two dimensional model corresponding to a lamp of infinite length. The results described in the article at hand base on a three dimensional stationary model [11,12]. The idea is to identify the onset of light flicker by the occurrence of instabilities of the stationary solution.…”