No abstract

We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to the desired order. The presented method provides a systematic and rigorous approach to the derivation, treatment and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirror examples.

Acoustic resonances in combustion systems like central heating boilers prohibit further technological advances in these systems. The design and construction is obstructed by acoustic problems because they are largely misunderstood, in spite of our increase in knowledge over the last decades. The flame often acts as an active element in the acoustic field, because the flame transfer function of acoustic waves has a large amplitude at low frequencies. Current models of the phase of the flame transfer function of Bunsen-type flames, based on kinematic behavior of the flame dynamics, completely miss the experimentally observed phase, unless the measured flow field is used in the model. In the current paper we analyze numerical results of the flame dynamics, flow field and flame transfer function found with a 2D detailed numerical model of the flow and structure of the flame on a multiple-slit burner. The model is validated with experiments of the flame dynamics (using chemiluminescence), flow dynamics (using PIV) and flame transfer function (using OH luminescence for the heat release fluctuations and heated wire probe for the acoustic distortions) on exactly the same configuration. A very good agreement is found which indicates the importance of predicting all the influences of the flow on the flame and vise-versa.

We present a formulation of the two-dimensional complete flux (CF) scheme in terms of local orthogonal coordinates adapted to the flow, i.e., one coordinate axis is aligned with the local velocity field and the other one is perpendicular to it. This approach gives rise to an advection-diffusion-reaction boundary value problem (BVP) for the flux component in the local flow direction. For the other (diffusive) flux component we use central differences. We will demonstrate the performance of the scheme for several examples.

We combine two-dimensional freeform reflector design with a scattering surface modeled using microfacets, i.e., small, specular, surfaces representing surface roughness. The model resulted in a convolution integral for the scattered light intensity distribution, which yields an inverse specular problem after deconvolution. Thus, the shape of a reflector with a scattering surface may be computed using deconvolution, followed by solving the typical inverse problem of specular reflector design. We found that the presence of surface scattering resulted in a few percentage difference in terms of reflector radius, depending on the amount of scattering in the system.