3D flame reconstruction and error calculation from a schlieren projection

Abstract

In this work a 3D flame reconstruction is performed from a 2D projection of the hot gases of a combustion flame. The projection is obtained using an optical schlieren technique. In this technique, a schlieren image is integrated linearly to obtain the hot gases, and then, a temperature field. Each row of the matrix representing the temperature distribution is fitted with a specific function, and its respective error is calculated. In this way, the projected matrix can be represented with the fitted functions. As a result of the procedure used in this research, a slice of the flame is obtained by assuming a cylindrical symmetry of it and multiplying the fitted function by itself. Finally, it was evaluated the mean error in calculations of temperature intensity in the flame under the cylindrical symmetry assumption obtaining an accuracy of 96% which validates the efficiency of our method.

3D non-axisymmetric temperature field measurement using rotating tomographic mechanism schlieren method

“…It is well known that when a light ray passes through an inhomogeneous medium, it suffers a deviation in its trajectory at a certain angle [10,[16][17][18][19]. This angle depends on the refractive index and the thickness of the field under test.…”

“…This angle depends on the refractive index and the thickness of the field under test. The ray propagation in an inhomogeneous medium is well described by the eikonal equation given in [17]: where n = n (x, y, z) is the refractive index of the medium, ds is the arc length defined as ds 2 = dx 2 + dy 2 + dz 2 , and dr is a position vector.…”

“…The light ray passes through the inhomogeneous medium in the z-direction from ζ 1 to ζ 2 , changing ds into dz and each displacement of dz generates a small angle deflection [17].…”

“…However, when the ray propagates through ζ 1 there is no deflection and equation ( 7) can be obtained as [17]:…”

“…where ∆x and ∆y are the infinitesimal displacements subtended by the angles ε x and ε y in the Z-X and Z-Y planes, respectively [17].…”