Measurement of the diffusion coefficient in a heated plane airstream

Abstract

In order to measure the diffusion coefficient of a heated plane airstream, a single laser beam is passed through the jet, perpendicularly to the flow direction. The thermic turbulence in the airstream causes random fluctuations of the refractive index. Consequently, the beam direction undergoes, in the flow, random perturbations. After having traversed the jet, the beam produces a luminous trace on a photoelectric cell placed outside the jet. An experimental setup for measuring the probabilities of the beam impact positions on the cell is described. From the Markovian process model, applied along the whole random path of the beam, it has been possible to compute these probabilities by solving the Einstein–Fokker–Kolmogorov equation. The diffusion coefficient can be determined by adjusting the numerical solution to agree with the experimental results. In addition, the calculation procedure gives the order of magnitude of an integral scale, characterizing the dimension of the turbulent structures in which the propagation of light can be considered rectilinear. A good agreement between the results and the published data obtained by means of the cold-wire anemometer technique proves the validity of the method.

Shape Optimization Using Genetic Algorithms and Laser Beam Propagation for the Determination of the Diffusion Coefficient in a Hot Turbulent Jet of Air

“…In the previous works [8] done under the same experimental conditions, the experimental value of the diffusion coefficient for the turbulent jet considered has been deduced (D µ = 2.20×10 −9 m −1 ) from the measurements of Gagnaire and Tailland [10], which were obtained by means of the well-known cold wire anemometer technique [11]. Moreover, by using the propagation of a thin laser beam through the hot turbulent jet, Pemha, Gay, and Tailland [8] have obtained the value D µ = 2.98 × 10 −9 m −1 .…”

“…In this paper, we are concerned with a thin laser beam, having initial diameter a = 0.8 mm, incident wavelength λ 0 = 6328 A, which propagates through a hot turbulent jet, created from a rectangular nozzle, according to the experimental conditions already described by Pemha, Gay and Tailland in [8], and by Ngo Nyobe and Pemha in [9]. The mean propagation direction is defined along the x axis, perpendicularly to the flow direction, with a mean propagation distance X = 200 mm.…”

“…If τ represents the unit vector tangent to the laser ray trajectory, s is the arc length of the laser ray curve, the well-known ray equation leads to the following form [1][2][3]8]:…”

“…By taking the square of (2), and using the fact that the deflection of the ray along the path σ is small, it can be shown [1,8] that the variance of ε is related to σ by the following equation:…”

“…where n 2 is the mean value of the refractive index, D µ is a quantity called the diffusion coefficient of the jet and defined as [1,8,9]:…”