A new technique using background oriented schlieren for temperature reconstruction of an axisymmetric open reactive flow

Abstract

A new technique, called 3D ray tracing, for refractive index field reconstruction of axisymmetric flows from displacement fields measured from Background Oriented Schlieren (BOS) experiments is developed and applied to a lean premixed methane/air reactive flow at Reynolds number of 4,000 on a 12 mm diameter circular burner. The temperature distribution is then calculated using a species independent direct relationship between refractive index, temperature, and ambient conditions. The error introduced by the approximation to reach this relationship is quantified using simulated flow fields and is found to be 8% within the inner unburnt region of the flow field, decreasing to 2% through the reaction zone, and then quickly reducing to 0% outside the flow field. The effect of random noise and reconstruction resolution on the accuracy of the method is assessed via application to synthetically generated data sets that mimic the characteristics of a heated air jet expelled into ambient. The novel 3D ray tracing allows for accurate temperature reconstructions of open axisymmetric reactive flows where 2D displacement fields are measured, which is shown to be a shortcoming of current direct methods in literature. Additionally, this is done without the need for any prior knowledge of flow field parameters; only ambient conditions to the system must be known. The simple experimental setup and low computational cost make this approach with BOS a good option for application into existing experimental combustion systems with minimal effort.

Temperature reconstruction of an axisymmetric enclosed reactive flow using simultaneous background oriented schlieren and infrared thermography

“…The rest of this section will describe the unique methods used to characterize the temperature of the flow field or solid in each region from outermost to innermost. To summarize, region one will be solved using the exact 3D ray tracing method presented in Wahls and Ekkad [28], region two will be determined using IR thermography, and region three will be characterized using a newly expanded version of the 3D ray tracing method. For the sake of brevity, a general overview of the 3D ray tracing method will be given here instead of the full mathematical formulation, and the reader is referred to the study of Wahls and Ekkad [28].…”

“…Referring to figure 2, it is seen that in region one the BOS camera's line of sight is directly to the background with no interference from the quartz liner, meaning the undisturbed ray paths can be mapped as directly parallel to the line of sight. With this condition met, the 3D ray tracing method can be applied to region one exactly as is described in Wahls and Ekkad [28] to reconstruct the refractive index field of the heated air surrounding the fused silica liner.…”

“…It is seen that equation ( 6) is dependent on local species concentration, which is infeasible to obtain during actual experiments. Also note that k i represents the Gladstone-Dale constant of each individual species, which is a tabulated value [28,34]. However if the flow field is at atmospheric pressure and composed of only air, then the C term is identical no matter if written for a point within in the flow or in ambient.…”

“…For this reason, noninvasive approaches are required for feasible full field temperature measurements, and several of these techniques used for measuring various flow parameters (temperature, density, mixture fraction, species concentration, etc) exist such as planar laser induced fluorescence (PLIF) [1][2][3][4][5][6][7][8][9], interferometry [10][11][12], and schlieren imaging. Schlieren imaging can be categorized further into conventional knife edge schlieren [13], rainbow schlieren [14,15], and BOS [11,[16][17][18][19][20][21][22][23][24][25][26][27][28]. Of these techniques, BOS is by far the simplest and most inexpensive to implement experimentally making it an attractive choice for researchers if it can be developed to the maturity of more established quantitative techniques such as PLIF, and in fact the purpose of this current work is to aid in this process.…”

“…Therefore, the novelty in this current work is the development of a refractive index reconstruction method for BOS experimental analysis capable of handling systems where the undisturbed ray paths are not necessarily parallel to the camera line of sight, in other words, an enclosed cylindrical system of any optically transparent material. This expanded technique is based on the 3D ray tracing technique presented in Wahls and Ekkad [28], which iteratively maps out ray paths in an axisymmetric flow using the measured displacements to calculate the angles that each ray enters and leaves the flow field in question. This reconstruction technique is an improvement from its predecessor, 2D ray tracing [24], as it maps each ray through 3D cylindrical rings as opposed to 2D circular rings.…”