Wide-range average temperature measurements of convective fluid flows by using a schlieren system

Abstract

In the schlieren method, the deflection of light by the presence of an inhomogeneous medium is proportional to the gradient of its refractive index. In the presence of temperature variations in a fluid flow, the refraction index is related to the gas density by the Gladstone-Dale constant, which depends on the nature of the gas and the wavelength of light propagating in the medium. The deflection of light in a schlieren system is represented by intensity variations on the observation plane. Then, for a digital camera, the intensity level registered in each pixel depends mainly on the refractive index variation of the medium and exposure time. Therefore, if we regulate the intensity value of each pixel by controlling the exposure time, it is possible to adjust the temperature value measurements. In this way, a specific exposure time of a digital camera allows us to measure a determined range of temperature values. For that reason, in this study we determine the range of temperatures that can be measured with a digital camera for different exposure times. By doing this, a wide range of average temperature value fields can be obtained by summing up the temperature contribution of each exposure time. The basic idea in our approach to measure temperature by using a schlieren system is to relate the intensity level of each pixel in a schlieren image to the corresponding knife-edge position measured at the exit focal plane of the system. Our approach is applied to the measurement of temperature fields of the air convection caused by a heated rectangular metal plate (7.3 cm×12 cm) and a candle flame. We found that the maximum temperature values obtained for exposure times of 31.3, 15.7, 7.9, 3.9, and 2 ms were 67.3°C, 122.6°C, 217.4°C, 364.3°C, and 524.0°C, respectively.

Simultaneous Schlieren-Shadowgraph Visualization and Temperature Measurement Fields of Fluid Flow Using One Color CCD Camera

“…Observe that each temperature field contributes specific details to the final result. Consequently, the temperature value close to the surface of the plate is consistent with the temperature set at the programmable rectangular metal plate [ 8 , 9 ]. In addition, we can observe that the optical technique presented in this work enhances the detail of the convective fluid flow temperature fields…”

“…In Equation (9) n 0 , and ρ 0 are the refractive index and density at reference temperature T 0 , respectively, and T and n m are the temperature and refractive index of interest. A deep discussion about determining calibration curves to calculate temperature fields can be found in other works [ 8 , 9 ].…”

“…The plate was placed in the work section with its width along the “z” axis in the experiments. For the analysis, we assume that close to the surface of the metal plate, where the fluid flow fluctuations are not so high, the behavior of the fluid can be considered nearly 2D [ 8 , 9 ]. Figure 5 shows Schlieren’s images that will be processed to determine temperature fields.…”

“…This study uses these two techniques to visualize and measure temperature fields. The Schlieren technique requires a calibration procedure to measure temperature fields [ 8 , 9 ]. In these optical techniques, we assume that the density and the refractive index of the fluid are linearly related through the Gladstone–Dale equation [ 12 ]: where ρ and n are the density and the refractive index of the gas, and K is the Gladstone–Dale’s constant.…”

“…Detailed visualization of the fluid flow behavior is of great importance in various branches of science [ 1 , 2 , 3 , 4 , 5 ]. On the other hand, temperature measurement fields in fluid flow are essential in several applications [ 6 , 7 , 8 , 9 , 10 ]. In addition, in some studies, it is necessary to detect two physical variables due to the phenomenon’s physical nature.…”