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The domain of science and engineering relies heavily on an in-depth comprehension of fluid dynamics, given the prevalence of fluids such as water, air, and interstellar gas in the universe. Euler equations form the basis for the study of fluid motion. This paper is concerned with the Cauchy problem of isentropic compressible Euler equations away from the vacuum. We use the integration method with the general test function f = f (r) , proving that there exist the corresponding blowup results of C 1 irrotational solutions for Euler equations and Euler equations with time-dependent damping in R n ( n ≥ 2 ), provided the density-independent initial functional is sufficiently large. We also provide two simple and explicit test functions f (r) = r and f (r) = 1 + r , to demonstrate the blowup phenomenon in the one-dimensional case. In particular, our results are applicable to the non-radial system. [ABSTRACT FROM AUTHOR]

Unlike the normal sizing method, the foam sizing had been proven to be a low-add-on technology. To investigate the effect of foam sizing, film thickness, sized-yarn evenness, and size penetration rate were necessary to evaluate the performances of foam-sized yarns. However, the conventional image analysis of sized-yarn cross sections primarily relied on artificial testing with a low efficiency. This paper proposed a novel dynamic method to measure the sized-yarn properties including film thickness, sized-yarn evenness, and size penetration rate based on yarn sequence images captured from a moving yarn. A method of dynamic threshold module was adopted to obtain threshold for segmenting yarns in the sequence images. K-means clustering algorithm was applied to segment pixels of the images into yarn and background. To further remove burrs and noise in the images, two judgment templates were carried out to extract the information of yarn core. The film thickness, sized-yarn evenness, and size penetration rate were measured based on the yarn core of each frame in sequence images. In order to compare with the experimental results of the dynamic method, the yarn properties of the same samples were tested by static and artificial testing. Results revealed that the proposed method could efficiently and accurately detect the film thickness, sized-yarn evenness, and size penetration rate.

This study was aimed at investigating the process optimization of foam sizing for cotton yarns. In this work, effects of major foam-sizing process factors including size concentration, blowing ratio, stirring speed, pre-wetting temperature, pre-drying temperature, squeezing pressure and drying temperature were studied on the hairiness (more than 3 mm) and abrasion resistance of foam-sized yarns. The combination of Plackett-Burman, steepest ascent path analysis and Box-Behnken design were adopted to optimize the foam-sizing process of cotton yarns. Results revealed that size concentration, blowing ratio and squeezing pressure were significant factors that affected the hairiness and abrasion resistance. Optimum hairiness and abrasion resistance were obtained when the cotton yarns were sized at size concentration of 19.33%, blowing ratio of 4.27 and squeezing pressure of 0.78kN. The theoretical values and the observed values were in reasonably good agreement and the deviation was less than 1%. Verifcation and repeated trial results showed that it has good reproducibility and imparts the foam sizing process of cotton yarns.