Investigation and prediction of slug flow characteristics in highly viscous liquid and gas flows in horizontal pipes

Slug flow characteristics in highly viscous liquid and gas flow are studied experimentally in a horizontal pipe with 0.074 m ID and 17 m length. Results of flow regime map, liquid holdup and pressure gradient are discussed and liquid viscosity effects are investigated. Applicable correlations which are developed to predict liquid holdup in slug body for low viscosity flow are assessed with high viscosity liquids. Furthermore, a mechanistic model is developed for predicting the characteristics of slug flows of highly viscous liquid in horizontal pipes. A control volume is drawn around the slug body and slug film in a slug unit. Momentum equations with a momentum source term representing the significant momentum exchange between film zone and slug body are applied. Liquid viscosity effects are considered in closure relations. The mechanistic model is validated by comparing available pressure gradient and mean slug liquid holdup data produced in the present study and those obtained from literature, showing satisfactory capabilities over a large range of liquid viscosity

Generalize Hilbert operator acting on Dirichlet spaces

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\gamma>0$, the Hankel matrix $\mathcal{H}_{\mu,\gamma}=(\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n+k}=\int_{0}^{\infty}t^{n+k}d\mu(t)$. formally induces the operator $$\mathcal{H}_{\mu,\gamma}=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty}\mu_{n,k}a_k\right)\frac{\Gamma(n+\gamma)}{n!\Gamma(\gamma)}z^n,$$ on the space of all analytic functions $f(z)=\sum_{k=0}^{\infty}{a_k}{z^k}$ in the unit disc $\mathbb{D}$. Following ideas from \cite{author3} and \cite{author4}, in this paper, for $0\leq\alpha<2$, $2\leq\beta<4$, $\gamma\geq1$. we characterize the measure $\mu$ for which $\mathcal{H}_{\mu,\gamma}$ is bounded(resp.,compact)from $\mathcal{D}_{\alpha}$ into $\mathcal{D}_{\beta}$.Comment: 7 page

Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations

Local Polynomial Regression Solution for Differential Equations with Initial and Boundary Values

Numerical solutions of the linear differential boundary issues are obtained by using a local polynomial estimator method with kernel smoothing. To achieve this, a combination of a local polynomial-based method and its differential form has been used. The computed results with the use of this technique have been compared with the exact solution and other existing methods to show the required accuracy of it. The effectiveness of this method is verified by three illustrative examples. The presented method is seen to be a very reliable alternative method to some existing techniques for such realistic problems. Numerical results show that the solution of this method is more accurate than that of other methods