The influence of boundary roughness characteristics on the rate of dissipation in a viscous fluid is analyzed using shape calculus from the theory of optimal control of systems governed by partial differential equations. To study the mapping D from surface roughness topography to the dissipation rate of a Navier-Stokes flow, expressions for the shape gradient and Hessian are determined using the velocity method. In the case of Couette and Poiseuille flows, a flat boundary is a local minimum of the dissipation rate functional. Thus, for small roughness heights the behavior of D is governed by the flat-wall shape Hessian operator, whose eigenfunctions are shown to be the Fourier modes. For Stokes flow, the shape Hessian is determined analytically and its eigenvalues are shown to grow linearly with the wavenumber of the shape perturbation. For Navier-Stokes flow, the shape Hessian is computed numerically, and the ratio of its eigenvalues to those of a Stokes flow depend only on the Reynolds number based on the wavelength of the perturbation. The consequences of these results on the analysis of the effects of roughness on fluid flows are discussed.

The high-temperature environment is a major factor that affects deep mining. Cooling has become a major expense, accounting for up to 25% of the total energy consumption of such mines. To address methods of cooling and the cooling cost, this paper studies the influence of the ventilation duct layout on the cooling effect. Six models were created in ICEM-CFD (3D modeling software), and the influence of cold airflow diffusion on the temperature of the mine environment was numerically simulated using ANSYS Fluent. Under the condition of the same ventilation volume, two models utilizing single pipe and double pipe scenarios were established, and six points were selected as the pipeline suspension position, forming six ventilation duct models. The cooling effect of each model was evaluated by analyzing the average temperature of the roadway section, the three-dimensional distribution of the roadway temperature and the velocity streamline of the whole roadway. The results show that the double-tube model has greater advantages than the single-tube model does, due to its superior local temperature, average temperature of the cross-section, range below 303 K, temperature uniformity and local wind speed. Among the models, model 4 (diameter of 0.5 m, 1.9 m away from the bottom of the roadway and 2.4 m away from the center of the circle) is the best pipeline layout scheme for comprehensive temperature values, roadway temperature uniformity and other factors. The average temperature is 299.3 K within 8 m from the mining face, which is 1.66 K lower than that of the single tube model. This configuration will increase the comfort of the mining environment and reduce cooling costs. These results can provide a reference for ventilation duct layouts of roadways in high temperature mines.

Abstract-Off-axis ellipsoid reflector based off-focus configuration for deastigmatism and circularization of an elliptical Gaussian beam is proposed. Mostly used off-axis ellipsoid reflector based conventional configuration is constructed by aligning the incident direction directed to one focus of the ellipsoid, which reflect the output beam to the another focus of the ellipsoid. However, such configuration is unavailable to deastigmatize and circularize an elliptical Gaussian beam. Therefore, the coupling efficiency between the reflected beam and an essentially circular beam is not well satisfied. In this case, an off-axis ellipsoid reflector based off-focus configuration is proposed to obtain better coupling efficiency. Different from the conventional configuration, in the proposed off-focus configuration, the incident beam direction is diverged from one focus of the ellipsoid. As a result, the coupling efficiency of no less than 99.9% (as compared with coupling efficiency of about 94.2% based on conventional configuration) can be obtained, which is verified with numerical calculations.

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