This paper presents the experimental results of the characteristics of hydraulic shock waves in an inclined chute contraction with consideration of the effects of sidewall deflection angle φ, bottom inclination angle θ and approach Froude number Fr0. Seventeen runs of laboratory experiments were conducted in the range of 27.45° ≤φ≤ 40.17°, 6.22°≤ θ ≤ 25.38° and 1.04 ≤ Fr0 ≤ 3.51. Based on the experimental data, three empirical dimensionless relations for the shock angle, maximum shockwave height, and corresponding position of maximum shockwave were obtained by regression analyses, respectively. These empirical relations would be useful for hydraulic engineers in designing chute contraction structures.

Based on the radial basis function (RBF) and the singular hybrid boundary node method (SHBNM), this paper presents an inherent meshless, boundary-only technique, which names dual reciprocity singular hybrid boundary node method (DRSHBNM), for numerical solution of various inhomogeneous equations. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method (DRM), while the general solution is solved by means of SHBNM, in which only requires discrete nodes constructed on the boundary of a domain, while several nodes in the domain are needed for the RBF interpolation. The treatment of singularity integration and the 'boundary layer effect' have been given by a series of effective approaches. Numerical examples for the solution of inhomogeneous equations show that high convergence rates and high accuracy with a small node number are achievable.

This study examines the parallel computing as a means to minimize the execution time in the optimization applied to thermohydrodynamic (THD) lubrication. The objective of the optimization is to maximize the load capacity of a slider bearing with two design variables. A global optimization method, DIviding RECTangle (DIRECT) algorithm, is used. The first approach was to apply the parallel computing within the THD model in a shared-memory processing (SMP) environment to examine the parallel efficiency of fine-grain computation. Next, a distributed parallel computing in the search level was conducted by use of the standard DIRECT algorithm. Then, the algorithm is modified to provide a version suitable for effective parallel computing. In the latter coarse-grain computation the speedups obtained by the DIRECT algorithms are compared with some previous studies using other parallel optimization methods. In the fine-grain computation of the SMP machine, the communication and overhead time costs prohibit high speedup in the cases of four or more simultaneous threads. It is found that the standard DIRECT algorithm is an efficient sequential but less parallel-computing-friendly method. When the modified algorithm is used in the slider bearing optimization, a parallel efficiency of 96.3% is obtained in the 16-computing-node cluster. This study presents the modified DIRECT algorithm, an efficient parallel search method, for general engineering optimization problems.

In this study, the effects of various endpoint constraints, including the first derivative, natural, quadratic, and not-a-knot endpoint constraints, on the time-line cubic spline interpolation are examined by solving the advection-diffusion equation with constant and variable velocities, and the viscous Burgers equation. The natural endpoint constraint could produce large numerical diffusion. The quadratic endpoint constraint can decrease the numerical diffusion from the natural endpoint constraint, but it could trigger large numerical oscillation. The first derivative endpoint constraint with higher-order central difference approximation has better simulated results than the natural and quadratic endpoint constraints. It can significantly reduce not only the numerical diffusion produced by the natural endpoint constraint, but also the numerical oscillation caused by the quadratic endpoint constraint. The applicability of the time-line cubic spline interpolation together with the not-a-knot endpoint constraint is limited, since the computational instability is caused while the Courant number is greater than unity. Therefore, as far as accuracy and applicability are concerned, the first derivative endpoint constraint with higher-order central difference approximation rather than the commonly used natural endpoint constraint should be a better choice for the time-line cubic spline interpolation.

Thermal buckling behaviour of rectangular laminated composite plates with initial geometrical imperfections is investigated in this article. The equilibrium, stability, and compatibility equations of an imperfect composite plate are derived using the first order shear deformation plate theory. The plate is assumed to be under longitudinal temperature rise. Resulting equations are used to obtain the thermal buckling load of the composite plate in closed-form solutions. The effect of initial imperfections on buckling loads are discussed.

The ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.

In this study an effective numerical approach is proposed for calculation of exhaust pipe flows. The flow inside an exhaust pipe is very complicated, since that flow involves pulsating hot gases with blast waves discharged from an internal combustion engine. In order to accurately simulate the complicated pulsating flow with the effects of heat transfer and friction at the duct wall, two systems of quasi-onedimensional model equations are employed, which resulted from the governing equations of the mass, momentum and energy conservation. One system of model equations with the terms of heat loss and wall friction results from the dimensionless governing equations based on dimensionless time variable t1 where t1 is defined as the dimensional time divided by the ratio of the pipe length to the time-average flow velocity at the pipe inlet. This system of model equations is numerically solved for a steady exhausted gas-flow without blast waves. The computed steady flow is referred as a basic flow. The other system of model equations without the terms of heat loss and wall friction results from the dimensionless governing equations based on dimensionless time variable t2, where t2 is defined as the dimensional time divided by the ratio of the pipe length to the speed of sound at the pipe inlet. The latter model is used for predicting exhausted gas-flows with blast waves. These two systems of model equations are solved by a th-order weighted essential non-oscillation scheme. It is found that the computed result of the peak pressures, temperature, and flow velocity at some check points for an exhaust pipe at different engine speeds agrees reasonably well with experimental data.

In present research, improvement of a microbubble generator's performance via reliance on fluid dynamics characteristics is studied numerically, and then some experiments are executed. In an elementary cylindrical microbubble generator, water flow enters the device via six diagonal nozzles, and passes a rotational path around a central motionless hub. This flow breaks the big bubbles entering the device by gas injection from air nozzles. The high-intensity turbulence and shear flow in this device is the cause of the air bubble breaking process. These small bubbles can be used to reduce frictional drag on the contact surface of moving solid bodies in water flow. To improve the operation of the apparatus, some suggested geometrical shapes were investigated numerically and were optimized based on the bubbles' effective breaking-up parameters. The experimental results illustrated good performance of the recent apparatus for generating smaller bubbles.

This paper studies the characteristics of a proposed reliability-dependent hazard rate function for composites under fatigue loading. The hazard rate function, in terms of reliability R, is in the form of e+c (1-R)p called (ecp) model, where e denotes the imbedded defects of material strength, c the coefficient of strength degradation, and p the memory characteristics of distributions of both applied stress and fatigue strength during the cumulative damage process. By taking a typical residual strength model in Monte Carlo simulation, this paper presents the time changing of the residual strength distribution and hazard rate of composite under various constant-amplitude cyclic stresses. The values of (e, c, p) are decided by fitting hazard rate function to the data generated in simulation. The results show that, under a suitable suggested value of e, p is a constant depending on the characteristics of stress distribution as well as the residual strength model used in Monte Carlo stimulation, and c is correlated to the maximum cyclic stress in a power-law relationship. Only by knowing the initial strength distribution and the maximum cyclic stress, the fatigue life can be easily estimated by integrating the reliability with time or its equivalent, i.e., the reciprocal of hazard rate function with reliability. Finally, by a proposed approximated equation of fatigue life, the (ecp) model is checked to be highly consistent with S-N curve in both the physical means and the equation form. The analysis presented here may be helpful in designing and maintenance planning of composite under fatigue loading.

This work studied the Rayleigh-Bénard convection under the first-order slip boundary conditions in both hydrodynamic and thermal fields. The variation principle was applied to find the critical Rayleigh number of instability. The exteneded relations of the critical Rayleigh number (Rc) and the wavenumber (ac) under partially slip boundary conditions were derived. The numerical results showed that both Rc and ac are decreasing with increasing the Knudsen number. The dependence of Rc on the Knudsen number (K) shows that when K≤10−3, the boundary can be considered as nonslip, while K≥10, it can be considered as free boundaries. The maximum change rate occurs when the Knudsen number is around 0.1, indicating that the system would be affected significantly in that range.

To improve the safety and automation of mechanical excavation methods used in tunnels, this present report studied the behavior of rock materials indented by a single cutter, based on the theory of indentation fracture mechanics. The development of microcracks during the indentation process and the correlation between microcracks and macrocracks was investigated using the nondestructive technique of acoustic emission. Microseismic activity of the microcracks received by the acoustic emission (AE) technique was used to interpret and represent the initiation and propagation of macrocracks. As the wedge angle increased, the maximum indentation force increased, but the nominal indentation pressure and the destructive indentation depth decreased. On the other hand, the direction of macrocrack propagation did not significantly change with the various wedge angles. Furthermore, the localization occurred earlier and the dimensionless radius of the elasto-plastic interface decreased with increased wedge angle. In addition, the dimensionless radius of the elasto-plastic interface obtained by the experiment was consistent with closed-form analytical solutions.