Pavement stresses due to tire impact

Road surfaces wear continually under the effects of vehicular motions in an environment of changing temperature, humidity, etc. Regulatory agencies need to set limits on vehicular loads, tire pressures, etc., in order to mitigate the damage caused by the traveling stress footprints of vehicular traffic. In order to understand and quantify the relationship between damage caused and the parameters influencing the forces generated by a moving vehicle on a road surface, it is necessary to construct a model for a mechanical system of vehicle body, suspension springs, axle, wheel rim and tire, transmitting forces back and forward to the road surface. The previous paragraph describes the broad problem presented to the workshop. In what follows we organize a simple mathematical model to represent the major components of the system, and we indicate how this model may be validated (or not) by tests and, if it is successful, how it can be used in a predictive capacity

Cavity flow past a slender pointed hydrofoil

A slender-body theory for the flow past a slender, pointed hydrofoil held at a small angle of Attack to the flow, with a cavity on the upper surface, has been worked out. The approximate solution valid near the body is seen to be the sum of two components. The first consists of a distribution of two-dimensional sources located along the centroid line of the cavity to represent the variation of the cross-sectional area of the cavity. The second component represents the crossflow perpendicular to the centroid line. It is found that over the cavity boundary which envelops a constant pressure region, the magnitude of the cross-flow velocity is not constant, but varies to a moderate extent. With this variation neglected only in the neighbourhood of the hydrofoil, the cross-flow is solved by adopting the Riabouchinsky model for the two-dimensional flow. The lift is then calculated by integrating the pressure along the chord; the dependence of the lift on cavitation number and angle of attack is shown for a specific case of the triangular plan form

Handgun Accuracy Problem

A laboratory test, aimed to check the compliance of the model with demand, indicates that consecutive fires of about 10 centers around a circular region with a radius of 10cm. The fact that the fires, though performed at the same conditions, do not target at the same point is called focusing uncertainty of the handgun. Furthermore, it is observed, that bullet velocity measured 10 meters from gun varies up to about 7m/s (around 340m/s) among the firing set of 10. There are about ten different models and each model seems to display a different magnitude of uncertainty and velocity deviation from the expected average. The company, being willing to produce more data at request, asks to see if the focusing uncertainty and variation in bullet velocities can somehow be correlated. And with some help from other disciplines, the fact behind such uncertainties? Experiment apparatus or manufacturing process. If latter, which manufacturing unit contributes more

Symmetry Breaking in Jetting

In the bubble-jet printing process, it has been observed that the drop that ultimately pinches off from the ink jet sometimes moves sideways rather than straight relative to the symmetry axis of the liquid jet. We examined various mechanisms that might lead to the deflection of the ink drop. In particular, we focused on whether the liquid filament that connects the lead drop to the nozzle is capable of supporting lateral waves which might propagate from the nozzle toward the lead drop and break the symmetry at pinch-off

Mathematical models in water environment protection

[Chinese

Evolution of an elliptical bubble in an accelerating extensional flow

Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed. The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known. The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small. In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw. The two bubbles had different final pressures and did not have fore-aft symmetry. An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment