A Nonlinear Analysis of the Wahl–Fischer Torsional Instability

This is an extension to a previous study of the Wahl–Fischer torsional instability problem (Infante and Doughty, “An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem”, J. Appl. Mech. Trans. ASME, 2020, 87(10), p. 101004). There, we provided a mathematical explanation of the reasons for the existence of torsional oscillations observed in numerical simulations and in actual mechanical devices such as the exhaust fan system studied by Wahl and Fischer. That explanation was mostly based on linear analysis. This paper presents an additional mathematical explanation of the nature and form of the large self-excited oscillations, due to the strongly nonlinear nature of the system and the large amplitude of these oscillations. Because the oscillations are large, their study requires the use of nonlinear methods.

Parametric Analysis of the Fixed Mirror Solar Concentrator for Medium Temperature Applications

The fixed mirror solar concentrator (FMSC) possesses a geometry that can produce thermal energy in medium temperature range. Due to its static reflector, the FMSC has several advantages when compared to other designs, such as being one of the best adapted for integration onto building roofs. An optical ray-tracing analysis of its geometry was presented in a previous paper (Pujol Nadal and Martínez Moll, 2012, “Optical Analysis of the Fixed Mirror Solar Concentrator by Forward Ray-Tracing Procedure,” Trans ASME J. Solar Energy Eng., 134(3), pp. 031009-1-14). The optical results were obtained in function of three design parameters: the number of mirrors N, the ratio of focal length and reflector width F/W, and the intercept factor γ (in order to represent different receiver widths). In this communication, the integrated thermal output of the same parameter combinations has been determined in order to find optimal values of the design parameters at a working temperature of 200 °C. The results were obtained for three different climates and two orientations (North-South and East-West). The results show that FMSC can produce heat at 200 °C with an annual thermal efficiency of 39, 44, and 48%, dependent of the location considered (Munich, Palma de Mallorca, and Cairo). The best FMSC geometries in function of the design parameters are exhibited for medium range applications.

Extension of Campbell's Major Resonance With Experimental Demonstration

The interaction of vibratory traveling waves in rotating and stationary axisymmetric components is examined. In the most general case, a resonance can occur when the wave propagation speed in a first structure is equal in magnitude and direction to the rotational velocity of an adjacent structure. When a backward wave in a rotor appears stationary, a major resonance, as discussed in Wilfred Campbell's classic paper (Campbell, W., 1924, “The Protection of Steam Turbine Disc Wheels from Axial Vibrations,” Trans ASME, 46, pp. 31–160), results. A related resonance has been observed when the wave propagation speed in the stator is equal to the physical speed of the adjacent rotor. A third mechanism is derived for resonance between a wave in rotor 1 and a co- or counter-rotating rotor 2. Description of a component test which demonstrated this final phenomenon is provided.

Unsteady turbulent plume models

Four existing integral models of unsteady turbulent plumes are revisited. We demonstrate that none of these published models is ideal for general descriptions of unsteady behaviour and put forward a modified model. We show that the most recent (top-hat) plume model (Scase et al. J. Fluid Mech., vol. 563, 2006, p. 443), and the earlier (Gaussian) plume models (Delichatsios J. Fluid Mech., vol. 93, 1979, p. 241; Yu Trans. ASME, vol. 112, 1990, p.186), are all ill-posed. This ill-posedness arises from the downstream growth of short-scale waves, which have an unbounded downstream growth rate. We show that both the top-hat and the Gaussian (Yu) models can be regularized, rendering them well-posed, by the inclusion of a velocity diffusion term. The effect of including this diffusive mechanism is to include a vertical structure in the model that can be interpreted as representing the vertical extent of an eddy. The effects of this additional mechanism are small for steady applications, and cases where the plume forcing can be considered to follow a power law (both of which have been studied extensively). However, the inclusion of diffusion is shown to be crucial to the general initial-value problem for unsteady models.

Contact Area and Static Friction of Rough Surfaces With High Plasticity Index

A model for the contact area and static friction of nominally flat rough surfaces and rough spherical surfaces is presented. The model extends previously published models, which are limited to plasticity index values below 8, to higher plasticity index values by accounting for fully plastically deformed asperities based on finite element results by Jackson and Green [2005, “A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat,” Trans. ASME, J. Tribol., 127, pp. 343–354]. The present model also corrects some deficiencies of the earlier models at very small plasticity index values below 0.5.

Flexural Waves in Fluid-Filled Tubes Subject to Axial Impact

We experimentally studied the propagation of coupled fluid stress waves and tube flexural waves generated through projectile impact along the axis of a water-filled tube. We tested mild steel tubes, 38–40 mm inner diameter and wall thicknesses of 0.8 mm, 6.4 mm, and 12.7 mm. A steel impactor was accelerated using an air cannon and struck a polycarbonate buffer placed on top of the water surface within the tube. Elastic flexural waves were observed for impact speeds of 5–10 m/s and plastic waves appeared for impact speeds approaching 20 m/s for a 0.8 mm thickness tube. We observed primary wave speeds of 1100 m/s in a 0.8 mm thickness tube, increasing to the water sound speed with 6.4 mm and 12.7 mm thickness tubes. Comparison of our measurements in the 0.8 mm thickness tube with Skalak’s water hammer theory indicates reasonable agreement between the predicted and measured peak strains as a function of the impact buffer speed (1956, “An Extension to the Theory of Water Hammer,” Trans. ASME, 78, pp. 105–116). For thick-walled tubes, the correlation between the experimentally determined peak pressures and strains reveals the importance of corrections for the through-wall stress distribution.

Forecasting: it is not about statistics, it is about dynamics

In 1963, the mathematician and meteorologist Edward Lorenz published a paper (Lorenz 1963 J. Atmos. Sci. 20 , 130–141) that changed the way scientists think about the prediction of geophysical systems, by introducing the ideas of chaos, attractors, sensitivity to initial conditions and the limitations to forecasting nonlinear systems. Three years earlier, the mathematician and engineer Rudolf Kalman had published a paper (Kalman 1960 Trans. ASME Ser. D, J. Basic Eng. 82 , 35–45) that changed the way engineers thought about prediction of electronic and mechanical systems. Ironically, in recent years, geophysicists have become increasingly interested in Kalman filters, whereas engineers have become increasingly interested in chaos. It is argued that more often than not the tracking and forecasting of nonlinear systems has more to do with the nonlinear dynamics that Lorenz considered than it has to do with statistics that Kalman considered. A position with which both Lorenz and Kalman would appear to agree.

A Thermal Law of the Wall for Separating and Recirculating Flows

The characteristics of the turbulent boundary layer near a separation point are studied here. The emphasis is on providing analytical expressions for the velocity and temperature near wall solutions which are also valid in the region of reverse flow. These expressions can then be used as boundary conditions in numerical schemes that use two-equation differential models. The paper proposes a new expression for the description of the near wall characteristic length which is shown to hold also in the reverse flow region. The specified velocity profiles are based on a previous formulation of the problem by Cruz and Silva Freire (IJHMT, 41, 2097 2111, 1998) but, as written here, they are presented for the first time. The temperature profiles near the wall are also described by a newly proposed expression that reduces to the logarithmic profile in the attached region, and assumes a minus half power law profile at the separation point. In the separated region, the logarithmic profile is recovered. All results are validated through the data of Vogel and Eaton (Trans. ASME JHT, 107, 922 929, 1985).