Dynamics of void collapse in shocked energetic materials: physics of void–void interactions

This work presents the response of a porous energetic material subjected to severe transient loading conditions. The porosities, represented by voids, entirely change the response of an otherwise homogeneous material. The variations in terms of energy distribution and maximum temperature reached in the material in the presence of heterogeneities (voids) but in the absence of chemical reactions are studied. This study also accounts for void–void interactions to enhance the understanding of the localization of energy in the material. It is observed that relative position of voids can have important consequence on energy distribution as well as rise in temperature of the energetic material. The relative position of voids further influences the interaction of secondary shock waves generated during the collapse of one void with the downstream voids. This interaction can either enhance or diminish the strength of the shock depending on the location of downstream voids. This work also reveals that the findings from mutual void–void interactions can be used to study systems with multiple voids. This is shown by analyzing systems with 10–25 % void volume fraction. The effect of void–void interactions are connected to the overall response of a chemically inert porous material to imposed transient loads.     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.     

Air–water flow characteristics in high-velocity free-surface flows with 50% void fraction

High-velocity free-surface flows are complex two-phase flows and limited information is available about the interactions between air and water for void fractions of about 50%. Herein a detailed experimental study was conducted in the intermediate flow region (C ∼ 50%) on a stepped spillway and the microscopic air–water flow characteristics were investigated. The results showed differences in water and droplet chord times with comparatively larger number of air chord times (0–2 ms), and larger number of water chord times (2–6 ms). A monotonic decrease of particle chord modes was observed with increasing bubble count rates. Several characteristic time scales were identified based upon inter-particle arrival time analyses of characteristic chord time classes as well as spectral analyses of the instantaneous void fraction signal. Chord times of 3–5 ms appeared to be characteristic time scales of the intermediate flow region having similar time scales compared to the local correlation and integral turbulent time scales and to time scales associated with bubble break-up and turbulent velocity fluctuations. A further characteristic time scale of 100 ms was identified in a frequency analysis of instantaneous void fraction. This time scale was of the same order of magnitude as free-surface auto-correlation time scales suggesting that the air–water flow structure was affected by the free-surface fluctuations.     

The ‘void’ structure in the wake of a self-oscillating flexible circular cylinder

We discuss the experimental vortex wake of a flexible circular cylinder undergoing vortex-induced vibration at low Reynolds number and a large cylinder aspect ratio. Hydrogen bubbles formed on the cylinder track the von Karman vortex cores. They show a characteristic ‘void’ structure. We propose a vortex skeleton model that includes a pinch-off of opposite-signed cores. Voids occurred at a node in streamwise vibration when close to an antinode in transverse cylinder vibration. A vibration model predicts the ratio of shedding frequency to natural cylinder vibration frequency necessary for void formation at specific spanwise locations.     

A new model for porous nonlinear viscous solids incorporating void shape effects – II: Numerical validation

The aim of this work is to critically assess the new model for porous, nonlinear viscous solids incorporating void shape effects proposed in Part I, by comparing its predictions with the results of some numerical micromechanical simulations. Two kinds of simulations are performed. First, the gauge surface of spheroidal representative volume elements, as considered in Part I, is determined for various values of the porosity, the aspect ratio of the void and the Norton exponent. This is done through minimization of the macroscopic viscous potential over a family of trial velocity fields especially adapted to the spheroidal geometry, which was proposed by Lee and Mear. Such simulations allow not only for satisfactory validation of the approximate analytical gauge surface proposed, but also for adjustment of the heuristic coefficients involved in the evolution equation for the void shape parameter. Second, the evolution in time of cylindrical cells subjected to various mechanical loads is determined by the finite element method. The quasi-periodicity of this new geometry is intended to approximately represent interactions between neighbouring voids. These simulations also reveal very good agreement between model predictions and numerical calculations, provided that the effect of the new geometry considered is accounted for by using a non-unity value for the analog of Tvergaard's famous “$q_1$” parameter for porous plastic solids.     

Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows

The development of a three-hole pressure probe with back-flushing combined with a conductivity probe, used for measuring simultaneously the magnitude and direction of the velocity vector in complex air–water flows, is described in this paper. The air–water flows envisaged in the current work are typically those occurring around the rotors of impulse hydraulic turbines (like the Pelton and Cross-Flow turbines), where the flow direction is not known prior to the data acquisition. The calibration of both the conductivity and three-hole pressure components of the combined probe in a rig built for the purpose, where the probe was placed in a position similar to that adopted for the flow measurements, will be reported. After concluding the calibration procedure, the probe was utilized in the outside region of a Cross-Flow turbine rotor. The experimental results obtained in the present study illustrate the satisfactory performance of the combined probe, and are encouraging toward its use for characterizing the velocity field of other complex air–water flows.     

Prediction of void fraction for gas–liquid flow in horizontal,upward and downward inclined pipes using artificial neural network

In this work, the ability of artificial neural networks (ANNs) to predict void fraction of gas–liquid two–phase flow in horizontal and inclined pipes was investigated. For this purpose, an ANN model was designed and trained using a total of 301 experimental data points reported in the literature for inclination angles between –20° and +20°. Pipe inclination angle as well as superficial Reynolds number of gas (Re_sg) and liquid (Re_sl) were chosen as input parameters of different structures of multilayer perceptron (MLP) neural networks, while the corresponding void fraction was selected as their output parameter. A hyperbolic tangent sigmoid and a linear function were employed as transfer functions of hidden and output layers, respectively, and Levenberg–Marquardt back propagation algorithm was used to train the networks. By trial–and–error method, a three–layer network with 10 neurons in the hidden layer was achieved as optimal structure of the ANN which made it possible to predict the void fraction with a high accuracy. Mean absolute percent error (MAPE) of 1.81% and coefficient of determination (R²) of 0.9976 for training data and MAPE of 1.52% and R² value of 0.9948 for testing data were obtained. Also for all data, MAPE of 1.95% and R² value of 0.9972 were calculated, and 96% data were within ±5% error band. In addition, the accuracy of the proposed ANN model was compared with the predictions from 17 void fraction correlations available in the literature for different flow patterns and horizontal and inclined flows. For all cases, the proposed ANN model gave better performance than all of the studied correlations. The results confirm the very good capability of the ANNs to predict the void fractions of gas–liquid flow in inclined pipes, regardless of flow pattern. Finally, by performing interpolation using the trained network, the void fraction values for some other conditions were predicted.     

Numerical modeling of the thermal–hydraulic behavior of wire-on-tube condensers operating with HFC-134a using homogeneous equilibrium model: evaluation of some void fraction correlations

This study presents a numerical evaluation of the influence of some void fraction correlations over the thermal–hydraulic behavior of wire-on-tube condensers operating with HFC-134a. The numerical model is based on finite volume method considering the homogeneous equilibrium model. Empirical correlations are applied to provide closure relations. Results show that the choice of void fraction correlation influences the refrigerant charge and pressure drop calculations, while no influences the heat transfer rate.