Towards Understanding Powder Behavior Via Simulation

The aim of this study was to investigate powder and tablet behavior at the level of mechanical interactions between single particles. Various aspects of powder packing, mixing, compression, and bond formation were examined with the aid of computer simulations. The packing and mixing simulations were based on spring forces interacting between particles. Packing and breakage simulations included systems in which permanent bonds were formed and broken between particles, based on their interaction strengths. During the process, a new simulation environment based on Newtonian mechanics and elementary interactions between the particles was created, and a new method for evaluating mixing was developed. Powder behavior is a complicated process, and many of its aspects are still unclear. Powders as a whole exhibit some aspects of solids and others of liquids. Therefore, their physics is far from clear. However, using relatively simple models based on particle-particle interaction, many powder properties could be replicated during this work. Simulated packing densities were similar to values reported in the literature. The method developed for describing powder mixing correlated well with previous methods. The new method can be applied to determine mixing in completely homogeneous materials, without dividing them into different components. As such, it can describe the efficiency of the mixing method, regardless of the powder's initial setup. The mixing efficiency at different vibrations was examined, and we found that certain combinations of amplitude, direction, and frequencies resulted in better mixing while using less energy. Simulations using exponential force potentials between particles were able to explain the elementary compression behavior of tablets, and create force distributions that were similar to the pressure distributions reported in the literature. Tablet-breaking simulations resulted in breaking strengths that were similar to measured tablet breaking strengths. In general, many aspects of powder behavior can be explained with mechanical interactions at the particle level, and single particle properties can be reliably linked to powder behavior with accurate simulations.

Influence of exhaust gas heating and L/D ratios on the discharge efficiencies for an activated carbon natural gas storage system

A transient 2D axi-symmetric and lumped parameter (LP) model with constant outflow conditions have been developed to study the discharge capacity of an activated carbon bed. The predicted discharge times and variations in bed pressure and temperature are in good agreement with experimental results obtained from a 1.82 l adsorbed natural gas (ANG) storage system. Under ambient air conditions, a maximum temperature drop of 29.5 K and 45.5 K are predicted at the bed center for discharge rates of 1.0 l min(-1) and 5.0 l min(-1) respectively. The corresponding discharge efficiencies are 77% and 71.5% respectively with discharge efficiencies improving with decreasing outflow rates. Increasing the LID ratio from 1.9 to 7.8 had only a marginal increase in the discharge efficiency. Forced convection (exhaust gas) heating had a significant effect on the discharge efficiency, leading to efficiencies as high as 92.8% at a discharge of 1.0 l min(-1) and 88.7% at 5 l min(-1). Our study shows that the LP model can be reliably used to obtain discharge times due to the uniform pressure distributions in the bed. Temperature predictions with the LP model were more accurate at ambient conditions and higher discharge rates, due to greater uniformity in bed temperatures. For the low thermal conductivity carbon porous beds, our study shows that exhaust gas heating can be used as an effective and convenient strategy to improve the discharge characteristics and performance of an ANG system. (C) 2013 Elsevier Ltd. All rights reserved.

PREDICTION OF TRANSITIONAL AND SEPARATED BOUNDARY LAYERS IN A COMPRESSOR CASCADE

Numerical simulations were performed of experiments from a cascade of stator blades at three low Reynolds numbers representative of flight conditions. Solutions were assessed by comparing blade surface pressures, velocity and turbulence intensity along blade normals at several stations along the suction surface and in the wake. At Re = 210,000 and 380,000 the laminar boundary layer over the suction surface separates and reattaches with significant turbulence fluctuations. A new 3-equation transition model, the k-k(L)-omega model, was used to simulate this flow. Predicted locations of the separation bubble, and profiles of velocity and turbulence fluctuations on blade-normal lines at various stations along the blade were found to be quite close to measurements. Suction surface pressure distributions were not as close at the lower Re. The solution with the standard k-omega SST model showed significant differences in all quantities. At Re = 640,000 transition occurs earlier and it is a turbulent boundary layer that separates near the trailing edge. The solution with the Reynolds stress model was found to be quite close to the experiment in the separated region also, unlike the k-omega SST solution. Three-dimensional computations were performed at Re = 380,000 and 640,000. In both cases there were no significant differences between the midspan solution from 3D computations and the 2D solutions. However, the 3D solutions exhibited flow features observed in the experiments the nearly 2D structure of the flow over most of the span at 380,000 and the spanwise growth of corner vortices from the endwall at 640,000.

An Experimental Study of Kerosene Combustion in a Supersonic Model Combustor Using Effervescent Atomization

Investigation of kerosene combustion in a Mach 2.5 flow was carried out using a model supersonic combustor with cross-section area of 51 mm × 70 mm and different integrated fuel injector/flameholder cavity modules. Experiments with pure liquid atomization and with effervescent atomization were characterized and compared. Direct photography, Schlieren imaging, and planar laser induced fluorescence (PLIF) imaging of OH radical were utilized to examine the cavity characteristics and spray structure. Schlieren images illustrate the effectiveness of gas barbotage in facilitating atomization and the importance of secondary atomization when kerosene sprays interacting with a supersonic crossflow. OH PLIF images further substantiate our previous finding that there exists a local high-temperature radical pool within the cavity flameholder, and this radical pool plays a crucial role in promoting kerosene combustion in a supersonic combustor. Under the same operation conditions, comparison of the measured static pressure distributions along the combustor also shows that effervescent atomization generally leads to better combustion performance than the use of pure liquid atomization. Furthermore, the present results demonstrate that the cavity characteristics can be different in non-reacting and reacting supersonic flows. As such, the conventional definition of cavity characteristics based on non-reacting flows needs to be revised.

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Statistical Simulation of Rarefied Gas Flows in Micro-Channels

Rarefied gas flows through micro-channels are simulated using particle approaches, named as the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method. In simulating the low speed flows in long micro-channels the DSMC method encounters the problem of large sample size demand and the difficulty of regulating boundary conditions at the inlet and outlet. Some important computational issues in the calculation of long micro-channel flows by using the IP method, such as the use the conservative form of the mass conservation equation to guarantee the adjustment of the inlet and outlet boundary conditions and the super-relaxation scheme to accelerate the convergence process, are addressed. Stream-wise pressure distributions and mass fluxes through micro-channels given by the IP method agree well with experimental data measured in long micro-channels by Pong et al. (with a height to length ratio of 1.2:3000), Shih et al. (l.2:4800), Arkilic et al. and Arkilic (l.3:7500), respectively. The famous Knudsen minimum of normalized mass flux is observed in IP and DSMC calculations of a short micro-channel over the entire flow regime from continuum to free molecular, whereas the slip Navier-Stokes solution fails to predict it.

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

Theoretical investigation of turbulent boundary layer over a wavy surface

The important features of the two-dimensional incompressible turbulent flow over a wavy surface of wavelength comparable with the boundary layer thickness are analyzed.

A turbulent field method using model equation for turbulent shear stress similar to the scheme of Bradshaw, Ferriss and Atwell (1967) is employed with suitable modification to cover the viscous sublayer. The governing differential equations are linearized based on the small but finite amplitude to wavelength ratio. An orthogonal wavy coordinate system, accurate to the second order in the amplitude ratio, is adopted to avoid the severe restriction to the validity of linearization due to the large mean velocity gradient near the wall. Analytic solution up to the second order is obtained by using the method of matched-asymptotic-expansion based on the large Reynolds number and hence the small skin friction coefficient.

In the outer part of the layer, the perturbed flow is practically "inviscid." Solutions for the velocity, Reynolds stress and also the wall pressure distributions agree well with the experimental measurement. In the wall region where the perturbed Reynolds stress plays an important role in the process of momentum transport, only a qualitative agreement is obtained. The results also show that the nonlinear second-order effect is negligible for amplitude ratio of 0.03. The discrepancies in the detailed structure of the velocity, shear stress, and skin friction distributions near the wall suggest modifications to the model are required to describe the present problem.

The effect of nozzle design on laser micro-machining of M2 tool steels

This paper shows how computational techniques have been used to develop axi-symmetric, straight, sonic-line, minimum length micro nozzles that are suitable for laser micro-machining applications. Gas jets are used during laser micro-machining processing applications to shield the interaction zone between laser and workpiece material, and they determine the machining efficiency of such applications. The paper discusses the nature of laser-material interactions and the importance of using computational fluid dynamics to model pressure distributions in short nozzles that are used to deliver gas to the laser-material interaction zone. Experimental results are presented that highlight unique problems associated with laser micro machining using gas jets.

Numerical simulations of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine

Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow. Copyright © 2006 by ASME.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

A numerical investigation of the flow structures and losses for turbulent flow in 90 degrees elbow bends

Computational fluid dynamic modelling was carried out on a series of pipe bends having R/r values of 1.3, 5, and 20, with the purpose of determining the accuracy of numerical models in predicting pressure loss data from which to inform one-dimensional loss models. Four separate turbulence models were studied: the standard k-epsilon model, realizable k-epsilon model, k-omega model, and a Reynolds stress model (RSM). The results are presented for each bend in the form of upstream and downstream pressure profiles, pressure distributions along the inner and outer walls, detailed pressure and velocity fields as well as overall loss values. In each case, measured data were presented to evaluate the predictive ability of each model. The RSM was found to perform the best, producing accurate pressure loss data for bends with R/r values of 5 and 20. For the tightest bend with an R/r value of 1.3, however, predictions were significantly worse due to the presence of flow separation, stronger pressure gradients, and high streamline curvature.

Implementation of Menter's Transition Model on an Isolated Natural Laminar Flow Nacelle

This study evaluates the implementation of Menter's gamma-Re-theta Transition Model within the CFX12 solver for turbulent transition prediction on a natural laminar flow nacelle. Some challenges associated with this type of modeling have been identified. The computational fluid dynamics transitional flow simulation results are presented for a series of cruise cases with freestream Mach numbers ranging from 0.8 to 0.88, angles of attack from 2 to 0 degrees, and mass flow ratios from 0.60 to 0.75. These were validated with a series of wind-tunnel tests on the nacelle by comparing the predicted and experimental surface pressure distributions and transition locations. A selection of the validation cases are presented in this paper. In all cases, computational fluid dynamics simulations agreed reasonably well with the experiments. The results indicate that Menter's gamma-Re-theta Transition Model is capable of predicting laminar boundary-layer transition to turbulence on a nacelle. Nonetheless, some limitations exist in both the Menter's gamma-Re-theta Transition Model and in the implementation of the computational fluid dynamics model. The implementation of a more comprehensive experimental correlation in Menter's gamma-Re-theta Transition Model, preferably the ones from nacelle experiments, including the effects of compressibility and streamline curvature, is necessary for an accurate transitional flow simulation on a nacelle. In addition, improvements to the computational fluid dynamics model are also suggested, including the consideration of varying distributed surface roughness and an appropriate empirical correction derived from nacelle experimental transition location data.