Numerical Simulation Results

In the simulation results shown in Fig. 8.6, variation of the steady-state amplitude of vibration vs. the axial force is plotted. In these simulations, parameter values are taken from Table 8.1. hi addition, the mass and the damping coefficient of the translating part are set to m = 1 kg and c = lO Ns/ m. First, notice that the self-locking condition is satisfied for the selected value of the constant coefficient of friction (i.e., fi = 0.218 tan(5.57°) = 0.0975). Also note that, using the selected parameters  

As shown in Fig. 8.6, at low values of applied axial force (approximately R 20 N), the origin is stable since R — r itan/lcxQ 0, which means that Nq 0 

From the eigenvalue analysis of Sect. 8.4, it is evident that regardless of the level of linear damping (Co), instability (due to Painleve s paradoxes) occurs whenever 

For simplicity, in the remainder of this chapter, it is assumed that Cx = 0. Note that from (8.15), now we have sgn(No) = sgn(/ ). In terms of systems parameters, the equilibrium point is unstable whenever the following inequalities hold simultaneously  

Expectedly, the instability conditions given by (8.21) are the same as the necessary conditions for the Painleve s paradoxes discussed in Sect. 8.1. Limiting our study to the case of Q 0 for simplicity. Fig. 8.7 shows that the phase plane of the system is divided by N = 0 and 6 = 0 lines into four regions. In these regions, the system s equation has either no solution or two solutions when kinematic constraint instability is active (i.e., conditions of (8.21) are satisfied). Based on the discussions in Sect. 8.2, the following conclusions are drawn for the behavior of the lead screw model  

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In this work, as for the spark ignition of combustible mixtures, the authors mainly introduce numerical simulation results that have been obtained until then in their laboratory. As can be seen, the authors firmly believe that the numerical simulation has a significant tool to grasp the mechanism of spark ignition, though in the quiescent mixture. 

Numerical simulation results of specific mixture consumption rates during flame quenching a channel with D = 4 mm. Time between the frames is At = 0.004 s = 0.729). 

Baranski and Lu [209] have carried out, applying microelectrodes, voltammetric studies on ammonium amalgam in propylene carbonate solutions at room temperatures. The sweep rates up to 80 V s were appropriate for the analysis of the formation kinetics of this compound. Experimental and numerical simulation results have shown that ammonium amalgam was formed via fast charge-transfer process and its first-order decomposition was characterized by the rate constant of about 0.6 s . Diffusion coefficient of NH4 radical in mercury was estimated to be about 1.8 X 10 cm s k The formal potential of NH4+ (aq)/NH4(Hg) couple was determined as—1.723 V (SHE). 

In Fig. 4 it can be observed that the numerical simulations result in viability profiles qualitatively similar to the experiment. However in contrast to the experiment, in the simulations a considerable fraction of the cells in the center remains viable. In addition the critical glucose level fitted is very high, 4.5 x 10 3 //mol mm-3 compared to the initial glucose concentration of 5 x 10 3 Hmol mm-3. 

Figure 1.171 Numerical simulation results obtained with a pulsed flow from the perpendicular inlet, (a) Mean velocity as a function of time in the inlet (dashed line) and in the perpendicular inlet (solid line). Contour levels of the mass fraction of one liquid in the VZ-plane cross-section taken 0.25 mm downstream of the confluence at various times marked on the previous curves are also given.

Figure 1.172 Numerical simulation results obtained with a pulsed flow from both inlets, one flow being at 90° phase difference to the other.

Comparison experiment with numerical simulation results... 

Fig. 10.48 Numerical simulation results of nonisothermal flow of HDPE, Melt Flow Index MFI = 0.1 melt obeying the Carreau-Yagoda model for a typical FCM model wedge of e/h — 3 and =15. (a) Velocity (b) shear rate and (c) temperature profiles [Reprinted by permission from E. L. Canedo and L. N. Valsamis, Non Newtonian and Non-isothermal Flow between Non-parallel Plate - Applications to Mixer Design, SPE ANTEC Tech. Papers, 36, 164 (1990).]...

This paper describes the development and operation of a continuous rotating annular chromatographic reactor (CRACR) for gas-solid reaction systems at elevated temperatures. Experimental and numerical simulation results for the dehydrogenation of cyclohexane on a Pt/Al2C>3 catalyst are presented. 

Experiments in our tubular SCWO reactors are described in [1], A model for SCWO in a Modar vessel reactor was published recently [2]. This paper will describe our present work on a model for tubular flow SCWO reactors. Some numerical simulation results will demonstrate the use of the model to understand time dependent temperature instabilities. The paper also presents first results to derive process parameters from operational process data. 

Numerical simulation results of batch and continuous drying models for slices of peppers in packed beds were presented in this work. The reported models were based on differential mass and energy balances in the dryer along with kinetic equations describing transport phenomena in individual particles and product quality deterioration. The shrinkage problem was... 

Numerical simulation results of the dynamics of the solute concentration (C) and the 0th moment (mo) (i.e., the particle number per unit volume) in a MSMPR precipitator initially filled with crystal free solvent and in a semi-batch crystallizer filled with crystal free solvent to 50% of its final volume, are shown in Figure... 

Figure 4.11 Effect of hydrodynamic interactions for spherical solutes in cylindrical fiber media. Adapted from [79] parameters for Equation 4-29 were obtained by fitting numerical simulation results. Each of the lines represents the variation of F with fiber volume fraction for systems with a particular value of 7. (which varies between 0.1 and 1 in this figure).

As an example. Figure 5 shows a comparison between results calculated from Equations 9 and 10 with numerical simulation results (data points) for initial mean log(K) =-15. A good agreement is... 

Figure 5. A comparison between results calculated from Equations 9 and 10 and numerical simulation results (data points).

To further test the value of the effective approach, numerical simulation results of transient water content are compared against the experimental results in Figure 3. A reasonable match between the numerical and the experimental results is obtained. 

First, the numerical simulation results show that the floor boreholes can transfer high stress to the deeper strata, the shallow strata stress can be reduced significantly. This result has ensured the stability of the large cross section mining roadway. But the convergence of roadway sides affected by floor drilling is not obvious. 

According to the literature, goaf float coal is prone to spontaneous combustion in oxygen concentration of 5% to 18% (Luo et al. 2002, Wang 2005). Numerical simulation results based on Fluent software can be used to calculate the distribution range... 

According to the numerical simulation results, the scope affected by the fracture of thick and hard critical stratum and main roof ranges 350 435 m from the open-off cut. 

The purpose of increasing permeability can be achieved at a lower pressure by using pulsating hydraulic fracturing. Meanwhile, the numerical simulation results can predict the fracturing... 

Comparison between numerical simulation results and site monitoring results... 

The Figure 5 is the curve of comparison between numerical simulation results and site monitoring results. It can be seen that the simulation is... 

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