Nonlinear Simulation

Plantwide management and optimization Economic Steady state, linear algebraic correlations or nonlinear simulator... 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

Figure 24 shows dynamic linear and nonlinear simulations of the gas temperatures at C = 0.17and = 0.38, and Fig. 25 shows the exit CO and C02 concentrations for a 50-sec disturbance in the inlet gas temperature from 573 to 601.65 K (a 5% increase) and in the inlet CO concentration from a mole fraction of 0.06 to 0.072 (a 20% increase). Again we find that only minor... 

Figure 3.45 gives a Matlab program for the nonlinear simulation of the autorefrigerated reactor. The specific case is the 90% conversion with a cooling water temperature in the condenser of 317 K. The reactor volume is 1.68 m3, and the reactor temperature TR is 353 K. The condenser area is 19.9 m2, and the condenser temperature Tc is 331 K. The temperature differential driving force is 331 - 317 = 14 K to transfer 0.237 MW. 

Li H., Colgate S. A., Wendroff B., and Liska R. (2001) Rossby wave instability of thin accretion disks III. Nonlinear simulations. Astrophys J. 551, 874-896. 

The expression derived by Despic and Bockris gives a potential dependence of especially when initial- and final-state profiles cross asymmetrically (see Fig. 15), i.e., when AFq is either a large exothermic or endothermic quantity, so that the transition state is, respectively, either close in configuration to the final state or to the initial state. The Tafel relation is consequently nonlinear simulated Tafel relations were calculated showing this behavior. 

It will be clear from the detailed analysis of a realistic process system that analytic linearization is unlikely to be a trivial exercise. The amount of detailed mathematical analysis often needed means that it cannot be recommended for every case. And certainly it should never be regarded as an alternative to full, nonlinear simulation. However, if the control engineer does carry out such a linear, block-diagram analysis and... 

After a constitutive model has been chosen, calibrated, and validated for a particular fluoropolymer, it becomes as easy to perform multiaxial deformation simulations as it is to simulate uniaxial deformation. If the material model considers time dependence, temperature dependence, or damage evolution, then thermomechanical or fatigue loading can also easily be simulated. Since almost all commercial finite element (FE) software packages allow for nonlinear simulations including considerations of large deformations, the key component of performing accurate finite element simulations lies within the specification and calibration of the constitutive model. 

The control structures identified by the controllability analysis are tested by full nonlinear simulation. Here the first task consists of implementing and tuning of controllers. The use of prescribed local control structures, or setting perfect control for fast loops simplifies this task and preserves the plantwide character of the analysis. 

Song et al (2006) proposed a multivariable purity control scheme using the m-parameters as manipulated variables and a model predictive control scheme based on linear models that are identified from nonlinear simulations. The approach proposed by Schramm, Griiner, and Kienle (2003) for purity control has been modified by several authors (Kleinert and Lunze, 2008 Fiitterer, 2008). It gives rise to relatively simple, decentralized controllers for the front positions, but an additional purity control layer is needed to cope with plant-model mismatch and sensor errors. Vilas and Van de Wouwer (2011) augmented it by an MPG controller based on a POD (proper orthogonal collocation) model of the plant for parameter tuning of the local PI controllers to cope with the process nonlinearity. 

Kiranoudis et al. [20] developed a dynamic model for the simulation of conveyor-belt dryers and proposed a SISO (single-input, single output) control scheme for the regulation of material moisture content. In a subsequent work, Kiranoudis et al. [21] extended the dynamic model of this process to include MIMO (multiple-input, multiple output) schane to control the material moistme content and temperature. In both works, PI controllers were appropriately tuned and nonlinear simulations were performed. 

Park, H., S. D. Heister Nonlinear simulation of free surfaces and atomization in pressure swirl atomizers, Phys. Fluids 18, 052103 (2006). 

Abstract Plain orifice, or pressure atomizers are the most commonly used atomizers due primarily to their simplicity and ease of manufacture. This chapter provides background on the characteristics of these devices in terms of spray production and general behavior. Classical linear theories are reviewed to provide a basis for theoretical droplet size predictions. More recent developments assessing the unsteadiness within these devices, and its role in spray production, is also provided in subsequent discussion. The chapter closes with modem nonlinear simulations of spray production using modem numerical techniques. 

J. H. Hilbing and S. D. Heister, Nonlinear simulation of a high-speed, viscous, liquid jet. Atomization Sprays, 8, 155-178, 1997. 

The adsorbents used in the Parex and Ebex processes are all various cationic forms of faujasite (Table 12.6). Due to the effect of liquid hold-up in the macropores, the effective separation factor fot a pelleted zeolite adsorbent is appreciably lower than the separation factor for the same material in unaggregated form. The number of theoretical stages required for any specified product purity decreases as the separation factor increases, but the relationship is highly nonlinear. Simulation studies reveal that for an economic process the minimum acceptable intrinsic separation factor between the extract and raffinate products is about 3. With a separation factor of less than... 

Preparation of 3D dynamic models suitable for a time history analysis of the racks which includes the assemblage of all racks in the SFP, all fluid coupling interactions, and mechanical couplings appropriate for a nonlinear simulation. 

Keywords Impedance standard, nonlinearity, simulation, four point measurment, HELIOS... 

Based on the above theoretical considerations, the dynamics of pattern formation in EHD instability has been modeled using LSA [236, 237, 241, 249, 250], and 3D nonlinear simulations [251, 252]. Linear stability analysis accounts for the forces acting on the film interface to determine the fastest mode of growth. The stability... 

The nonlinear simulation was used to illustrate the closed-loop response of the controlled variable X2 following a 30 percent increase in feed composition. The results are shown in Figure 21.4b with the feedback-only dual and PID algorithms. Control is immensely improved with the feedforward action. The slight deviation in X2 with feedforward control is due to inaccuracies in the linear model and the long sampling time relative to the process dead time. The... 

Again, for a certain interval of Z [AOT] the interface between the two ME can be destabilised, and in this case it deforms into fingers that grow vertically and symmetrically with time across the interface (see Fig. 6(b)). These structures are successfully predicted by the analysis of the density profile obtained from the cross-diffusion model in analogous conditions and the phenomenology favourably compares with nonlinear simulations. 

Budroni, M.A. Cross-diffusion-driven hydrodynamic instabilities in a double-layer system general classification and nonlinear simulations. Phys. Rev. E 92(6), 063007 (2015)... 

Beer M, Liebscher M (2008) Designing robust structures a nonlinear simulation based approach. Comput Struct 86 1102-1122... 

Zhao H, Yuan Y, Ye Y (2012) Simplified nonlinear simulation of steel-concrete composite beams. J Construct Steel Res 71 83-91... 

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