Gear integrator

Note PSpice does not support the Gear integration option. It instead relies on a modified trapezoidal-Gear integration algorithm for transient timestep operation. 

PSpice does not offer the option of switching to Gear integration, instead a combination of trapezoidal and gear integration is always used. 

Figure 8.53 IsSpice results of Colpitts oscillator (Gear integration).

The approximating scheme converts the system of partial differential equations to a set of ordinary differential equations in the axial spatial coordinate. The detailed equations are contained in Yu et al. (2). The advantage of reduction in this manner is that the transient location of the combustion zone does not have to be known a priori, but can be found in the course of the integrations. Gear integration, which is designed for stiff systems, is used to solve the two point boundary value problem in the axial direction. 

Gear C W 1966 The numerical integration of ordinary differential equations of various orders ANL 7126... 

The reaction rate equations give differential equations that can be solved with methods such as the Runge-Kutta [14] integration or the Gear algorithm [15]. 

With these reaction rate constants, differential reaction rate equations can be constructed for the individual reaction steps of the scheme shown in Figure 10.3-12. Integration of these differential rate equations by the Gear algorithm [15] allows the calculation of the concentration of the various species contained in Figure 10.3-12 over time. This is. shown in Figure 10.3-14. 

In the electronics industry. Pis find wide appHcations as a dielectric material for semiconductors due to thermal stabiHty (up to 400°C) and low dielectric constant. Pis are being considered for use in bearings, gears, seals, and prosthetic human joints. The intended part can be machined or molded from the PI, or a film of PI can be appHed to a metallic part. Because of their superior adhesion, dielectric integrity, processing compatibUity, and lack of biological system impact. Pis have been used in many biological appHcations with particular success as body implants. 

With the introduction of Gear s algorithm (25) for integration of stiff differential equations, the complete set of continuity equations describing the evolution of radical and molecular species can be solved even with a personal computer. Many models incorporating radical reactions have been pubHshed. 

Packages exist that use various discretizations in the spatial direction and an integration routine in the time variable. PDECOL uses B-sphnes for the spatial direction and various GEAR methods in time (Ref. 247). PDEPACK and DSS (Ref. 247) use finite differences in the spatial direction and GEARB in time (Ref. 66). REACOL (Ref. 106) uses orthogonal collocation in the radial direction and LSODE in the axial direction, while REACFD uses finite difference in the radial direction both codes are restricted to modeling chemical reactors. 

Ordinaiy differential Eqs. (13-149) to (13-151) for rates of change of hquid-phase mole fractious are uouhuear because the coefficients of Xi j change with time. Therefore, numerical methods of integration with respect to time must be enmloyed. Furthermore, the equations may be difficult to integrate rapidly and accurately because they may constitute a so-called stiff system as considered by Gear Numerical Initial Value Problems in Ordinaiy Differential Equations, Prentice Hall, Englewood Cliffs, N.J., 1971). The choice of time... 

For both the finite difference and collocation methods a set of coupled ordinaiy differential eqiiafions results which are integrated forward in time using the method of hnes. Various software packages implementing Gear s method are popular. 

Other timing switch gear works with electronic digital clocks. The 1-s time interval derived from the mains frequency is counted in an integrating counter. The... 

Figure 1-4. Cross-seotion of an expander with integral gear for power reoovery.

The more reeent eombination of standardized eompressor modules and eustomized eomponents with integrally geared radial turbines has opened new possibilities. Integrally geared radial turboexpanders represent eonsiderable design flexibility and this, in turn, allows... 

Figure 4-36. A single integral gear box connects one or more expanders to several compressor stages. (Source GHH-Borsig.)...

In the case of nitrous acid plants, application of integrally geared process gas radial turbines and compressors are used in plants with capacities ranging from 120-600 t/day and higher. For air compression, up to three compressor stages are connected in series. To increase efficiency, the inlet temperature of the individual stages is reduced by using two external intermediate coolers. 

Figure 4-39. Integrally geared multistage compressor. (Source Demag Delaval.)...

The first documented use of dry gas seals in turboexpanders was in 1989. At that time, an ethylene plant in Scotland worked with a dry gas seal manufacturer to retrofit a turboexpander-integral gear-generator package. The partial success of that project was sufficiently encouraging for both user plant and turboexpander manufacturer to undertake a redesign of all three expander stages. Dry face or gas seals were installed at that time. 

The main power source is a 2,200 kW rated motor, which drives two high-speed pinions through integral gears. The first stage of the compressor operates at 17,900 rpm, while the second and third stages operate at 21,800 rpm. The unit is controlled by a local control system, but operators can also monitor the operating parameters from the plant control room. 

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