Local streaming velocity

If the shear rate is low and the thermostat is not applied to the direction of mean flow, most of these methods work well. At this point some comments about the implementation of the thermostat in the system under shear flow should be made. In a fluid under shear flow the velocity of the particles can be divided into two contributions the contribution due to the local stream velocity and the contribution due to thermal motion. The thermostat should act only on the thermal part of the particle velocity, and since this is unknown a priori, it is difficult to implement the thermostat on the velocity component in the direction of the flow. It was shown previously that inappropriate thermostat can bias the flow [9,84]. There are several ways of addressing this problem, for example, by applying the thermostat only on the y and/or z velocity components (the induced flow moves in the x direction). 

The original scheme utilized Gaussian isokinetic thermostats, whereas in Eqs. [217] we have replaced it with a Nose-Hoover thermostat. In this equation, the true local streaming velocity is given by iyy, + Usi(q,). In principle, there are no restrictions on u i, so the steady state velocity can be of any form hence, Evans and Morriss refer to Eqs. [217] as profile-unbiased thermostats (PUT). The PUT scheme requires only a reasonable prescription for determining the true local streaming velocity. 

It is interesting to observe that the original Evans-Morriss PUT equations of motion [Eqs. (217)] place the momenta in an unusual frame the p s are neither in the laboratory frame, nor are they truly thermal. The quantity being thermostated, hence the true thermal momentum, is p - mUgi. Since it is at least aesthetically desirable to have direct access to the peculiar momenta, a simple change of variables can be applied. In the process, the phase space is extended to include a dynamical variable for the local streaming velocity. The new equations of motion become ... 

As an acoustic wave travels through a medium, it can be absorbed. Because of the absorption of momentum in the direction of the sound field, flow is initiated in this direction. Local variations in intensity and energy absorption lead to local streaming velocities of the order of several centimeters per second. Finite amplitude waves create acoustic streaming due high absorption of higher harmonic components [14, 15]. 

Clear evidence exists that beyond the linear regime the synthetic thermostat influences the results. The role of the heat removing mechanism becomes especially important at high shear rates where the assumption of the linear velocity profile (iyyi is incremented in the position equation of equations 27) of the SLLOD shear flow is unrealistic. To allow the formation of kink instabilities in the velocity profile (turbulent flow) the simple thermostating scheme of equations (27) mast be replaced by a profile unbiased thermostat which makes no assumption about the local streaming velocity. ... 

Local air velocity The air velocity in the zone in which the design conditions have to be met. Or, the air velocity recorded at a specific location in a space or in a jet stream. 

We can do this simply only by making the approximation that P(c,z) P(c). This will be valid only when the streaming velocity V is much less than a, the most probable speed. (F , and the integrations become rather difficult. In such a case, however, when the plate is moving with molecular velocities, the use of a local Maxwellian velocity is probably very bad and the entire treatment breaks down. 

The aij values are the stoichiometric coefficients for component j in reaction i, ri is the rate of reaction i, uS is the local solids stream velocity, t is real time, and z is distance measured from the bottom of the reactor. 

To use the technique for our system of equations, we first make the assumption that the solids stream velocity is piecewise constant for very small axial sections of the reactor, i.e., for the local integration step. The solids velocity still varies significantly within the gasifier, but its change is assumed piecewise rather than continuous. 

However, this somewhat low average value should be tempered by the realization that local free stream velocities may be higher, and that the hot spots will be higher by about 70-90%. 

Larger structures have lower calculated deposition velocities as a result of their larger Reynolds numbers. This effect will be partially countered by higher free-stream velocities for taller structures. Blunt objects will tend to have lower average deposition as a result of their zones of separated flow. This may not pertain to local hot spots, however. 

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