Velocity deficit

In the abstract of the paper (Ref 36a, p 1920) it is stated The limiting slope of he detonation velociry-wave front curvature locus for small- velocity deficits is obtained under an assumption concerning the "reaction zone length as related to the charge diameter and the radius of curvature of the wave front. The model is an extension to two dimensions of von Neumann s classical theory of the plane wave detonation... 

Thus, to recap the derivation, consider the situation shown in Fig. 9.21. As discussed in Chapter 5, it is assumed that lumps from layer 2 arrive at layer 1 with a velocity deficit of ... 

Now, the lump of fluid from 2 will arrive at l with a velocity deficit (as mentioned before, du/dy is taken as positive) that is given by ... 

TABLE 6.1. Comparison of calculated and observed fractional velocity deficit at 1-atm pressure in I-cm radius tubes [58]... 

Figure 6.5 Top view of canopy. Circles represent cylindrical stems of diameter d. Behind each stem is a recirculation zone (black) of length yd, where y is an 0(1) function Re. The wake downstream of each recirculation zone has length (Co ) 1 (light gray). Where wakes overlap (dark gray), the velocity deficit is the linear sum of individual wake deficits. Particles 1, 2, 3 released together at x = 0 and t = 0 pass through different velocity zones and travel different longitudinal distances (x1,x2,x3) in time, t, such that the spatial variance in the velocity field produces longitudinal dispersion.

Next, consider the wakes downstream of the recirculation zone. White and Nepf [643]derived the following expression for the velocity deficit, uw, in the wake of a cylinder (stem) located at x = 0 and y = 0 within an array of cylinders,... 

The skin friction coefficient varies with Re, the Mach number, M, (when it involves incompressible fluids of local speeds less than the sonic speed, 1), and the character of the boundary layer. The momentum transferred between the air and the body surface appears as a velocity deficit in the viscous wake behind the body. 

For experiments in which the equivalence ratio was greater than 0.2, it was found that the measured velocity was lower than that predicted by CJ calculations. This was not unexpected — previous studies have reported velocity deficits for spray detonation. It was found that the velocity deficit increased with equivalence ratio. Liquid mass loading also increases with equivalence ratio. It is therefore possible that this effect is due to gcis-phase saturation or to processes that tend to slow the evaporation rate of the droplets (e.g., cooling due to latent heat). It can be further noted that the velocity deficit increases with decreasing fuel pressure (i.e., with increasing droplet diameter). This may also be attributable to a decreased rate of evaporation. Velocity deficit and its causes will be explored in more detail in future experiments. 

For effective use of the developed model, information on the induction time and droplet evaporation rates, as a function of the local conditions in the shock-heated mixture, is needed. Currently, in the absence of such information, parametric studies with various constant induction times and droplet evaporation rates have been carried out. The predicted detonation velocity as a function of the initial droplet size is shown in Fig. 11.6 for a nominalJP-lO-oxygen mixture with an equivalence ratio of 0.12. A d -law evaporation with a rate of 0.1 cm /s and an induction time for the fuel-vapor of 1 //s was used for this series of simulations. The velocity deficit observed previously in many experimental studies of multiphase detonations is predicted by the numerical model. In the absence... 

The trace material, after being released, is swept along with the flow. If one does not resolve the motion of single particles, qualitative itrformation on the flow structure (streamhnes, vortices, separated flow regimes) becomes available from the observed pattern. The identification of the motion of individual tracers provides quantitative information on the flow velocity, provided that there is no velocity deficit between the tracer and the fluid. Only in the case of fluorescent (or phosphorescent) tracers is it... 

The following typical combustion velocities have been observed the turbulent deflagration mode with a velocity of some dozens of meters per second in lean mixtures the sound deflagration mode, high-speed deflagration with 800-1,000 m/ s velocities, when the combustion front moves with the local sound speed relative to the reaction products the quasi-detonation mode when the velocity spectra exceeds 1,100 m/s, but is 200-500 m/s less than the CJ detonation velocity. The quasi-detonation mode velocity deficit, in comparison with thermodynamic defined values, is explained by impulse losses due to interactions with walls and obstacles. 

The work [40] deals with the redistribution of filler particles in the process of injection molding. In this case nonuniform distribution may occur both in the cross-section of a sample and along its length. Both kinds of nonuniformity are linked together if particle moves away from the mold walls it enters the zone of high velocity flow, therefore, a deficit of particles near the walls should be accompanied with a surplus of them far from the inlet. It should be noted that all the works mentioned consider spherical particles there are no theoretical or experimental studies of the redistribution of particles of other shapes, say, fibers or bars. 

Introducing the concentration deficit due to loss of radiogenic element times r as the new variable v(r, t), not to be confused with a velocity, we obtain... 

These authors used the global average piston velocity determined by Broecker and Peng (391 by the radon deficit method, 2.8 m/day. The Othmer-Thakar relationship was used to calculate the diffusivity of DMS, which has never been determined experimentally. Since the calculated diffusivity for DMS (1.2 x 10-5 cm2/s) is similar to that calculated for radon, the radon deficit piston velocity was assumed to apply to DMS without correction. The DMS concentrations used in this study were based on more than 600 surface ocean samples from a variety of environments. The global area weighted concentration used for the calculation was 102.4 ng S/l, resulting in a flux of 39 x 1012 g S/yr. 

Figure 4. Box model results compared to Caribbean transect data ((6), solid symbols). Units are m/day for Vp and 106 molecule/cm3 for midday maximum OH. (a) Runs using piston velocities obtained from the radon deficit (V Rn = 3.1) and SFg lake study (VpSF6 = 2.2) wind speed relationships. Midday maximum OH concentrations (shown on plot) were adjusted to give mean DMS levels in agreement with the shipboard data, (b) Model runs with lower piston velocities and lower OH showing less diurnal variation. Conditions used were (a) Vp = 1.7, OH = 8.0 (b) Vp = 1.1, OH = 5.0 (c) Vp = 0.6, OH = 3.0.

Sensorimotor deficits imitating peripheral nerve involvement were reported (Back and Mrowka 2001). Ulnar and median nerve-like deficit were due to infarcts located in the thalamus and the corona radiate (Lampl et al. 1995). We have seen two patients with radial nerve-like deficits due to cortical ischemic lesions of the cortical presentation of the hand in the motor cortex. Normal nerve conduction velocity and MRI help to clarify these cases. 

Obviously the theory of evaporation from large areas is quite complex, requiring computer evaluation even if all relevant data were available. There is, however, a vast amount of accumulated experimental data about water evaporation, and if we can establish the relationship between water and pesticide evaporation, we can use this material for prediction. The evaporation of water over a large area can always be viewed either as a small- or large-scale process. Thus, we can measure total evaporation from a lake in relation to wind conditions and the humidity and temperature of the air as it reaches the lake, or from small identical open vessels floated at various locations on the lake surface. The first would show an average rate roughly proportional to the 3/2 power of the lake diameter (if circular), to the 1/2 power of the wind velocity, and to the humidity deficit of the incoming air. The second would show a rate approximately proportional to the local humidity deficit but more nearly proportional to vessel area. 

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