Evolución de la dirección y gestión de recursos humanos

660 640 620 600 580 conduction 560 convection _ j I 20 40 60 time (s) 80 100 0.50 640 0.45 620 0.40 0.35 a . 0.30 580 0.25 0.20 560 0.15 100 20 Q. 0> x: time (s)

Figure 7.10 Comparison o f predicted temperature profiles for four descriptions of heat loss. Numerical simulations. Reactants: n-heptane/oxygen. RH:02 =1 : 1 (by vol.). po = 62 torr. To = 559 K (286 °C). Cylindrical batch reactor. Volume = 330 cm^.

Figure 7.11 Predicted temperature and n-heptane consumption profiles. Curve a, temperature; curve b, n-heptane. Numerical simulations. Reactants: n- heptane/oxygen. RH:02 = 1:1 (by vol.). po = 62 torr. To = 559 K (286 °C). Cylindrical batch reactor. Volume = 330 cm Mode o f heat loss: Conduction.

620 1 2 600 S. E B 580 560 — — b 20 40 60 time (s) 80 100 'c o 0.40 I 0.35 I (D 0.30 0) -9 0.25 0.20 0.15 620 0.35 E ro 600 0.30 580 0.25 0.20 560 0.15 100 time (s)

Figure 7.12 Predicted temperature and n-heptane consumption profiles. Curve a, temperature; curve b n-heptane. Numerical simulations. Reactants: n- heptane/oxygen. RHiOi = 1:1 (by vol.). p„ = 62 torr. To = 559 K (286 °C). Cylindrical batch reactor. Volume = 330 cm^. Mode o f heat loss: Convection (inside reactor).

Figure 7.13 Predicted temperature and n-heptane consumption profiles. Curve a, temperature; curve b n-heptane. Numerical simulations. Reactants: n- heptane/oxygen. RH:02 = 1:1 (by vol.). po = 62 torr. To = 559 K (286 °C). Cylindrical batch reactor. Volume = 330 cm^. Mode o f heat loss: Convection (outside reactor).

Chapter Seven

Results and Discussion— Heat Losses

7,4,4 The preferred choice o f heat loss model

Having established that different descriptions o f heat loss yield different solutions to the numerical simulations, a choice is made as to which description is the most suitable, in terms o f closeness to physical reality and also how well the respective numerical simulations match experimental observations. With respects to the latter requisite one may well argue that from Table 7.1 the inclusion o f any o f the heat loss descriptions yield solutions that far from match experimental observations. However, since multiple cool flames are detected experimentally, some form o f heat loss must necessarily be included and so a compromise should be expected when attempting to describe the heat loss pertinent for this particular experiment. As for the physical reality o f the experiment, Ashmore et al. (1967) have suggested that for Rayleigh numbers (Ra) lower than 600 conduction prevails, whilst for Ra > 600 convection dominates.

The dimensionless Ra is the product o f the Prandtl number (Pr) and the Grashof number (Or):

Ra = Pr.Gr (7.12)

CpM p^r^gPAT (7 ,1 3 )

k • p'

where: Cp = specific heat capacity at constant pressure p = kinematic viscosity

k = thermal conductivity p = density

r = radius o f reactor

g = acceleration due to gravity P = coefficient o f thermal expansion

AT = temperature difference between “hot” and “cold” parts o f mixture.

Values for air are adopted in calculating the relevant parameters for Ra for all numerical simulations for ease and rapidity o f calculation. For the range o f temperatures encountered during experimental trials, approximately 500 K to 800 K, Pr may be taken as constant («0.7) (Welty, Wicks & Wilson, 1984). Values for the sub-group (gpp^/p^) o f the Grashof number are tabulated in Welty, Wicks & Wilson (1984) as a function o f temperature and for the temperature range o f concern have values o f order zero

(1/K.cm^). The reactor has an internal radius o f 4.3 cm, so r^ = 79.51 cm^. For values o f the sub-group (gppVp^) greater than 1.5 K'\cm'^, ie. for temperatures below approximately 800 K, Gr = AT.O(2); where O denotes order. Thus Ra = 0.7Gr (since Pr is approximately constant) = 0.7AT.0(2). The temperature difference required for the onset o f convection is given by

AT= — ( 7. 14)

0.70(2) 0.70(2)

The maximum temperature difference required occurs when Gr = 100.AT, giving AT = 8.5 K. Calculated values o f Ra from numerical simulations suggest that the critical value o f Ra is exceeded for temperature differences o f 3-5 K. Such temperature differences are achieved in the early stages o f propagation o f the first cool flame. This result, combined with the assumption that a steady-state temperature profile exists at any instant, persuades one to consider convection rather than conduction as the more pertinent description o f heat loss.

7.5 Further considerations

Convective processes rely upon fluid motion. For the system in question this motion arises from temperature, and hence density, differences occurring in the gaseous mixture contained within the reactor, and is termed natural convection. Assuming that a temperature increase, due to chemical reaction, occurs in some part o f the gaseous mixture located centrally in the reactor, then the hotter part o f the fluid rises to the top o f the reactor and is replaced by cooler fluid moving in from the bottom o f the reactor. The resulting flow pattern is shown in fig. (7.14). A thermal boundary layer and a velocity boundary layer, not necessarily o f equal thickness, will exist at the reactor walls and it is the thermal boundary layer which provides resistance to heat transfer from the higher temperature bulk fluid (the fluid exterior to the boundary layer).

Since a circulation o f the gaseous mixture occurs due to natural convection, it follows that temperature, and concentration, variations will exist within the reactor. Since the rate o f reaction is a function o f temperature and concentration, it is possible that the spatial variations introduced by natural convective motion will lead to variations in the reaction rate at different parts o f the mixture. This implies that with significant spatial variations in the reaction rate different parts o f the mixture react at different times, a situation similar to the occurrence o f knocking in a spark-ignition engine. Spatial

Chapter Seven Results and Discussion— Heat Losses

variations variations in temperature and concentration may be reduced if the velocities in the bulk o f the fluid, i.e. the fluid exterior to the boundary layer, are large enough to reduce the thickness o f the boundary layer. This may be achieved by stirring the mixture by means o f a mechanical stirrer, in which case the convection is classified as forced and a higher heat transfer rate, than natural convection, is encountered.

gravity

reactor wall, T,

Figure 7.14 Natural convection flow pattern in a cylinder

Spatial variations in temperature and concentration may be most significant when a temperature rise first occurs in the reacting mixture, i.e. when steady-state temperature and velocity profiles within the reactor are yet to be established. Spatial variations will almost certainly be important if reaction initially occurs in some small part o f the gaseous mixture. In the preceding sections o f this chapter the part o f the gaseous mixture where reaction took place was called the reacting mixture and was defined as the entire contents o f the vessel, effectively assuming that the boundary layer is thin enough to allow the approximation that the volume o f the reacting mixture is the volume o f the reactor. If, however, the reacting mixture were not the entire contents o f the vessel but some portion o f it then potentially large spatial concentrations may arise. The (now smaller) volume o f the reacting mixture reacts before the rest o f the bulk fluid and will have a different product distribution, particularly after cool flame propagation. That initial reaction may occur in some small part o f the gaseous mixture stems from the observation o f “hot spots” in spark-ignition engines responsible for knocking (Griffiths & Barnard, 1995).

7.6 Summary

In this chapter the influence o f different descriptions for heat loss on the predicted behaviour o f the chemical model have been explored. Unfortunately, for certain initial conditions the numerical simulations compare poorly with experimental observations, regardless o f the description o f heat loss. However, different descriptions o f heat loss do appear to yield different solutions to the numerical simulations. Two-stage ignition is only simulated when there is no heat loss (adiabatic case) and multiple cool flames are only possible when some form o f heat loss is included. The magnitude o f heat loss significantly affects the predicted behaviour o f the chemical model (conduction and convection cases) although one should take into account the mode o f heat transfer that is most likely to apply to the physical situation.

Chapter Eight Results and Discussion— Kinetic Analysis