Density ratios

S has been approximated for flames stabili2ed by a steady uniform flow of unbumed gas from porous metal diaphragms or other flow straighteners. However, in practice, S is usually determined less directly from the speed and area of transient flames in tubes, closed vessels, soap bubbles blown with the mixture, and, most commonly, from the shape of steady Bunsen burner flames. The observed speed of a transient flame usually differs markedly from S. For example, it can be calculated that a flame spreads from a central ignition point in an unconfined explosive mixture such as a soap bubble at a speed of (p /in which the density ratio across the flame is typically 5—10. Usually, the expansion of the burning gas imparts a considerable velocity to the unbumed mixture, and the observed speed will be the sum of this velocity and S. ... 

The preceding equations, which have assumed that both the air and the water vapor benave as ideal gases, are sufficiently accurate for most engineering calculations. If it is desired to remove the restriction that water vapor oehave as an ideal gas, the aclual density ratio should be used in place of the molecular-weight ratio in Eqs. (12-5) and (12-6). 

It is interesting to generalise this solution for any core skin density ratio. Fig. 2.20 shows how the optimum skin thickness varies with D. This is independent of the solid material density or modulus but is based on a weight... 

Fig. 2.20 Variation of optimum skin thickness with core skin density ratio...

Once the piston-driven flow field is known, the flame-driven flow field is found by fitting in a steady flame front, with the condition that the medium behind it is quiescent. This may be accomplished by employing the jump conditions which relate the gas-dynamic states on either side of a flame front. The condition that the reaction products behind the flame are at rest enables the derivation of expressions for the density ratio, pressure ratio, and heat addition... 

A f = Liquid gradient per row of caps, uncorrected, in. if) = Relative froth density, ratio of froth density to clear liquid density ... 

The Haring-Blum cathode is divided into two equal plane areas, distant f 1 and fj from a common anode, and a quantity called the primary current density ratio P is defined as... 

Since, however, at any given pressure there is for all substances a unique value of the density ratio pjpy evaluated at the saturation temperature, Eq. (36) may be rewritten as... 

This allows the pressure, which has significance only when the fluid experiencing it is named, to be replaced by a dimensionless group of properties which has significance for all fluids. Thus, the first requirement in constructing a model of a system is that the inlet pressures should be selected so that the density ratio of the two phases in the model is the same as that in the system... 

Solution In a real problem, the individual values for k, V, and Qi would be known. Their values are combined into the dimensionless group, kVIQi . This group determines the performance of a constant-density reactor and is one of the two parameters needed for the variable-density case. The other parameter is the density ratio, r = Pmommer/Ppoiymer- Setting kVIQtn = 1 gives T = 0.5 as the fraction unreacted for the constant-density case. The individual values for k, V, Qi , Pmommer, and Ppoiymer can be assigned as convenient, provided the composite values are retained. The following... 

Eddie, Y. N. and Liu, N., "Stress-Density Ratio Slip-corrected... 

Hasegawa, T. and Nishikado, K., Effect of density ratio on flame propagation along a vortex tube. Proceedings of the Combustion Institute, 26, 291-297, 1996. 

Consider a planar premixed flame front, such as that sketched in Figure 5.1.1. For the moment, we will be interested only in long length scales and we will treat the flame as an infinitely thin interface that transforms cold reactive gas, at temperature and density T p, into hot burnt gas at temperature and density T, A.-The flame front propagates at speed Sl into the xmbumt gas. We place ourselves in the reference frame of the front, so cold gas enters the front at speed = Su and because of thermal expansion, the hot gases leave the front at velocity 14 = Sl(Po/a)- The density ratio, Po/Pb, is roughly equal to the... 

Si is the laminar flame velocity, the function Z(co) is the heat response function Equation 5.1.16, whose real part is plotted in Figure 5.1.10. The function f(r, giJ is a dimensionless acoustic structure factor that depends only on the resonant frequency, a , the relative position, r, of the flame, and the density ratio Pb/Po-... 

Using Pe = vh/k and Nu ar /k, where h is the vessel width, V the flame speed v = Sl , where > 1 is the density ratio across the flame), and r the flame radius, a quenching radius... 

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