Gases motion

Chapcer 4. GAS MOTION IN A LONG TlfBE AT THE LIMIT OF BULK DIFFUSION AND VISCOUS FLOW... 

Chapter 6. SOME IMPORTANT EXPERIMENTAL RESULTS ON GAS MOTION IN POROUS MEDIA And capillaries... 

Real-life premixed flame fronts are rarely planar. Of course, if the flow is turbulent, gas motion will continuously deform and modify the geometry of the flame front, see Chapter 7. However, even when a flame propagates in a quiescent mixture, the front rapidly becomes structured. In this chapter, we will discuss hydrodynamic flame instability, thermo-diffusive instability, and thermo-acoushc instability. 

The gas motion near a disk spinning in an unconfined space in the absence of buoyancy, can be described in terms of a similar solution. Of course, the disk in a real reactor is confined, and since the disk is heated buoyancy can play a large role. However, it is possible to operate the reactor in ways that minimize the effects of buoyancy and confinement. In these regimes the species and temperature gradients normal to the surface are the same everywhere on the disk. From a physical point of view, this property leads to uniform deposition - an important objective in CVD reactors. From a mathematical point of view, this property leads to the similarity transformation that reduces a complex three-dimensional swirling flow to a relatively simple two-point boundary value problem. Once in boundary-value problem form, the computational models can readily incorporate complex chemical kinetics and molecular transport models. 

When considering that all the dimensionless values are functions of the dimensionless values y, tu A where A (A=r/VTJt) is the only variable, Sedov stated that the gas motion is automodeling, and the problem of detg it is reduced to integration of ordinary differential equations... 

Gas Motion Under the Action of Short-Duration Pressure (Impulse) 107... 

In order to complete the solution of the problem of gas motion under the action of a short impulse, we must not only find the exponents and dimensionless functions, which is accomplished by integrating the ordinary differential equations. We must also determine the numerical coefficients A and B in the formulas. 

What problems face the theory of combustion The theory of combustion must be transformed into a chapter of physical chemistry. Basic questions must be answered will a compound of a given composition be combustible, what will be the rate of combustion of an explosive mixture, what peculiarities and shapes of flames should we expect We shall not be satisfied with an answer based on analogy with other known cases of combustion. The phenomena must be reduced to their original causes. Such original causes for combustion are chemical reaction, heat transfer, transport of matter by diffusion, and gas motion. A direct calculation of flame velocity using data on elementary chemical reaction events and thermal constants was first carried out for the reaction of hydrogen with bromine in 1942. The problem of the possibility of combustion (the concentration limit) was reduced for the first time to thermal calculations for mixtures of carbon monoxide with air. Peculiar forms of propagation near boundaries which arise when normal combustion is precluded or unstable were explained in terms of the physical characteristics of mixtures. 

In order to interpret this recently discovered, but absolutely fundamental fact, we shall consider more carefully the conditions of the gas motion. The flame functions as a piston, and the dependence written above of the gas velocity on the flame velocity, w — (n—l)u, is valid insofar as the combustion products do not cool. Therefore, for detonation to occur the ratio of the drag and heat transfer is of particular importance. It is precisely in rough tubes that conditions are most favorable the increased drag accelerates the establishment of the velocity profile, while the heat transfer remains practically unchanged by the introduction of roughness. 

We presented the theory as applied to ignition of a mixture at the closed end of a tube. Ignition at some distance from the closed end increases the amount of the substance which burns in unit time (since combustion will propagate in both directions from the point of ignition), and will accelerate the gas motion which depends on its expansion during combustion. And indeed, experiment shows some decrease in the distance at which detonation appears. 

In contrast, for ignition at the open end of a tube the expanding combustion products flow out into the atmosphere and create much lower compression and gas motion before the flame front. However, as the flame moves... 

But it is easy to see that the same results will be valid for any other means of heat transfer as well, for example, by a cold flow of explosive mixture blowing over the igniting surface. It is only necessary that within a thin boundary layer near the igniting surface—within several units variation of 6 and —the influence of the gas motion not be felt, and a purely conductive regime take place (one corresponding to the plane case so that... 

The problem considered in this paper of a self-sustaining propagation wave of flame is closely related to self-similar solutions of the second kind, considered by Ya.B. in his paper, Gas Motion Under the Action of Short-Duration Pressure (Impulse) (see article 9 of the present volume) nearly twenty years later. Indeed, we are dealing here with wave-like solutions, for instance,... 

Studying anew the differential equations of heat conduction, diffusion, gas motion and chemical kinetics under the conditions of a chemical reaction (flame) propagating in a tube, through a narrow slit or under similar conditions, using the methods of the theory of similarity we find the following dimensionless governing criteria ... 

Thus, it is not the absolute value of D, but its ratio with k that determines the character of the phenomena. Convection blurs the effect in convective motion the particles of gas which carry quantities of material and heat are in the ratio of the concentration to the product of the specific heat and temperature, which corresponds to equality of the effective (related to the gas motion) coefficients of diffusion and thermal diffusivity. In all cases radiation from the surface of the catalyst lowers its temperature Tr. 

Consider the condition, which determines the velocity of the curved flame front propagation in the channel. Inside the stagnation zone filled by combustion products the pressure is constant and is equal to the value at infinity (when x = oo). Because of Bernoulli s integral along the streamline restricting the stagnation zone, the gas motion velocity remains unchanged. Since at x = oo the flow is plane-parallel (ptJO = const, v — 0), distributions of velocity u and of the stream function are associated with the vorticity distribution ... 

The dependence e vs a derived from Eq. (36) is plotted on Fig. 4 as a dotted line. Solutions of Eq. (36) and of Eq. (27) show good agreement only at small values (e < 0.05) as would be expected, because the assumptions used in Eq. (32) are valid only at sufficiently small amplitudes A /A -C 1. Note that the changes of the gas motion before and after the curved front were considered indirectly through value /(a) taken from the Landau theory for a small disturbance. 

In the scheme considered, as shown above, the convex flame front affects the hydrodynamics of the gas flow, and forms some velocity distribution ahead of it. This is associated with the pressure difference at the flame front. In other words, it is always necessary to solve a conjugate problem on the front propagation and the gas motion. Restricting the analysis by the first term in the series describing the flow field before the flame and taking into account the corresponding shape of the flame front, as was shown,... 

The velocity distribution ahead of the flame front in the room coordinate system is shown in Fig. 13. As seen from the figure, the gas motion is accompanied by the rotation and displacement of fluid elements, since the velocities near the axis and walls are directed in opposite directions. The rotation centers of each of the fluid elements are behind the flame front. But the flow is potential and u = curl u = 0. In the coordinate system of the flame front, the velocities near the axis and walls have the same direction (see Fig. 2). 

Because free gas (or gas-saturated water) is less dense than either water or sediments, it will percolate upward into the region of hydrate stability. Kvenvolden suggested that a minimum residual methane concentration of 10 mL/L of wet sediment was necessary for hydrate formation. The upward gas motion may be sealed by a relatively impermeable layer of sediment, such as an upper dolomite layer (Finley and Krason, 1986a) or the upper siltstone sequence, as in the North Slope of Alaska (Collett et al., 1988). Alternatively, permafrost or hydrate itself may act as an upper gas seal. These seals can also provide traps for free gas that has exsolved from solution, and the seals can subsequently act to provide sites for hydrate formation from the free gas. 

Two types of trays are most common sieve trays and valve trays. A sieve tray is a simple perforated plate. Gas issues from the perforations to give a multiorifice effect liquid is prevented from descending the perforations or weeping by the upward motion of the gas. At low gas flow rates, the upward gas motion may be insufficient to prevent weeping. 

The use of a helium-verified computer model to predict gas motion can be extended to compare leakage from vehicles fueled with a variety of fuels. 

Figure 1. Eulerian/Langrangian formulation of solid-gas motion...

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