Regression rate

Step 1. Determine the linear regression rate of the liquid surface (i.e., the rate at which the liquid level would fall as a result of vaporization by radiant heat from the burning vapor above it, assuming no addition of incoming liquid) ... 

N. E. Cohen, 13th Symp (Int) Combust (Proc) (1970), 1019—29 CA 76, 61471 (1972) To analyze and explain the mechanism of combustion of powdered metals in contact with a solid oxidizer (AP) with the powdered metal dispersed in solid AP (I), the combustion of various compressed I-Al and I-Mg mixts in N2 under various conditions in a high-pressure window bomb was studied. The regression-rate laws of the mixts at high and low pressures, the pressure limits for deflagration, and the structures of the combustion zone and of the surface were detd. The burning rate of various I-Al mixts, as a function of pressure, I particle size, and mixt ratio was determined by cinematography. The combustion was difficult to achieve... 

Basic to the sandwich model is the two-temperature concept. According to this concept, the linear regression rate of the fuel and oxidizer sandwiches must be nearly identical i.e.,... 

The principal difficulty with these equations arises from the nonlinear term cb. Because of the exponential dependence of cb on temperature, these equations can be solved only by numerical methods. Nachbar has circumvented this difficulty by assuming very fast gas-phase reactions, and has thus obtained preliminary solutions to the mathematical model. He has also examined the implications of the two-temperature approach. Upon careful examination of the equations, he has shown that the model predicts that the slabs having the slowest regression rate will protrude above the material having the faster decomposition rate. The resulting surface then becomes one of alternate hills and valleys. The depth of each valley is then determined by the rate of the fast pyrolysis reaction relative to the slower reaction. 

Let us examine some more details of this methanol problem. The regression rate of the surface is, for a liquid density of 0.79 g/cm3,... 

In other study,79 Samuelsson and coworkers (Sweden) investigated the efficacy of either ECT or radiotherapy or a combination of the two in destroying experimental colon carcinoma tumor in rats. The combined treatment resulted in tumor growth inhibition, and, total regression was obtained in 75% of the cases with radiotherapy alone, 75% of the tumors remained. As mentioned above78 with ECT alone, the regression rate was 50%, the same as surgery alone. 

Nevertheless, a diffusion mechanism generally prevails and because it is the slowest step, it determines the regression rate. In evaporation, the mechanism is the conduction of heat from the surrounding atmosphere to the surface in ablation, it is the conduction of heat through the boundary layer in droplet burning, it is the rates at which the fuel diffuses to approach the oxidizer, etc. 

As the combustion proceeded, the bed surface regressed downwards and reached the first thermocouple (Tl), and after some time the second one (T2), and then the third one (T3). Since the time elapsed for the combustion front to regress between the thermocouples was measured (derived from temperature curves), and the distances between the thermocouples were fixed, the regression rate could be calculated. From the ratio between the air flow and regression rate the bed stoichiometric ratio could be obtained. 

Since the burning surface temperature, T, is dependent on the regression rate of the propellant, it should be determined by the decomposition mechanism of the double-base propellant. An Arrhenius-type pyrolysis law represented by Eq. (3.61) is used to determine the relationship between the burning rate and the burning surface temperature. 

Experimental observation indicates that the AP particles within the matrix of a double-base (DB) propellant appear to burn and regress in size spherically on the burning surface. Thus, the regression rate of the particles appears to depend on their instantaneous diameter. The average burning rate of each AP particle is determined as a function of pressure, as shown in Fig. 8.3. The burning rate is represented by r p = where Kj is independent of pressure, r p is the burning rate... 

Region (2) is assumed to regress at approximately the same rate as the AP particles, as given by Eq. (8.1). Thus, the burning rate of an AP-CMDB propellant is expressed as the fractionally weighted sum of the two different regression rates ... 

Other developments go into the direction of adding up to approx. 10 % aluminum hydride (A1H3) or LiAlH4 to the HTPB fuel in order to increase the regression rate and deliver a specific impulse of up to 370 s. 

FIGURE 7.3. The normal regression rate of black powder as a function of pressure at 25°C [83]. 

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