PULSATION AND VIBRATION
FLAME FRONT STABILITY IN LIQUID FUEL DROPLET COMBUSTION C. C. MIESSE Aeroief-General Corp., Azusa, Calif.
H E previous analysis on the oscillation of the flame front between two unlike droplets in a liquid bipropellant system (3) has been extended t o the case of a single fuel droplet burning in a n oxidizer atmosphere. B y determining the radial concentration distribution of the oxidizing vapor, applying Fick’s first law of diffusion, and following the method of Burke and Schumann (Z), the mass flow rate of the oxidizing vapor to the spherical flame front varies inversely as the radius of the fuel droplet. Under these conditions, the steady-state flame front position varies directly with the radius of the fuel droplet, and stability is ensured if the flame front radius is at least three halves of the droplet radius. This condition can be expressed explicitly in terms of the stoichiometric mixture ratio and the physical properties of the two constituents, exclusive of the size of the fuel droplet. If, however, it is assumed t h a t the mass flow rate of the oxidizing vapor is independent of the radius of the fuel droplet, then the ratio of the steady-state flame front radius t o the droplet radius is a function of the droplet radius, and the stability criterion involves the radius of the fuel droplet. Although this assumption was made without theoretical confirmation, the experimental observations of Burgoyne and Cohen ( 1 )indicate t h a t the ratio of flame front t o droplet radii varies in a manner similar t o t h a t derived under the assumption of constant oxidizer flow rate. Under this assumption, stability is increased as the size of the droplet decreases. The following conclusions are common t o both assumptions: 1. Stability is increased by a n increase in the vaporization ratio of the fue1 droplet. 2. Stability increases with a n increase in the stoichiometric mixture ratio. 3. Stability is increased as the diffusion rate of the oxidizer flow is decreased. literature Cited (1) Burgoyne, J. H., and Cohen, L., Proc. Rov. SOC.(London), A225,
375 (1954). S.P., and Schumann, T. E. W., IND.ENG.CHEM.,20,998-
(2) Burke,
length and 0.5 inch i n diameter, were held in a vertical position. T h e lower end of the sample was placed in t h e distilled water of the transducer and the upper end was placed in t h e heat treating furnace. T h e ultrasonic frequencies used were 400 and 1000 kilocycles. The ultrasonic treated samples of 0.07% carbon hypoeutectoid steel had finer grain size and greater hardness than the reference samples which had undergone the same heat treating cycle but with no ultrasonic treatment. When either the intensity or the frequency of the ultrasonic energy was increased, t h e grain size was further decreased. The grain size of the ultrasonic treated samples of 1.05% carbon hypereutectoid steel w,s coarser than t h a t of the reference sample. The samples treated a t the louest intensity had t h e coarsest grain size while higher intensities produced grain size which approached the grain size of the nontreated samples. Samples treated a t 1000 kilocycles showed a grain size slightly smaller t h a n t h e samples treated at 400 kilocycles. Hardness values showed a relationship similar t o t h a t of t h e grain size. T h e lamellar layers of ferrite and iron carbide making up t h e pearlite crystals in t h e 1.05% carbon steel were definitely thicker in t h e ultrasonic treated samples than in the untreated ones.
SONIC VELOCITY MEASUREMENTS IN STUDY OF LIQUID AND LIQUID SOLUTION PROPERTIES F. C. COLLINS, M. H. NAVIDI, AND L. P. FRIEDMAN Departmenf o f Chemisfry, Polytechnic Institute of Brooklyn, Brooklyn I , N. Y.
S
ONIC velocity is a convenient measurement for the study of liquid properties in addition to the customary measurements of specific volume, vapor pressure, specific heat, heat of vaporization, and dielectric constant. The adiabatic compressibility so obtained is related t o other thermodynamic variables and is useful for correlations among liquids and for interpreting the microscopic structure of the given liquids. By use of the free volume theory, the following equation can be obtained which gives the ratio of the incompressible molar volume V oto the actual volume V without additional assumptions ( 3 )
1004 (1928). (3) Miesse, C. C., Fifth Symposium (International) on Combustion, Reinhold, New York, 1955.
-
ULTRASONIC EFFECT O N POLYMORPHIC TRANSFORMATION OF STEEL H. V. FAIRBANKS AND F. J. DEWEZ, JR.’ Chemical hgineering Dept., Wesf Virginio University, Morgantown, W. Va.
In Equation 1 us is the measured sonic velocity and the other symbols have their customary meaning. Data of this kind have been used in connection with a free volume theory of viscosity and diffusion for simple liquids (3). The viscosity term vCwhich arises from the transport of momentum across the bodies of molecules upon collision is 2 u(MRT)1’2 5 T ” V [ l - (VO/V)1’3]
Ilc = - _ _
T
HE purpose of this investigation was t o determine the effects of ultrasonic energy on 0.07 and 1.05% carbon steels during polymorphic transformation, or annealing. T h e steel samples used were slowly cooled during t h e transformation in which the iron changed from a face-centered cubic structure t o a hodycentered cubic structure. The ultrasonic energy was produced b y means of a bowlshaped crystal of barium titanate and was coupled to the steel samples through distilled water. The steel samples, 8 inches in 1
Present address, U. S. Steel Corp., Pittsburgh, Pa.
June 1955
where u is the molecular collision diameter. Equation 2 does not take account of attractive intermolecular interactions but, nevertheless, yields numerical values for the viscosity coefficient of the order of one third of the experimental value?. I n the case of binary solutions, deviations from regular behavior are due t o differences in intermolecular forces between unlike species, variation in number of nearest neighbors, and nonrandom mixing. Sonic velocity provides a n additional experimental variable for the evaluation of these several effects. Sonic
INDUSTRIAL AND ENGINEERING CHEMISTRY
1181
