Heat transfer rates have been measured for forced flow of supercritical carbon dioxide normal to a horizontal heated cylinder. The 0.006 inch diameter cylinder was held at various constant temperatures by a feed-back bridge circuit. Free convection results are also included. The effects of bulk fluid temperature, bulk fluid pressure, and surface temperature were studied for a range of bulk fluid temperature and pressure of from 0.8 to 1.4 times the critical temperature and pressure for several free stream velocities from zero to three feet per second. The temperature difference between the heated cylinder and the bulk fluid was varied from 1 deg F to 320 deg F. Flow fields of all data runs were observed. Still photographs and high speed movies have been taken at operating conditions of interest. In a supercritical fluid the heat transfer rate increases smoothly and monotonically with increasing temperature difference, increasing velocity, and increasing pressure. In fluid with the bulk temperature below the pseudo-critical temperature the heat transfer coefficient shows large peaks when the cylinder temperature is near the pseudocritical temperature. Peaks are largest when the bulk fluid pressure is near the critical pressure. The heat transfer coefficient decreases with increasing temperature difference when the bulk fluid temperature is above the pseudo-critical temperature. The heat transfer rate noteably increases with increasing pressure only when vapour-like fluid is in contact with the heated cylinder. Supercritical forced flow has been compared to forced flow boiling. The supercritical case does not exhibit the characteristic strong maxima in heat transfer rate shown in forced flow nucleate boiling. Heat transfer rates at larger temperature differences are very similar in forced flow film boiling and supercritical forced flow heat transfer. With this horizontal, constant temperature cylinder, no "bubble-like" or "boiling-like" mechanisms of heat transfer were observed in supercritical free or forced convection. The flow field and heat transfer rate in free convection were found to be very unstable and sensitive to small temperature disturbances in the bulk fluid. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A physical model and a numerical solution procedure has been developed to predict heat transfer behaviour in supercritical fluids. A major area of concentration was the modelling of the turbulent components of shear stress and heat flux. Traditionally, the turbulent fluxes are modelled by algebraic expressions such as the familiar mixing length methods. However, the use of this technique has not been entirely satisfactory. Newer methods for constant-property flows which model turbulent fluxes by considering the transport of quantities such as turbulent kinetic energy and the dissipation rate of turbulence have been extended to supercritical fluids. This involves the solution of two additional partial differential equations that are solved simultaneously with the equations of continuity, energy, and momentum. The numerical scheme has been developed on a completely two-dimensional basis by extending the Pletcher-DuFort-Frankel finite difference method. Computed results for velocity and temperature profiles as well as wall temperature distributions exhibited reasonable agreement with previous experimental data and therefore indicate the viability of the present method. Computations were carried out for supercritical carbon dioxide flowing through a circular duct in the reduced pressure range 1.0037 to 1.098. A consideration of the influence of buoyancy on the mean momentum balance permitted the calculation of unusual velocity profiles in this investigation. The existance of such velocity profiles had been accepted previously but the nature of their growth along a pipe has probably not been suggested previous to this work. No attempt was made to include buoyancy generated turbulence or additional fluctuating property correlations in this work, but suggestions are made regarding possible avenues of approach. Some of the incidental outcomes of this work were a new continuous universal velocity profile implicit in cross stream distance an a new mixing length distribution for turbulent pipe flows. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Thesis. 1977. Ocean E.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 93-95. / by Osie "V". Combs, Jr. / Ocean E.

The thermophysical properties of supercritical CO₂ and H₂O-CO₂ mixtures are reviewed and their computation and prediction improved through theory and experiment. A resolution is attempted among inconsistencies between and within data sets, including P-V-T measurements, phase equilibrium experiments and equations of state. Pure carbon dioxide: Equations of state for CO₂ (Kerrick & Jacobs, 1981; Bottinga & Richet, 1981; Holloway, 1977) are based solely on P-V-T data up to 8 kbar and lead to deviations from phase equilibrium data at pressures greater than 10-20 kbar. Mathematical programming analysis has been applied to the fitting of parameters for an equation of state using simultaneously constraints from phase equilibrium and P-V-T data. Phase equilibrium data up to 42 kbar are used to define a feasible region for the adjustable parameters in free energy space. Each half-bracket places an inequality constraint on the fugacity of CO₂ provided the thermophysical properties of the solid phases are known. Except for magnesite thermophysical data from the mineral data base of Berman (1988) were used. A least squares objective function served to optimize parameters to P-V-T data. The enthalpy of formation of magnesite was revised on the basis of recent low pressure phase equilibrium experiments by Philipp (1988) to —1112.505 kj/mole. Piston-cylinder experiments were performed to constrain the equilibrium magnesite ⇌ periclase + CO₂ at high pressure. The equilibrium boundary is located at 12.1(±1) kbar, 1173-1183 °C (±10), and at 21.5(±1) kbar, 1375-1435 °C (±10). A van der Waals type equation of state with five adjustable parameters has been developed for CO₂. The function is smooth and continous above the critical region, behaves well in the high and low pressure limits, and the calculation of ʃ VdP for free energy does not require numerical integration. Computed free energies are consistent with all phase equilibrium data at high pressure, and computed volumes agree reasonably with P-V-T measurements. The proposed equation is: [ Equation omitted ] with B₁ = 28.0647, B₂ = 1.7287.10⁻⁴, B3 = 83653, A₁ = 1.0948.10⁹, A₂ = 3.3 7 47.10⁹, and R = 83.147, in units of Kelvin, bar and cm³/mole. The equation is recommended up to 50 kbar and above 400 K with reasonable extrapolation capabilities. A FORTRAN source code to evaluate the volume and fugacity is provided. Thermophysical properties for the calcium carbonate polymorphs calcite-I, IV, V, and aragonite were derived that are consistent with phase equilibrium experiments. Data required for further improvement include high pressure phase equilibria involving CO₂, constraints on the thermal expansion of magnesite, and P-V-T data to resolve inconsistencies among existing measurements. Water-carbon dioxide mixtures: The two widely used equations of state for H₂O-CO₂ mixtures are those proposed by Kerrick & Jacobs (1981) and by Holloway (1977)-Flowers (1979). Evaluation of existing equations and data is difficult due to inconsistencies among experimental studies. P-V-T-X data by Franck ＆ Todheide (1959) are inconsistent with data by Greenwood (1973) and Gehrig (1980), and cannot be reconciled with measured phase equilibria in H₂O-CO₂ fluid mixtures. Data by Greenwood and Gehrig are in loose agreement but extend only to 600 bar and do not constrain activities at higher pressures. A procedure is developed for using experimental phase equilibrium constraints to put limits on the fugacities of components of the fluid mixture. Inconsistencies among phase equilibrium studies are discussed. It is concluded that the data base available is not yet adequate to derive a reliable equation of state for H₂O-CO₂ mixtures. Future work must include P-V-T-X measurements to 8 kbar and phase equilibrium studies to resolve inconsistencies. These can constrain deviations from ideal mixing in the fluid phase, and constrain specific volumes at high pressures where P-V-T-X data connot be obtained. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The objectives of this work are to measure phase equilibria in the carbon dioxide + pyrrole system and to correlate and predict the phase behavior of this system with a thermodynamic model. This binary system is of interest due to the growing applications of supercritical carbon dioxide as a solvent or reaction medium for pyrrole. Polypyrrole is an electrically conducting polymer of interest in a number of applications such as anti-static coatings. Pyrrole has also been used as a reactant in enzymatic reaction. Knowledge of the phase behavior of carbon dioxide + pyrrole system is therefore necessary for evaluating optimal conditions and feasibility of such applications. Phase equilibria in the carbon dioxide + pyrrole system were measured at 313 K, 323 K, and 333 K using a synthetic method. Liquid-vapor (LV) phase behavior and liquid-liquid (LL) phase behavior were observed. The pressure in the experiments ranged from 84 to 151.1 bar. The Patel-Teja equation of state and the Mathias-Klotz-Prausnitz mixing rule with two temperature independent parameters was able to correlate the phase equilibrium data satisfactorily and was used to predict the phase behavior at other temperatures. A pressure-temperature diagram was then constructed from these calculations and suggests that the carbon dioxide + pyrrole system exhibit type IV phase behavior in the classification of Scott and van Konynenburg.