Degassing of a nonlinearly viscous liquid flowing over the heated surface of a tapered rotor

Abstract

Degassing is widely used in the chemical, food, microbiological, and other industries. Degassing is performed by heating an aerated liquid while simultaneously stirring. Such a procedure has low efficiency, consumes much energy, and does not guarantee a high quality of degassing. Degassing in a centrifugal field in a thin-film liquid flow is an order of magnitude more efficient and provides the required quality of degassing. However, broad implementation of this process is constrained by the lack of deep theoretical studies and their based process design procedure.Let us consider degassing of a nonlinearly viscous liquid flowing over the heated inner surface of a tapered rotor in a special conical coordinate system ( l , ϕ , z ) ( Fig. 1). The aerated liquid is fed at constant volume flow rate q l to the center of a truncated tapered rotor rotating at constant angular velocity ω . When touching the horizontal part of the tapered rotor, the liquid is decelerated in the radial direction and accelerated in the tangential direction; i.e., a spatial boundary layer forms. At radius r , this layer reaches the film surface. Thus, there are three regions of the flow of the liquid fed to the center of the rotating rotor, namely, potential flow region 1 , spatial boundary layer region 2 , and thinfilm flow region 3 (Fig. 1). In region 3 , all of the liquid fed to the rotor is set in rotary motion and the integral continuity equation is valid. The size of the horizontal part of the tapered rotor is chosen so that r 0 ≥ r ; this prevents the rotor from flooding and ensures the thin-film liquid flow over the inner surface of the rotor at velocity components v l , v ϕ , and v z .In considering the degassing, we assume that the flow of the aerated liquid is laminar, waveless, and axisymmetric. It is supposed that the rise of gas bubbles to the liquid film surface and their penetration through the interface do not distort the flow pattern. The gravity, the surface tension, and the friction of the film against the gas medium can be ignored. We also assume that T w = const and ∂ T / ∂ z | z = h = 0. Since the maximal velocity of the relative motion of a babble and the liquid is vanishingly small in comparison with the volume-average aerated flow velocity, we use a quasi-homogeneous model of degassing. We also suppose that the physicomechanical properties of the gas in the quasi-homogeneous medium almost do not affect the rheological constants of the dispersion medium.Abstract -The flow of a nonlinearly viscous power-law liquid over the heated inner surface of a tapered rotor is considered. The form of a solution is found that enables one to reduce the complete partial differential equations of rheodynamics and convective heat transfer to a set of ordinary differential equations. The set is integrated numerically by the Runge-Kutta method using a procedure of reduction to a Cauchy problem by Newton's method. The velocity, temperature, and pressure fields in the liquid film are determined. Two steps of degassing are considered, namel...

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