Numerical Solution of the Flow of Power-Law Gel Propellants in Converging Injectors

Abstract

The governing equations of the steady, incompressible, isothermal, laminar flow of a power‐law, shear‐thinning gel propellant in a converging injector were formulated. The equations were transformed to a ψ–ω system, then discretized and solved. A numerical algorithm was developed for the solution of the flowfield. A parametric investigation was conducted to evaluate the effect of the injector geometry and the flow rate on the velocity and viscosity fields, for various gel propellants. In comparison to a straight injector, a convergent one can produce additional decrease in the mean apparent viscosity of the fluid. The mean apparent viscosity decreases significantly with increasing the convergence angle of the injector. In general, increasing the gel flow rate results in a decrease of the mean apparent viscosity of the fluid. Increasing the gellant content of gel propellants results in an increase of the fluid viscosity that decreases when the gel flows through the injector. Gels of different gellant content that flow through the same geometry injector exhibit similar relative reduction in viscosity.

Investigation of the Effective Parameters on Preparation of the Gelled IRFNA

“…Based on the reports, the rheological behavior of the gelled propellant follows the power model. Therefore, in the current study power model was used as follows [16]:…”

Wall friction effects and viscosity reduction of gel propellants in conical extrusion

“…The two conditions (16) and (17) with the normalization (18b) supplement the solution of the third-order differential Eq. (13) for the velocity profile f(Â).…”

“…The integration constant in (37) is determined from the condition at the wall (˛) = m, which follows from (16) and (36), and is evaluated iteratively using numerical solutions of (37). The velocity profile f(Â) is then determined from (36) as:…”

“…During the last decades studies have been made on steady laminar conical converging flow of Newtonian [4][5][6] and nonNewtonian fluids, such as dilute polymer solutions [7], Mises perfectly plastic solids [8] and Ostwald de Waele pseudo-plastic or dilatant fluids [9][10][11][12][13][14][15][16]. Most of these studies assume a small conical convergent angle, no inertia and a non-slip boundary condition along the rigid conical-shaped channel wall.…”

“…Since shear viscosity is non-uniform over an arbitrary cross-section of the flow field, a cross-sectional average viscosity is being used [16,20]. In fact, it has been shown in [21] that mass averaged shear viscosity correlates with atomization characteristics of non-Newtonian fluids.…”