This work focuses on the use of a finitevolume solver to describe the wallbounded cyclonic flowfield that evolves in a swirldriven thrust chamber. More specifically, a nonreactive, coldflow simulation is carried out using an idealized chamber configuration of a squareshaped, rightcylindrical enclosure with eight tangential injectors and a variable nozzle size. For simplicity, we opt for air as the working fluid and perform our simulations under steady, incompressible, and inviscid flow conditions. First, a meticulously developed mesh that consists of tetrahedral elements is generated in a manner to minimize the overall skewness, especially near injectors; second, this mesh is converted into a polyhedral grid to improve convergence characteristics and accuracy. After achieving convergence in all variables, our three velocity components are examined and compared to an existing analytical solution obtained by Vyas and Majdalani (Vyas, A. B., and Majdalani, J., “Exact Solution of the Bidirectional Vortex,” AIAA Journal, Vol. 44, No. 10, 2006, pp. 22082216). We find that the numerical model is capable of predicting the expected forced vortex behavior in the inner core region as well as the free vortex tail in the inviscid region. Moreover, the results appear to be in fair agreement with the Vyas–Majdalani solution derivedmore »
On the generalized Beltramian motion of the bidirectional vortex in a rightcylindrical cyclone with a hollow core
In this work, an exact inviscid solution is developed for the incompressible Euler equations in the context of a bidirectional, cyclonic flowfield in a rightcylindrical chamber with a hollow core. The presence of a hollow core confines the flow domain to an annular swirling region that extends into a toroid in threedimensional space. The procedure that we follow is based on the Bragg–Hawthorne framework and a judicious assortment of boundary conditions that correspond to a wallbounded cyclonic motion with a cylindrical core. At the outset, a selfsimilar stream function is obtained directly from the Bragg–Hawthorne equation under the premises of steady, axisymmetric, and inviscid conditions. The resulting formulation enables us to describe the bidirectional evolution of the socalled inner and outer vortex motions, including their fundamental properties, such as the interfacial layer known as the mantle; it also unravels compact analytical expressions for the velocity, pressure, and vorticity fields, with particular attention being devoted to their peak values and spatial excursions that accompany successive expansions of the core radius. By way of confirmation, it is shown that removal of the hollow core restores the wellestablished solution for a fully flowing cylindrical cyclone. Immediate applications of cyclonic flows include liquid and more »
 Award ID(s):
 1761675
 Publication Date:
 NSFPAR ID:
 10340985
 Journal Name:
 Physics of Fluids
 Volume:
 34
 Issue:
 4
 Page Range or eLocationID:
 043603
 ISSN:
 10706631
 Sponsoring Org:
 National Science Foundation
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This work presents an exact solution of Euler's incompressible equations in the context of a bidirectional vortex evolving inside a conically shaped cyclonic chamber. The corresponding helical flowfield is modeled under inviscid conditions assuming constant angular momentum. By leveraging the axisymmetric nature of the problem, a steadystate solution of the generalized Beltramian type is obtained directly from first principles, namely, from the Bragg–Hawthorne equation in spherical coordinates. The resulting stream function representation enables us to fully describe the ensuing swirldominated motion including its fundamental flow characteristics. After identifying an isolated singularity that appears at a cone divergence halfangle of 63.43°, two piecewise formulations are provided that correspond to either fluid injection or extraction at the top section of the conical cyclone. In this process, analytical expressions are readily retrieved for the three velocity components, vorticity, and pressure. Other essential flow indicators, such as the theoretically preferred mantle orientation, the empirically favored locus of zero vertical velocity, the maximum polar and axial velocities, the crossflow velocity, and other such terms, are systematically deduced. Results are validated using limiting process verifications and comparisons to both numerical and experimental measurements. The subtle differences between the present model and a strictly Beltramian flowfield aremore »

We vary the inflow properties in a finitevolume solver to investigate their effects on the computed cyclonic motion in a rightcylindrical vortex chamber. The latter comprises eight tangential injectors through which steadystate air is introduced under incompressible and inviscid conditions. To minimize cell skewness around injectors, a fine tetrahedral mesh is implemented first and then converted into polyhedral elements, namely, to improve convergence characteristics and precision. Once convergence is achieved, our principal variables are evaluated and compared using a range of inflow parameters. These include the tangential injector speed, count, diameter, and elevation. The resulting computations show that wellresolved numerical simulations can properly predict the forced vortex behavior that dominates in the core region as well as the free vortex tail that prevails radially outwardly, beyond the point of peak tangential speed. It is also shown that augmenting the mass influx by increasing the number of injectors, injector size, or average injection speed further amplifies the vortex strength and all peak velocities while shifting the mantle radially inwardly. Overall, the axial velocity is found to be the most sensitive to vertical displacements of the injection plane. By raising the injection plane to the top half portion of the chamber, themore »

We vary the inflow properties in a finitevolume solver to investigate their effects on the computed cyclonic motion in a rightcylindrical vortex chamber. The latter comprises eight tangential injectors through which steadystate air is introduced under incompressible and inviscid conditions. To minimize cell skewness around injectors, a fine tetrahedral mesh is implemented first and then converted into polyhedral elements, namely, to improve convergence characteristics and precision. Once convergence is achieved, our principal variables are evaluated and compared using a range of inflow parameters. These include the tangential injector speed, count, diameter, and elevation. The resulting computations show that wellresolved numerical simulations can properly predict the forced vortex behavior that dominates in the core region as well as the free vortex tail that prevails radially outwardly, beyond the point of peak tangential speed. It is also shown that augmenting the mass influx by increasing the number of injectors, injector size, or average injection speed, further amplifies the vortex strength and all peak velocities while shifting the mantle radially inwardly. Overall, the axial velocity is found to be the most sensitive to vertical displacements of the injection plane. By raising the injection plane to the top half portion of the chamber, themore »

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