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 conical cyclone
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 are more »
 Award ID(s):
 1761675
 Publication Date:
 NSFPAR ID:
 10340987
 Journal Name:
 Physics of Fluids
 Volume:
 34
 Issue:
 3
 Page Range or eLocationID:
 036604
 ISSN:
 10706631
 Sponsoring Org:
 National Science Foundation
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