 Award ID(s):
 1916979
 NSFPAR ID:
 10238803
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 900
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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null (Ed.)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 derived under similarly inviscid conditions, and thus resulting in a quasi complexlamellar profile. In this work, we are able to ascertain the axial independence of the swirl velocity no matter the value of the outlet radius, which confirms the key assumption made in most analytical models of wallbounded cyclonic motions. Moreover, the pressure distribution predicted numerically is found to be in fair agreement with both theoretical formulations and experimental measurements of cyclone separators. The bidirectional character of the flowfield is also corroborated by the axial and radial velocity distributions, which are found to be concurrent with theory. Then using parametric trade studies, the sensitivity of the numerical simulations to the outlet diameter of the chamber is explored to determine the influence of outlet nozzle variations on the mantle location and the number of mantles. Since none of the cases considered here promote the onset of multiple mantles, we are led to believe that more factors are involved in producing more mantles than one. Besides the exit diameter, the formation of a multiple mantle structure may be influenced by the physical boundary conditions, nozzle radius, inlet curvature, and length. In closing, we show that the latter plays a significant role in controlling the development of backflow regions inside the chamber.more » « less

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 hybrid rocket engines, swirldriven combustion devices, as well as a multitude of heat exchangers, centrifuges, cyclone separators, and flow separation devices that offer distinct advantages over conventional, nonswirling systems.more » « less

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 also highlighted and discussed. The conically cyclonic configuration considered here is relevant to propulsive devices, such as vortexfired liquid rocket engines with tapered walls; meteorological phenomena, such as tornadoes, dust devils, and fire whirls; and industrial contraptions, such as cyclonic flow separators, collectors, centrifuges, boilers, vacuum cleaners, cement grinders, and so on.more » « less

SUMMARY We present a new, 3D model of seismic velocity and anisotropy in the Pacific upper mantle, PAC13E. We invert a data set of singlestation surfacewave phaseanomaly measurements sensitive only to Pacific structure for the full set of 13 anisotropic parameters that describe surfacewave anisotropy. Realistic scaling relationships for surfacewave azimuthal anisotropy are calculated from petrological information about the oceanic upper mantle and are used to help constrain the model. The strong age dependence in the oceanic velocities associated with plate cooling is also used as a priori information to constrain the model. We find strong radial anisotropy with vSH > vSV in the upper mantle; the signal peaks at depths of 100–160 km. We observe an age dependence in the depth of peak anisotropy and the thickness of the anisotropic layer, which both increase with seafloor age, but see little age dependence in the depth to the top of the radially anisotropic layer. We also find strong azimuthal anisotropy, which typically peaks in the asthenosphere. The azimuthal anisotropy at asthenospheric depths aligns better with absoluteplatemotion directions while the anisotropy within the lithosphere aligns better with palaeospreading directions. The relative strengths of radial and azimuthal anisotropy are consistent with Atype olivine fabric. Our findings are generally consistent with an explanation in which corner flow at the ridge leads to the development and freezingin of anisotropy in the lithosphere, and shear between the lithosphere and underlying asthenosphere leads to anisotropy beneath the plate. We also observe large regions within the Pacific basin where the orientation of anisotropy and the absoluteplatemotion direction differ; this disagreement suggests the presence of shear in the asthenosphere that is not aligned with absoluteplatemotion directions. Azimuthalanisotropy orientation rotates with depth; the depth of the maximum vertical gradient in the fastaxis orientation tends to be age dependent and agrees well with a thermally controlled lithosphere–asthenosphere boundary. We observe that azimuthalanisotropy strength at shallow depths depends on halfspreading rate, with higher spreading rates associated with stronger anisotropy. Our model implies that corner flow is more efficient at aligning olivine to form latticepreferred orientation anisotropy fabrics in the asthenosphere when the spreading rate at the ridge is higher.

A computational study of vorticity reconnection, associated with the breaking and reconnection of vortex lines, during vortex cutting by a blade is reported. A series of Navier–Stokes simulations of vortex cutting with different values of the vortex strength are described, and the different phases in the vortex cutting process are compared to those of the more traditional vortex tube reconnection process. Each of the three phases of vortex tube reconnection described by Melander & Hussain ( Phys. Fluids A, vol. 1(4), 1989, pp. 633–635) are found to have counterparts in the vortex cutting problem, although we also point out numerous differences in the detailed mechanics by which these phases are achieved. Of particular importance in the vortex cutting process is the presence of vorticity generation from the blade surface within the reconnection region and the presence of strong vortex stretching due to the ambient flow about the blade leading edge. A simple exact Navier–Stokes solution is presented that describes the process by which incident vorticity is stretched and carried towards the surface by the ambient flow, and then interacts with and is eventually annihilated by diffusive interaction with vorticity generated at the surface. The model combines a Hiemenz straining flow, a Burgers vortex sheet and a Stokes first problem boundary layer, resulting in a nonlinear ordinary differential equation and a partial differential equation in two scaled time and distance variables that must be solved numerically. The simple model predictions exhibit qualitative agreement with the full numerical simulation results for vorticity annihilation near the leadingedge stagnation point during vortex cutting.more » « less