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1. Effects of Varying Characteristic Injection Parameters and Geometric Configurations on the Cyclonic Flowfield in a Bidirectional Vortex Chamber Using Velocity Inlet Conditions

   https://doi.org/10.2514/6.2023-0136  

   Sharma, Gaurav; Majdalani, Joseph (January 2023, AIAA SCITECH 2023 Forum)

   We vary the inflow properties in a finite-volume solver to investigate their effects on the computed cyclonic motion in a right-cylindrical vortex chamber. The latter comprises eight tangential injectors through which steady-state 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 well-resolved 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, the flow character is markedly altered, and an axially unidirectional vortex is engendered, particularly, with no upward motion or mantle formation. Conversely, the tangential and radial velocities are found to be axially independent and together with the pressure distribution prove to be the least sensitive to injection plane relocations. 

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2. Effects of nozzle inlet size and curvature on the flow development in a bidirectional vortex chamber

   https://doi.org/10.1063/5.0066121  

   Sharma, Gaurav; Majdalani, Joseph (September 2021, Physics of Fluids)

   A finite-volume solver is used to describe the cyclonic motion in a cylindrical vortex chamber comprising eight tangential injectors and a variable nozzle size. The simulations are performed under steady, incompressible, and inviscid flow conditions with air as the working fluid. First, we apply a fine tetrahedral mesh to minimize cell skewness, particularly near injectors. Second, this mesh is converted into a polyhedral grid to improve convergence characteristics and precision. After achieving convergence, the velocity components are evaluated and compared to existing analytical solutions. We find that well-resolved numerical simulations can accurately predict the expected forced vortex behavior in the core region as well as the free vortex tail in the outer region. We also confirm that the swirl velocity remains axially invariant irrespective of the outlet radius. Similarly, we are able to ascertain that the axial and radial velocities embody the bidirectional nature of the motion. As for the computed pressure distribution, it is found to agree quite well with both theoretical formulations and experimental measurements of cyclone separators. Then using a parametric trade study, the effect of nozzle variations on the internal flow character, mantle structure, and recirculation zones is systematically investigated. Apart from the exit diameter, we find that the nozzle length and inlet curvature can substantially affect the internal flow development including the formation of backflow regions, recirculation zones, and mantle excursions. Finally, an empirical relation is constructed for the nozzle radius of curvature and shown to effectively suppress the emergence of recirculation and backflow regions. 

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3. Exact Beltramian solutions for hemispherically bounded cyclonic flowfields

   https://doi.org/10.1063/5.0063743  

   Williams, Langston_L; Majdalani, Joseph (September 2021, Physics of Fluids)

   This study focuses on the development of two analytical models that describe the wall-bounded cyclonic flowfield in a hemispherical domain. The closed-form solutions that we pursue are motivated by the need to characterize the swirling bidirectional motion engendered in an upper stage thrust chamber, namely, the VR35K-A VORTEX® engine, conceived and developed by Sierra Nevada Corporation. Our analysis proceeds from the Bragg–Hawthorne formulation, which is quite effective in the treatment of steady, inviscid, and axisymmetric flows. In this work, we show that two rotational solutions may be derived for particular specifications of the stagnation head and tangential angular momentum expressions that appear in the Bragg–Hawthorne equation. Then, with the parental streamfunctions in hand, other properties of interest are deduced and these include the main velocity and pressure variations, vorticities, crossflow velocities, extensional and shearing strain rates, virtual energy dissipation rates, and both axial and polar mantle distributions; the latter consist of pairs of rotating, non-translating interfacial layers, separating the so-called inner and outer bidirectional and bipolar regions, respectively. More specifically, two Beltramian solutions are identified with mantles that appear at 50% and 61.06% of the chamber radius, respectively. By matching the outlet radius of the chamber to the mantle location in the equatorial plane, the outflow is permitted to exit the chamber seamlessly. In both models, the axial and radial velocities vary linearly with the injection speed and a characteristic inflow parameter consisting of a geometric ratio of the inlet area and the chamber radius squared. 

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4. High-Fidelity Modeling and Simulation of Primary Breakup fo a Gasoline Surrogate Jet

   Zhang, Bo; Ling, Yue (May 2019, Proc. ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems 30th Annual Conference on Liquid Atomization and Spray Systems)

   In the present work, we model and simulate the injection and atomization of a gasoline surrogate jet by detailed numerical simulation. The surrogate fuel has a low volatility and thus no phase change occurs in the process. The nozzle geometry and operation conditions are similar to the Engine Combustion Network (ECN) “Spray G”. We focus the present study on the near field where inter-jet interaction is of secondary importance. Therefore, we have considered only one of the eight jets in the original Spray G injectors. The liquid is injected from the inlet into a chamber with stagnant gas. A tangential component of velocity is introduced at the inlet to mimic the complex internal flow in the original spray G injector, which leads to the jet deflection. A parametric study on the inlet tangential velocity is carried out to identify the proper value to be used. Simulations are performed with the multiphase flow solver, Basilisk, on an adaptive mesh. The gas-liquid interface is captured by the volume-of-fluid method. The numerical results are compared to the X-ray experimental data for the jet deflection angle and the temporal variation of penetration length. The vortex dynamics in the near field are also presented by the assistance of the vortex-identification criterion. 

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5. Effect of Variable Outlets on the Nonreactive Flowfield of a Right-Cylindrical Cyclonic Chamber

   https://doi.org/10.2514/6.2020-3823  

   Sharma, Gaurav; Majdalani, Joseph (August 2020, 2020 AIAA Propulsion and Energy Forum)

   null (Ed.)

   This work focuses on the use of a finite-volume solver to describe the wall-bounded cyclonic flowfield that evolves in a swirl-driven thrust chamber. More specifically, a non-reactive, cold-flow simulation is carried out using an idealized chamber configuration of a square-shaped, right-cylindrical 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. 2208-2216). 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 complex-lamellar 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 wall-bounded 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. 

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