scholarly journals On the Beltramian motion of the bidirectional vortex in a conical cyclone

2017 ◽  
Vol 828 ◽  
pp. 708-732
Author(s):  
Timothy A. Barber ◽  
Joseph Majdalani
Keyword(s):  
Cross Sections ◽  
Accurate Determination ◽  
Cross Flow ◽  
Numerical Data ◽  
Divergence Angle ◽  
Rocket Engines ◽  
Bulk Motion ◽  
Half Angle ◽  
Liquid Rocket ◽  
Flow Variables

In this work, an exact Eulerian model is used to describe the steady-state motion of a bidirectional vortex in a conical chamber. This particular model is applicable to idealized representations of cyclone separators and liquid rocket engines with slowly expanding chamber cross-sections. The corresponding bulk motion is assumed to be non-reactive, rotational, inviscid and incompressible. Then, following Bloor & Ingham (J. Fluid Mech., vol. 178, 1987, pp. 507–519), the spherical Bragg–Hawthorne equation is used to construct a mathematical model that connects the solution to the swirl number and the cone divergence angle. Consequently, a self-similar formulation is obtained independently of the cone’s finite body length. This enables us to characterize the problem using closed-form approximations of the principal flow variables. Among the cyclonic parameters of interest, the mantle divergence angle and the maximum cross-flow velocity are obtained explicitly. The mantle consists of a spinning cone that separates the circumferential inflow region from the central outflow. This interfacial layer bisects the fluid domain at approximately 60 per cent of the cone’s divergence half-angle. Its accurate determination is proven asymptotically using two different criteria, one being preferred by experimentalists. Finally, recognizing that the flow in question is of the Beltramian type, results are systematically described over a range of cone angles and spatial locations in both spherical and cylindrical coordinates; they are also compared to available experimental and numerical data.

scholarly journals Extended semi-analytical model for the prediction of flow and concentration fields in a tangentially-fired furnace

2013 ◽  
Vol 17 (4) ◽  
pp. 1233-1243
Author(s):  
Amin Lotfiani ◽  
Shahram Khalilarya
Keyword(s):  
Analytical Model ◽  
Cross Sections ◽  
Cross Flow ◽  
Numerical Data ◽  
Solution Procedure ◽  
Zone Model ◽  
Extended Model ◽  
Cfd Simulations ◽  
Jet Trajectory ◽  
Computational Fluid Dynamics Cfd

Tangentially-fired furnaces (TFF) are one of the modified types of furnaces which have become more attractive in the field of industrial firing systems in recent years. Multi-zone thermodynamic models can be used to study the effect of different parameters on the operation of TFF readily and economically. Flow and mixing sub-model is a necessity in multi-zone models. In the present work, the semi-analytical model previously established by the authors for the prediction of the behavior of coaxial turbulent gaseous jets is extended to be used in a single-chamber TFF with square horizontal cross-sections and to form the flow and mixing sub-model of the future multi-zone model for the simulation of this TFF. A computer program is developed to implement the new extended model. Computational fluid dynamics (CFD) simulations are carried out to validate the results of the new model. In order to verify the CFD solution procedure, a turbulent round jet injected into cross flow is simulated. The calculated jet trajectory and velocity profile are compared with other experimental and numerical data and good agreement is observed. Results show that the present model can provide very fast and reasonable predictions of the flow and concentration fields in the TFF of interest.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

EVALUATION OF SMD EFFECTS ON CHARACTERISTIC LENGTHS OF LIQUID ROCKET ENGINES USING ETHANOL/LOX AND RP-1/LOX

2020 ◽  
Author(s):  
Maurício Sá Gontijo ◽  
Gustavo Alexandre Achilles Fischer ◽  
FERNANDO DE SOUZA COSTA
Keyword(s):  
Rocket Engines ◽  
Liquid Rocket Engines ◽  
Liquid Rocket

scholarly journals Elastic Electron Scattering from Methane Molecule in the Energy Range from 50–300 eV

2021 ◽  
Vol 22 (2) ◽  
pp. 647
Author(s):  
Jelena Vukalović ◽  
Jelena B. Maljković ◽  
Karoly Tökési ◽  
Branko Predojević ◽  
Bratislav P. Marinković
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Electron Gun ◽  
Methane Molecule ◽  
Edge Plasma ◽  
Electron Interaction ◽  
Outer Planet ◽  
Elastic Electron

Electron interaction with methane molecule and accurate determination of its elastic cross-section is a demanding task for both experimental and theoretical standpoints and relevant for our better understanding of the processes in Earth’s and Solar outer planet atmospheres, the greenhouse effect or in plasma physics applications like vapor deposition, complex plasma-wall interactions and edge plasma regions of Tokamak. Methane can serve as a test molecule for advancing novel electron-molecule collision theories. We present a combined experimental and theoretical study of the elastic electron differential cross-section from methane molecule, as well as integral and momentum transfer cross-sections in the intermediate energy range (50–300 eV). The experimental setup, based on a crossed beam technique, comprising of an electron gun, a single capillary gas needle and detection system with a channeltron is used in the measurements. The absolute values for cross-sections are obtained by relative-flow method, using argon as a reference. Theoretical results are acquired using two approximations: simple sum of individual atomic cross-sections and the other with molecular effect taken into the account.

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