Effect of the Coil Angle in an Inductively Coupled Plasma Torch: A Novel Two-Dimensional Model

A two-dimensional model has been developed for the calculation of the electromagnetic (EM) fields generated by spiral coil currents, in order to obtain a better representation of the actual configuration used in a typical inductively coupled plasma (ICP) torch. In order to obtain the EM fields in a two-dimensional model, the change of EM field in tangential direction is neglected and the coil is assumed to be a concentric cylinder. In order to justify our assumption, the EM, flow and temperature fields resulting from five-ring coil and concentric cylinder coil are compared and the results are almost the same except for the EM field in the vicinity of the coil. In the case of the spiral coil, the coil current is inclined with respect to the horizontal plane. Therefore current in the cylinder coil is assumed to have the same inclined angle, which is split into tangential and axial components. The axial electric field and hence an axial current in plasma is induced by the axial component of the spiral coil current. Charge density is accumulated in the plasma, since the axial current cannot form a loop. In order to obtain the EM field and the charge distribution in the plasma generated by the spiral coil, the equations of axial vector potential and electrostatic potential have been derived. Due to the swirling Lorentz force (J_z×B_r) an axisymmetrical swirling fluid model is used to simulate the plasma flow in an axisymetrical configuration. With an inclined angle of the coil current being 3.7° and the frequency being 3 MHz, computational results show that the swirling Lorentz force causes plasma swirling with a maximum speed of 3.41 m/s near the plasma center when the injected sheath gas and central gas are not swirling. In these conditions, the real and imaginary parts of the maximum electrostatic potential are 0.95 V and 1.66 V, respectively. When the electrostatic field is neglected, the swirling velocity of the plasma is 3.95 m/s.     

The efect of the couple stress parameter and Prandtl number on the transient natural convection flow over a vertical cylinder

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefcient and Nusselt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.     

Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure

Elastic analysis of a functionally graded thick-walled cylindrical pressure vessel is analytically studied in the present research. Gradation is considered for all mechanical properties along the thickness direction based on a power function. The constitutive relations are developed in the general cylindrical coordinate system for an axisymmetric pressurized cylinder. For simulation of these two deformation components, first order shear deformation theory is considered. The FG cylinder is subjected to longitudinally non-uniform pressure along the length of the cylinder. The present problem is applicable for simulation of non-uniform pressurized cylinder by fluids or gases.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

Issue Information

Three‐dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set‐up, which restricts the development of intrinsic wake structure, leads to an over‐prediction of the onset point of the secondary wake instability (Re_cr). A best practice of the numerical set‐up is presented for the accurate prediction of Re_cr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Re_cr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set‐up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Re_cr, while the periodic boundary condition is recommended for simulating the wake structures above Re_cr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Free convection of a dusty‐gas flow along a semi‐infinite vertical cylinder

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.     

Trace gas detection of benzene,toluene, p-, m- and o-xylene with a compact measurement system using cantilever enhanced photoacoustic spectroscopy and optical parametric oscillator

A compact measurement system based on a novel combination of cantilever enhanced photoacoustic spectroscopy (CEPAS) and optical parametric oscillator (OPO) was applied to the gas phase measurement of benzene, toluene, and o-, m- and p-xylene (BTX) traces. The OPO had a band width (FWHM) of 1.3 nm, was tuned from 3237 to 3296 nm in steps of 0.1 nm and so spectra of BTX at different concentrations were recorded. The power emitted by the OPO increased from 88 mW at 3237 nm to 103 mW at 3296 nm. The univariate detection limits (3σ, 0.951 s) for benzene, toluene, p-, m- and o-xylene at 3288 nm were 12.0, 9.8, 13.2, 10.1 and 16.0 ppb, respectively. Multivariate data analysis using science-based calibration was used to resolve the interference of the analytes. The multivariate detection limits (3σ, 3237–3296 nm, 591 spectral points each 0.951 s) for benzene, toluene, p-, m- and o-xylene in the multi-compound sample, where all other analytes and water interfere were 4.3, 7.4, 11.0, 12.5 and 6.2 ppb, respectively. Without interferents, the multivariate detection limits varied between 0.5 and 0.6 ppb. The sum of the cross-selectivities (3237–3296 nm, 591 spectral points, each 0.951 s) per analyte were below 0.05 ppb/ppb, with an average of 0.038 ppb/ppb. The cross-selectivity of water to the analytes was on average 1.22 × 10⁻⁴ ppb/ppb. The OPO is small in size (L × W × H 125 × 70 × 45 mm), commercially available, and easy to operate and integrate to setups. The combination with sensitive CEPAS enables compact measurement systems for industrial as well as environmental trace gas monitoring.     

Start‐up of electrophoresis of an arbitrarily oriented dielectric cylinder

An analytical study is presented for the transient electrophoretic response of a circular cylindrical particle to the step application of an electric field. The electric double layer adjacent to the particle surface is thin but finite compared with the radius of the particle. The time‐evolving electroosmotic velocity at the outer boundary of the double layer is utilized as a slip condition so that the transient momentum conservation equation for the bulk fluid flow is solved. Explicit formulas for the unsteady electrophoretic velocity of the particle are obtained for both axially and transversely applied electric fields, and can be linearly superimposed for an arbitrarily‐oriented applied field. If the cylindrical particle is neutrally buoyant in the suspending fluid, the transient electrophoretic velocity is independent of the orientation of the particle relative to the applied electric field and will be in the direction of the applied field. If the particle is different in density from the fluid, then the direction of electrophoresis will not coincide with that of the applied field until the steady state is attained. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.