The elementary plane‐wave model for hologram ray tracing

This work presents a semi-analytical technique based on the Green’s function and uniform-piston driven model to determine the end-correction length [Formula: see text] in an axially long flow-reversal end chamber muffler having an end-inlet and an end-outlet. The semi-analytical procedure is based on the 3D analytical uniform piston-driven model for obtaining the impedance [Z] matrix parameters and numerically evaluating the frequency [Formula: see text] at which the imaginary part of the cross-impedance parameter [Formula: see text] crosses the frequency axis at the first instance. The frequency [Formula: see text] corresponds to the low-frequency peak in the transmission loss (TL) spectrum of the axially long flow-reversal end-chamber muffler obtained a priori to its computation by considering the influence of higher order evanescent transverse modes. The effective chamber length (and thence, the end-correction length) in the low-frequency range are determined by using the expression for resonance frequency of a classical quarter-wave resonator. This method is employed to determine the end-correction in axially long elliptical cylindrical end chambers and circular cylindrical end chambers (with or without a rigid concentric circular pass-tube). The TL graph predicted by the 1D axial plane wave model (incorporating the end-correction length) is shown to be in an excellent agreement with that obtained by the 3D analytical approach and an experimental result (from literature) up to the low-frequency limit, thereby validating the semi-analytical technique. Parametric studies are conducted using the proposed semi-analytical method to investigate and qualitatively explain the effect of angular location and offset distance of the end ports and the pass-tube diameter on the end-correction length, thereby yielding important insights into the influence of transverse evanescent modes on dominant axial plane wave modes of the axially long end-chamber. Development of an empirical end-correction expression in a flow-reversal circular end-chamber with offset inlet and outlet ports is a practically useful contribution of this work.

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Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Annales Geophysicae ◽

10.5194/angeo-22-101-2004 ◽

2004 ◽

Vol 22 (1) ◽

pp. 101-113 ◽

Cited By ~ 68

Author(s):

A. Viljanen ◽

A. Pulkkinen ◽

O. Amm ◽

R. Pirjola ◽

T. Korja ◽

...

Keyword(s):

Magnetic Field ◽

Plane Wave ◽

Electric Field ◽

Wave Model ◽

Local Magnetic Field ◽

Geomagnetic Variation ◽

Geoelectric Field ◽

Geomagnetically Induced Currents ◽

The Baltic ◽

Current Systems

Abstract. The method of spherical elementary current systems provides an accurate modelling of the horizontal component of the geomagnetic variation field. The interpolated magnetic field is used as input to calculate the horizontal geoelectric field. We use planar layered (1-D) models of the Earth's conductivity, and assume that the electric field is related to the local magnetic field by the plane wave surface impedance. There are locations in which the conductivity structure can be approximated by a 1-D model, as demonstrated with the measurements of the Baltic Electromagnetic Array Research project. To calculate geomagnetically induced currents (GIC), we need the spatially integrated electric field typically in a length scale of 100km. We show that then the spatial variation of the electric field can be neglected if we use the measured or interpolated magnetic field at the site of interest. In other words, even the simple plane wave model is fairly accurate for GIC purposes. Investigating GIC in the Finnish high-voltage power system and in the natural gas pipeline, we find a good agreement between modelled and measured values, with relative errors less than 30% for large GIC values. Key words. Geomagnetism and paleomagnetism (geomagnetic induction; rapid time variations) – Ionosphere (electric field and currents)

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