THE LOCATION OF SPHERICAL CAVITIES USING A TRIPOTENTIAL RESISTIVITY TECHNIQUE

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 780-784 ◽  
Author(s):  
G. M. Habberjam
Keyword(s):  
Magnetic Field ◽  
Apparent Resistivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Spherical Body ◽  
Numerical Results ◽  
Detailed Account ◽  
Conducting Sphere ◽  
Spherical Cavities ◽  
Conductivity Contrast

The surface gravitational and magnetic field anomalies due to a contrasting spherical body at depth are well known and appear in geophysical textbooks. The corresponding problem of the anomaly in apparent resistivity arising from such a body, owing to its conductivity contrast, is less frequently referred to because of the lengthy potential solutions involved. In electrical interpretation, few potential solutions exist for buried bodies of limited three‐dimensional extent, and consequently the simplest of these problems, the buried sphere, has received particular attention. Following early work by Hummel (1928), Webb (1931) produced potential solutions for this problem, and more recently Lipskaya (1949) has derived solutions and computed extensive numerical results. For the particular case of an infinitely conducting sphere, Van Nostrand (1953) has computed comprehensive numerical solutions, and more recently Van Nostrand and Cook (1966) presented a very detailed account of work on the buried sphere.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

scholarly journals Analytical and Numerical Solutions for the Thermal Problem in a Friction Clutch System

Computation ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 122
Author(s):  
Laith A. Sabri ◽  
Katarzyna Topczewska ◽  
Muhsin Jaber Jweeg ◽  
Oday I. Abdullah ◽  
Azher M. Abed
Keyword(s):  
Numerical Solution ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Results ◽  
Three Dimensional Model ◽  
Thermal Problem ◽  
Friction Clutch ◽  
Dry Conditions ◽  
The Difference ◽  
Element Technique

The dry friction clutch is an important part in vehicles, which has more than one function, but the most important function is to connect and disconnect the engine (driving part) with driven parts. This work presents a developed numerical solution applying a finite element technique in order to obtain results with high precision. A new three-dimensional model of a single-disc clutch operating in dry conditions was built from scratch. As the new model represents the real friction clutch including all details, the complexity in the geometry of the clutch is considered one of the difficulties that the researchers faced using the numerical solution. The thermal behaviour of the friction clutch during the slip phase was studied. Meanwhile, in the second part of this work, the transient thermal equations were derived from scratch to find the analytical solution for the thermal problem of a clutch disc in order to verify the numerical results. It was found, after comparison of the numerical results with analytical results, that the results of the numerical model are very accurate and the difference between them does not exceed 1%.

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls

1972 ◽  
Vol 56 (1) ◽  
pp. 121-141 ◽  
Author(s):  
J. S. Walker ◽  
G. S. S. Ludford ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Flow Direction ◽  
Three Dimensional ◽  
Side Wall ◽  
Transverse Magnetic ◽  
Wall Boundary ◽  
Strong Transverse

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.

scholarly journals Analytical Particular Solutions of Multiquadrics Associated with Polyharmonic Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chia-Cheng Tsai
Keyword(s):  
Laurent Series ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Results ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Particular Solutions

We derive two- and three-dimensional analytical particular solutions of multiquadrics (MQ) associated with the polyharmonic operators, named as the polyharmonic multiquadrics (PMQs). The methods of undetermined coefficients are constructed by observing the first few orders of the PMQs which are obtained by the symbolic software,Mathematica. By expanding the PMQs into the Laurent series, the unknown coefficients of the PMQs can be determined. The homogeneous parts of the PMQs are suitably arranged so that the PMQs are hierarchically unique and infinitely differentiable.Mathematicacodes are provided for obtaining the PMQs of arbitrary orders. The derived PMQs are validated by numerical solutions for Poisson’s equation. Numerical results indicate that the solutions obtained by the PMQs are more accurate than those by the MQ.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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