scholarly journals Solutions without Space-Time Separation for ADS Experiments: Overview on Developments and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
B. Merk ◽  
V. Glivici-Cotruţă
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Space Time ◽  
Experimental Results ◽  
Time Dependent ◽  
Special Configuration ◽  
Time Separation ◽  
Function Solution ◽  
Boundary Source ◽  
Good Agreement

The different analytical solutions without space-time separation foreseen for the analysis of ADS experiments are described. The SC3A experiment in the YALINA-Booster facility is described and investigated. For this investigation the very special configuration of YALINA-Booster is analyzed based on HELIOS calculations. The results for the time dependent diffusion and the time dependentP1equation are compared with the experimental results for the SC3A configuration. A comparison is given for the deviation between the analytical solution and the experimental results versus the different transport approximations. To improve the representation to the special configuration of YALINA- Booster, a new analytical solution for two energy groups with two sources (central external and boundary source) has been developed starting form the Green's function solution. Very good agreement has been found for these improved analytical solutions.

scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

Numerical Calculation of Pressure Fluctuations in the Volute of a Centrifugal Fan

2005 ◽  
Vol 128 (2) ◽  
pp. 359-369 ◽  
Author(s):  
Rafael Ballesteros-Tajadura ◽  
Sandra Velarde-Suárez ◽  
Juan Pablo Hurtado-Cruz ◽  
Carlos Santolaria-Morros
Keyword(s):  
Fluid Dynamics ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Power Spectra ◽  
Operating Conditions ◽  
Experimental Results ◽  
Time Dependent ◽  
Centrifugal Fan ◽  
Wall Pressure Fluctuations ◽  
Good Agreement

In this work, a numerical model has been applied in order to obtain the wall pressure fluctuations at the volute of an industrial centrifugal fan. The numerical results have been compared to experimental results obtained in the same machine. A three-dimensional numerical simulation of the complete unsteady flow on the whole impeller-volute configuration has been carried out using the computational fluid dynamics code FLUENT®. This code has been employed to calculate the time-dependent pressure both in the impeller and in the volute. In this way, the pressure fluctuations in some locations over the volute wall have been obtained. The power spectra of these fluctuations have been obtained, showing an important peak at the blade passing frequency. The amplitude of this peak presents the highest values near the volute tongue, but the spatial pattern over the volute extension is different depending on the operating conditions. A good agreement has been found between the numerical and the experimental results.

Guidelines for Design of Dividing Manifolds With Discharge Uniformly Distributed at Different Positions Along the Device Axis

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Honggang Yang ◽  
Yi Wang ◽  
Xiaojing Meng ◽  
Dong Li ◽  
Xiaofan Cai
Keyword(s):  
Experimental Data ◽  
Analytical Solution ◽  
Governing Equation ◽  
Analytical Solutions ◽  
Dimensionless Parameter ◽  
Operating Conditions ◽  
Experimental Results ◽  
Practical Operation ◽  
Discharge Distribution

Abstract For practical operation of dividing manifolds, the discharge uniformity is a property generally required. To investigate the dependence of discharge uniformity on the manifold geometry and operating conditions, analytical solution to the governing equation, Bajura's equation, was secured. Furthermore, examples were derived by substituting experimental data into the analytical solutions; the resultant curves of discharge distribution indicated essential agreement between the theoretical and experimental results. For evaluating the property of discharge distribution, a uniformity index, U, was introduced. The calculated results of U showed a well-defined dependence of uniformity on the dimensionless parameter, γ, and a maximum of U presented around 1.44 of γ.

Fast Computation of Frictional Energy Dissipation in Rough Contacts Under Partial Slip

2008 ◽  
Author(s):  
Simon Medina ◽  
Daniele Dini ◽  
Andrew V. Olver ◽  
David A. Hills
Keyword(s):  
Energy Dissipation ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Partial Slip ◽  
Fast Computation ◽  
Integration Technique ◽  
Frictional Energy ◽  
Contact Compliance ◽  
Frictional Energy Dissipation ◽  
Good Agreement

The multilevel multi-integration technique has been used here to numerically solve the normal and tangential loading of rough surfaces, employing the theory of Ciavarella [1] & Ja¨ger [2] to determinine the tangential shear tractions. Regular asperity surfaces, for which analytical solutions have previously been reported, have been analysed and results showed good agreement with the analytical solution. Random Gaussian surfaces have also been investigated to assess the effect of roughness on contact compliance and frictional energy dissipation.

Nitric Oxide Formation in Diesel Engines

1974 ◽  
Vol 188 (1) ◽  
pp. 477-483 ◽  
Author(s):  
H. Çakir
Keyword(s):  
Nitric Oxide ◽  
Nitrogen Oxides ◽  
Analytical Solutions ◽  
Diesel Engines ◽  
Operating Conditions ◽  
Experimental Results ◽  
Combustion Model ◽  
Oxide Formation ◽  
Nitric Oxide Formation ◽  
Good Agreement

A combustion model is presented to account for the nitric oxide formation in diesel engines at all operating conditions. The paper tries to introduce the concept of variable air-fuel ratio estimated to exist during diesel combustion. Analytical solutions are found to be in good agreement with experimental results. Further investigations will be directed to diesel engines having combustion systems other than the M.A.N.-FM system, and to possible remedies to reduce the formation of nitrogen oxides.

Analytical Solution to Transient Asymmetric Heat Conduction in a Multilayer Annulus

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Prashant K. Jain ◽  
Suneet Singh ◽  
Rizwan-uddin
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Series Solution ◽  
Double Series ◽  
The Other ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Explicit Dependence

In this paper, we present an analytical double-series solution for the time-dependent asymmetric heat conduction in a multilayer annulus. In general, analytical solutions in multidimensional Cartesian or cylindrical (r,z) coordinates suffer from existence of imaginary eigenvalues and thus may lead to numerical difficulties in computing analytical solution. In contrast, the proposed analytical solution in polar coordinates (2D cylindrical) is “free” from such imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of transverse (radial) eigenvalues on those in the other direction.

Particle Entrainment in a Bounded Rotating Flow With a Drain

1998 ◽  
Vol 120 (4) ◽  
pp. 676-679 ◽  
Author(s):  
J. Mang ◽  
E. Minkov ◽  
U. Schaflinger ◽  
M. Ungarish
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Time Dependent ◽  
Rotating Flow ◽  
Centrifugal Separation ◽  
Ekman Layers ◽  
Dependent Flow ◽  
Bathtub Vortex ◽  
Oseen Vortex ◽  
Good Agreement

A bathtub vortex is usually formed at the axis of a drain. In the presence of such a vortex, gravity separation of solid impurities lighter than the embedding fluid is modified by centrifugal separation and viscous resuspension. Both mechanisms are responsible for the agglomeration of impurities at the axis of the vortex. From there the impurities are easily sucked into the outlet. In the investigated case, a viscous fluid with a given initial rotation is spinning down in a container with endplates both at the bottom and the top. The amount of fluid withdrawn through a circular hole in the center of the vortex is constantly replaced by a radial influx. The resulting time-dependent flow was solved by means of a finite difference method taking into account the influence of Ekman layers at the bottom and the top. Subsequently, the process of centrifugal separation of particles lighter than the embedding fluid was studied in the aforementioned flow field. The results were compared with the particle motion in a classical Oseen vortex. For a simplified case an analytical solution was derived and compared with the corresponding numerical solution. Both results were found to be in good agreement.

Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

2005 ◽  
Vol 42 (6) ◽  
pp. 1705-1717 ◽  
Author(s):  
Li Li ◽  
Michel Aubertin ◽  
Tikou Belem
Keyword(s):  
Numerical Modeling ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Earth Pressure ◽  
The State ◽  
Experimental Results ◽  
State Of Stress ◽  
Earth Pressures

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.Key words: backfill, earth pressure, 3D openings, analytical solutions, trenches, mining stopes.

On the Propagation Buckling and Effects in Ultra-Long Deep Subsea Pipelines

2011 ◽  
Author(s):  
Hossein Khalilpasha ◽  
Faris Albermani
Keyword(s):  
Experimental Investigation ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Numerical Results ◽  
Series Of Experiments ◽  
Buckle Propagation ◽  
Subsea Pipelines ◽  
Good Agreement

This paper considers buckling propagation in ultra-long deep subsea pipelines. Experimental investigation of buckle propagation in ultra-deep pipelines was conducted to verify the analytical solutions proposed by the authors in a previous paper [1]. A series of experiments were designed and conducted to calibrate the equations and verify the analytical and numerical results. The tests include tensile coupon tests, ring squash tests and buckle propagation tests on intact and dented Aluminum pipes with three different D/t ratios. The results are in good agreement with the proposed analytical solution.

Application of Artificial Intelligence To Predict Time-DependentMud-Weight Windows in Real Time

SPE Journal ◽  
2021 ◽  
pp. 1-21
Author(s):  
Dung T. Phan ◽  
Chao Liu ◽  
Murtadha J. AlTammar ◽  
Yanhui Han ◽  
Younane N. Abousleiman
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Analytical Solution ◽  
Real Time ◽  
Analytical Solutions ◽  
Wellbore Stability ◽  
Time Dependent ◽  
Processing Unit ◽  
Inference System ◽  
Drilling Operations

Summary Selection of a safe mud weight is crucial in drilling operations to reduce costly wellbore-instability problems. Advanced physics models and their analytical solutions for mud-weight-window computation are available but still demanding in terms of central-processing-unit (CPU) time. This paper presents an artificial-intelligence (AI) solution for predicting time-dependent safe mud-weight windows and very refined polar charts in real time. The AI agents are trained and tested on data generated from a time-dependent coupled analytical solution (poroelastic) because numerical solutions are prohibitively slow. Different AI techniques, including linear regression, decision tree, random forest, extra trees, adaptive neuro fuzzy inference system (ANFIS), and neural networks are evaluated to select the most suitable one. The results show that neural networks have the best performances and are capable of predicting time-dependentmud-weight windows and polar charts as accurately as the analytical solution, with 1/1,000 of the computer time needed, making them very applicable to real-time drilling operations. The trained neural networks achieve a mean squared error (MSE) of 0.0352 and a coefficient of determination (R2) of 0.9984 for collapse mud weights, and an MSE of 0.0072 and an R2 of 0.9998 for fracturing mud weights on test data sets. The neural networks are statistically guaranteed to predict mud weights that are within 5% and 10% of the analytical solutions with probability up to 0.986 and 0.997, respectively, for collapse mud weights, and up to 0.9992 and 0.9998, respectively, for fracturing mud weights. Their time performances are significantly faster and less demanding in computing capacity than the analytical solution, consistently showing three-orders-of-magnitude speedups in computational speed tests. The AI solution is integrated into a deployed wellbore-stability analyzer, which is used to demonstrate the AI’s performances and advantages through three case studies.

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