On the stability and settling of suspended solids in settling ponds. Part I. Piece-wise linear consolidation analysis of sediment layer

1983 ◽  
Vol 20 (4) ◽  
pp. 817-826 ◽  
Author(s):  
Raymond N. Yong ◽  
Steven K. H. Siu ◽  
Donald E. Sheeran
Keyword(s):  
Finite Difference ◽  
Large Strain ◽  
Constant Load ◽  
Sediment Layer ◽  
Iterative Technique ◽  
Computer Technique ◽  
Consolidation Model ◽  
The Stability ◽  
Solids Content ◽  
Settling Ponds

The resultant large overall strains resulting from the consolidation of low solids content slurry sediments, such as those obtained in settling ponds, are predicted and compared with actual results for two sludge settling ponds. The computer technique developed in association with the piece-wise linear consolidation model permits inclusion of self-weight and eliminates restrictions such as small strains, constant load, and constant material consolidation parameters by solving the governing equations using the finite difference iterative technique. Good agreement between predicted and measured field values for the two ponds has been obtained. Keywords: large-strain consolidation, settling ponds, sediments, piece-wise linear consolidation, finite difference, iterative technique.

scholarly journals Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting

2020 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Bolat Duissenbekov ◽  
Abduhalyk Tokmuratov ◽  
Nurlan Zhangabay ◽  
Zhenis Orazbayev ◽  
Baisbay Yerimbetov ◽  
...  
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Equations ◽  
Constant Load ◽  
Time Interval ◽  
Test Case ◽  
Algebraic Equations ◽  
Nonlinear Properties ◽  
Finite Difference Equations ◽  
Concrete Shells

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.

scholarly journals The Effect of RME-1-Butanol Blends on Combustion, Performance and Emission of a Direct Injection Diesel Engine

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2941
Author(s):  
Wojciech Tutak ◽  
Arkadiusz Jamrozik ◽  
Karol Grab-Rogaliński
Keyword(s):  
Diesel Engine ◽  
Heat Release ◽  
Direct Injection ◽  
Specific Energy Consumption ◽  
Combustion Process ◽  
Constant Load ◽  
Combustion Stability ◽  
Performance And Emission ◽  
Energy Share ◽  
The Stability

The main objective of this study was assessment of the performance, emissions and combustion characteristics of a diesel engine using RME–1-butanol blends. In assessing the combustion process, great importance was placed on evaluating the stability of this process. Not only were the typical COVIMEP indicators assessed, but also the non-burnability of the characteristic combustion stages: ignition delay, time of 50% heat release and the end of combustion. The evaluation of the combustion process based on the analysis of heat release. The tests carried out on a 1-cylinder diesel engine operating at a constant load. Research and evaluation of the combustion process of a mixture of RME and 1-butanol carried out for the entire range of shares of both fuels up to 90% of 1-butanol energetic fraction. The participation of butanol in combustion process with RME increased the in-cylinder peak pressure and the heat release rate. With the increase in the share of butanol there was noted a decrease in specific energy consumption and an increase in engine efficiency. The share of butanol improved the combustion stability. There was also an increase in NOx emissions and decrease in CO and soot emissions. The engine can be power by blend up to 80% energy share of butanol.

Accuracy contours in (nT, λ) space in electrochemical digital simulations

1991 ◽  
Vol 56 (1) ◽  
pp. 20-41 ◽  
Author(s):  
Dieter Britz ◽  
Merete F. Nielsen
Keyword(s):  
Finite Difference ◽  
Linear Sweep Voltammetry ◽  
Stability Factor ◽  
Dimensionless Time ◽  
Simulation Techniques ◽  
Rational Algorithm ◽  
The Stability ◽  
Transport Problems ◽  
Current Approximation ◽  
Digital Simulations

In finite difference simulations of electrochemical transport problems, it is usually tacitly assumed that λ, the stability factor Dδt/δx2, should be set as high as possible. Here, accuracy contours are shown in (nT, λ) space, where nT is he number of finite difference steps per unit (dimensionless) time. Examples are the Cottrell experiment, simple chronopotentiometry and linear sweep voltammetry (LSV) on a reversible system. The simulation techniques examined include the standard explicit (point- and box-) methods as well as Runge-Kutta, Crank-Nicolson, hopscotch and Saul’yev. For the box method, the two-point current approximation appears to be the most appropriate. A rational algorithm for boundary concentrations with explicit LSV simulations is discussed. In general, the practice of choosing as high a λ value when using the explicit techniques, is confirmed; there are practical limits in all cases.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

scholarly journals A Finite-Difference Wavenumber-Time Domain Method for Sound Field Prediction in a Uniformly Moving Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Bichun Dong ◽  
Runmei Zhang ◽  
Chuanyang Yu ◽  
Huan Li
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Sound Pressure ◽  
Sound Field ◽  
Time Domain Method ◽  
Practical Significance ◽  
Moving Medium ◽  
Domain Method ◽  
Aero Engines ◽  
The Stability

Sound field prediction has practical significance in the control of noise generated by sources in a flow, for example, the noise in aero-engines and ventilation systems. Aiming at accurate and flexible prediction of time-dependent sound field, a finite-difference wavenumber-time domain method for sound field prediction in a uniformly moving medium is proposed. The method is based on the second-order convective wave equation, and the wavenumber-time domain representation of the sound pressure field on one plane is forward propagated via a derived recursive expression. In this paper, the recursive expression is first deduced, and then numerical stability and dispersion of the proposed method are analyzed, based on which the stability condition is given and the correction of dispersion related to the transition frequency is made. Numerical simulations are conducted to test the performance of the proposed method, and the results show that the method is valid and robust at different Mach numbers.

Effect of various treatments on consolidation of oil sands fluid fine tailings

2018 ◽  
Vol 55 (8) ◽  
pp. 1059-1066 ◽  
Author(s):  
G. Ward Wilson ◽  
Louis K. Kabwe ◽  
Nicholas A. Beier ◽  
J. Don Scott
Keyword(s):  
Shear Strength ◽  
Oil Sands ◽  
Large Strain ◽  
Regulatory Requirements ◽  
Freeze Thaw ◽  
Treatment Processes ◽  
Fine Tailings ◽  
Fluid Fine Tailings ◽  
Solids Content ◽  
And Storage

Regulatory policy and regulations in Alberta require oil sands companies to reduce their production and storage of fluid fine tailings by creating deposits that can be reclaimed in a timely manner. To meet the regulatory requirements, some companies are adding flocculants to the fluid fine tailings and then using thickeners, inline flocculation or centrifuges to increase the solids content. Freeze–thaw and drying processes are then used to further dewater the tailings. The effects of flocculating, thickening, and freeze–thaw treatments were investigated by performing large-strain consolidation and shear strength tests on these treated fluid fine tailings. The consolidation and shear strength results were then compared with those of untreated fluid fine tailings. All of the treatments increased the hydraulic conductivity of the fluid fine tailings to some degree, but had little to no effect on the compressibility and shear strength. The effects of the treatment processes are discussed and evaluated.

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