Search results for: Algebraic%20Fractions

Authors: Mikhail Gritskevich, Sebastian Hohenstein

Abstract:

The paper presents the results of a detailed assessment of several modern Reynolds Averaged Navier-Stokes (RANS) turbulence models for prediction of C3X vane film cooling at various injection regimes. Three models are considered, namely the Shear Stress Transport (SST) model, the modification of the SST model accounting for the streamlines curvature (SST-CC), and the Explicit Algebraic Reynolds Stress Model (EARSM). It is shown that all the considered models face with a problem in prediction of the adiabatic effectiveness in the vicinity of the cooling holes; however, accounting for the Reynolds stress anisotropy within the EARSM model noticeably increases the solution accuracy. On the other hand, further downstream all the models provide a reasonable agreement with the experimental data for the adiabatic effectiveness and among the considered models the most accurate results are obtained with the use EARMS.

Keywords: Discrete holes film cooling, Reynolds Averaged Navier-Stokes, Reynolds stress tensor anisotropy, turbulent heat transfer.

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Authors: A. Majid Bahari, Kourosh Hejazi

Abstract:

Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds- Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model.

Keywords: Buoyant flows, Buoyant k-ε turbulence model, saline gravity current.

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Authors: E.Darzi

Abstract:

In this study, a reformer model simulation to use refinery (Farashband refinery, Iran) waste natural gas. In the petroleum and allied sectors where natural gas is being encountered (in form of associated gas) without prior preparation for its positive use, its combustion (which takes place in flares, an equipment through which they are being disposed) has become a great problem because of its associated environmental problems in form of gaseous emission. The proposed model is used to product syngas from waste natural gas. A detailed steady model described by a set of ordinary differential and algebraic equations was developed to predict the behavior of the overall process. The proposed steady reactor model was validated against process data of a reformer synthesis plant recorded and a good agreement was achieved. H2/CO ratio has important effect on Fischer- Tropsch synthesis reactor product and we try to achieve this parameter with best designing reformer reactor. We study different kind of reformer reactors and then select auto thermal reforming process of natural gas in a fixed bed reformer that adjustment H2/CO ratio with CO2 and H2O injection. Finally a strategy was proposed for prevention of extra natural gas to atmosphere.

Keywords: Fischer-Tropsch, injection, reformer, syngas, waste natural gas.

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

Abstract:

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: Noura Boudiaf, Allaoua Chaoui

Abstract:

To analyze the behavior of Petri nets, the accessibility graph and Model Checking are widely used. However, if the analyzed Petri net is unbounded then the accessibility graph becomes infinite and Model Checking can not be used even for small Petri nets. ECATNets [2] are a category of algebraic Petri nets. The main feature of ECATNets is their sound and complete semantics based on rewriting logic [8] and its language Maude [9]. ECATNets analysis may be done by using techniques of accessibility analysis and Model Checking defined in Maude. But, these two techniques supported by Maude do not work also with infinite-states systems. As a category of Petri nets, ECATNets can be unbounded and so infinite systems. In order to know if we can apply accessibility analysis and Model Checking of Maude to an ECATNet, we propose in this paper an algorithm allowing the detection if the ECATNet is bounded or not. Moreover, we propose a rewriting logic based tool implementing this algorithm. We show that the development of this tool using the Maude system is facilitated thanks to the reflectivity of the rewriting logic. Indeed, the self-interpretation of this logic allows us both the modelling of an ECATNet and acting on it.

Keywords: ECATNets, Rewriting Logic, Maude, Finite-stateSystems, Infinite-state Systems, Boundness Property Checking.

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Authors: Robersy Sánchez, Ricardo Grau

Abstract:

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represent one or more hypothetical bases with unspecific pairing. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvements of a primitive DNA repair system could make possible the transition from the ancient to the modern genetic code. Our results suggest that the Watson-Crick base pairing and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as the transition from the former to the later. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences.

Keywords: Genetic code vector space, primeval genetic code, power spectrum.

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Authors: Dragos Nicolae VIZIREANU

Abstract:

One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.

Keywords: 3D shape decomposition representation, mathematical morphology, gray scale interframe interpolation

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: Leila Vafajoo, Farhad Khorasheh, Mehrnoosh Hamzezadeh Nakhjavani, Moslem Fattahi

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In the present study, a procedure was developed to determine the optimum reaction rate constants in generalized Arrhenius form and optimized through the Nelder-Mead method. For this purpose, a comprehensive mathematical model of a fixed bed reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3 catalyst was developed. Utilizing appropriate kinetic rate expressions for the main dehydrogenation reaction as well as side reactions and catalyst deactivation, a detailed model for the radial flow reactor was obtained. The reactor model composed of a set of partial differential equations (PDE), ordinary differential equations (ODE) as well as algebraic equations all of which were solved numerically to determine variations in components- concentrations in term of mole percents as a function of time and reactor radius. It was demonstrated that most significant variations observed at the entrance of the bed and the initial olefin production obtained was rather high. The aforementioned method utilized a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method was demonstrated by comparing the predicted values of the kinetic constants using the proposed method with a series of experimental values reported in the literature for different systems.

Keywords: Dehydrogenation, Pt-Sn/Al2O3 Catalyst, Modeling, Nelder-Mead, Optimization

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Authors: N. Outili, A-H. Meniai

Abstract:

Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Juhee Lee, Yongjun Lee

Abstract:

In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.

Keywords: Finite volume method, fluid flow, laminar flow, unstructured grid.

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Authors: Mohamed Ghorab

Abstract:

Local generated and distributed system for thermal and electrical energy is sighted in the near future to reduce transmission losses instead of the centralized system. Distributed Energy Resources (DER) is designed at different sizes (small and medium) and it is incorporated in energy distribution between the hubs. The energy generated from each technology at each hub should meet the local energy demands. Economic and environmental enhancement can be achieved when there are interaction and energy exchange between the hubs. Network energy system and CO₂ optimization between different six hubs presented Canadian community level are investigated in this study. Three different scenarios of technology systems are studied to meet both thermal and electrical demand loads for the six hubs. The conventional system is used as the first technology system and a reference case study. The conventional system includes boiler to provide the thermal energy, but the electrical energy is imported from the utility grid. The second technology system includes combined heat and power (CHP) system to meet the thermal demand loads and part of the electrical demand load. The third scenario has integration systems of CHP and Organic Rankine Cycle (ORC) where the thermal waste energy from the CHP system is used by ORC to generate electricity. General Algebraic Modeling System (GAMS) is used to model DER system optimization based on energy economics and CO₂ emission analyses. The results are compared with the conventional energy system. The results show that scenarios 2 and 3 provide an annual total cost saving of 21.3% and 32.3 %, respectively compared to the conventional system (scenario 1). Additionally, Scenario 3 (CHP & ORC systems) provides 32.5% saving in CO₂ emission compared to conventional system subsequent case 2 (CHP system) with a value of 9.3%.  

Keywords: Distributed energy resources, network energy system, optimization, microgeneration system.

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Authors: Padmanabhan Balasubramanian, Ryuta Arisaka

Abstract:

Factoring Boolean functions is one of the basic operations in algorithmic logic synthesis. A novel algebraic factorization heuristic for single-output combinatorial logic functions is presented in this paper and is developed based on the set theory paradigm. The impact of factoring is analyzed mainly from a low power design perspective for standard cell based digital designs in this paper. The physical implementation of a number of MCNC/IWLS combinational benchmark functions and sub-functions are compared before and after factoring, based on a simple technology mapping procedure utilizing only standard gate primitives (readily available as standard cells in a technology library) and not cells corresponding to optimized complex logic. The power results were obtained at the gate-level by means of an industry-standard power analysis tool from Synopsys, targeting a 130nm (0.13μm) UMC CMOS library, for the typical case. The wire-loads were inserted automatically and the simulations were performed with maximum input activity. The gate-level simulations demonstrate the advantage of the proposed factoring technique in comparison with other existing methods from a low power perspective, for arbitrary examples. Though the benchmarks experimentation reports mixed results, the mean savings in total power and dynamic power for the factored solution over a non-factored solution were 6.11% and 5.85% respectively. In terms of leakage power, the average savings for the factored forms was significant to the tune of 23.48%. The factored solution is expected to better its non-factored counterpart in terms of the power-delay product as it is well-known that factoring, in general, yields a delay-efficient multi-level solution.

Keywords: Factorization, Set theory, Logic function, Standardcell based design, Low power.

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Authors: Mingren Shi, Michael Renton

Abstract:

There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

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Authors: Padmanabhan Balasubramanian, C. Hari Narayanan

Abstract:

This paper discusses a new, systematic approach to the synthesis of a NP-hard class of non-regenerative Boolean networks, described by FON[FOFF]={mi}[{Mi}], where for every mj[Mj]∈{mi}[{Mi}], there exists another mk[Mk]∈{mi}[{Mi}], such that their Hamming distance HD(mj, mk)=HD(Mj, Mk)=O(n), (where 'n' represents the number of distinct primary inputs). The method automatically ensures exact minimization for certain important selfdual functions with 2n-1 points in its one-set. The elements meant for grouping are determined from a newly proposed weighted incidence matrix. Then the binary value corresponding to the candidate pair is correlated with the proposed binary value matrix to enable direct synthesis. We recommend algebraic factorization operations as a post processing step to enable reduction in literal count. The algorithm can be implemented in any high level language and achieves best cost optimization for the problem dealt with, irrespective of the number of inputs. For other cases, the method is iterated to subsequently reduce it to a problem of O(n-1), O(n-2),.... and then solved. In addition, it leads to optimal results for problems exhibiting higher degree of adjacency, with a different interpretation of the heuristic, and the results are comparable with other methods. In terms of literal cost, at the technology independent stage, the circuits synthesized using our algorithm enabled net savings over AOI (AND-OR-Invert) logic, AND-EXOR logic (EXOR Sum-of- Products or ESOP forms) and AND-OR-EXOR logic by 45.57%, 41.78% and 41.78% respectively for the various problems. Circuit level simulations were performed for a wide variety of case studies at 3.3V and 2.5V supply to validate the performance of the proposed method and the quality of the resulting synthesized circuits at two different voltage corners. Power estimation was carried out for a 0.35micron TSMC CMOS process technology. In comparison with AOI logic, the proposed method enabled mean savings in power by 42.46%. With respect to AND-EXOR logic, the proposed method yielded power savings to the tune of 31.88%, while in comparison with AND-OR-EXOR level networks; average power savings of 33.23% was obtained.

Keywords: AOI logic, ESOP, AND-OR-EXOR, Incidencematrix, Hamming distance.

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