A Study of the Effects of Baffles on Rotating Compressible Flows

1989 ◽  
Vol 56 (3) ◽  
pp. 710-712
Author(s):  
Max D. Gunzburger ◽  
Houston G. Wood ◽  
Rosser L. Wayland
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Compressible Flows ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Gas Centrifuge ◽  
Mass Injection ◽  
Flow Domain ◽  
The Mathematical Model ◽  
Element Algorithm

Onsager’s pancake equation for the fluid dynamics of a gas centrifuge is modified for the case of centrifuges with baffles which render the flow domain doubly connected. A finite element algorithm is used for solving the mathematical model and to compute numerical examples for flow fields induced by thermal boundary conditions and by mass injection and extraction.

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

scholarly journals THERMOPHYSICS AND FLUID DYNAMICS. Special Chapters

2018 ◽  
Author(s):  
Alexander M. Molchanov
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Thermal Radiation ◽  
Gas Dynamics ◽  
Numerical Algorithms ◽  
Fluid Flows ◽  
Postgraduate Students ◽  
High Enthalpy ◽  
Scientists And Engineers ◽  
The Mathematical Model

The textbook is devoted to the description of the mathematical model of gas dynamics and thermal radiation of turbulent high-enthalpy gas and multiphase flows under conditions of thermal and chemical nonequilibrium.The book is a intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and fluid flows and also for students and postgraduate students who specialize in heanumerical gas and fluid dynamics.

scholarly journals Performance Analysis and Modeling of Microplastic Separation through Hydro Cyclones

2021 ◽  
Author(s):  
Fabio Borgia
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Computational Fluid Dynamics ◽  
Cfd Modeling ◽  
Separation Device ◽  
Operation Conditions ◽  
Computational Fluid Dynamics Cfd ◽  
Solid Liquid ◽  
Solid Liquid Separation ◽  
The Mathematical Model

The filtering hydro cyclone is a solid–liquid separation device, generally conical in shape. The hydro cyclone allows the separation of microplastics from water, to facilitate micro-recycling. To test the capabilities of a hydro cyclone at separating microplastics from water, Rietema’s standard sizes, mathematical and computational fluid dynamics (CFD) modeling were used. The results show that, even dough the mathematical model in unreliable when considering parameters out-side standard operation conditions, hydro cyclone microplastic separation can be achieved at 98% efficiency. Particles reach the outlet on average in 1.5 s for a flow velocity of 2 m/s, and denser microplastics end up in the underflow.

Mathematical model of anomalous thermoviscous non-newtonian fluid dynamics in a circular pipe

2012 ◽  
Vol 9 (2) ◽  
pp. 139-142
Author(s):  
S.F. Khizbullina
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Circular Pipe ◽  
Incompressible Fluid Flow ◽  
The Mathematical Model ◽  
Continuum Dynamics ◽  
Viscosity Dependence ◽  
The Continuum

On the basis of the continuum dynamics equations the mathematical model of evolution of an incompressible fluid flow in a circular pipe is developed taking into account non-newtonian properties of fluid and non-monotone viscosity dependence on temperature. The qualitative flow picture of anomalous thermoviscous non-newtonian fluid is similar to the flow picture of the anomalous thermoviscous newtonian fluid. Existence of viscosity anomaly leads to reduction of fluid hydraulic resistance.

Validation: What, Why and How

2016 ◽  
Author(s):  
Luís Eça ◽  
Guilherme Vaz ◽  
Arjen Koop ◽  
Filipe Pereira ◽  
Hugo Abreu
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Flat Plate ◽  
Parameter Uncertainty ◽  
Physical Reality ◽  
Physical Models ◽  
The Mathematical Model ◽  
Modelling Error ◽  
Quantities Of Interest

Offshore and Naval engineering have relied on physical models, i.e. experimental fluid dynamics (EFD), for several decades. Although the role of experiments in engineering is still unquestionable, some of the limitations of physical models, as for example domain size (blockage and scale effects), can be addressed using mathematical models, i.e. computational fluid dynamics (CFD). However, to gain confidence in the use of CFD it is fundamental to determine the modelling accuracy, i.e. to determine the difference between the “physical reality” and the selected mathematical model. The quantification of the modelling error is the goal of Validation. It must be emphasized that Validation applies to the mathematical model (and not the code) and is performed for selected flow quantities (the so-called quantities of interest). Ideally, Validation would be performed comparing an exact measurement of the “physical reality” with the exact solution of the selected mathematical model. However, exact measurements do not exist and mathematical models for turbulent flows do not have analytical solutions. Therefore, procedures must be developed to take into account experimental and numerical uncertainties. Furthermore, the exact values of the flow parameters as for example Reynolds number, fluid viscosity or inlet turbulence quantities are often unknown, which leads to the so-called parameter uncertainty that also has to be dealt within the assessment of the modelling error. The main goal of this paper is to demonstrate that the very popular designation of “code X is validated” is meaningless without saying what is the mathematical model embedded in the code, what are the quantities of interest for the specific application and what is the Validation uncertainty imposed by the experimental, numerical and parameter uncertainties. Furthermore, we also illustrate that Validation is not a pass or fail exercise. A modelling error of 10% may be acceptable for a given application, whereas 1% may not be enough for a different one. To this end, we present the application of the ASME V&V 20 Validation procedure for local set points and the metric for multiple set points to several practical test cases: prediction of transition from laminar to turbulent regime for the flow over a flat plate; flow around a circular cylinder; flow around the KVLCC2 tanker and current loads in shallow water for a LNG carrier. In most of these exercises, parameter uncertainty is assumed to be zero, which is an assumption often required for the so-called practical calculations due to the computational effort required to address it. Nonetheless, as an illustration of its application, the flow over the flat plate includes parameter uncertainty for the specification of the inlet turbulence quantities.

scholarly journals Reenactment of a bollard pull test for a double propeller tugboat using computational fluid dynamics

2015 ◽  
Vol 8 (17) ◽  
pp. 9
Author(s):  
Adan Vega ◽  
David López Martínez
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Computational Fluid Dynamics ◽  
Numerical Calculation ◽  
Cfd Simulations ◽  
The Real ◽  
Pull Test ◽  
Pull Tests ◽  
The Mathematical Model ◽  
Real Test

Use of CFD simulations is an affordable and trustworthy way of determining a vessel’s capacity before its construction. This study focuses in simulating a bollard pull of a specific tugboat and comparing the results with those of the real test to which it was subjected after construction. In compliance with the regulations of the classification societies regarding these types of tests, simulations will be carried out to study the bollard pull tests of a double propeller two boat. The results showed that the mathematical model is suitable for a numerical calculation of the bollard pull tests.

scholarly journals Coordinating a three level supply chain with multiple retailers

2021 ◽  
Author(s):  
Shahzad Naqvi
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Supply Chain Coordination ◽  
Research Work ◽  
The Other ◽  
Total Cost ◽  
Numerical Examples ◽  
Conflicting Interests ◽  
Order Quantities ◽  
The Mathematical Model

The objective of this research is to highlight the factors that can optimize the total cost of a centralized supply chain through coordination of order quantities amongst the players in a supply chain. Survey of earlier research reveals that players in a supply chain usually have conflicting interests, such as reducing inventories and increasing profitability. Thus, to make coordination feasible, it is essential to provide proper incentives to individual players. Munson and Rosenblatt (2001) were the first to discuss coordination in a three level supply chain with a single player at each level. On the other hand, Viswanathan and Piplani (2001) are believed to be the first to consider cooordination in a two level supply chain with a single vendor and multiple retailers. This research extends upon these works by investigating coordination in a three level supply chain with multiple retailers. This is done by incorporating the model of Viswanathan and Piplani (2001) into that of Munson and Rosenblatt (2001). A new mathematical model is developed, with numerical examples presented and results discussed. When players in a supply chain agree to coordinate, it is possible to have some of the players benefiting more than others in the chain, if not losing. The mathematical model developed in this research work guarantees that the local costs for the players either remain the same as before coordination, or decrease as a result of coordination. Furthermore, this research work assumes that savings generated from coordination should be distributed among the players of the chain. This led to developing a scheme to fairly distribute savings amongst the players of the supply chain. Results indicate that even though players may have conflicting interests in the supply chain, coordination is recommended and should be pursued.

scholarly journals Analysis of Repairable Geo/G/1 Queues with Negative Customers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Doo Ho Lee ◽  
Kilhwan Kim
Keyword(s):  
Mathematical Model ◽  
Performance Measures ◽  
Generating Functions ◽  
Time Distribution ◽  
System Size ◽  
Repair Process ◽  
Negative Customers ◽  
Numerical Examples ◽  
Sojourn Time Distribution ◽  
The Mathematical Model

We consider discrete-time Geo/G/1 queues with negative customers and a repairable server. The server is subject to failure due to a negative customer arrival. As soon as a negative customer arrives at a system, the server fails and one positive (ordinary) customer is forced to leave. At a failure instant, the server is turned off and the repair process immediately begins. We construct the mathematical model and present the probability generating functions of the system size distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given to show the influence of negative customer arrival on the performance measures of the system.

scholarly journals Coordinating a three level supply chain with multiple retailers

2021 ◽  
Author(s):  
Shahzad Naqvi
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Supply Chain Coordination ◽  
Research Work ◽  
The Other ◽  
Total Cost ◽  
Numerical Examples ◽  
Conflicting Interests ◽  
Order Quantities ◽  
The Mathematical Model

The objective of this research is to highlight the factors that can optimize the total cost of a centralized supply chain through coordination of order quantities amongst the players in a supply chain. Survey of earlier research reveals that players in a supply chain usually have conflicting interests, such as reducing inventories and increasing profitability. Thus, to make coordination feasible, it is essential to provide proper incentives to individual players. Munson and Rosenblatt (2001) were the first to discuss coordination in a three level supply chain with a single player at each level. On the other hand, Viswanathan and Piplani (2001) are believed to be the first to consider cooordination in a two level supply chain with a single vendor and multiple retailers. This research extends upon these works by investigating coordination in a three level supply chain with multiple retailers. This is done by incorporating the model of Viswanathan and Piplani (2001) into that of Munson and Rosenblatt (2001). A new mathematical model is developed, with numerical examples presented and results discussed. When players in a supply chain agree to coordinate, it is possible to have some of the players benefiting more than others in the chain, if not losing. The mathematical model developed in this research work guarantees that the local costs for the players either remain the same as before coordination, or decrease as a result of coordination. Furthermore, this research work assumes that savings generated from coordination should be distributed among the players of the chain. This led to developing a scheme to fairly distribute savings amongst the players of the supply chain. Results indicate that even though players may have conflicting interests in the supply chain, coordination is recommended and should be pursued.

Free and Forced Longitudinal Vibrations of Rods

2018 ◽  
Vol 931 ◽  
pp. 47-53 ◽  
Author(s):  
Khusen P. Kulterbaev ◽  
Lyalusya A. Baragunova ◽  
Maryana M. Shogenova
Keyword(s):  
Mathematical Model ◽  
Numerical Methods ◽  
Free Vibration ◽  
Cross Section ◽  
Forced Oscillations ◽  
Constant Cross Section ◽  
Longitudinal Vibrations ◽  
Numerical Examples ◽  
The Mathematical Model ◽  
Forced Longitudinal Oscillations

Free and forced longitudinal oscillations of homogeneous rods of constant cross section are considered. Analytical and numerical methods for solving problems are used. With free vibration, numerical examples are shown for a rod with a jammed and free end and for a rod with a concentrated non-deformable mass at the end, due to which the mathematical model accordingly changes. Forced oscillations are considered for distributed and concentrated loads. The eigenmodes of oscillations characteristic for continually discrete sisites are obtained.

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