On the cellular patterns in thermal convection

1964 ◽  
Vol 18 (4) ◽  
pp. 481-498 ◽  
Author(s):  
J. T. Stuart
Keyword(s):  
Mathematical Model ◽  
Convective Motion ◽  
Theoretical Work ◽  
Experimental Conditions ◽  
Cellular Pattern ◽  
Precise Knowledge ◽  
A Cell ◽  
Definition Of ◽  
New Formulation ◽  
The Mathematical Model

In the theory of thermal convective instability between two horizontal planes there are many solutions that are periodic in the horizontal co-ordinates, while in experiment convection is observed to take place in cellular patterns. It is often assumed, or decided after insufficient argument, that the periodic solutions of the mathematical model ‘explain’ or correspond to these patterns, but a completely satisfactory discussion of this correspondence has not been given. Indeed, with certain mathematical solutions ambiguities arise as to what cell centres and cellular boundaries are. A detailed discussion has recently become especially necessary because attempts are being made to predict which particular cellular pattern will occur in given experimental conditions.In this paper the topic is studied afresh and the question is asked: what features, in the mathematical model, correspond to what an experimentalist observes in cellular convective motion? In answer a definition of a cell is formulated which relates certain surfaces in the flow field of the mathematical model to steady vertical cellular boundaries that are observed in experiment, and which shows where the cell centres lie. In particular the classical hexagonal cellular pattern, of the mathematical model, is shown to be the prototype pattern of what is experimentally observed. On the other hand the square and so called ‘rectangular’ cases of linearized theory are shown not to correspond truly to square and rectangular cells at all. The new formulation is especially relevant to theoretical work on the prediction of cell shape and direction of flow in cells, since precise knowledge of the shapes of the cellular boundaries and locations of cell centres is essential if predictions are to be compared with observation.

Mathematical model of the artificial muscle with two actuators

2020 ◽  
pp. 095440622094156
Author(s):  
Ljubinko B Kevac ◽  
Mirjana M Filipovic ◽  
Ana M Djuric
Keyword(s):  
Mathematical Model ◽  
Control Structure ◽  
Artificial Muscle ◽  
Parallel Robot ◽  
Simulation Results ◽  
Proportional Derivative Controller ◽  
Definition Of ◽  
The Mathematical Model ◽  
The Given ◽  
Very High

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 326-336 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
D. B. Spalding
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Combustion Process ◽  
Three Dimensional ◽  
Solution Algorithm ◽  
Physical Models ◽  
Turbulence Energy ◽  
Experimental Conditions ◽  
Diffusion Controlled ◽  
The Mathematical Model

The paper presents a mathematical model for three-dimensional, swirling, recirculating, turbulent flows inside can combustors. The present model is restricted to single-phase, diffusion-controlled combustion, with negligible radiation heat-transfer; however, the introduction of other available physical models can remove these restrictions. The mathematical model comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy, its dissipation rate, and the mean square of concentration fluctuations. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variables at all internal grid nodes. The prediction procedure, composed of the mathematical model and its solution algorithm, is applied to predict the fields of variables within a representative can combustor; the results are compared with corresponding measurements. The predicted results give the same trends as the measured ones, but the quantitative agreement is not always acceptable; this is attributed to the combustion process not being truly diffusion-controlled for the experimental conditions investigated.

DRY SLIDING WEAR BEHAVIOR OPTIMIZATION OF STIR CAST LM6/ZrO2 COMPOSITES BY RESPONSE SURFACE METHODOLOGY ANALYSIS

2016 ◽  
Vol 40 (3) ◽  
pp. 351-369 ◽  
Author(s):  
G. Karthikeyan ◽  
G.R. Jinu
Keyword(s):  
Mathematical Model ◽  
Response Surface Methodology ◽  
Response Surface ◽  
Wear Behavior ◽  
Wear Test ◽  
Stir Casting ◽  
Dry Sliding Wear ◽  
Experimental Conditions ◽  
Weight Percentage ◽  
The Mathematical Model

LM6 was reinforced with various percentages of ZrO2 particles by using stir casting method. The prepared samples were subjected to tensile and wear test at variable loads by using a pin-on-disc wear tester. The curve fitting technique was used to develop the respective linear, logarithmic, polynomial, power law equations. The wear worn surface and surface roughness of the specimen were studied. Response Surface Methodology (RSM) was used to minimize the number of experimental conditions and develop the mathematical model between the key process parameters namely weight percentage of ZrO2, load and sliding distance. Analysis of Variance technique was applied to check the validity of the developed model. The mathematical model developed for the specific wear rate was predicted at 99% confidence level and some useful conclusions were made.

scholarly journals ANGULAR MOVEMENT PROGRAM CALCULATION PROCEDURE SPACECRAFT WHEN TAKING THE SURFACE OF THE EARTH IN AREA MODE

2019 ◽  
Vol 27 (4) ◽  
pp. 86-100
Author(s):  
Oleg Viktorovich Lutz ◽  
Galina Alexandrovna Borshchova ◽  
Evgeny Dmitrievich Yarmolchuk ◽  
Alexander Alekseevich Manoilenko
Keyword(s):  
Mathematical Model ◽  
Angular Motion ◽  
Field Of View ◽  
Method Of Calculation ◽  
Angular Movement ◽  
The Earth ◽  
Program Calculation ◽  
Large Width ◽  
Definition Of ◽  
The Mathematical Model

Currently increased interest in satellite images of the Earth's surface with high resolution terrain  (1 to 10 m). To obtain such images, you must use a long focus optical system (OS) having a limited field of view that does not allow the images of the large width. To increase the effectiveness of shooting in modern space systems (SS) Earth observation provides the opportunity after shooting a segment of the Earth's surface to redirect the OS to another area and spend it shooting. With sufficient speed shift OS it is possible to survey two or more adjacent parcels, which is almost equivalent to the corresponding increase in the width of the field of view of the removing apparatus. In this connection there is the task of restoring the OS, which is solved by the use of appropriate hardware and software control the angular movement of the removing apparatus. When creating the SS there is also the need to solve the following tasks: calculation of the program angular motion in a given length of the removable sections and a predetermined number of adjacent strips to be shot, with the purpose of definition of system requirements, spacecraft (SC) control and calculation under given characteristics of the system orientation of the SC possible number of the maximum length and remove adjacent portions of the surface of the Earth. To solve these tasks the mathematical model software of angular motion of the SC. Given the necessary initial data, mathematical model and method of calculation of kinematic parameters of a software angular motion of a SC in the mode of area highway shooting adjacent sections of the Earth's surface located at a predetermined distance from a trace route SC; examples and results of numerical calculations of the programmes angular motion by moving the instrument in remote sensing.

scholarly journals ROS-based Toolbox for Motor Parameter Identification of Robotic Manipulators

2021 ◽  
Author(s):  
Ulici Ioana-Anamaria ◽  
Codrean Alexandru ◽  
Tassos Natsakis
Keyword(s):  
Mathematical Model ◽  
Parameter Identification ◽  
Robotic Manipulators ◽  
Velocity Control ◽  
Precise Knowledge ◽  
Depth Study ◽  
Motor Parameter ◽  
The Mathematical Model ◽  
Stable Control ◽  
Individual Motor

For many applications, a precise knowledge of the model of the robot is necessary for accurate and stable control. However, it is not always feasible or desirable to perform from scratch an in-depth study of the robot model, especially if it is not an element of concern for the respective application. In this article we present a methodology for identifying motor parameters of a robotic manipulator. We discuss the mathematical model and introduce an extensible toolbox with velocity-control based methodology for a fast identification of individual motor parameters. The results show that we can identify individual parameters even for joints that are commercialised as of the same type.

scholarly journals Machine Directional Register System Modeling for Shaft-Less Drive Gravure Printing Machines

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shanhui Liu ◽  
Xuesong Mei ◽  
Jian Li ◽  
Li'e Ma
Keyword(s):  
Mathematical Model ◽  
System Modeling ◽  
System Model ◽  
Experimental Setup ◽  
Gravure Printing ◽  
Servo Motor ◽  
Definition Of ◽  
The Mathematical Model ◽  
Register Error ◽  
Control Accuracy

In the latest type of gravure printing machines referred to as the shaft-less drive system, each gravure printing roller is driven by an individual servo motor, and all motors are electrically synchronized. The register error is regulated by a speed difference between the adjacent printing rollers. In order to improve the control accuracy of register system, an accurate mathematical model of the register system should be investigated for the latest machines. Therefore, the mathematical model of the machine directional register (MDR) system is studied for the multicolor gravure printing machines in this paper. According to the definition of the MDR error, the model is derived, and then it is validated by the numerical simulation and experiments carried out in the experimental setup of the four-color gravure printing machines. The results show that the established MDR system model is accurate and reliable.

The Estimation of the Thermal Properties of Refractory Materials According to the Temperatures Acceleration Curve at the Blast Furnace Blowing-In

2015 ◽  
Vol 1095 ◽  
pp. 476-482 ◽  
Author(s):  
A.N. Dmitriev ◽  
Maxim O. Zolotykh ◽  
Yury A. Chesnokov ◽  
Oleg Yu. Ivanov ◽  
Galina Yu. Vitkina
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Blast Furnace ◽  
Thermal Properties ◽  
Thermal Conductivity Coefficient ◽  
Refractory Materials ◽  
Different Types ◽  
Definition Of ◽  
The Mathematical Model

In a laying of a hearth it is usually used to ten different types of the flameproof materials. The characteristics of materials declared by the manufacturer can differ from the actual. For creation of the mathematical model [1, 2] temperatures distributions in a laying of the concrete furnace it is necessary to know thermal conductivity of materials of the specific parties used at construction of the furnace. Definition of the thermal conductivity coefficient allows adapt mathematical model for specific conditions of use. The technique of determination of thermal properties of refractory materials on the temperatures acceleration curve at blowing-in of the blast furnace is described.

Improving the Performance of a Two Way Flow Control Valve, Using a 3D CFD Modeling

2014 ◽  
Author(s):  
Emma Frosina ◽  
Adolfo Senatore ◽  
Dario Buono ◽  
Michele Pavanetto ◽  
Micaela Olivetti ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Flow Control ◽  
Fluid Dynamic ◽  
Control Valve ◽  
Operating Conditions ◽  
Cfd Modeling ◽  
Flow Control Valve ◽  
Development Costs ◽  
Definition Of ◽  
The Mathematical Model

The paper introduces a methodology aimed to optimize the performance of hydraulic components; in particular the design of a new two way flow control valve studying the valve internal fluid-dynamic behavior will be introduced. The methodology is based on the definition of a CFD tridimensional fluid-dynamic model. In fact, the model can help engineers to develop the best geometry, to optimize the valve performance, reducing the prototyping requirement and finally the time-to-market and, consequently, the development costs. At first, the original spool internal geometry has been evaluated and studied to tune the mathematical model and to validate it comparing its results with the data obtained through an experimental campaign. Then, the same approach has been applied to investigate several different internal spool geometries to define the best one in all operating conditions. A limited number of solutions have been prototyped and tested to verify the mathematical model predictions, in order to find the best configuration whose performances are consistent with the assigned objective for the component.

A Mathematical-Numerical Model to Calculate Load Distribution, Contact Stiffness and Transmission Error in Involute Spur Gears

2009 ◽  
Author(s):  
Mehdi Mohammadpour ◽  
Iraj Mirzaee ◽  
Shahram Khalilarya
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Load Distribution ◽  
Contact Stiffness ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Meshing Stiffness ◽  
Definition Of ◽  
The Mathematical Model

This paper firstly presents a mathematical model in order to calculate the load distribution, single contact stiffness and meshing stiffness as well as transmission error. in this way, there is no need to use finite element like methods and also the calculation time is dramatically reduced. Presented method is based on definition of a statically undetermined problem that is formulated using energy method. Some assumptions considered to convert this problem to a statically determined problem and get the mathematical models. Then a numerical method is employed in order to solve the mathematical model using a double iteration flowchart to close the problem. This model is flexible to adapt for any modification in spur gear profile geometry. Finally, this model is verified using previous works that have been utilized finite element and experimental model.

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