On the Dynamics of a Rotary Compressor: Part 1 — Mathematical Modeling

1993 ◽  
Author(s):  
Sisir K. Padhy
Keyword(s):  
Experimental Validation ◽  
Sensitivity Study ◽  
Solution Procedure ◽  
Rotary Compressor ◽  
Kutta Method ◽  
Air Conditioners ◽  
Runge Kutta Method ◽  
Bearing Dynamics ◽  
The Mathematical Model ◽  
Theoretical Results

Abstract The rotary compressor has been used in room air conditioners as well as in refrigerators for many years. Although a number of published papers has been reported on rotary compressor, in the area of dynamics only a few are found. In addition only one paper describes experimental validation with some agreement with theoretical results. Again the effect of various operating pressures and temperatures, rotational speed of shaft etc. is not fully covered in any published literature. The present paper analyzes the rotary compressor dynamics in detail. The mathematical model, the solution procedure using Runge-Kutta method, and the bearing dynamics are described. The second part of this papers describes the experimental validation and sensitivity study using different variables that affect the compressor dynamics.

Lubrication Analysis of a Rolling Piston Rotary Compressor: Part 2: Experimental Validation and Results

1994 ◽  
Vol 208 (2) ◽  
pp. 95-104
Author(s):  
S K Padhy
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Validation ◽  
Sensitivity Study ◽  
Rotary Compressor ◽  
Oil Flow ◽  
Different Dimensions ◽  
Rolling Piston ◽  
The Mathematical Model ◽  
Good Agreement

In this paper the experiments conducted for the measurement of oil flow in the rotary compressor are described. The experimental data are compared against the theoretical prediction from the mathematical model developed (1) and a good agreement is found. In addition, experimental data from previously published literature are also used to verify the mathematical model. A sensitivity study is carried out to predict the behaviour of the rotary compressor for the oil flow at different conditions and with different dimensions.

On the Dynamics of a Rotary Compressor: Part 2 — Experimental Validation and Sensitivity Analysis

1993 ◽  
Author(s):  
Sisir K. Padhy
Keyword(s):  
Experimental Validation ◽  
Sensitivity Study ◽  
Rotary Compressor ◽  
Dynamics Model ◽  
The Coefficient Of Friction ◽  
The Moment ◽  
Discharge Pressure ◽  
Roller Radius ◽  
Theoretical Results ◽  
Good Agreement

Abstract This paper describes the experimental validation of the rotary compressor dynamics model [1]. Roller velocity is measured using video technology and a very good agreement is found with the theoretical results. A sensitivity study using different variables that affect the compressor dynamics is also carried out. It is found that the coefficient of friction at the vane and roller plays an important role in roller velocity. The dynamics of roller is influenced by the clearances, the roller radius, the vane radius, eccentricity of the shaft, the frictional behavior between the roller ends and the bearing plates, the discharge pressure of the compressor as well as the moment of inertia of roller.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

Dynamic Analysis of a Rotary Compressor

1994 ◽  
Vol 116 (2) ◽  
pp. 639-646 ◽  
Author(s):  
S. K. Padhy
Keyword(s):  
Dynamic Analysis ◽  
Experimental Validation ◽  
Complete Analysis ◽  
Rotary Compressor ◽  
Air Conditioners

The rotary compressor is used in room air conditioners and refrigerators. Although a number of papers have been published on rotary compressors, in the area of dynamics only a few are found, and they lack a complete analysis. In this paper the rotary compressor dynamics is modeled in detail and experimental validation is presented. The effects of some variables on the dynamics are also described.

scholarly journals A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Legendre Polynomials ◽  
Algebraic System ◽  
The Novel ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Novel Coronavirus ◽  
The Mathematical Model

Abstract Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.

Applications of Numerical Simulation of Solar Cooker Type Box With Multi-Step Inner Reflector

Solar Energy ◽  
2003 ◽  
Author(s):  
H. Terre´s-Pen˜a ◽  
P. Quinto-Diez
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Thermal Conversion ◽  
Numerical Results ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Energetic Analysis ◽  
The Mathematical Model ◽  
Solar Rays

It is shown a mathematical model of a solar box cooker with multi-step inner reflector and the numerical results for two applications has been analyzed. These applications are 1. Numerical simulation of operation of solar box cooker with multi-step inner reflector in Tanta, Egypt and 2. Numerical simulation of solar box cooker with multi-step inner reflector for 10 hours of operation. In the case 1, is analyzed a solar box cooker constructed and evaluated in Tanta, Egypt [1]. The experimental results that was obtained are compared with the numerical results that was obtained for the mathematical model. The case 2, is an evaluation of numerical results that was obtained for the operation of 10 hours for solar box cooker constructed in the Laboratorio de Ingenieri´a Te´rmica e Hidra´ulica Aplicada (LABINTHAP) in Me´xico City. [4] The solar box cooker is integrated by a covert that was made with double glass, this is use with two purposes, reduce the loss heat convection with outer and to generated the greenhouse effect with inner of cooker. In the inner of cooker there are a mirrors arrangement in inclined position (inner reflectors) placed in angles of 30°, 45° and 75°, these helped to reflex the solar rays in direction to the cook recipient. The recipient also received the solar rays in the upper part (lid). The mathematical model that was obtained from energetic analysis, is formed for five differential equations system no linear and the fourth Runge-Kutta method is used to resolve it. The numerical solution of the equations system is obtained with a computational software in C++. This work is a contribution to the application of numerical methods and computational for development of the solar energy used in thermal conversion equipments. The use of these techniques to solve the mathematical model is important to contribute in the evaluation and design of solar box cookers with multi-step inner reflector.

scholarly journals Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor

2020 ◽  
Vol 16 (3) ◽  
pp. 311
Author(s):  
Susi Agustianingsih ◽  
Rina Reorita ◽  
Renny Renny
Keyword(s):  
Optimal Control ◽  
Minimum Cost ◽  
Sir Model ◽  
Human Populations ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Susceptible Group ◽  
Minimum Costs

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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