A mathematical model is developed to estimate the pressure response of an insulated electric air compressor. A pressure switch is modeled as a comparator and the electric motor as an amplifier. It is assumed that the compressed air is a perfect gas when applying the isentropic process. In addition, the effect of a step, ramp and sinusoidal functions of disturbance signals on the air pressure has been studied. A good agreement was obtained when comparing the predicted results with the measured values obtained from the experimental test that was done using a (1.32 kW, 23 litter and 8 bar) electric reciprocating air compressor. In addition, the same behavior of the predicted results was obtained when compared with results of a previously published article. It was found that the time constant of this control system is directly proportional with the value of the spring constant that is inserted inside the pressure switch and with the volume of air storage vessel, and it is inversely proportional with the gain of the amplifier and with the effective cross -sectional area of the pressure switch diaphragm and it is independent of the value of operating pressure set point. In addition, when the value of disturbance signal is positive, it will increase the output pressure response and when it is negative, it will decrease it.
In this paper, the performance of a six blades axial type wind turbine has been studied experimentally to estimate the wind power, the electrical generated power and-the modified power-coefficient of the wind-turbine. This study was conducted under different operating conditions assuming steady-state, incompressible and isothermal air flow through the wind-turbine. The range of operating condition was (2 to 5.6 m/s wind speed), (10% to 100% of electrical load that is applied on the terminals of the electrical generator) and (10° to 80° blades angle of the wind-turbine). A good agreement was obtained when comparing the results of the present work with those of a previously published article. The predicted results showed that increasing the wind speed and-the blades angle of the wind-turbine will increase the generated power from the wind-turbine. The maximum-value of the modified power-coefficient was (0.57) at a wind velocity value of (5.6 m/s) and at a blades angle value of (80°). It is found that it's not recommended to operate the wind-turbine at (80°) blades angle associated with a wind speed range that is above (3.8 m/s) due to a high level of wind-turbine vibration.
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal conductivity. It is found that the characteristics of the thermal insulation material and the pressure value between its particles have a major effect on the rate of heat transfer and temperature profile.
Cold startup of boiler is the process of boiler operation with water at ambient temperature and pressure with all intake and discharge valves are fully closed to permit fast development of pressure. A mathematical model is developed to estimate the pressure response during cold startup of a perfectly insulated steam generator unit. A commercial type pressure switch is used in this unit to control and maintain the desired set point of the steam operating pressure. This mathematical model assume that the thermal properties of t he supplied liquid water are temperature dependent. It is based on a novel Pressure Marching Technique that is coded using a FORTRAN language computer program. The maximum percentage error of (8.24 %) was obtained when comparing the predicted results of the mathematical model with the measured values obtained from the experimental test that was done using a (2 kW) electric steam generator unit with a volume of (30 litter) and maximum operating pressure of (8 bar). In addition, the same behavior of the predicted results was obtained when compared with results of a previously published article. It was found that the time constant of the pressure control system is directly proportional with its operating pressure set point and with the volume of the steam generator and its void fracti on. A (50%) increase in the pressure set point will increase the time constant by (66.16%). Increasing the boiler volume by (166.667%) will increase the time constant by (166.677%) and increasing the boiler void fraction by (150%) will increase the time constant by (23.634%). The time constant is inversely proportional with the heating power of the steam generator. A (100%) increase in the heating power will decrease the time constant by (50%). The time constant is independent of the initial water temperature. Also, it was found that the time delay to start water evaporation is directly proportional with the volume of the steam generator. A (166.667%) increase in boiler volume will increase the time delay by (166.65%). The time delay is inversely proportional with the initial water temperature and with the heating power and void fraction of the steam generator. A (38.889%) increase in the initial water temperature will decrease the time delay by (8.882%). Increasing the heating power by (100%) will decrease the time delay by (50%) and increasing the boiler voi d fraction by (150%) will decrease the time delay by (16.665%). The time delay is independent on the operating pressure set point.
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