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Transients
Published in William Bolton, Engineering Science, 2020
The product RC has the unit of time and so we define time constant as τ = RC. The significance of the time constant is that the bigger the time constant the smaller the initial rate of discharging of the capacitor and the longer it will take to completely discharge.ExampleA capacitor is charged to a voltage of 12 V. It is then allowed to discharge through a resistance of 2 kΩ. What will be (a) the initial circuit current, (b) the circuit current when the voltage across the capacitor has dropped to 2 V? Initially the voltage across the capacitor is 12 V and so the voltage across the resistor is –12 V. The initial current is thus –12/2000 = –0.006 A = –6 mA.When the voltage across the capacitor has dropped to 2 V the voltage across the resistor will be –2 V and so the circuit current is –2/2000 = –0.001 A = –1 mA.
System Response
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
where the time constant provides a measure of how quickly the response reaches a steady state. Linear, second-order systems are modeled as x¨+2ζωnx˙+ωn2x=f(t), x(0)=x0, x˙(0)=x˙0
Analysis of Power Cables Conducting Fast Transient Loads
Published in Robert E. Henry, Models for Design, 2017
If the bundle is installed in a galvanized conduit in free air, (7.1) becomes more complicated. Now, there is a resistance between the bundle and the conduit, and a second resistance between the conduit and free air. Also, the conduit’s thermal capacitance affects the heating time. First, because of proximity effect, the resistance has increased, increasing the heating time. Second, the conduit doesn’t begin to heat up in the beginning. It doesn’t have heat generated in it like the bundle, so it begins to heat up after the bundle starts to transfer heat to it, which happens only as the bundle heats up. And the conduit’s thermal capacitance adds to that of the system. With both resistance and system capacitance increased, the time constant is increased. (Here again, the small radial temperature difference through the conduit wall is neglected.)
Development of a detection system for gas-phase aromatics and other molecules ionizable by soft X-rays demonstrated using methyl salicylate
Published in Aerosol Science and Technology, 2023
Dong-Bin Kwak, Seong Chan Kim, George W. Mulholland, Miles C. Owen, Changhyuk Kim, Handol Lee, David Y.H Pui
To determine how quickly the total number or volume concentration reaches the steady state through the soft X-ray detection method, we compared the sensor time constant (τ) and sensor response time (5τ). The time constant is usually defined as the rise time to reach 63.2%, i.e., 1–1/e, of its steady-state response. Because we have already obtained the calibration curve for ppbv-level MeS vapor concentrations at stable mode (Equations (6) and (7)), the value of steady-state response is assumed to be the same value of the correlated results. Sensor time constant and sensor response time of total number and volume concentration measurements are presented in Table 3. Sensor time constant and sensor response time decrease with the increase of MeS vapor concentrations. Furthermore, both the sensor time constant and sensor response time of total number concentration is two times shorter than those of total volume concentration. This is due to the fact that the particle formation of MeSNPs has a series of stage changes during the soft X-ray irradiation as described in Figure 3.
Parametric study on dynamic behaviours of basic Organic Rankine Cycle recovering waste heat with thermal power fluctuations
Published in International Journal of Green Energy, 2021
Lei Wang, Xiaoli Yu, Jie Wu, Zhi Li, Yan Huang, Rui Huang
The evaporating pressure and superheat degree of working fluid are the most important parameters during the operating process of ORC system. The evaporating pressure determines the average temperature of working fluid absorbing heat from the heat source while the superheat degree is an important indicator for system safety. Figure 5 shows the response curves of evaporating pressure and superheat degree under different step-change ratio (SCR) of heat source. It can be found that in Figure 5a, when the SCR of heat source is different, the response curves of the evaporating pressure of working fluid shows the same trend, all of which increases rapidly when the step occurs, and enters a slow equilibrium process after reaching the peak. The difference is the extreme value of evaporating pressure increases with the rise of SCR. The time constant is usually used to evaluate the response speed of parameters in the dynamic systems. When SCR = 3%, 6% and 10%, the time constants of evaporating pressure are 5.4 s, 5.1 s and 4.8 s, respectively. It can be seen that there is a slight difference in the time constants, which is mainly because the Reynolds number increases when the heat source temperature suddenly increases. The larger Reynolds number leads to an increase in the convective heat transfer coefficient and a slightly faster response speed of the evaporating pressure of working fluid.
Effects of controls and floor construction of radiant floor heating systems for residential application with high variability of solar gains
Published in Science and Technology for the Built Environment, 2020
Sébastien A. Brideau, Ian Beausoleil-Morrison, Michaël Kummert
Some of the earliest experimental work on radiant panel heating was performed by Algren and Ciscel (1949). They measured the time constant of a radiant slab on grade (without slab insulation) with the use of a small experimental structure. Time constant is defined here as the time it takes for a system given a step input to reach approximately 63.2% of its steady-state value. They found a time constant of almost 4 h for the floor surface temperature, and about 5 h for the air temperature. These long-time constants show that thermal mass in embedded-tube systems can be significant. Due to these potentially long response times, appropriate controls of radiant floors are crucial, especially when the heating or cooling load is highly variable. For residential applications, a large amount of south-facing glazing could result in high variability in solar gains, especially during the shoulder seasons. Adequate controls are important in that case, in order to prevent overheating.