The density of a substance (ρ) is defined as its mass per unit volume and is therefore the reciprocal of its specific volume. If the temperature of the fluid is lower than the saturation temperature for the existing pressure, it is called a subcooled fluid (implying the temperature is lower than the saturation temperature for the given pressure) or a compressed fluid (implying the pressure is lower than the saturation temperature for the existing pressure). greater than the saturation pressure for the given temperature).
Numerical example
Dividing by M, the molecular weight, gives the equation of state on a unit mass basis. The above equation of state is called the ideal gas equation of state.
Work and Heat
At very low density, all gases and vapors approximate ideal-gas behavior, with the P-v-T relationship given by the ideal-gas equation of state. Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature to another system (or the environment) at a lower temperature due to the temperature difference between the two systems.
The First Law of Thermodynamics
The first law of thermodynamics
Let us consider each of the terms of the first law as written for the system and transform each term into an equivalent form applicable to the control volume (Fig. 5.5). Schematic for a first law analysis of a control volume, showing heat and work as well as mass crossing the control surface.
The Second and Third Laws of Thermodynamics
The meaning of Clausius' inequality can be illustrated by considering the simple cycle of a steam power plant shown in Figure. The cycle consisting of the reversible process A and the irreversible process C is an irreversible cycle.
The Steam Cycle
Elbow (Bend)
Diffuser
Orifice
Header-To-Feeder Nozzles
However, there are some peculiarities that make most of the pumps in the CANDU plant a little different. First, most CANDU pumps are of the nuclear type: the pumps are manufactured according to nuclear regulations and standards. Heat Transport pumps operate at high temperature and pressure, where sealing the pump shaft is a real challenge.
The actual pump operating head and flow rate are determined by the intersection of the two curves. QL = flow from high pressure side to low pressure side of pump ev = Q.
Heat Transport System of Full Pressure, Pressurizer Connected This configuration provides the greatest margin against system depressurization
Since the critical value of σchas was found to depend on both the normal specific velocity and the suction specific velocity, the relation. In order to obtain σc, the critical value of NPSH must be used in the evaluation of S. During this period it is essential to ensure sufficient net positive suction head (NPSH) to prevent pump cavitation.
Heat Transport System at Reduced Pressure, Pressurizer Connected The primary heat transport system pumps may be operated with the pressurizer
Heat Transport System at Full Pressure, Pressurizer Isolated The pumps can be operated with “solid mode” pressure control if necessary
Several events can lead to reduced HTS pressure (and therefore low NPSH) during operation: these include loss of D2O feed pumps and false opening of the liquid relief valves. 3] Bean, H.S., “Fluid Gauges: Their Theory and Application”, the American Society of Mechanical Engineers, 6th edition, 1971. 6] Idelchik, I.E., “Handbook of Hydraulic Resistance: Coefficients of Local Resistance and of Friction”, Israel Program for Scientific Translation Ltd., AEC-tr-6630, 1966.
Introduction
Two-Phase Flow Theory and Definitions
It is often useful to use the part of the total mass flow that consists of vapor or liquid. It is defined as the ratio between the average velocity of the vapor Ug and that of the liquid Uf. So if the total mass flow of the mixture is W, the vapor flow rate is xW and the liquid flow rate is (1-x)W, where x is the quality in the section of interest.
The void fraction in the section under consideration is the ratio of the vapor phase volume to the total volume within the section. For the small portion of the channel considered, this is the same as the ratio of the cross-sectional area of the vapor Ag to the total cross-sectional area of the channel.
Flow Regimes
Groeneveld and Leung (16) have recently recommended the flow regime map of Taitel and Dukler for use with components of the CANDU heat transport system, particularly the fuel array, in horizontal flow. developed a sound mechanical model for predicting the transition between flow regimes inside diabatic and adiabatic horizontal pipes. The Taitel-Dukler flow regime map shown in Figure 12 is valid for very wide ranges of pressure, quality, mass flow, and pipe diameter. Hewitt and Roberts (1) have developed a flow regime map shown in Figure 13 from observations on low-pressure water-air-water and high-pressure steam-water flows in small-diameter vertical pipes.
Groeneveld and Leung (16) tentatively recommended the flow regime map of Taitel and Dukler for use with CANDU vertical flow heat transfer system components. At different pressures and pipe diameters, the flow regime map can vary to a certain extent.
Basic Models
The homogeneous model considers the two-phase flow as a homogenized mixture (pseudo-fluid) possessing average fluid properties. It ignores any effect flow patterns may have on the two-phase flow and ignores interaction between the phases. The effect of mass velocity on the two-phase friction multiplier has been widely reported.
Martinelli-Nelson developed one of the first models for the two-phase pressure drop, based on the basic assumptions of the separated flow model. However, it has the same shortcoming as that of Martinelli-Nelson, in that it does not correctly represent the effect of the mass flow on the two-phase friction multiplier.
Pressure Gradients and Pressure Drops
The entrained flow approach therefore satisfactorily accounts for the effect of mass velocity on the void fraction, as seen in the model and the separated flow equation, and the empirical Comay expression used to provide the required relationship between the void fraction and the independent flow pattern. The entrainment model is only valuable if the entrainment rate is significant compared to the total volumetric flow rate (u– . gi> 0.05 j). The following analysis assumes one-dimensional flow, a variation of the adiabatic flow across the region so that x is constant, and pressure changes that are small compared to the total pressure so that ρfan and ρg do not change significantly.
For two-phase flow, the calculation of the total pressure change in a sudden expansion can be calculated as follows. We can see that for the same mass flow and areas, since x is less than α, the pressure rise in two-phase flow is greater than in one-phase flow.
Void Fraction Correlations
Under all conditions, the error on the predicted mean density decreases with increasing mass velocity. The predictive power of the von Glahn correlation becomes worse as the phase density ratio decreases and with increased velocity. Mass velocity has little effect on the prediction of this correlation except for large phase density ratios, when an increase in mass velocity improves the predicted value.
It can be noted that the homogeneous model predicts the highest void for a given grade. The careful selection of the solution scheme together with the use of appropriate correlations is of utmost importance in solving two-phase phenomena.
Notation
Freidel, L., "Average Void Fraction and Frictional Pressure Drop: Comparison of Some Correlations with Experimental Data", Paper A7, European Meeting of the Two-Phase Flow Group, Grenoble, 1977. In this lesson we will briefly describe situations in which - phase current occurs and to assess the consequences on the overall behavior of the reactor. Critical flows occur when the velocity of the two-phase mixture is controlled by its upper limit, i.e.
Under poor conditions, a two-phase mixture at the pump inlet can cause severe vibrations that can deteriorate the pump's hydraulics or break a pipe. In many scenarios, the pressure and supply control of the HT cannot eliminate void formation and the HT operates under two-phase flow conditions.
Critical Flows
Critical flows occur when the velocity of the two-phase mixture is controlled by its upper limit, that is, the speed of sound of the mixture. In two-phase flow, two similar expressions can be written for coexisting liquid and vapor phases with the above mass flow rates as: pTP) and (∆pTP) account for the two-phase pressure drops due to liquid and vapor, respectively. Using the lumped model it can be shown that the specific volume of the mixture is related to vf and vgby.
The liquid partially turns into vapor, as the pressure drops along the channel, the specific volume of the mixture ν reaches its maximum value at the outlet. The critical pressure ratio was found to vary with L/D for shorter channels but appeared to be independent of initial pressure in all cases.
Pumps Operation
The Darlington two-phase pump tests demonstrated the ability of the pump sets to withstand operation under rough two-phase flow conditions without damage or loss of function. The toughness of the other HT pump sets has also been proven in the previous Bruce two-phase pump tests as well as the Pickering two-phase pump tests. However, severe vibration of the test loop pipes, especially at low frequencies, was encountered during two-phase pump tests.
Darlington two-phase pump tests show that large-amplitude pressure pulses occur mainly at low frequencies. The Darlington biphasic pump test was not designed to measure biphasic wave velocity.
Natural Circulation
If the pumps are not running, single-phase thermosyphoning is not expected to occur in the intact loop. Otherwise, temporary reverse duct flow and collapse of the duct space, end fitting and part of the exhaust supply may occur. Oscillating channel flow can be expected under certain conditions after blowing off steam in the standing start phenomenon.
Unstable or oscillating water column in the full reflux condensation mode occurred for a certain range of steam flow. As the steam flow was reduced, the longest tube developed a steady water column in the vicinity of the pressure drop-flow characteristic curve where the tube itself would have exhibited fill and dump mode.
An essential, and often the most uncertain, part of any heat exchanger analysis is the determination of the overall heat transfer coefficient. Its value depends on the operating temperature, fluid velocity and service life of the heat exchanger. The overall heat transfer coefficient can be determined from knowledge of the hot and cold fluid convection coefficients and fouling factors and shape.
It is now logical to define the effectiveness, ε as the ratio of the actual heat transfer rate for a heat exchanger to the maximum possible heat transfer rate. To define a specific form of the effectiveness-NTU relation, Equation 5.6, consider a parallel-flow heat exchanger for which Cmin= Ch. In heat exchanger design calculations, it is more convenient to work with E-NTU relationships of the form.
From knowledge of the type and size of the heat exchanger and the fluid flow rate, the NTU and (Cmin/Cmax) values can be calculated and ε can then be determined from the corresponding graph (or equation).
Natural Convection Region
The first is called saturated (or bulk) boiling because the liquid is held at saturation temperature. Main boiling regimes in swimming pools Boiling of water at atmospheric pressure and saturation temperature Ts, from an electrically heated platinum wire.
