Pseudocritical Rapid Energy Dissipation Analysis of Base-Load Electrical Demand Reduction on Nuclear Steam Supply System

Effect of pseudocritical rapid energy dissipation (PRED) from Pressurizer in nuclear steam supply system of Pressurized Water Reactor, where a single event as common cause failure, of considerable reduction of base-load electricity demand causes the temperature of the reactor coolant system (RCS) to increase, and corresponding pressure increases in pressurizer and steam gene-rators above set-points. The study employed the uses of MATLAB/Simulink library tools, to experimentally modelled pressure control as PRED, where the momentum of transport of kinematic viscosity fraction above pseudocritical point dissipated as excess energy, to maintain the safety of the Pressurizer and RCS and keep the water from boiling. The result demonstrated the significance of pressure vector and Prandlt number as heat transfer coefficients that provided detailed activities in 2-D contour and 3-D graphics of specific internal energy and other parameterization of fluid in the pressurizer.


Introduction
A considerable reduction of base-load electricity demand generated by nuclear into action, to compensate for the demand reduction of the base-load, since the amount of heat released from the nuclear chain reaction must be proportional to the amount of heat taking away for generation of electrical energy.
The Pressurizer in NPP maintains the pressure of reactor coolant system (RCS), preserves the threshold parameters through the steady state operations, and regulates the pressure during the transient process of the Reactor. The Pressurizer pressure control system (PPCS) forms part of the IPCS of the nuclear steam supply system (NSSS) of the Pressurized Water Reactor (PWR) [1]. It offers three main functions: 1) to protect the reactor from trip, 2) to protect the reactor from changes in reactivity and 3) to protect the activation of pressure relief valve [2]. The introduction of Pseudocritical rapid energy dissipation (PRED) pressure control, seeks to maintain the safety of the Pressurizer and the RCS.
The Pressurizer operates on three main functions that take place concurrently; 1) the dynamics of temperature variation, 2) the rise and fall of pressure values and 3) the variation of water/steam levels. The rod control system regulates the in-core rod position, the power and the power distribution. The input of the pressurizer pressure is the deviation from a set-point, while the output drives proportional spray controller, to actuate heaters and power relief valve within fixed operating points. The other system controllers provide ex-core integrated plant control by synchronization of fluid flow and control signal activities.
Most of the reactors in operation today are about 40 -50 years older. The assessment of existing Instrumentation and control (I & C) systems, and its modernization needs in terms of obsolete systems and the impact of failure rate, the NSSS-I & C appeared to be of high priority for modernization [3], the NSSS has reach its operational limits and condition (OLC). The nuclear I & C system serves as nerve center of NPP [4], to coordinate activities of thousands of components and equipment [5], that allow the plant operators to monitor the safe operation of NPP. The advances made by the evolution of digital technology have improved operations of automation and control systems, and yet the nuclear industry remains conservative with the use of analogue systems, hence the need for the proposed modern PRED I & C system. The level control of pressurizer represent balance of injection of water inflow into the reactor coolant system and water letdown into the chemical and volume control system (CVCS) [6]. The two-phase simulation model of compressibility involving the thermodynamic equilibrium revealed sub-critical evaporation with large variation of liquid compressibility factor and density [7].
A two-phase turbulence model where interfacial turbulence accounts for pseudoturbulence in liquid bubble-induced mixing [8]. The hyperbolic transition model of two-phase fast depressurization is highlighted on six equations of two-phase model, for accurate tabulation of equation of state (EoS) for thermodynamic equilibrium recovery, for depressurization of water-steam system [9]. Which referred to PWR with water as coolant with highly non-linear behavior of two-phase, model provided thermodynamic separation between water and steam independent of each other.
Modern instrumentation and control system was used to examine the effect heat transfer of fluid properties, MATLAB/Simulink library tools was used to: 1) design a model of pseudocritical rapid energy dissipation I & C system, where thermophysical properties of the two-phase fluid characteristics with introduction of three thermodynamic property sensors. Analyze pseudocritical saturation line, the effect of specific internal energy, pressure vector and other parameterization of fluid content of Pressurizer. Evaluated the effect of heat transfer coefficient (Prandtl number) and momentum of the transport of the kinematic viscosity, as pseudocritical rapid energy dissipation from pressurizer.

Theories
The pressurizer relief line connect the pressurizer safety and relief valve to the pressurizer relief tank with the input coming from refueling water and storage tank.
The energy conservation in the pressurizer sometimes referred to in the study as pipe or open-channel can be expressed as [10].

( )
where, M is the fluid mass inside the pressurizer, A m  and B m  are the mass flow rate into the pipe through port A and B, while u I is the specific internal energy of the fluid inside the pressurizer, ϕ A is the energy flow rate into the pressurizer through port A. While ϕ B is the energy flow rate into the pressurizer through port B, and Q H is the heat flow rate into the pressurizer through the pressurizer wall represented by port subscript H is the thermal conductive insulator.
The energy conservation in the pressurizer is given by the energy balance equation as expressed in "Equation (2)" [11]: where: P A is the pressure at port A, S is the cross-sectional area of the pressurizer, V A is the specific volume of the fluid at port A, F visc,A is the viscous friction force is port A, I A is the fluid inertia at port A which is further expressed as in where L is the length of the pressurizer in the half pipe adjacent to port B.
Similarly, for port B, the energy conservation in the pressurizer can be ex- The heat flow rate inside the walls of the pressurizer and the internal fluid volume was modelled as ( ) where, h coeff is the average heat transfer coefficient, S surf is the surface area, T H is the pressurizer wall temperature and T I is the temperature of the fluid in the pressurizer.
The heat transfer coefficient rely on the phase of the fluid. With subcooled liquid and superheated vapour conditions, [12] the coefficient was modelled as: The asterisk represent a value of the phase under consideration (liquid or vapour). While N u is the average Nusselt number in the pipe, k I is the average thermal conductivity in the pressurizer, and D h is the hydraulic diameter. , The subscript M refers to specific value of two-phase mixture and SL is the saturated liquid.
The Nusselt number have effect on convective and conductive heat transfer coefficient, for laminar flow assumed as constant, while the Reynolds number acts on the inertia and viscous forces applied when the value is smaller than the laminar flow [13].
The Gnielinski correlation [14], expressed in "Equation ( where, f is the friction factor of the pressurizer, Re is the Reynolds number and Pr I is the Prandtl number.
The friction factor was evaluated as: where, ε r is the roughness of the pressurizer inner walls. The Reynolds number was expressed as: where the subscript Avg represent an average value between the ports, S is the cross-sectional area, v I is the specific volume and v I is the kinematic viscosity.
For the two-phase mixture, the Nusselt number for turbulent flow correlation expressed by Cavallini and Zecchin [15] was utilized as in "Equation (11)".
where subscript SL represent the saturated liquid and SV saturated vapor, x I is the vapour quality and v is the specific volume.
The Reynolds number of the saturated liquid is expressed as The conservation of mass balance in the pressurizer was modelled according to Equation (13) where, ρ is the fluid density, I p  is the pressure inside the pressurizer, V is the volume of fluid, A m  is the mass flow rate into the pipe through port A, B m  is the mass flow rate into the pipe through port B and ε M is the correction term density partial derivation of transition phase boundaries.
The density partial derivative using cubic polynomial function of subcooled blended with superheated vapour in two-phase mixture domain was accounted for according to "Equation (14)".
where the ε M is the cubic polynomial function introduces the numerical error has always a single inflection point. M is the fluid mass in the pressurizer and is expressed as where v I as the specific volume of the fluid in the pressurizer, τ is the phase change time constant.
In the laminar regime, the Reynolds number limit value in port A was specified by: and the half pipe adjacent to port B by: where, f shape is the pipe shape factor, L eff is the effective pipe length and D h is the hydraulic diameter of the pipein the turbulent regime, the Reynolds number limit for port A was specified according to "Equation (18)".
while in the half pipe adjacent to port B, it was specified as World Journal of Nuclear Science and Technology In Equations "(18)" and "(19)", f A is the Darcy friction factor for turbulent flow in the half pipe adjacent to port A and f B is the Darcy friction factor for turbulent flow in the half pipe adjacent to port B.
The Darcy friction factor [16] for the turbulent to port A was modelled by utilizing Haaland equation for ports A and B as expressed in Equations "(20)" and "(21)" respectively.
The half pipe adjacent to port B 2 1.11 The Darcy friction factor formulates the friction losses in the pressurizer sim-

Methods
The

Results
The thermodynamic analysis of fluid properties has been widely studied in 1D graphics. However, such representation does not provide detail illustration compared to the 2-D contour and the 3-D graphics. The thermodynamic properties sensor in PRED provided the plot of the magnitude and phase of the temperature, specific enthalpy, specific volume and specific entropy against time at reference zero of the fluid in one-dimensional (1D) display ( Figure 3).
The temperature values simulated for 10 seconds appeared to be constant, however, the range of temperature measured in degree Celsius ranges from 280 degree Celsius to 330 degree Celsius for specified time.
The spectrum analyzer plotted the noise power spectral density (Figure 4) that illustrated the peak as finder and distortion measurement of specified number of harmonics with the corresponding power measured in dBm/Hz. The  device under test (DUT) was the pressure and internal energy sensor where selected peak finder provided corresponding peak values and frequencies was determined. The Gaussian reference plot provided complementary cumulative distribution function (CCDF), where the average maximum power in decibels was measured.
The Spectrum Analyzer displayed the results of the fundamental frequencies of the total harmonics distortion (THD), where the frequency variation was considered as the sum of the internal energy of the water, the steam produced, the pressure and the volume of fluid within the pressurizer. The distortion measured by six harmonics at different frequencies with different power levels measured in decibels equals −400.38 dBm.

Effect of Pseudocritical Saturation
The flow dynamics of the two-phase have effect on the fluid inertia, the viscous friction losses and the convective heat transfer within the pressurizer. The volume of the fluid is assumed to be constant, where the pressure and temperature of the fluid affect the thermal conservation of the pressurizer.
The proposed PRED function coordinates activities of the heaters to compensate for the heat loss of the pressurizer to achieve equilibrium between steam and water. The subcooled liquid has normalized internal energy defined as: where, ū is the normalized internal energy of the fluid, u is the specific internal energy of the fluid, ū min is the minimum specific internal energy and L sat u is the specific internal energy of the liquid at saturation as shown in Equations "(22)" to "(24)".
The changes in the internal energy of the pressurizer depends on specific volume of the liquid, the temperature and the pressure, due to the energy balance of the chemical reaction ( Figure 5). The Pressure vector (0.001 and 100) coordinates the pressure values that provided the grid surface points. The pressure of the liquid is within the minimum values, why the pressure above the pseudocritical saturation approaches the maximum value.
At The specific volume (m 3 /kg) of the liquid (Table 1) represented the pressure vector and internal energy at specific grid point, where the boundary of saturation above or at the critical pressure is equal to vapour specific volume.
At the critical pressure the properties of the water gradually changes from liquid with small compressibility and high density to gaseous with low density and high compressibility. The physical properties of the liquid such as specific enthalpy, specific heat and density also changes with the changing temperatures, resulting in subcooled liquid and superheated steam as shown Equation (6) and Equations "(22)" and "(23)". World Journal of Nuclear Science and Technology  The superheated vapour of the normalized internal energy was expressed as, where, ū max is the maximum specific internal energy and V sat u is the specific internal energy of saturated vapour.
The specific entropy around the saturation boundary as per unit mass of liquid and vapour at saturation, where the liquid phase and vapour phase changes to mixture state in Figure 6.
Where the pressure vector at the upper part of the pressurizer registered 62.8 bar, the base remain at the minimum range with values of 0.001417 bar. While the specific internal energy ranges between 117 and 3933 kJ/kg/K and the specific entropy (kJ/kg/K) registered variable figures at different levels ( Table 2).
The normalized internal energy of the two-phase mixture was evaluated as defined below:          Table 4 and Table 5.
The resultant manipulations provided graphical illustrations of two dimension The kinematic viscosity at point a remains as low as 0.1276 mm 2 /s, that at point e is extremely as high at the value of 26,940 mm 2 /s ( Table 6). The kinematic viscosity of the fluid in the pressurizer is the inherent shear stress to flow, where the kinematic of liquid decreases with temperature and increases with temperature for gasses.
The thermal conductivity of specific liquid depends on the nature of that liquid, where thermal conductivity of water differs from other solid and liquids ( Figure 10). The thermal conductivity of water changes due to temperature changes that correspond to the changes of atomic vibration frequency of the liquid.
In addition, the analysis of the thermal conductivity of liquid in NSSS pressurizer, where the thermal conductivity (W/m/K) values is a fraction of the thermal properties with the values from points a to e ranging between 0.4381 to 0.7361 as shown in Table 7.   Figure 10. Effect of transport thermal conductivity. Figure 11. Pseudocritical rapid energy dissipation from Pressurizer.

Conclusions
The "Pseudocritical rapid energy dissipation (PRED) from Pressurizer in Nuclear steam supply system", the study affirmed the significance of heat transfer coefficient between conductive and convective heat transfer with the Nusselt number as the ratio of convective heat transfer and conductive heat transfer. The