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# atw 2018-03v6

## atw

atw Vol. 63 (2018) | Issue 3 ı March ENVIRONMENT AND SAFETY 160 in Figure 4. Following the Newtonian mechanics, the uniform gravitational field without air resistance can show the terminal velocity shows [The Physics Classroom, 2016], v(t)= -gt+ v o (1) So, one can find the pressure using Bernoulli’s principle [Clancy, 2006], (2) The coolant quantity is obtained by mass flow rate [Potter, 2007], ṁ = v(t)∙ρ (3) Therefore, using continuity equation [Potter, 2007], Q = ṁ ∙A = v(t) ∙ ρ ∙ A(4) where, v o is the initial velocity (m/s) v(t) is the vertical velocity to time t (m/s) g is the gravitational acceleration (9.8 m/s 2 ) z is the elevation of the point ρ is the density of the water (1,000 kg/m 3 ) ṁ is the mass flow rate (kg/m 2 s) Q is the mass rate (kg/s) A is the area (m 2 ) 2.3 Configuration of the drone The water tank is carried out by the drone where the mechanics of the flying robotics is exploited. There is the mechanical analysis of the drone for nuclear engineering applications in the below equations [Cho and Woo, 2016]. The mathematical forms of the movement of the flying is described as the flight dynamics in which three kinds of the parameters are done as roll, pitch, and yaw. These are angles of rotation in three dimensions about the vehicle’s center of mass [NASA, 2014]. The configurations are shown in Figure 5 [The Smithsonian’s National Air and Space Museum, 2014]. In the control of the four thrust forces from four rotors, there are three angles Ø, θ, ψ and the altitude z to make the six motions and then the control inputs are [Jeong and Jung, 2014], (5) where, k pø , k iø , k dø are the proportional-integral-derivative (PID) controller gains for the roll angle control, k pθ , k iθ , k dθ are PID controller gains for the pitch angle control, and k pψ , k iψ , k dψ are PID controller gains for the yaw angle control, respectively. Furthermore, the altitude control of PID controller is as follows [Jeong and Jung, 2014], (6) where, m is the mass, g is the gravitational acceleration, and then V z is, (7) where, k pz , k iz , k dz are PID controller gains for the altitude control and altitude data zs are obtained using a sonar sensor. 2.4 System dynamics (SD) Algorithm The SD was created by Dr. Jay Forrest in MIT around 1960s in which the scientific and technological matters as well as social and humanities are quantified as the mathematical SD modeling [SDS, 2014]. The interested event is described by the Boolean values and the designed modeling could show the event scenarios. There are several kinds of characteristics as the complexed non-linear manipulations in the problems. The event flows backward in the modeling, which is a particular merit in the SD modeling. The event quantification could be the stocking of the values of the event which is called as ‘Level’. In addition, the cause loop is seen by the event flows, which is like the flow chart in the computer programming. Each calculation is done as the time step in which the time interval is decided by the author. The software in this study is Vensim code system as the window version 6.3 [Ventana, 2016]. There are the comparisons between the SD and conventional safety assessments, probabilistic safety assessment (PSA), in Table 3. The event values are made by the Boolean value based quantifications with calculation interval of designed time step. Hence, the realtime calculations are reasonably possible in SD which is basically the dynamical simulations. There are several companies for the SD software in the world. 2.5 Modeling of the event The modeling of the event is constructed by passive system sequences. Designed scenarios are initiated by the loss of coolant accident (LOCA) and it is needed to find the integrity of reactor [Ha, 2006]. So, the conventional event tree is made which is in Figure 6. Based on the event tree, the SD modeling in done in Figure 7 which is modified from conventional work during early 1,000 minutes. The characteristics of the SD are reflected in the modeling where the non-linear algorithm is expressed. The line is used as the curved line as well as the straight line so that the event flow could be drawn without any PSA Theory Random number based Boolean value Probability Event Non-linear lines Event tree, Fault tree Result Relative value Probability value Graphics Colorful Black & white Topic Variable Variable Dynamics Time step based Operator manipulated Real-time Possible Impossible Speed Quick Time needed Commercialization Very active Moderate | | Fig. 5. Three parameters’ motions. | | Tab. 3. Comparisons between the SD and PSA. Environment and Safety Applied Reliability Assessment for the Passive Safety Systems of Nuclear Power Plants (NPPs) Using System Dynamics (SD) ı Yun Il Kim and Tae Ho Woo

atw Vol. 63 (2018) | Issue 3 ı March | | Fig. 6. Event tree of event. | | Fig. 7. SD modeling. Event | | Tab. 4. List of event value. | | Fig. 8. Causes tree of SD modeling. Content LOCA (if then else(random 0 1 () < 0.8, 0, 1)) / Reactor Piping Integrity if then else(random 0 1 () < 0.3, 0, 1) Alarm Alert if then else(random 0 1 () < 0.5, 0, 1) * LOCA * Piping Integrity Manual Actions if then else(random 0 1 () < 0.4, 0, 1) * Alarm Alert * Piping Integrity Reactor SCRAM if then else(random 0 1 () < 0.6, 0, 1) * Manual Actions *Piping Integrity Coolant Tank Integrity if then else(random 0 1 () < 0.5, 0, 1) Flying Integrity if then else(random 0 1 () < 0.3, 0, 1) Drone Action Coolant Tank Integrity * Flying Integrity Emergency Cooling by Operator if then else(random 0 1 () < 0.5, 0, 1) * Drone Action *Reactor SCRAM Reactor if then else(random 0 1 () < 0.5, 0, 1) + Emergency Cooling by Operator + 0.001 restriction. One of most important merits in SD is used as the feedback algorithm in which Reactor is connected to LOCA. This means the final event, Reactor, affects to the initial event, LOCA. There are some cartoon shapes which could give the operator the sign of meaning. In the arrow line, the plus sign means the additive values of the event. In Table 4, the values of the event are shown, which are decided by expert’s judgments. In the case of Piping Integrity, if the randomly generated number between 0 and 1 is lower than 0.3, the value is 0.0. Otherwise it is 1.0. So, the Boolean value is obtained. The others are similar to this case. In the case of LOCA and Reactor, the values are accumulated using the ‘Level’ function in which the values are summed up by the designed time step. 3 Results The simulation is performed for the SD modeling. Using passive system of the free-fall of coolant, the designed scenarios are quantified. Figure 8 is the causes tree of SD modeling which is from the Figure 7. There are results of the modeling. In Figure 9, there are the cause tree’s results of SD modeling as (a) Reactor and (b) LOCA. In ­Figure 9 (a), the possibility for LOCA is shown. The Y-axis has the relative value where the value is stabilized after it increases abruptly. In the final stage as Reactor in Figure 9 (b), the integrity of the reactor is increased. 4 Conclusions The complex algorithm of the SD modeling is done in the passive cooling system. The free-fall could be another kind of the nuclear passive system which is different from the conventional passive systems as gravity and natural circulation. There are some finding in this study as follows, • The nuclear passive system is modeled using the free-fall concept. • System dynamics (SD) based algorithm is performed for nuclear accident. • More realistic safety assessment is described. • New kind of nuclear safety analysis is done successfully The nuclear passive system by the free-fall is successfully modeled for the LOCA accident. Conventional passive systems of gravity or natural circulation could be performed when the piping systems are not damaged. However, in the Fukushima and Chernobyl cases, the piping was blown ENVIRONMENT AND SAFETY 161 Environment and Safety Applied Reliability Assessment for the Passive Safety Systems of Nuclear Power Plants (NPPs) Using System Dynamics (SD) ı Yun Il Kim and Tae Ho Woo