# atw 2018-03v6 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

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