Cooling Tank Control Assignment - Desklib

COOLING TANK CONTROL
ASSIGNMENT
INSTITUTIONAL AFFILIATION
LOCATION
INSTRUCTOR (PROFESSOR)
STUDENT NAME
STUDENT ID NUMBER
DATE OF SUBMISSION
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TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................2
PROBLEM STATEMENT..........................................................................................................2
ASSUMPTIONS..........................................................................................................................2
SYSTEM PARAMETERS..........................................................................................................2
COOLING TANK CONTROLLER DESIGN TASKS..................................................................3
PART I.........................................................................................................................................3
PART II........................................................................................................................................9
PART III....................................................................................................................................10
PART IV....................................................................................................................................12
PART V......................................................................................................................................15
PART VI....................................................................................................................................16
DISCUSSION................................................................................................................................17
Process modeling.......................................................................................................................17
Control systems..........................................................................................................................19
Heat transfer in Thermodynamics..............................................................................................21
CONCLUSION..............................................................................................................................22
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INTRODUCTION
PROBLEM STATEMENT
A hot liquid flow is coming to the tank with flow rate F and temperature T0. The liquid in
the tank is cooled by a jacket cooling water with flow rate Fc and inlet temperature Tcin. The
outlet temperature of cooling water is Tcout. By controlling the jacket cooling water flow rate, the
outlet temperature of the tank, T, can be maintained at a desired level.
ASSUMPTIONS
(i) The cooling tank is properly insulated to avoid heat transfer to the surroundings.
(ii) The amassing of energy in the tank walls and cooling jacket is considered negligible
compared to the accumulation of energy in the liquid.
(iii) It the liquid in the tank is well-mixed and the system is initially at steady state and the
physical properties of the liquid and tank environment are constant.
SYSTEM PARAMETERS
The system parameters of the cooling tank that define the inlet and the outlet are,
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COOLING TANK CONTROLLER DESIGN TASKS
PART I
DESIGN: COOLING TANK CONTROL
Steady state balance equations of the cooling water tank
For an unsteady state mass balance of the cooling water tank, the rate of accumulation of the
mass in the tank is equivalent to the rate of mass at the inflow minus the rate at which the water
flows out.
d (Vρ )
d t =w1+ w2 −w
The unsteady state component balance is
d (Vρx )
dt =w1 x1+ w2 x2−wx
For the corresponding steady-state model is given as,
w1+ w2 −w=0
w1 x1 +w2 x2−wx=0
In the steady state equation of the cooling tank, the laws of conservation hold following a
number of theoretical models of chemical processes. In thermodynamics, the rate of energy
accumulation is the difference between the convection energy rate of the incoming water and the
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convection energy rate of the water flowing out taking into consideration the mesh rate of head
addition to the system as a result of surrounding and the net amount of work accomplished on the
system by the ambiances. The total energy of a thermodynamic system is the sum of its internal
energy, the kinetic energy, and the potential energy. The energy balance is given as,
d
U∫¿
dt =−∆ ( w ^H ) +Q ¿
Using molar quantities, the enthalpy per mole and molar flow rate are used such that,
d U∫¿
dt =−∆ ( ~w ~
H ) +Q ¿
Revisiting the cooling process,
ρ dV
dt =w1+ w2−w
ρ d ( Vx )
dt =w1 x1+ w2 x2−wx
The system is differentiated using the chain rule such that,
ρV dx
dt + px dV
dt =w1 x1 +w2 x2−wx
Further,
ρV dx
dt + x ( w1 +w2−w )=w1 x1 +w2 x2−wx
Simplifying the terms by eliminating the common terms in the equation,
dV
dt = 1
p ( w1+ w2−w )
dx
dt = w1
Vρ ( x1−x ) + w2
Vρ ( x2−x )
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In the cooling tank scenario, it is possible to determine the amassing of the internal energy such
that,
d
U∫¿
dt =ρVC dT
dt ¿
For the cooling tank with a temperature T with an enthalpy H,
^H− ^H ref =C ( T −T ref )
^Href =0
^H=C ( T −T ref )
At the inlet valve section,
^Hi=C ( Ti −Tref )
The convection energy is given as,
−∆ ( w ^H )=w [ C ( T i−T ref ) ]−w [ c ( T −T ref ) ]
VρC dT
dt =wC ( Ti −T ) +Q
At the outlet valve section,
^Hout =C ( T out−T ref )
The convection energy is given as,
−∆ ( w ^Hout )=w [ C ( T out−T ref ) ]−w [ c ( T out−T ref ) ]
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