Dynamic model for the paper machine headbox
Explain and derive the Dynamic model for the paper machine headbox?
Expert
We'll first develop a dynamic model for the paper machine headbox.A stock balance around the headbox. A suffix hb refers to the head box. Accumulation = Input – Outputdmhb/dt = ρqin – ρqoutNow ρ, is the stock density, but since the consistancy is 0.5% only, ρ = ρw = Water densityd(ρVhb)/dt = ρqin – ρqoutdVhb/dt = qin – qoutAhbdh/dt = qin – qoutwhere, Ahb, is the c/s area of header and assumed to be constant. qout, is the flow out of the header, and is only through slice, and can be written as, CAs(2gh)1/2, where As, is the cross sectional area of slice perpendicular to the flow, and C is characteristic constant coefficient for the slice.Hence, Ahbdh/dt = qin – CAs(2gh)1/2,To find, we can write Bernoulli's equation between Vacuum Degasser and Headbox. Suffix vd refers to vacuum degasser. Pvd/ρ + W = (Phb + ρgh)/ρ + V2/2 V = {2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2 qin = AinV = Ain{2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2Hence the dynamic model is, Ahbdh/dt = Ain{2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2 – CAs(2gh)1/2,where the rate of stock height change in head box is related to the pressure in vacuum degasser and height. We have to linearize the non linear dynamic model. So that the effective model will be,τdh'/dt = KpP'hb + Khh',So as we see the the response of the height of stock to variations in vacuum degasser pressure is first order lag. We don't know the dynamics of level sensor or transmitter, but we'll assume it's also first order lag. Hence the effective system will be a second order. And hence it'll be oscillatory, and we propose the PID controller for level control by manipulating the speed of fan pump. Using MATLAB control toobox and given values of the parameters in the problem, we approximately find the following controller parameter settings. Kc = 9.6, τI = 2.3 min, τD = 3.5 min.Similarly, a propotional integral controller is proposed for pressure control in head box.The pressure in the head box is related to in flow of air, which is controlled by PI controller. The air is available at pressure of 300 kPa. dPhb/dt = f(Qin), where is the inlet flow rate of air. This will be pure capacitive system, hence we propose PI controller. We find the controller parameters for this, Kc = 14.5, τI = 4.5 min.
Process Flow Diagram: A Process Flow Diagram or System Flow Diagram exhibits the relationships among the main components in the system. It too has fundamental information regarding the material balance for the process.
Ergonomics: This is concerned with how easy (comfort, complexity) the product is to use by the targeted market. Physical human dimensions must be considered when designing the driver's seating, instruments, and controls in a car. Slight variations bet
Air at 20 m/s, 260 K, 75 kPa with 5 kg/s flows into a jet engine and it flows out at 500 m/s, 800 K, 75 kPa. What is the change (power) in flow of kinetic energy?
Product appearance: Strongly influenced by the Industrial Designer, the general style? of the product is significant as this will have an influence on materials and manufacturing procedures to be used. The product should be able to grab the customer's
The oil pump is drawing 25 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are of 8 cm and 12 cm, respectively. When the pressure rise of oil in the pump is measured to be 250 k
Difference between pressure vessel & column: The Pressure vessels (cylinder or tank) are utilized to store fluids under pressure. If the pressure vessel are design in the form of column to separate the gas at u
Draw a frequency-response curves for a damped single degree of freedom system subjected to a harmonic excitation under three different damping ratios. System has a natural frequency of ωn as the forcing frequency of the excitation is ω. Describe
Explain the two Solar thermal DHW and Solar DHW Solar thermal systems n brief?
What is meant by the term LILO?
theories for the origin of petroleum, methods for detection of petroleum deposits, fractional distillation
18,76,764
1936182 Asked
3,689
Active Tutors
1419902
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!