Shock waves and expansion waves Rayleigh flow Fanno flow Assignment

Normal shocks Figure 12.24: Control volume for flow across a normal shock wave

Normal shocks Figure 12.65: normal shock wave above the wing of an L-1011 commercial jet aircraft.

h-s diagram

h-s diagram What do the states on the Fanno line and the Rayleigh line represent? What do the intersection points of these two curves represent? ANSWER: The Fanno line represents the states that satisfy the conservation of mass and energy equations. The Rayleigh line represents the states that satisfy the conservation of mass and momentum equations. The intersections points of these lines represent the states that satisfy the conservation of mass, energy, and momentum equations.

Oblique shock wave How do oblique shock wave occur? How do oblique shock wave differ from the normal shock wave? Oblique shocks occur when a gas flowing at supersonic speeds strikes a flat or inclined surface. Normal shock waves are perpendicular to flow whereas inclined shock waves, as the name implies, are typically inclined relative to the flow direction. Also, normal shocks form a straight line whereas oblique shocks can be straight or curved, depending on the surface geometry. In addition, while a normal shock must go from supersonic (Ma > 1) to subsonic (Ma < 1), the Mach number downstream of an oblique shock can be either supersonic or subsonic.

Questions 12.64 Air enters a normal shock at 18kPa, 205K and 740m/s. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number and stagnation pressure downstream the shock. shock wave AIR 1 2

Question 12.75

Rayleigh flow Flow with heat transfer and negligible friction.

Understanding the fundamental… What is the characteristic aspect of Rayleigh flow? What are the main assumptions associated with Rayleigh flow? Answer: The characteristic aspect of Rayleigh flow is its involvement of heat transfer. The main assumptions associated with Rayleigh flow are: the flow is steady, one-dimensional, and frictionless through a constant-area duct, and the fluid is an ideal gas with constant specific heats.

Rayleigh flow Steady one-dimensional flow of an ideal gas with constant specific heat through a constant-area duct with heat transfer with negligible friction. Continuity equation  eq 12.50 X-momentum equation  eq 12.51 Energy equation  eq 12.53 or 12.54 Entropy change  eq 12.55 Equation of state  eq 12.56 Control volume for flow in a constant-area duct with heat transfer and negligible friction.

Rayleigh line(T-s diagram)

Rayleigh flow (a summary)

Question 12.91 Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches 52kJ/kg, the flow is observed to be choked and the velocity and the static pressure are measured to be 620m/s and 270kPa. Disregarding frictional losses, determine the velocity, static temperature and static pressure at the duct inlet.

Fanno flow Adiabatic duct flow with friction. Wall friction is significant and should be considered when studying flow through long flow sections, e.g. long ducts where the cross section is very small.

Understanding the fundamental… What is the characteristic aspect of Fanno flow? What are the main assumptions associated with Fanno flow? Answer: The characteristic aspect of Fanno flow is its consideration of friction. The main assumptions associated with Fanno flow are: the flow is steady, one-dimensional, and adiabatic through a constant-area duct, and the fluid is an ideal gas with constant specific heats.

Fanno flow Steady one-dimensional flow of an ideal gas with constant specific heat through a constant-area duct with friction. Continuity equation  eq 12.70 X-momentum equation  eq 12.71 Energy equation  eq 12.72 or 12.73 Entropy change  eq 12.74 Equation of state  eq 12.75 Control volume for flow in a constant-area duct with friction.

Fanno flow Steady one-dimensional flow of an ideal gas with constant specific heat through a constant-area duct with heat transfer with negligible friction. Considering all Fanno flow tend to reach Ma =1, it is convenient to use the critical point (i.e. at sonic state) as the reference point and to express flow properties relative to critical point properties. The actual duct length, L can be determined from equation 12.91. The length, L* represents the length distance between a given section where the Ma number and a real or imaginary section where Ma*=1.

Fanno flow (summary)

Question 12.115 Air enters a 5cm diameter adiabatic duct at Ma1=0.4, T1=550K and P1=200kPa. The average friction factor for the duct is estimated to be 0.016. if the Ma number at the duct exit is 0.8, determine the duct length, temperature, pressure, and the velocity at the duct exit.

Assignment II Questions: 12.40 Submission: 12.69 11 MAY 2012 12.79 12.90 12.111 Submission: 11 MAY 2012 Venue: Admin office level 2