Boundary Layer Flow 17 - Compressible Boundary Layer Flow

Question 1

What does viscosity cause?

Answer 1

Aerodynamic drag

Question 2

What does thermal conduction cause?

Answer 2

Aerodynamic heating

Question 3

Viscous flow analysis

Answer 3

Skin friction and heat transfer at the surface
Complete solution of viscous flow field needed

Question 4

Wall boundary conditions

Answer 4

No-slip condition velocity at wall
Constant temperature at wall
Unsteady heat transfer
Adiabatic wall case (zero heat transfer)

Question 5

Considerations for compressible viscous equations

Answer 5

Exact analytical solutions of complete N-S equations exist for only a few very specialised cases (all of which are laminar)
Equations are frequently simplified by making appropriate approximations about the flow
In modern times, solutions of full viscous flow equations can be obtained numerically using CFD

Question 6

Properties of BL equations

Answer 6

Steady
2D
Re»1
Dimensional analysis
Thickness«length
Freestream outside BL is frictionless and adiabatic, may be isentropic

Question 7

Effect of compressibility on velocity profiles over insulated flat plate

Answer 7

BL thickness becomes large at large Mach numbers

Question 8

Effect of compressibility on temperature profiles over insulated flat plate

Answer 8

As Mach number increases temperature increases significantly

Question 9

Effect of compressibility of velocity profiles over a cold flat plate

Answer 9

Rapid BL thickness growth as Mach number increases
General effect of cold wall is to reduce BL thickness

Question 10

Effect of compressibility of temperature profiles over a cold flat plate

Answer 10

Temperature levels much lower than insulated plate case, pressure is same, from equation of state density is much higher in cold wall case, thinner BL can accommodate same mass flow
Peak temperature inside BL is indication of amount of viscous dissipation
Rapidly growing effect of this viscous dissipation as Mach number increases

Question 11

What are compressibility effects?

Answer 11

To make BL solutions a function of Mach number, Prandtl number and wall-to-freestream temperature ratio
Generally, compressibility reduces drag coefficient and increases thickness
Warmer wall also reduces drag coefficient

Question 12

Effect of increasing Mach number for turbulent BL

Answer 12

Reduces drag coefficient at constant Re
Effect is stronger on turbulent flow results