With the increase in shock layer temperature, how is the pressure and density of shock layer going to change?
I see this problem from the perspective of 'viscous interaction' of Hypersonic flows. I am not sure whether my answer is applicable to your case.
So in Hypersonic flows over flat plates, a viscous layer (boundary layer) starts developing over the flat plate downstream. Now the velocity decrease due to viscous forces causes temperature to rise (your case of increasing T, remember enthalpy is constant since no heat is added). Since, pressure downstream is same for a particular oblique shock angle, therefore from ideal gas law we see that for increase T, density decreases. This causes the flow at a particular mass flow rate to pass via a bigger volume. Implying the boundary layer increases. The increase in layer causes flow deflection angle to slightly increase (theta) causing stronger shocks at same upstream Mach number. Hence the Pressure static increases but total Pressure decreases. The density decreases as earlier mentioned.
Let me know if I messed up somewhere....
@aditya praksh singh in your case pressure normal to the direction of boundary layer is fixed (constant) and temperature increases due to viscous dissipation which causes the density to increase(by p=density*RT) ... and hence increases the boundary layer thickness ...
i want to know if heat is added in shock layer by means of exothermic reaction how it's going to effect the pressure and temperature???
I don't know if my answer fits your question exactly...
Shock layer exists for real gas, it depends on thermodynamic properties. Usually, we talk of adiabatic shock layer, no heat is added from the exterior. That means that the upstream and downstrem condition are exactly the same you have for the inviscid case.
A similar argument can be deduced from one-dimensional theory (Fanno flow). In the shock layer you reach the maximum of entropy at M=1
You can read details in many classical books
one picture about the shock wave in the compressible boundary layer is attached, I think it is helpful to you.
@Fillipo I want to know if temperature is increased in shock layer by means of exothermic reaction (blunt body coating ) in shock layer what would be its after effects ?
Again, the way to understand the effects is to consider a simple model such as the one-dimensional viscous flow (Fanno flow) with additional heat (Raileigh flow), The exothermic reaction produces the heat flux acting on the flow and appears in the energy equation. It is a driving force.
As a result of the increasing of temperature (but within the range of ideal gas) the effects are on the enthalpy and on the sound velocity that increase. More complex is the case when temperature is so high that the model of ideal gas fails. You have to consider ionization and dissociation effects.
Details of the theories can be found in classical books such as Zucrow or Kundu...
@Filippo thanks alot ....how its going to change shock stand -off distance within the limit of prefect gas ...
- Badges
- Science topic
- Similar topics
- Thermodynamics
- Pressure