PRANDTL MEYER SHOCK PROBLEM
PRANDTL MEYER SHOCK PROBLEM
Introduction:
- In this project, We will be working on the literature review on shock flows and assosiated boundary conditions.
- We will be analysing the shock flow for different SGS temperature for different velocities and processing the results.
Shock Wave:
- Shock wave, strong pressure wave in any elastic medium such as air, water, or a solid substance, produced by supersonic aircraft, explosions, lightning, or other phenomena that create violent changes in pressure.
- An object such as jet is said to have supersonic speed if it travels faster than the speed of sound. such speed is defined using mach number
- In particular, shock waves travel faster than sound, and their speed increases as the amplitude is raised, but the intensity of a shock wave also decreases faster than that of a sound wave, because some of the energy of the shock wave is expended to heat the medium in which it travels.
- Shock waves alter the mechanical, electrical, and thermal properties of solids and, thus, can be used to study the equation of state(a relation between pressure, temperature, and volume) of any material.
- Wave front pile up along the side, the wave crests overlap with one another and form a large amplitude wave known as shock wave.
- A sonic boom is the sound associated with the shock waves created whenever an object travelling through the air travels faster than the speed of sound. Sonic booms generate enormous amounts of sound energy.
Prandtl Meyer Expansion fan:
- A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner.
- The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point.
Shock Flow Boundary Condition:
- Neumann Bounadry Condition:
- The Neumann boundary condition is a type of boundary condition when imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is going to take on the boundary of the domain. It specifies the normal derivative of funtion on surface. The zero gradient means all variables are set to a constant value at outlet boundary, then it can only be true when you extend the outlet location very far away from flow domain. \'Zero Gradient\' means that the variable is \'fully developed\' on the inflow portion of the opening
- Boundary Condition used in Shock Flow:
- Inlet Boundary Condition: In inlet boundary conditions, the distribution of all flow variables needs to be specified at inlet boundaries mainly flow velocity. This type of boundary conditions are common and specified mostly where inlet flow velocity is known.
- Outlet Boundary Condition: The zero normal gradient (NE) is used. It means all variables are set to a constant value at outlet boundary, then it can only be true when you extend the outlet location very far away from flow domain. \'Zero Gradient\' means that the variable is \'fully developed\' on the inflow portion of the opening. This means neumann boundary condition say that the outlet condition is dependent on the initial condition.
- Top & Bottom Boundary: The slip wall condition is used because viscous effects at the wall are negligible.
- Front & Back Boundary: Two_D boundary condition is used.
Solver : Density based steady solver
Regions & Initialization:
CASE-1:
- Velocity = 680m/s(Super-sonic)
CASE-2:
- Velocity = 100m/s(Sub-sonic)
Grid Control:
- Base Grid Size:
dx=dy=dz=0.8
- Adaptive Mesh Refinement:
- Sub-grid criterion:
- 0.01K
- 0.05K
- 0.1K
Simulation Results:
Base setup:
Surface with edge contour:
CASE-1:
- Velocity = 680m/s
- SGS = 0.01K
- Velocity = 680m/s
- SGS = 0.05K
- Velocity = 680m/s
- SGS = 0.1K
Explanation:
CASE-1:
- By Analyzing the graph of temperature we can see that the temperature is decreasing at outlet, that is because, the outlet condition is set to zero normal gradient(NE) so the outlet condition is depend on the initial condition and also the variable is fully developed on the inflow position. So to manage the temperature difference it reduces and attain the steady state.
- And the Mach at the outlet is increasing this is because the outlet velocity is also increases from the initial condition.
- Mach Number = Velocity of object / Speed of sound wave.
CASE-2:
- Velocity = 100m/s
- SGS = 0.01K
- Velocity = 100m/s
- SGS = 0.05K
- Velocity = 100m/s
- SGS = 0.1K
Explanation:
CASE-2:
- By Analyzing the graph of temperature we can see that the temperature is increased at outlet, that is because, the outlet condition is set to zero normal gradient(NE) so the outlet condition is depend on the initial condition and also the variable is fully developed on the inflow position so to manage that the temperature is increased because the initial condition velocity is higher than the inflow condition.
- So to cope with the inflow condition velocity, the temperature is increased. Because molecules at higher temperature have more energy thus they can vibrate faster and as the result the velocity is increased and both attains the steady state.
- And the Mach at the outlet is increasing this is because the outlet velocity is also increases from the initial condition.
- Mach Number = Velocity of object / Speed of sound wave.
Effect of SGS Parameter on Shock Location:
- The Adaptive mesh refinement is depending on the value of sub grid criterion. Here we are using temperature criterion, that is when the curvature of temperature is greater than certain value the mesh is refined. And thus the SGS is decreased we get the more refined mesh on the shock location and vice-versa. We can visualize it by seeing the total cell graph, When the SGS parameter is low, the cell count is increased and as the result we get the more refined mesh on the shock location. And also you can see that the AMR starts from (5000) cycles because we provided that as start time.