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What is shock wave? Like an ordinary wave a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discountinous , change in pressure ,temperature, and density of the medium. because of this, shock waves propagate in a manner different from that of ordinary acoustic waves.…
Arun Reddy
updated on 01 Jul 2022
What is shock wave?
Like an ordinary wave a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discountinous , change in pressure ,temperature, and density of the medium. because of this, shock waves propagate in a manner different from that of ordinary acoustic waves. In physics a shock wave is a type of propagating disturbance that moves faster than the local speed of sound in the medium.
When the speed of a source exceeds the speed of sound the wavefronts lag behind the source in a cone-shaped region with the source at the vertex. The edge of the cone forms a supersoincs wavefront with unusually large amplitude called a shockwave. the shockwave from a supersoinc object is a cone composed of overlapping spherical wavefronts. the regionbehind the source and the shock wave called a shock layer is the region with high pressure temparature and density, then the free flowing fluids.
Types of flow according to mach number:
MACH NUMBER is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
M=u/c
where: M=is the mach number,
u=is the local flow velocity with respect to the boundaries
c=is the speed of sound in the medium.
*subsonic flow: When the fluid velocity is lower than the acoustic speed (m<1) then the fluid flow is called subsonic. however mach number of the flow changes while passing over an object or through a duct. hence for simplicity flow is counsider as subsonic if the mach number is in the range of 0-0.8.
*Transonic flow: When the flow mach number is in range 0.8-1.2 it is called transonic flow. Highly unstable and mixed subsonic and supersonic flows are the main feature of theis regime.
*Soinc flow: When flow mach number is 1 it is called sonic flow.
*Supersonic flow: When the flow machn number is more than everywhere in the domain then it is called as supersonic flow.
*Hypersonic flow: When the flow mach number is more than 5 then it is called as hypersonic flows.
PRANDTL-MEYER EXPANSION FAN:
A supersonic expansion fan, technically know as prandtl-meyer expansion fan, a two dimensional simple wave is a centred expansion process that occur when a supersoinc flow turns around a convex corner. the fan consists of an infinite number of mach waves, diversing 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.
there are some marked difference between shock waves and expnasion fans. across a shock wave the mach number decreases the static pressure increases and there is a loss of total pressure because the process is irreversible. through an expansion fan the mach number increases the static pressure decreases and the total pressure remain constant. expansion fans are isentropic.
An expansion wave emanating from a sharp convex corner is known as a centred expansion which is commonly known as the prandtl-meyer expansion wave.
Boundary condition used for shock flow simulation:
- Dirichlet boundary condition
-Neumanm boundary condition
-Mixed boundary condition
-Robin boundaty condition
Geometry:
MESH:
SOLVER PARAMETER:
BOUNDARY CONDITIONl:
Inlet boundary
1 INFLOW CONDITION
2 Velocity=680m/s
3 Temperature=286.1 K
4 Turbulence model-RNG K-Epsilon
Outlet boundary
1 Outflow condition
2 Temperature=286.1
3 Mixture=Air
Wall
1 Wall boundary
2 Temperature=300K
3 Velocity=statinory
4 Temperature=Law of wall
5 Turbulent kinetic energy-Zero normal gradient
6 Turbulent Dissipation- wall model
RESULTS:
FOR SGS 0.05
MESH:
TOTAL CELL COUNT:
MACH NUMBER:
PRESSURE COUNTOUR:
TEMPERATURE COUNTOUR:
TEMPERATURE ANIMATION:
FOR SGS 0.03
MESH
TOTAL CELL COUNT:
MACH NUMBER:
PRESSURE CONTOUR:
TEMPERATURE CONTOUR:
TEMPERATURE ANIMATION:
https://youtu.be/wnm5-J29HfM
FOR SGS 0.01
MESH:
TOTAL CELL COUNT:
MACH NUMBER:
PRESSURE CONTOUR:
TEMPERATURE CONTOUR:
TEMPERATURE ANIMATION:
https://youtu.be/HvdzaINDLLs
CONCLUSION:
*The cell differ for the all cases with different SGS . it is clear that for the law value of SGS the cell count is maximum. as mentioned when sub grid temperature become greater than SGS value the mesh is refined.
* Through result we can understand that the SGS value has no effect on the location of the shock waves. they occur at the vicinity of the sharp coner. as mentioned above when the sub grid temperature becomes greater than SGS value the mesh is refined. there fore increases the cell count and computational time.
*the edges of the curvature of temperature and pressure becomes fine as the SGS value gets finer. going through above links mentioned we can observed that the shocks waves generated are infinite and edges are very coarse.
*after some time edges get finer and this because of the adaptive mesh refinement technique which enables to get an accurate result at a particular point locally.
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