Karteikarten
Shock waves
Karten in diesem Stapel (50)
- 1At what Mach can flow no longer be considered incompressible0.3
- 2Variables for incompressible vs compressibleFor incompressible just volume and pressure (no heating by work)
For compressible also use energy and density - 3What happens at greater than Mach 1Shock waves form
- 4What physically causes shock wavesCan be either a strong impulse or wave steepening such as water waves
- 5Key TakeawaysDescribe the characteristics of elastic, plastic and shock waves
Be familiar with simple equations of state
Can use the Rankine equations and equation of state to calculate shock state
Describe the governing equations of compressible flow
Describe the concept of artificial viscosity
Describe the method for treating elasto-plastic flow - 6Rankine Huguinot equationsCalculates conservation of mass, momentum and energy across the shock wave
Ie what is the state of a shock wave - 7Does pressure in a fluid support shearNo shear wave in fluid
- 8Pressure wave in a solidCan support shear waves as well as longitudinal
Stress proportional to the speed of the particle - 9Can waves be superimposedElastic and plastic waves can, shock waves cannot
- 10What happens when a wave hits a free surfaceDepending on the density and velocity of the material on either side of the interface will dictate the ratio of energy that is transmitted/reflected
- 11Low impedance to high impedancePressure is conserved at the interface. A stronger pressure waves is transfered into the high impedance material. To balance the pressure the reflected wave is still positive
When all of deformation is elastic can just superimpose waves - 12What is the Hugoniot elastic limitWaves that exceed this Hugoniot elastic limit break into elastic precursor and slower plastic wave
- 13What is the effect of the shock wave being strongerTravels faster than the elastic sound speed
Wave speed gets higher the harder you hit it
- 14What are the Rankine Hugeniot equationsU is the shock wave speed
u is the particle waves speed
Shock wave speed is not constant in a medium - relates to pressure
- 15Are shock waves isentropicNo they are not. Create waste heat
- 16What do perfectly elastic waves conserveConserve mass, momentum, energy and are reversible (isentropic and adiabatic)
- 17Rayleigh lineThe discontinuity line when you jump from pre shock to post shock in pressure/volume diagram
- 18What is area under pressure-volume diagrams curveEquivilent to energy
- 19Hugoniot curve (Diagram and def)The curve that connects the line of all of the different shock states
- 20What happens in front of the shock frontAlmost instantaneous increase in properties - pressure, internal energy, density
- 21The equation needed to close the hugoniot equation listThe equation of state
- This is material specific
Very complex for composite materials
Hugoniot curve is also a line of the phase diagram surface - 22Some simple equations of stateD
- 23Gamma Cb Mie-Grüneise equation of state Pref and ErefThe ratio of specific heats
The bulk sound speed
Pressure and internal energy along some reference line
- 24Stiffened gas equationThe result of the coupling of the perfect gas and liquid (low pressure ) equations of state
- 25Relationship between shock wave and speed of the material in generalLinear relationship between shock wave and the speed of the material
- 26Conservation of momentum (Lagrangian)
- 27Conservation of energy (This is different for compressible flow)
- 28Lagrangian reference frame Eulerian reference frame Conservative formFollows the particle of material as it moves around (material reference frame)
The third form
- 29Conservation of mass both reference framesProduct rule and material derivative is the key way to get between three reference frames
- 30—Because this is the only combination that gives a scalar + scalar
Uses product rule
- 31Material Derivative
- 32Definition of deviatoric stressd
- 33Why can't you use the energy equation for shock wavesCan't simulate shock waves using energy equation as there is no entropy term
- 34Shock velocity vs material velocity Rarefaction release waveShock velocity is always faster than the material velocity
Behind the material velocity you have a rarefaction release wave. Moves the opposite way to the shock wave
Can solve using Reimann methods - 35An alternative to Reimann problemUse artificial viscocity
Its actually a pressure
Used to smear the discontinuity across a few cells, this represents the discontinuity - 36Temperature behind/in front of shockIn front of shock gas it hot
Behind the shock the gas is hot - 37What happens if you don't use artificial viscocity Where do you apply qOscillations
Only use artifical viscocity at the shock front
Can cause artificial heating - 38Pressure from the stress tensor
- 39Deviatoric stressesAct to deform the shape of the material
The stresses with the pressure term taken out
Describes materials resistant to deformation - 40Stress tensor for inviscid fluidSij = 0
- 41Deviatoric stress related to strain
- 42Yield limit for metals vs brittle materialsmetals - depends on strain, strain rate and temp. This is as these factors determined dislocation motion
brittle materials - also depends on pressure - 433d stress tensor6 independent components in a symmetric tensor
Can rotate the reference frame such that all diagonal components vanish and just principal diagonal stresses on the diagonal - 44Reference frame for failure due to principal stressesFor isotropic material where materials reference frame does not affect properties this means that principal stresses are key
- 45Stress invariantsInvariants a way to combine all of the stresses into one scalar number. A measure of how different the stresses are in different directions
The bigger J2 is the bigger the distortion effect - 46Wilkins radial returnCalculate square root of J2 and compare with yield stress.
- 47What detemines a metals strengthIn metals the strength is determined by dislocations
- 48Why do dislocations depend on temperature What happens when strain rate increases What happens when strain increasesDislocation motion is dominated by waiting time at other dislocation, this is aided with thermal energy
Dislocation motion is resisted by thermal vibrations (phonon drag)
Density of dislocations increases impeding movement - 49Conservation of momentumMomentum = mass * velocity
For conservation momentum2 = momentum1 + impulse over the time domain
For impulse it is the pressure differential across the area between the time steps time the cross sectional area - 50—
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- Contitnuum Mechanics Karteikarten am Shock waves, erstellt von Oliver Boom am 03/01/2019.
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- Oliver Boom
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