1 / 60

Gas Dynamics, Lecture 7 (Shocks & Point Explosions) see: astro.ru.nl/~achterb/

Prof. dr. A. Achterberg, Astronomical Dept. , IMAPP, Radboud Universiteit. Gas Dynamics, Lecture 7 (Shocks & Point Explosions) see: www.astro.ru.nl/~achterb/. Summary of shock physics. Shocks occur in supersonic flows; Shocks are sudden jumps in velocity, density and pressure;

mare
Download Presentation

Gas Dynamics, Lecture 7 (Shocks & Point Explosions) see: astro.ru.nl/~achterb/

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Prof. dr. A. Achterberg, Astronomical Dept. , IMAPP, RadboudUniversiteit Gas Dynamics, Lecture 7(Shocks & Point Explosions)see: www.astro.ru.nl/~achterb/

  2. Summary of shock physics • Shocks occur in supersonic flows; • Shocks are sudden jumps in velocity, density and pressure; • Shocks satisfy flux in = flux out principle for - mass flux - momentum flux - energy flux

  3. Flux in = flux out: three jump conditions;Case of a normal shock Three conservation laws means three fluxes for flux in = flux out! Mass flux Momentum flux Energy flux Three equations for three unknowns: post-shock state (2) is uniquely determined by pre-shock state (1)!

  4. “Bernoulli” in shock jump:

  5. Shock strength and Mach Number 1D case: Shocks can only exist if Ms>1 ! Weak shocks:Ms=1+ with << 1; Strong shocks: Ms>> 1.

  6. Weak shock:

  7. From jump conditions:

  8. Weak shock ~ strong sound wave! Sound waves:

  9. Very strong normal shock

  10. Strong shock: P1<< 1V12 Approximate jump conditions: put P1 = 0!

  11. Conclusion for a strong shock:

  12. Jump conditions in terms of Mach Number:the Rankine-Hugoniot relations Shocks all have S > 1 Compression ratio: density contrast Pressure jump

  13. Oblique shocks: four jump conditions! (1) (2) (3) (4)

  14. Oblique shocks: tangential velocity unchanged!

  15. From normal shock to oblique shocks: All relations remain the same if one makes the replacement: θis the angle between upstream velocity and normal on shock surface

  16. From normal shock to oblique shocks: All relations remain the same if one makes the replacement: θis the angle between upstream velocity and normal on shock surface Tangential velocity along shock surface is unchanged

  17. Example from Jet/Rocket engines:over-expanded jet exhaust

  18. Under-expanded jet exhaust

  19. Bell X1 Rocket Plane

  20. “Diamond” shocks in Jet Simulation

  21. Summary: Fundamental parameter of shock physics: Mach Number Rankine-Hugoniot jump conditions: Strong shock limit

  22. Application: point explosions Trinity nuclear test explosion, New Mexico, 1945 Supernova remnant Cassiopeia A

  23. Tycho’s Remnant (SN 1572AD)

  24. Sedov scaling law for point explosions (1) Assumptions: Explosion takes place in uniform medium with density ρ; → spherical expanding fireball! Total available energy: E. Point explosion + uniform medium: no EXTERNAL scale imposed on the problem!

  25. Sedov scaling law for point explosions (2) Dimensional analysis: Sedov: fireball radius ~ Sedov radius RS

  26. Supernova explosions Steps: Photo dissociation of Iron in hot nucleus star:  loss of (radiation) pressure! Collapse of core under its own weight  formation of proto-neutron star when ρ ~ 1014 g/cm3 Gravitational binding energy becomes more negative:  positive amount of energy is lost from the system! 4. Core Bounce shock formation and ejection envelope

  27. Evolution of a massive star (25 solar masses) Core collapse: t ~ 0.2 s (!) Collapse onset: photo-dissociation of iron

  28. Processes around collapsed core

  29. Available energy: Gravitational binding energy:

  30. Lots of things happen………

  31. Where does the energy go? neutronization core:

  32. Supernova Blast Waves • Main properties: • Strong shock propagating through the Interstellar Medium; • (or through the wind of the progenitor star) • Different expansion stages: • - Free expansion stage (t < 1000 yr) R  t • - Sedov-Taylor stage (1000 yr < t < 10,000 yr) R  t 2/5 • - Pressure-driven snowplow (10,000 yr < t < 250,000 yr) R  t 3/10

  33. Free-expansion phase: R=Vexpt Energy budget: Expansion speed:

  34. Sedov-Taylor stage: R ~ RS ~ t2/5 • - Expansion decelerates due to swept-up mass; • Interior of the bubble is reheated due to reverse shock; • Hot bubble is preceded in ISM by strong shock: • the supernova blast wave.

  35. Shock relations for strong (high-Mach number) shocks:

  36. Pressure behind strong shock (blast wave) Pressure in hot SNR interior

  37. At contact discontinuity: equal pressure on both sides! This procedure is allowed because of high sound speeds in hot interior and in shell of hot, shocked ISM: No large pressure differences are possible!

  38. At contact discontinuity: equal pressure on both sides! Relation between velocity and radius gives expansion law!

  39. Step 1: write the relation as difference equation

  40. Step 2: write as total differentials and………

  41. ……integrate to find the Sedov-Taylor solution

  42. Alternative derivation: Energy Conservation shock speed = expansion speed Deceleration radius Rd:

More Related