Skip to main content

Shock Waves

Com­press­ible flow is the area of flu­id me­chan­ics that deals with flu­ids in which the flu­id den­si­ty varies sig­nif­i­cant­ly in re­sponse to a change in pres­sure. Com­press­ibil­i­ty ef­fects are typ­i­cal­ly con­sid­ered sig­nif­i­cant if the Mach num­ber (the ra­tio of the flow ve­loc­i­ty to the lo­cal speed of sound) of the flow ex­ceeds 0.3. Ap­pli­ca­tions for com­press­ible flow in­clude the aero­dy­nam­ics of high speed air­crafts, the flow through the tur­bo com­pres­sor, tur­bine and noz­zle of a jet en­gine, the de­ploy­ment of airbags etc..

The most dis­tinct dif­fer­ences be­tween the com­press­ible and in­com­press­ible flow mod­els are that the com­press­ible flow mod­el al­lows for the ex­is­tence of shock waves and choked flow. Shock waves are an im­por­tant as­pect of com­press­ible flow and oc­cur in most prac­ti­cal sit­u­a­tions where su­per­son­ic flow ex­ists. Shock waves form when the speed of a gas changes by more than the speed of sound.At the re­gion where this oc­curs sound waves trav­el­ing against the flow reach a point where they can­not trav­el any fur­ther up­stream and the pres­sure pro­gres­sive­ly builds in that re­gion, and a high pres­sure shock wave rapid­ly forms.

This ver­i­fi­ca­tion test case first in­tro­duced by G.A. Sod con­sists of a tube closed at both ends, with a di­aphragm sep­a­rat­ing a re­gion of high-pres­sure gas on the left from a re­gion of low pres­sure gas on the right. When the di­aphragm is re­moved, an ex­pan­sion wave trav­els to the left and a shock wave to the right (Read more).
This ver­i­fi­ca­tion test case shows the im­pact of an in­com­ing oblique shock wave on a sol­id wall. The re­flec­tion of a shock wave is al­so a shock wave thus di­vid­ing the flu­id do­main in three zones with three dis­tinct flu­id ve­loc­i­ties, pres­sure, den­si­ty and tem­per­a­ture that can be solved an­a­lyt­i­cal­ly (Read more).
This val­i­da­tion test case shows how the solver han­dles the com­plex in­ter­ac­tions that oc­cur when an oblique shock wave im­pacts a sol­id wal­l's bound­ary lay­er (Bound­ary lay­er sep­a­ra­tion, first re­flect­ed shock wave up­stream of the in­ci­dent shock wave im­pact, ex­is­tence of a sec­ond re­flect­ed shock wave, etc..) (Read more).
A spe­cial poster ses­sion was run dur­ing the 18th In­ter­na­tion­al Sym­po­sium on Shock Waves, held on Ju­ly 21 - 26, 1991, in Sendai, Japan where the 2-D pla­nar shock wave dif­frac­tion over a 90 de­gree sharp cor­ner was se­lect­ed as a bench­mark prob­lem for com­press­ible CFD codes (Read more).
This bench­mark­ing test case fea­tures an in­com­ing su­per­son­ic flow in a wind tun­nel meet­ing a step. Once the flow reach­es the step, shock waves ap­pear and are re­flect­ed on the dif­fer­ent wind tun­nel bound­aries. The ob­jec­tive of this test case is to study the de­vel­op­ment of the flow through time and specif­i­cal­ly the vary­ing im­pact lo­ca­tions of the shock waves (Read more).
Mod­ern high speed air­crafts usu­al­ly fly in tran­son­ic flows where there is mixed sub- and su­per­son­ic lo­cal flow in the same flow­field (typ­i­cal­ly with freestream Mach num­bers from M = 0.7 or 0.8 to 1.3). Usu­al­ly the su­per­son­ic re­gion of the flow is ter­mi­nat­ed by a shock wave, al­low­ing the flow to slow down to sub­son­ic speeds. This bench­mark­ing test case stud­ies the in­vis­cid flow over a clas­sic NACA air­foil at tran­son­ic speed (Read more).