When an object moves faster than the
speed of sound,
and there is an abrupt decrease in the flow area,
are generated. Shock waves
are very thin regions in the gas where the
change by a large amount.
In many flow problems multiple shocks are present. The shocks
may intersect with each other and with the surfaces generating them.
On this page we present the physics which govern the
intersection of two shock waves and include a Java program that
you can use to investigate these flow problems.
On the slide we show two problems involving two unequal wedges,
wedge "a" and wedge "b".
On the left side of the figure, wedge "b" is located downstream
of wedge "a" and the problem is called the double wedge problem.
On the right side of the figure, wedge "b" is located opposite to
wedge "a" and the problem is called the opposed wedges problem.
The general physics of both problems is the same. A supersonic
flow at Mach number M is flowing from left to right. We will
call the free stream region zone "0" as shown in red. Wedge "a"
generates a shock wave with the conditions downstream of this shock noted
as zone "1". The flow in zone "1" is parallel to wedge "a" and
the conditions are specified by the
oblique shock relations given on another page.
Wedge "b" also generates a shock wave with the conditions downstream of
this shock noted as zone "2". The flow in zone "2" is
parallel to wedge "b" and the
conditions in zone "2" are again given
by the oblique shock relations. For the double wedge problem the upstream
conditions for zone "2" are the conditions in zone "1".
For the opposed wedge problem
the upstream conditions for zone "2" are the free stream conditions of zone "0".For both problems
the shocks generated by the two wedges intersect at some point in the flow.
For the double wedge problem, the two shocks coalesce into a third shock
with downstream conditions noted as zone "3". The flow in zone "3" is parallel
to wedge "b" and the upstream conditions for zone "3" are the free stream
conditions of zone "0". The flow is zone "3" has passed through one oblique
shock while the flow in zone "2" has gone through two shocks. In general,
the static pressure in zone "2" will not match the static pressure in zone "3".
Because of this mismatch, a weak shock or
expansion fan is generated in the flow and a
new zone "4" is created. The flow direction and static pressure in zone "4"
must be the same as the conditions in zone "3". But in general, the total
pressure and Mach number are not the same in zone "4" and zone "3" because of
the different number and strength of shocks that the two flows have
encountered. A slip surface is generated between zones "3" and "4" and
some flow variables change across this line.
In the opposed wedges problem the
shocks pass through each other and form two additional shocks. The flow in
zone "3" is now parallel to wedge "a", while the flow in zone "4" is parallel
to wedge "b". Upstream conditions for zone "3" are the zone "1" conditions;
upstream conditions for zone "4" are the zone "2" conditions. Once again the
flow direction and static pressure in zone "3" and zone "4" must be the
same. These conditions set the strength of the two new shocks (3 and 4).
And again, a slip surface is generated between zones "3" and "4". The shock
wave for zone "3" then intersects and
from wedge "a", while the shock wave from zone "4" intersects
and reflects from wedge "b".
In all of the shock refections and intersections the Mach number of the flow
is decreased. Eventually, the Mach number in some zone becomes too low
to support an oblique shock and a terminal,
normal shock is formed.
Here's a Java program which solves the two crossed shock problems.
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The user must select which flow problem to study by pushing the appropriate button
on the blue bar at the top.
Input to the program can be made
using the sliders, or input boxes at the lower left. To
change the value of an input variable, simply move the slider. Or
click on the input box, select and replace the old value, and
hit Enter to send the new value to the program.
Output from the program is displayed
in output boxes at the lower right.
The user selects the Zone to display by using the choice button.
The flow variables are presented as ratios to the previous zone (up)
and to the free stream value (0).
The graphic at the top shows the wedges in red and green
and the shock wave generated by the wedge as a line. The line is colored
blue for an oblique shock and magenta when the shock is a normal shock.
The user can move the display by clicking on the graphic, holding down,
and dragging the graphic. You can zoom in or out of the graphic by
using the slider at the left of the display.
If you loose the graphic, click on "Find"
to restore the initial display.
To restore the initial conditions click on "Reset".
The ShockModeler simulation program, shown above, can also be used to study
the generation and reflection of shock waves and the devlopment of expansion fans. A
of the program is available at this web site.
If you are an experienced user of this simulator, you can use a
of the program which loads faster on your computer and does not include these instructions.
You can also download your own copy of the program to run off-line by clicking on this button: