Example:
The tank shown rolls along a level track. Water received from a jet is retained in the tank. The tank is to
accelerate from rest toward the right with constant acceleration, a. Neglect wind a
Continuous-Duty Wind Tunnels
Continuous duty wind tunnels utilize a compressor to produce the driving pressure gradient for the flow. In
order to minimize the required compressor power, the wind tunne
Image from: http:/history.nasa.gov/SP-440/ch5-6.htm
Notes:
1.
There is a fixed amount of time for which the device will operate at the design test section Mach
number, MaTS, since the tank mass will d
Again, in order to minimize the compressor power requirements, the losses in the system should be
minimized. The ideal case (shown below) is to have an isentropic deceleration from supersonic to subso
Example:
A blowdown wind tunnel exhausting to atmospheric pressure (14.7 psia) is to be designed. The test section
cross-sectional area is specified to be 1 ft2, and the desired test section Mach numb
Supersonic Wind Tunnel Design
There are three common designs for supersonic wind tunnels:
1. high-pressure gas storage tanks (and/or vacuum tanks) for blowdown wind tunnels,
2. a compressor and diffus
Example:
A converging-diverging nozzle, with an exit to throat area ratio, Ae/At, of 1.633, is designed to operate with
atmospheric pressure at the exit plane, pe = patm.
a. Determine the range(s) of
A converging-diverging nozzle with pressure taps along the
length of the device. The flow is from left to right.
The pressure ratio as a function of the axial distance in the CD nozzle for various bac
4.
The location of a shock wave for a back pressure in the range corresponding to case 3 and case 5 can
be determined through iteration.
a. Assume a location for the shock wave (e.g. pick a value for
Now consider what happens if we make the 2nd throat just a little bit larger than the 1st throat. As we
decrease the back pressure we will reach a case where the flow in the 1st throat becomes choked
and we decrease the back pressure further, then the shock will be swallowed by the 2nd throat and the flow
within the test section will, at last, be supersonic (shown below).
Mat2 > 1
Mat1 = 1
p01
MaT
3.
Over-speeding the diffuser is often impractical. For example, consider a diffuser designed to operate
at a Mach number of 1.7 (Ai/A* = Ai/At = 1.338). The critical Mach number for swallowing the sh
As the upstream Mach number increases, the sonic area approaches the throat area, i.e. A* At, and the
shock moves closer to the inlet (the shock gets weaker and less flow needs to be diverted around t
Supersonic Diffuser Design
Another application where the efficient deceleration of a supersonic flow is of interest is a supersonic
diffuser at the inlet of aircraft jet engines. The flow entering a j
Example:
Consider a supersonic wind tunnel starting as shown in the figure below. The upstream nozzle throat area
is 1.25 ft2, and the test section design Mach number is 2.50. As the tunnel starts, a
5.
In real nozzles flows, the flow will typically separate from the nozzle walls as a result of the large
adverse pressure gradient occurring across a shock wave. Interaction of the shock with the sep
Once the wind tunnel is running and weve decreased the 2nd throat area, we should try to minimize the
stagnation pressure loss through the shock wave in the 2nd diverging section (and, hence, increase
Example:
A converging-diverging nozzle, with Ae/At = 1.633, is designed to operate with atmospheric pressure at the
exit plane. Determine the range(s) of stagnation pressures for which the nozzle will
Notes:
1. The critical back pressure ratio corresponding to case 3 can be found from the isentropic relations (the
flow throughout the entire device is isentropic). Assume that the geometry, and hence
Example:
A jet of water is deflected by a vane mounted on a cart. The water jet has an area, A, everywhere and is
turned an angle with respect to the horizontal. The pressure everywhere within the jet
Example:
A variable mesh screen produces a linear and axi-symmetric velocity profile as shown in the figure. The
static pressure upstream and downstream of the screen are p1 and p2 respectively (and a
The LME for Non-Inertial Frames of Reference
Recall that Newtons 2nd law holds strictly for inertial (non-accelerating) frames of reference. Now lets
consider frames of reference that are non-inertial
Example:
Incompressible fluid of negligible viscosity is pumped, at total volume flow rate Q, through a porous
surface into the small gap between closely spaced parallel plates as shown. The fluid has
Now apply the linear momentum equation in the X-direction to the same control volume.
d
u X dV + u X ( u rel dA ) = FB, X + FS , X
dt
where
d
dt
CV
CV
u
X
(3.82)
dV = 0
CV
r=R
u X ( u rel dA ) = V12
Substitute.
Fx = 2 V 2 RH
(3.75)
To determine V, apply conservation of mass to the same control volume.
d
dV + u rel dA = 0
dt
where
d
dt
CV
CS
dV = 0
(3.76)
(steady flow)
CV
= dA
=
u rel dA = Q +
Now apply the linear momentum equation in the X-direction to the same control volume.
d
u X dV + CS u X ( urel dA ) = FBX + FSX
dt CV
where
d
u X dV = 0 (steady flow)
dt CV
d
d
dA ) = V 2 hw + (
Example:
Water is sprayed radially outward through 180 as shown in the figure. The jet sheet is in the horizontal
plane and has thickness, H. If the jet volumetric flow rate is Q, determine the result