How to account for and set the temperatur​e in testing

Question

The problem is this: I'm setting up an airflow resistance test and I need to account for temperature and barometric pressure. However, I don't know how to setup LabVIEW to account for these variables.

Answer 1

Devont:
Actually this issue is a fairly complex problem in aerodynamics. I am
an aerospace engineer who has developed computer code for this very
purpose in a couple of wind tunnels. When you say you are setting up
an airflow "resistance" test, what physical (aerodynamic) properties
are you trying to measure? Tunnel flow velocity? Mass flow?
Aerodynamic properties on a test model? (lift and drag coefficients,
center of pressure, gross forces?)
If you are trying to measure air flow velocity through a wind tunnel
test section, then the next question is what type of sensor system are
you using to do this? A pitot-static probe? A hot wire anenometer?,
an LDV (doppler laser)? Each has different techniques for getting
back flow properties.
Also what kind of tunnel is this? Low speed subsonic (say less <100
M/s) Mid speed subsonic <0.6 Mach? Transonic 0.8 to 1.2 Mach?
Supersonic 1.2 to 4.0 Mach? Hypersonic (say >4.0 Mach?) This will
make a great deal of difference in computing flow properties.
Mach number is a ratio of the flow velocity to the local speed of
sound where;
M=v/a where a is the speed of sound.
a=(gamma*r*t)^0.5
where gamma is the ratio of specific heats Cp/Cv, r is the gas
constant, and t is the absolute temperature. Gamma is a constant up to
about mach 4 but really starts to fall apart after that so this speed
of sound equation becomes a lot less useful for hypersonic analysis.
At low speeds gamma for air is approximately 1.4, r is about 287 for
air. At STP, the speed of sound is about 340 meters/second.
What is the scale of your tunnel? What is the density altitude of
your tunnel? What is the fluid medium in your tunnel? (Is it regular
air or something else?) These play into computing flow properties
because they affect a dimensionless flow property called the Reynolds
number which affects how the flow in the tunnel behaves.
You will need to consider also humidity which affects the density of
the fluid medium in your tunnel. Water vapor has a molecular weight
of 18. Dry air (0% RH) has a molecular weight of about 28.9. The
more water vapor you have, the lighter the sample volume of "air" will
be. The ability of air to retain water vapor is a function of
temperature, so a relative humidity of 100% at 0 degrees C will
contain much less water vapor than a relative humidity of 20% at 30
degrees C.
Because of something called the "boundary layer" the velocity profile
will be faster in the center of your tunnel than at the walls. It
will resemble something like a U shape for higher Reynolds numbers and
for very low Reynolds numbers may look more like a parabola. Reynolds
number is computed by:
Re=rho*V*L/mu
where rho is the air density, V is the flow velocity, and mu is a
property called the kinematic viscosity which is a function of
temperature.
The Reynolds number, like the Mach number, the Nusselt number, and a
few other fluid dynamics properties is a dimensionless ratio. Flows
with a similar dimensionless property should behave more or less the
same. This is called similitude.
Mass flow calculations first require that you know the air speed
profile of your tunnel and then you will need to compute the density
of the air in the tunnel and then perform an integration process to
calculate the actual mass flow through a particular plane of interest
in the tunnel.
Also, even when you put a test probe into the tunnel to measure the
flow in the tunnel, this will interfere with the free flow to a
certain of the tunnel. To minimize this, the test probes have to be
carefully designed and their size needs to be much smaller than the
overall tunnel dimensions. Later when you put a test model in the
tunnel, it and it's mounting system will also have an interference
effect on the tunnel that has to be accounted for.
To give a simple (perhaps an overly simple) answer to your question,
temperature and barometric pressure will play into your problems of
computing forces in that they affect the density of the fluid medium
in your tunnel via the unified gas law (which is a combined expression
of Charles and Boyles laws for perfect gases):
PV=nRT
or
Pv=rT
where rho, the density is the inverse of v, so this is sometimes
written as:
P/rho=rT
This only applies for perfect gases though. A perfect gas is one
where the constant pressure and constant volume specific heats (Cv,
and Cp) are fixed. The hotter and more dense the fluid medium, the
less true these equations become.
Temperature in these equations doesn't mean the common ways that we
ordinarily talk about temperature when cooking or talking about the
weather. Instead of C or F, temperature in the gas law must be on an
absolute scale such as Kelvin or Rankin. 0 degrees Kelvin or
Rankine=-273.15 degrees C or -459.67 degrees F. One Kelvin degree=1.8
Rankine degrees but both start at the same point of absolute zero.
For standard atmospheric conditions (called STP for standard
temperature and pressure), 1 cubic meter of air weighs about 1.226 kg.
You have to calculate the density of air at non standard conditions
by solving algebraically for the above gas law equation.
r is called the gas constant and can be derived from the universal gas
constant R (8314 units I can't remember of the top of my head but it
involves kJ/kg.mole or something like) by deviding by the molecular
weight of the gas in question. If the gas is a mixture then you will
have to apply the partial pressures rule to come up with an averaged
molecular weight of the mixture. Dry air contains mostly nitrogen
which has an atomic weight of 28 (about 79%), and then oxygen (about
20%) which has an atomic weight of 32, and the balance (about 1%)of
inert gases (Helium, argon, krypton, etc.) which have much smaller
atomic weights. For dry air r (small r that is) is about 287.
If the air is not dry, then you have to account for the water vapor in
the air by figuring out what partial pressure of water vapor is in the
air and then performing an average between the water vapor portion and
the other components of the air. Wator vapor only has a molecular
weight of 18 (1 Oxygen + 2 Hydrogens=18) and so is lighter than dry
air and tends to make the air less dense.
The partial pressure of water vapor that can be supported in the air
is a function of temperature that more or less grows exponentially
with temperature. I'm sure if you search the web you can find several
empirical equations for this. Relative Humidity (RH) is an expression
of how much water vapor is in an air sample versus the maximum that
can be supported at the current temperature of the air sample but what
you really want is the partial pressure of water vapor in the air.
There are sensors that can give this to you by measuring the
electrical conductivity of the air. Dry air is actually a very good
insulator, whereas water vapor decreases the insulating property of
the air.
All other things remaining equal, increasing the humidity will
decrease the density of the air.
All other things remaining equal, increasing the temperature will
result in decreasing density while decreasing temperature will result
in increasing density. If the temperature in your tunnel is different
than standard then you will need to account for this.
Tunnels generally heat up the air by the way when they accelerate the
air through the fan and also through boundary layer friction with the
tunnel walls. Many tunnels actually have heat exchangers to keep the
air from getting too hot. You will need to make sure you measure the
temperature at the same point thats you are measuring the static and
stagnation pressures in your your tunnel so that you can account for
its effects. Standard temperature is 15 degrees C or 59 degrees F.
For conversion purposes, 15 degrees Celsius =288.15 degrees Kelvin= 59
degrees Fahrenheit=518.6 degrees Rankine.
All other things remaining equal, increasing pressure will result in
increasing density, while decreasing pressure will result in
decreasing density. Barometric pressure is usually given by the
weather service as inches or millimeters of mercury or sometimes
millibars. For conversion purposes, 29.92
inHg=760mmHg=1000millibars=14.7 psi= 101325 Pascals pressure. If the
pressure in your tunnel is different than standard then you will need
to account for this.
Depending on tunnel velocity, you will also have to consider
stagnation versus static properties. Stagnation properties are what
you measure if you bring the flow at a point to a complete stop, i.e.
the kinetic (as opposed to random thermal) energy in the sample is
completely converted thermal energy. How you do this depends on what
speed of sample you are trying to measure and is the subject of whole
books. Suffice it to say that at low speeds there is little
difference between stagnation and static properties but the faster you
go, the less resemblance they bear to one another.
Compressibility is another issue. At low speeds air is
incompressible, but at higher speeds v>100m/sec, compressibility
becomes worth accounting for in your measurments.
At higher temperatures and velocities, (high supersonic, or
hypersonic, or high temperature >500 degrees C), the constant pressure
and constant volume (Cp and Cv) specific heat assumptions break down
and so does the gas law. The simplifications that can be made for
using the ratio of Cp/Cv (called gamma) also break down because Cp and
Cv and therefore gamma all stop being constants. Solving flow
problems in this regime becomes much more complex requiring numerical
models for Cp and Cv and requiring numerical (as opposed to simple
analytical) methods to compute flow properties.
Once you know the flow density, you can calculate air speed. For
lower speed low temperature tunnels (low subsonic) you can use a
simple incompressible Bernoulli equation for converting pitot-static
pressure to air speed. At higher speeds and temperatures this depends
on the regime (transonic, supersonic, hypersonic, etc.)
The Bernoulli equation is simply:
Pstagnation=Pstatic+1/2 rho * velocity^2
For lower speed supersonic, the isentropic gas relations are sometimes
used.
In any event, you have to be sure to get your units right. If you use
metric, pressure is Pascals (Newtons/m^2), rho is kg/m^3 and velocity
is meters/sec. It's harder in U.S/U.K units because of conversions
between slugs and pounds etc.
Also you have to consider the concept that there will be a steady
state average that you will measure and a transient/turbulent portion
that will occur for each parameter that you measure (temperature,
pressure, RH, etc.) that you will need to account for.
Once you know the air speed and the density, you can compute their
product - mass flow. Mass flow then can be used for other purposes
such as calculating performance properties if you are testing a jet
engine or propeller or something.
Hot wire anenometers work by heating a wire and measuring the
resistance of the wire. The faster the air flow past the wire
filament, the more it will cool. I don't remember the equations off
of the top of my head but I believe that there is a square rule
involved. Hot wires work better at lower speeds than pitot-static
sensors but both become less effective the slower you go.
LDV's are neat, high tech toys that I haven't had a chance to work
with yet but they measure the airspeed by measuring the doppler shift
in the light emitted by a laser beam going through the flow, much like
doppler (WX-88) weather radar works. They actually measure the speed
of the air more directly than the pitot-static or hot wire methods are
probably simpler to implement from an equations point of view but they
are very very expensive.
In conclusion, I know I have written a lot of stuff up here that
probably sounds pretty intimidating with regards to solving your
problem. It would help to eliminate some of this by telling us more
about your test problem so that we can make the appropriate
simplifying assumptions. Tell us more about the details.
Douglas De Clue
LabVIEW developer (and degreed Georgia Tech aerospace engineer)
[email protected]
Devont wrote in message news:<50650000000800000025530000-1027480788000@exc​hange.ni.com>...
> The problem is this: I'm setting up an airflow resistance test and I
> need to account for temperature and barometric pressure. However, I
> don't know how to setup LabVIEW to account for these variables.