AME 341b—Mini Talk Prep
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Lecture 6 “Jets, Plumes, and Self Similarity”
SLIDE 7
-
Jets
o
Two different regions in every jet
Laminar
Turbulent
SLIDE 8
-
Turbulent Jets
o
Laminar Flow
Have streams of flow which do not interfere with each other
No friction between any two layers
Same velocity between each of them and they’re going continuously straight
Also called potential core
Purely laminar flow
Seen in beginning of jet
Assume streak of flow with continuous velocity all the way
o
Turbulent Flow
Squeezing/friction suddenly
interact with each other, rubbing out, one goes faster than the other, see eddies “twirls”
Seen in second half of jet
Not easy to understand
Too random to predict
SLIDE 9
-
A class of free shear flows (no effect due to boundaries) is called laminar flow
-
Shear flow
occurs when 2 streams of jet are at different velocities
o
Turbulence occurs when 2 streams of jet are at different velocities
-
Flow 1, U1; Flow 2 U2
o
U2 > U1 (one is moving faster than the other)
o
Will create a twisting motion called “eddies”
o
Variation of velocity between two adjacent layers is what’s creating the turbulence
o
If you plot this, (velocity as x-axis and y as the distance)…
Mathematical way of representing turbulence
Strong velocity gradient (large dU
dy
) as move across y
-
What will be the velocity profile as we progress in time and space?
o
Something happens as increase space for it to move
o
Will not be exactly same as go in time
o
Profile is expanding as moving away from the origin
Changing in x and changing in time
o
How does mathematical formulation dU
dy
change as you progress in time?
grow or shrink? it’ll go to zero
As go away, velocity gradient (difference between the two velocities will reduce because system is losing energy as moving forward and forward)
Slowly, the velocity gradient is going to reduce and the turbulence intensity also reduces but still exists
dU
dy
will become smaller
-
SLIDE 10
-
Free shear slows
o
Characteristics
Important in everyday life
There are shear flows everywhere
Evolve in both t and x
Expands in x
Unstable; usually turbulent
Having a perfect flow means a really good phenomenon
Difficult to study
Poorly understood
Want to predict by math; mathematical model
However, up to this day, there is “NO” closed form solution (yet)
that allows us to predict particle motion in turbulent flows
As engineers we perform experiments to construct simplified empirical
models to help predict flow phenomenon
o
“empirical” no mathematical form but done enough experimentation over the years that can still predict some phenomenon of turbulence based on experimental proof
SLIDE 11
-
Reynold’s Number (1 number to rule it all in fluid flow)
o
o
Fluids! ^
-
If Reynold’s number is small, the flow tendency is to be laminar
-
If Reynold’s number is very large, the flow tendency is to be turbulent
-
Values for Re range from 10
−
1
to 10
6
o
When Re very small, it is laminar
o
Always represent to 2 significant figures (i.e., Re = 13060 ~ 130000)
o
When Re 10
6
or higher, it is turbulent
o
o
As long as ground experiment to the same Re number and to the same conditions, can say that for the same Re number on the airplane will be same method
o
“Grounding factor”; one number to rule it all in the fluid flow
o
Why did we use Re number??? HAVE TO EXPLAIN THIS
SLIDE 12
-
Turbulent Jet Empirical Profile
o
Assume ambient velocity of air is 0 m/s
No particles moving around this structure
o
Velocity uj should be greater than uamb (ambient velocity)
If want to make something move or flow, have to be more velocity/energy inside the system
As time and space progresses, velocity profile will expand
o
Clear laminal flow: Potential core
Easiest to predict because laminar flow
Whatever velocity have at uj will be the same a the tip of the potential core
Velocity is going to be the same length where laminar flow
Top-hat profile
-
Collect velocity profile at different locations
o
Wherever have best laminar flow (center), will have same velocity as see at uj but
as go away from the center towards the end, velocity reduces and profile drops
o
-
Once cross potential core what happens?
o
Collecting data of turbulent flow once cross the potential core
o
Profiles are now turbulent flow
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o
In the center will have the max and it will not be equal to uj
Will be much less than uj
But still reducing as go away from the center
-
Profiles
o
Jet boundary (cone)
o
Fully developed zone (fully developed turbulent flow)
Don’t have any more laminar flow; after potential core
Whatever you’re recording is purely turbulent
When cross boundaries of the potential core, will interact with the surrounding layers and create swirls or eddies and because of that, slowly will see turbulence increase as move away from P
0
When have two layers moving at different velocities (outside layer is at zero velocity and one at higher velocity than the other one), there will be friction which will create eddies which creates turbulence which is not technically easy to predict
o
Unmixed flow typically ends at 5D
D is the diameter of the nozzle
Any data after 5D, only then will get fully developed turbulent region
o
Collecting data at different profiles to understand how the profile of velocity changes as go away from the nozzle
-
Experimental Model Hypothesis
o
The model hypothesis is…
At sufficiently large Reynold’s number (10 to the power of four or greater;
will create a flow inside the lab with greater than 10 to the power of four Re number) turbulence reaches a universal state (state at which it doesn’t matter about anything else but have a condition that we can understand)where local flow dynamics depends only on the local conditions
-
Find Umax of each profile and divide the whole profile by Umax (called unorm; varying from 0 to 1)
o
Dividing all velocity data with the highest velocity seen in profile (first normalization)
o
So velocity only varying from 0 to 1
o
Calculate y distance from that value
On y axis divide by y/2 (second normalization performing; on y-axis)
o
Once plot all profiles ontop of eachother, will see that they will exactly match after the fully developed region (x = 6D, x = 8D)
o
This phenomenon experimentally proves
only way as engineers to predict what happens in turbulent flow; self-
similarity
o
Can predict profile at 10D based on this
o
Not proved in the potential core
o
Only proved in the fully developed region and that’s how we can predict turbulent
flows in engineering
o
Have to normalize; phenomenon is called self-similarity
-
Will use pitot tube o
Sensor that measures velocity
o
Run at different profiles
-
Self-similar region is ground
SLIDE 13
-
Self similar region
o
Fully turbulent flow
-
Shear layer
o
Turbulent boundary
SLIDE 14
-
Assume that velocity coming from the nozzle is going to be U
0
all the way which will
end at 5D will D = diameter
o
Find D value from measuring the diameter of the jet nozzle
-
Max velocities should reduce and y distances should increase
-
Lecture 7 “Traverse Recap & Dynamic Pressure & Measurement”
SLIDE 3
In lab
-
Know where motor is at all times when using a step motor
SLIDE 29
-
Potential Core
-
Self-similar Region
-
Shear Layer
o
Self-similar region is approaching the surrounding environment
o
In theory, even if had some wind or air movement in room, the velocity inside the jet is so much larger than what’s happening on the outside so can consider all the surrounding area as negligible or that not that much is going on
o
Thinking about difference in velocity between the self-similar region and the exterior, going to have some reaction or mixing where those two regions intersect
o
Complex flow movement happening at that boundary
-
Velocity profile
o
Velocity is initial velocity, U
0
o
Length of potential core is approximately 5D (5 diameters)
o
Self-similar region; start with velocity profile
At subsequent distances away, over distance away from potential core (velocity profiles called self-similar because when they are normalized and plot on top of each other, they collapse into similar shape that follow this empirical behavior)
-
Each dot is each sample\
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o
-
o
Hypothesis that the flow profiles in a fully developed region evolve in a self-
similar fashion
If this hypothesis true, this means that one system at a given Reynold’s number can be used to predict the behavior of another system at the same Reynold’s number
Useful because if you want to be testing something in plane design, way too expensive and not feasible to build an entire plane to measure a potential design
Use idea of Reynold’s number similarity to get the same flow state and to understand
Look up advantages of Reynold’s number
o
Conclusions are valid across space transformation
PLOT UNCERTAINTIES
SLIDE 33
-
Pitot Static Tube
o
Analysis of flow: Bernoulli’s Equation (type of conservation of energy)
Assume:
Fluid medium is incompressible
Have isothermal process
o
SLIDE 34
-
SLIDE 38
-
Measuring pressure
o
Open ends of U-shaped tube, at static equilibrium
o
Velocity not happening in the same medium as the fluid inside of the monometer
So have ratio of fluid density to the air density which represents the change between the two states because just using some liquid to do this operation based on the density that’s causing this pressure change on the other end
Solution for velocity based on a height change and known parameters of the system
SLIDE 39
-
Manometers are 2
nd
order systems
o
Has a finite time constant
o
No oscillating response
o
State is such that ζ
≫
1
(overdamped system)
An overdamped system has a response like such
Never overshoot, no oscillations, just approach step value
Highly overdamped systems can be approximated by a first order system because they have similar type of step response
Can make direct comparisons
o
-
What is response time to use a manometer to record values?
o
System is so slow that it is effectively averaging all values
o
Basically giving smoothed out variations of what’s actually happening in real life
-
Can use frequency response of 1
st
order system as well
o
o
Expecting attenuation at 1 Hz for the manometer
o
How fast can information from the system? Quite slow…
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Talking about averaging: anything that’s happening under the 1 Hz time period is essentially being lost
Expect to see eddies at edge of self-similarity region
Have so much going on that can this give spatial results?
-
Can’t measure fluctuations
o
Going to get overall large scale behavior but not small behavior
SLIDE 42
-
For the system in E13, the manometer has 2 main disadvantages
o
1. Can’t read directly into computer
o
2. Long averages, thus, sparse measurements
Can’t capture small fluctuations
SLIDE 43
-
Thus use Pressure Transducer
-
Response time is on the order of 0.0005 seconds o
Can take the data density that need
o
Turbulent eddies in some regions; now able to quantify this smaller scale behavior
in time
SLIDE 47
-
Need to have uncertainty o
Take points, go around and take more points
-
Talk about limitations and assumptions
-
Think about pitot tube response
o
Ideal case
Straight on; no angle
o
In reality
While looks straight on, pitot tube at a slight angle
Have some offset in angle of incidence of U
0
and pitot tube
u f
(
α
)
If this is the case and thinking of geometry and how much of that velocity would actually be entering the front of the pitot tube? How that would change what’s being measured by the pitot tube itself?
Lecture 8 “MiniTalks”
SLIDE 3
-
Include different type of examples of turbulent jets
o
Where see turbulent jets in real life?
o
i.e., turbulent jet in snow-making machine
-
Why important as an engineer to study this?
SLIDE 5
-
D: nozzle
-
Regions
o
1. Potential Core
o
2. Shear Layer
Boundary between the actual flow and the zero velocity
Approaching the surrounding environments
o
3. Self-Similar Region
-
Questions to answer in presentation
o
What happens in the potential core?
What kind of flow do you see?
Laminar flow
o
What is the difference between the self-similar region and the potential core?
SLIDE 6
-
Done an experiment where want to take velocity profiles by collecting data at different locations on the curve & want velocity profiles at different “D’s”
o
i.e., 1D, 2D, 5D…..
-
Profiles after 5D where see a self-similar region
o
No theoretical value for this prediction, can still use empirical data and predictions SLIDE 7
-
Ultimate goal is to talk about the self-similar region
-
SLIDE 8
-
Normalization
o
Trying to match all different data sets into one single graph by doing normalization
o
Normalize by taking the highest point (max value for that profile), divide all values with that max value, U
c
, and the peak will be “1”
-
If take different number of samples for different profiles, the highest point, U
c
, will not be the same.
o
How can predict if no consistency of catching the right point each time?
Anchor/ground the system (12:14)
“Anchor” or “ground”: make everything relative to a certain point; referring all data to a particular point
Grounding to the ½ value of top velocity profile u
c
& using that to predict U
c
to normalize
Bottom range should change from -2 to 2 and max value should be 1
Use U value at y ½ to approximate U
c
Because of symmetry, have y ½ on both sides
Because of symmetry can assume that at least two locations where have same value at y ½
Find average of the two estimated values SLIDE 9
-
Turbulence Intensity
o
Turbulence exists but will intensity of turbulence be the same at every location? No.
-
Plot U vs t
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o
See some variation on top and bottom, will not be constant value
o
Where σ
is the standard deviation of that particular value of U(t)
-
Turbulence intensity is o
U
'
U
c
where U
c
is the max velocity o
Will help understand any turbulence better
o
Know how much turbulence exists as well as how much intensity is in certain parts
SLIDE 10
-
If plot turbulence intensity, U’, with respect to y, can see the turbulence intensity increases, becomes flat, increases, and then become flat again
o
Wherever there are definitely eddies, which means there is nonlaminar flow and it
is continuously mixing of velocities of different flows, should see some intensity
o
Becomes flat because of perfectly laminar flow (should get very smooth movement without any standard deviation of variance) and that’s why get a zero value o
o
How can you identify the potential core mathematically? (12:18)
By graphs
By plotting 1D, 2D, etc…
Can see where flatlining ends and that’s immediately where potential core ended
Beyond that, get fully turbulent area where see intensity going all the way to the max value
o
Turbulence intensity become almost nonzero after 5D for most of the cases
After 5D, any D you pick is going to be a fully turbulent region
SLIDE 12
-
So what?
-
Outline
o
Why should we study this?
o
What did we study?
o
How did we study this?
o
Explain, “if I can estimate this dynamically similar region, I can make predictions
based on the Re number (based on inertial/viscous flow)…”
Conclude that this is true and point to a model hypothesis
Explain by using graphs
SLIDE 13
-
Logistics
o
5-minute talk time-limit
o
Concise & clear
o
Have a story outline/narrative
Slides
Have clear path, don’t jump around slides
o
Well-rehearsed
o
Be professional
o
5-6 slides max
SLIDE 14
-
Assignment Components
o
Have to use powerpoint slides AND have to print them
o
Abstract/Title Page
First slide
250 word max-
one paragraph
Add color, bold, italics, underline, etc. to make words stand out
No long sentences
Meaningful title, name
What did you observe, what did you do?, what did you observe?, what is reynold’s numbers?, what flows studying?
Not just ‘Turbulent Jets’
Preview of the whole paper/experiment/data/talk
Technically correct
Spend at least 30 seconds talking about it
o
Plots
Worth 70% of grade goes to the plots
Must be printed; NO LAPTOP
MAKE SURE CENTERED; OVERLAP ON SAME PLOT
so that can make the argument that they are self similar
When showing the plots talk about…
Why you are doing this?
How are you doing this?
What you got so far?
o
Talking
PRACTICE
BE 15 MINUTES EARLY
SLIDE 15
-
Plots
o
Organized
Organized in the right order
i.e,. start with profiles first vs. starting with turbulence intensity
o
Careful Units
SI units
o
Annotations
Easier for reader to read
o
NO DEFAULTS
Color
Make it so easy for reader to read
o
How many do you actually need?
4-5 graphs
SLIDE 16
-
No gridlines
-
No Title
-
Multiple series with color, different line style, legend
-
x-label, y-label
-
Remove box
-
Zoom in for comparisons between two graphs
-
Print in color so can differentiate between different series
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o
Also add contrast to differentiate
-
Add in centerline to prove symmetric around zero
-
Make sure that all graphs have same decimal values -
Uncertainty
-
Annotations
o
1-on-1 with a staff member (two copies required)
Why 5V for Channel 2 (Fan) not sufficient? -
Reynold’s number too low
-
Speed of fan so low that will not have 10
4
and won’t see similarity in the data
12 V
-
Speed of fan so high that have 10
4
Pitot tube investigation (12:50)
-
Flow always parallel to opening in a perfect case scenario
o
In reality not the case
-
What if pitot tube is angled?
o
This will happen in experiment because although tube and fan pointing at each other, flow of air will be at an intersection with the tube
-
At what angle will get 0 velocity being recorded on the system?
o
Why is something weird happening at the edges of graphs?
o
Maximum angle can reach before get 0 velocity
% pitot tube detects pressure
% transducer converts pressure to voltage
% vi converts voltage to velocity
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