Applied Fluid Mechanics Flashcards
0
Q
Types of measurement quantities
A
Local, global
Direct, indirect
1
Q
Purpose of measurements
A
Validation: were the correct equations solved ?
Verification: were the equations solved correctly?
2
Q
3 steps of DoE
A
Isolate the phenomenon
Choose the right tool for the problem
Design the experiment backwards
3
Q
St
A
Strouhal number
Oscillating velocity/mean velocity
For oscillating flows
4
Q
Eu
A
Euler number
Pressure forces/inertial forces
For pumps, cavitation
5
Q
Re
A
Reynolds number
Inertial forces/viscous forces
Almost always used
6
Q
Fr
A
Froude number
Kinetic energy/potential energy
For free surface flows, where gravity is important.
7
Q
Ma
A
Mach number
Flow velocity/sonic velocity
For compressible flows (Ma>0.2)
8
Q
Similar solution
A
When two flows with same BC also have same Re, St, Ma and Fr.
9
Q
Buckingham Pi-Theory
A
Pi=n-r
Pi: nb of dimensionless quantities
n: nb of influencing quantities
r: nb of basic quantities (MLT)
10
Q
Requirements on wind tunnels
A
Reproduction of the problem’s flow
Defined conditions (perfect, worst case)
Transferability
11
Q
Eiffel type: class, parts
A
Open-circuit
Inlet, settling chamber, test section, fan, diffusor
12
Q
Blower tunnel
A
Fan at entrance-> no diffuser/test section necessary
13
Q
Göttinger type
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Closed loop
Corner vanes
Heat exchanger
Wide angle diffuser
14
Q
Ma dependences in supersonic tunnels
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Only on ratio of cross-section at nozzle exit and throat. Not on power input as long as it is enough to produce sonic speed at the throat.
15
Q
Supersonic tunnels: characteristics, types
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Convergent-divergent nozzle upstream of test section, diffuser with second throat (breakdown shock)
Blow-down, suck-down
16
Q
Pressure tunnels: types
A
Low density
High-speed
17
Q
Turbulence dissipates
A
turbulent kinetic energy into heat
18
Q
Turbulence energy transfer cascade process
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Energy transfer from large to small scales through deformation work on vortices, induced by strain rates.
Rapid increase of vorticity component in stretching direction, slow decrease in compression direction.
19
Q
Diffusivity in turbulence
A
Increased rates of momentum, heat and mass transfer. Increase of exchange surface.
20
Q
Turbulent Reynolds number
A
uL/nu
Molecular diffusion time scale/ turbulence time scale
21
Q
Meaning of RMS
A
Standard deviation
22
Q
Turbulence level
A
Tu,i = u_i,rms/u_1,av
23
Q
Nyquist criteria
A
f_sampling>2f_max
24
Rough estimate of L_t
Time for one large eddy to pass. Half the channel height is a good estimate for the maximum size if large eddies, over velocity.
25
L_t
Integral time scale
| Rough measure of the interval over which the velocity u(t) is correlated with itself.
26
Skewness
Describes symmetry of PDF
=0 for Gauss
av(a^3)/arms^3
27
Flatness/Kurtosis
Describes width of PDF
=3 for Gauss
av(a^4)/a_rms^4
28
Method for calculating autocorrelation R
Align graphically the series u'(t) with u'(t+tau), multiply them vertically and compute the average product.
29
Normalized function condition
<=1
30
Autocorrelation of stationary process: characteristic
Symmetry around tau=0 where r=1
31
Energy spectrum: operation
Fourier transform of autocorrelation function.
| Energy spectrum and autocorrelation function are a Fourier transformation pair.
32
Integral of all energy spectrum is
Turbulent kinetic energy and R(tau=0)
33
Energy spectrum of spatial autocorrelation is function of
Wavenumber vector Kj
34
Total turbulent shear stress
Molecular momentum transport (viscosity and grad) + turbulent momentum transport (fluctuations)
35
Velocity profile close to the wall
Depends only on local relevant parameters, not on free stream velocity of channel height/boundary layer thickness.
36
Wall shear velocity
u_tau=sqrt(tau_W/rho)
37
Viscous units
u+=avg(u_1)/u_tau
| y+=y.u_tau/nu
38
Universal law of the wall
Log region
| u+=1/K ln y+ + C
39
Layers of turbulent BL
Viscous sublayer: y+>nu_t u+=y+
| Buffer region: 550 nu<
40
Definition static pressure, use in fluid mechanics
Force per unit area imposed by the flow onto a boundary parallel to the streamline.
Distribution around an object defines its flow resistance or buoyancy. Determines the velocity or volume flow based on Bernouilli.
41
Variation of pressure in wall-normal direction
None (boundary layer theory according to Prandtl)
| p at wall = p in free stream
42
Reference form of wall tappings
Perfect straight drill
43
Dependencies of p error in wall tappings
Diameter, length, burr height, velocity utau
44
Method for calculating Delta p
Calculate all dimensionless parameter in Pi equation
| Read Pi on diagram of relevant tapping
45
Static pressure measurements access
Wall tappings
Static pressure tube
PSP
46
Problem with static pressure tubes
Blockage effect from shaft and head
47
Assumption with pitot tubes
Hydrostatic pressure can be neglected
48
Dependency of ptot in pitot tubes
```
Flow angularity
Diameter ratio (.6)
```
49
Conrad sensor
2 slanted pitot tubes
+: no angle dependency
-: linear angle dependency
50
Condition for velocity measurement with pitot tube, solutions
Static pressure is known
| Wall taping, prandtl tube.
51
Pressure transducers
Liquid manometers
Spring manometers
Multi-point pressure measurements
Wall microphones
52
Types of liquid manometers
Cistern (diff. areas)
Bets
Inclined tube
53
Types of spring manometers
Plate, membrane, spring
Bourdon (circular tube)
Electromechanical (strain gauge, induction)
54
Multi-point pressure measurement
Scani valve, electronic scanning system
| Stationary: tapping connected with tube. Instationary: wall microphone.
55
Wall microphones: type, parameter
```
Capacitor microphone
Dead volume (volume between measurement point and membrane, needs to be reduced for better frequency response, equal for arrays
```
56
Max frequency for pressure sensors
1000Hz
57
Tool for resistance measurement for hot wires
Wheatstone bridge
58
Wheatstone bridge in balance when
U_B=0
59
Types of anemometer for hot wires
Constant Current Anemometer -> small quick fluctuations, limited in frequency by thermal inertia.
Constant Temperature Anemometer -> standard, no thermal inertia influence
60
Overheat ratio
Rw/R3=1+alpha(T-Ta)
| Higher ratio improves response but decreases lifetime
61
Influences on quality of hot wire measurements
Overheat ratio
Geometry, sleeves
Anemometer quality
Calibration: velocity, dynamic calibration
62
Hot wire in turbulence
Reynolds decomposition of voltage, calculation of turbulence level without calibration.
63
Hot wire measurement of very low turbulent intensities
Parallel hot wire probe. Cross correlation technique. Tu= .1-.2%
64
Hot film
Metallization of thin nickel layer on quartz substrate
65
Advantages/disadvantages of HWA
Unbeatable frequency, excellent signal to noise ratio, analog output
Intrusive, not sense-specific, calibration, sensitive to T, pointwise, sensitive to particles
66
% skin friction on commercial aircraft
50% of the flow resistance
67
Skin friction due to
wall shear stress
68
Viscous sublayer
y+<=5
69
Property of turbulent flows
Asymmetrical PDF of wall shear stress
70
Wall shear stress measurement devices
Wall shear stress balances
Hot films, hot wires (surface, pulse, wall)
Pressure sensor (Preston, surface fence, Stanton, surface)
Optical (oil film, LDA, micro pillar)
71
Measurement of direction of tau_W
V-shaped hot film (2 sensors)
| Hot film oriented in stream wise direction
72
Preston sensor
Pitot tube on wall
73
Diameter ratio for pitot tubes
d/D= .6
74
Advantage of surface fences
Relatively insensitive to varying boundary conditions -> can be used in more complex flows
75
Oil film laser interferometry
Tau_W from gradient dy/dx
76
Flow rate measurements
Turbine-/impeller-type meters
| Differential pressure measurement, Venturi nozzle and tube
77
Pressure losses in differential pressure measurements
prop to square of volume flux
78
Viscosity effects in differential pressure measurements
Higher power requirements
Recirculation bubbles
Narrower cross section (mu=A2/A0, m=A1/A0)
79
Flow coefficient
Combines all correction factor in estimation of volume flux in differential pressure measurement.
80
Venturi nozzle
Separation prevented with curved entrance section
81
Most significant deviation of flow coefficient
Swirl components -> use of flow straighteners
82
Design parameter of flow straightener
L>2D
83
Purpose of visualization techniques
Qualitative analysis
Preliminary information
Quantitative information in some cases
84
Types of visualization techniques
Surface
Density based
Tracers
85
Surface visualization techniques
Wool threads
Oil film
PSP, TSP
86
PSP principle
Oxygen quenching. p/,pO/,I\
87
TSP principle
Thermal quenching, T/, I\
88
Identification of flow structures with oil film visualization
Distribution on surface or drying speed
89
Important by oil film visualization technique
Oil viscosity, must remain on surface but be affected by local flow structures
90
Density based visualization techniques
Shadowgraphy
Schlieren
Mach-Zehnder Interferometer
Moiré or Ronchi interferometer
91
Density changes caused by...
Compressibility effects, temperature variations, concentration variations
92
Principle of Schlieren
Density gradients distorts collimated light which focuses imperfectly. Resulting pattern is a planar distribution of grey levels.
93
Moiré or Ronchi interferometer principle
Pattern gets deformed when visualized through a field of variable density
94
Mach Zehnder interferometer in practice
Slight tilt of one mirror by angle alpha induces a phase shift and interference pattern with fringe distance Delta x = lambda/alpha
Density gradients induce deviation from reference line proportional to local density.
95
Pathline
Trajectory of a single particle as a function of time
96
Streakline
All particles that have passed through one point. Sum of pathlines of single particles from that point.
97
Timeline
Set of oarticles set at an instant in time and displaced in time
98
Streamline
Tangent is parallel to local velocity at that point
99
Flow lines in stationary flows
Pathlines, streamlines, streaklines coincide
100
Introduction of particles
Far enough upstream, at average velocity, upstream of contraction ratio in wind tunnels
101
Flow lines in turbulent flows
Too strong mixing -> anisotropic particles such as aluminum flakes
102
Acronym laser
Light Amplification by Stimulated Emission of Radiation
103
Specific qualities of lasers
```
Coherence
Monochromatic
Small divergence
Extreme short pulse duration
High intensities
```
104
Condition for interference
Spatial coherence
| Polarization
105
Proportionality of emission of LIF
To concentration and temperature
106
Neutrally buoyant particles
Have no slip velocity up-uf
107
Particles response time for turbulent flows
Should be in the same order of magnitude as the characteristic flow time tau_f. Stoke number=tau/tau_f< 1%
108
Maximum acceptable particle diameter for turbulent flow tracing
Depends on the smallest eddies at which significant turbulent kinetic energy exists
109
PTV
Particle tracking velocimetry
| Follows one particle in a known time
110
Tracer selection
Follow the flow: small, density close to fluid
| Scatter light: big, large differences in refractive indices
111
Light scattered by small particles is a function of
```
Ratio of refractive indices
size
shape
orientation
Polarization
Observation angle
Laser power
```
112
Tracer stokes number
Tau/tau_F= change in flow speed with time/how good can the particle follow<.1
113
Origin of wave diffraction
Bending around small obstacles
| Spreading past small openings
114
Particle image scales with
Particle diameter
Light intensity
Distance particle camera
115
Improper focusing
Particle image becomes gradually darker, blurry.
116
Particle image density for different techniques
Low Nsource<=10 PIV
| High Ns>1 laser speckle velocimetry
117
Important properties of light source for tracer illumination
Short pulse
High power
Uniformity in measurement plane
Narrow light sheet
118
Optimal pulse delay by PIV
Compromise between
Reasonable particle displacement
Loss of particles
Realtive error decreases with delay increasing
Approximation with finite difference: error / with delay \
119
Imperfect images in PIV
Lens aberrations, limited optical access
120
Displacement-correlation peak detectability
Ratio of the highest correlation peak to the second highest
121
Loss of correlation due to
Out of plane motion, in plane motion.
122
PIV multipass
Window shifting in 2nd exposure -> weak influence of inplane losses
With shifting: velocity=window shift+highest correlation
123
Multigrid PIV
Sub domain can only host one particle
124
Dynamic range by PIV
(Delta Xmax - Delta Xmin)/Delta Xmin
125
Spurious vector in PIV occur with...
random acceleration peak exceeds amplitude of displacement correlation peak because of insufficient particle images, large displacements, high spatial velocity gradient, strong background, light sheet inhomogeneity. About 5% in good PIV
126
Limitations of PIV
Velocity gradients (BL)
Pixel blur at wall
Inhomogenous seeding density
Peak locking
127
Assumptions in PIV
Uniform displacement within interrogation region
Tracers follow flow
Homogeneous distribution
128
LDA response to particle velocity
Linear -> no calibration
129
Fringe spacing depends on
Laser wavelength, half beam intersection angle
130
Doppler signal in fringe pattern
Particles going through the fringe pattern in the measurement volume will scatter light with a frequency proportional to its velocity perpendicular to the fringe planes.
131
Doppler fringe signal split up
Pedestal, modulation.
132
Measuring volume is defined by....
Amplitude of the modulation (e-2 of max)
133
From of measuring volume
Elipsoid
134
Detection volume
Elipsoid exceeding signal threshold, depends on particle.
135
LDA MV optimization
Beam waist
| Beam expansion before focus
136
LDA amplitude depends on
Particle size
137
Directional sensitivity in LDA
Slight frequency shift with Bragg cell -> fringes are moving
138
Difference between signal and data processing
Signal : estimates characteristic parameters from signal such as velocity of particle
Data: use these parameters from many signals to derive flow related quantities such as statistical properties
139
Unique for LDA data processing
Irregular sample times
| Correlation of particles arrival rate correlated with velocity
140
Doppler burst signal is used to...
Determinate the particle's velocity, arrival time, residence time, evtly acceleration
141
Refractive index matching
Mix 2 Diesel oils, exact adjustment to Duran glass n with temperature
142
Advantages of LDA
```
Non-intrusive
No calibration
High spatial and temporal accuracy
Simultaneous multi-component
Reverse flow possible
```
143
Disadvantages LDA
```
Noisier than hot wire
Careful seeding
Velocity gradients (integration over MV, leads to overestimation of mean and variance)
Optical access
Expensive and complex
```
144
Turbulence arise from
High Re
145
Taylor's frozen field hypothesis
Move a probe rapidly through the flow if rapid enough
146
Reynolds shear stress
av(u1'u2') = R.u1,rms.u2,rms
147
Correlation in Reynolds shear stress
Negative correlation (ejection, sweep)
148
Assumptions for Bernouilli equation
stationary flow
Non viscous fluid
Constant density
Along streamline
149
Hydrostatic pressure
Pressure inside the fluid
150
Error in liquid manometers
Due to meniscus
151
Image calibration in PIV
Coordinate transformation with grid
152
PIV is considered non-intrusive because...
Concentrations <10^-6 particles per m3
153
Amplitude distribution in beam waist
Gaussian beam: strong increase
154
LDA in practice
Not a point measurement
Limited temporal resolution because of sampling frequency
Noise from detector, multiple particles, electronics, ambient light
Particles may not follow the flow!
155
Bernouilli equation derivation
From Euler equation with hypotheses of stationarity, 1D.
| Integration along a streamline. g.s=g.h.
156
Mean Square error
av((av(uM)-av(u))^2)=2av(u'^2)Lt/T
157
Prevent flow separation in wind tunnel
Wide angle diffusor: screens, turbulence generators, slits
| Fan: long nacelle
158
Statistically independent samples
N=T/2Lt
| Sampling once every two Lt is adequate
159
Normalized autocorrelation with
Variance^2 (urms^2)
