Applied Fluid Mechanics Flashcards
Types of measurement quantities
Local, global
Direct, indirect
Purpose of measurements
Validation: were the correct equations solved ?
Verification: were the equations solved correctly?
3 steps of DoE
Isolate the phenomenon
Choose the right tool for the problem
Design the experiment backwards
St
Strouhal number
Oscillating velocity/mean velocity
For oscillating flows
Eu
Euler number
Pressure forces/inertial forces
For pumps, cavitation
Re
Reynolds number
Inertial forces/viscous forces
Almost always used
Fr
Froude number
Kinetic energy/potential energy
For free surface flows, where gravity is important.
Ma
Mach number
Flow velocity/sonic velocity
For compressible flows (Ma>0.2)
Similar solution
When two flows with same BC also have same Re, St, Ma and Fr.
Buckingham Pi-Theory
Pi=n-r
Pi: nb of dimensionless quantities
n: nb of influencing quantities
r: nb of basic quantities (MLT)
Requirements on wind tunnels
Reproduction of the problem’s flow
Defined conditions (perfect, worst case)
Transferability
Eiffel type: class, parts
Open-circuit
Inlet, settling chamber, test section, fan, diffusor
Blower tunnel
Fan at entrance-> no diffuser/test section necessary
Göttinger type
Closed loop
Corner vanes
Heat exchanger
Wide angle diffuser
Ma dependences in supersonic tunnels
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.
Supersonic tunnels: characteristics, types
Convergent-divergent nozzle upstream of test section, diffuser with second throat (breakdown shock)
Blow-down, suck-down
Pressure tunnels: types
Low density
High-speed
Turbulence dissipates
turbulent kinetic energy into heat
Turbulence energy transfer cascade process
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.
Diffusivity in turbulence
Increased rates of momentum, heat and mass transfer. Increase of exchange surface.
Turbulent Reynolds number
uL/nu
Molecular diffusion time scale/ turbulence time scale
Meaning of RMS
Standard deviation
Turbulence level
Tu,i = u_i,rms/u_1,av
Nyquist criteria
f_sampling>2f_max
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.
L_t
Integral time scale
Rough measure of the interval over which the velocity u(t) is correlated with itself.
Skewness
Describes symmetry of PDF
=0 for Gauss
av(a^3)/arms^3
Flatness/Kurtosis
Describes width of PDF
=3 for Gauss
av(a^4)/a_rms^4
Method for calculating autocorrelation R
Align graphically the series u’(t) with u’(t+tau), multiply them vertically and compute the average product.
Normalized function condition
<=1
Autocorrelation of stationary process: characteristic
Symmetry around tau=0 where r=1
Energy spectrum: operation
Fourier transform of autocorrelation function.
Energy spectrum and autocorrelation function are a Fourier transformation pair.
Integral of all energy spectrum is
Turbulent kinetic energy and R(tau=0)
Energy spectrum of spatial autocorrelation is function of
Wavenumber vector Kj
Total turbulent shear stress
Molecular momentum transport (viscosity and grad) + turbulent momentum transport (fluctuations)
Velocity profile close to the wall
Depends only on local relevant parameters, not on free stream velocity of channel height/boundary layer thickness.
Wall shear velocity
u_tau=sqrt(tau_W/rho)
Viscous units
u+=avg(u_1)/u_tau
y+=y.u_tau/nu
Universal law of the wall
Log region
u+=1/K ln y+ + C
Layers of turbulent BL
Viscous sublayer: y+>nu_t u+=y+
Buffer region: 550 nu«nu_t u+=1/K.ln(y+) + C
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.
Variation of pressure in wall-normal direction
None (boundary layer theory according to Prandtl)
p at wall = p in free stream
Reference form of wall tappings
Perfect straight drill
Dependencies of p error in wall tappings
Diameter, length, burr height, velocity utau
Method for calculating Delta p
Calculate all dimensionless parameter in Pi equation
Read Pi on diagram of relevant tapping
Static pressure measurements access
Wall tappings
Static pressure tube
PSP
Problem with static pressure tubes
Blockage effect from shaft and head
Assumption with pitot tubes
Hydrostatic pressure can be neglected
Dependency of ptot in pitot tubes
Flow angularity Diameter ratio (.6)
Conrad sensor
2 slanted pitot tubes
+: no angle dependency
-: linear angle dependency
Condition for velocity measurement with pitot tube, solutions
Static pressure is known
Wall taping, prandtl tube.
Pressure transducers
Liquid manometers
Spring manometers
Multi-point pressure measurements
Wall microphones
Types of liquid manometers
Cistern (diff. areas)
Bets
Inclined tube
Types of spring manometers
Plate, membrane, spring
Bourdon (circular tube)
Electromechanical (strain gauge, induction)
Multi-point pressure measurement
Scani valve, electronic scanning system
Stationary: tapping connected with tube. Instationary: wall microphone.
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
Max frequency for pressure sensors
1000Hz
Tool for resistance measurement for hot wires
Wheatstone bridge
Wheatstone bridge in balance when
U_B=0
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
Overheat ratio
Rw/R3=1+alpha(T-Ta)
Higher ratio improves response but decreases lifetime
Influences on quality of hot wire measurements
Overheat ratio
Geometry, sleeves
Anemometer quality
Calibration: velocity, dynamic calibration
Hot wire in turbulence
Reynolds decomposition of voltage, calculation of turbulence level without calibration.
Hot wire measurement of very low turbulent intensities
Parallel hot wire probe. Cross correlation technique. Tu= .1-.2%
Hot film
Metallization of thin nickel layer on quartz substrate
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
% skin friction on commercial aircraft
50% of the flow resistance
Skin friction due to
wall shear stress
Viscous sublayer
y+<=5
Property of turbulent flows
Asymmetrical PDF of wall shear stress
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)
Measurement of direction of tau_W
V-shaped hot film (2 sensors)
Hot film oriented in stream wise direction
Preston sensor
Pitot tube on wall
Diameter ratio for pitot tubes
d/D= .6
Advantage of surface fences
Relatively insensitive to varying boundary conditions -> can be used in more complex flows
Oil film laser interferometry
Tau_W from gradient dy/dx
Flow rate measurements
Turbine-/impeller-type meters
Differential pressure measurement, Venturi nozzle and tube
Pressure losses in differential pressure measurements
prop to square of volume flux
Viscosity effects in differential pressure measurements
Higher power requirements
Recirculation bubbles
Narrower cross section (mu=A2/A0, m=A1/A0)
Flow coefficient
Combines all correction factor in estimation of volume flux in differential pressure measurement.
Venturi nozzle
Separation prevented with curved entrance section
Most significant deviation of flow coefficient
Swirl components -> use of flow straighteners
Design parameter of flow straightener
L>2D
Purpose of visualization techniques
Qualitative analysis
Preliminary information
Quantitative information in some cases
Types of visualization techniques
Surface
Density based
Tracers
Surface visualization techniques
Wool threads
Oil film
PSP, TSP
PSP principle
Oxygen quenching. p/,pO/,I\
TSP principle
Thermal quenching, T/, I\
Identification of flow structures with oil film visualization
Distribution on surface or drying speed
Important by oil film visualization technique
Oil viscosity, must remain on surface but be affected by local flow structures
Density based visualization techniques
Shadowgraphy
Schlieren
Mach-Zehnder Interferometer
Moiré or Ronchi interferometer
Density changes caused by…
Compressibility effects, temperature variations, concentration variations
Principle of Schlieren
Density gradients distorts collimated light which focuses imperfectly. Resulting pattern is a planar distribution of grey levels.
Moiré or Ronchi interferometer principle
Pattern gets deformed when visualized through a field of variable density
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.
Pathline
Trajectory of a single particle as a function of time
Streakline
All particles that have passed through one point. Sum of pathlines of single particles from that point.
Timeline
Set of oarticles set at an instant in time and displaced in time
Streamline
Tangent is parallel to local velocity at that point
Flow lines in stationary flows
Pathlines, streamlines, streaklines coincide
Introduction of particles
Far enough upstream, at average velocity, upstream of contraction ratio in wind tunnels
Flow lines in turbulent flows
Too strong mixing -> anisotropic particles such as aluminum flakes
Acronym laser
Light Amplification by Stimulated Emission of Radiation
Specific qualities of lasers
Coherence Monochromatic Small divergence Extreme short pulse duration High intensities
Condition for interference
Spatial coherence
Polarization
Proportionality of emission of LIF
To concentration and temperature
Neutrally buoyant particles
Have no slip velocity up-uf
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%
Maximum acceptable particle diameter for turbulent flow tracing
Depends on the smallest eddies at which significant turbulent kinetic energy exists
PTV
Particle tracking velocimetry
Follows one particle in a known time
Tracer selection
Follow the flow: small, density close to fluid
Scatter light: big, large differences in refractive indices
Light scattered by small particles is a function of
Ratio of refractive indices size shape orientation Polarization Observation angle Laser power
Tracer stokes number
Tau/tau_F= change in flow speed with time/how good can the particle follow<.1
Origin of wave diffraction
Bending around small obstacles
Spreading past small openings
Particle image scales with
Particle diameter
Light intensity
Distance particle camera
Improper focusing
Particle image becomes gradually darker, blurry.
Particle image density for different techniques
Low Nsource<=10 PIV
High Ns>1 laser speckle velocimetry
Important properties of light source for tracer illumination
Short pulse
High power
Uniformity in measurement plane
Narrow light sheet
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 \
Imperfect images in PIV
Lens aberrations, limited optical access
Displacement-correlation peak detectability
Ratio of the highest correlation peak to the second highest
Loss of correlation due to
Out of plane motion, in plane motion.
PIV multipass
Window shifting in 2nd exposure -> weak influence of inplane losses
With shifting: velocity=window shift+highest correlation
Multigrid PIV
Sub domain can only host one particle
Dynamic range by PIV
(Delta Xmax - Delta Xmin)/Delta Xmin
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
Limitations of PIV
Velocity gradients (BL)
Pixel blur at wall
Inhomogenous seeding density
Peak locking
Assumptions in PIV
Uniform displacement within interrogation region
Tracers follow flow
Homogeneous distribution
LDA response to particle velocity
Linear -> no calibration
Fringe spacing depends on
Laser wavelength, half beam intersection angle
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.
Doppler fringe signal split up
Pedestal, modulation.
Measuring volume is defined by….
Amplitude of the modulation (e-2 of max)
From of measuring volume
Elipsoid
Detection volume
Elipsoid exceeding signal threshold, depends on particle.
LDA MV optimization
Beam waist
Beam expansion before focus
LDA amplitude depends on
Particle size
Directional sensitivity in LDA
Slight frequency shift with Bragg cell -> fringes are moving
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
Unique for LDA data processing
Irregular sample times
Correlation of particles arrival rate correlated with velocity
Doppler burst signal is used to…
Determinate the particle’s velocity, arrival time, residence time, evtly acceleration
Refractive index matching
Mix 2 Diesel oils, exact adjustment to Duran glass n with temperature
Advantages of LDA
Non-intrusive No calibration High spatial and temporal accuracy Simultaneous multi-component Reverse flow possible
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
Turbulence arise from
High Re
Taylor’s frozen field hypothesis
Move a probe rapidly through the flow if rapid enough
Reynolds shear stress
av(u1’u2’) = R.u1,rms.u2,rms
Correlation in Reynolds shear stress
Negative correlation (ejection, sweep)
Assumptions for Bernouilli equation
stationary flow
Non viscous fluid
Constant density
Along streamline
Hydrostatic pressure
Pressure inside the fluid
Error in liquid manometers
Due to meniscus
Image calibration in PIV
Coordinate transformation with grid
PIV is considered non-intrusive because…
Concentrations <10^-6 particles per m3
Amplitude distribution in beam waist
Gaussian beam: strong increase
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!
Bernouilli equation derivation
From Euler equation with hypotheses of stationarity, 1D.
Integration along a streamline. g.s=g.h.
Mean Square error
av((av(uM)-av(u))^2)=2av(u’^2)Lt/T
Prevent flow separation in wind tunnel
Wide angle diffusor: screens, turbulence generators, slits
Fan: long nacelle
Statistically independent samples
N=T/2Lt
Sampling once every two Lt is adequate
Normalized autocorrelation with
Variance^2 (urms^2)
