A combination of a source and a sink of equal strength, where the distance between them a -> 0
Stagnation point (definition)
Where velocity due to the uniform flow and velocity due to the source cancel eachother out
Ideal fluid flow assumes that..?
Fluid is incompressible (Div u = 0)
No viscous effects affecting the flow (n=0)
Flow field is irrotational (vorticity = 0, Curl u = 0)
A flow in which the streamlines are concentric circles
Source or sink
Fluid flowing radially outward from the origin
Volumetric flow rate, per unit length, (m) is given by
+ve m = strength of the source
-ve m = strength of the sink
Vortex - flow defined by?
Is a vortex irrotational?
Yes, because rotation refers to the orientation of the flow element, not the path followed by the element
Doublet - flow defined by?
Flow past a half-body
Flow past a half body diagram
Equation of the streamline passing
through the stagnation point
Max width of the half-body
2 pi b
Streamlines around half body
Flow around a stationary cylinder
Combines a doublet with a uniform flow
Flow past a rotating cylinder
Vortex + stationary flow past cylinder
(ie vortex + doublet + uniform flow)
Streamline patterns dep't on circulation
Hot wire anemometry
Used to measure and analyse the microstructures in turbulent gas and liquid flows
Based on heat conducted in a tiny thread
Works on the principle that the heat lost (convection) is a function of the velocity of the fluid.
Records instantaneous velocity at a point - can be used for statistical analysis to describe the flow conditions
Can be constant current (CCA) or, more usually, constant temperature (CTA) probe
Each probe has to be individually calibrated
Hot wire anemometry pro's
Fast response rate (400Hz fluctuations measured)
High spatial resolution (small eddies to 1/10mm can be seen)
Little disturbance of the flow due to small sensor size
High dynamic range - velocities from cm/s to 100s of m/s can be measured w almost constant sensitivity
Hot wire anemometry - Principles of operation
- Thin wire is mounted in supports and placed in the flow
- Power through wire related to heat transfer
- Heat transfer related to the velocity of the fluid
The probe is one arm of a Wheatstone Bridge - as the velocity increases, the resistance decreases
Hot wire anemometry - assumptions
- Heat transfer mainly via convection, ie
- Radiation losses are small
- Conduction loss to supports = small
- Fluid has constant properties
- Velocity = normal to wire, does not change over the length of the probe
Relationship between the resistive/drag forces acting on an object and the physical properties of the fluid
The resistice forces acting on an object are related to the drag coefficient. Since this depends on Re, the density and viscosity of the fluid affect the resistive forces/drag.
Hot wire anemometry considerations
Wire should be as short as possible
Aspect ratio (l/d) should be high (to minimise the effects of end losses)
Wire should resist oxidation until high temperatures (needs good sensitivity, high signal to noise ratio)
Temperature coefficient of resistance should be high (for high sensitivity, signal to noise ratio and frequency response)
Wires of less than 5 µm diameter cannot be reliably drawn.
Hot wire anemometry - Types of probes?
1D: Minature, Film, Gold plated, hybrid
Laser Doppler Anemometry (LDA)
Non-intrusive measurements (optical
Absolute measurement technique (no
V high accuracy
V high spatial resolution due to small
Tracer particles (seeding) are required
Can be 1, 2 or 3D depending on the number of paired beams directed at
the measurement volume
Advantages and disadvantages with the use of forward and backscatter configurations for experimental velocity measurements when using LDA
- Optics are more difficult to align
- Vibration sensitive
- More space is required to accommodate both nets of optics
- High data rates are possible because more light can be collected - forward scatter ensures the maximum amount of light is recieved by the optics
- Easy to align optics and whole system is more user friendly
- Not so much space required
- Less light collected
Briefly discuss the benefits of non-dimensionalising Navier Stokes eqns to introduce Reynolds number
It introduces a basis of dynamic similarity between two viscous flows. Geometrically similar situations can be modelled. This can be done if similar kinematic boundary conditions are used. Scaling can be considered.
Simplified -> Stokes and Eulers eqns
Stokes and Eulers eqns
Particle Image Velocimetry
Flow is illuminated in the target area with a light sheet, cross-correlating the interrogation areas from each pulse of light allows particle displacement (hence velocity) to be found.
- Non-intrusive measurements (optical technique)
- Calibration required for high accuracy.
- V high spatial resolution due to small measurement volume
- Tracer particles (seeding) are required
- Use of a stereoscopic approach permits all three velocity components to be recorded (for normal PIV = two)
LDA advantages and disavantages
High spatial and temporal resolution
No need for calibration
Ability to measure in reversing flows
Complicated to use
Needs lots of space around the pipe for the optics, particularly in forward scatter mode. . Not possible unless optical access available within the pipe.
Engineering: determine parameters in turbulence mode, develop, extend, refine models, investigate model limits
Theoretical fluid mechanics :verify model predictions, verify theoretical predictions, verify new concepts
Conceptual ideas: search for new ideas
Probe selection - Hot wire anemometry
Probes are primarily selected on basis of:
Fluid medium; 1D/2D/3D; Expected velocity range; Quantity to be measured (velocity, wall shear stress, etc); Required spatial resolution; Turbulence intensity and fluctuation frequency in the flow; Temperature variations; Contamination risk; Available space around the measuring point
Use wire probes whenever possible:
better frequency response
can be repaired
Use film probes for rough environments
worse frequency response
cannot be repaired
protected against mechanical and chemical action
Principles of LDA
Non intrusive technique, 3D, high accuracy, laser beams intersect and create a measurement volume with a Gaussian intensity distribution.The light is scattered and measured with a particular frequency. The system gives velocity and size of particle.
PIV +ves and -ves
non intrusive, good correlation, fast tracking, vortical recognition, stereoscopic approach permits all three velocity components to be recorded.
careful __ seed size, a lot of memory required, powerful lasersPIV for 3D
Stereoscopic PIV utilises two cameras with separate viewing angles (ideally 90° apart) to extract the z-axis displacement of the particles.
The lens plane and object plane intersect in a common line. Therefore, the resulting planes provide the mapping of the real velocity.
Both cameras must be focused on the same spot in the flow and must be properly calibrated to have the same point in focus
u rms = √(u' bar²)/u bar
Laser for LDA
Monochrome (wavelength = l)
Low divergence (collimator)
Gaussian intensity distribution
- Need to be small enough to accurately follow all the flow pattern but large enough to scatter the light effectively
- Particle v = flow v
- Particles ~ magnitude as λ of laserbeam
- Even in well seeded flows, particles = tiny % of flow, no effect upon
A Bragg cell is often used as the beam splitter. It is a glass crystal with a vibrating piezo crystal attached. The vibration generates acoustical waves acting like an optical grid.
The output of the Bragg cell is two beams of equal intensity with frequencies f0 and fshift. These are focused into optical fibres bringing them to a probe.
Forward scatter and side scatter (off-axis)
- Difficult to align,
- Vibration sensitive
- Easy to align
- User friendly
An eddy describes the motion of a limited
volume of fluid that breaks away from its surroundings due to some disturbance.
Velocity at a point
Velocity at a point = steady (mean)
component + instantaneous turbulent component
TIx = TIy = TIz at a given point
TIx,TIy and TIz have the same three values at all points in the fluid.
Explain why the flow behind a plane oblique shock wave may
be supersonic, although the flow behind a plane shock wave normal to the flow
must be subsonic
The normal component of velocity is reduced by the passage through the shock, but the tangential component is unchanged. So although (where )
The resulting Mach number may be greater than one.
Ratio of speed of an object moving through a fluid and local speed of sound (in the medium)
Mach number < 1, lower than the speed of sound
and have the opposite sign, as when the pipe expands, the velocity decreases; when the pipe size decreases, the velocity increases
Mach no > 1, higher than the speed of sound
and have the same sign, as when the pipe expands, the velocity increases
This is not in contradiction to continuity as A increases and V increases but density decreases
Mach number ~ 1
Sudden discontinuities in pressure, density and velocity