Fluid mechanics

A combination of a source and a sink of equal strength, where the distance between them a -> 0

Where velocity due to the uniform flow and velocity due to the source cancel eachother out

• 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 

• 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
• 

Yes, because rotation refers to the orientation of the flow element, not the path followed by the element

2 pi b

• Combines a doublet with a uniform flow
• 

• Vortex + stationary flow past cylinder
• (ie vortex + doublet + uniform flow)
• 

• 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

• 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
• Continuous signal

• - 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

• - 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

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.

• 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.

• 1D: Minature, Film, Gold plated, hybrid
• 2D, 3D
• 

• Non-intrusive measurements (optical
• technique)
• Absolute measurement technique (no
• calibration required)
• V high accuracy
• V high spatial resolution due to small
• measurement volume
• Tracer particles (seeding) are required
• Can be 1, 2 or 3D depending on the number of paired beams directed at
• the measurement volume

• Forward scatter
• -  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

• Backward scatter
• -  Easy to align optics and whole system is more user friendly
• -  Not so much space required
• -  Less light collected

• 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

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)

• +ves
• Non-intrusive measurement
• High spatial and temporal resolution
• No need for calibration
• Ability to measure in reversing flows

• -ves
• 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.

• Industrial: investigate technical problems, check technical specifications, verify performance, improve performance
• 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

• 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:
•  relatively inexpensive
•  better frequency response
•  can be repaired

• Use film probes for rough environments
•  more rugged
•  worse frequency response
•  cannot be repaired
•  electrically insulated
•  protected against mechanical and chemical action

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.

• +ves
• non intrusive, good correlation, fast tracking, vortical recognition, stereoscopic approach permits all three velocity components to be recorded.

• -ves
• 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

• Monochrome (wavelength = l)
• Coherent
• Linearly polarised
• 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

• Backscatter
• - 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 = 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.

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)

M = 

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