Fluid mechanics

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  1. Doublet (definition)
    A combination of a source and a sink of equal strength, where the distance between them a -> 0
  2. Stagnation point (definition)
    Where velocity due to the uniform flow and velocity due to the source cancel eachother out
  3. 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)
  4. Bernoulli's equation
    Image Upload 1
  5. Vortex (definition)
    A flow in which the streamlines are concentric circles Image Upload 2
  6. Source or sink
    • Fluid flowing radially outward from the origin Image Upload 3
    • Volumetric flow rate, per unit length, (m) is given by Image Upload 4
    • +ve m = strength of the source
    • -ve m = strength of the sink
    • Image Upload 5
  7. Vortex - flow defined by?
    Image Upload 6Image Upload 7
  8. Is a vortex irrotational?
    Yes, because rotation refers to the orientation of the flow element, not the path followed by the element
  9. Doublet - flow defined by?
    Image Upload 8Image Upload 9
  10. Flow past a half-body
    Image Upload 10
  11. Flow past a half body diagram
    Image Upload 11
  12. Equation of the streamline passing
    through the stagnation point
    Image Upload 12
  13. Max width of the half-body
    2 pi b
  14. Streamlines around half body
    Image Upload 13
  15. Flow around a stationary cylinder
    • Combines a doublet with a uniform flow
    • Image Upload 14
  16. Flow past a rotating cylinder
    • Vortex + stationary flow past cylinder
    • (ie vortex + doublet + uniform flow)
    • Image Upload 15
  17. Streamline patterns dep't on circulation
    Image Upload 16

    Image Upload 17
  18. 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
  19. 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
    • Continuous signal
  20. 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
    • Image Upload 18

    The probe is one arm of a Wheatstone Bridge - as the velocity increases, the resistance decreases
  21. 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
  22. 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.
  23. 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.
  24. Hot wire anemometry - Types of probes?
    • 1D: Minature, Film, Gold plated, hybrid
    • 2D, 3D
    • Image Upload 19
  25. Laser Doppler Anemometry (LDA)
    • 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
  26. Advantages and disadvantages with the use of forward and backscatter configurations for experimental velocity measurements when using LDA
    • 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
  27. 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
  28. Stokes and Eulers eqns
  29. 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)
  30. LDA advantages and disavantages
    • +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.
  31. Why measure?
    • 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
  32. 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:
    •  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
  33. Principles of LDA
    Image Upload 20
  34. 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.
  35. PIV +ves and -ves
    • +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
  36. Stereo PIV
    • 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

    Image Upload 21
  37. Turbulent Intensity
    • Image Upload 22
    • u rms = √(u' bar²)/u bar
  38. Laser for LDA
    • Monochrome (wavelength = l)
    • Coherent
    • Linearly polarised
    • Low divergence (collimator)
    • Gaussian intensity distribution
  39. LDA particles
    • - 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
  40. Bragg cell
    • 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.
  41. LDA Configurations
    • Forward scatter and side scatter (off-axis)
    • - Difficult to align,
    • - Vibration sensitive

    • Backscatter
    • - Easy to align
    • - User friendly
    • Image Upload 23
  42. Eddy
    • An eddy describes the motion of a limited
    • volume of fluid that breaks away from its surroundings due to some disturbance.
  43. RMS
    Image Upload 24
  44. Velocity at a point
    • Velocity at a point = steady (mean)
    • component + instantaneous turbulent component
  45. Turbulence:


    TIx = TIy = TIz    at a given point

    TIx,TIy and TIz have the same three values at all points in the fluid.
  46. Turbulence intensity
    Image Upload 25
  47. 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  Image Upload 26 (where Image Upload 27)

    The resulting Mach number Image Upload 28 may be greater than one.Image Upload 29
  48. Mach number
    Ratio of speed of an object moving through a fluid and local speed of sound (in the medium)

    M = Image Upload 30
  49. Subsonic
    Mach number < 1, lower than the speed of sound

    Image Upload 31 and Image Upload 32 have the opposite sign, as when the pipe expands, the velocity decreases; when the pipe size decreases, the velocity increases
  50. Supersonic
    Mach no > 1, higher than the speed of sound

    • Image Upload 33 and Image Upload 34 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
  51. Sonic
    Mach number ~ 1

    Image Upload 35
  52. Shockwave
    Sudden discontinuities in pressure, density and velocity
Card Set
Fluid mechanics
fluid mechanics
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