Lecture 3: Fundamentals of Fluid Flow: fluid properties and types; Boundary layer structure; unidirectional flows

Transcription

1 GEOL 440 Sedimentology and stratigraphy: processes, environments and deposits Lecture 3: Fundamentals of Fluid Flow: fluid properties and types; Boundary layer structure; unidirectional flows

2 Why study process?: linking form to mechanism Fluid Flow (Turbulence) coherent turbulent structures, Reynolds stresses turbulence enhancement & attenuation Fluid Turbulence large-scale outer layer structures?? flow separation form roughness, eddy shedding, outer flow structures local transport rate flow separation Sediment Transport Bed Morphology

3 So, what do we need to know: Flow types Flow processes How these control sediment movement or control/influence sedimentation How these are represented in the rock record

4 To begin: What forces control the behavior of fluids: Inertial forces Gravitational forces Viscous forces

5 Osborne Reynolds ( )

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7 Laminar versus Turbulent flow How do we characterise these? Reynolds number: Re = ρul μ inertial forces (= resistance to fluid acceleration) viscous forces (resistance to fluid deformation) where ρ = density, u = velocity, l = length scale, μ = molecular viscosity If.. Re < <Re<2000 Re > 2000 laminar transitional turbulent But why is this important?

8 Laminar and turbulent flows have different ability to support particles of a particular size distance of sediment transport The deposits of laminar and turbulent flows may have different geometry (laminar) debris flow versus (turbulent) turbidity current The deposits of laminar and turbulent flows may have different internal organisation laminated and massive beds, clean (mud-poor) sand versus dirty (mud-rich) sand The deposits of laminar and turbulent flows may have different textural properties heterogeneities, granulometric trends, permeability barriers, pore fluid flow

9 Life in high Reynolds number flows car dog

10 Life in low Reynolds number flows

11 Influence of gravity expressed by the Froude number, Fr = inertial William Froude ( ) Fr = u gl inertial forces (= resistance to fluid acceleration) gravitational forces where u = velocity, l = length scale, g = acceleration due to gravity viscosity

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14 Froude number: some examples in rivers Fr = 1.2 Fr = 0.4 Fr 0.8

15 Newtonian/non-Newtonian fluids Bingham plastic non-newtonian: pseudo-plastic, shear-thinning apparent viscosity decreases with shear rate (mayonnaise) Newtonian constant mol. viscosity non-newtonian: dilatant, shear-thickening apparent viscosity increases with shear rate shear rate (fluid deformation) 15

16 BEWARE!! Laminar = Non-Newtonian

17 SOME EXAMPLES Turbulent, Newtonian flows: River flows Low-density turbidity currents Air flows Laminar, Newtonian flows: Low-velocity contour currents Pore fluid flows Settling river plumes Shear-thickening flows: Grain flows Shear-thinning flows: Basal part of high-density turbidity currents Muddy debris flows with cohesive strength

18 Turbulent, Newtonian flow density (turbidity) current

19 Turbulent, Newtonian flow fluvial current

20 Shear-thinning non-newtonian flow muddy debris flow previous pulse new pulse

21 Shear-thickening non-newtonian flow grain flow water surface sand avalanche flow direction 7 cm dune base of flume 21

22 Daniel Bernoulli ( ) Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases.

23 Flow over a fixed boundary.

24 u =(τ/ρ) 0.5 τ =ρdu/dy log y dy du y o or roughness height U

25 To derive the bed shear stress: 1) Depth slope produce: τ =ρgys 2) Velocity profile: will look at this in lab class

26 Structure of Turbulent Boundary Layer y outer flow Root-mean-square velocity fluctuations.. turbulence intensity U turbulence generation layer viscous sublayer

27 Velocity as a vector quantity w v u u = downstream v = vertical (positive for upwards flow) w = cross-stream (positive for flow towards the right bank)

28 EACH velocity component can be split into a mean and fluctuating part: i.e. u = u mean +/- u u = u mean +/- u v = v mean +/- v w = w mean +/- w v mean = 0 If we simplify and consider downstream and vertical components of flow (u and v) τ r = ρu v..thus provides a turbulent shear stress Reynolds stress

29 Flow Separation: separation reattachment

30 Flow Separation:

31 Flow Separation:

32 Shear layers and Kelvin-Helmholtz instabilities c.3 km

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34 Flow Separation and KH importance in sedimentology: Think about location and magnitude of maximum turbulent shear stresses

35 Boundary layers and roughness (grains): Roughness increases vertical mixing and may destroy viscous sublayer

36 Main issues from this lecture. Flow types and states Flow Separation Velocity profile and bed shear stress Reading: B&D, Chapter 5, p ; Boggs Chapter 2, 21-33