Advanced Transport Phenomena
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Advanced Transport Phenomena - Leaderboard
Advanced Transport Phenomena - Details
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| 🇬🇧 | 🇬🇧 |
| Describe what happens when an ideal fluid moves past a straight smooth solid boundary | Fluid velocity is unaffected by presence of boundary. Mutual force between fluid and solid is normal to surface. Drag is zero. |
| Give an example of a rheopectic fluid | Coal-slurries, |
| Give an example of a rheopectic fluid | Coal-slurries, |
| Describe what happens when a real fluid moves past a straight smooth solid boundary | Fluid adjacent to boundary is brought to rest (relative to boundary). Large velocity gradient exists in a thin layer of fluid near boundary, in which velocity increases from zero to free stream velocity, U. Large velocity gradient means shear stress plays a significant role in BL. Shear stress gives rise to drag force on boundary. |
| Give an example of a rheopectic fluid | Coal-slurries, |
| What are the implications of a rough boundary? | Calculations studied assume boundary is smooth. If boundary is rough, viscous sub-layer becomes disrupted. If roughness elements are large enough, they completely break up the laminar sub-layer. |
| Give an example of a rheopectic fluid | Coal-slurries, |
| Describe the pressure changes across a flat smooth boundary layer. | Since BL is thin, velocity components normal to surface are very small, hence pressure changes across BL are negligible (for flat, smooth surface, not cylinders). |
| What are the implications of a rough boundary? | Calculations studied assume boundary is smooth. If boundary is rough, viscous sub-layer becomes disrupted. If roughness elements are large enough, they completely break up the laminar sub-layer. |
| Describe the pressure changes across a curved surface, e.g. cylinder. | If the BL is curved, streamline curvature will cause velocity gradients. |
| Describe the thickness of the BL. | As velocity in BL approaches free stream aymptotically, there is no definite thickness of BL. BL does not have a uniform thickness, but develops in direction of main stream flow. Nominal thickness is defined, e.g. limit definted as point where when u=0.99u0 |
| Why are BLs important? | BLs influence drag on surface and mass and heat transfer rates. BLs in velocity gradients can be thought of as analogous to temperature gradients and concentration gradients. The 3 BL types are distinct from one another. If physical properties remain constant, then velocity BL will be unaffected by temp & conc BLs. |
| Describe the boundary layer on a flat plate | BL starts with zero thickness at leading edge. BL increases in downstream direction. Near leading edge, flow is laminar in BL. Thickness of BL increases more in turbulent area. Flow is all BLs begins as laminar, then goes through transition area where large eddies are formed, then develops into turbulent. All BLs become turbulent if surface is sufficiently long. |
| Describe skin friction in laminar flow | Skin friction is the viscous drag on a surface. It is proportional to the velocity gradient in the BL evaluated at the surface. |
| What is Inviscid flow? | These are areas of flow where viscous effects are negligible (inviscid assumption or irrotational flow region). Flow is inviscid/irrotational in regions where velocity has not yet diffused. |
| What are properties of stream functions? | Curves of constant Ψ are streamlines of the flow. Streamlines are tangent to velocity field. At steady steady: streamlines approx equal path lines. Difference in value of Ψ from one streamline to another is equal to the volume flow rate per unit width between the two streamlines. |
| What are the conditions of velocity potential? | Must be a solution of laplace equation. Satisfy boundary conditions (inviscid flow assumption), such as no flux through solid surfaces, uniform flow away from objects. Flow is determined by kinermatics only, Euler equations are a constraint on the pressure required for the flow. Can be used for uniform flows, flow around objects (cylinders) or flow around corners. |
| How do real fluids behave at the surface? | No slip conditions at surface, viscous effects generate shear at the surface. |
| What does the thickness, δ, of BL depend on? | Displacement thickness Momentum thickness Energy thickness |
| What is displacement thickness? | Displacement thickness is the distance the wall must be placed to keep the same flow rate as the inviscid flow. |
| What is momentum thickness? | Thickness such that rho * u0 *Θ^2 is a direct measure of momentum lost through viscous effects. |
| What are the assumptions for momentum applied to BL? (this is used for deriving force equation) | Steady state flow. Density constant. No pressure gradient in flow direction (only for flat plates, not cylinders). |
| What are the two dimensionless coefficients? | Skin friction coefficient, Cf. Drag coefficient, Cd. |
| What are the BL boundary conditions at y=0? | No slip at boundary surface (u=0). Shear stress at boundary must be finite (differential is finite). Equation of motion satisfied (double differential =0). |
| What are the BL boundary conditions at outer edge, y=δ? | No discontinuinity of velocity profile (u=u0). No "kink" in velocity profile (differential=0). For smooth transitions, need double differential=0. |
| What are the steps to calculate BL thickness, force, shear stress, etc? | Check BCs. Get δ* and Θ in terms of δ. Get δ. Apply to required parameter. |
| What is the multilayer model? | Multilayer model is an extension of the adaptations made with the viscous sub-layer. Approximate analysis of turbulent BL made with power law and laminar sub-layer inclusion (however still oversimplified). Investigate turbulent velocity profile in immediate vicinity of laminar sub-layer (u=δ'). |
| What are the implications of a rough boundary? | Calculations studied assume boundary is smooth. If boundary is rough, viscous sub-layer becomes disrupted. If roughness elements are large enough, they completely break up the laminar sub-layer. |
| What are the types of time dependent fluids? | Thixotropic Rheopectic |
| What is a thixotropic fluid? | Shear thinning fluids where structural interactions (apparent viscosity) decrease with time at a constant shear rate. |
| Give an example of a thixotropic fluid. | Paraffin oil, gelatine, creams. |
| What is a rheopectic fluid? | Shear-thickening fluids that increase in apparent viscosity with time, at a constant shear rate. |
| Give examples of time independent fluids | Shear-thinning Shear-thickening Viscoelastic materials - Bingham plastic & Herschel-Bulkley model |
| What are the two types of non-Newtonian fluids? | Time independent. Time dependent. |
| Give an example of a rheopectic fluid | Coal-slurries, |
| What is rheology? | Rheology is the study of deformation and flow of matter, i.e. response to stress and strain. |
| What are the motivations for rheological study? | Direct impact on design of processing equipment. Allows insight into material structure. Used in raw material and process control. Relevance to consumer acceptability. |
| What are the difficulties associated with rheology? | Very wide range of materials to study. Any material will have different rheology under different conditions (temp, pressure). |
| What are the two types of non-Newtonian fluids? | Time independent. Time dependent. |
| Give examples of time independent fluids | Shear-thinning Shear-thickening Viscoelastic materials - Bingham plastic & Herschel-Bulkley model |
| What are the types of time dependent fluids? | Thixotropic Rheopectic |
| What is a thixotropic fluid? | Shear thinning fluids where structural interactions (apparent viscosity) decrease with time at a constant shear rate. |
| Give an example of a thixotropic fluid. | Paraffin oil, gelatine, creams. |
| What is a rheopectic fluid? | Shear-thickening fluids that increase in apparent viscosity with time, at a constant shear rate. |
| Give an example of a rheopectic fluid | Coal-slurries, |
| When is the Cauchy versus Hencky form of rate of strain used? | Cauchy - for solids which remember its original shape, Lo. Hencky - for materials which do not remember Lo. |
| What is the definition of stress? | Stress = force per unit area. Units of N/m2, or Pa. It may be tensile, compressive or shear. Small element may be considered in terms of Cartesian coordinates x, y, z. |
| When are normal stresses considered positive or negative. | Positive - tensile stresses (acting outward) Negative - compressive stresses (acting inward) |
| On any given surface of an element, how many stresses are acting? | 3 stresses acting: 2 shear stresses 1 normal stress Therefore only 9 separate quantities are required to completely describe the state of stress in a material. |
| What is a elastic (Hookean) solid? | An elastic solid has no viscous properties and does not flow. Follows Hooke's law of elasticity where stress-strain curve is a straight line through the origin. Perfectly elastic: stress = constant * strain E.g. rubber. |
| What is a Newtonian liquid? | Has no elastic properties. Newtonian liquids obey Newton's law of viscosity where shear stress-shear rate curve is a straight line through origin. i.e. shear stress = constant * shear rate. E.g. water, most aqueous solutions, silicones. |
| What is the cause of viscosity in a liquid? | Cohesion is the predominant cause of viscosity in a liquid. As cohesion decreases with temperature, therefore so does viscosity. |
| What are the advantages of rotational viscometers? | Given sample can be sheared for as long as is desired, so changes in time can be observed. Uniform shear rate can be applied throughout sample. |
| What is the main disadvantage of rotational viscometers? | Excessive rise in temperature incurred at high shear rates. |
| What is a concentric cylinder viscometer? | In a concentric cylinder viscometer, the material is confined between vertical coaxial cylinders, one of which can be rotated at various speeds while the torque on the other is measured. |
| What is a cone and plate viscometer? | A cone and plate viscometer consists of a flat plate and a cone of radius R having a very obtuse angle. Cone's axis is normal to plate and its apex just touches the plate surface. |
| What is a parallel plate viscometer? | A parallel plate viscometer is an instrument which consists of two parallel circular plates of radius R separated by a narrow gap of height h. One plate rotates at a steady angular velocity Ω, and the torque T on the other plate is measured. |
| What does the Rabinowitsch-Mooney equation show? | Gives the shear rate at the pipe wall for the laminar flow of a time-independent fluid, in which the derivative is evaluated at a particular value of τw. |
| What is the generalised Reynolds number for? | The generalised Reynolds number is used to get unique friction factor-Reynold's number curve for laminar flow. |
| What are viscoelastic materials? | Materials which possess varying degrees of viscous as well as elastic properties. |
| What parameter is λ for Maxwell liquids? | Λ is known as the relaxation time or characteristic time of a Maxwell liquid. Dimensions of time. |
| What is the Voigt model/ Kelvin model? | Viscoelastic material but more solid-like behaviour compared to Maxwell model. Obtained by assembling a spring and dashpot in parallel. Strain is same for both elements and stresses are additive. |
| What is the Maxwell model? | A Maxwell material is the most simple model viscoelastic material showing properties of a typical liquid. Stress same for both elements and strains are additive. |
| What parameter is λ for Voigt model liquids (delayed elasticity)? | Λ is referred to as the retardation time. |
| What is the generalised Voigt model analogous to? | The generalised Voigt model is analogous to a viscoelastic solid |
| What does it mean if one of the elements in the generalised Voigt model has a zero modulus? | System is left with a simple dashpot which does allow unlimited viscous flow. System therefore could be considered as a viscoelastic liquid. |
| What is the creep function φ (t)of a viscoelastic material? | The creep function, φ (t) , of a viscoelastic material is defined as the strain per unit stress expressed as a function of time when the relaxed material is suddenly subjected to a constant stress. |
| What is the creep function useful for? | The creep function is perhaps the most convenient method of specifying the properties of a viscoelastic material which has predominantly solid properties, i.e. a material which is capable of supporting its own weight without appreciable distortion as compared with a liquid which flows and must be confined |
| What are the typical operating modes of a dynamic testing rheometer? | Strain sweep Frequency sweep Isothermal time sweep |
| Describe strain sweep in a dynamic rheometer | In strain sweep, the strain amplitude is varied over a wide range. This mode is used to determine the limits of linear viscoelastic behaviour; in the linear region, the rheological properties are strain independent. |
| Describe Frequency sweep in a dynamic rheometer | Frequency sweep is a common mode of dynamic testing because it shows how the viscous and elastic behaviours of the material change with the rate of application of strain, i.e. the frequency of the harmonic strain input ω. |
| Describe isothermal time sweep in a dynamic rheometer | Isothermal time sweep: in this mode the frequency and amplitude of the input strain are kept constant. This test can reveal structural changes in materials with thixotropic characteristics. A time sweep can be conducted in conjunction with a controlled increase in temperature. Such a test would reveal if there are any drastic changes in rheological behaviour that are caused by heating such as in protein substances or starch pastes. |
| What are the three dimensionless groups used in viscoelasticity problems? | Reynolds number, Re Deborah number, De Weissenberg or elasticity number, We |
| What does Re measure? | Re is a measure of the relative importance of inertial and viscous forces |
| What does De measure? | De is a measure of the degree of viscoelasticity of a material, i.e. whether it will act as a solid or liquid. De<<1 corresponds to a slow deformation of the fluid. De>>1 corresponds to fast deformation, behaviour like an elastic solid. |
| What does We measure? | Alternative to De. Measures relaxation time, determined from steady flow. |