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IB Engineering > 2P4 Thermofluid Mechanics > Flashcards

2P4 Thermofluid Mechanics Flashcards

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1
Q

What are the methods of mixing in turbulent compared to laminar flows?

A

Turbulent - large scale eddie mixing
Laminar - molecular diffusion at small scales

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2
Q

For laminar flow through a pipe what different dimensionless groups for wall friction (cf) can be formed for wall shear stress?

A
  1. Dynamic τ/0.5ρV^2 for higher Re
  2. Viscous τ/0.5μ(V/D)
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3
Q

What is a measure of roughness in a pipe?

A

k/D, where k is the characteristic length scale of the roughness, and D is the diameter of the pipe.

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4
Q

Under what conditions does the flow stay laminar in terms of roughness?

A

When k/D «1.

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5
Q

What is the specific steady flow availability function?

A

b = hi - T0si

where T0 is the environmental temperature

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6
Q

What is the maximum power that can be extracted between two flow states?

A

mdot (b1-b2)

where b is the specific steady flow availability function

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7
Q

What is exergy?

A

The difference between b1 and b0 where b0 is the specific steady-flow availability of the environemnet.

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8
Q

What is the specific energy unavailable for work?

A

=T0(S1-S0)

the energy unavailable is fixed by the entropy flow rate

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9
Q

How can you rewrite the availability equation in terms of work out?

A

m(b2-b1) = -Wx + integral(1-T0/T)dQ -T0Sirr

interesting because it contains carnot efficiency

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10
Q

Give three examples of irreversibility in a flow

A
  1. viscous dissipation in boundary layers
  2. viscous mixing of flows of different velocity
  3. heat transfer accross a finite ΔT
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11
Q

What is a limitation of the air-standard Joule cycle?

A

Accross combustor there is a 2-4% drop in pressure.

Combustion changes gas composition and therefore its thermodynamic properties.

Turbine and compressor have irreversibilities, so they are not isentropic, loss of available power.

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12
Q

What is the 2-property rule?

A

In the absence of external effects, the state of a pure substance is fixed by the values of 2 independent property

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13
Q

What is the triple line?

A

Where all three phases can exist together.

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13
Q

What is the saturated liquid line?

A

Where the fluid is wet saturated (left hand side)

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14
Q

What is the critical point.

A

The max temperature where liquid and vapor phases can exist. Above which, there is no distinction.

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15
Q

What is the heat transfer called during melting?

A

latent heat of fusion.

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16
Q

What is the heat transfer called during melting?

A

latent heat of vaporisation

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17
Q

How is dryness fraction defined?

A

x = mass of vapour/total mass

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18
Q

What is Poiseuille flow?

A

Flow between two stationary plates driven by a constant pressure gradient.

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19
Q

What assumptions can be made about viscous flow down a slope?

A

Laminar
Streamlines straight and parallel
Pressure, and velocity does not depend on distance down the slope
Shear stress at surface is zero.

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20
Q

What is Couette flow?

A

one plate moves in a set of parallel plates, no pressure gradient.

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21
Q

What happens in combined Couette and poiseuille flow?

A

Can get flow reversal depending on adverse of favourable pressure gradient.

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22
Q

How do you derive the expression for the growth of a boundary on a plate in a free stream?

A

use the navier stokes equation to scale pressure, intertia and viscous terms.

In x direction you can show that the way the thickness grows.

In y direction can show that the perpendicular pressure gradient is neglibible

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23
Q

Where can Bernoulli be used for the flow of a free stream over a fixed plate?

A

Bernoulli can be used outside the boundary layer where viscous effects are neglibible but not inside the boundary layer.

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24
What happens to a boundary layer in a favourable pressure gradient?
Fuller boundary layer
25
What happens to a boundary layer in an adverse pressure gradient?
Depleted boundary layer, up to flow reversal. Can be derived from thinking of a Couette flow.
26
What happens to pressure around a ellipse placed in a free stream?
high p at stagnation point, low p at top and bottom due to curvature of streamlines, high p at other end of ellipse (if inviscid)
27
What is the consequence of adverse pressure gradient on backside of objects?
Can lead to flow reversal and therefore seperation.
28
What determines whether flow will reverse inside an adverse pressure gradient?
Competing effects of pressure gradient and diffusion of momentum from external flow towards the wall. There is more diffusion of momentum when the flow is more viscous, making it more robust to seperation.
29
How can seperation be delayed?
By injection high-momentum fluid directly into the boundary layer, which means the boundary layer can stay attached more easily. By using suction on the wing, to suck in the lower momentum fluid.
30
What happens after transition to turbulence?
Weak viscous forces, flow breaks down into small disorganised eddies
31
What effect does turbulence have on the growth of the boundary layer?
It quickens the growth of the boundary layer, as turbulence increases the rate of momentum transfer between surface and free stream. This leads to a fuller profile than laminar. Higher skin friction due to steeper gradient at wall.
32
What effect does turbulence have on seperation?
More robust against flow reversal, delays seperation due to fuller boundary layer.
33
How can turbulence be created?
By 'tripping' the flow such as the dimples in golf balls.
34
How is form drag created?
By the seepration of the flow, the pressure behind the object won't return to the high p seen in an inviscid flow.
35
What causes laminar boundary layers to become unstable and transition to turblunece?
Because their velocity profiles contain an inflexion point. This leads to seperation, unless the flow is very viscous
36
How can boundary layers re-attach?
Turbulence after seperation causes the velocity profile to become fuller, this new profile may be robust enough to overcome adverse pressure gradient, and reattach creating a seperation bubble.
37
What is the thermal resistance in a solid?
L/λA
38
What is the thermal resistance of a fluid?
1/hA, where h is the coefficient of heat transfer
39
Whats the generalised expression for thermal resistance?
Rth = T1-T2/Qdot
40
What is the thermal resistance of an annular body?
ln(r2/r1)/2πLλ
41
What is notable for thermal resistance of insulator ona pipe?
Thermal resistance intially decreases, then increases again.
42
What is the 1D transient heat diffusion equation?
∂T/∂t = α∂2T/∂x2
43
How can the 1D unsteady heat conduction equation be derived?
By considering a slab of planar material, which has energy accumulation per unit volume G, and a heat flux in qx and heat flux out qx+dx
44
What non-dimensional group for transient heat conduction?
Fourier Number Fo, time/characteristic time for heat diffusion through body ατ/s^2 where s is the characteristic dimension of the body. Can be found through dimensional analysis that t = x^2/α
45
How can lumped heat capacity anlaysis be modelled in the circuit analogy of heat transfer?
as a capactor with value cρV Time constant of onduction is cρV/hA
46
When is the lumped capacity model valid?
When Bi <0.1
47
What does the Biot number tell you?
Internal thermal resistance/surface thermal resistance (s/λA)/(1/hA)=hs/λ s is the characteristic legnth of the solid.
48
What is the overall heat transfer coefficient, U?
UA = 1/Rth,overall
49
What is the log mean temperature difference and why is it useful?
Qdot = UAΔT where ΔTm = ΔT2-ΔT1/ln(ΔT2/ΔT1) 2 and 1 refer to ends of the heat exchanger
50
Define the effectiveness (ε) of a heat exhanger
Actual heat exchange /max possible heat exchange (achieved in counter flow) ε = mhch(Thin - Thout)/ mc min (Thin - Tcin)
51
Condition for incompressibility:
Temperature fluctuations are less than 0.1 of background temperature, Mach number less than 0.3
52
What is the Stanton Number?
Heat flux/characteristic heat flux heat transfer coefficient/thermal capacity of the fluid
53
What is the Prandtl number?
momentum diffusivity/thermal diffusivity ν/α
54
What happens when Prandtl number equals 1?
Momentum diffusivity = thermal diffusivit , non-dimensional equations of heat and momentum transfer are identical, non-dimensional solutions are identical, direct analogy between thermal and mechanical fields.
55
What is Reynold's analogy?
If Pr=1, then St = 0.5cf Need high wall friction for high heat transfer.
56
What is the equivalent of the Reynold's number for natural convection?
The grasshof number, Which uses a scaling velocity, based on the Bouyant forces
57
How do you do dimensional analysis for natural convection?
Group β ΔT and g together as these are one independent dimensional quantity.
58
What is β for natural convection?
Coefficient of expsnaion 1/v dv/dT
59
WHat dimensionless relationship is usually true for natural convection problems?
Nu = fn (Gr Pr)
60
Define black body
idealised object that will completely absorb all radiation upon it emit the largest amount of energy per unit area possible for a given temperatr=ure
61
What is the difference between monochromatic emissivity and total emissivity?
mono chromatic = ελ = radiation emmited per unit area between λ and dλ / Ebλ Total emissivity = emission from real surfcae/ emission from black body at same temp = integral ( ελ Ebλdλ)/σT^4
62
Define grey body
monochromatic emissivity is constant
63
In radiation what does ρ, α, and τ stand for?
ρ is reflectivity α is absorptivity τ is transmissivity Most bodys τ =0 (opaque)
64
What is Kirchoff's identity?
ε=α, absorptivity is equal to emissivity,
65
What is G and J for radiation problems?
G = irradiation, the total radiation incident on a surface per unit time and area J = radiosity = the total radiation leaving a surface per unit time and area.
66
Equation relating J and G.
J = εEb +ρG = εEb + (1-ε)G => G = (J-εEb)/(1-ε)
67
What is Qdot for radiation?
Qdot = (Eb-J)/(1-ε/εΑ)
68
How does the circuit analogy work for radiation?
Eb is the first node, the resistance is (1-ε)/εΑ which then leads to J the radiosity, which then leads to a shape factor.
69
What is true about shape factors?
Reciprocity A1F12 = F2F21
70
WHat is space resistance?
1/A1F12, wich is the resistance between two radiosities.
71
What is the expression for heat transfer when 1 object is completely enclosed by another?
little object ->1 Qdot = A1 ε1 ( σT1^4 - σT2^4). Does not depend on emissivity of the outer body

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