Solutions to questions from chapter 9 in GEF Cloud Physics

Transcription

1 Solutions to questions from chapter 9 in GEF Cloud Physics i.h.h.karset@geo.uio.no Problem 1 What is the difference between collision, coalescence and collection? Problem 2 Name and very briefly explain the different categories of growth by collection illustrated in Figure 1. Problem 3 a) What is the definition and the value of the mean free path in air, λ air? b) What is the definition of the Reynolds number? c) The drag force in some regimes are a sum of two different forces. Which? Problem 4 When a particle is falling through the air, it experiences a drag-force. The behaviour of this drag-force is varying with the size of the particle. Which drag-force regimes do we have, and how large are the particles in the different regimes? Which particles do we Figur 1: Figure 9.1 from the book. 1

2 Figur 2: Figure 9.3 from the book. typically find in the different regimes? Also say something about the behaviour of the drag-force or it s impact on the fall speed in the different regions. Problem 5 Link the equations below to the different regimes: v p,drizzle = k drizzle D p v p = µ air ρ air N Re D p v p = ρ pg 18µ air D 2 p v p = π ρ p 6C F M ρ air g c air D p Problem 6 v p = ρ pg 18µ air ( λ ) air Dp 2 D p a) What is typical fall speed for a cloud droplet? And a raindrop? b) What is the grey-shading in Figure 3 indicating? 2

3 Figur 3: Figure 9.5 from the book. Problem 7 a) What is the definition of the Davies number? b) When looking at ice crystals, give an expression for the Davies number. c) When looking at ice crystals, the Davies number can be written as N Da = 2gρ aira µ 2 air c D2+b d c How do we get this, and what is a, b, c and d saying something about? d) How can we use the Davies number to calculate the fall speed of the crystal? e) Explain Figure 4 and Figure 5. f) What is the typical fall speed of an unrimed ice crystal? And how is riming affecting the fall speed? Problem 8 Explain Figure 6 and link it to the equation below: E = A eff A geom = πy 2 c π(r L + r S ) 2 3

4 Figur 4: Figure 9.7 from the book. Figur 5: Figure 9.10 from the book. Figur 6: Figure 9.11 from the book. 4

5 Figur 7: Figure 9.12 from the book. Problem 9 a) Figure 7 shows how the collision efficiency is varying with the size of the small droplets. What is the different curves with different N Re -values expressing? b) There is a threshold value for the smaller droplets. Why? And how large is this value? c) Why is E in Figure 7 decrasing after reaching a certain size of the smaller droplets, and then increasing again? d) What does it mean when E is larger than 1, and how can this happen? e) What is the treshold value for the collector drop? Problem 10 a) Why isn t the collection efficiency, E c, equal to the collision efficiency? b) How is the coalescence efficiency, ɛ, varying with the size of the smaller droplets? And why is that so? Link the explanation up the the Weber number: N W e = ρ LV r L (v L v S ) 2 σ LV c) How is the collection efficiency, E c changing with r droplet, and why is that so? d) What is a typical value for the collision efficiency when the droplets are larger than the treshold value of 5 µm? 5

6 Figur 8: Figure 9.14 from the book. Problem 11 a) Why isn t raindrops getting bigger than a couples of mm? b) We have three types of breakups of drops caused by collisions with other drops. What do we call them? Explain how the collisions happens, and link each of them up to one of the illustrations in Figure 9. c) Which breakup mechanism is the most common? d) Link the different breakup mechanisms up to the histograms in Figure 10. What is indicated by the arrows? e) How can breakups broaden the droplet spectra? Problem 12 a) What do we mean by mixed-phase collection processes? And which processes are included here? b) What is riming, and what is it also called? c) What do we mean by cutoff crystal size when talking about riming, and what is this size for plates and columns? d) What is the difference between riming and capture nucleation? e) How large are the coalescence efficiency during capture nucleation? f) Explain Figure 12 and link it to Figure 11. 6

7 Figur 9: Figure about disruption. Figur 10: Figure about disruption. Figur 11: Figure 9.20 from the book 7

8 Figur 12: Figure 9.21 from the book Figur 13: Figure 9.22 from the book Problem 13 a) What is the difference between aggregation and the other cathegories of growth by collection? b) What is adhesion? c) What is causing the high values of large snowflakes (aggregates) in Figure 13? Problem from the book Consider a small liquid drop of size D = 20 µm falling from rest in the Earth s atmosphere, the density and viscosity of which can be taken as ρ air = 1 kgm 3 and µ air = Pa s, repectively. Start with the fundamental physical principles and develop the mathematics that would allow you to calculate the speed v of the drop as a function of time t. In terms of the physical variables, what is the steady-state fall velocity and the time constant τ to achieve this terminal velocity? Are we justified in assuming that the cloud droplet is always falling at its terminal fall speed? 8