Differential emissivity based evaporable particle measurement
A differential emissivity imaging device for measuring evaporable particle properties can include a heated plate, a thermal camera, a memory device, and an output interface. The heated plate can have an upper surface oriented to receive falling evaporable particles. The evaporable particles have a particle emissivity and the upper surface has a plate surface emissivity. The thermal camera can be oriented to produce a thermal image of the upper surface. A memory device can include instructions that cause the imaging device to calculate a mass of the individual evaporable particle via heat conduction using a calculated surface area and an evaporation time.
1. A differential emissivity imaging device for measuring evaporable particle properties, comprising:
a) a heated plate with an upper surface oriented to receive falling evaporable particles, the evaporable particles having a particle emissivity and the upper surface having a plate surface emissivity;
b) a thermal camera oriented to produce a thermal image of the upper surface;
c) at least one memory device including instructions that, when executed by at least one processor, cause the imaging device to:
i. identify individual evaporable particles from the thermal image by identifying differences between the particle emissivity and the plate surface emissivity,
ii. determine a plate surface radiative temperature and a droplet radiative temperature as a function of a time until the droplet is evaporated,
iii. determine a surface area of the droplet, and
iv. calculate a mass of the individual evaporable particle via heat conduction using the surface area and the time; and
d) an output interface to communicate the evaporable particle properties including the mass to an output device.
2. The imaging device of claim 1 , wherein the upper surface is roughened to increase evaporation rate of the droplet.
3. The imaging device of claim 1 , wherein the plate temperature is maintained below a Leidenfrost point during evaporation of the droplet.
4. The imaging device of claim 1 , wherein the particle emissivity is at least 0.4 higher than the plate surface emissivity.
5. The imaging device of claim 1 , wherein the mass is calculated using:
S
Δ
T
∫
dm
+
L
∫
dm
=
∫
0
Δ
t
(
k
/
d
)
A
(
t
)
(
T
p
-
T
w
(
t
)
)
dt
where S is specific heat capacity of the droplet, ΔT is a temperature difference between an initial and final temperature of the droplet, m is mass of the droplet, L is latent heat of vaporization of the droplet, k is thermal conductivity of the plate, d is thickness of the plate, A(t) is plan area of the droplet as a function of time, T p (t) is the plate temperature, and T w (t) is surface temperature of the droplet as a function of time.
6. The imaging device of claim 1 , further comprising an optical camera oriented to produce a plurality of optical images of falling evaporable particles above the heated plate.
7. The imaging device of claim 6 , wherein the instructions further include at least one of:
a) calculating fall speed from the plurality of optical images,
b) determining an evaporable particle height prior to impact with the upper surface,
c) determining a second comparative surface area of the droplet after impact of the evaporable particle with the upper surface, and
d) calculating evaporable particle density using the evaporable particle height and the mass.
8. The imaging device of claim 7 , wherein the instructions further include calculating at least one of:
a) a precipitation flux using the mass and the fall speed,
b) a precipitation rate using total mass loss per image frame, sampling frequency, and surface area of the heated plate,
c) a number density using number of evaporable particles per unit volume, the fall speed, and time lapse,
d) a visibility using a sum of cross-sectional area of evaporable particles on the heated plate, surface area of the heated plate, and an average fall velocity of the evaporable particles calculated from the fall speed, wherein the evaporable particles are hydrometeors, and
e) a precipitation type using initial temperature drop of the heated plate.
9. The imaging device of claim 8 , wherein the precipitation rate is calculated as:
Δ
mv
ρ
A
where Δm is total mass loss of hydrometeors for a single thermal image, v is sampling frequency, p is density of water, and A is surface area of the heated plate.
10. The imaging device of claim 8 , wherein the visibility is 3.912/Q where
Q
=
2
Σ
A
A
p
v
p
t
where A is cross sectional area of all hydrometeors on the heated plate at a sample time, A p is the area of the heated plate, v is average fall speed of hydrometeors at the sample time, and t is the sample time.
11. The imaging device of claim 7 , wherein the fall speed is calculated by forming a light sheet perpendicular to an imaging axis of the optical camera.
12. The imaging device of claim 1 , wherein the output interface is a display or a data connection.
13. The imaging device of claim 1 , comprising:
at least one memory device including instructions that, when executed by the at least one processor, cause the imaging device to:
i. identify changes in temperature of the upper surface as a function of time, and
ii. calculate a wind speed and optionally a wind direction via heat convection using the plate temperature, and a surface area; and
an output interface to communicate the wind speed and optionally the wind direction to an output device.
14. The imaging device of claim 13 , wherein the wind speed is calculated via thermal image velocimetry.
15. The imaging device of claim 14 , wherein wind direction and turbulent variability are also calculated via thermal image velocimetry.
16. The imaging device of claim 13 , wherein the plate surface emissivity is a low emissivity.