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A Review on Thermal Design of Liquid Droplet Radiator System

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Abstract

Liquid Droplet Radiator (LDR) system is regarded as a quite promising waste heat rejection system for aerospace engineering. A comprehensive review on the state-of-the-art of LDR system was carried out. The thermal design considerations of crucial components such as working fluid, droplet generator and collector, intermediate heat exchanger, circulating pump and return pipe were reviewed. The state-of-the-art of existing mathematical models of radiation and evaporation characteristics of droplet layer from literatures were summarized. Furthermore, thermal designs of three LDR systems were completed. The weight and required planform area between the rectangular and triangular LDR systems were respectively compared and the evaporation models for calculating the mass loss were evaluated. Based on the review, some prospective studies of LDR system were put forward in this paper.

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Abbreviations

dA :

area differential element

c p :

specific heat capacity

D :

diameter of nozzle

D ab :

diffusion coefficient of liquid molecule

D ab,0 :

initial diffusion coefficient of liquid molecule

d :

diameter of droplet

E ev :

evaporation rate of the droplet

E n(x):

\(E_n(x)=\int_{0}^{1} \mu^{n-2}e^{(-x/\mu)}d\mu\)

F :

function of temperature profile

F :

frequency

f :

friction factor, dimensionless

G :

function of optical thickness or radius in profile of Ĩ1/4

h :

enthalpy

h sl :

latent heat of phase change

h r :

heat transfer coefficient of each droplet

I :

source function in absorbing-scattering layer; \(\tilde{I}=\pi{I}/\sigma{T_i^4}\)

I λ :

radiation intensity

I λ,b :

radiation intensity of black body

j :

Colburn factor, dimensionless

k :

dimensionless wave number, k=πDF/u

L :

length of droplet layer

M :

molecular weight

ṁ :

rate of mass loss per unit area

N :

the number of droplet layers

n :

the number of droplets per unit volume

P :

radiation power of the droplet layer

p :

pressure

p 0 :

saturated vapor pressure of plane surface

Q ev :

evaporation loss rate of the droplet layer

Q r :

overall radiation heat flux

q ev :

evaporation loss rate of per area of the droplet layer

q m :

evaporation mass flux of the droplet layer

q r :

radiation heat flux per area

R :

radius of droplet

R′:

universal gas constant, 8.3145 J/(mol·K)

r :

radius

S :

thickness of droplet layer

s :

spacing of droplet

T :

temperature

T e :

effective radiation temperature

T m :

melting point temperature

T rf :

the reference temperature

T 0 :

inlet temperature of droplet layer

T 1 :

outlet temperature of droplet layer

T ∞ :

the environment temperature

t :

time

U :

function of velocity profile

u :

velocity

V :

volume

dV :

volume differential element

W :

width of droplet layer

X :

shape factor matrix

X :

dimensionless variable, X=x/D

x :

coordinate

y :

coordinate

d:

droplet

j:

liquid jet

l:

the length direction of droplet layer

M:

mean value

s:

the thickness direction of droplet layer

v:

vapor

w:

the width direction of droplet layer

l:

liquid phase

s:

solid phase

′:

dummy variable of integration

α :

absorption coefficient of droplet layer

α 0 :

absorptivity of the droplet

β :

growth factor

γ :

surface tension coefficient

ε :

emittance

ε fd :

emittance of droplet layer in “fully developed” transient region

ζ :

radiation emission per unit volume

Θ :

dimensionless normalized temperature

θ :

defined angle

κ :

optical thickness

κ D :

optical thickness of the droplet layer

λ :

thermal conductivity

ρ :

density

ρ d :

specific mass of the droplet

ρ s :

specific mass of the droplet layer

ρ r :

electrical resistivity

σ :

Stefan-Boltzmann constant, σ=5.67×10−8 W/(m2·K)

σ s :

scattering coefficient of droplet layer

ϕ :

defined angle

Ω :

Albedo for scattering =σs/(σ+σs)

ω :

solid angle

LDHX:

Liquid Droplet Heat Exchanger

LDR:

Liquid Droplet Radiator

OSF:

Offset Strip Fin

SSR:

Solid Surface Radiator

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Acknowledgement

This work was supported by the Basic Science Center Program for Ordered Energy Conversion of the National Natural Science Foundation of China (No.51888103) and Shaanxi Innovation Capability Support Plan (2018TD-014).

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  1. State Key Laboratory of Multiphase Flow in Power Engineering, **’an Jiaotong University, **’an, 710049, China

    Daotong Chong, Maoguo Zhu, Quanbin Zhao, Weixiong Chen & Junjie Yan

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  1. Daotong Chong
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  2. Maoguo Zhu
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  3. Quanbin Zhao
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Correspondence to Junjie Yan.

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Chong, D., Zhu, M., Zhao, Q. et al. A Review on Thermal Design of Liquid Droplet Radiator System. J. Therm. Sci. 30, 394–417 (2021). https://doi.org/10.1007/s11630-021-1419-2

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