Simulation and experimental study on the evolution of droplet size distribution during spray drying of mannitol

doi:10.16085/j.issn.1000-6613.2018-0752

Abstract

Abstract:

Computer simulation and experimental study were carried out on the evolution of droplet size distribution during spray drying of mannitol dissolved in water. The shrink rate of the diameter of a droplet during spray drying was treated as a negative growth rate in the population balance (PB) model which was obtained using the reaction engineering approach (REA).The integration of PB and REA yielded the PBREA model, which was solved using a high-resolution numerical method. The drying time of droplets of varied sizes, the change of the mean moisture content of droplets and the droplet size distribution were simulated under different spray drying conditions. The results showed that the drying time increased with the increase of droplet diameter. The ratio of the predicted and measured particle mean diameters was between 1.0 to 1.5, and the span was from 0.61 to 0.89. The errors were analyzed and attributed to three main factors: error due to the statistical analysis of droplet and particle sizes, the difference in drying a single static droplet and a group of droplets in motion, and the empirical thermal conductivity and diffusion coefficient values. Images were collected and analyzed to obtain droplet and particle size distributions with the Buchi 290 spray dryer. The simulated and experimental results showed that the PBREA model could effectively predict the mean diameter and span of particles during spray drying process.

Key words: drying, particle size distribution, mathematical modelling, population balance, reaction engineering approach

摘要：

利用群体粒数衡算（population balance，PB）计算机模拟和实验研究了甘露醇水溶液的喷雾干燥过程中液滴的粒度分布的变化规律。液滴干燥过程中的颗粒粒度的萎缩速率，在群体粒数衡算模型中描述为液滴的逆（或负）生长项，通过单个液滴反应动力学方法（reaction engineering approach，REA）获得。基于单个液滴干燥的反应工程方法模型REA和群体粒数衡算模型PB集成建立了PBREA模型。PBREA 模型的求解是通过高分辨率数值方法。本文模拟研究了不同工况下，不同粒径液滴的干燥时间、液滴平均含湿量以及液滴粒度分布随时间的变化。结果显示，液滴粒径越大，干燥时间越长，模型预测的颗粒平均粒径为实验值的1.0~1.5倍，粒度分布跨度是实验值的0.61~0.89倍。模拟误差主要来源于液滴及颗粒粒径分布统计精度、单个静止液滴与群体运动液滴干燥的差异、热导率及扩散系数是经验值3个方面。在使用Buchi 290 小型喷雾干燥仪进行的实验中，使用了图像采集和分析方法得到了液滴及颗粒的数密度分布，并和模拟结果做了对比。结果表明该模型可以有效地预测喷雾干燥过程中干燥颗粒的平均粒度及分布跨度。

关键词: 干燥, 粒度分布, 数学模拟, 群体粒数衡算模型, 反应工程方法

CLC Number:

Feng LÜ, Yang ZHANG, Caiyun MA, Xuezhong WANG. Simulation and experimental study on the evolution of droplet size distribution during spray drying of mannitol[J]. Chemical Industry and Engineering Progress, 2019, 38(02): 772-778.

吕凤, 张扬, 马才云, 王学重. 甘露醇喷雾干燥过程中液滴粒度分布变化的群体粒数衡算模拟和实验研究[J]. 化工进展, 2019, 38(02): 772-778.

Figures/Tables 10

工况	入口温度/℃	母液中甘露醇的质量分数/%	雾化气体流量/L·min^-1	出口温度/℃	产率/%	D ₅₀/μm	分布跨度	产品含湿量/%
A	135	10	4.1	86	71.3	9.36	1.62	0.38
B	135	10	5.95	85	84.4	7.24	1.39	1.22
C	135	15	4.1	86	72.7	11.76	1.57	0.70
D	135	15	5.95	85	80.2	8.01	1.44	0.74

样品编号	实验值/μm			实验值分布跨度	PBREA模拟值/μm			PBREA模拟值分布跨度	REA模拟值 D ₅₀/μm	PBREA模拟值/ 实验值		REA D ₅₀模拟值/实验值
样品编号	D ₁₀	D ₅₀	D ₉₀	实验值分布跨度	D ₁₀	D ₅₀	D ₉₀	PBREA模拟值分布跨度	REA模拟值 D ₅₀/μm	D ₅₀	分布跨度	REA D ₅₀模拟值/实验值
A	3	6	12	1.5	5.00	9.00	17.00	1.33	11.58	1.50	0.89	1.93
B	2	5	12	1.3	5.00	7.00	11.00	0.86	8.86	1.40	0.66	1.77
C	3	9	17	1.6	6.00	10.50	18.00	1.14	13.40	1.17	0.71	1.59
D	3	7	12	2	3.50	7.00	12.00	1.21	8.30	1.00	0.61	1.19

初始液滴平均直径/μm	颗粒与液滴平均粒径的比值/%
初始液滴平均直径/μm	实验值	PBREA模拟值	REA模拟值
17	35.29	52.94	68.12
13	38.46	53.85	68.12
21	42.86	50.00	63.83
14	50.00	50.00	63.83

A	——		液滴的表面积， m²
a ₁, a ₂, a ₃	——		拟合系数
b	——		REA模型中液滴粒径变化的系数
$c_{p}$	——		液滴的定压比热容， kJ/(kg·K)
D	——		液滴或颗粒直径， m
D ₁₀ ，D ₅₀ ，D ₉₀	——		累积粒度分布分别为10%， 50%和90%时对应的颗粒直径
$D_{f}$	——		扩散系数， $m^{2} / s$
G	——		液滴或颗粒的萎缩速度，m/s
h	——		传热系数， $W / (m^{2} ? K)$
$h_{m}$	——		传质系数， m/s
k	——		时间步长
$k_{f}$	——		热导率， $W / (m ? K)$
L	——		特征尺寸
m	——		质量， kg
Pr	——		普朗特数
Q	——	种群的密度函数
R	——	气体常数
Re	——	雷诺数
T	——	温度， K
t	——	时间， s
X	——	液滴或颗粒的含湿量， kg水/kg固体
z	——	尺寸步长
ΔH	——	水的气化潜热， $k J / k g$
ρ	——	密度， $k g / m^{3}$
$? E$	——	干燥过程中的活化能， J/mol
上、下角标
b	——	干燥气体
c	——	平衡状态下的参数
d	——	液滴
s	——	表面
sat	——	饱和状态下的参数
t	——	时间
v	——	蒸汽
0	——	初始状态下的数值
L	——	特征尺寸

A	——		液滴的表面积， m²
a ₁, a ₂, a ₃	——		拟合系数
b	——		REA模型中液滴粒径变化的系数
$c_{p}$	——		液滴的定压比热容， kJ/(kg·K)
D	——		液滴或颗粒直径， m
D ₁₀ ，D ₅₀ ，D ₉₀	——		累积粒度分布分别为10%， 50%和90%时对应的颗粒直径
$D_{f}$	——		扩散系数， $m^{2} / s$
G	——		液滴或颗粒的萎缩速度，m/s
h	——		传热系数， $W / (m^{2} ? K)$
$h_{m}$	——		传质系数， m/s
k	——		时间步长
$k_{f}$	——		热导率， $W / (m ? K)$
L	——		特征尺寸
m	——		质量， kg
Pr	——		普朗特数
Q	——	种群的密度函数
R	——	气体常数
Re	——	雷诺数
T	——	温度， K
t	——	时间， s
X	——	液滴或颗粒的含湿量， kg水/kg固体
z	——	尺寸步长
ΔH	——	水的气化潜热， $k J / k g$
ρ	——	密度， $k g / m^{3}$
$? E$	——	干燥过程中的活化能， J/mol
上、下角标
b	——	干燥气体
c	——	平衡状态下的参数
d	——	液滴
s	——	表面
sat	——	饱和状态下的参数
t	——	时间
v	——	蒸汽
0	——	初始状态下的数值
L	——	特征尺寸

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