基于焓耗散數(shù)的絕熱型溶液除濕/再生器性能預(yù)測解析模型

彭冬根, 曹 卓

彭冬根, 曹 卓

(南昌大學(xué) 工程建設(shè)學(xué)院, 江西 南昌 330031)

1 前言

溶液除濕是一種利用表面水蒸氣分壓力較低的水溶液吸收空氣中水分的除濕方法，由于驅(qū)動能源品味要求低[1-3]、可以改善室內(nèi)空氣品質(zhì)[4]等優(yōu)勢被研究人員所關(guān)注。在除濕過程中，吸濕性溶液與濕空氣直接接觸進(jìn)行水分與熱量的傳遞[5]，因此溶液除濕過程是一個傳熱與傳質(zhì)相耦合的過程[6-8]，給除濕/再生器數(shù)學(xué)模型建立及求解造成困難。

Lazzarin等[9]分析并建立了絕熱型填料塔內(nèi)空氣與溶液之間傳熱傳質(zhì)的一維模型。代彥軍等[10]建立除濕/再生器內(nèi)叉流降膜除濕的傳熱傳質(zhì)過程數(shù)學(xué)模型。Varela等[11]通過雷諾-普朗特數(shù)和雷諾-施密特數(shù)給出溶液除濕/再生過程中傳熱傳質(zhì)的一般關(guān)系式。Ren等[12]在常見的溶液除濕/再生工況下將溶液平衡濕度比與溫度的關(guān)系進(jìn)行線性逼近。Babakhani等[13]給出可以預(yù)測各種變量在再生器內(nèi)分布情況的解析解。Zhang等[14]基于傳質(zhì)單元數(shù)(NTUm)模型分析了熱泵驅(qū)動的溶液除濕系統(tǒng)性能。Liu等[15]在NTUm的基礎(chǔ)上提出用效率表示的除濕/再生器解析模型。上述研究從傳熱傳質(zhì)角度發(fā)展了除濕/再生器數(shù)學(xué)模型，但皆未從裝置不可逆性的角度進(jìn)行建模，無法分析裝置不可逆性程度對除濕/再生器性能影響。

式中：Q=mcT，為物體質(zhì)量，kg；c為物體的比定容熱容，kJ×kg-1×K-1；為熱力學(xué)溫度，K；Q為物體所含的熱能，kJ。

式中：q,a為干空氣的質(zhì)量流量，kg×s-1；a為濕空氣中水蒸氣與干空氣的質(zhì)量比。

式中：q,s為溶液質(zhì)量流量，kg×s-1；eq為與溶液表面平衡時的空氣的等效比焓，kJ×kg-1；s為溶液比焓，kJ×kg-1；

為方便后文解析推導(dǎo)，在分析溶液與空氣的熱質(zhì)交換時作如下假設(shè)：

1) 由于除濕/再生過程水分遷移率和溶液流率相比較小，假設(shè)溶液流量不變；

2) 忽略除濕/再生介質(zhì)與環(huán)境之間散熱損失，假設(shè)除濕/再生器為絕熱；

3) 不考慮除濕/再生器內(nèi)可能存在的局部積液及局部渦流現(xiàn)象，假設(shè)溶液與空氣在填料表面均勻分布；

4) 不考慮溶液和空氣沿與其流動垂直方向的熱濕傳遞，假設(shè)順逆流除濕/再生過程為一維模型；

5) 由于除濕/再生溫濕度變化較窄，假設(shè)溶液和空氣物性參數(shù)為常數(shù)；

6) 只考慮溶液與空氣的熱質(zhì)交換最終處于穩(wěn)態(tài)的結(jié)果，假設(shè)除濕/再生過程為穩(wěn)態(tài)。

以逆流除濕過程為例，微元面積內(nèi)的傳熱傳質(zhì)過程如圖1所示，圖中q,a,in、q,s,in分別為進(jìn)口空氣和溶液的質(zhì)量流量，kg×s-1；a,in、a,out、s,in和s,out分別為進(jìn)、出口空氣和溶液的比焓，kJ×kg-1。

根據(jù)2.2節(jié)假設(shè)，可以得到逆流除濕過程的能量守恒微分方程如下：

積分得

式中：為在微元面積上傳遞的全熱量，kW。

將式(6)代入式(8)得

為方便計算，在此定義系數(shù)，如式(11)所示：

式中：eq,in和eq,out分別為與進(jìn)、出口溶液平衡的空氣比焓，kJ×kg-1。

將式(11)代入式(8)并在整個除濕/再生器的面積上進(jìn)行積分，得到

對方程(15)左側(cè)進(jìn)行積分得

在除濕/再生器中，其焓效率定義為

定義*為與溶液平衡狀態(tài)下空氣與溶液之間的等效熱容比，如下：

式中：c,s為溶液的比定壓熱容，kJ×(kg×K)-1；c,eq為與溶液平衡時的空氣的比熱容，kJ×(kg×K)-1。

將式(20)與(17)代入式(13)可得

圖2 除濕/再生器中焓耗散數(shù)Eh*與焓效率eh的關(guān)系

式中：為溶液與空氣之間的傳熱系數(shù)，kW×(m2×K)-1；c,a為空氣的比定壓熱容，kJ×(kg×K)-1。

在除濕/再生器中，NTU與焓效率的關(guān)系如式(23)和(24)所示[15,30]，且在形式上分別與文獻(xiàn)[29]中順流、逆流換熱器的NTU和換熱效率的關(guān)系式一致：

順流：

逆流：

式中：為溶液和空氣間傳熱傳質(zhì)的路易斯數(shù)(近似為1[28,30])

順流：

逆流：

圖3 除濕/再生器中焓耗散數(shù)Eh*與傳熱單元數(shù)NTU的關(guān)系

溶液與空氣之間的能量守恒方程見式(7)。

溶液與空氣之間的質(zhì)量守恒方程為

式中：a,in、a,out分別為進(jìn)口、出口濕空氣中水蒸氣與干空氣的質(zhì)量比；s,in、s,out分別為除濕/再生器進(jìn)、出口溶液中溶質(zhì)與溶液質(zhì)量比。

傳熱系數(shù)和傳質(zhì)系數(shù)m可分別由空氣側(cè)的顯熱、含濕量和焓的增量方程決定：

式中：a,in和a,out分別為進(jìn)口、出口的空氣熱力學(xué)溫度，K；Δm為對數(shù)平均溫差，K。

式中：eq,in、eq,out分別表示與進(jìn)口、出口溶液濕熱平衡的濕空氣中水蒸氣與干空氣質(zhì)量比。

對于含濕量或溫度出現(xiàn)交叉的情況而言，采取以下選擇策略：

1) 當(dāng)溶液與空氣之間的溫度不存在交叉時，聯(lián)立方程(28)、(29)與(31)可以得到方程(33)：

2) 當(dāng)溶液與空氣之間的溫度存在交叉時，聯(lián)立方程(30)和(31)得

聯(lián)立方程(7)、(13)、(28)和(34)可以通過除濕/再生器工質(zhì)進(jìn)口狀態(tài)計算得到其出口狀態(tài)。

5 解析模型驗證

為了驗證除濕/再生器解析模型的精確性，本研究將該解析模型計算結(jié)果與數(shù)值模型計算結(jié)果及實驗結(jié)果分別進(jìn)行了對比及分析誤差。

5.1 數(shù)值模型驗證

氣液流量比定義為

表1 除濕/再生器基準(zhǔn)工況

圖5 再生工況下解析模型與數(shù)值模型結(jié)果對比

圖4和5分別顯示了通過數(shù)值模型和解析模型計算得到的除濕率和再生率及兩者相對誤差隨氣液流量比和傳熱單元數(shù)NTU的變化情況。從圖中可以看出，當(dāng)其他參數(shù)不變情況下，隨和NTU的增加，除濕/再生過程中的除濕率和再生率均逐漸升高。在模擬范圍內(nèi)，解析模型結(jié)果與數(shù)值模型結(jié)果的相對誤差在±6%以內(nèi)，平均誤差為3.4%。另外，圖4(a)與4(b)中的相對誤差分別在=0.8及NTU=1.5時發(fā)生突變，前者是因為除濕工況下，隨著的增大，除濕率逐漸增加，空氣釋放的冷凝熱也增加，溶液除濕溫度隨之升高。在本研究選定的基準(zhǔn)除濕工況下，當(dāng)≤0.7時，解析模型選取對數(shù)平均溫差來計算。而當(dāng)增大到0.8時，選取對數(shù)平均含濕量差來計算解析模型，模型切換過程導(dǎo)致了誤差趨勢的突變，但絕對值大小仍在允許范圍內(nèi)，結(jié)果的精度可接受。圖4(b)的原因與之類似。

5.2 實驗驗證

文獻(xiàn)[32]中實驗得到的除濕與再生工況數(shù)據(jù)可被用于驗證逆流除濕/再生器解析模型，實驗分別采用聚丙烯RauschertHiflow環(huán)和LiCl水溶液作為填料和除濕劑，填料塔為圓柱體直徑為25.4 cm、高為60 cm、比表面積為210 m2×m-3，實驗工況見表2。

表2 文獻(xiàn)[32]中除濕/再生器實驗工況

圖6 解析模型與實驗結(jié)果對比

6 解析模型預(yù)測結(jié)果分析

對于除濕和再生過程來說，水分的傳遞量是主要考慮的問題，因此采用濕效率來評價除濕/再生器的性能：

圖7 不同工況下除濕/再生過程焓耗散數(shù)Eh*對濕效率ew的影響

Fig.7 Effects of the enthalpy entransy dissipation number Eh* on humidity efficiency ew under varying conditions

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An analytical model for predicting the performance of adiabatic dehumidifier/regenerator based on enthalpy entransy dissipation numbers

PENG Dong-gen, CAO Zhuo

(School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China)

In order to study the irreversibility of coupled heat and mass transfer processes of parallel/counter flow solution dehumidification/regeneration, a concept of enthalpy entransyEwas proposed，and the enthalpy entransy dissipation numberE*of solution dehumidification/regeneration was deduced. Its relationship with the equivalent heat capacity ratio*, the number of heat transfer unit (NTU) and the enthalpy efficiencywere obtained, respectively. Moreover, an analytical model of dehumidifier/regenerator based onE*was established, and the effect of the enthalpy entransy dissipation numberE*on the performance of dehumidifier/regenerator was analyzed. The results show that theE* shows negative linearity relationship with the,and it increases with the decrease of* and decreases to a stable value with the increase of NTU. The degree of heat and mass transfer processes taking place between the solution and air is deeper whenE* is smaller, while their processes tend to stop whenE* approaches 1.0. At constantE*, the solution inlet temperature and the flow-rate ratio have more significant effects on the performance of the device.

dehumidification / regeneration; enthalpy entransy; analytical model; irreversibility; heat and mass transfer

1003-9015(2022)04-0543-11

TU834.9

A

10.3969/j.issn.1003-9015.2022.04.010

2021-08-12；

2021-11-17。

國家自然科學(xué)基金(51766010)；江西省研究生創(chuàng)新專項資金(YC2019-S002)；南昌市高效制冷知識創(chuàng)新團隊(2018-CXTD-004)。

彭冬根(1975-)，男，江西吉安人，南昌大學(xué)教授，博士。

彭冬根，E-mail：ncu_hvac2013@163.com

彭冬根, 曹卓. 基于焓火積 耗散數(shù)的絕熱型溶液除濕/再生器性能預(yù)測解析模型[J]. 高?；瘜W(xué)工程學(xué)報, 2022, 36(4): 543-553.

：PENG Dong-gen, CAO Zhuo. An analytical model for predicting the performance of adiabatic dehumidifier/regenerator based on enthalpy entransy dissipation numbers [J]. Journal of Chemical Engineering of Chinese Universities, 2022, 36(4): 543-553.