彭冬根，張小松（.南昌大學(xué)建筑工程學(xué)院，南昌33003；.東南大學(xué)能源與環(huán)境學(xué)院，南京0096）

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應(yīng)用于太陽能集熱再生系統(tǒng)的除濕效率模型

彭冬根1，張小松2
（1.南昌大學(xué)建筑工程學(xué)院，南昌330031；2.東南大學(xué)能源與環(huán)境學(xué)院，南京210096）

摘要：溶液除濕裝置是太陽能空氣預(yù)處理分級溶液集熱/再生系統(tǒng)的重要組成部分，預(yù)測填料預(yù)除濕器空氣出口參數(shù)變化是這種新型溶液再生系統(tǒng)設(shè)計時必須考慮的。文章通過定義濕度效率和等焓率預(yù)測填料型溶液除濕器的空氣出口參數(shù)，采用實驗和理論相結(jié)合的方法，分析影響濕度效率和等焓率變化的因素。發(fā)現(xiàn)當(dāng)液氣比小于2.0時，溶液和空氣入口參數(shù)變化對濕度效率影響顯著；溶液和空氣入口溫度對等焓率影響大；隨液氣比增加，濕度效率增加，等焓率下降。文章最后通過線性擬合方法得到濕度效率和等焓率的數(shù)學(xué)表達(dá)式，為太陽能空氣預(yù)處理分級溶液集熱再生系統(tǒng)理論建模提供理論基礎(chǔ)。

關(guān)鍵詞：模型；太陽能；溶液除濕；濕度效率；等焓率；液氣比

彭冬根，張小松.應(yīng)用于太陽能集熱再生系統(tǒng)的除濕效率模型[J].農(nóng)業(yè)工程學(xué)報，2016，32（01）：206-211.doi：10.11975/j.issn.1002-6819.2016.01.029 http://www.tcsae.org

Peng Donggen, Zhang Xiaosong.Dehumidification efficiency model for solar thermal regeneration system[J].Transactions of the Chinese Society of Agricultural Engineering（Transactions of the CSAE）, 2016, 32（01）: 206－211.（in Chinese with English abstract）doi：10.11975/j.issn.1002-6819.2016.01.029 http://www.tcsae.org

0　引言

太陽能溶液除濕蒸發(fā)冷卻空調(diào)系統(tǒng)[1-4]由于具有低能耗而受到越來越多關(guān)注，太陽能溶液再生裝置[5-7]是該系統(tǒng)最重要部件之一。作者設(shè)計一種新型太陽能溶液再生系統(tǒng)——太陽能空氣預(yù)處理分級溶液集熱再生系統(tǒng)，其中需采用一種溶液預(yù)除濕裝置。國內(nèi)外學(xué)者對各種溶液除濕裝置性能進(jìn)行大量實驗[8-9]和理論研究。理論研究所采用的模型主要有有限差分模型[10-11]、效率模型[12-13]和簡化模型[14]。效率模型以其簡單和精確性較高而成為國內(nèi)外學(xué)者研究熱點。文獻(xiàn)[15]仿照冷卻塔的效率模型，推導(dǎo)出用于填料除濕器的ε—NTU效率模型，并和實驗和數(shù)值模型計算結(jié)果進(jìn)行比較。Martin綜合大量實驗研究結(jié)果，擬合出一組新型填料除濕/再生過程的濕度效率公式[16]。文獻(xiàn)[17]對絕熱型和內(nèi)冷型溶液除濕器的各種效率模型進(jìn)行較為詳細(xì)介紹。文獻(xiàn)[18]定義焓效率、溫度效率和濕度效率，并對數(shù)值模擬結(jié)果進(jìn)行線性回歸得到3個效率的擬合關(guān)系式。清華大學(xué)Liu等給出順流、逆流和叉流3種流態(tài)的全熱效率和濕度效率的解析模型[19]。Ren在近似定義溶液平衡濕度與溶液溫度和含水量呈線形變化基礎(chǔ)上，推導(dǎo)出溶液除濕過程中溶液和空氣間傳熱傳質(zhì)勢差的理論解，并進(jìn)一步得到絕熱和內(nèi)冷型填料除濕過程的ε—NTU理論解析模型[20-21]。本文采用一個經(jīng)試驗驗證的填料除濕數(shù)值模型進(jìn)行溶液除濕效率理論分析，并定義等焓率表征溶液除濕的空氣出口溫度變化。最后得到填料除濕過程的空氣濕度效率和等焓率的數(shù)學(xué)表達(dá)式，為太陽能空氣預(yù)處理分級溶液集熱再生系統(tǒng)數(shù)學(xué)模型建立提供理論基礎(chǔ)。

1　叉流填料除濕裝置及流程

本文選用規(guī)則填料（蒙特GLASdekII介質(zhì)），其裝置及填料結(jié)構(gòu)圖片見圖1（a）所示，外形尺寸為0.5 m（寬）×0.5 m（高）×0.3 m（長）。為計算方便，填料中空氣流動通道可近似為三角形和菱形，通道的當(dāng)量直徑采用三角形和菱形兩種幾何形狀作為計算依據(jù)，見圖1（b）。文中試驗所用填料器的空隙率及比面積見圖1（c）。

本文采用的填料除濕流程見圖2，底部溶液槽內(nèi)溶液通過溶液泵進(jìn)入填料除濕裝置上部的溶液噴管，溶液在填料內(nèi)靠重力作用由上向下流動與空氣直接接觸，由于空氣中水蒸氣分壓力高于溶液表面水蒸氣壓力，溶液吸收空氣中水分被稀釋，較干燥空氣排出填料裝置，稀釋后溶液匯聚與溶液槽。為保證填料除濕裝置能連續(xù)運行，溶液槽分別設(shè)有濃溶液液入口和稀溶液出口，它們分別和太陽能空氣預(yù)處理分級溶液集熱再生系統(tǒng)中的一級太陽集熱再生裝置的溶液出口和進(jìn)口相連。系統(tǒng)中設(shè)置一個換熱器對循環(huán)溶液進(jìn)行預(yù)冷以改變除濕溶液入口溫度。

2　叉流除濕模型及實驗驗證

按照除濕溶液與空氣流動方向不同，可以將填料除濕裝置分為順流、逆流[22]與叉流[23]3種形式，本文中采用的是叉流式填料除濕裝置。在分析溶液和空氣熱、質(zhì)交換中，采用如下假設(shè)：

圖1　填料結(jié)構(gòu)及參數(shù)Fig.1 Structure and parameters of packing

圖2　填料除濕流程圖Fig.2 Schematic diagram of packed bed dehumidifier

1）溶液和空氣熱、質(zhì)交換過程是穩(wěn)態(tài)的，物性參數(shù)為常數(shù)；

2）填料除濕裝置與環(huán)境之間不存在熱、質(zhì)交換，為絕熱除濕過程；

3）溶液均勻噴灑，傳熱與傳質(zhì)界面相同；

4）只考慮在溶液和空氣流動方向上的熱濕傳遞，因此叉流除濕過程簡化為二維傳熱傳質(zhì)問題；

5）只考慮溶液和空氣在流動方向的對流傳熱、傳質(zhì)，忽略它們的導(dǎo)熱和質(zhì)量擴(kuò)散。

假設(shè)填料除濕裝置高度為H，m；長度為Z，m；寬度為W，m。x軸與溶液噴淋方向一致，z軸與空氣流動方向一致。叉流除濕過程的溶液和空氣能量和質(zhì)量守恒方程分別為：

溶液中鹽分質(zhì)量守恒方程為：

式中ma，ms為空氣和溶液質(zhì)量流量，kg/s；ha，hs為空氣和溶液比焓，kJ/kg；Ya為空氣含濕量，kg/kg；ξ為溶液中含鹽分濃度。

空氣側(cè)能量和質(zhì)量傳遞方程為：

式中heL為溶液平衡含濕量，kg/kg；hfg為水的蒸發(fā)潛熱，kJ/ kg；劉易斯數(shù)Le和傳質(zhì)單元數(shù)NTUm定義為：

式中h為傳熱系數(shù)，kW/（m2·K）；hm為傳質(zhì)系數(shù)，kg/（m2·s）；Cpa為空氣比熱容，kJ/（kg·K）；A為填料面積，m2。

為驗證叉流除濕模型假設(shè)及模型求解正確性，文中利用第1節(jié)介紹的實驗裝置進(jìn)行變空氣流量除濕實驗并和理論模擬結(jié)果進(jìn)行比較，兩組比較結(jié)果見圖3所示。圖3比較空氣出口溫度Ta，out和除濕率mde，顯示除濕率的模擬和實驗值相差在5%內(nèi)，空氣出口溫度的模擬和實驗值相差在0.5℃內(nèi)，比較結(jié)果顯示理論模擬和實驗結(jié)果相一致。

3　填料器除濕效率模型及理論分析

填料除濕器的性能可通過2個除濕效率——濕度效率εy和全熱效率εh來預(yù)測，其計算式分別為：

式中Ya，in，Ya，out為空氣進(jìn)、出口含濕量，kg/kg；YeL，in為溶液入口平衡含濕量, kg/kg；ha，in，ha，out為空氣進(jìn)、出口比焓，kJ/kg；heL，in為溶液入口平衡比焓，kJ/kg。

式（8）能較好表征空氣除濕過程含濕量變化，但同時由于空氣除濕過程會釋放水蒸氣中潛熱致使空氣出口溫度升高，因此有必要對除濕過程中空氣溫度變化進(jìn)行定義。盡管式（9）的全熱效率綜合了空氣濕度和溫度變化但不直觀，需定義一個單獨變量來表征空氣溫度變化程度。文獻(xiàn)[18]類似換熱器原理直接定義溫度效率，但是溶液除濕過程伴隨溫度和濕度的耦合作用與純換熱原理有本質(zhì)區(qū)別。

圖3　叉流除濕實驗和模擬比較Fig.3 Comparison between results of experiments and simulation of cross-flow dehumidification

為此，文中定義等焓率εeh為溶液除濕過程空氣吸收顯熱占整個除濕潛熱的比值，見式（10）。如果空氣在除濕器內(nèi)進(jìn)行等焓除濕（即溶液除濕釋放的潛熱完全被空氣吸收）時，等焓率εeh=1；如果空氣進(jìn)行等溫除濕時，等焓率εeh=0。一般來說εeh界于0～1之間，如果εeh＜0說明空氣除濕過程不但要釋放潛熱而且要釋放顯熱，這是由于溶液溫度低于空氣入口溫度所致；如果εeh＞1說明空氣不但完全吸收釋除濕過程放潛熱而且要部分吸收溶液釋放的顯熱，這是由于溶液溫度高于空氣入口溫度所致。

式中Ta，in，Ta，out為空氣進(jìn)、出口溫度，℃。

由于實驗裝置結(jié)構(gòu)單一，實驗參數(shù)變化受局限，為此文中采用數(shù)值模擬方法研究溶液和空氣入口參數(shù)及填料結(jié)構(gòu)參數(shù)變化對濕度效率及等焓率影響。

圖4為溶液（LiCl-H2O[24]）入口參數(shù)變化對除濕效率作用，圖中比表面積和除濕長度乘積aZ為110。圖4（a）為0.29 kg/kg和0.34 kg/kg兩種不同溶液入口濃度下除濕效率比較。從圖中比較可知，當(dāng)LiCl溶液濃度從0.29上升0.34時，濕度效率略提高0.022～0.033，提高幅度達(dá)2.6～4.7%；等焓率降低0.08～0.11，降幅達(dá)20～30%。圖4（b）為15℃和25℃兩種不同溶液入口溫度下除濕效率比較。當(dāng)溶液入口溫度由15℃上升到25℃時，濕度效率上升，特別是在液氣比小于1.0時濕度效率提高更明顯。在等焓率的變化上，溶液入口溫度變化對其影響巨大，當(dāng)Ts，in＜Ta，in時等焓率εeh為負(fù)值，這是由于空氣通過對流傳熱向溶液釋放顯熱，而除濕潛熱也完全被溶液吸收；反之則溶液和空氣同時吸收除濕潛熱，空氣除濕的等焓率為正值且小于1.0，并隨液氣比增大而有所降低。

圖5為空氣入口參數(shù)變化對除濕效率的影響，圖中比表面積和除濕長度乘積aZ為110。圖5（a）為9.6g/kg和12.3g/kg兩種不同空氣入口含濕量下除濕效率比較。圖中比較可知，當(dāng)空氣入口含濕量從12.3 g/kg下降到9.6 g/kg時，濕度效率隨液氣比下降而提高0.017～0.075，提高幅度2～10%；等焓率上升0.3左右，說明空氣除濕潛熱越小，其越接近的等焓過程。圖5（b）為20℃和30℃兩種不同空氣入口溫度下除濕效率比較。空氣入口溫度越高，濕度效率越低，并且液氣比越低空氣入口溫度變化對濕度效率影響越大。空氣入口溫度對等焓率的作用與溶液入口溫度相似，表現(xiàn)為當(dāng)空氣入口溫度高于溶液溫度時等焓率為負(fù)，反之則為正。

綜上分析可知，當(dāng)液氣比大于2.0時，溶液和空氣入口參數(shù)變化對濕度效率的影響并不明顯，但是對等焓率的影響卻非常顯著，特別是入口溫度變化會直接導(dǎo)致等焓率的巨大波動，甚至出現(xiàn)負(fù)值情況。

除液氣比及入口參數(shù)對濕度效率存在影響外，填料器物理結(jié)構(gòu)尺寸也是影響除濕效率的重要因素。Chung[25]采用復(fù)合變量（aZ）衡量填料尺寸結(jié)構(gòu)，它表示填料比表面積a和填料空氣流道長度Z乘積，是一個無量綱量。圖6 為aZ=110和180兩種規(guī)格的填料器的除濕效率比較。由圖可知，當(dāng)aZ由110提高到180時，濕度效率提高0.1左右，但是等焓率基本重合，說明隨空氣流道長度增加濕度效率提高明顯，但除濕潛熱在空氣和溶液間的分配比例基本維持不變。

綜合上述除濕效率性能分析數(shù)據(jù)，可得到類似Chung提出的LiCl溶液叉流除濕濕度效率及等焓率數(shù)學(xué)表達(dá)式，見式（11）～（13）。等焓率數(shù)學(xué)模型擬合分為εeh＞0和εeh＜0兩種情況，其中包括等溫除濕過程線方程α，其物理含義為當(dāng)填料進(jìn)行空氣等溫除濕時，溶液和空氣入口溫度所需滿足的比例關(guān)系，見式（14）。當(dāng)溶液和空氣入口溫度滿足式（14）時，等焓率εeh計算值為零。

圖4　溶液入口參數(shù)對除濕效率影響Fig.4 Effect of inlet parameters of solution on dehumidification effectiveness

圖5　空氣入口參數(shù)對除濕效率影響Fig.5 Effect of inlet parameters of air on dehumidification effectiveness

圖6　填料結(jié)構(gòu)參數(shù)對除濕效率影響Fig.6 Effect of structure parameters of packing on dehumidification effectiveness

其中，α為等溫除濕過程線，具體表達(dá)式如下：

Γ為無量綱蒸汽壓力，如下：

式中：Pw為與溶液等溫度的純水飽和水蒸氣分壓力，Pa；Ps為溶液表面水蒸氣分壓力，Pa。

上述擬合公式中，濕度效率擬合平均誤差為4%；等焓率擬合平均誤差為7%。

4　結(jié)論

1）文章介紹一種叉流規(guī)則填料除濕裝置結(jié)構(gòu)及實驗流程；通過提出叉流除濕過程物理假設(shè)，建立叉流除濕控制方程，并與相關(guān)實驗結(jié)果對比驗證模型正確性。

2）當(dāng)LiCl溶液濃度從0.29 kg/kg上升0.34 kg/kg時，濕度效率提高幅度達(dá)2.6%～4.7%；等焓率降低降幅達(dá)20%～30%。當(dāng)溶液入口溫度由15℃上升到25℃時，濕度效率在液氣比小于1.0時提高明顯；當(dāng)溶液入口溫度小于空氣入口溫度時等焓率為負(fù)值。當(dāng)空氣入口含濕量從12.3 g/kg下降到9.6 g/kg時，濕度效率提高幅度達(dá)2%～10%；等焓率上升0.3左右；空氣入口溫度越高，濕度效率越低，當(dāng)高于溶液溫度時等焓率為負(fù)。當(dāng)填料比表面積和填料空氣流道長度乘積（aZ）由110提高到180時，濕度效率提高0.1左右，但是等焓率基本重合。另外，濕度效率隨液氣比增加而增加；等焓率隨液氣比增加而下降。

3）最后文章利用線性回歸方法對所有理論計算結(jié)果進(jìn)行擬合得到濕度效率和等焓率隨溶液和空氣流量以及入口參數(shù)變化的擬合關(guān)聯(lián)式，擬合結(jié)果具有較好精度。

[參考文獻(xiàn)]

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Dehumidification efficiency model for solar thermal regeneration system

Peng Donggen1, Zhang Xiaosong2
（1.School of Civil Engineering and Architecture, Nanchang University, Nanchang, 330031, China; 2.School of Energy and Environment, Southeast University, Nanjing, 210096, China）

Abstract:Solar liquid desiccant air-conditioning system has attracted many attentions because of low-energy consumption, and solar liquid regenerator is one of important units in that system.A novel solar liquid regenerator designed by the author is the solar air-pretreatment solution grading collector/regenerator.The proposed liquid regeneration system needs a packed bed dehumidifier, and the prediction of outlet parameters of air in that dehumidifier must be considered for the design of the novel solar liquid regeneration system.A structured packing dehumidifier was designed and the systemic experiments were made at Southeast University in Nanjing, China in 2009.The structured packing dehumidifier has the size of 0.5 m（width）×0.5 m（height）×0.3 m（length）with cross-flow mode.In order to increase flow rate of desiccant solution, instead of injecting directly strong solution into the interior of packed bed, a circulation solution pump was used for supplying solution for the dehumidifier.At the same time, a water-cooled heat exchanger was used to cool circulating solution in advance to control inlet temperature of solution.The experiments were performed under varying conditions including varying flow rates of air and solution and their inlet parameters.However, because of single structure of the experimental unit and limited variation range of experimental parameters, a method of numerical stimulation was used in this paper to study the effects of the inlet parameters of solution and air and the structure parameters of packing on the humidity effectiveness and the isenthalpic effectiveness.The previously experimental data were used to validate numerical model.For this purpose, several assumptions in physics were made, which were followed by the models of cross-flow dehumidification.The numerical simulation showed that as the concentration of LiCl solution increased from 0.29 to 0.34 kg/kg, the humidity effectiveness was increased by 2.6%～4.7% and the isenthalpic effectiveness was reduced by 20%～30%.As the inlet temperature of solution rose from 15 to 25℃, the humidity effectiveness went up, especially when the liquid-gas ratio was less than 1.0.As for isenthalpic effectiveness, the solution inlet temperature had large impact on it and when the inlet temperature of solution was less than that of air, the isenthalpic effectiveness was negative.As the air humidity ratio at the inlet dropped from 12.3 to 9.6 g/kg, the humidity effectiveness was increased by 2%～10% and the isenthalpic effectiveness was increased by about 0.3.The higher inlet temperature of airflow yields the lower humidity effectiveness, and when the liquid-gas ratio is low, the effect of air's inlet temperature on humidity effectiveness is high.The effect of air's inlet temperature on isenthalpic effectiveness is similar to solution's inlet temperature, which shows when the inlet temperature of air is higher than that of solution, the isenthalpic effectiveness is negative and otherwise it is positive.As the product of area per unit volume and length of air flow channel increased from 110 to 180, the humidity effectiveness was increased by about 0.1, however, the isenthalpic effectiveness was basically unchanged.Therefore, the humidity effectiveness increases with the increasing of the inlet temperature, the concentration of solution, the area per unit volume as well as the length of air flow channel, and decreases with the increase in humidity ratio and air temperature at the inlet.The isenthalpic effectiveness is affected dramatically by inlet temperatures of air and solution.Structure parameters of packing have little effect on the isenthalpic effectiveness.Moreover, with the increasing of the liquid-gas ratio, the humidity effectiveness increases and the isenthalpic effectiveness decreases.Finally, 2 equations about humidity effectiveness and isenthalpic effectiveness were obtained by applying a nonlinear regression to rearrange numerical simulation results, which provide the theoretical basis for the modeling of solar air-pretreatment solution grading collector/regenerator.

Keywords:models; solar; liquid desiccant dehumidification; humidity effectiveness; isenthalpic effectiveness; ratio of flowrate of solution to air

作者簡介：彭冬根（1975-），男，博士，副教授，主要從事太陽能制冷空調(diào)研究，南昌南昌大學(xué)建筑工程學(xué)院，330031。Email: ncu_hvac2013@163.com

基金項目：國家自然科學(xué)基金項目（51266010）；江西省科技支撐計劃項目（20123BBG70195）

收稿日期：2015-08-07

修訂日期：2015-11-16

中圖分類號：TK511.3

文獻(xiàn)標(biāo)志碼：A

文章編號：1002-6819（2016）-01-0206-06

doi：10.11975/j.issn.1002-6819.2016.01.029