人工林杉木干燥过程传热传质数值模拟
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摘要
干燥过程中的传热传质速率影响锯材的干燥质量与干燥能耗，传热传质数学模型可以定量分析干燥过程中水分与热量的传递规律，为优化干燥工艺与节能减排提供理论基础。因此，开展木材干燥传热传质数学模型构建与分析的研究具有重要的理论意义和实际价值。
本文以杉木（Cunninghamia lanceolata [Lamb.] Hook.）人工林木材作为试验材料，建立了早晚材密度沿径向分布的数学模型；基于这一密度分布数学模型，考虑了木材早晚材密度不均匀性对木材干燥的影响，分别建立径切板与弦切板干燥过程中传热传质的一维数学模型；并采用X射线扫描法与称重法分别监测干燥过程中无疵小试件的含水率分布规律与锯材平均含水率的经时变化规律，验证了传热传质模型的准确性与可行性；最后，以径切板传热传质数学模型为依据，定性分析了干燥介质、物性参数、锯材厚度对干燥速率的影响。主要结论如下：
1、通过正弦波函数定量描述了树木生长环境中温度周期性变化，函数拟合的决定系数为0.907；利用分段线性函数定量描述了树木生长环境中降雨量的周期性变化；由此所得的树木生长速率模型可准确分析温度与降雨量对树木生长速率的影响。基于树木生长速率模型所构建的早晚材密度分布模型准确描述了木材密度沿径向的分布规律，为木材密度在宏观与微观上的内在联系提供了理论依据，也为定量分析早晚材密度不均匀性对木材干燥的影响提供了数学基础。
2、利用菲克扩散定律（Fick's law of diffusion）与傅里叶定律（Fourier law）分别表征了木材干燥过程中的传质与传热过程。基于径切板与弦切板在干燥过程中水分移动方向上不同的密度分布函数，分别建立了木材干燥传热传质的“多场-相变-扩散”一维数学模型，并利用有限差分数学方法及Fortran语言编写计算程序，结合定解条件，得出了木材干燥传热传质数学模型的数值解。
3、通过切片法验证了X射线扫描法在分层含水率测定中的适用性，两种方法测量的分层含水率无显著差异（P>0.05），表明X射线扫描法能准确获得木材含水率分布。利用该方法，实测了径切板与弦切板的无疵小试件在干球温度60℃（湿球温度40℃）与干球温度90℃（湿球温度75℃）时分层含水率随时间的变化规律，并分别与径切板与弦切板传热传质模型所得的分层含水率进行比较，曲线拟合较好，表明木材传热传质模型可以反映木材干燥过程中含水率的分布状况；通过径切板与弦切板在不同干湿球温度（45℃/25℃、60℃/40℃、75℃/55℃与90℃/75℃）下的干燥试验，测定了木材的平均含水率随时间变化的规律，并与木材传热传质模型计算结果进行比较，二者吻合较好，进一步表明本研究所构建的木材传热传质模型能反映木材干燥的传热传质行为。
4、通过对干燥传热传质模型的理论分析，在木材恒速干燥阶段，干燥速率取决于表面蒸发率，而干燥介质是表面蒸发率的主要影响因子；干燥介质的温度越高、相对湿度越小、流动速度越大，则木材干燥速率越快；但当干燥介质流动速度超过1.5m/s时，木材干燥速率增加不明显。在减速干燥阶段，干燥速率取决于体积蒸发率与界面蒸发率，而木材自身物性是体积蒸发率与界面蒸发率的主要影响因子；等效质扩散率与导热系数越大、木材厚度越小，则干燥速率越快；但与等效质扩散率相比，导热系数对木材干燥速率的影响较小。
Drying quality and energy consumption was influenced by heat and mass transfer ratesduring the sawn drying. The transfer law of moisture and heat during wood drying can bedescribed quantitatively by heat and mass model, which provided theoretical basis foroptimizing drying process and energy conservation. Therefore, the reaserch on heat and masstransfer model building and analysis had important theoretical significance and practical value.
A mathematical model about earlywood and latewood density radial distribution wasestablished by taking Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) plantation woodas an example. Based on this model, considering the effect of non-uniform earlywood andlatewood density on wood drying, two one-dimensional mathematical model were establishedfor separately describing heat and mass transfer in quarter-sawn lumber and flat-sawn lumberdrying process. Moisture content (MC.) distribution in small flawless and average MCvariation in sawn lumber during drying was separately detected by X-ray method and weighingmethod, which was used for testing the accuracy and feasibility of the mass and heat transfermodels. In the end, based on the models about heat and mass transfer in quarter-sawed lumber,the effect of drying medium, physical parameters, lumber thickness on drying rate wasqualitatively analyzed. The results showed that:
1. Tree growth temperature cycling was quantitively described by sine wave function, andthe function fitting coefficient of determination was0.907. Cyclical changes in rainfall duringtree growth was quantitively described by piecewise linear function. Tree growth rate modelgot from them can accurately analyze temperature and rainfall effects on tree growth rate. Themodel about earlywood and latewood density based on tree growth rate model can accuratelydescribe wood density ridial distribution, which provided theoretical basis for the wood densityon the macro and micro intrinsic link, as well as mathematical foundation for quantitivelyanalyzing effects of earlywood and latewood non-uniform density on wood drying.
2. Heat and mass transfer during wood drying process was separately expressed byFourier law and Fick's law of diffusion. Based on the density distribution function ofquarter-sawed lumber and flat-sawed lumber drying, a one-dimensional mathematical modeldescribing heat and mass transfer “multi field-phase transitions-diffusion” was established.Using finite difference method and FORTRAN language programming, with boundaryconditions, numerical solutions of this model was obtained.
3. Using slicing method to test the applicability of X-ray scanning method in layer MCdetection. The result showed that there was no significant differece between them (P>0.05),and we can get accurate MC distribution in wood by X-ray scanning method. With this method,layer MC variation of quarter-sawed lumber and flat-sawed lumber under dry bulb temperature60℃(wet bulb temperature40℃) and dry bulb temperature90℃(wet bulb temperature75℃)were detected. Then, it compared with the result got from heat and mass transfer model. Itindicated that the model can reflect the MC distribution during wood drying process. Thevariation of average MC got from drying test that quarter-sawed lumber and flat-sawed lumberunder different dry bulb temperature and wet bulb temperature was good agreement with theresult obtained from heat and mass transfer model. Therefore, it showed that the heat and masstransfer model can reflect heat and water transfer in wood drying.
4. Through the heat and mass transfer model, we can can draw some condusions: in woodconstant drying stage, drying rate depended on the surface evaporation rate, and dryingmedium was main factors affecting the rate of surface evaporation. The higher the dryingmedium temperature, the smaller the relative humidity, the greater the flow rate, and the fasterthe drying rate of sawn drying. When the flow rate of the air surpassed1.5m/s，it had nosignificant effects on wood drying rate. In the slowly drying stage, drying rate depended onvolume evaporation rate and interface evaporation rate, which were determined by woodphysical properties. The equivalent mass diffusion rate and thermal conductivity had positivecorrelation with wood drying rate; while timber thickness had negative correlation with drying rate. The effect of thermal conductivity was smaller than equivalent mass diffusion rate.
本文以杉木（Cunninghamia lanceolata [Lamb.] Hook.）人工林木材作为试验材料，建立了早晚材密度沿径向分布的数学模型；基于这一密度分布数学模型，考虑了木材早晚材密度不均匀性对木材干燥的影响，分别建立径切板与弦切板干燥过程中传热传质的一维数学模型；并采用X射线扫描法与称重法分别监测干燥过程中无疵小试件的含水率分布规律与锯材平均含水率的经时变化规律，验证了传热传质模型的准确性与可行性；最后，以径切板传热传质数学模型为依据，定性分析了干燥介质、物性参数、锯材厚度对干燥速率的影响。主要结论如下：
1、通过正弦波函数定量描述了树木生长环境中温度周期性变化，函数拟合的决定系数为0.907；利用分段线性函数定量描述了树木生长环境中降雨量的周期性变化；由此所得的树木生长速率模型可准确分析温度与降雨量对树木生长速率的影响。基于树木生长速率模型所构建的早晚材密度分布模型准确描述了木材密度沿径向的分布规律，为木材密度在宏观与微观上的内在联系提供了理论依据，也为定量分析早晚材密度不均匀性对木材干燥的影响提供了数学基础。
2、利用菲克扩散定律（Fick's law of diffusion）与傅里叶定律（Fourier law）分别表征了木材干燥过程中的传质与传热过程。基于径切板与弦切板在干燥过程中水分移动方向上不同的密度分布函数，分别建立了木材干燥传热传质的“多场-相变-扩散”一维数学模型，并利用有限差分数学方法及Fortran语言编写计算程序，结合定解条件，得出了木材干燥传热传质数学模型的数值解。
3、通过切片法验证了X射线扫描法在分层含水率测定中的适用性，两种方法测量的分层含水率无显著差异（P>0.05），表明X射线扫描法能准确获得木材含水率分布。利用该方法，实测了径切板与弦切板的无疵小试件在干球温度60℃（湿球温度40℃）与干球温度90℃（湿球温度75℃）时分层含水率随时间的变化规律，并分别与径切板与弦切板传热传质模型所得的分层含水率进行比较，曲线拟合较好，表明木材传热传质模型可以反映木材干燥过程中含水率的分布状况；通过径切板与弦切板在不同干湿球温度（45℃/25℃、60℃/40℃、75℃/55℃与90℃/75℃）下的干燥试验，测定了木材的平均含水率随时间变化的规律，并与木材传热传质模型计算结果进行比较，二者吻合较好，进一步表明本研究所构建的木材传热传质模型能反映木材干燥的传热传质行为。
4、通过对干燥传热传质模型的理论分析，在木材恒速干燥阶段，干燥速率取决于表面蒸发率，而干燥介质是表面蒸发率的主要影响因子；干燥介质的温度越高、相对湿度越小、流动速度越大，则木材干燥速率越快；但当干燥介质流动速度超过1.5m/s时，木材干燥速率增加不明显。在减速干燥阶段，干燥速率取决于体积蒸发率与界面蒸发率，而木材自身物性是体积蒸发率与界面蒸发率的主要影响因子；等效质扩散率与导热系数越大、木材厚度越小，则干燥速率越快；但与等效质扩散率相比，导热系数对木材干燥速率的影响较小。
Drying quality and energy consumption was influenced by heat and mass transfer ratesduring the sawn drying. The transfer law of moisture and heat during wood drying can bedescribed quantitatively by heat and mass model, which provided theoretical basis foroptimizing drying process and energy conservation. Therefore, the reaserch on heat and masstransfer model building and analysis had important theoretical significance and practical value.
A mathematical model about earlywood and latewood density radial distribution wasestablished by taking Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) plantation woodas an example. Based on this model, considering the effect of non-uniform earlywood andlatewood density on wood drying, two one-dimensional mathematical model were establishedfor separately describing heat and mass transfer in quarter-sawn lumber and flat-sawn lumberdrying process. Moisture content (MC.) distribution in small flawless and average MCvariation in sawn lumber during drying was separately detected by X-ray method and weighingmethod, which was used for testing the accuracy and feasibility of the mass and heat transfermodels. In the end, based on the models about heat and mass transfer in quarter-sawed lumber,the effect of drying medium, physical parameters, lumber thickness on drying rate wasqualitatively analyzed. The results showed that:
1. Tree growth temperature cycling was quantitively described by sine wave function, andthe function fitting coefficient of determination was0.907. Cyclical changes in rainfall duringtree growth was quantitively described by piecewise linear function. Tree growth rate modelgot from them can accurately analyze temperature and rainfall effects on tree growth rate. Themodel about earlywood and latewood density based on tree growth rate model can accuratelydescribe wood density ridial distribution, which provided theoretical basis for the wood densityon the macro and micro intrinsic link, as well as mathematical foundation for quantitivelyanalyzing effects of earlywood and latewood non-uniform density on wood drying.
2. Heat and mass transfer during wood drying process was separately expressed byFourier law and Fick's law of diffusion. Based on the density distribution function ofquarter-sawed lumber and flat-sawed lumber drying, a one-dimensional mathematical modeldescribing heat and mass transfer “multi field-phase transitions-diffusion” was established.Using finite difference method and FORTRAN language programming, with boundaryconditions, numerical solutions of this model was obtained.
3. Using slicing method to test the applicability of X-ray scanning method in layer MCdetection. The result showed that there was no significant differece between them (P>0.05),and we can get accurate MC distribution in wood by X-ray scanning method. With this method,layer MC variation of quarter-sawed lumber and flat-sawed lumber under dry bulb temperature60℃(wet bulb temperature40℃) and dry bulb temperature90℃(wet bulb temperature75℃)were detected. Then, it compared with the result got from heat and mass transfer model. Itindicated that the model can reflect the MC distribution during wood drying process. Thevariation of average MC got from drying test that quarter-sawed lumber and flat-sawed lumberunder different dry bulb temperature and wet bulb temperature was good agreement with theresult obtained from heat and mass transfer model. Therefore, it showed that the heat and masstransfer model can reflect heat and water transfer in wood drying.
4. Through the heat and mass transfer model, we can can draw some condusions: in woodconstant drying stage, drying rate depended on the surface evaporation rate, and dryingmedium was main factors affecting the rate of surface evaporation. The higher the dryingmedium temperature, the smaller the relative humidity, the greater the flow rate, and the fasterthe drying rate of sawn drying. When the flow rate of the air surpassed1.5m/s，it had nosignificant effects on wood drying rate. In the slowly drying stage, drying rate depended onvolume evaporation rate and interface evaporation rate, which were determined by woodphysical properties. The equivalent mass diffusion rate and thermal conductivity had positivecorrelation with wood drying rate; while timber thickness had negative correlation with drying rate. The effect of thermal conductivity was smaller than equivalent mass diffusion rate.
引文
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