Üzümlerin mikrodalga kurutma eğrilerinin ve sıcaklık değişiminin matematiksel modellenmesi

Modeling of drying curves and temperature profiles of microwave-assisted convective drying of grapes

Özet

Bu çalışmada, Türkiye'nin önemli ihraç ürünlerinden olan üzümün kuruması esnasında kararmaya neden olan Polifenol Oksidaz enziminin, çocuklarda ve yaşlılarda astım, isilik ve mide rahatsızlıklarına neden olabilen sülfıt kullanılmadan inaktive edilmesi ve aynı zamanda da kuruma hızının arttırılması amaçlanmıştır. Mikrodalga yardımlı konvektif kurutma, konvansiyonel kurutma yöntemlerine göre daha hızlı olduğundan ve gıda maddesinde bulunan dipolar su molekülleri ile etkileşebilmesinden dolayı etkin bir kurutma işlemine olanak sağlamaktadır. Gıda içindeki sıcaklık artışının modellenmesi mikrodalga ısıtma ve kurutma işleminin kontrolü açısından önem arz etmektedir. Kurutma hızını daha da arttırmak ve iyi bir son ürün elde edebilmek amacıyla üzümler kurutma işleminden önce 40°C sıcaklığındaki etil oleat ve potasyum karbonat içeren çözelti içine 3 dakika süreyle daldırılmış veya 90°C'deki buharla 140 saniye süreyle haşlanarak önişlenmişlerdir. Üzümler önişlemlerden sonra mikrodalga yardımlı konvektif kurutucuda 0,25 W/g başlangıç mikrodalga güç oranı ve 60°C. sıcaklığında ortalama 1.8 m/s hızındaki hava ile kurutulmuşlardır. Matlab programının Eğri Yaklaştırma (CFT) araç kutusu kullanılarak kuruma eğrileri literatürdeki ince tabaka modelleri ile tanımlanmışlardır. Kuruma esnasındaki sıcaklık değişimleri fiber optik prob kullanılarak ölçülmüş ve Matlab programının Kısmi Diferansiyel Denklem (PDE) araç kutusu kullanılarak matematiksel olarak modellenmiş ve simüle edilmiştir. Matematiksel modelde mikrodalga enerjisi hacimsel ısı üretim kaynağı olarak kabul edilmiş ve kuruma esnasında meydana gelen ve ince tabaka modelleriyle hesaplanan nem kaybı, evaporatif ısı kaybı olarak modele dahil edilmiştir. Sonuçları literatürdeki çalışmalar ile karşılaştırdığımızda, mühendislik açısından gerekli yakınsaklık sağladığı gözlenmiştir.

Abstract

Raisin is an important export product of Turkey and darkens during drying due to the enzyme Polyphenol Oxidase (PRO). To prevent browning reactions, these products are sulfited. Ingestion of sulfites can lead to asthmatic attacks, rashes and abdominal upset especially for elderly people and children. For these reasons sulfites are either prohibited or subject to very low limits in USA. Thompson seedless grapes were used in this study. Grapes were dipped into 2% ethyl oleate (v/v) and 5% potassium carbonate solution (m/v) at 40°C for 3 minutes and were blanched with steam at 90°C for 140 seconds. The aims of these pretreatments were to accelerate drying rate and to inactivate PPO without the use of sulphur dioxide. Pretreated grapes were dried in a microwave-assisted convective dryer. Center temperature profile of grapes were obtained using a fiber optic probe. It was observed that 0.25 W/g initial power ratio combined with 60°C convective air produced better end-product thus in this study drying curves and temperature profiles were modeled at this selected condition.The thin layer drying models were used to describe the drying curves of both pretreated and untreated grapes. Using curve fitting tool (CFT) of Matlab software, non-linear regression analysis were performed to thin layer models. Regression coefficient (R2), Sum of Squares Due to Error (SSE) and Root Mean Square Error (RMSE) were adopted to evaluate the goodness of fit in each model. Among the thin layer models, drying curves of microwave-assisted drying of both untreated and pretreated grapes at 0.25 W/g initial power ratio and 60°C convective air temperature could be accurately described by all of the applied thin-layer models. For all cases the R2 were greater than 0.97 and SSE and RMSE were close to zero. In order to compare the moisture loss with time, derivative of logarithmic model with respect to time was taken. It was found that moisture loss of untreated and chemically dipped grapes could be considered as same however, moisture loss of steam blanched grapes were 2.30 times higher than untreated and chemically dipped grapes until 300 minutes drying.It is critical to have knowledge of dielectric properties, relative dielectric constant and relative dielec- tric loss factor, of materials which are the most important physical properties in microwave heating. In this study dielectric properties of grapes were calculated using descriptive equations for fruits and vegetables. In these equations dielectric properties of materials were related with temperature and moisture content. Within the temperature range of this study, temperature had negligible effect on the values of dielectric properties of grapes. Thus during microwave-assisted convective drying of grapes, only moisture dependent dielectric properties were taken into consideration. Electric field in the grapes was calculated through calorimetry. Since the penetration depth of microwave energy was less than radius of grape, integral average of electric field within the grape was calculated. The thermophysical properties, density, specific heat and heat conduction coefficient of grapes were also calculated using descriptive equations. The results were in close agreement with the literature.Experimental center temperature of grapes was modeled using a one dimensional heat equation which uses microwave energy as a heat generation source term. The main assumptions to solve this equation were that the initial temperature and moisture content of grapes were uniform, both heat and moisture flows in radial direction and heat losses due to radiation were negligible. For simulations Partial Differential Equation Toolbox of Matlab was used. Generic Scalar equation type was selected and the partial differential equation was specified to be parabolic type. Since Matlab requires boundary conditions to be specified to solve the time and space dependent differential equation, Neumann boundary condition was selected due to constant heat flux provided by convective air with a velocity of 1.8 m/s and temperature at 60°C. Since Thompson seedless grapes could be approximated to cylinders, both the boundary conditions and the differential equation were expressed in cylindrical coordinates.It was found that the maximum difference between experimental and simulation values were 4°C was during initial heating up period. However, after then the difference was less than 1°C. Since the phase changes of grapes were not incorporated into the model, sudden increase in temperature below 56% moisture content could not be predicted by the proposed simulation model.