Hareketli sınır değer problemi olarak tahıl hidrasyonu modellerinin sayısal çözümleri üzerine
Yükleniyor...
Dosyalar
Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ege Üniversitesi, Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez çalışmasında, farklı sınır koşulları altında sabit ve değişken difüzyon katsayılı, bir boyutlu soya fasülyesi hidrasyon modellerinin sayısal çözümleri incelenmiştir. Bir difüzyon modeli olarak ele alınabilen soya fasülyesi hidrasyon modellerinin çözümleri sabit hacim ve değişken hacim altında incelenmiştir. Literatürde Hsu model olarak bilinen, hidrasyon boyunca hacmin değişmediğinin varsayıldığı modelin klasik sonlu fark yöntemleriyle çözümleri incelenmiş, kararlılık analizi yapılmış ve literatürdeki sonuçla karşılaştırılmıştır. Daha sonra, soya fasülyesinin yarıçapının hareketini ifade eden bir fonksiyon yardımıyla hacim değişimi göz önüne alınarak modelin sayısal çözümü yapılmış ve su alım oranları sabit hacimdeki durumla karşılaştırılmıştır. Devam eden bölümde ise hareketli sınır değer problemi olarak ele alınan soya fasülyesi hidrasyon modellerinin sayısal çözümlerine değinilmiştir. Ele alınan modeller, farklı sınır koşulları altında hem sabit difüzyon katsayılı hem de değişken difüzyon katsayılı durumlarda dördüncü ve altıncı mertebeden kompakt sonlu fark yöntemlerinin değişken uzay ızgarası (variable space grid) ve sınır sabitleme (boundary immobilization) yöntemleriyle birlikte düşünülmesiyle çözülmüştür. Elde edilen sonuçlar literatürdeki sonuçla karşılaştırılmıştır. Son olarak, sabit difüzyon katsayılı, yüzey sınırın hidrasyonun başında denge nemine ulaştığı sınır koşuluna sahip soya fasülyesi hidrasyon modeli için kısıtlı integral yönteminden faydalanarak yarıçapın hareketinin ifade edildiği bir diferansiyel denklem elde edilerek, sayısal çözümler yapılmıştır. Elde edilen sonuçlar literatürdeki diğer yöntemlerle karşılaştırılmıştır.
In this thesis, numerical solutions of one dimensional soybean hydration models with constant and variable diffusion coeffcient under different boundary conditions were investigated. The solutions of soybean hydration models, which can be considered as a diffusion model, have been investigated under constant volume and variable volume. The model which is assumed to have no change in volume during hydration known as Hsu model in the literature was solved by using classical finite difference methods. Stability analysis is made and compared with the result in the literature. Then, the numerical solution of the model was solved considering the volume variation by means of a function expressing the movement of the radius of the soybean and the water intake rates were compared with the situation in the constant volume. In the following section, numerical solutions of soybean hydration models which are considered as moving boundary value problem have been mentioned. The models discussed were solved by the fourth and sixth order compact finite difference methods with variable space grid and boundary immobilization methods under both constant diffusion coefficients and variable diffusion coefficients with different boundary conditions. Stability and sensitivity analyzes of the methods were performed. Finally, soybean hydration model with constant diffusion coeffcient and boundary condition reached to equilibrium moisture at the beginning of hydration at surface were investigated. A differential equation expressing the motion of radius is obtained by using the constrained integral method and numerical solution was made. The results obtained were compared with other methods in the literature.
In this thesis, numerical solutions of one dimensional soybean hydration models with constant and variable diffusion coeffcient under different boundary conditions were investigated. The solutions of soybean hydration models, which can be considered as a diffusion model, have been investigated under constant volume and variable volume. The model which is assumed to have no change in volume during hydration known as Hsu model in the literature was solved by using classical finite difference methods. Stability analysis is made and compared with the result in the literature. Then, the numerical solution of the model was solved considering the volume variation by means of a function expressing the movement of the radius of the soybean and the water intake rates were compared with the situation in the constant volume. In the following section, numerical solutions of soybean hydration models which are considered as moving boundary value problem have been mentioned. The models discussed were solved by the fourth and sixth order compact finite difference methods with variable space grid and boundary immobilization methods under both constant diffusion coefficients and variable diffusion coefficients with different boundary conditions. Stability and sensitivity analyzes of the methods were performed. Finally, soybean hydration model with constant diffusion coeffcient and boundary condition reached to equilibrium moisture at the beginning of hydration at surface were investigated. A differential equation expressing the motion of radius is obtained by using the constrained integral method and numerical solution was made. The results obtained were compared with other methods in the literature.
Açıklama
Anahtar Kelimeler
Hareketli Sınır Değer Problemleri, Stefan Problemi, Soya Fasülyesi Hidrasyon Modeli, Sonlu Fark Yöntemleri, Kompakt Sonlu Fark Yöntemleri, İntegral Yöntemi, Moving Boundary Problems, Stefan Problem, Soybean Hydration Model, Finite Difference Methods, Compact Finite Difference Methods, Heat Balance Integral Method
