AbstractThe present research features the problems of wheat processing. Wheat processing has its own specific features. For instance, the process of gluten extrusion forming is very complex since it is associated with the visco-elastic and adhesive properties of raw gluten. The article discusses the results of applying the numerical finite difference method to the Navier-Stokes equation in the case of the one-dimensional problem when a cooled viscoelastic material has to pass through circular nozzles. The paper also features the obtained surface model of velocity evolution and some averaged results for the possible automation of the process. The viscosity properties of raw gluten are variable and depend on temperature, chemical composition, and properties of the raw material. Modeling makes it possible to characterize the properties of the material and its behavior in various situations. Such research demands neither additional time nor significant costs. The authors identified patterns of movement for raw gluten in the extrusion molding unit and selected the most appropriate automation system to control the speed of its movement to the molding assembly in the grinder feed screw. The significance of the research is obvious for subsequent physical and mathematical modeling of heat and mass transfer processes of vacuum freezing and drying and granulating of gluten extrusions. The results of the research presented in the article are consistent with the available information on this topic. The present approach to solving the problem of choosing the best rational hydrodynamic regimes was applied due to the complexity of the experimental determination of velocity fields and the difficulty of analyzing the Navier-Stokes system of hydrodynamic differential equations with variable proportionality coefficients.
KeywordsNavier-Stokes equation, numerical methods, non-Newtonian fluids, technical means of process control
- Aleksanyan IYu, Buynov AA. Vysokointensivnaya sushka pishchevykh produktov. Penosushka. Teoriya. Praktika. Modelirovanie [High-intensity food drying. Foam drying. Theory. Practice. Modeling]. Astrakhan: Astrakhan State Technical University; 2004. 380 p. (In Russ.).
- Vanin SV, Kolpakova VV. Funktsionalʹnye svoystva sukhoy pshenichnoy kleykoviny raznogo kachestva [Functional properties of dry wheat gluten of different quality]. News of Institutes of higher education. Food Technology. 2007;296(1):21–24. (In Russ.).
- Ananʹev PA, Volkov PK, Pereverzev AV. Issledovanie korrektnosti kraevykh zadach dlya uravneniy Navʹe-Stoksa v estestvennykh peremennykh [Correctness of boundary value problems for the Navier-Stokes equations in natural variables]. Mathematical Models and Computer Simulations. 2004;16(7):68–76. (In Russ.).
- State Standard 31934-2012. Wheat gluten. Specifications. Moscow: Standartiform; 2013.
- Demidovich BP, Maron IA, Shuvalova EhZ. Chislennye metody analiza. Priblizhenie funktsiy, differentsialʹnye i integralʹnye uravneniya [Numerical analysis methods. Approximation of functions, differential and integral equations]. St. Petersburg: Lan; 2010. 400 p. (In Russ.).
- Volkov PK. On the source of motion of liquids. Yugra State University Bulletin. 2011;21(2):8–28. (In Russ.).
- Lapchik MP, Ragulina MI, Khenner EK. Ehlementy chislennykh metodov [Elements of numerical methods]. Moscow: Akademia; 2007. 224 p. (In Russ.).
- Nugmanov AH-H, Maximenko YuA, Aleksanian AI, Aleksanian OA. Investigation of physical and chemical properties of minced fish, dry vegetable premixes and their mixtures. Vestnik of Astrakhan State Technical University. Series: Fishing Industry. 2018;(2):135–148. (In Russ.). DOI: https://doi.org/10.24143/2073-5529-2018-2-135-148.
- Markin EE, Skachkov PP. Solution of the navier stokes complete system of equations with parallelization of the computation process. European Student Scientific Journal. 2017;(2):70–78. (In Russ.).
- Pontryagin LS. Obyknovennye differentsialʹnye uravneniya [Ordinary differential equations]. Moscow: Lenand; 2019. 336 p. (In Russ.).
- Shkhalakhov DS, Nesterenko AA. Ispolʹzovanie rastitelʹnykh belkov v myasnoy promyshlennosti posredstvom dobavleniya belkovozhirovoy ehmulʹsii [Use of vegetable proteins in meat industry by adding a protein-fat emulsion]. Young Scientist. 2016;127(23):109–111. (In Russ.).
- Wang ZJ. High-order methods for the Euler and Navier-Stokes equations on unstructured grids. Progress in Aerospace Sciences. 2007;43(1–3):1–41. DOI: https://doi.org/10.1016/j.paerosci.2007.05.001.
- Wang L, Mavriplis DJ. Adjoint-based h-p adaptive Discontinuous Galerkin methods for the compressible Euler equations. 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition; 2009; Orlando, USA. Orlando, USA, 2009.
- Tan Z, Le DV, Li Z, Lim KM, Khoo BC. An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane. Journal of Computational Physics. 2008;227(23):9955–9983. DOI: https://doi.org/10.1016/j.jcp.2008.08.013.
- Powell CE, Silvester DJ. Preconditioning Steady-State Navier--Stokes Equations with Random Data. SIAM Journal on Scientific Computing. 2012;34(5):A2482–A2506. DOI: https://doi.org/10.1137/120870578.
- Bruyatskiy EV, Kostin AG, Nikiforovich EI, Rozumnyuk NV. Metod chislennogo resheniya uravneniy Navʹe-Stoksa v peremennykh skorostʹ–davlenie [Numerical solution method of the Navier-Stokes equations in velocity – pressure variables]. Prikladna gidromekhanika [Applied Hydromechanics]. 2008;10(2):13–23. (In Russ.).