Numerička analiza fermentacijskog spremnika za proizvodnju piva

undergraduate thesis

• Title (english): Numerical analysis of fermentation tank for beer production
• Author: Luka Labar
• Mentor: Ivica Skozrit (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2022-03-03, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Tema ovog rada je numerička analiza fermentacijskog spremnika za proizvodnju piva. Na početku rada dan je kratki uvod o proizvodnji piva te o spremnicima za fermentaciju istog. Za odabrani spremnik iskoristivog volumena 1000 l i ukupnog volumena 1200 l izvršen je analitički i numerički proračun. Geometrija odabranog spremnika sastavljena je od konusne, sferne i dvije cilindrične ljuske te od tanke kružne ploče. Prije samog proračuna dan je kratki teorijski uvod o tankim kružnim pločama i ljuskama te o metodi konačnih elemenata (MKE). Analitički proračun proveden je primjenom jednadžbi izvedenih iz teorije tankih kružnih ploča i ljuski. Za svaki dio spremnika određeni su i u dijagramu prikazani radijalni pomaci i zakreti. Također, određena su naprezanja na kritičnim mjestima spremnika. Primjenom Trescine teorije čvrstoće na tim mjestima određena su ekvivalentna naprezanja te je na osnovu najvećeg dobivenog naprezanja provjerena čvrstoća spremnika u odnosu na granicu elastičnosti odabranog materijala spremnika. Numerički proračun izveden je primjenom programskog paketa Abaqus® koji se temelji na metodi konačnih elemenata (MKE). Verifikacija konačnih elemenata za ovu analizu napravljena je na primjeru jedne cilindrične ljuske opterećene konstantnih tlakom. Različitim vrstama konačnih elemenata i različitim gustoćama mreže prikazana je konvergencija rješenja te je na taj način opravdana upotreba konačnih elemenata za glavni proračun. Provedbom glavnog proračuna određeni su radijalni pomaci i zakreti svakog dijela spremnika te ekvivalentna naprezanja na kritičnim mjestima. Radijalni pomaci i zakreti prikazani su u dijagramima te grafički na cijelom spremniku i u detaljnijem pogledu u blizini spojeva. Ekvivalentna naprezanja određena su primjenom Trescine i von Misesove teorije čvrstoće te su ista prikazana grafički na cijelom spremniku i u detaljnijem pogledu za svako kritično mjesto. Za najveće naprezanje dobiveno Trescinom teorijom čvrstoće provjerena je čvrstoća spremnika u odnosu na granicu elastičnosti odabranog materijala spremnika. Rezultati dobiveni primjenom obje metode uspoređeni su. Radijalni pomaci i zakreti uspoređeni su u preklopljenim dijagramima, a ekvivalentna naprezanja dobivena primjenom Trescine teorije čvrstoće uspoređena su tablično te je prikazana relativna pogreška numeričkog rješenja.

Abstract (english)

The topic of this paper is the numerical analysis of the fermentation tank for beer production. At the beginning of the paper, a brief introduction was presented on the production of beer and fermentation tanks. Analytical and numerical calculations were performed for the selected tank with a usable volume of 1000 l and a total volume of 1200 l. The geometry of the selected tank consists of one conical, one spherical and two cylindrical shell and a thin circular plate. Before the calculation, a brief theoretical introduction on thin circular plates and shells and on the finite element method (FEM) was presented. Analytical calculation was performed using equations derived from the theory of thin circular plates and shells. Radial displacements and rotations were determined for each part of the tank and shown in the diagram. Also, stresses were determined at critical places of the tank. By applying Tresca’s failure theory, equivalent stresses were determined at these places, and based on the highest stress obtained, the strength of the tank was examined in relation to the elastic limit of the selected tank material. Numerical calculation was performed using the Abaqus® software package based on the finite element method (FEM). Verification of finite elements for this analysis was made on the example of one cylindrical shell loaded with constant pressure. Different types of finite elements and different mesh densities show the convergence of solutions, thus justifying the use of finite elements for the main calculation. By applying main calculation radial displacements and rotations were determined for each part of the tank as well as the equivalent stresses at critical places. Radial displacements and rotations are shown in diagrams and graphically throughout the tank and in a more detailed view near the joints. Equivalent stresses were determined using Tresca’s and von Mises failure theory and are shown graphically throughout the tank and in more detailed view for each critical place. For the highest stress obtained by Tresca’s failure theory, the strength of the tank in relation to the elastic limit of the selected tank material was examined. The results obtained using both methods were compared. Radial displacements and rotations are compared in overlapping diagrams and the equivalent stresses obtained by applying Tresca’s failure theory are compared by the means of table and the relative error of the numerical solution is shown.

• Keywords: Abaqus®; cilindar; čvrstoća; fermentacija; konus; ljuska; metoda konačnih elemenata (MKE); naprezanje; numerička analiza; ploča; sfera; spremnik; Tresca
• Keywords (english): Abaqus®; cone; cylinder; fermentation; finite element method (FEM); numerical analysis; plate; shell; sphere; strength; stress; tank; Tresca
• Language: croatian
• URN:NBN: urn:nbn:hr:235:387185
• Study programme: Title: Mechanical Engineering; specializations in: Design, Process and Energy Engineering, Production Engineering, Engineering Modelling and Computer Simulation, Marine Engineering, Industrial Engineering and Management, Materials Engineering; Course: Engineering Modelling and Computer Simulation; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-02-24 07:23:15