Study Group Problems
Problem 1: Mathematical Simulation of A Glass Furnace
Industry: Glass
Industry Representative: Eddie Ferreira
Moderator: Gideon Fareo
Student Moderator: Ashleigh Hutchinson
Problem Statement
To improve and control a process optimally, it is necessary to understand and measure the important parameters. This is no different for a glass melting furnace. The chemistry and physics is complex and interdependent. Furthermore, the very high temperatures employed make it very difficult to measure and see everything that is important. However, by making certain assumptions and simplifying it is possible to simulate the process using mathematical models. The accuracy of the simulation depends on the assumptions made and the models used.
It is fairly simple to model the glass flow using the three conservation laws:
- Continuity:
- Momentum conservation:
- Energy conservation:
The general purpose CFD code Ansys Fluent? is implemented at PFG Building Glass to model the glass flows and the combustion space which solves the conservation equations and selected physical models.
The steps involved in solving a CDF problem are:
- Define the modeling goals
- Create the model geometry and mesh
- Set up the solver and physical models
- Compute and monitor the solution
- Examine and save the results
- Consider revisions to the numerical model parameters if necessary
The study group is asked to implement sub-models in step 3 above for the following two processes:
- The batch melting of glass
- The fining and refining process
The end goal is for the models to be implemented and tested in C or Ansys Fluent?.
Modeling Goals
- Model the batch melting process
- Options
- Inputs: empirical constants defining chemical reaction rates, specie properties
- Physical models: reaction rates, specie diffusivity, source terms
- Assumptions
- Computational domain boundaries
- Boundary conditions
- Mesh resolution
During the melting process, a blanket of foam (batch) made up of various chemical by-products forms on top of the molten glass (melt). The batch blanket is constantly melting into the melt. The task is to model the formation and evolution of this batch blanket and its interaction with the melt.
- Model the fining and refining process
- Options
- Inputs: empirical constants defining chemical reaction rates, specie properties
- Physical models: gas diffusion and bubble growth
- Assumptions
- Computational domain boundaries
- Boundary conditions
- Mesh resolution
During the melting process after the batch has melted, the temperature gets high enough for fining gases to be created by chemical reactions. These gases diffuse through the melt into existing bubbles in the melt. The task is to model this diffusion process and the evolution of these bubbles and their dependence and interdependence on temperature.
Mathematical simulation of glass furnace MISG 2013.pdf
Download further information:
GlassribbondPilkingtonMISG2013.pdf, L.A.B. Pilkington (11Mb pdf)
hinchlister2008.pdf, S. Chiu-Webster, E. J. Hinch and J. R. Lister
howellockendon2007.pdf, H. J. J. Gramberg, P. D. Howell and J. R. Ockendon
Problem 2: Predicting Glass Ribbon Shape in the Tin Bath
Industry: Glass
Industry Representative: Eddie Ferreira
Moderator: TBD
Student Moderator: TBD
Problem Statement
During the forming process, the glass-melt flows on top of a bath of molten tin. The forming of glass is essential to the final dimensions of the glass ribbon. The interaction of the bath (tin flows, heating, cooling and forming equipment) with the ribbon is complex and bi-directional i.e. the ribbon shape can affect the bath flow and vice versa. The final dimension of the ribbon is set by customer requirements. The final glass ribbon can suffer optical distortion, related to the forming of the ribbon in the tin bath, which impacts negatively on the quality of the glass product.
A model is required that will predict the ribbon shape in the bath based on typical operational parameters. This will help determine better operating parameters for prevailing conditions in the bath or to trouble shoot optical distortion.
Modeling Goals
- The differential equation describing the ribbon deformation.
- The method of supplying the boundary conditions.
- A method of solving for the ribbon shape given operational parameters.
- A method of coupling the ribbon shape with commercial CFD solvers.
Predicting glass ribbon shape MISG 2013.pdf
Download for further information:
Narayanaswamy1977.pdf, 0. S. Narayanaswamy
Presentation of report back to industry
Predicting glass ribbon MISG 2013.pdf
Problem 3: Optimal management strategy for white rhinoceros
Industry / sector: Conservation / game ranching
Industry representative: Michael ‘t Sas-Rolfes
Moderator:
Student Moderator:
Problem statement
South Africa’s white rhino population is under increasing threat from illegal killing (poaching) to supply the demand for rhino horn in East Asia. As a response to this threat, some rhino owners are taking defensive measures such as dehorning live animals and adopting intensive management practices (elevated stocking rates with supplementary feeding, sometimes outside the rhinos’ natural habitat or traditional range).
Conservationists and certain other interest groups (eco-tourists, trophy hunters) wish to ensure the continued survival of an extensively managed (‘wild’) white rhino population, that is not subject to such interventions – i.e. rhinos are not dehorned, overstocked, artificially fed or otherwise genetically manipulated. However, to maintain rhinos in such extensive conditions is more costly (especially in terms of increasing security needs).
At this time trade in rhino horn is illegal, both within South Africa and to international markets. Some rhino owners argue that reestablishing a legal trade could provide an additional source of income to offset protection costs, thereby helping with rhino conservation. However, such a move would most likely benefit intensive owner/managers more than extensive owner/managers.
Given various production and cost parameters, we can determine the likely effect of a change in trade policy and various demand parameters (as reflected by the market price of rhino horn). If rhino specialists can specify a minimum viable population of rhinos to retain under extensive conditions, we can also determine whether and when a legal trading regime might threaten the so-called wild populations, and we can also determine whether intensive managers may need to subsidize the protection costs borne by extensive managers and to what extent.
Modelling goals
- Model the production functions of three types of producers: intensive, extensive and illegal to determine optimal harvesting levels (this is an optimal control problem)
- Model the interaction between the three types of producers under two different strategies: legal trade and illegal trade
- Model the effects of changing demand conditions (using prices as a proxy)
Intensive production function
Costs: Fences, feedstock, security, dehorning
Revenues: Live sales, horn sales (under legal trade)
Extensive production function
Costs: Fences, security, veterinary
Revenues: Conservation subsidies, tourism, trophy hunting, live sales
Illegal harvest function
Costs: equipment, transport, bribes, probable cost of punishment
Revenues: horn sales
Presentation of report back to industry
FinalpressRhinoMISG2013.pdf
Problem 4: Optimal flat glass shapes
Industry: Glass
Industry representative: Riaan von Wielligh
Moderators: Dario Fanucchi and Montaz Ali
Student Moderator:
Problem ststement
In the glass Industry our group manufacture and caters for various segments of the South African and International markets in terms of glass quality and application.
In the Domestic Automotive stream we manufacture glass from sand and supply finished glass components to the Local Motor manufacturers, the replacement glass for vehicles on the road as well as replacement glass for vehicles in Europe.
As manufacturer of glass we receive forecast from Manufacturers and Distributors of glass which must be consolidated and converted to manufacturing requirements. Because of unpredictability of the requirements and the wide range of products that we offer as a group we need to rationalise the range of flat sizes that we produce as input to produce the final shapes in our Automotive Glass manufacturing division.
An optimisation model is required where the group can enter our flat glass forecast requirements and the model will calculate the optimal flat glass shapes that we need to manufacture in anticipation of the actual orders received.
Real data will be provided to solve the problem, it will be a 2D optimisation problem where the input will be provided in square or rectangular shapes and the output, must be provided as a manufacturing requirement in a square or rectangular shapes, taking into consideration the manufacturing constraints of the process
Modelling Goals
To minimise the glass wastage from the manufacturing process to the final shape produced for our customer base. (The cutting up of a larger shape to a smaller final shape)
The model must take the various manufacturing parameters of the production lines that produce the required glass shapes into consideration.
There are also product attributes that must be taken into consideration: Colour, Thickness and orientation.
At the end of the day a model is required to convert a Forecasted requirement into an optimal Manufacturing requirement, taking into consideration the physical process constraints.
Click here to download the data file for the glass optimisation problem.
Presentation of problem statement
Domestic automotive glass optimisation problem