# Publications

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## 2005 |

Jemcov, ALeksandar; Mathur, Sanjay Nonlinear Parameter Estimation in Inviscid Compressible Flows in Presence of Uncertainties Conference CFD2005 Conference CFD Society of Canada, CFD Society of Canada 2005. Abstract | Links | BibTeX | Tags: AEM, Algorithm, C++, Compressible, Flow, SEM, Velocity @conference{jemcov2005nonlinear, title = {Nonlinear Parameter Estimation in Inviscid Compressible Flows in Presence of Uncertainties}, author = { ALeksandar Jemcov and Sanjay Mathur}, url = {https://www.researchgate.net/profile/Aleksandar_Jemcov/publication/265161046_NONLINEAR_PARAMETER_ESTIMATION_IN_INVISCID_COMPRESSIBLE_FLOWS_IN_PRESENCE_OF_UNCERTAINTIES/links/54009fa20cf2c48563ae5881.pdf?origin=publication_detail_rebranded&ev=pub_int_prw_xdl&msrp=Eb6hxD11VAw8qlL87p7OgqEvootFE1qcP1%2B29eaQTXDZQJsA8p7cxhtWYujmiizIS6g9Ghe%2Fs%2FiKlYpqUkiuGg%3D%3D_xyhmRLK3POGJnefHrNX7GIlJ13cJFypuToDg6Wh3WROQGJDU9efiaEfVb4Ncmlvxom8DUrMXvQfMj5PjopEZKw%3D%3D&inViewer=1}, year = {2005}, date = {2005-01-01}, booktitle = {CFD2005 Conference CFD Society of Canada}, organization = {CFD Society of Canada}, abstract = {The focus of this paper is on the formulation and solution of inverse problems of parameter estimation using algorithmic differentiation. The inverse problem formulated here seeks to determine the input parameters that minimize a least squares functional with respect to certain target data. The formulation allows for uncertainty in the target data by considering the least squares functional in a stochastic basis described by the covariance of the target data. Furthermore, to allow for robust design, the formulation also accounts for uncertainties in the input parameters. This is achieved using the method of propagation of uncertainties using the directional derivatives of the output parameters with respect to unknown parameters. The required derivatives are calculated simultaneously with the solution using generic programming exploiting the template and operator overloading features of the C++ language. The methodology described here is general and applicable to any numerical solution procedure for any set of governing equations but for the purpose of this paper we consider a finite volume solution of the compressible Euler equations. In particular, we illustrate the method for the case of supersonic flow in a duct with a wedge. The parameter to be determined is the inlet Mach number and the target data is the axial component of velocity at the exit of the duct.}, keywords = {AEM, Algorithm, C++, Compressible, Flow, SEM, Velocity}, pubstate = {published}, tppubtype = {conference} } The focus of this paper is on the formulation and solution of inverse problems of parameter estimation using algorithmic differentiation. The inverse problem formulated here seeks to determine the input parameters that minimize a least squares functional with respect to certain target data. The formulation allows for uncertainty in the target data by considering the least squares functional in a stochastic basis described by the covariance of the target data. Furthermore, to allow for robust design, the formulation also accounts for uncertainties in the input parameters. This is achieved using the method of propagation of uncertainties using the directional derivatives of the output parameters with respect to unknown parameters. The required derivatives are calculated simultaneously with the solution using generic programming exploiting the template and operator overloading features of the C++ language. The methodology described here is general and applicable to any numerical solution procedure for any set of governing equations but for the purpose of this paper we consider a finite volume solution of the compressible Euler equations. In particular, we illustrate the method for the case of supersonic flow in a duct with a wedge. The parameter to be determined is the inlet Mach number and the target data is the axial component of velocity at the exit of the duct. |

## 2001 |

Stephens, Darrin W Studies on modelling circulation in sugar vacuum pans PhD Thesis James Cook University, 2001. Abstract | Links | BibTeX | Tags: Axi-Symmetric, Calandria, Circulation, Flow, Heat Transfer, Mass Flow Rate, Model, Modelling, Quasi-Static, Saturation, Vacuum Pan @phdthesis{stephens2001studies, title = {Studies on modelling circulation in sugar vacuum pans}, author = {Darrin W Stephens}, doi = {10.13140/RG.2.1.4325.1048}, year = {2001}, date = {2001-01-01}, school = {James Cook University}, abstract = {This thesis presents an investigation into mathematical modelling of natural circulation in high grade batch vacuum pans. Batch vacuum pans are an important part of a sugar factory, with the circulation in such vessels being a key factor in successful sucrose extraction. The flow within a batch vacuum pan is laminar with three phases (molasses, crystal and vapour) present, and is driven by buoyancy, which results from vapour formation due to boiling. Numerical modelling of natural circulation in batch vacuum pans has been limited in the past by computational power and available computer software, and has suffered from the necessity for very restrictive assumptions to make modelling possible. The thesis uses computational fluid dynamics (CFD) as a tool to develop an improved batch vacuum pan model to investigate the detailed distribution of velocity and temperature within a batch vacuum pan at various stages throughout the strike. A segmented modelling approach has been developed where the vacuum pan is divided into two segments: the space inside the calandria tubes (the calandria tube segment), and the remaining part consisting of a downtake and the space above and below the calandria (the external flow segment). The external flow segment is modelled using the standard CFD approach, whereas the calandria tube segment is represented by a one-dimensional finite volume model. The two segments are coupled together to obtain the overall model of the entire vacuum pan. The calandria tube segment is the key to the vacuum pan model as the majority of the driving force for natural circulation is developed from the vapour formed due to boiling within the calandria tubes. The one-dimensional constant wall temperature tube model developed within this thesis demonstrates, for most parameters, reasonable agreement with previous experimental data. The tube model results have been presented in the form of characteristic curves showing pressure difference, heat transfer and evaporation rate as functions of mass flow rate. These curves provide a new insight into the boiling process within calandria tubes. Improvement of the one-dimensional model predictions would require more experimental data pertaining to the volume fraction distribution in the axial and radial directions, as well as an improved correlation for the boiling heat transfer coefficient. Quasi-static, two-dimensional, axi-symmetric CFD simulations of the vacuum pan were performed for three discrete levels of filling, representing the start, middle and end of the batch process. It was found that the magnitude of the flow speed through the tubes decreases drastically with increasing level within the vacuum pan. This reduction has two causes: first, the effect of increased viscosity with increasing head; and second the effect of the increased boiling point with increasing head. Both of these effects combine to give a much lower heat transfer rate within the tubes, thus producing less vapour to drive the flow. As the head above the calandria increases, the size, strength and existence of recirculation zones also increases. These recirculation zones do not provide any assistance in circulating the flow through the tubes. The simulations provide an improved understanding of the mechanisms producing natural circulation and allow suggestions of possible improvements to vacuum pan designs. With the large change in fluid viscosity from start to finish of the boiling process, combined with the change in saturation profile due to the increasing head, it is difficult to conceive a batch vacuum pan design that will operate at the maximum heat transfer and evaporation point for all times during the strike. The model developed produces a preliminary tool for analysis of vacuum pan operation, and may be applied to both batch and continuous pans. The segmented modelling approach, which is a novel contribution of this work, also provides a framework for future model improvements as new experimental data becomes available.}, keywords = {Axi-Symmetric, Calandria, Circulation, Flow, Heat Transfer, Mass Flow Rate, Model, Modelling, Quasi-Static, Saturation, Vacuum Pan}, pubstate = {published}, tppubtype = {phdthesis} } This thesis presents an investigation into mathematical modelling of natural circulation in high grade batch vacuum pans. Batch vacuum pans are an important part of a sugar factory, with the circulation in such vessels being a key factor in successful sucrose extraction. The flow within a batch vacuum pan is laminar with three phases (molasses, crystal and vapour) present, and is driven by buoyancy, which results from vapour formation due to boiling. Numerical modelling of natural circulation in batch vacuum pans has been limited in the past by computational power and available computer software, and has suffered from the necessity for very restrictive assumptions to make modelling possible. The thesis uses computational fluid dynamics (CFD) as a tool to develop an improved batch vacuum pan model to investigate the detailed distribution of velocity and temperature within a batch vacuum pan at various stages throughout the strike. A segmented modelling approach has been developed where the vacuum pan is divided into two segments: the space inside the calandria tubes (the calandria tube segment), and the remaining part consisting of a downtake and the space above and below the calandria (the external flow segment). The external flow segment is modelled using the standard CFD approach, whereas the calandria tube segment is represented by a one-dimensional finite volume model. The two segments are coupled together to obtain the overall model of the entire vacuum pan. The calandria tube segment is the key to the vacuum pan model as the majority of the driving force for natural circulation is developed from the vapour formed due to boiling within the calandria tubes. The one-dimensional constant wall temperature tube model developed within this thesis demonstrates, for most parameters, reasonable agreement with previous experimental data. The tube model results have been presented in the form of characteristic curves showing pressure difference, heat transfer and evaporation rate as functions of mass flow rate. These curves provide a new insight into the boiling process within calandria tubes. Improvement of the one-dimensional model predictions would require more experimental data pertaining to the volume fraction distribution in the axial and radial directions, as well as an improved correlation for the boiling heat transfer coefficient. Quasi-static, two-dimensional, axi-symmetric CFD simulations of the vacuum pan were performed for three discrete levels of filling, representing the start, middle and end of the batch process. It was found that the magnitude of the flow speed through the tubes decreases drastically with increasing level within the vacuum pan. This reduction has two causes: first, the effect of increased viscosity with increasing head; and second the effect of the increased boiling point with increasing head. Both of these effects combine to give a much lower heat transfer rate within the tubes, thus producing less vapour to drive the flow. As the head above the calandria increases, the size, strength and existence of recirculation zones also increases. These recirculation zones do not provide any assistance in circulating the flow through the tubes. The simulations provide an improved understanding of the mechanisms producing natural circulation and allow suggestions of possible improvements to vacuum pan designs. With the large change in fluid viscosity from start to finish of the boiling process, combined with the change in saturation profile due to the increasing head, it is difficult to conceive a batch vacuum pan design that will operate at the maximum heat transfer and evaporation point for all times during the strike. The model developed produces a preliminary tool for analysis of vacuum pan operation, and may be applied to both batch and continuous pans. The segmented modelling approach, which is a novel contribution of this work, also provides a framework for future model improvements as new experimental data becomes available. |

## 2000 |

McBain, Geordie D; Stephens, Darrin W Low Grash of number convective heat transfer across a spherical cavity Inproceedings Proc. of the 7th Australasian Heat and Mass Transfer Conference, 2000. Abstract | Links | BibTeX | Tags: Cavity, Flow, Grashof, Heat Transfer, Model, Modelling, Temperature @inproceedings{mcbain2000low, title = {Low Grash of number convective heat transfer across a spherical cavity}, author = {Geordie D McBain and Darrin W Stephens}, doi = {10.13140/RG.2.1.4194.0324}, year = {2000}, date = {2000-01-01}, booktitle = {Proc. of the 7th Australasian Heat and Mass Transfer Conference}, abstract = {The increase in heat transfer rate across a spherical fluid-filled cavity embedded in a highly conducting solid with a horizontal temperature gradient is investigated analytically and numerically. Analytically, the low Grashof number asymptotic expansion is extended to second-order for the temperature field. This provides the lowest order correction to the overall Nusselt number. This prediction and the associated flow and temperature fields are compared with specially obtained numerical solutions of the full nonlinear equations. Agreement is excellent for Rayleigh numbers less than a few thousand.}, keywords = {Cavity, Flow, Grashof, Heat Transfer, Model, Modelling, Temperature}, pubstate = {published}, tppubtype = {inproceedings} } The increase in heat transfer rate across a spherical fluid-filled cavity embedded in a highly conducting solid with a horizontal temperature gradient is investigated analytically and numerically. Analytically, the low Grashof number asymptotic expansion is extended to second-order for the temperature field. This provides the lowest order correction to the overall Nusselt number. This prediction and the associated flow and temperature fields are compared with specially obtained numerical solutions of the full nonlinear equations. Agreement is excellent for Rayleigh numbers less than a few thousand. |

Atkinson, Bruce J; Stephens, Darrin W; Harris, Jonathan A; Schneider, Phil A The net pressure driving force due to boiling in calandria tubes. Inproceedings Hogarth, DM (Ed.): Australian Society of Sugar Cane Technologists, 2000. Abstract | Links | BibTeX | Tags: Boiling, Calandria, Evaporation, Flow, Mass Flow Rate, Model, Pressure, Temperature, Thermodynamic, Two-Phase, Vacuum Pan @inproceedings{atkinson2000net, title = {The net pressure driving force due to boiling in calandria tubes.}, author = {Bruce J Atkinson and Darrin W Stephens and Jonathan A Harris and Phil A Schneider}, editor = {DM Hogarth }, doi = {10.13140/RG.2.1.1998.5762}, year = {2000}, date = {2000-01-01}, booktitle = {Australian Society of Sugar Cane Technologists}, journal = {Proceedings of the 2000 Conference of the Australian Society of Sugar Cane Technologists held at Bundaberg, Queensland, Australia, 2 May to 5 May 2000.}, volume = {22}, abstract = {Vapour formation due to boiling in calandria tubes provides the driving force for natural circulation in vacuums pans. The net pressure difference generated across a calandria tube is determined by the average density deficit in the tube relative to the downcomer (i.e. the amount of vapour in the tube) and the pressure loss due to friction and acceleration. This paper presents a mathematical model of the two-phase flow of molasses and vapour in calandria tube assuming equilibrium thermodynamics and steady state conditions. The model can predict the net pressure driving force and the evaporation rate produced by a tube as a function of parameters such as heat input, mass flow rate, liquid height above the calandria and boiling point elevation. Additionally, the model yields detailed profiles of temperature, absolute pressure, volume fraction and other variables as a function of distance along the calandria tube. Results are presented in the form of characteristic curves representing the net pressure difference available to drive natural circulation as a function of applied heat and mass flow rate. The circulation rate and evaporation rate in natural circulation lop may be determined by matching the appropriate characteristic curve to the system response curve for the loop. An example is presented to illustrate the application of the model.}, keywords = {Boiling, Calandria, Evaporation, Flow, Mass Flow Rate, Model, Pressure, Temperature, Thermodynamic, Two-Phase, Vacuum Pan}, pubstate = {published}, tppubtype = {inproceedings} } Vapour formation due to boiling in calandria tubes provides the driving force for natural circulation in vacuums pans. The net pressure difference generated across a calandria tube is determined by the average density deficit in the tube relative to the downcomer (i.e. the amount of vapour in the tube) and the pressure loss due to friction and acceleration. This paper presents a mathematical model of the two-phase flow of molasses and vapour in calandria tube assuming equilibrium thermodynamics and steady state conditions. The model can predict the net pressure driving force and the evaporation rate produced by a tube as a function of parameters such as heat input, mass flow rate, liquid height above the calandria and boiling point elevation. Additionally, the model yields detailed profiles of temperature, absolute pressure, volume fraction and other variables as a function of distance along the calandria tube. Results are presented in the form of characteristic curves representing the net pressure difference available to drive natural circulation as a function of applied heat and mass flow rate. The circulation rate and evaporation rate in natural circulation lop may be determined by matching the appropriate characteristic curve to the system response curve for the loop. An example is presented to illustrate the application of the model. |

## 1999 |

Stephens, Darrin W; Harris, Jonathan A Modelling convective boiling of molasses Conference 2nd International Conference on CFD in the Minerals and Processing Industries, CSIRO, Melbourne, Australia, 1999. Abstract | Links | BibTeX | Tags: Boiling, Flow, Heat Transfer, Model, Modelling, ODE, Pressure, Two-Phase @conference{stephens1999modelling, title = {Modelling convective boiling of molasses}, author = {Darrin W Stephens and Jonathan A Harris}, doi = {10.13140/RG.2.1.2359.0242}, year = {1999}, date = {1999-01-01}, booktitle = {2nd International Conference on CFD in the Minerals and Processing Industries, CSIRO, Melbourne, Australia}, abstract = {One-and two-dimensional numerical models of forced convective boiling of molasses in a calandria tube are described. The flow in the tube is considered to be composed of two phases (molasses and steam). The one-dimensional model solves a simplified set of ODEs describing the non-equilibrium boiling process. The two-dimensional model is based on the Eulerian/Eulerian multi-phase approach as implemented in the CFX-4.2 CFD code, and solves for the distribution of volume fraction and the temperature and velocity of each phase, along with global parameters such as pressure drop and evaporation rate. Solutions are presented for a case with similar conditions to those expected in a batch vacuum pan. The results show that the flow in the tube is complex and multi-dimensional. Vapour forms both at the wall (due to direct heating) as well as in the centre (due to bulk boiling). The observed features of the flow from the numerical simulation are qualitatively similar to available experimental observations made by previous investigators, although quantitative agreement has yet to be achieved.}, keywords = {Boiling, Flow, Heat Transfer, Model, Modelling, ODE, Pressure, Two-Phase}, pubstate = {published}, tppubtype = {conference} } One-and two-dimensional numerical models of forced convective boiling of molasses in a calandria tube are described. The flow in the tube is considered to be composed of two phases (molasses and steam). The one-dimensional model solves a simplified set of ODEs describing the non-equilibrium boiling process. The two-dimensional model is based on the Eulerian/Eulerian multi-phase approach as implemented in the CFX-4.2 CFD code, and solves for the distribution of volume fraction and the temperature and velocity of each phase, along with global parameters such as pressure drop and evaporation rate. Solutions are presented for a case with similar conditions to those expected in a batch vacuum pan. The results show that the flow in the tube is complex and multi-dimensional. Vapour forms both at the wall (due to direct heating) as well as in the centre (due to bulk boiling). The observed features of the flow from the numerical simulation are qualitatively similar to available experimental observations made by previous investigators, although quantitative agreement has yet to be achieved. |

## 1998 |

Stephens, Darrin W; Harris, Jonathan A Numerical modelling of two-phase flow a benchmark solution Conference Australasian Fluid Mechanics Conference, 13 , 1998. Abstract | Links | BibTeX | Tags: Eulerian, Flow, Heat Transfer, MATLAB, Model, Modelling, Multiphase, ODE, Two-Phase @conference{stephens1998numerical, title = {Numerical modelling of two-phase flow a benchmark solution}, author = {Darrin W Stephens and Jonathan A Harris}, doi = {10.13140/RG.2.1.2621.1681}, year = {1998}, date = {1998-01-01}, booktitle = {Australasian Fluid Mechanics Conference}, journal = {continuity}, volume = {13}, abstract = {This paper explores a simple test problem that can be used for the validation of Eulerian two-phase flow CFD models. Validation results are presented for a commercial CFD code with multi-phase flow capability, namely CFX-4.2, produced by AEA Technology. The results show that CFX-4.2 exhibits virtually perfect agreement with all 12 test cases over a full range of input parameters using a very moderate mesh.}, keywords = {Eulerian, Flow, Heat Transfer, MATLAB, Model, Modelling, Multiphase, ODE, Two-Phase}, pubstate = {published}, tppubtype = {conference} } This paper explores a simple test problem that can be used for the validation of Eulerian two-phase flow CFD models. Validation results are presented for a commercial CFD code with multi-phase flow capability, namely CFX-4.2, produced by AEA Technology. The results show that CFX-4.2 exhibits virtually perfect agreement with all 12 test cases over a full range of input parameters using a very moderate mesh. |