Lower Dimensional Model for Modeling the Heat Transfer and Detailed Reactions Inside Long Channels

Paper from the AFRC 2015 conference titled Lower Dimensional Model for Modeling the Heat Transfer and Detailed Reactions Inside Long Channels

Many applications like fuel reformers, cracking furnaces, fuel cells have the shell and tube configurations, typically consisting of a large number of thin long channels having chemical reactions inside the channels. The channels exchange heat with the fluid in the outer domain. In order to have accurate numerical predictions, it is required to have detailed chemistry calculations inside the channels. However, the number of channels in these types of applications is generally very high. Therefore, the resolution of detailed chemistry inside the thin pipes with three dimensional CFD computations is computationally expensive. In the current work, a methodology is developed for coupling the one dimensional (1D) solution inside the non-permeable channels with the 3D outer flow in shell and tube type of configurations. In the proposed lower dimensional model, called the channel model, the 1D channels have detailed reactions while the outer 3D flow can be reactive or non-reactive. The channel is discretized into 1D grid points and a parabolic solver is used to solve the species transport and energy equations inside the channel. The channel is assumed to have a plug flow but the flow and the mixture properties inside the channel can have the axial variations. Since, the channel walls are non-permeable; the two zones are coupled only through the heat transfer. ANSYS R15 was used to perform the simulations.

Lower Dimensional Model for Modeling the Heat Transfer and Detailed Reactions Inside Long Channels AFRC 2015 INDUSTRIAL COMBUSTION SYMPOSIUM Sept 9-11, 2015 Anchal Jatale ANSYS Inc. 1 © 2011 ANSYS, Inc. July 10, 2015 Rakesh Yadav ANSYS Inc. Stefano Orsino ANSYS Inc. Motivation • Fuel Reformers, Cracking Furnaces, Fuel Cells have the shell and tube configurations with large number of thin long channels having chemical reactions inside the channels • Use of Computational Fluid dynamics to model heat exchange from tubes to outside is increasing and help industry to improve the process. • Accurate modeling requires the use of detailed chemistry inside the channels. • Resolution of detailed chemistry in large number of thin channels is computationally very expensive. 2 © 2011 ANSYS, Inc. July 10, 2015 The major hurdle for numerical analysis especially CFD to grow further is total run time. Proposed Solution • The thin long channels are represented with lower dimensional modeling approach, where the flow and other governing equations are solved in 1D. • The flow outside the channels is modeled using three dimensional control volumes. • Flow inside the channel and the outer flow coupled only through the heat transfer coefficients. • The model is known as Channel Model in ANSYS Fluent. 3 © 2011 ANSYS, Inc. July 10, 2015 Channel Model: Concepts and Numerical Formulation • The flow inside the channels is assumed to be plug flow and hence no radial variation is considered • The volume of a channel is discretized into one dimensional grid points and a parabolic solver is used to solve the species transport and energy equations inside the channel. • Though the radial variation of the flow is ignored inside the channel, the flow and the mixture properties inside the channel can have the axial variations • The coupling approach offers the flexibility to model the flow inside the channels and outer domain independently. - Flow can be turbulent and non-reacting in the outer domain while it may be laminar and reacting inside the channels - Can use different methodologies for resolving the chemistry and modeling the turbulence chemistry closures 4 © 2011 ANSYS, Inc. July 10, 2015 Flow inside the Channel • 5 © 2011 ANSYS, Inc. Flow is assumed to be a plug flow: - Flow variables radially uniform - Axial diffusion of heat and species are ignored July 10, 2015 Heat Transfer Calculations • Convective heat transfer source : • Tw is averaged from the 3D outer flow temperature field on the resolved channel wall • The heat transfer coefficient is calculated as : Where: Kc :gas-phase thermal conductivity Dc : channel diameter Nu: can be calculated from empirical correlations • 6 The plug flow equations are solved with a stiff ODE solver using time steps based on the grid size ( size of the channel element) and the local channel velocity © 2011 ANSYS, Inc. July 10, 2015 Outer Flow in the domain • The energy solution of the outer flow uses a prescribed heat flux boundary condition at the channel walls from the solution of the reacting channel Under relaxation parameter Channel heat gain/loss 7 © 2011 ANSYS, Inc. July 10, 2015 Heat flux from previous iteration 1D Channel Model Features • No mesh inside the channels • Channels can be curvilinear • The channel can have variable cross-section • Detailed chemistry in the tube (plug flow) • Ability to define porous medium inside the channel • Surface reactions option available 8 © 2011 ANSYS, Inc. July 10, 2015 Validation of Results • Channel model results were compared with fully resolved cases for different cases • Channel model results were compared with experimental data for different mechanisms and cases 9 © 2011 ANSYS, Inc. July 10, 2015 Case 1: Straight Channels Two reacting channels with different materials with non reacting outer flow. Results of the channel model are compared with full simulation (mesh inside Channels is resolved) Bulk Mean Temperature 10 © 2011 ANSYS, Inc. July 10, 2015 Channel wall Temperature Case 2: Curved Chanel with Variable Area • Channel Inlet: Premixed H2-air mixture • Mass fraction of H2 : 0.015 and O2 0.23 • The channel inlet mass flow rate: 0.445 kg/s. • The reactions inside the channel are solved using a single step global mechanism for H2-O2 11 © 2011 ANSYS, Inc. July 10, 2015 Validating With Experimental Data • Simple 15 m long, 2-tube furnace was used to demonstrate the model features • Flow outside the tubes is non reactive, only heat transfer is taking place • 12 Chemistry for 2 application was taken from the literature and results were reproduced using this model © 2011 ANSYS, Inc. July 10, 2015 inlet tubes outlet Case 3: Ethane Cracking • The reaction mechanism of steam cracking of ethane to form ethylene for 8 species is taken from K.M. Sundaram et. al1 and implemented into the fluent to reproduce some of the results 1) K.M. Sundaram, and G. F. Forment , "Modeling of Thermal Cracking Kinetics. 1. Thermal Cracking of Ethane, Propane and Their Mixtures", Chem. Eng. Sci., 32, 601, 1977. 13 © 2011 ANSYS, Inc. July 10, 2015 Boundary and Initial Conditions • Inlet tube conditions - Temperature : 1053 K - Flow rate : 0.0025 Kg/s ( residence time 45-50 s) - Species Mass faction : C2H6-0.4 , H2O-0.6 • Outside Tube conditions - No Reactions only Heat transfer - Air at 1323 K and 1 m/s velocity 14 © 2011 ANSYS, Inc. July 10, 2015 Comparison to Simulation Results Fluent is able to produce the cracking products close to the literature values ( Final mixture do have other species too, but due to lack of experimental values only normalized mole % of 4 of the species is compared) 15 © 2011 ANSYS, Inc. July 10, 2015 Reacting Channel Variables along the Channel Length 16 © 2011 ANSYS, Inc. July 10, 2015 Case 4: Steam Reformer • Chemical mechanism from S. Lee et. al2 was taken and implemented into the fluent to reproduce some of the results 2) S. Lee, J. Bae, S. Lim and J. Park, "Improved configuration of supported nickel catalysts in a steam reformer for effective hydrogen production from methane", Journal of Power Sources, 180, 506-515, 2008. 17 © 2011 ANSYS, Inc. July 10, 2015 Boundary and Initial Conditions • Inlet tube conditions - Temperature : 1173 K - Flow rate : 0.0005 Kg/s ( residence time 100-125 s) - Pressure : 101325 pa - Species Mass faction : CH4-0.33 , H2O-0.67 ( S:C ~2) - Nickel Catalyst : Porosity 0.6 • Outside Tube conditions - No Reactions only Heat transfer - Air at 1323 K and 1 m/s velocity 18 © 2011 ANSYS, Inc. July 10, 2015 Comparison to Simulation Results Simulation results for Mole/ Mole of CH4 are close to the literature values at S:C ratio 2 The hydrogen production is close to 70 % which is also comparable to the literature values 19 © 2011 ANSYS, Inc. July 10, 2015 Reacting Channel Variables along the Channel Length Dip because of endothermic reactions 20 © 2011 ANSYS, Inc. July 10, 2015 Case 5: Industrial level Geometry :Steam Reformer Burners Tube Outlet Tube Inlet 90 m long tube, 15m x 3m x 6m main chamber 21 © 2011 ANSYS, Inc. July 10, 2015 Boundary and Initial Conditions • Inlet tube conditions - Temperature : 1173 K - Flow rate : 0.005 Kg/s ( residence time 40-45 s) - Pressure : 101325 pa - Species Mass faction : CH4-0.33 , H2O-0.67 ( S:C ~2) - Nickel Catalyst : Porosity 0.6 • Outside Tube conditions - 8 Natural gas burners heating the furnace 22 © 2011 ANSYS, Inc. July 10, 2015 Mesh ~3 million cells 23 © 2011 ANSYS, Inc. July 10, 2015 Comparison to Simulation Results The hydrogen production is 68 % and CO production is 15 % which is also comparable to the literature values 24 © 2011 ANSYS, Inc. July 10, 2015 Temperature Profiles in the Domain 25 © 2011 ANSYS, Inc. July 10, 2015 Conclusions • Modeling of detailed chemistry inside thin channels can become quite cumbersome. • Channel model remove the need of meshing/resolving long channels and solve the flow inside them by 1D solver • The 1D model is coupled with outside 3D model through heat transfer coefficient. • The results of Channel model were matching quite well with both Fully resolved model as well as experimental data. • Channel model gives results ~2 times faster than fully resolved model. • It also allow for modeling zonal combustion ( different reaction mechanisms inside and outside the tubes) Channel model is an efficiency approach for modeling the finite rate chemistry inside thin long channels 26 © 2011 ANSYS, Inc. July 10, 2015