Modelling of a Thermal Spraying Controller Using MATLAB/Simulink

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1 Modelling of a Thermal Sraying Controller Using MATLAB/Simulink D.Barth, IA Gorlach Deartment of Mechatronics NMMU Port Elizabeth, South Africa Igor.Gorlach@nmmu.ac.za G Gruhler Faculty of Engineering Reutlingen University, Reutlingen, Germany gerhard.gruhler@reutlingen-university.de Abstract There are a number of thermal sraying systems, which are based on air flame rocesses. Stable control of such systems is difficult to achieve due to the comlexity of the combustion rocess in a small burner and varying rocess arameters. Therefore, modelling of a system control can rovide useful information in otimising the erformance of thermal sraying systems. In this research, a simulation model of a thermal sray controller was develoed using MATLAB/Simulink software. The model was evaluated by comaring the simulated and actual rocess arameters. The obtained results indicate that the develoed model of system controller rovides the main required control arameter, the fuel-air ratio, which corresonds with the otimal value used in the actual control of the thermal sraying system. Keywords MATLAB/Simulink, modeling, control I. Introduction Thermal sraying rocesses based on combustion rocesses where air is used as an oxidizer are less common than rocesses with oxygen. However, air flame based sraying rocesses can rovide a number of advantages, for examle: lower combustion temerature, which reduces a formation of brittle hases of WC and reduced running costs (Ref ). In designing a thermal sraying system controller, it is imortant to achieve an otimal combustion rocess, while keeing the controller simle, chea yet robust. Hence, modelling of the rocesses inside of a thermal sraying system is a valuable simulation tool, which can be alied to achieve the desired erformance of a thermal sraying system. Recent analyses of combustion rocesses focus on control concets, which are based mainly on low-order modelling. A relatively new aroach is multidimensional simulation, in which an unsteady Navier-Stokes flow solver is couled with a control algorithm. However, this method of control would be too comlex for a basic thermal sraying system. A number of concets of combustion control have been develoed for internal combustion engines and turbines, which are mainly divided in two categories (Ref ): Oerating oint control (OPC) and Active combustion control (ACC). In OPC, certain arameters, such as: the stoichiometric ratio in a required range is maintained. In ACC, the mixture roerties (e.g. fuel flow rate) are modulated by the controller to imrove the combustion characteristics or to limit combustion ressure oscillations, (Ref ). Modelling secifically oxy flame combustion and thermal sraying rocesses was resented in (Ref 4-7). In this research, the modelling aroach is based on the oerating oint control strategy using MATLAB/Simulink, which is a tool extensively used in engineering calculations, for examle in (Ref 8). The model consists of sub-models of various stages and units of the control system, such as: the air and fuel suly, the combustion rocess, the combustion chamber and the nozzle. The model was alied and evaluated on the system controller described in Ref 9. II. Theoretical Background A. Combustion Model The combustion model is based on a low order aroach of combustion simulation (Ref 0). The model includes the calculation of the adiabatic flame temerature and the comosition of the exhaust gas. The adiabatic flame temerature is the temerature that would be achieved if the combustion occurred in an adiabatic, hence in an ideal insulated combustion chamber. Because no heat exchange occurs with the environment, the temerature of the exhaust gas is the same as the flame temerature. In a real alication, there is of course always a heat exchange with the environment. Hence the temeratures of the exhaust gas calculated with this method will be higher than in reality. The adiabatic flame temerature or the exhaust gas temerature is calculated as follows, (Ref 0): where reresents the mass flow rate of the exhaust gas, and the secific heats of air and the exhaust gas, the air temerature, the lower heating value of the fuel. The comosition of the exhaust gas is influencing the adiabatic flame temerature and it also affects the oerating conditions of the accelerating nozzle. It is assumed that the reaction between fuel and air can be described by a single () 9

2 global reaction. In the case of kerosene the reaction is as follows: () In reality, the combustion of kerosene and air consist of several elementary reactions and would also result in the generation of and. The secific heat of the exhaust gas is calculated using the mass fractions of the exhaust gas comonents. Similar to the secific heat calculation, the molar mass of the exhaust gas can be calculated by using the molar fractions of the exhaust gas comonents: where reresent the molar fractions, the molar masses of. B. Combustion Chamber Model It is assumed that ressure and temerature in the combustion chamber are constant and location-indeendent. Furthermore it is assumed that the ideal gas law is alicable. In this case the ressure in the combustion chamber is calculated as follows: where reresents the mass of the mixture, the volume of the combustion chamber, the temerature of the exhaust gas, the secific gas constant of the exhaust gas. C. Accelerating Nozzle Model The jet velocity at the exit of a de Laval nozzle is calculated with the following formula: (5) where reresents the temerature at the inlet of the nozzle, the ressure at the inlet of the nozzle, the ratio of secific heats of the gas, the ideal gas constant, the ressure at the exit of the nozzle. () (4) where reresents the cross-sectional area at nozzle throat, the ressure at the inlet of the nozzle, the secific volume of the gas. D. Fuel and Air Suly Systems Models For modelling the air and fuel suly systems, a ie with a ressure dro due to friction and turbulence is alied. Using the Bernoulli equation, neglecting the influence of gravity, the flow rate can be calculated as follows: where A reresents the cross-sectional area of the ie, _ the ressure at the inlet of the ie, _ the ressure at the outlet of the ie, ρ the density of the fuel, α the flow coefficient. The model of the fuel system is derived from equation (7) using the ressure of fuel instead of and the combustion chamber ressure instead of. To reresent the roortional valve, the cross-sectional area can be modified by multilying it with a factor. Similar to the fuel system, the air system can be modelled. It is assumed that the air flow is incomressible. By combining the models of the combustion chamber and the nozzle, the model of the thermal sray gun is generated. For modelling of the whole thermal sraying, the fuel and air suly models are added to the model of the sray gun. III. The above mentioned formulae were used for develoing the MATLAB/Simulink models of the HVAF thermal sraying system (Figs. -5). (7) MATLAB/Simulink Models Time delays are used in the adiabatic flame temerature model in order to revent an algebraic loo (Fig. ). An algebraic loo occurs if the forward and the feedback branches of a signal ath only consist of direct feedthrough blocks. Direct feedthrough blocks, are blocks where the inut signals are directly assed to the outut, such as Gain, Product or Sum blocks. Ignoring the articles of sraying material due to their negligible mass in comarison with the amount of the conveying exhaust gas, the mass flow rate through the nozzle is calculated as follows: (6) GMSA Chair of Mechatronics and the Landesstiftung Baden- Württemberg. 9

3 Fig: Simulink model of the adiabatic flame temerature 94

4 Fig : Simulink model of the calculation of the exhaust gas roerties 95

5 m_fuel T_chamb m_f uel R_chamb kaa_chamb Adiabatic Flame Temerature T R kaa T 4 m_out s Integrator 96.e-6 R m V Ideal Gas Law [e5] IC 4 V_chamber Fig : Simulink model of the combustion chamber 4 _a a_in m_f uel T R T_in R_in u_out u m_fuel kaa m_out Combustion Chamber kaa_in m_out _in Nozzle m Fig 4: Simulink model of the thermal sray gun -C_air _air-in _back Air system v _air -C_fuel 0.85 _f uel setoint-v alv e m_f uel valve_os _back Fuel system v _f uel m_f uel u m Scoe jet 05 _a a HVAF gun Fig 5: Simulink model of the HVAF thermal sray controller 96

6 IV. RESULTS Exerimentally, the fuel/air ratio for a sustainable thermal sraying rocess, with owder as a sraying material, was determined as 0.0. For evaluation of the develoed MATLAB/Simulink model, selected signals from the model were comared with measurement data of the real rocess on the thermal sraying system controller, which are shown in Table I. TABLE I: AIR FLAME PROCESS PARAMETERS Parameter Value Air flow rate (kg/s) 0.4 Pressure in combustion chamber (MPa) Fuel flow rate (kg/s) Fuel ressure (MPa) Prior to the evaluation, the model was arameterised by adjusting the arameters A and α in the air and the fuel system blocks according to measurements that where erformed in a narrow range around the tyical oerating oint of the thermal sray gun. As the control of combustion in the thermal sraying rocess is an oerating oint control, oscillations in the signals are of minor interest, as long as the amlitude is small and the mean value can be seen as constant (Fig. 6). fuel flow rate in m /s x 0-6 simulated measured time in s Fig 6: Simulated and measured fuel flow rate The simulated and the measured air flow rate were comared. Because the mass flow rate of air was not measured directly, but calculated by equation from the measurement data of the air ressure, the air flow rate and the air temerature sensor, it could result in an adding u of the measurement errors. Due to this fact the focus of the arameterisation of the model was on the flow rate and not on the mass flow rate of air. V. CONCLUSION In this research, a simulation MATLAB/Simulink model of an air fame thermal sray controller was develoed. The core of the model is a low order combustion model, which is sufficient for simulation and control of the combustion rocess for thermal sraying. The model was evaluated by comaring the simulated rocess arameters with the actual rocess control arameters used by the controller. The obtained results indicate that the develoed model rovides the fuel-air ratio, which corresonds with the value used in the actual control of the thermal sraying system. The simulation model consists of a number of sub-models reresenting the elements of the system. Hence, the model can be easily modified or exanded, deending on the design requirements. Acknowledgment The authors would like thank the GMSA Chair of Mechatronics and the Landesstiftung Baden-Württemberg for their suort of this roject. References [] I. Gorlach, Low-cost HVAF for thermal sraying of WC-Co, Proceedings of the International Thermal Sray Conference, on CD- ROM, May 4-7, 009 (Las Vegas, Nevada), 78-7 [] M. Koller and A. Kilchenmann, The next Ste in intelligent Gun Technology: EvoLink for Plasma Sraying, Proceedings of the International Thermal Sray Conference, on CD-ROM, May -5, 00 (Singaore), [] J. Hermann, A. Orthmann, S. Hoffmann, P. Berenbrink,. Combination of Active Instability Control and Passive Measures to Prevent Combustion Instabilities in a 60MW Heavy Duty Gas Turbine, NATO RTO Meeting on Active Control Technology; Braunschweig, 000 (Germany) [4] M. Li, and P.D. Christofides, Modeling and Control of High-Velocity Oxygen-Fuel (HVOF) Thermal Sray, A Tutorial Review. Journal of Thermal Sray Technology, Online First(TM) (serial on the Internet), 009 [5] K. Bobzin, N. Bagcivan and M. Schäfer, Mathematical Modelling and Simulation of a Kerosene Driven HVOF-Process, Proceedings of the International Thermal Sray Conference, on CD-ROM, May -5, 00 (Singaore), [6] U. Rueedi and A. Kilchenmann, Process Measurement and Data Storage, Integrated in a Thermal Sray Gun, Proceedings of the International Thermal Sray Conference, on CD-ROM, May 4-7, 009 (Las Vegas, Nevada), [7] R. Schmitt, J. Doeren, K. Bobzin, E. Lugscheider, F. Ernst, Imlementation of Modern Networks into Modern Process Control Equiment, Proceedings of the International Thermal Sray Conference, on CD-ROM, May 5-8, 006 (Seattle, Washington) [8] T.V. Light, I.A.Gorlach, G.J Wiens, Dynamic Modelling of a Low-cost CNC milling machine. Proceedings of the WSEAS International Conference on Systems, July 0, (Corfu, Greece) [9] D. Barth, I.A. Gorlach, G. Gruhler, Develoment of a Novel Controller for a HVAF Thermal Sray Process, Proceedings of the International Conference on Cometitive Manufacturing (Coma 0), January 00, (Stellenbosch, South Africa) [0] B. Ele, R Leithner, W. Linzer, H. Walter, Simulation von Kraftwerken und wärmetechnischen Anlagen. st ed. Sringer, New York,