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Thermal Performance Evaluation in Gas Turbine Aero Engines Accessory Gearbox

Thermal Performance Evaluation in Gas Turbine Aero Engines Accessory Gearbox International Journal of Turbomachinery Propulsion and Power Article Thermal Performance Evaluation in Gas Turbine Aero Engines Accessory Gearbox Soheil Jafari * , Ahmed Bouchareb and Theoklis Nikolaidis Centre for Propulsion Engineering, School of Aerospace, Transport and Manufacturing (SATM), Cranfield University, Cranfield MK43 0AL, UK; a.bouchareb@cranfield.ac.uk (A.B.); t.nikolaidis@cranfield.ac.uk (T.N.) * Correspondence: S.Jafari@cranfield.ac.uk Received: 14 February 2020; Accepted: 24 August 2020; Published: 26 August 2020 Abstract: This paper presents a methodological approach for mathematical modelling and physics-based analysis of accessory gearbox (AGB) thermal behavior in gas turbine aero engines. The AGB structure, as one of the main sources of heat in gas turbine aero engines, is firstly described and its power losses will be divided into load-dependent and no-load dependent parts. Di erent mechanisms of heat generation are then identified and formulated to develop a toolbox for calculation of the churning, sliding friction, and rolling friction losses between contact surfaces of the AGB. The developed tool is also capable of calculating the heat loss mechanisms in di erent elements of the AGB, such as gears, bearings, and seals. The generated model is used to simulate and analyze the AGB thermal performance in the di erent flight phases in a typical flight mission, where the obtained results are validated against publicly available data. The analysis of the results confirms the e ectiveness of the proposed method to estimate the heat loss values in the AGBs of gas turbine aero engines and to predict the thermal loads of the AGB in di erent flight phases. The developed tool enables the gas turbine thermal management system designers to deal with the generated heats e ectively and in an optimal way. Keywords: thermal management systems; accessory gearbox; gas turbine aero engines; heat loss mechanisms; thermal performance evaluation 1. Introduction Gas turbine engine (GTE) manufactures are facing huge challenges in developing the next generation of GTEs to meet all requirements, due to the increase of fuel price, power and eciency demands, and limitations and restrictions set by governments and organizations (e.g., the Advisory Council for Aviation Research and Innovation in Europe has a target of a 75% reduction in CO emissions and a 90% reduction of NOx emissions by 2050) [1,2]. One of these challenges is to deal with huge thermal loads generated by advanced GTEs components. The engine thermal management system (TMS) should be able to manage these heat loads in an optimal feature to get a safe and reliable operation for the engine. In other words, the main duty of the GTE TMS is to use engine heat sinks (oil, fuel, and air) to manage the thermal loads generated by engine heat sources (gearboxes, bearings, generators, pumps, etc.). There are a few studies in the literature focusing on the thermal management challenges and potential solutions for GTEs. An analytic review on this topic has recently been done by the authors [3], in which the di erent aspects, current challenges, and potential solutions for the TMS design procedure in new and next generation of GTEs were studied in detail. One of the main challenges in this field is the lack of physics-based models for thermal loads calculation in di erent TMS components to enable researchers and manufacturers to predict and analyze the thermal loads in each component at di erent flight phases, based on the geometry, mechanical loads, input and output Int. J. Turbomach. Propuls. Power 2020, 5, 21; doi:10.3390/ijtpp5030021 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2020, 5, 21 2 of 10 powers, and other design parameters. This kind of model will enable TMS designers to do a precise sensitive analysis on design and operational parameters, as well as to get a reliable vision about the next generation of TMSs for GTEs [4]. The gearbox is one of the most important elements in gas turbine TMS as a noticeable amount of heat load is generated by this component [5]. So, it is significant to predict its power loss during the design phase to improve the mechanical system design through di erent perspectives. For instance, reducing gear operating temperature will contribute to better lubrication, less oil degradation, and improving the gear lifetime by improving the resistance to scung and micro-pitting [6]. Therefore, this paper will focus on developing a physics-based tool to calculate the thermal load generated by di erent elements of the accessory gearbox (AGB) in gas turbine aero engines. 2. Accessory Gearbox Heat Loss Mechanisms The accessory gearbox drives the accessories of the engine like generator, fuel and oil pumps, hydraulic pumps, etc. So, it is an essential element for the operation of the engine or the aircraft on which it is mounted. The power loss mechanisms inside gearbox can be separated into two groups: no-load dependent losses and load-dependent losses. No-load dependent losses include churning losses caused by gears, seals, and bearings, and load-dependent losses are frictional losses caused by gears and bearings [7]. No-load dependent losses mainly consist of Windage and churning power losses, the churning losses are one of the main power losses especially at high oil fill level and rotational speeds [8]. This type of power loss occurs between gears even without torque transmission in the rotation of mechanical components and it is related to the density, viscosity, and immersion depth of the components on a sump lubricated gearbox, and it also depends on the internal design of gearbox casing and operating conditions. No-load losses of rolling bearings mainly depend on the size, type, and bearing arrangement, immersion depth, and lubricant viscosity [9]. Load-dependent power losses occur because of contacts between the gears’ teeth during power transmitting, which are mainly depends on friction coecient, transmitted power, and sliding velocity in the contact area between teeth [9]. The dependence of no-load losses on the lubricant viscosity and the frictional losses is influenced by the oil characteristics and the ability to provide low friction coecient and lubricant film. This is important to increase gearbox eciency and to enhance gears and bearings life [10]. Most studies have focused on power loss, and gear eciency is related to the planetary gear system, power gearbox (PGB). Some of these studies have focused on spin power losses, but most of the studies have investigated mechanical losses. These studies provide a significant database for predicting power loss in gears, but it considers only a single gear pair. The review of these studies discloses the need for a model can predict the power loss in the AGB for typical aero-engine. The accessory gearbox consists of sets of spur gears connected to each other, each gear drives one element, such as the generator, or pump. The power losses can be divided into load-dependent and no-load dependent according to their mechanical component and their relation to transmitted torque that generates them [3]. In this way, the total power loss (PL) can be subdivided into no-load and load dependent related to gears (PL + PL ), bearings (PL + PL ), and no-load dependent for G0 G B0 B seals (PL ). S0 The total power losses in the accessory gearbox are the sum of all sources of losses in each contact pairs and single elements inside generated by load and no-load losses equal to the heat evacuation from AGB to the environment [9]. PL = PL + PL + PL + PL + PL = Q (1) G0 G B0 B S0 AGB The share of power losses between di erent sources strongly depends on the gearbox design configuration. Int. J. Turbomach. Propuls. Power 2020, 5, 21 3 of 10 3. Mathematical Modelling of Heat Losses The physics-based model for heat loss calculation is described in this section. 3.1. No-Load Dependent Losses Depending on the input speed and power, gearbox design and lubricant characteristics, the no-load dependent losses are a very important source of heat dissipation within an accessory gearbox. Due to the complicated design of the AGB, it is not straightforward to generate a model that consists of a general formulation to assess this mechanism of power loss. The main objective of this study is to accurately predict the power losses considering friction torque loss in the meshing gears. 3.1.1. Gears Churning Loss In recent decades, many studies have investigated the influence of the energy loss mechanism and parameters on power loss in the gearbox. Boness (1989) [10] investigated the influence of diameter and oil fill level on a disk and drove an empirical formulation through experiments. Terekhov (1975) [11] studied single meshing gears rotating immersed in a fluid and developed an empirical equation using a dimensionless moment coecient from several experiments. Höhn et al. [12] developed an empirical formation through experimental work, and concluded that reducing oil level can reduce the churning loss but not the gear temperature. Gear churning losses is the main source of power loss for splash lubricated gears, which is generated by rotating gears totally or partly immersed in fluid lubrication. Changenet et al. [13] developed a mathematical model for calculating the gear churning loss based on the series of experimental tests, and carried out a comprehensive dimensional analysis to tune the model. In this paper, this model is selected, since it overcomes some of the limitations of the previous research in gear churning losses from accuracy, validity range, and reliability points of view. The model proposed by Changenet et al. [13] depends on the regime of the flow and Reynolds number that defines the laminar-turbulent transition determined by experimental results. It is very dicult to determine the transition of the laminar-turbulent regime inside an oil sump, due to the infinite combination parameters and design features [14]. Gear churning power loss is mainly responsible for no-load dependent losses and depends on rotational speed, immersion area and depth, gear geometry, lubricant density, and viscosity, as shown in Equation (2): 3 3 PL =  W A R C (2) G0 i m where  is the lubricant density, W is the rotational speed in rad/s, A is immersion surface area, R = is the pitch radius, and the C expression has been determined depending on the flow regime: W.Rp b For Rec = < 6000 0 1 0.45 0.1 B C h V B oil C 0.21 0.21 B C C = 1.36B   Fr Re C (3) @ A D D W.r b For Rec = > 9000 0 1 ! ! 0.1 0.85 0.35 B C h b V B C oil 0.88 B C C = 3.644  B    Fr C (4) @ A D D where h is the immersion depth, D is the gear pitch diameter, V is the oil volume,  is the lubricant oil kinematic viscosity, b is the tooth face width, Fr = Froude number, depending on gear parameters 2 2 W R W R = , Re = Reynolds number = . It should be mentioned that this formulation and corresponding flow regimes are valid for the steady-state operating condition. Int. J. Turbomach. Propuls. Power 2020, 5, 21 4 of 10 3.1.2. Bearings Churning Loss The bearing churning losses are mainly depending on the bearing geometry and type, speed and lubricant viscosity. 2/3 7 3 3 PL = W  f  10  (n  )  d  10 (5) B0 0 oil where f is bearing coecients of loss,  is the dynamic viscosity, n is the rotation speed, and d is 0 oil m the mean diameter. 3.1.3. Seals Churning Loss The seal churning losses are mainly occurring between seal tip and shaft in the contact zone. However, many studies have been investigated on seals losses but this phenomenon still not well understood, due to small of the contact zone and dicult to parametrize. With regard to [15,16], the seal losses mainly depend on seal diameter and shaft speed. Equation (5) is used to predict the seal losses, but this formula does not consider the oil viscosity: 6 2 P = 7.69  10  d  n (6) Seal i where d is the shaft diameter. 3.2. Load Dependent Losses Load dependent losses include gear mesh loss and power loss in bearings that could be calculated as follows: 3.2.1. Power Loss in Meshing Gears Generally, the power loss due to gear mesh is determined by the normal load, relative rolling and sliding between lubricated meshing gears. Friction interaction between meshing gears must be considered as it is influenced by all characterized elements. The main contributors to power loss are the friction coecient and load distribution along the line of contact of meshing gear [3]. This study will consider the friction coecient and load distribution constant along the line of contact. Ohlendorf [17], has introduced the equation to calculate the load-dependent for spur gears. PL = P   H (7) G in m v where  : mean friction coecient along the path of the contact [18], H : is the gear loss factor. P : m in is the power input. 3.2.2. Power Loss in Bearings According to Wimmer et al. [16], the bearings load dependent loss mainly depends on the load applied, mean diameter, and friction coecient of the bearings: 2 2 PL =  n  F + F  f  d (8) B 1 m R A where F + F is the radial and axial load applied, f is the bearings friction coecient, d is the R A 1 m mean diameter. Finally, by adding the values of Equations (2), (5)–(8) and putting them in Equation (1), the total heat loss in the accessory gearbox will be calculated. 4. Results Analysis The equations described in previous sections have been used to generate a simulation toolbox in MATLAB environment to calculate di erent power loss mechanisms in di erent elements of accessory Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 5 of 11 4. Results Analysis Int. J. Turbomach. Propuls. Power 2020, 5, 21 5 of 10 The equations described in previous sections have been used to generate a simulation toolbox in MATLAB environment to calculate different power loss mechanisms in different elements of gearbox for gas turbine engines. The toolbox is able to predict the heat load values in the AGB, due to accessory gearbox for gas turbine engines. The toolbox is able to predict the heat load values in the friction and churning losses in gears and bearing and seals for each element. AGB, due to friction and churning losses in gears and bearing and seals for each element. It should be mentioned that in this study, the simulation model includes only the elements that have It should be mentioned that in this study, the simulation model includes only the elements that huge impacts on the total power losses while ignoring other elements (e.g., de-oiler). The schematic of have huge impacts on the total power losses while ignoring other elements (e.g., de-oiler). The accessory gearbox gear set configuration for an aero-engine is shown in Figure 1, it mainly consists of a schematic of accessory gearbox gear set configuration for an aero-engine is shown in Figure 1, it set of spur gears connected to drive each element at di erent speed ratios and power, a ball bearing, mainly consists of a set of spur gears connected to drive each element at different speed ratios and and gear shaft, seals, a gearbox housing. According to [19], the typical speed of each element in the power, a ball bearing, and gear shaft, seals, a gearbox housing. According to [19], the typical speed accessory gearbox at maximum power output, such as fuel pump, generator, and oil pump, are listed of each element in the accessory gearbox at maximum power output, such as fuel pump, generator, in Table 1. and oil pump, are listed in Table 1. Figure 1. Schematic of accessory gearbox (AGB) gear set configuration. Figure 1. Schematic of accessory gearbox (AGB) gear set configuration. Table 1. Accessory gearbox drives speeds. Table 1. Accessory gearbox drives speeds. Component Speed Ratio to HP Spool Component Speed Ratio to HP Spool Oil Pump 0.62 Oil Pump 0.62 Generator 1.79 Generator 1.79 Fuel Pump 0.9 Fuel Pump 0.9 Hydraulic Pump 0.5 Hydraulic Pump 0.5 In this study, the power loss model of the accessory gearbox is simulated through operating in In this study, the power loss model of the accessory gearbox is simulated through operating in a di erent flight phase, wide range of operating conditions, with an input power and speed varied a different flight phase, wide range of operating conditions, with an input power and speed varied for each flight condition, according to engine manufacturer, the speed and power input data in the for each flight condition, according to engine manufacturer, the speed and power input data in the accessory gearbox are taken from real engine of CFM56 family through di erent flight phases. The first accessory gearbox are taken from real engine of CFM56 family through different flight phases. The row of the Table 2 presents the core engine power. A percentage of this power will be transmitted to first row of the Table 2 presents the core engine power. A percentage of this power will be transmitted the AGB at di erent flight phases. With regard to Rolls-Royce [20] and Pratt & Whitney [21], the AGB to the AGB at different flight phases. With regard to Rolls-Royce [20] and Pratt & Whitney [21], the drives the accessories, fuel pumps, oil pumps, generators etc., by handling between 400–500 hp. AGB drives the accessories, fuel pumps, oil pumps, generators etc., by handling between 400–500 hp. The second raw presents the percentage of high-pressure rotational speed (from [19]), which is used as The second raw presents the percentage of high-pressure rotational speed (from [19]), which is used the input for the AGB physics-based model. as the input for the AGB physics-based model. The simplified model of AGB internal structure of gears is shown in Figure 1. Reference [22] Table 2. Accessory gearbox speed and engine core power during flight phases. provides basic design parameters of the spur gear, which are also listed in Table 3. Take Begin End Start End Begin End Conditions Idle Climb Approach O Climb Climb Cruise Cruise Descent Descent HP Power (kW) 825 24700 23200 14100 9700 8570 7260 5080 1090 6870 Speed (%) 0.28 0.88 0.88 0.92 0.91 0.88 0.88 0.80 0.69 058 The simplified model of AGB internal structure of gears is shown in Figure 1. Reference [22] provides basic design parameters of the spur gear, which are also listed in Table 3. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 6 of 11 Table 2. Accessory gearbox speed and engine core power during flight phases. Take Begin End Start End Begin End Conditions Idle Climb Approach Off Climb Climb Cruise Cruise Descent Descent HP Power (kW) 825 24700 23200 14100 9700 8570 7260 5080 1090 6870 Speed (%) 0.28 0.88 0.88 0.92 0.91 0.88 0.88 0.80 0.69 058 Int. J. Turbomach. Propuls. Power 2020, 5, 21 6 of 10 Table 3. Design parameters of AGB. Table 3. Design parameters of AGB. Parameter Index Unites Value Parameter Index Unites Value 𝛽 ° Base helix angle 10 Base helix angle 10 Bearing mean diameter 𝑑 𝑚 0.20 Bearing mean diameter d m 0.20 𝑑 𝑚 Pitch diameter 0.35 Pitch diameter d m 0.35 −6 Immersed area 𝐴 𝑚 1.0996 × 10 𝑖 2 6 Immersed area A m 1.0996  10 ℎ 𝑚 Gear immersion depth 0.22 Gear immersion depth h m 0.22 Shaft diameter 𝑑 𝑚 0.2 Shaft diameter d m 0.2 Oil volume V m 0.0012 𝑉 𝑚 Oil volume oil 0.0012 𝑙𝑜𝑖 N of teeth (Oil Pump) z - 77 N of teeth (Oil Pump) z - 77 N of teeth (Fuel Pump) z - 75 N of teeth (Fuel Pump) z - 75 N of teeth (Generator) z - 20 N of teeth (Generator) z - 20 N of teeth (Hydraulic Pump) z - 67 N of teeth (Hydraulic Pump) z - 67 Figure 2 shows the power loss toolbox generated with the graphical user interface (GUI) in Figure 2 shows the power loss toolbox generated with the graphical user interface (GUI) in MATLAB (R2019a) to enable the user to analyze di erent heat load mechanisms in di erent AGB MATLAB (R2019a) to enable the user to analyze different heat load mechanisms in different AGB elements separately and/or in total. elements separately and/or in total. Figure 2. Accessory gearbox heat load calculation toolbox. Figure 2. Accessory gearbox heat load calculation toolbox. By applying the flight phases of Table 2 to the model generated in MATLAB, the results of the By applying the flight phases of Table 2 to the model generated in MATLAB, the results of the heat load in different elements of the AGB according to different heat loss mechanisms are generated, heat load in di erent elements of the AGB according to di erent heat loss mechanisms are generated, and will be analyzed here. and will be analyzed here. Figure 3 shows the friction loss in all AGB elements, where the gear connected to the generator Figure 3 shows the friction loss in all AGB elements, where the gear connected to the generator has the highest friction loss in take-off condition compared to other elements, which mainly depends has the highest friction loss in take-o condition compared to other elements, which mainly depends on the friction coefficient and the load applied to the meshing gears. on the friction coecient and the load applied to the meshing gears. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Figure 4 confirms that the bearings friction losses are influenced directly by the applied load and speed. This figure is also showing a direct relation between the power loss value and the increase of speed and power transmitted. Figure 3. Power losses due to gear friction. Figure 3. Power losses due to gear friction. Figure 4. Power losses due to bearing friction. Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses where the oil properties change with oil temperature and operating conditions. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 5. Power losses due to gear churning. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, 21 7 of 10 Figure 3. Power losses due to gear friction. Figure 4 confirms that the bearings friction losses are influenced directly by the applied load and speed. This figure is also showing a direct relation between the power loss value and the increase of speed and power transmitted. Figure 3. Power losses due to gear friction. Figure 4. Power losses due to bearing friction. Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses where the oil properties change with oil temperature and operating conditions. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. Figure 4. Power losses due to bearing friction. Figure 4. Power losses due to bearing friction. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses level influences the churning power loss, the losses increase with increasing the immersion level of where the oil properties change with oil temperature and operating conditions. where the oil properties change with oil temperature and operating conditions. the gear teeth. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 5. Power losses due to gear churning. Int. J. Turbomach. Propuls. Power 202Figure 0, 5, x FO 5. R P Power EER REV losses IEW due to gear churning. 8 of 11 Figure 5. Power losses due to gear churning. Figure 6. Power losses due to bearing churning. Figure 6. Power losses due to bearing churning. Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load The fuel pump has a high loss compared to the generator due to the influence of gear diameter. dependent loss, and less important in the total losses. It can be seen that the seals losses varied with It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of the density and dynamic viscosity of the oil. The churning losses at take-o condition seem to have the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. Figure 7. Power losses due to seals friction. By adding the values of different heat loss mechanisms, Figure 8 shows the total power loss predicted in accessory gearbox components. It can be seen that:  The gear set connected to the generator creates the highest value of loss in comparison with other elements due to the high power transmitted which causes high friction between the gears as the friction coefficient change with power transmitted.  The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic pump is less than 2 kW in all flight phases.  The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine components) is valid, as the generated heat loads would be very small (in the order of 1 kW and less). Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 8 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, 21 8 of 10 a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 6. Power losses due to bearing churning. Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load dependent loss, and less important in the total losses. It can be seen that the seals losses varied with dependent loss, and less important in the total losses. It can be seen that the seals losses varied with speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. Figure 7. Power losses due to seals friction. Figure 7. Power losses due to seals friction. By adding the values of different heat loss mechanisms, Figure 8 shows the total power loss By adding the values of di erent heat loss mechanisms, Figure 8 shows the total power loss predicted in accessory gearbox components. It can be seen that: predicted in accessory gearbox components. It can be seen that:  The gear set connected to the generator creates the highest value of loss in comparison with other The gear set connected to the generator creates the highest value of loss in comparison with other elements due to the high power transmitted which causes high friction between the gears as the elements due to the high power transmitted which causes high friction between the gears as the friction coefficient change with power transmitted. friction coecient change with power transmitted.  The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic pump is less than 2 kW in all flight phases. The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic  The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine pump is less than 2 kW in all flight phases. components) is valid, as the generated heat loads would be very small (in the order of 1 kW and The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine less). components) is valid, as the generated heat loads would be very small (in the order of 1 kW and less). Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 9 of 11 Figure 8. Total power loss for each element in AGB. Figure 8. Total power loss for each element in AGB. By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory gearbox gearbox through all flight conditions. The model presented in this work seems to perform quite well through all flight conditions. The model presented in this work seems to perform quite well in overall in overall power loss prediction in AGB, given the proper geometry and operating conditions. The power loss prediction in AGB, given the proper geometry and operating conditions. The overall losses overall losses followed the trend of the friction losses because of the high heat generated between the followed the trend of the friction losses because of the high heat generated between the friction surfaces friction surfaces compared to the heat produced by the gears and bearing digging in the oil. compared to the heat produced by the gears and bearing digging in the oil. A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat load generated by the AGB for an 18 klbs engine at take-off condition is 17 kW. The case study of this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the generated tool is 21.6 kW. The linear relationship works very well between these two values. However, more case studies and analyses are required to confirm and enhance the reliability and validity of the generated tool. Figure 9. Overall power loss in AGB. 5. Conclusions A MATLAB tool for predicting different heat loss mechanisms, as well as heat load values in accessory gearbox components of gas turbine aero engines, was developed based on the physics- based modelling approach. The tool is capable of calculating load-dependent and no-load dependent heat losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear mesh loss and bearing friction loss at different flight phases. The heat losses could also be calculated in different gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show that the friction losses in gears and bearing generate the majority of the heat load in the AGB. Moreover, between different elements of the AGB, the gear set connected to the generator creates the highest amount of heat loss in comparison with other elements. The heat load value is maximum at the take-off condition due to the high transmitted power and the highest rotational speed. This value Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 9 of 11 Figure 8. Total power loss for each element in AGB. By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory gearbox through all flight conditions. The model presented in this work seems to perform quite well in overall power loss prediction in AGB, given the proper geometry and operating conditions. The overall losses followed the trend of the friction losses because of the high heat generated between the friction surfaces compared to the heat produced by the gears and bearing digging in the oil. A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat load generated by the AGB for an 18 klbs engine at take-off condition is 17 kW. The case study of this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the generated tool is 21.6 kW. The linear relationship works very well between these two values. Int. HoJ. wev Turbomach. er, moPr reopuls. case Power studi 2020 es ,a5n , 21 d analyses are required to confirm and enhance the reliability 9 of an 10 d validity of the generated tool. Figure 9. Overall power loss in AGB. Figure 9. Overall power loss in AGB. 5. Conclusions A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat A MATLAB tool for predicting different heat loss mechanisms, as well as heat load values in load generated by the AGB for an 18 klbs engine at take-o condition is 17 kW. The case study of accessory gearbox components of gas turbine aero engines, was developed based on the physics- this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the based modelling approach. The tool is capable of calculating load-dependent and no-load dependent generated tool is 21.6 kW. The linear relationship works very well between these two values. However, heat losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear more case studies and analyses are required to confirm and enhance the reliability and validity of the mesh loss and bearing friction loss at different flight phases. The heat losses could also be calculated generated tool. in different gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show 5. Conclusions that the friction losses in gears and bearing generate the majority of the heat load in the AGB. A MATLAB tool for predicting di erent heat loss mechanisms, as well as heat load values in Moreover, between different elements of the AGB, the gear set connected to the generator creates the accessory gearbox components of gas turbine aero engines, was developed based on the physics-based highest amount of heat loss in comparison with other elements. The heat load value is maximum at modelling approach. The tool is capable of calculating load-dependent and no-load dependent heat the take-off condition due to the high transmitted power and the highest rotational speed. This value losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear mesh loss and bearing friction loss at di erent flight phases. The heat losses could also be calculated in di erent gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show that the friction losses in gears and bearing generate the majority of the heat load in the AGB. Moreover, between di erent elements of the AGB, the gear set connected to the generator creates the highest amount of heat loss in comparison with other elements. The heat load value is maximum at the take-o condition due to the high transmitted power and the highest rotational speed. This value for the case study is 21.6 kW, which is in good agreement with the reported experimental data in the literature. The tool could be used for thermal management system designers for di erent gas turbine aero-engines and di erent missions, because all design parameters (geometry, oil characteristics, load, and rotational speed) are considered in a physics-based feature in the tool, and could be tuned for other applications. Author Contributions: Conceptualization, S.J.; Data curation, A.B.; Formal analysis, A.B.; Investigation, A.B.; Methodology, A.B.; Project administration, S.J.; Resources, T.N.; Software, A.B.; Supervision, T.N.; Writing—original draft, S.J.; Writing—review & editing, T.N. and S.J. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. References 1. Directorate-General for Research and Innovation; Directorate-General for Mobility and Transport. Flightpath 2050, Europe’s Vision for Aviation Maintaining Global Leadership & Serving Society’s Needs; Report of the High-Level Group on Aviation Research; Publication oce of the EU: Brussels, Belgium, 2011. 2. Jafari, S.; Nikolaidis, T. Turbojet engine industrial min-max controller performance improvement using fuzzy norms. Electronics 2018, 7, 314. [CrossRef] Int. J. Turbomach. Propuls. Power 2020, 5, 21 10 of 10 3. Jafari, S.; Nikolaidis, T. Thermal management systems for civil aircraft engines: Review, challenges and exploring the future. Appl. Sci. 2018, 8, 2044. [CrossRef] 4. Rolls Royce Deutschland Ltd. & Co KG. Heat Exchange System for A Power Gearbox, A Power Gearbox and A Turbo Engine with A Power Gear Box. Patent No. EP3244039 A1, 22 June 2017. 5. Nutakor, C.; Kłodowski, A.; Sopanen, J.; Mikkola, A.; Pedrero, J.I. Planetary gear sets power loss modeling: Application to wind turbines. Tribol. Int. 2017, 105, 42–54. [CrossRef] 6. Magalhães, L.; Martins, R.; Locateli, C.; Seabra, J. Influence of tooth profile and oil formulation on gear power loss. Tribol. Int. 2010, 43, 1861–1871. [CrossRef] 7. Martins, R.C.; Cardoso, N.F.R.; Bock, H.; Igartua, A.; Seabra, J.H.O. Power loss performance of high pressure nitrided steel gears. Tribol. Int. 2009, 42, 1807–1815. [CrossRef] 8. Hu, X.; Jiang, Y.; Luo, C.; Feng, L.; Dai, Y. Churning power losses of a gearbox with spiral bevel geared transmission. Tribol. Int. 2019, 129, 398–406. [CrossRef] 9. Fernandes, C.M.; Marques, P.M.; Martins, R.C.; Seabra, J.H. Gearbox power loss. Part I: Losses in rolling bearings. Tribol. Int. 2015, 88, 298–308. [CrossRef] 10. Boness, R.J. Churning Losses of Discs and Gears Running Partially Submerged in Oil. In Proceedings of the ASME International Power Transmission and Gearing Conference, Chicago, IL, USA, 7–9 April 1989; Volume 1, pp. 355–359. 11. Terekhov, A.S. Hydraulic losses in gearboxes with oil immersion. Russ. Eng. J. 1975, 55, 7–11. 12. Höhn, B.R.; Michaelis, K.; Vollmer, T. Thermal Rating of Gear Drives: Balance between Power Loss and Heat Dissipation; American Gear Manufacturers Association: Alexandria, VA, USA, 1996. 13. Changenet, C.; Leprince, G.; Ville, F.; Velex, P. A note on flow regimes and churning loss modeling. J. Mech. Des. 2011, 133, 121009. [CrossRef] 14. Fernandes, C.M.; Martins, R.C.; Seabra, J.H. Torque loss of type C40 FZG gears lubricated with wind turbine gear oils. Tribol. Int. 2014, 70, 83–93. [CrossRef] 15. Concli, F. Low-loss gears precision planetary gearboxes: Reduction of the load dependent power losses and eciency estimation through a hybrid analytical-numerical optimization tool. Forschung im Ingenieurwesen 2017, 81, 395–407. [CrossRef] 16. Wimmer, J.A. Lastverluste von Stirnradverzahnungen: Konstruktive Einflüsse, Wirkungsgradmaximierung, Tribologie. Doctoral Dissertation, Technische Universität München, München, Germany, 2006. 17. Ohlendorf, H. Verlustleistung und Erwärmung von Stirnrädern. Doctoral Dissertation, Technische Universität München, München, Germany, 1958. 18. Fernandes, C.M.; Marques, P.M.; Martins, R.C.; Seabra, J.H. Gearbox power loss. Part III: Application to a parallel axis and a planetary gearbox. Tribol. Int. 2015, 88, 317–326. [CrossRef] 19. Feehally, T. Electro-Mechanical Interaction in Gas Turbine-Generator Systems for More-Electric Aircraft. Doctoral Dissertation, The University of Manchester, Manchester, UK, 2012. 20. The Jet Engine; 7 Accessory drives; Rolls-Royce: Birmingham, UK, 1986; pp. 65–71, ISBN 0-902121-04-9. 21. The Aircraft Gas Turbine Engine and Its Operation, Part No. PWA 182408 PWA Oper. Instr. 200, Installation Engineering; Pratt & Whitney: East Hartford, CT, USA, 1988; pp. 3-45–3-47. 22. Niemann, G.; Winter, H. Maschinenelemente. II: Getriebe allgemein, Zahnradgetriebe-Grundlagen, Stirnradgetriebe; Springer: Berlin/Heidelberg, Germany, 2003. 23. Streifinger, H. Fuel/oil system thermal management in aircraft turbine engines. In Proceedings of the RTO Meeting Proceedings, Symposium, Design Principles and Methods for Aircraft Gas Turbine Engines, Toulouse, France, 11–12 July 1998; pp. 12–24. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (http://creativecommons.org/licenses/by-nc-nd/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Turbomachinery, Propulsion and Power Multidisciplinary Digital Publishing Institute

Thermal Performance Evaluation in Gas Turbine Aero Engines Accessory Gearbox

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International Journal of Turbomachinery Propulsion and Power Article Thermal Performance Evaluation in Gas Turbine Aero Engines Accessory Gearbox Soheil Jafari * , Ahmed Bouchareb and Theoklis Nikolaidis Centre for Propulsion Engineering, School of Aerospace, Transport and Manufacturing (SATM), Cranfield University, Cranfield MK43 0AL, UK; a.bouchareb@cranfield.ac.uk (A.B.); t.nikolaidis@cranfield.ac.uk (T.N.) * Correspondence: S.Jafari@cranfield.ac.uk Received: 14 February 2020; Accepted: 24 August 2020; Published: 26 August 2020 Abstract: This paper presents a methodological approach for mathematical modelling and physics-based analysis of accessory gearbox (AGB) thermal behavior in gas turbine aero engines. The AGB structure, as one of the main sources of heat in gas turbine aero engines, is firstly described and its power losses will be divided into load-dependent and no-load dependent parts. Di erent mechanisms of heat generation are then identified and formulated to develop a toolbox for calculation of the churning, sliding friction, and rolling friction losses between contact surfaces of the AGB. The developed tool is also capable of calculating the heat loss mechanisms in di erent elements of the AGB, such as gears, bearings, and seals. The generated model is used to simulate and analyze the AGB thermal performance in the di erent flight phases in a typical flight mission, where the obtained results are validated against publicly available data. The analysis of the results confirms the e ectiveness of the proposed method to estimate the heat loss values in the AGBs of gas turbine aero engines and to predict the thermal loads of the AGB in di erent flight phases. The developed tool enables the gas turbine thermal management system designers to deal with the generated heats e ectively and in an optimal way. Keywords: thermal management systems; accessory gearbox; gas turbine aero engines; heat loss mechanisms; thermal performance evaluation 1. Introduction Gas turbine engine (GTE) manufactures are facing huge challenges in developing the next generation of GTEs to meet all requirements, due to the increase of fuel price, power and eciency demands, and limitations and restrictions set by governments and organizations (e.g., the Advisory Council for Aviation Research and Innovation in Europe has a target of a 75% reduction in CO emissions and a 90% reduction of NOx emissions by 2050) [1,2]. One of these challenges is to deal with huge thermal loads generated by advanced GTEs components. The engine thermal management system (TMS) should be able to manage these heat loads in an optimal feature to get a safe and reliable operation for the engine. In other words, the main duty of the GTE TMS is to use engine heat sinks (oil, fuel, and air) to manage the thermal loads generated by engine heat sources (gearboxes, bearings, generators, pumps, etc.). There are a few studies in the literature focusing on the thermal management challenges and potential solutions for GTEs. An analytic review on this topic has recently been done by the authors [3], in which the di erent aspects, current challenges, and potential solutions for the TMS design procedure in new and next generation of GTEs were studied in detail. One of the main challenges in this field is the lack of physics-based models for thermal loads calculation in di erent TMS components to enable researchers and manufacturers to predict and analyze the thermal loads in each component at di erent flight phases, based on the geometry, mechanical loads, input and output Int. J. Turbomach. Propuls. Power 2020, 5, 21; doi:10.3390/ijtpp5030021 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2020, 5, 21 2 of 10 powers, and other design parameters. This kind of model will enable TMS designers to do a precise sensitive analysis on design and operational parameters, as well as to get a reliable vision about the next generation of TMSs for GTEs [4]. The gearbox is one of the most important elements in gas turbine TMS as a noticeable amount of heat load is generated by this component [5]. So, it is significant to predict its power loss during the design phase to improve the mechanical system design through di erent perspectives. For instance, reducing gear operating temperature will contribute to better lubrication, less oil degradation, and improving the gear lifetime by improving the resistance to scung and micro-pitting [6]. Therefore, this paper will focus on developing a physics-based tool to calculate the thermal load generated by di erent elements of the accessory gearbox (AGB) in gas turbine aero engines. 2. Accessory Gearbox Heat Loss Mechanisms The accessory gearbox drives the accessories of the engine like generator, fuel and oil pumps, hydraulic pumps, etc. So, it is an essential element for the operation of the engine or the aircraft on which it is mounted. The power loss mechanisms inside gearbox can be separated into two groups: no-load dependent losses and load-dependent losses. No-load dependent losses include churning losses caused by gears, seals, and bearings, and load-dependent losses are frictional losses caused by gears and bearings [7]. No-load dependent losses mainly consist of Windage and churning power losses, the churning losses are one of the main power losses especially at high oil fill level and rotational speeds [8]. This type of power loss occurs between gears even without torque transmission in the rotation of mechanical components and it is related to the density, viscosity, and immersion depth of the components on a sump lubricated gearbox, and it also depends on the internal design of gearbox casing and operating conditions. No-load losses of rolling bearings mainly depend on the size, type, and bearing arrangement, immersion depth, and lubricant viscosity [9]. Load-dependent power losses occur because of contacts between the gears’ teeth during power transmitting, which are mainly depends on friction coecient, transmitted power, and sliding velocity in the contact area between teeth [9]. The dependence of no-load losses on the lubricant viscosity and the frictional losses is influenced by the oil characteristics and the ability to provide low friction coecient and lubricant film. This is important to increase gearbox eciency and to enhance gears and bearings life [10]. Most studies have focused on power loss, and gear eciency is related to the planetary gear system, power gearbox (PGB). Some of these studies have focused on spin power losses, but most of the studies have investigated mechanical losses. These studies provide a significant database for predicting power loss in gears, but it considers only a single gear pair. The review of these studies discloses the need for a model can predict the power loss in the AGB for typical aero-engine. The accessory gearbox consists of sets of spur gears connected to each other, each gear drives one element, such as the generator, or pump. The power losses can be divided into load-dependent and no-load dependent according to their mechanical component and their relation to transmitted torque that generates them [3]. In this way, the total power loss (PL) can be subdivided into no-load and load dependent related to gears (PL + PL ), bearings (PL + PL ), and no-load dependent for G0 G B0 B seals (PL ). S0 The total power losses in the accessory gearbox are the sum of all sources of losses in each contact pairs and single elements inside generated by load and no-load losses equal to the heat evacuation from AGB to the environment [9]. PL = PL + PL + PL + PL + PL = Q (1) G0 G B0 B S0 AGB The share of power losses between di erent sources strongly depends on the gearbox design configuration. Int. J. Turbomach. Propuls. Power 2020, 5, 21 3 of 10 3. Mathematical Modelling of Heat Losses The physics-based model for heat loss calculation is described in this section. 3.1. No-Load Dependent Losses Depending on the input speed and power, gearbox design and lubricant characteristics, the no-load dependent losses are a very important source of heat dissipation within an accessory gearbox. Due to the complicated design of the AGB, it is not straightforward to generate a model that consists of a general formulation to assess this mechanism of power loss. The main objective of this study is to accurately predict the power losses considering friction torque loss in the meshing gears. 3.1.1. Gears Churning Loss In recent decades, many studies have investigated the influence of the energy loss mechanism and parameters on power loss in the gearbox. Boness (1989) [10] investigated the influence of diameter and oil fill level on a disk and drove an empirical formulation through experiments. Terekhov (1975) [11] studied single meshing gears rotating immersed in a fluid and developed an empirical equation using a dimensionless moment coecient from several experiments. Höhn et al. [12] developed an empirical formation through experimental work, and concluded that reducing oil level can reduce the churning loss but not the gear temperature. Gear churning losses is the main source of power loss for splash lubricated gears, which is generated by rotating gears totally or partly immersed in fluid lubrication. Changenet et al. [13] developed a mathematical model for calculating the gear churning loss based on the series of experimental tests, and carried out a comprehensive dimensional analysis to tune the model. In this paper, this model is selected, since it overcomes some of the limitations of the previous research in gear churning losses from accuracy, validity range, and reliability points of view. The model proposed by Changenet et al. [13] depends on the regime of the flow and Reynolds number that defines the laminar-turbulent transition determined by experimental results. It is very dicult to determine the transition of the laminar-turbulent regime inside an oil sump, due to the infinite combination parameters and design features [14]. Gear churning power loss is mainly responsible for no-load dependent losses and depends on rotational speed, immersion area and depth, gear geometry, lubricant density, and viscosity, as shown in Equation (2): 3 3 PL =  W A R C (2) G0 i m where  is the lubricant density, W is the rotational speed in rad/s, A is immersion surface area, R = is the pitch radius, and the C expression has been determined depending on the flow regime: W.Rp b For Rec = < 6000 0 1 0.45 0.1 B C h V B oil C 0.21 0.21 B C C = 1.36B   Fr Re C (3) @ A D D W.r b For Rec = > 9000 0 1 ! ! 0.1 0.85 0.35 B C h b V B C oil 0.88 B C C = 3.644  B    Fr C (4) @ A D D where h is the immersion depth, D is the gear pitch diameter, V is the oil volume,  is the lubricant oil kinematic viscosity, b is the tooth face width, Fr = Froude number, depending on gear parameters 2 2 W R W R = , Re = Reynolds number = . It should be mentioned that this formulation and corresponding flow regimes are valid for the steady-state operating condition. Int. J. Turbomach. Propuls. Power 2020, 5, 21 4 of 10 3.1.2. Bearings Churning Loss The bearing churning losses are mainly depending on the bearing geometry and type, speed and lubricant viscosity. 2/3 7 3 3 PL = W  f  10  (n  )  d  10 (5) B0 0 oil where f is bearing coecients of loss,  is the dynamic viscosity, n is the rotation speed, and d is 0 oil m the mean diameter. 3.1.3. Seals Churning Loss The seal churning losses are mainly occurring between seal tip and shaft in the contact zone. However, many studies have been investigated on seals losses but this phenomenon still not well understood, due to small of the contact zone and dicult to parametrize. With regard to [15,16], the seal losses mainly depend on seal diameter and shaft speed. Equation (5) is used to predict the seal losses, but this formula does not consider the oil viscosity: 6 2 P = 7.69  10  d  n (6) Seal i where d is the shaft diameter. 3.2. Load Dependent Losses Load dependent losses include gear mesh loss and power loss in bearings that could be calculated as follows: 3.2.1. Power Loss in Meshing Gears Generally, the power loss due to gear mesh is determined by the normal load, relative rolling and sliding between lubricated meshing gears. Friction interaction between meshing gears must be considered as it is influenced by all characterized elements. The main contributors to power loss are the friction coecient and load distribution along the line of contact of meshing gear [3]. This study will consider the friction coecient and load distribution constant along the line of contact. Ohlendorf [17], has introduced the equation to calculate the load-dependent for spur gears. PL = P   H (7) G in m v where  : mean friction coecient along the path of the contact [18], H : is the gear loss factor. P : m in is the power input. 3.2.2. Power Loss in Bearings According to Wimmer et al. [16], the bearings load dependent loss mainly depends on the load applied, mean diameter, and friction coecient of the bearings: 2 2 PL =  n  F + F  f  d (8) B 1 m R A where F + F is the radial and axial load applied, f is the bearings friction coecient, d is the R A 1 m mean diameter. Finally, by adding the values of Equations (2), (5)–(8) and putting them in Equation (1), the total heat loss in the accessory gearbox will be calculated. 4. Results Analysis The equations described in previous sections have been used to generate a simulation toolbox in MATLAB environment to calculate di erent power loss mechanisms in di erent elements of accessory Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 5 of 11 4. Results Analysis Int. J. Turbomach. Propuls. Power 2020, 5, 21 5 of 10 The equations described in previous sections have been used to generate a simulation toolbox in MATLAB environment to calculate different power loss mechanisms in different elements of gearbox for gas turbine engines. The toolbox is able to predict the heat load values in the AGB, due to accessory gearbox for gas turbine engines. The toolbox is able to predict the heat load values in the friction and churning losses in gears and bearing and seals for each element. AGB, due to friction and churning losses in gears and bearing and seals for each element. It should be mentioned that in this study, the simulation model includes only the elements that have It should be mentioned that in this study, the simulation model includes only the elements that huge impacts on the total power losses while ignoring other elements (e.g., de-oiler). The schematic of have huge impacts on the total power losses while ignoring other elements (e.g., de-oiler). The accessory gearbox gear set configuration for an aero-engine is shown in Figure 1, it mainly consists of a schematic of accessory gearbox gear set configuration for an aero-engine is shown in Figure 1, it set of spur gears connected to drive each element at di erent speed ratios and power, a ball bearing, mainly consists of a set of spur gears connected to drive each element at different speed ratios and and gear shaft, seals, a gearbox housing. According to [19], the typical speed of each element in the power, a ball bearing, and gear shaft, seals, a gearbox housing. According to [19], the typical speed accessory gearbox at maximum power output, such as fuel pump, generator, and oil pump, are listed of each element in the accessory gearbox at maximum power output, such as fuel pump, generator, in Table 1. and oil pump, are listed in Table 1. Figure 1. Schematic of accessory gearbox (AGB) gear set configuration. Figure 1. Schematic of accessory gearbox (AGB) gear set configuration. Table 1. Accessory gearbox drives speeds. Table 1. Accessory gearbox drives speeds. Component Speed Ratio to HP Spool Component Speed Ratio to HP Spool Oil Pump 0.62 Oil Pump 0.62 Generator 1.79 Generator 1.79 Fuel Pump 0.9 Fuel Pump 0.9 Hydraulic Pump 0.5 Hydraulic Pump 0.5 In this study, the power loss model of the accessory gearbox is simulated through operating in In this study, the power loss model of the accessory gearbox is simulated through operating in a di erent flight phase, wide range of operating conditions, with an input power and speed varied a different flight phase, wide range of operating conditions, with an input power and speed varied for each flight condition, according to engine manufacturer, the speed and power input data in the for each flight condition, according to engine manufacturer, the speed and power input data in the accessory gearbox are taken from real engine of CFM56 family through di erent flight phases. The first accessory gearbox are taken from real engine of CFM56 family through different flight phases. The row of the Table 2 presents the core engine power. A percentage of this power will be transmitted to first row of the Table 2 presents the core engine power. A percentage of this power will be transmitted the AGB at di erent flight phases. With regard to Rolls-Royce [20] and Pratt & Whitney [21], the AGB to the AGB at different flight phases. With regard to Rolls-Royce [20] and Pratt & Whitney [21], the drives the accessories, fuel pumps, oil pumps, generators etc., by handling between 400–500 hp. AGB drives the accessories, fuel pumps, oil pumps, generators etc., by handling between 400–500 hp. The second raw presents the percentage of high-pressure rotational speed (from [19]), which is used as The second raw presents the percentage of high-pressure rotational speed (from [19]), which is used the input for the AGB physics-based model. as the input for the AGB physics-based model. The simplified model of AGB internal structure of gears is shown in Figure 1. Reference [22] Table 2. Accessory gearbox speed and engine core power during flight phases. provides basic design parameters of the spur gear, which are also listed in Table 3. Take Begin End Start End Begin End Conditions Idle Climb Approach O Climb Climb Cruise Cruise Descent Descent HP Power (kW) 825 24700 23200 14100 9700 8570 7260 5080 1090 6870 Speed (%) 0.28 0.88 0.88 0.92 0.91 0.88 0.88 0.80 0.69 058 The simplified model of AGB internal structure of gears is shown in Figure 1. Reference [22] provides basic design parameters of the spur gear, which are also listed in Table 3. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 6 of 11 Table 2. Accessory gearbox speed and engine core power during flight phases. Take Begin End Start End Begin End Conditions Idle Climb Approach Off Climb Climb Cruise Cruise Descent Descent HP Power (kW) 825 24700 23200 14100 9700 8570 7260 5080 1090 6870 Speed (%) 0.28 0.88 0.88 0.92 0.91 0.88 0.88 0.80 0.69 058 Int. J. Turbomach. Propuls. Power 2020, 5, 21 6 of 10 Table 3. Design parameters of AGB. Table 3. Design parameters of AGB. Parameter Index Unites Value Parameter Index Unites Value 𝛽 ° Base helix angle 10 Base helix angle 10 Bearing mean diameter 𝑑 𝑚 0.20 Bearing mean diameter d m 0.20 𝑑 𝑚 Pitch diameter 0.35 Pitch diameter d m 0.35 −6 Immersed area 𝐴 𝑚 1.0996 × 10 𝑖 2 6 Immersed area A m 1.0996  10 ℎ 𝑚 Gear immersion depth 0.22 Gear immersion depth h m 0.22 Shaft diameter 𝑑 𝑚 0.2 Shaft diameter d m 0.2 Oil volume V m 0.0012 𝑉 𝑚 Oil volume oil 0.0012 𝑙𝑜𝑖 N of teeth (Oil Pump) z - 77 N of teeth (Oil Pump) z - 77 N of teeth (Fuel Pump) z - 75 N of teeth (Fuel Pump) z - 75 N of teeth (Generator) z - 20 N of teeth (Generator) z - 20 N of teeth (Hydraulic Pump) z - 67 N of teeth (Hydraulic Pump) z - 67 Figure 2 shows the power loss toolbox generated with the graphical user interface (GUI) in Figure 2 shows the power loss toolbox generated with the graphical user interface (GUI) in MATLAB (R2019a) to enable the user to analyze di erent heat load mechanisms in di erent AGB MATLAB (R2019a) to enable the user to analyze different heat load mechanisms in different AGB elements separately and/or in total. elements separately and/or in total. Figure 2. Accessory gearbox heat load calculation toolbox. Figure 2. Accessory gearbox heat load calculation toolbox. By applying the flight phases of Table 2 to the model generated in MATLAB, the results of the By applying the flight phases of Table 2 to the model generated in MATLAB, the results of the heat load in different elements of the AGB according to different heat loss mechanisms are generated, heat load in di erent elements of the AGB according to di erent heat loss mechanisms are generated, and will be analyzed here. and will be analyzed here. Figure 3 shows the friction loss in all AGB elements, where the gear connected to the generator Figure 3 shows the friction loss in all AGB elements, where the gear connected to the generator has the highest friction loss in take-off condition compared to other elements, which mainly depends has the highest friction loss in take-o condition compared to other elements, which mainly depends on the friction coefficient and the load applied to the meshing gears. on the friction coecient and the load applied to the meshing gears. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Figure 4 confirms that the bearings friction losses are influenced directly by the applied load and speed. This figure is also showing a direct relation between the power loss value and the increase of speed and power transmitted. Figure 3. Power losses due to gear friction. Figure 3. Power losses due to gear friction. Figure 4. Power losses due to bearing friction. Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses where the oil properties change with oil temperature and operating conditions. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 5. Power losses due to gear churning. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 7 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, 21 7 of 10 Figure 3. Power losses due to gear friction. Figure 4 confirms that the bearings friction losses are influenced directly by the applied load and speed. This figure is also showing a direct relation between the power loss value and the increase of speed and power transmitted. Figure 3. Power losses due to gear friction. Figure 4. Power losses due to bearing friction. Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses where the oil properties change with oil temperature and operating conditions. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. Figure 4. Power losses due to bearing friction. Figure 4. Power losses due to bearing friction. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, Figures 5 and 6 show the losses due to gear and bearing churning in all AGB components, a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses respectively. Regarding Section 3, the fluid viscosity and density index influence the churning losses level influences the churning power loss, the losses increase with increasing the immersion level of where the oil properties change with oil temperature and operating conditions. where the oil properties change with oil temperature and operating conditions. the gear teeth. The fuel pump has a high loss compared to the generator due to the influence of gear diameter. It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in the density and dynamic viscosity of the oil. The churning losses at take-off condition seem to have a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 5. Power losses due to gear churning. Int. J. Turbomach. Propuls. Power 202Figure 0, 5, x FO 5. R P Power EER REV losses IEW due to gear churning. 8 of 11 Figure 5. Power losses due to gear churning. Figure 6. Power losses due to bearing churning. Figure 6. Power losses due to bearing churning. Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load The fuel pump has a high loss compared to the generator due to the influence of gear diameter. dependent loss, and less important in the total losses. It can be seen that the seals losses varied with It can be seen that the impact of the oil temperature on the churning power losses is mainly reflected in speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of the density and dynamic viscosity of the oil. The churning losses at take-o condition seem to have the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. Figure 7. Power losses due to seals friction. By adding the values of different heat loss mechanisms, Figure 8 shows the total power loss predicted in accessory gearbox components. It can be seen that:  The gear set connected to the generator creates the highest value of loss in comparison with other elements due to the high power transmitted which causes high friction between the gears as the friction coefficient change with power transmitted.  The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic pump is less than 2 kW in all flight phases.  The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine components) is valid, as the generated heat loads would be very small (in the order of 1 kW and less). Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 8 of 11 Int. J. Turbomach. Propuls. Power 2020, 5, 21 8 of 10 a high value on all AGB components, due to change the viscosity of the oil. Additionally, the oil fill level influences the churning power loss, the losses increase with increasing the immersion level of the gear teeth. Figure 6. Power losses due to bearing churning. Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load Finally, Figure 7 shows the power loss produced by shaft seals which is considered as no-load dependent loss, and less important in the total losses. It can be seen that the seals losses varied with dependent loss, and less important in the total losses. It can be seen that the seals losses varied with speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of speed through all flight conditions. The results presented in Figures 3–7 confirms that the majority of the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. the heat load in accessory gearbox is generated by gear and bearing friction mechanisms. Figure 7. Power losses due to seals friction. Figure 7. Power losses due to seals friction. By adding the values of different heat loss mechanisms, Figure 8 shows the total power loss By adding the values of di erent heat loss mechanisms, Figure 8 shows the total power loss predicted in accessory gearbox components. It can be seen that: predicted in accessory gearbox components. It can be seen that:  The gear set connected to the generator creates the highest value of loss in comparison with other The gear set connected to the generator creates the highest value of loss in comparison with other elements due to the high power transmitted which causes high friction between the gears as the elements due to the high power transmitted which causes high friction between the gears as the friction coefficient change with power transmitted. friction coecient change with power transmitted.  The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic pump is less than 2 kW in all flight phases. The oil and fuel pump gear sets have the next ranks in generating heat loads. The loss in hydraulic  The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine pump is less than 2 kW in all flight phases. components) is valid, as the generated heat loads would be very small (in the order of 1 kW and The assumption of neglecting other elements (e.g., de-oiler and heat transfer from the engine less). components) is valid, as the generated heat loads would be very small (in the order of 1 kW and less). Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 9 of 11 Figure 8. Total power loss for each element in AGB. Figure 8. Total power loss for each element in AGB. By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory gearbox gearbox through all flight conditions. The model presented in this work seems to perform quite well through all flight conditions. The model presented in this work seems to perform quite well in overall in overall power loss prediction in AGB, given the proper geometry and operating conditions. The power loss prediction in AGB, given the proper geometry and operating conditions. The overall losses overall losses followed the trend of the friction losses because of the high heat generated between the followed the trend of the friction losses because of the high heat generated between the friction surfaces friction surfaces compared to the heat produced by the gears and bearing digging in the oil. compared to the heat produced by the gears and bearing digging in the oil. A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat load generated by the AGB for an 18 klbs engine at take-off condition is 17 kW. The case study of this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the generated tool is 21.6 kW. The linear relationship works very well between these two values. However, more case studies and analyses are required to confirm and enhance the reliability and validity of the generated tool. Figure 9. Overall power loss in AGB. 5. Conclusions A MATLAB tool for predicting different heat loss mechanisms, as well as heat load values in accessory gearbox components of gas turbine aero engines, was developed based on the physics- based modelling approach. The tool is capable of calculating load-dependent and no-load dependent heat losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear mesh loss and bearing friction loss at different flight phases. The heat losses could also be calculated in different gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show that the friction losses in gears and bearing generate the majority of the heat load in the AGB. Moreover, between different elements of the AGB, the gear set connected to the generator creates the highest amount of heat loss in comparison with other elements. The heat load value is maximum at the take-off condition due to the high transmitted power and the highest rotational speed. This value Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 9 of 11 Figure 8. Total power loss for each element in AGB. By adding all values in Figure 8, Figure 9 shows the overall power loss occurs in accessory gearbox through all flight conditions. The model presented in this work seems to perform quite well in overall power loss prediction in AGB, given the proper geometry and operating conditions. The overall losses followed the trend of the friction losses because of the high heat generated between the friction surfaces compared to the heat produced by the gears and bearing digging in the oil. A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat load generated by the AGB for an 18 klbs engine at take-off condition is 17 kW. The case study of this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the generated tool is 21.6 kW. The linear relationship works very well between these two values. Int. HoJ. wev Turbomach. er, moPr reopuls. case Power studi 2020 es ,a5n , 21 d analyses are required to confirm and enhance the reliability 9 of an 10 d validity of the generated tool. Figure 9. Overall power loss in AGB. Figure 9. Overall power loss in AGB. 5. Conclusions A comparison of the results with the value reported in [23] shows that the total accessory gearbox power loss is quite close to the experimental value reported by manufacturers. In [23], the total heat A MATLAB tool for predicting different heat loss mechanisms, as well as heat load values in load generated by the AGB for an 18 klbs engine at take-o condition is 17 kW. The case study of accessory gearbox components of gas turbine aero engines, was developed based on the physics- this paper is a CFM56-5 like with the thrust value of 25 klbs and the heat load calculated by the based modelling approach. The tool is capable of calculating load-dependent and no-load dependent generated tool is 21.6 kW. The linear relationship works very well between these two values. However, heat losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear more case studies and analyses are required to confirm and enhance the reliability and validity of the mesh loss and bearing friction loss at different flight phases. The heat losses could also be calculated generated tool. in different gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show 5. Conclusions that the friction losses in gears and bearing generate the majority of the heat load in the AGB. A MATLAB tool for predicting di erent heat loss mechanisms, as well as heat load values in Moreover, between different elements of the AGB, the gear set connected to the generator creates the accessory gearbox components of gas turbine aero engines, was developed based on the physics-based highest amount of heat loss in comparison with other elements. The heat load value is maximum at modelling approach. The tool is capable of calculating load-dependent and no-load dependent heat the take-off condition due to the high transmitted power and the highest rotational speed. This value losses in AGB structure including churning loss in gears, bearings, and seals, as well as gear mesh loss and bearing friction loss at di erent flight phases. The heat losses could also be calculated in di erent gear sets in the AGB, including gear sets connected to the generator, oil pump, fuel pump, and hydraulic pump. The results of the simulation of a complete mission for a CFM56-5 AGB show that the friction losses in gears and bearing generate the majority of the heat load in the AGB. Moreover, between di erent elements of the AGB, the gear set connected to the generator creates the highest amount of heat loss in comparison with other elements. The heat load value is maximum at the take-o condition due to the high transmitted power and the highest rotational speed. This value for the case study is 21.6 kW, which is in good agreement with the reported experimental data in the literature. The tool could be used for thermal management system designers for di erent gas turbine aero-engines and di erent missions, because all design parameters (geometry, oil characteristics, load, and rotational speed) are considered in a physics-based feature in the tool, and could be tuned for other applications. Author Contributions: Conceptualization, S.J.; Data curation, A.B.; Formal analysis, A.B.; Investigation, A.B.; Methodology, A.B.; Project administration, S.J.; Resources, T.N.; Software, A.B.; Supervision, T.N.; Writing—original draft, S.J.; Writing—review & editing, T.N. and S.J. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. References 1. Directorate-General for Research and Innovation; Directorate-General for Mobility and Transport. Flightpath 2050, Europe’s Vision for Aviation Maintaining Global Leadership & Serving Society’s Needs; Report of the High-Level Group on Aviation Research; Publication oce of the EU: Brussels, Belgium, 2011. 2. Jafari, S.; Nikolaidis, T. Turbojet engine industrial min-max controller performance improvement using fuzzy norms. Electronics 2018, 7, 314. [CrossRef] Int. J. Turbomach. Propuls. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Journal

International Journal of Turbomachinery, Propulsion and PowerMultidisciplinary Digital Publishing Institute

Published: Aug 26, 2020

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