Proceedings of ASME Turbo Expo 2018 Turbomachinery Technical Conference and Exposition GT2018 June 11-15, 2018, Oslo, Norway

GT2018-75386 Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021

EXPERIMENTAL INVESTIGATION OF AN INVERTED FOR EXHAUST GAS ENERGY RECOVERY

Ian Kennedy Zhihang Chen University of Bath University of Bath Bath, UK Bath, UK

Bob Ceen Simon Jones Colin D Copeland Axes Design Ltd HIETA Technologies Ltd University of Bath Malvern, UK Bristol, UK Bath, UK

ABSTRACT the vehicle. A window of opportunity still remains for this until Exhaust gases from an internal (ICE) alternatives such as electric vehicles become more readily contain approximately 30% of the total energy released from available and cost effective. Recovering energy from exhaust combustion of the fuel. In order to improve fuel economy and gases is one key means of improving the efficiency of ICE reduce emissions, there are a number of technologies available powered vehicles. Turbomachinery can be used to recover this to recover some of the otherwise wasted energy. The inverted energy using technologies such as the IBC, which is shown Brayton cycle (IBC) is one such technology. schematically on Fig. 1. The purpose of the study is to conduct a parametric experimental investigation of the IBC. Hot air from a Coolant turbocharger test facility is used. The system is sized to operate exchanger using the exhaust gases produced by a 2 litre turbocharged engine at motorway cruise conditions. A number of parameters Electric are investigated that impact the performance of the system such C T as turbine inlet temperature, system drop and machine inlet temperature. The results confirm that the output power is strongly affected by the turbine inlet temperature and system pressure Exhaust Engine gas drop. The study also highlights the packaging and performance advantages of using a 3D printed to reject the FIGURE 1: excess heat. Due to rotordynamic issues, the speed of the system was limited to 80,000 rpm rather than the target 120,000 rpm. The IBC can operate using hot gases at as low as However, the results show that the system can generate a specific atmospheric pressure or lower. This makes it applicable to any of up to 17 kJ/kg at 80,000 rpm. At full speed it is estimated industry where such gases are available, not just the automotive that the system can develop approximately 47 kJ/kg, which industry. It also represents one of the few types of heat recovery represents a of approximately 5%. that does not need to impose any additional backpressure on the internal combustion engine. Such backpressure is often viewed INTRODUCTION as detrimental to its performance due to the increase in pumping In the automotive industry, government legislation requires loss and combustion instability. manufacturers of ICE powered vehicles to meet stringent targets The cycle has been studied for a number of years by for exhaust gas emissions. Emissions such as NOx and different groups for various applications. For example, in 1919 hydrocarbons can be reduced through techniques such as exhaust Kohler [1] invented a process for operating combustion gas recirculation or catalysis, but production of CO2 is inevitable with expansion to sub atmospheric pressure and compression when hydrocarbon fuels are combusted. CO2 emissions of ICE back to ambient. A steam generator and condenser were powered vehicles can be reduced through improved efficiency of proposed to cool the gases after expansion. Hingst [2] proposed

1 Copyright © 2018 ASME a number of variants of the IBC with cooling after the turbine IBC could increase electrical efficiency by about 5%, at the using surface or spray type coolers. Hodge [3] evaluated the expense of thermal efficiency. thermal efficiency and specific work output of the cycle over a A number of papers have compared IBC performance with range of temperatures and pressure ratios. The thermal efficiency that of other heat recovery techniques. Copeland and Chen [16] was shown to increase with turbine inlet temperature. The compared the performance of an IBC with turbocompounding optimum pressure ratio was also demonstrated to increase with and the pressurized Brayton cycle, when applied as a bottoming turbine inlet temperature. The disadvantage that the cycle cycle to a turbocharged engine. They found that the requires larger components due to the operation at reduced IBC had superior performance, provided that the turbomachinery Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 pressure was also noted. efficiencies are high enough. They compared the results in terms Various studies have investigated the performance of the of specific work and thermal efficiency. Bianchi and De Pascale IBC as a bottoming cycle for devices such as gas turbines. [17] compared the IBC (with and without condensation of water) Wilson et al. [4] investigated the business case of adding a fan with the and the organic . They downstream of a fitted with a downstream boiler. The compared the cycle performance using a number of different intent was to increase net power out through a greater expansion efficiency metrics based on heat used, heat available and ratio across the existing turbine by expanding to atmospheric efficiency compared with an ideal reversible cycle. They found pressure and below. A standalone IBC device operating off of hot that the gave the highest efficiency using gases was also studied. The findings were up to 10 percent return all efficiency metrics, particularly at low heat source on investment for the standalone device and up to 30 percent for temperatures. The Stirling engine and IBC both had efficiencies the addition of a fan. Holmes [5] investigated the addition of an that increased with heat source temperature, with the Stirling induced draft fan to a marine gas turbine and found an increase engine having superior efficiency compared with the IBC. in power and efficiency of approximately 9%. Condensation improved the IBC efficiency to close to the Frost [6] proposed a combined Brayton and Stirling efficiency for high IBC turbomachinery polytropic where the Ericsson cycle is a bottoming cycle with expansion to efficiency. Lu et al [18] compared the performance of a very low pressure (0.04 bar absolute). The bottoming cycle is turbocharged engine with IBC versus a turbocompounding effectively an inverted cycle with isothermal compression as in system with decoupled turbine and continuously variable the Ericsson cycle. They predicted an efficiency similar to that transmission driven compressor. They found that both systems of a combined Brayton and Rankine cycle. Tsujikawa et al. [7] offered a significant improvement in fuel efficiency and power investigated intercooling in an IBC, finding that three stages can output at full load. Bhargava et al [19] compared the IBC with improve thermal efficiency by approximately ten percent. They the pressurized Brayton and the organic Rankine cycle in a found that a Brayton cycle with an IBC as a bottoming cycle had cogenerative application as a gas turbine bottoming cycle. a thermal efficiency of over 60% for a turbine inlet temperature Performance was evaluated using an energy saving index, with of 1500°C. Fuji et al. [8] showed that the IBC could either the Rankine cycle giving the best performance for most gas replace a Rankine cycle as a bottoming cycle or could be used as turbines followed by the IBC and then the pressurized Brayton an alternative to recuperation. Agnew et al. [9] showed that cycle. overall efficiency could be improved with higher inverted cycle Another means to evaluate and compare cycle performance inlet pressures when used as a bottoming cycle. is based on exergy efficiency. Zheng et al [20] investigated the Alabdoadaim et al. [10] investigated a combined Rankine, exergy efficiency and losses in a Braysson cycle. They found that Brayton and two parallel inverted Brayton cycles, and found that the exergy efficiency was higher than for a Brayton cycle and the system had a maximum thermal efficiency of 54%, achieved that the largest exergy loss was for combustion. Zhang et al [21] by altering the expansion ratio of the second inverted Brayton performed an exergy analysis on the system proposed in [12], cycle. Alabdoadaim et al. [11] studied a combined Rankine, finding the largest exergy losses to be in the followed Brayton and inverse Brayton cycle and attained a maximum by the heat exchanger. Chen et al [22] used exergy analysis to thermal efficiency of 57.7%. Alabdoadaim et al. [12] also studied optimize the performance of a combined intercooled a combined Brayton and inverse Brayton cycle. They found that regenerative Brayton and inverse Brayton cycle. They found that a system with regeneration could achieve an efficiency of at low pressure ratios regeneration could significantly improve 49.36%. efficiency and at high pressure ratios intercooling had a marked Bianchi et al [13] investigated the use of an IBC for impact on efficiency. repowering existing gas turbines. They found that the cycle could Some investigations have been conducted into the increase the electrical efficiency by up to 30%. application of the IBC to microturbines. Henke et al [23] Tsujikawa et al [14] proposed an atmospheric pressure simulated the use of an IBC in a micro gas turbine combined heat turbine to recovery energy from a solid oxide fuel cell. The and power (CHP) plant. They noted that for small systems, small system was effectively an inverted Brayton cycle with two stage turbocharger components are needed and these suffer from high intercooled compression. The combined system had a thermal losses such as losses due to tip leakages. The losses can be efficiency of over 65%. reduced by using an IBC where the components are larger for the Bianchi et al [15] studied the IBC as a gas turbine bottoming same mass flow rate. They investigated using exhaust gas cycle for a cogenerative application. They found that using the recirculation (EGR) to improve the efficiency of the

2 Copyright © 2018 ASME microturbine CHP unit, finding that total efficiency could be temperature, speed (expansion ratio), turbine inlet temperature improved by up to 15% by using an EGR rate of 85%. Tanaka et and system pressure drop. A CAD screenshot of the test rig is a [24] studied the development of a 50 kW micro gas turbine shown in Fig. 2. operating on the inverted Brayton cycle. They predicted an Heat electrical efficiency of 10% and simulated its application to an Turbine exchanger industrial furnace and a biomass boiler. Bianchi et al [25] Cold air out simulated the addition of an IBC to two different types of micro gas turbine. They found that the addition could give a relative Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 4 improvement of electrical efficiency of about 10%. Few studies have been conducted that have applied the IBC 2 to piston engines to recover heat from exhaust gases. Murray 3 Bailey [26] compared the IBC with the pressurized Brayton and organic Rankine cycles as a waste heat recovery system for a 1 diesel truck engine. The findings were that the IBC gave a fuel consumption improvement of about 6%, which was more than the pressurized Brayton (~ 4% improvement) but less than the Hot air in organic Rankine cycle (~ 12% improvement). Chen et al [27] Rotrex Torque Compressor applied the IBC to a gasoline engine to determine the benefits drive meter over the Worldwide Harmonized Light Vehicle Test Procedure. The analysis was conducted using pre-catalyst temperatures, at a FIGURE 2: TEST SETUP SHOWING KEY COMPONENTS number of fixed turbomachinery isentropic efficiencies. They The test facility used to perform the experiments is an noted that for most applications, it would be desirable to locate electrically heated hot-gas stand used primarily for turbocharger the system downstream of the catalyst. The inlet pressure to the testing. As such, the system was operated using air rather than system was set to atmospheric, so that there was no detrimental exhaust gas. The air to run the rig was dried air supplied by an effect on engine performance. The results for a single stage upstream compressor. The inlet pressure to the rig was controlled system were an improvement in fuel consumption of up to 3% using a valve and the inlet temperature was varied using an for 80% efficient turbomachinery and up to 1.4% for 75% electric heater. efficient turbomachinery. After expansion in the turbine, the air was cooled using Despite the large number of studies there have been very few water supplied from a cooling system capable of controlling the experimental investigations using the IBC. Agelidou et al [28] water inlet temperature and hence the compressor inlet operated a conventional micro gas turbine on an inverted cycle temperature. The heat was rejected through a 3D printed Inconel and were unable to produce a positive power output due to high heat exchanger. The heat exchanger has very high performance mechanical losses. Inoue et al [29] built a 3.5 kW recuperated heat transfer surfaces resulting in an effectiveness that was found microturbine operating on the inverted Brayton cycle. It was to be approximately 97% for a pressure drop of 1.5 kPa at 50 g/s. referred to as an atmospheric pressure turbine and achieved a The high heat transfer surfaces, combined with the fact that it is maximum thermal efficiency of 8.7%. 3D printed, means that the packaging of it is very flexible and it In summary the literature on the IBC is predominantly can be designed to occupy small spaces found on modern analytical studies assessing its performance as a bottoming cycle vehicles. and comparing it with other heat recovery techniques. In this The speed of the device was controlled using a Rotrex drive paper an experimental study of the IBC is conducted to evaluate dynamometer that could supply or extract shaft power. A high the effect of various parameters on its performance. There are a speed torquemeter was used to measure the torque and speed number of unique aspects to this work in comparison to the precisely to derive the power generated directly off of the shaft available literature. First, to authors’ knowledge, it is the first of the IBC device. Thus, while bearing losses are included in the experimentally based parametric study of the subatmospheric data in this paper, any losses in energy conversion (e.g. electric cycle. Secondly, a unique additively manufactured heat generator) are not. exchanger is used that offers an excellent tradeoff between Both the turbine and compressor used in the study were effectiveness and pressure drop. This tradeoff is key to the trimmed versions of commercially available turbomachines. The performance of the cycle as others have shown. volutes and compressor diffuser were optimized for the design conditions. The design was conducted using CFD and the EXPERIMENTAL SETUP resulting design is shown below in Fig. 3. A test rig was designed and constructed to investigate the performance of an IBC system. The system was sized to operate using the exhaust gases produced by a 2 litre turbocharged gasoline engine in a motorway cruise condition. This corresponds to a flow rate of 55 g/s at temperatures of up to 750 °C. The parameters to be investigated were compressor inlet

3 Copyright © 2018 ASME Bearing Vacuum housing pump

Sight PID glass controller Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 Relief valve

Heat pump exchanger

Water Hot out water in

FIGURE 5: BEARING LUBRICATION SYSTEM

The lubrication system is shown on Fig. 5. One of the unusual aspects of the cycle with respect to turbomachinery design is that it operates under vacuum. That is the turbine outlet and compressor inlet pressures are both subatmospheric. Thus the FIGURE 3: TURBOMACHINERY HOUSING DESIGNED AND lubrication system must be able to operate under vacuum to MANUFACTURED FOR THIS TESTING avoid oil being pumped into the system during operation. The

vacuum pressure was set to automatically track a pressure just The heat exchanger (Fig. 4) was designed and below the compressor inlet pressure. The oil was heated using manufactured by HiETA Technologies Ltd. who offer ultra-high hot water to give the required viscosity. A sight glass was performance heat exchangers using the Selective Laser Melting installed to monitor the oil exiting the bearing housing to ensure Additive Manufacturing (AM) technique. The design freedom there was no excessive aeration. Note that while this system with AM enables the use of very efficient heat transfer surfaces proved very successful to limit oil ingestion in the tests, it is that offer a much more advantageous tradeoff between pressure anticipated that a productionized version of the device would drop and effectiveness. Since both these parameters influence likely address this through more detailed sealing design – which compressor work, and therefore IBC power output directly, the was not the focus of the study here. heat exchanger is key to the success of the heat recovery cycle.

FIGURE 4: SELECTIVELY LASER MELTED, HIGH PERFORMANCE HEAT EXCHANGER

4 Copyright © 2018 ASME TABLE 1: TEST RIG MEASUREMENTS

Sensor Parameter Sensor type Accuracy torque Phase shift meter ± 0.0011 Nm

rotational speed Phase shift meter ± 0.05% Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 turbine inlet pressure Pressure transducer ± 250 Pa turbine inlet 4 x K type ± 2.5 °C or temperature thermocouple ± 0.75%*T turbine outlet Pressure transducer ± 500 Pa pressure turbine outlet K type ± 2.5 °C or temperature thermocouple ± 0.75%*T compressor inlet Pressure transducer ± 80 Pa pressure compressor inlet ±(0.15 + Class A PRT temperature 0.002∗T) compressor outlet Pressure transducer ± 500 Pa pressure compressor outlet ±(0.15 + Class A PRT temperature 0.002∗T) mass flow rate Calibrated v-cone ±0.5%

v-cone pressure drop Pressure transducer ± 16 Pa v-cone upstream Pressure transducer ± 280 Pa pressure Vcone upstream ±(0.15 + Class A PRT FIGURE 6: INVERTED BRAYTON CYCLE WITH HIGH temperature 0.002∗T) SPEED DYNAMOMETER INSTALLED IN HOT GAS STAND

The rig was instrumented with guidance from SAE J1826 PERFORMANCE ANALYSIS [30], SAE J1723 [31] and ASME PTC 10 [32]. Turbine inlet In the following analysis, a semi-perfect gas is assumed temperature was measured using four K type thermocouples and where the specific heat at constant pressure 푐 is assumed to be the outlet temperature using a single K type. Compressor inlet 푝 a function of temperature only. The analysis begins with the and outlet temperatures were measured using class A PRTs at compressor, as the calculated turbine work and efficiency depend depths as recommended by SAE J1723. The pipework was on the compressor work. On Fig. 2, 1 refers to the turbine inlet, insulated between the measurement locations and the IBC 2 to turbine outlet, 3 to compressor inlet and 4 to compressor system. Whenever temperature is measured in a flow the actual outlet. The compressor total to static pressure ratio 푃푅 is temperature measured is a value between the static and total 푐 푇푆 given by temperature. ASME PTC 10 notes that for air if the velocity is below 38 m/s the velocity temperature is negligible. Since the 푝4 푃푅푐 푇푆 = (1) velocities measured were all below this value, the measured 푝03 temperatures were taken to be total temperature. Brun and Kurz The compressor specific work 푤푐 is calculated using [33] showed that this leads to a negligible compressor isentropic efficiency uncertainty. 푐푝 + 푐푝 푤 = 3 4 (푇 − 푇 ) (2) Pneumatically averaged pressures were measured at 푐 2 04 03 compressor and turbine inlet and outlets using pressure transducers. The air mass flow rate was measured upstream of In Eq. (2), the average value of specific heat is evaluated based the heaters using a V-Cone flow meter. Torque was measured on the inlet and outlet temperatures, assuming a linear variation with a phase shift type torque meter that also measured the speed. with temperature. 푐푝 is determined from the ratio of specific Details of the measurements taken are given in Table 1. Figure 6 훾 using 훾푅 shows the system as installed in the hot gas stand. 푐 = (3) 푝 훾 − 1

5 Copyright © 2018 ASME The individual components of uncertainty 푢 can be 훾 for air is calculated using 푥푖 evaluated using either a type A method or a type B method. For (4) 훾 = 1.42592 − 8.03974(10−5)T type A the uncertainty is calculated from a series of readings using statistical methods. Type B is calculated using other which is from SAE J1826. The compressor total-to-static methods such as engineering judgement. ISO 5168:2005 isentropic efficiency, 휂푐 푇푆 is then recommends that if an uncertainty contribution is less than 20%

훾−1 of the largest contribution, it can be ignored. Since many Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 훾 (푃푅푐 ) − 1 readings have been taken at each operating point, the standard 휂 = 푇푆 (5) 푐 푇푆 푇 deviation of the mean is small and type A related uncertainty due 04 − 1 to uncertainty in the mean can be ignored. This leaves only type 푇03 B uncertainty, which is consistent with the approach taken in The turbine work is challenging to measure directly, due to the other uncertainty analyses of turbocharger test results such as difficulty in accurately measuring the temperature of the flow at Olmeda et al [35], Guillou [36] and Mohtar et al [37]. the turbine exit. The typical approach in turbocharger testing is When attempting to measure a turbocharger performance to assume that the turbine work is equal to the compressor work parameter such as temperature or pressure according to a times a factor to account for mechanical losses. Because this standard, there are a number of different sources of uncertainty. factor is unknown, a factor of unity is used and the turbine work ISO 5168:2005 gives the following categories: effectively includes these losses. Since this device can produce  Calibration uncertainty work output 푤표, the turbine specific work 푤푡 is equal to  Data acquisition uncertainty. For example, arising from signal conditioning. This was minimized where possible by 푤 = 푤 + 푤 (6) 푡 푐 표 overall system calibration. The turbine total to total pressure ratio is  Data processing uncertainty. For example uncertainty due to curve fitting. 푝  Uncertainty due to methods. This can include errors in 푃푅 = 01 푡 푇푇 (7) locating sensors according to the standard, disturbance 푝02 caused by installed instrumentation, environmental effects on the instrument, drift, hysteresis and repeatability. and the turbine total-to-total isentropic efficiency, 휂푡 푇푇 is given by: The uncertainty due to methods is typically the main source of 푤푡 uncertainty. Hence, this analysis will focus on errors related to 휂푡 푇푇 = 훾−1 the accuracy of the instrumentation as stated by the 1 훾 (8) manufacturers, neglecting other sources of uncertainty. 푐푝푇01 (1 − ( ) ) 푃푅푡 푇푇 The results are presented using coverage factor of 2, meaning that there is an approximately 95% probability that the 훾 is calculated based on the average expansion temperature result lies within the specified bounds. In the absence of using the measured turbine outlet temperature. information about the probability distribution of sensor accuracy, the distributions are assumed to be rectangular, and the accuracy UNCERTAINTY ANALYSIS is divided by √3 to give the standard uncertainty. This is a To assess the reliability of results and to analyze trends, an conservative assumption as it is possible that they could follow, uncertainty analysis is necessary. Since the uncertainties are for example, a normal distribution where dividing by a larger small when compared with the measured values, a first order number would give the standard uncertainty. Taylor series approximation can be used to estimate the The quantities to be plotted and hence those for which an uncertainties in the quantities of interest. An excellent overview uncertainty calculation is required for are: of this approach is given in ISO 5168:2005 [34].  Compressor, turbine and net specific work For a given derived quantity 푦 that depends on a number of  Compressor and turbine pressure ratios variables 푥 , its relative standard uncertainty 푢 is found by: 푖 푦  Compressor and turbine efficiencies 푁 Uncertainty in all the relevant quantities was calculated for 휕푦 푥 2 √ 푖 (9) individual data points using the method outlined above. The 푢푦 = ∑ [ 푢푥푖] 휕푥푖 푦 equations are omitted for brevity and the results are plotted as 푖=1 error bars in the results section. Equation (9) may be applied if there is no correlation One point to note is that where 푛 sensors measure the same between the input variables. Correlation arises when the same parameter, some studies such as Guillou [36] reduce the instrument is used to make several measurements or where uncertainty by √푛. In this study, no such reduction is applied as instruments are calibrated against the same reference. In this it is judged that there will be some variation in the true experiment separate instruments were used for each temperature over the area of the ducts. measurement and calibration error will be assumed to be negligible, making the application of Eq. (9) valid.

6 Copyright © 2018 ASME One final source of error is that when a change is made to HEAT TRANSFER AND MECHANICAL LOSSES the parameter studied, every other factor cannot be held perfectly When interpreting experimental results arising from equal. For example, if the turbine inlet temperature is varied, the changes to the parameter investigated, it is important to identify speed or compressor inlet temperature cannot be controlled to all the transmission mechanisms through which the net work exactly the same value for each test point. output is affected. Obviously, when the rotational speed is increased, the COMPUTATION FLUID DYNAMIC MODELLING bearing losses will increase, and this will reduce the net work Although modeling the system in CFD is not a core part of output. In the analysis above, bearing losses are included in the Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 this paper, it did form a useful tool to evaluate turbomachinery turbine efficiency. Increased bearing losses would not affect the efficiencies under the test conditions. Thus, for completeness, true turbine or compressor work, but would reduce the work the models are briefly presented here. output. They would also not affect the thermodynamically The computational domain consists of two distinct regions calculated compressor work. The bearing losses reduce the for both compressor and turbine, shown in Fig. 7; an inlet domain turbine specific work in Eq. (6). This in turn reduces the and a single flow passage. All computational grids are structured calculated turbine efficiency in Eq. (8). hexahedral meshes. Another mechanism affecting the results is heat transfer. Heat is transferred due to convection from the hot turbine gases to the housing where it can be lost to atmosphere, lost to the oil or cooling water, or transmitted to the compressor gas through the housing, oil or water. When modelling the turbocharger using a lumped model, it is often assumed that the heat transfer from the turbine gas occurs before expansion and the heat transfer to the compressor gas occurs after compression [38]. Furthermore, heat transfer to the atmosphere can occur between the measurement location and the inlet / exit of the turbomachinery, despite insulation. FIGURE 7: CFD MODEL OF THE COMPRESSOR [LEFT] Heat transfer effectively means that there is less heat AND TURBINE [RIGHT] INCLUDING INLET DOMAIN AND available in the turbine gases for expansion. If all the heat VOLUTE transfer occurs at the turbine inlet, the turbine can be considered For both compressor and turbine, the inlet and volute as having the same efficiency but a lower inlet temperature. domain are stationary, while the single passage is set as a rotating From Eq. (8), the lower turbine inlet temperature will reduce the domain. Correspondingly, interfaces between rotating and true turbine work. If the compressor gas is heated or cooled only stationary domains are designated as frozen rotor interfaces, thus after compression, there is no effect on the compressor work. ensuring conservation of mass, momentum and energy as the Hence ,the net work output of the system is reduced. frame of reference changes. Having discussed the effect of heat transfer on net work output, the analysis will now consider the effect on the TABLE 2: CFD BOUNDARY CONDITIONS turbomachinery efficiencies calculated from an experimentally determined net work output. Analysis Type Steady State Starting with the compressor, heat transfer to the compressor Medium Air, gas from the housing after compression tends to increase 푇04. Walls Hydraulically Smooth, No Slip Heat loss in the downstream pipe between the exit and the Total Temperature and measurement location tends to decrease 푇04. The net effect could Inlet Pressure be either an overestimate or underestimated 푇04. This will affect Outlet Mass Flow Outlet the specific work (Eq. (2)) and the compressor efficiency (Eq. Turbulence Model k − ω SST (5)). With regard to the turbine, in Eq. (6) the error in compressor Advection Scheme High Resolution Turbulence specific work leads to an error in turbine specific work in the Table 2 summarizes the boundary conditions used same direction, to give the required work output. In Eq. (8) there throughout the simulations for both compressor and turbine. is an overestimation of 푇 due to heat transfer. Errors in both Turbulence closure for the Reynolds stress tensor is achieved by 01 푇 and the turbine specific work then lead to an error in turbine using Menter’s k-ω shear stress transport (SST) turbulence 01 efficiency. model. Finally, iterative convergence is deemed to be obtained The effect of heat transfer on 푇 in particular (and hence on as soon as the normalized root mean squared (RMS) residuals 04 compressor work and efficiency) is more pronounced at lower decrease below 10e−6, and total to total isentropic efficiency and speeds. This is due to a number of reasons. The main factor is total pressure ratio have settled to stationary levels. that at low speeds, the compressor power is small and the

temperature rise across the compressor is small. This means that any heat transfer will give a large relative error in 푇04. Heat

7 Copyright © 2018 ASME transfer to the atmosphere will be reduced due to the lower exit RESULTS AND DISCUSSION temperature, but it could still be very significant as a fraction of For the results presented below, specific work has been the compressor temperature rise. plotted as the dependent variable. Changes to the independent The lower gas temperature in the compressor also leads to variable will affect the operating point and hence the efficiency an increased temperature difference between the turbine gas and of the turbomachinery, so turbine and compressor efficiencies the compressor gas, which tends to give more heat transfer to the from CFD and pressure ratios are also plotted. The work required compressor gas. Another factor to consider for convective heat to pump the coolant for the heat exchanger is negligible, so this transfer to the compressor gas is that the gas velocity will be has not been included in the results. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 lower at the lower rotational speed. This leads to a lower The system was designed to operate at a target speed of convective heat transfer coefficient between the compressor 120,000 rpm but due to rotordynamic issues the speed was housing and the gas. limited to approximately 80,000 rpm. Baseline conditions of In order to determine the effect that heat transfer may be 70,000 rpm, 550°C turbine inlet temperature and approximately having on the measured efficiencies, the efficiencies from CFD 10°C compressor inlet temperature were chosen, to compare the were compared with the experimental results for the same effect of changes to the system. The speed reduction was not reduced mass flow rate. The results are presented in Fig. 8. sufficient to detrimentally affect the uncertainty of the results presented. 0.85 The effect of turbine inlet temperature is given in Fig. 9. The compressor ηTS (experiment) results show that net specific work increases with turbine inlet 0.83 turbine ηTT (experiment) temperature. For a hypothetical device with only inlet 0.81 compressor ηTS (CFD) temperature changing, this is to be expected from the equation turbine ηTT (CFD) 0.79 for turbine work. However, in reality the operating points of the 0.77 turbomachinery have also changed. The pressure ratios show that the change in operating point is small. The efficiency plot shows 0.75 that the compressor efficiency is essentially unchanged but the 0.73 turbine has moved to a less efficient operating point. This tends Efficiency 0.71 to reduce the impact of raised inlet temperature on turbine work and hence on net specific work. Nonetheless, the trend of 0.69 increased inlet temperature leading to more net specific work is 0.67 clearly demonstrated. 0.65 The results for changing system pressure difference are 820 845 870 895 920 shown on Fig. 10. Increasing system pressure drop has had the effect of increasing the turbine pressure ratio. The net effect of Turbine inlet temperature (K) raised inlet pressure has been to increase the pressure FIGURE 8: COMPARISION OF CFD AND EXPERIMENTAL downstream of the turbine and hence to reduce the compressor ISENTROPIC EFFICIENCIES pressure ratio. At the same time the compressor efficiency has reduced slightly, leading to no net effect on the compressor The results in Fig. 8 show that the experimentally specific work. The increased turbine pressure ratio has led to determined compressor efficiency is higher than the CFD more turbine work, despite the efficiency dropping. Therefore predicted efficiency by a few percentage points. From the raising the inlet pressure has increased the net specific work. preceding discussion, if the CFD is accurate, this must be due to Figure 11 demonstrates the effect of compressor inlet heat transfer downstream of the compressor leading to a reduced temperature on the performance of the system. From Eq. (5), for 푇04 and hence a lower temperature rise across the compressor. a constant isentropic efficiency, the expected effect of increasing This translates into a lower compressor work and hence a lower the compressor inlet temperature is to increase the work required turbine efficiency than the CFD. Part of the turbine difference is to drive the compressor. The net specific power does indeed also bearing losses. Therefore, it was decided to plot CFD trend downwards. The compressor efficiency is unchanged but predicted efficiencies rather than experimentally determined the increase in turbine efficiency is an effect that would tend to efficiencies, to determine the true trend in efficiency when a increase net specific power rather than reduce it. change is made to the studied parameter. It is important to note that while the compressor and turbine efficiencies are important parameters to understand and design the IBC device, the one measurement of ultimately paramount importance to this experiment is the shaft power delivered by the device. Thus, despite the challenges in characterizing the individual efficiencies thermodynamically, the specific power of the device is known with high confidence.

8 Copyright © 2018 ASME 30 60 30 60 net net compressor compressor turbine turbine 20 50 20 50 Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021

10 40 10 40 Specific work (kJ/kg) Specific work (kJ/kg) Specific work (kJ/kg) Specific work (kJ/kg)

0 30 0 30 820 845 870 895 920 0 2.5 5 Turbine inlet temperature (K) System pressure drop (kPa)

1.45 1.45 compressor PR TS turbine PR TT compressor PR TS turbine PR TT

1.4 1.4 Ratio Ratio 1.35 1.35

1.3 1.3 820 845 870 895 920 0 2.5 5 Turbine inlet temperature (K) System pressure drop (kPa)

0.78 0.78 compressor ηTS turbine ηTT 0.77 0.77

0.76 0.76

0.75 0.75

0.74 0.74 CFD predicted CFD predicted efficiency 0.73 compressor ηTS turbine ηTT 0.73 CFD predicted CFD predicted efficiency

0.72 0.72 820 845 870 895 920 0 2.5 5 System pressure drop (kPa) Turbine inlet temperature (K)

FIGURE 9: SPECIFIC WORK AND TURBOMACHINERY FIGURE 10: SPECIFIC WORK AND TURBOMACHINERY PERFORMANCE AS A FUNCTION OF TURBINE INLET PERFORMANCE AS A FUNCTION OF SYSTEM PRESSURE TEMPERATURE DROP

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30 60 30 60 net net compressor compressor turbine 20 50 turbine 20 50 Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021

10 40 10 40 Specific work (kJ/kg) Specific work (kJ/kg) Specific work (kJ/kg) Specific work (kJ/kg) 0 30 0 30 64000 68000 72000 76000 80000 12 14 16 18 20 22 24 26 28 30 32 34 Speed (rpm) Compressor inlet temperature (°C)

1.55 1.45 compressor PR TS compressor PR TS turbine PR TT 1.5 turbine PR TT

1.4 1.45 Ratio

Ratio 1.4 1.35 1.35

1.3 1.3 64000 68000 72000 76000 80000 12 14 16 18 20 22 24 26 28 30 32 34 Speed (rpm) Compressor inlet temperature (°C) 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 compressor ηTS turbine ηTT CFD predicted CFD predicted efficiency 0.73 compressor ηTS turbine ηTT CFD predicted CFD predicted efficiency 0.72 64000 68000 72000 76000 80000 0.72 12 14 16 18 20 22 24 26 28 30 32 34 Speed (rpm) Compressor inlet temperature (°C) FIGURE 12: SPECIFIC WORK AND TURBOMACHINERY PERFORMANCE AS A FUNCTION OF SPEED FIGURE 11: SPECIFIC WORK AND TURBOMACHINERY PERFORMANCE AS A FUNCTION OF COMPRESSOR INLET The effect of changes in speed are given on Fig. 12. The TEMPERATURE trend from Fig. 12 is that increasing speed leads to increasing

10 Copyright © 2018 ASME turbine and compressor work, with a net increase in work due to the data provided in Fig. 13 as a useful comparison of the tradeoff the greater increase in turbine work with speed. The CFD results between pressure drop and effectiveness. As this figure have indicated that the efficiencies don’t change significantly. demonstrates, the Selective Laser Melting additive The specific work increase of each device is therefore manufacturing process provides very impressive performance predominantly due to increased pressure ratio. The turbine outlet with effectiveness values of over 99% whilst only imposing a pressure reduces with increases in speed. This confirms the trend 2.5-3.5kPa pressure drop. It is the authors’ belief that it is this shown by Copeland and Chen [16] that specific work and cycle extraordinary performance that helps make the inverted Brayton efficiency increase as turbine outlet pressure decreases. cycle a viable heat recovery strategy. It is also useful to note that Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 However, this trend peaks at an optimum system pressure ratio the smaller heat exchanger core does indeed produce lower that depends on the exhaust temperature and component pressure drop (1.5-2kPa) but at the expense of lower efficiencies. Thus, it is clear that the present system has not effectiveness. Depending on the target application for the cycle, reached peak operating pressure ratio since at 80,000 rpm, it is the design of the two performance metrics could be optimized still some way off the target design point of 120,000 rpm. for maximum power.

1.00

0.99

0.98

0.97

High Eff HX [10C coolant] 0.96 High Eff HX [20C coolant]

Heat Heat exchanger effectiveness Lower Eff HX [20C coolant] 0.95 0.0420 0.0460 0.0500 0.0540 Mass flow (kg/s) 4.00

3.50

3.00 FIGURE 14: 1D GAS-DYNAMIC MODEL OF THE 2.50 EXPERIMENTAL IBC SYSTEM

2.00 To estimate the performance of the system over a broader range (kPa) 1.50 of operation, and in particular the design point of the machine, a 1D gas dynamic model was created utilizing CFD generated 1.00 High Eff HX [10C coolant] turbomachinery performance maps. A commercially available code was used here, GT-Power, due to its wide use in the 0.50 High Eff HX [20C coolant] automotive industry. GT-Power uses maps with corrected

Heat Heat exchanger pressure drop Lower Eff HX [20C coolant] 0.00 parameters, to account for variations in inlet conditions. The heat 0.0420 0.0460 0.0500 0.0540 exchanger model was represented by the relationship shown in Fig. 13. Finally, a mechanical loss could be estimated by Mass flow (kg/s) introducing the experimentally measured conditions at the FIGURE 13: HEAT EXCHANGER EFFECTIVENESS AND boundaries of the model and comparing the predicted power to PRESSURE LOSS the experimental values. Here, an assumption of constant torque (hence linear frictional power with speed) proved a reasonable The final important experimental data to be presented is the approach. The predicted pressure ratios had a mean error of performance of the heat exchanger. The heat exchanger was +3.5% and a maximum error of +4.7% versus the experimental designed to target very high effectiveness numbers since a future results. The predicted powers had a mean absolute error of 5.7% research interest is to study water condensation. For comparison, and a maximum deviation of -12.7% from the experimental a second heat exchanger was also tested with a smaller core and results. Although more work could be done to develop this

11 Copyright © 2018 ASME model, the comparison with the available data set provided NOMENCLATURE enough confidence to be able to estimate the performance at the 푐푝 specific heat at constant pressure design inlet conditions of 55g/s flow rate and 750°C with the unit 푚̇ mass flow rate rotating at 120,000 rpm. The predicted performance at these 푝 pressure conditions is given in Table 3. 푃푅 pressure ratio 푅 specific gas constant TABLE 3: PERFORMANCE AT DESIGN CONDITIONS 푇 temperature Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 푢 relative standard uncertainty speed 120,000 rpm 푤 specific work flow 55 g/s turbine inlet temperature 750°C Greek Symbols coolant inlet temperature 10°C 훾 ratio of specific heats turbine pressure ratio 2.23 휂 efficiency turbine efficiency TT 74.3% Subscripts compressor efficiency TS 71.8% 푐 compressor heat exchanger pressure drop 3.55 kPa 표 out bearing losses 0.29 kW 푡 turbine net power (after losses) 2.56 kW 푇푆 total to static net specific work (after losses) 46.5 kJ/kg 푇푇 total to total

CONCLUSIONS Abbreviations An inverted Brayton cycle system has been successfully AM additive manufacturing demonstrated experimentally. This is the first experimental CFD computational fluid dynamics parametric study of the cycle. Moreover, it is also one of the very IBC inverted Brayton cycle few works in the public domain that provide experimental results ICE internal combustion engine from an inverted Brayton cycle. PRT platinum resistance thermometer Although operation at the full design speed was not possible SST shear stress transport due to rotordynamic issues, the system was still able to operate at 80,000 rpm and produce a specific work output of REFERENCES approximately 17 kJ/kg. [1] Kohler, C., 1919, “Verfahren zum Betriebe von Increasing turbine inlet temperature and system pressure Verbrennungsturbinen mit mehreren Druckstufen,” drop were shown to increase specific work output. Increased Deutsches Pat. 339590 (Filed 4 October 1919; Publ. 29 July compressor inlet temperature slightly reduced specific work 1921). output. Specific work also increased with speed. The results were [2] Hingst, R., 1944, “Verfahren zur Energieerzeugung aus in line with what would be expected from a thermodynamic Gasen und Gasdampfgemischen niederen Druckes, z. B. analysis of the system. Abgasen von Brennkraftmaschinen,” Deutsches Pat. Whenever changes were made to the independent parameter 852015 (Filed 12 May 1944; Publ. 9 October 1952). studied, this affected the operating point of the turbomachinery [3] Hodge, J., 1955, Cycles and Performance Estimation, and the related efficiencies. The efficiency changes for the Butterworths Scientific Publications, London, England. compressor were small, suggesting that the compressor was [4] Wilson, D. G. and Dunteman N. R., 1973, “The Inverted operating in a region where the efficiency is fairly constant. On Brayton Cycle for Waste-Heat Utilization,” In ASME Gas the other hand, the turbine efficiency was sensitive to changes in Turbine Conference and Products Show, Washington, D.C., operating point, which contributed to some of the measured April 8-12, 1973. difference in work output. The turbomachinery efficiencies were [5] Holmes, R. T., 1976, “An inverted Brayton cycle application predicted by the CFD to be slightly lower at the design speed of to naval marine gas turbines,” Master of Science in 120,000 rpm than at the tested speeds, suggesting that further Mechanical Engineering, Massachusetts Institute of optimization could yield a higher output at the design speed. Technology. Finally, an estimate of the work output of the system was [6] Frost, T., Anderson, A., and Agnew, B., 1997, “A Hybrid made using a GT-Power model. This predicted a specific work Gas Turbine Cycle (Brayton/Ericsson): An Alternative to output of 47 kJ/kg, which corresponded to a thermal efficiency Conventional Combined Gas and Steam Turbine Power of 5%. Plant,” Proc. Inst. Mech. Eng., Part A, 211 (2), pp.121–131. ACKNOWLEDGEMENT [7] Tsujikawa, Y., Ohtani, K., Kaneko, K., Watanabe, Y., and The authors would like to acknowledge the support of Fujii, S., 1999, “Conceptual Recovery of Exhaust Heat Innovate UK in funding this research. From a Conventional Gas Turbine by an Inter-Cooled

12 Copyright © 2018 ASME Inverted Brayton Cycle,” In ASME International Gas [20] Zheng, J., Sun, F., Chen, L., and Wu, C., 2001, “Exergy Turbine and Aeroengine Congress and Exhibition, analysis for a Braysson cycle,” Exergy Int. J., 1, pp. 41-45. Indianapolis, IN, June 7–10, 1999. [21] Zhang, Z., Chen, L., and Sun, F., 2012, “Exergy analysis for [8] Fujii, S., Kaneko, K., Otani, K., and Tsujikawa, Y., 2001, combined regenerative Brayton and inverse Brayton “Mirror Gas Turbines: A Newly Proposed Method of cycles,” Int. J. Energy Environ., 3, pp. 715-730. Exhaust Heat Recovery,” ASME J. Eng. Gas Turbines [22] Chen, L., Ni, D., Zhang, Z., and Sun, F., 2016, “Exergetic Power, 123 (3), pp. 481–486. performance optimization for new combined intercooled [9] Agnew, B., Anderson, A., Potts, I., Frost, T., and regenerative Brayton and inverse Brayton cycles,” Appl. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 Alabdoadaim, M., 2003, “Simulation of Combined Brayton Therm. Eng., 102, pp. 447-453. and Inverse Brayton Cycles,” Appl. Therm. Eng., 23 (8), pp. [23] Henke, M., Monz, T., and Aigner, M., 2013, “Inverted 953–963. Brayton Cycle With Exhaust Gas Recirculation—A [10] Alabdoadaim, M., Agnew, B., and Alaktiwi, A., 2004, Numerical Investigation,” ASME J. Eng. Gas Turbines “Examination of the performance envelope of combined Power, 135 (9), 091203. Rankine, Brayton and two parallel inverse Brayton cycles,” [24] Tanaka, K., Inoue, K., Kitajima, J., Kazari, M., Nitta, S., Proc. Inst. Mech. Eng., Part A, 218, pp. 377-385. Tsujikawa, Y., and Kaneko, K., 2007, “The Development of [11] Alabdoadaim, M., Agnew, B., and Potts, I., 2006, 50kW Output Power Atmospheric Pressure Turbine (APT),” “Examination of the performance of an unconventional In ASME Turbo Expo, Montreal, Canada, May 14-17, 2007. combination of Rankine, Brayton and inverse Brayton [25] Bianchi, M., De Pascale, A., and Negri di Montenegro, G., cycles,” Proc. Inst. Mech. Eng., Part A, 220, pp. 305-313. 2005, “Micro Gas Turbine Repowering With Inverted [12] Alabdoadaim, M., Agnew, B., and Potts, I., 2006, Brayton Cycle,” In ASME Turbo Expo, Reno, NV, June 6- “Performance analysis of combined Brayton and inverse 9, 2005. Brayton cycles and developed configurations,” Appl. [26] Murray Bailey, M., 1985, “Comparative Evaluation of Three Therm. Eng., 26, pp.1448-1454. Alternative Power Cycles for Waste Heat Recovery from the [13] Bianchi, M., Negri di Montenegro, G., Peretto, A., and Exhaust of Adiabatic Diesel Engines,” Lewis Research Spina, P., 2005, “A Feasibility Study of Inverted Brayton Center, National Aeronautics and Space Administration, Cycle for Gas Turbine Repowering,” ASME J. Eng. Gas Cleveland, OH, Report No. NASA TM-86953. Turbines Power, 127 (3), pp. 599–605. [27] Chen, Z., Copeland, C., Ceen, B., Jones, S., and Agurto [14] Tsujikawa, Y., Kaneko, K., and Suzuki, J., 2004, “Proposal Goya, A., 2017, “Modeling and Simulation of an Inverted of the Atmospheric Pressure Turbine (APT) and High Brayton Cycle as an Exhaust-Gas Heat-Recovery System,” Temperature Fuel Cell Hybrid System,” JSME Int. J. Series ASME J. Eng. Gas Turbines Power, 139 (8), 081701. B Fluids and Therm. Eng., 47, pp. 256-260. [28] Agelidou, E., Monz, T., Huber, A., and Aigner, M., 2017, [15] Bianchi, M., Negri di Montenegro, G., and Peretto, A., 2002, “Experimental investigation of an inverted Brayton cycle “Inverted Brayton Cycle Employment for Low-Temperature micro gas turbine for CHP application,” In ASME Turbo Cogenerative Applications,” ASME J. Eng. Gas Turbines Expo, Charlotte, North Carolina, June 26–30, 2017. Power, 124 (3), pp. 561–565. [29] Inoue, K., Harada, E., Kitajima, J., and Tanaka, K., 2006, [16] Copeland, C., and Chen, Z., 2016, “The benefits of an “Construction and Performance Evaluation of Prototype inverted brayton bottoming cycle as an alternative to Atmospheric Pressure Turbine (APT)” In ASME Turbo turbocompounding,” ASME J. Eng. Gas Turbines Power, Expo, Barcelona, Spain, May 8–11, 2006. 138 (7), 071701. [30] SAE International Surface Vehicle Recommended Practice, [17] Bianchi, M., and De Pascale, A., 2011, “Bottoming cycles “Turbocharger Gas Stand Test Code,” SAE Standard J1826, for electric energy generation: Parametric investigation of Rev. Mar. 1995. available and innovative solutions for the exploitation of [31] SAE International Surface Vehicle Standard, “Supercharger low and medium temperature heat sources,” Appl. Energy, Testing Standard,” SAE Standard J1723, 1995. 88 (5), pp. 1500-1509. [32] ASME Performance Test Code, “Performance Test Code on [18] Lu, P., Brace, C., Hu, B., and Copeland, C., 2017, “Analysis and Exhausters,” ASME PTC 10-1997, 1997. and Comparison of the Performance of an Inverted Brayton [33] Brun, K., and Kurz, R., 2001, “Measurement Uncertainties Cycle and Turbocompounding With Decoupled Turbine and Encountered During Gas Turbine Driven Compressor Field Continuous Variable Transmission Driven Compressor for Testing,” ASME J. Eng. Gas Turbines Power, 123 (1), pp. Small Automotive Engines,” ASME J. Eng. Gas Turbines 62–69. Power, 139 (7), 072801. [34] ISO Standard, “Measurement of fluid flow – Procedures for [19] Bhargava, R.K., Bianchi, M., and De Pascale, A., 2011, the evaluation of uncertainties,” BS ISO 5168:2005, 2005. “Gas Turbine Bottoming Cycles for Cogenerative [35] Olmeda, P., Tiseira, A., Dolz, V., and García-Cuevas, L.M., Applications: Comparison of Different Heat Recovery 2015, “Uncertainties in power computations in a Cycle Solutions,” In ASME Turbo Expo, Vancouver, British turbocharger test bench,” Measurement, 59, pp. 363-371. Columbia, June 6-10, 2011. [36] Guillou, E., 2013, “Uncertainty and Measurement Sensitivity of Turbocharger Compressor Gas Stands,” In

13 Copyright © 2018 ASME SAE 2013 World Congress & Exhibition, Detroit, MI, April 16-18, 2013. [37] Mohtar, H., Chesse, P., and Chalet, D., 2012, “Describing Uncertainties Encountered during Laboratory Turbocharger Compressor Tests,” Experimental Techniques, 36, pp. 53- 61. [38] Olmeda, P., Dolz, V., Arnau, F.J., and Reyes-Belmonte, M.A., 2013, “Determination of heat flows inside Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT2018/51173/V008T26A003/3768225/v008t26a003-gt2018-75386.pdf by guest on 28 September 2021 turbochargers by means of a one dimensional lumped model,” Math. Comput. Modell., 57, pp. 1847-1852.

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