Exergy-Based Aerothermodynamic Evaluation of a Turbocharger Turbine Under Pulsating Flow: An Experimental Power-Based Approach

Abstract

This experimental study investigates the aerothermodynamic performance of a turbocharger turbine under steady and pulsating flow conditions across various turbine inlet temperatures (TITs) and pulsation frequencies. A power-based approach was implemented to quantify turbine heat transfer for diabatic scenarios over a range of operating turbocharger speeds. The results reveal that higher TITs significantly increase heat transfer under steady flow, driven by enhanced thermal gradients; while pulsating flow amplifies heat transfer by up to 63.6% due to intensified turbulence and frequent boundary layer disruptions. The exergy analysis shows that pulsating flow increases exergy destruction compared to steady flow, primarily due to pressure and velocity fluctuations that intensify flow friction and turbulence. At higher pulsation frequencies, exergy destruction decreases slightly, while heat transfer exergy loss becomes more prominent, reflecting a shift in the exergy balance. These higher frequencies, representative of real engine conditions, drive the flow toward quasi-steady behavior, further shaping the aerothermodynamic performance of the turbine. These findings provide valuable insights into the effects of pulsating flow on turbine heat transfer and exergy losses, offering practical implications for optimizing turbocharger turbine performance under realistic operating conditions.

1. Introduction

The automotive industry is undergoing significant transformations to meet stringent environmental regulations and consumer demands for better performance and fuel efficiency. Turbocharging is a critical technology for enhancing the efficiency and performance of internal combustion engines (ICEs), both for conventional and alternative fuels.

The development of hydrogen combustion engines (H2 ICE) is gaining traction as a promising solution for CO₂—neutral combustion and sustainable mobility, particularly in sectors where electrification is challenging, such as heavy-duty commercial vehicles [1].

Hydrogen combustion engines encounter distinct challenges, such as the need to maintain lean-burn combustion to control NOx emissions and the difficulty of achieving sufficient torque and power density due to hydrogen fuel’s low density. Turbocharging plays a crucial role in overcoming these obstacles by significantly improving volumetric efficiency and enabling higher power outputs. The low energy density and gaseous state of hydrogen demand higher intake air or boost pressure, making the turbocharger essential in ensuring that the engine maintains its performance and efficiency [2].

The synergy between turbocharging and hydrogen combustion technologies could pave the way for high-efficiency and carbon-free powertrain system, marking a significant step forward in the automotive industry’s quest for sustainability.

Problem Statement and Solution Approach

The conventional performance evaluation of turbochargers on a hot gas test bench follows the SAE J922 and SAE 1826 standards, in which the turbocharger is being measured under steady-state gas flow and assuming adiabatic conditions. However, under engine operating conditions, a turbocharger turbine is exposed to a pulsating flow, leading to deviations from the performance metrics obtained under steady-state gas-stand flow conditions. Additionally, due to the minimal distance between the turbine (hot side) and the compressor (cold side) of the turbocharger, a significant temperature gradient is established. Combined with the high exhaust gas temperatures, this increases heat transfer rates, further accelerating the degradation of turbine performance. Therefore, the conventional performance evaluation of turbochargers on a hot gas test fails to account for the inherent aerothermodynamic effects resulting from pulsating flow and heat transfer [3].

The non-adiabatic (diabatic) behavior and heat transfer within turbochargers tend to overshadow the calculated aerodynamic turbine expansion work when assuming an adiabatic process, resulting in an overestimation of the calculated turbine power and isentropic efficiency [3], followed by Equations (1) and (2).

$${\eta }_{is}={\displaystyle \frac{P_{T,eff}}{P_{is}}}={\displaystyle \frac{{\dot{m}}_T{c}_{p,T}(T_3-T_4)}{P_{is}}}$$

(1)

$${P_{T,eff}=P}_{T,corr}+{\dot{Q}}_T$$

(2)

As shown in Equations (1) and (2), eliminating turbine heat transfer rate (${\dot{Q}}_T$) results in a higher calculated turbine power ($P_{T,eff}$) as it considers the turbine expansion as an adiabatic process governed solely by the turbine flow temperature difference. Consequently, this leads to an overestimation of the turbine’s isentropic efficiency. To correct these computational discrepancies arising from the adiabatic assumption, $P_{T,eff}$ must be refined by applying a correction that accounts for the heat transfer rate as shown in Equation (1). must be refined by applying a correction that accounts for the heat transfer rate.

Thus, a detailed understanding of heat flows in turbochargers is crucial and extends beyond current methodologies. Some studies [4,5] have developed experimental models to determine internal heat transfers and estimate corrected turbine and compressor efficiencies, based on specific geometric assumptions and simplifications. Recent research has introduced various experimental and numerical methods to approximate heat transfer in turbochargers, including sophisticated conjugate heat transfer (CHT) simulations with varying levels of complexity [6,7,8,9]. These methods predominantly rely on geometric data, requiring significant computational resources and extensive measurement campaigns, leading to increased measurement time compared to conventional turbocharger mapping techniques.

To simplify and overcome these complexities, a novel power-based approach was introduced by the author of [10], which eliminates the effects of turbochargers heat transfer rate from direct experimental hot gas measurements. This method has been validated through several comparisons with CFD and CHT simulations [7,11,12], showing satisfactory agreement between experimental and simulated results. Moreover, this method relies on standard turbocharger mapping measurements, eliminating the need for additional measurements or modifications. Consequently, it avoids extending measurement time and increasing complexity. The feasibility and reliability of this approach were further demonstrated in [13], which evaluated the performance impacts of various turbocharger designs and introduced a new criterion for comparing adiabatic measurements with stand measurements. This study validates the robustness of adiabatic experimental techniques, which are foundational for assessing the heat transfer impacts and efficiency variations across different turbocharger configurations.

From a thermodynamic perspective, applying the energy balance to the turbocharger using the standard model adheres to the first law of thermodynamics. However, the first law alone is insufficient to fully comprehend the aerothermodynamic behavior of the turbocharger, including losses due to heat transfer and internal irreversibilities.

Several researchers have explored advanced methodologies to address these limitations. For instance, A. Diango et al. conducted an exergy analysis and optimization for small turbomachines operating under non-adiabatic conditions. Their findings indicate that the turbine performance, as typically represented in adiabatic maps, is overestimated and requires recalculation to account for thermal losses [14].

Brötz et al. further developed this field by deriving exergetic efficiency, incorporating the second law of thermodynamics. They compared isentropic and exergetic efficiencies using a high-pressure radial fan, revealing significant differences under partial-load conditions. Their findings show that the thermal energy in the flow significantly contributes to exergy, highlighting the necessity of integrating thermal considerations into efficiency calculations [15]

S. M. Lim et al. conducted different numerical exergy analysis using CFD, which was validated with experimental data. Their findings indicate that aerothermodynamic performance cannot be fully captured by energetic considerations alone. They observed that losses due to heat transfer and internal irreversibilities during the expansion process vary significantly, ranging from 8 to 15 times depending on the operating conditions. Moreover, the total irreversibilities substantially exceed the generated power, underscoring the necessity of accounting for these factors in performance evaluations [16,17,18].

S.K. Bakhshmand et al. in [3] conducted an experimental study to investigate the non-adiabatic performance of an automotive turbocharger turbine under steady flow using a novel power-based approach. This study performed energy and exergy analyses to account for heat transfer effects. By implementing the power-based approach, the amount of heat transfer in the turbine was calculated, and the results quantified the lost available work due to heat transfer and internal irreversibilities. This provided a comprehensive understanding of turbocharger performance by considering both the first and second laws of thermodynamics.

Further research has explored the impact of pulsating flow on turbocharger performance. Internal combustion engine exhaust gases cause unsteady turbine operation due to pulsating flow. A. Rezk et al. used three-dimensional CFD models coupled with a one-dimensional engine model to analyze realistic pulsating flows in turbocharger turbine. A square wave pulsating flow showed the highest unsteadiness with 92.6% maximum mass flow accumulation, while a sawtooth wave, with gradual changes, had 88.9%. These extremes highlight the need to consider unsteady flow effects in performance evaluations [19].

R. Mosca’s research have significantly advanced understanding in this area. Key findings include the substantial impact of the exhaust manifold on flow fields and heat transfer, the primary effect of pulse amplitude on turbine performance. They also observed that increasing pulse amplitude improves turbine power despite increased heat transfer and internal irreversibilities. Moreover, their exergy analysis revealed that pulse amplitude is the main factor affecting the exergy budget, improving turbine work up to 9.4% [20,21,22]. Additionally, they developed a neural network model that accurately predicted unsteady turbine performance, providing a rapid and efficient alternative to complex simulations and experiments [23].

Several studies have employed 0D/1D simulation methodologies to enhance the modeling of engine-turbocharger interactions under transient conditions. A 0D/1D simulation approach for real driving emissions (RDE) cycles was developed by A. Marinoni et al. in [24], where a high-fidelity engine model was validated to capture transient variations in load and rotational speed, demonstrating the effectiveness of predictive solvers in modeling turbocharger effects on performance and emissions. In a related study, they introduced a co-simulation framework that integrated a 1D thermo-fluid dynamic engine model with a vehicle model, enabling real-time assessment of turbocharger behavior. Their research, applied to a hybrid city bus, fully coupled the turbocharger and engine models, improving simulation accuracy while maintaining computational efficiency [25]. Furthermore, D. Misul et al. conducted 1D simulations of hydrogen-fueled internal combustion engines, evaluating turbocharging and supercharging strategies to optimize power density and efficiency, particularly addressing the challenges posed by hydrogen’s low energy density. While these studies demonstrate the effectiveness of 0D/1D simulations, they primarily focus on performance and emissions, with limited emphasis on detailed turbocharger heat transfer analysis [26].

This paper seeks to further advance the aerothermodynamic investigation of a passenger car turbocharger by extending the understanding of turbine heat transfer to account for the complex effects of pulsating flow under real engine-like conditions. While conventional studies often focus on steady flow scenarios, this work moves beyond by integrating pulsating flow conditions into the experimental setup, providing a more realistic assessment of turbine performance. A novel power-based approach is employed to estimate turbine heat losses under diabatic conditions, offering a robust method for capturing heat transfer dynamics in scenarios that closely resemble real-world operations. Initially, the turbocharger was measured on a hot gas test bench under standard steady flow conditions. Subsequently, a pulse generator was used to measure the turbocharger’s performance under pulsating conditions across various operating points. Measurements were conducted under both adiabatic and diabatic conditions to better understand the pure effects of heat transfer and to verify the results obtained from the power-based approach. Turbine heat losses have been estimated for both steady and pulsating conditions using the power-based approach, demonstrating the impacts of pulsation on turbine heat transfer and its interplay with aerothermodynamic performance, while also providing inputs for further exergy-based analysis.

2. Materials and Methods

2.1. Experimental Setup

Measurements were carried out on the turbocharger hot gas test bench at the Chair of Powertrain Technologies, Technical University of Berlin (see Figure 1a). Hot gas for the turbine is generated either by electric heater up to 200 °C or by a combustion chamber up to 1050 °C covering a wide temperature range at turbine inlet. The electric heater, used exclusively for adiabatic measurements, supplies compressed air with a uniform composition similar to atmospheric air. In contrast, the combustion chamber, used for diabatic measurements, burns diesel fuel, generating a mixture of air and combustion gases. However, the sufficient mixing space before the turbine ensures a uniform temperature distribution across the measurement section. The gas is supplied by sets of electrical screw air compressors capable of delivering up to 1400 kg/h for a combustion air pressure of up to 4 bar. Temperatures and pressures are recorded at both the inlet and outlet of the turbine and compressor sides of the turbocharger. The exhaust gas flow, prepared in this manner, is directed to the turbine, which drives the compressor operating within a completely independent air stream. The compressor’s load is regulated by two parallel throttles, allowing for the determination of the turbine and compressor operating maps under steady-state conditions.

To generate the engine-like pulsating flow, a cylinder head was installed upstream of the turbine. This cylinder head contains four cylinders, but two were closed during these tests to generate larger pulse amplitudes compared to four-cylinder mode. The two-cylinder operation was found to produce a high-amplitude, uniform pulsating flow, making it the optimal configuration for the experiment. The pulse generator includes an internal oil circuit and external water cooling, enabling operation at hot exhaust gas temperatures. The camshaft, which operates the exhaust valves, is driven by an electric motor. The camshaft’s rotational speed is adjustable, and its position is precisely recorded using a reference mark sensor. This sensor provides the temporal reference for turbine inlet and outlet pressures measured with high temporal resolution. Figure 1b, provides an overview of schematic setup of the pulse generator.

Furthermore, to monitor the pulsating regime of the flow and capture the pulsating gas pressure, piezoresistive sensors were placed at the edge of the flow, corresponding to the static pressure. These air-cooled sensors achieve an accuracy of 0.5% (FS) with temperature compensation. The sensors have a measuring range from 0.1 to 10 bar absolute and are typically operated within a range of about 1 to 3 bar absolute. Their short response time makes them ideal for detecting exhaust pulses at various frequencies. Additionally, another pressure sensor was installed at the turbine outlet to accurately measure the turbine pressure ratio. The results of the measured pressure at the inlet and outlet of the turbine for sample measurement point, where turbocharger rotational speed is 173,000 rpm and the average turbine inlet temperature (T3) is set to 400 °C are shown in Figure 2. The results are captured at a pulse frequency of 33.3 Hz, which corresponds to a camshaft speed of 1000 rpm in two-cylinder operation of the pulse generator.

2.2. Adiabatic and Diabatic (i.e., Non-Adiabatic) Measurement Conditions

For the adiabatic measurement of the turbocharger in both steady and pulsating flow conditions, the testing conditions are adjusted to minimize temperature gradients, which drive heat transfer. Consequently, the turbine inlet temperature is aligned with the compressor outlet temperature and the mean oil temperature (T₃ = T₂ = T_oil,mean) [6,7,17]. To minimize heat transfer effects, a maximum allowable temperature deviation of 2 °C was established. These temperatures are key adjustable parameters for controlling internal heat transfer during turbocharger measurements. Furthermore, maintaining lower operating temperatures is generally advantageous to reduce thermal interactions between the turbocharger and its surroundings. Additionally, the turbocharger is fully insulated to limit heat transfer to the surroundings. It should be noted that during adiabatic testing, turbine power is mainly derived from the mass flow rather than the specific enthalpy (temperature) drop. This leads to fewer speed lines being measured in comparison to hot test due to the pressure and mass flow constraints of the test bench. Additionally, achieving the necessary temperature alignments for near-adiabatic conditions takes significantly longer compared to standard diabatic tests.

Diabatic measurements of the turbocharger were conducted on the hot gas test bench under both steady and pulsating flow conditions. The steady-state measurements without pulsating flow were conducted for both turbine inlet temperatures (T₃) of 400 °C and 600 °C. During pulsating flow measurements, the maximum inlet temperature of the turbine (T₃) was set to 400 °C due to cooling limitations of the pulse generator. To minimize heat losses to the environment, all measurement pipes were insulated; however, the turbocharger itself was left uninsulated to accurately replicate the heat-loss conditions observed in real-world applications. Additionally, to accurately measure the turbine outlet temperature (T₄) and create a more homogeneous temperature field, a mixing device was installed in the measurement pipe downstream of the turbine [27].

2.3. Turbine Heat Transfer Estimation Using Power-Based Approach

Heat transfer within a turbocharger is unavoidable and complicates the accurate calculation of aerodynamic performance maps using hot gas test bench data. On the other hand, the conventional turbocharger measurement standards SAE J922 and SAE 1826, recommend a turbine inlet temperature of 600 °C, while simultaneously assuming adiabatic conditions. Consequently, quantifying heat transfer is crucial for enhancing turbocharger matching in 0D/1D engine simulation processes. To address this, a novel method has been developed at TUB [11,28], which directly determines turbocharger heat transfer from hot gas test bench data. This approach enables the derivation of corrected aerodynamic maps and isentropic efficiencies for the turbocharger by eliminating the impact of heat transfer during hot gas measurements, despite the presence of heat transfer within the turbocharger. It also accounts for conduction, convection, and radiation collectively, capturing total turbine heat dissipation without isolating individual modes. Additionally, it does not require adiabatic measurements or detailed turbocharger geometrical data which are commonly required by other advanced methods.

The method is based on a standard turbocharger SAE map, utilizing all available measured data and relise on the isentropic and effective powers of the compressor and turbine obtained from hot gas measurement data, as illustrated in Figure 3. The key idea behind using the isentropic compressor power (ICP) on the horizontal axis is that it depends solely on the compressor inlet temperature and pressure ratio as illustrated in Equation (3), both of which remain largely unaffected by heat transfer. Figure 4 shows the comparison between the calculated isentropic compressor power in adiabatic and diabatic scenarios for the compressor at different turbocharger speeds, with the maximum flow rate at the choke point for each speed. It demonstrates that, as mentioned, the compressor isentropic power is mostly independent of heat transfer, with minimal differences between the diabatic and adiabatic scenarios. This allows for a comparison between adiabatic and diabatic test results. By plotting isentropic compressor power against effective turbine power, a similarity between adiabatic and diabatic speed lines is observed, forming the basis of the approach.

$$P_{C,is}={\dot{m}}_C{c}_{p,C}{T}_1({\mathsf{\Pi }}_C^{{\displaystyle \frac{k-1}{k}}}-1)$$

(3)

From Figure 3, it can be observed that the line connecting operating points at maximum isentropic compressor power in each speed line under adiabatic conditions converges toward the origin, where the compressor power is zero, reflecting zero turbine power. The only difference between diabatic and adiabatic lines in y axis (zero power line) is a vertical offset, representing the amount of heat transfer in the turbine. By shifting the turbine’s effective power results from the hot gas test bench, the corrected values of turbine power can be calculated as follows:

$$P_{T,corr}=P_{T,eff}-{\dot{Q}}_T$$

(4)

The heat transfer in the turbine ${\dot{Q}}_T$ can be directly estimated using the power-based approach, (see Figure 3) and the calculated turbine $P_{T,eff}$, is carried out considering the turbine expansion as an adiabatic process, as follows:

$$P_{T,eff}={\dot{m}}_T{c}_{p,T}(T_3-T_4)$$

(5)

This method eliminates the need for direct measurements of bearing friction losses, as the power-based approach inherently accounts for mechanical losses. Turbocharger friction losses can instead be estimated using the following equation:

$$P_{Frictionloss}=P_{T,Corr}-P_{C,Corr}$$

(6)

2.4. Flow Exergy Methodology

As previously noted, thermodynamic analyses of turbochargers generally depend on energy balances based on the first law of thermodynamics, typically assuming an adiabatic process. When heat transfer is considered in turbochargers, the first law is essential for precise energy accounting when deriving the turbine performance map from experimental data. However, relying only on the first law is insufficient for identifying and quantifying aerothermodynamic losses due to heat loss in a turbocharger turbine. This limitation highlights the need for additional methods, such as exergy analysis, to provide a more thorough thermodynamic understanding of heat transfer losses, taking into account the irreversibilities in each process.

This study seeks to experimentally quantify the aerothermodynamic losses and the impact of heat transfer and pulsating flow on a passenger car small turbocharger turbine. Exergy analysis, also known as second-law analysis, is based on the second law of thermodynamics and goes beyond traditional energy balance calculations.

The equations for the first and second laws of thermodynamics for a diabatic turbine can be formulated as follows:

1

law of thermodynamics (energy balance):

$$P_{T,corr}=\left({\dot{H}}_3-{\dot{H}}_4\right)-{\dot{Q}}_T$$

(7)

2

law of thermodynamics (entropy balance):

$${\dot{S}}_{gen}=-\left({\dot{S}}_3-{\dot{S}}_4\right)+{\displaystyle \frac{{\dot{Q}}_T}{T_b}}$$

(8)

Considering the hot gas as an ideal gas with a constant specific heat capacity, which is determined using polynomial regression as a function of temperature at the turbine’s mean temperature, accounting for different gas compositions at each measurement point. The changes in enthalpy and entropy in Equations (7) and (8) can be calculated as follows:

$${\dot{H}}_3-{\dot{H}}_4={\dot{m}}_T{c}_{p,T}\left(T_3-T_4\right)$$

(9)

$${\dot{S}}_3-{\dot{S}}_4={\dot{m}}_T\left(c_{p,T}ln\left({\displaystyle \frac{T_3}{T_4}}\right)-Rln\left({\displaystyle \frac{p_3}{p_4}}\right)\right)$$

(10)

Exergy is defined as the maximum theoretical useful work obtainable from a given quantity of a substance as the system reaches equilibrium with its environment, referred to as the dead state (where ${P=P}_0$ and ${T=T}_0$). In this dead state, the system is in thermal and mechanical equilibrium with the environment, and no more turbine power can be extracted from the working fluid.

The specific exergy transfer of a flow in state (i) is defined as follows:

$$e_i=\left(h_i\left(T,p\right)-h_0\right)-T_0\left(s_i(T,p\right)-s_0)$$

(11)

Consequently, the total exergy of a flow in state (i) would be as follows:

$${\dot{E}}_i={\dot{m}}_i{e}_i$$

(12)

Figure 5, illustrates the schematic graph of the turbine, highlighting the key points of exergy flow input, output, and losses. This visualization, followed by detailed explanations, will clarify the different exergy components, including the inlet and outlet exergies, turbine power, heat transfer exergy, and exergy destruction as follows:

• Exergy at the turbine inlet ($\dot{E_3}$) represents the available maximum useful work in the fluid flow before expansion and defined as:

  $${\dot{E}}_3=\left(\dot{H_3}-\dot{H_0}\right)-T_0(\dot{S_3}-\dot{S_0})$$

  (13)
• Exergy at the turbine Outlet ($\dot{E_4}$) represents the remained available maximum useful work in the fluid flow after expansion and defined as:

  $${\dot{E}}_4=\left({\dot{H}}_4-{\dot{H}}_0\right)-T_0(\dot{S_4}-\dot{S_0})$$

  (14)
• Turbine power ($P$) is the mechanical power produced by the turbine, representing the useful work generated during its operation.
• Exergy due to heat transfer ($\dot{E_Q}$) encompasses the exergy associated with heat transfer across system boundaries. It is expressed as:

  $${\dot{E}}_Q={\dot{Q}}_T(1-{\displaystyle \frac{T_0}{T_b}})$$

  (15)

  where ${\dot{Q}}_T$ is the heat transfer rate, $T_0$ is the ambient temperature, and $T_b$ is the boundary temperature at which the heat transfer occurs.
• Exergy Destruction (${\dot{E}}_D$) represents the losses associated with irreversible within the system, quantifying inefficiencies due to factors such as friction, turbulence, and non-ideal gas behavior. It is defined as:

  $${\dot{E}}_D=T_0{\dot{S}}_{gen}$$

  (16)

  where $T_0$ is the ambient temperature and ${\dot{S}}_{gen}$ is the rate of entropy generation and is calculated from second law of thermodynamics (Equation (8)).

Furthermore, the exergy balance of the turbine is being carried out by combining the first and second laws of thermodynamics (Equations (7) and (8)), as follows:

$${\dot{E}}_{in}={\dot{E}}_{out}+{\dot{E}}_D\to {\dot{E}}_3={\dot{E}}_4+P_{Corr}+{\dot{E}}_Q+{\dot{E}}_D$$

(17)

$$\underset{{\dot{E}}_F}{\underbrace{\left(\dot{H_3}-\dot{H_4}\right)-T_0(\dot{S_3}-\dot{S_4})}}=\underset{{\dot{E}}_P}{\underbrace{P_{Corr}}}+\underset{{\dot{E}}_L}{\underbrace{{\dot{Q}}_T\left(1-{\displaystyle \frac{T_0}{T_b}}\right)}}+\underset{{\dot{E}}_D}{\underbrace{T_0{\dot{S}}_{gen}}}$$

(18)

The fuel exergy term (${\dot{E}}_F)$ in equation, represents the total available exergy from the turbine expansion process. This fuel exergy concept extends beyond the conventional definition of fuel (such as gasoline, diesel, etc.).

The individual components of fuel exergy are divided into three distinct terms:

• Product exergy rate (${\dot{E}}_P$): the useful work produced by a system;
• Exergy destruction rate (${\dot{E}}_D$): exergy destroyed due to internal irreversibilities;
• Exergy loss rate (${\dot{E}}_L$): exergy lost due to heat losses.

The following section presents the results of the experimental analysis, highlighting the impact of heat transfer and internal irreversibilities in both steady and pulsating flow on the individual exergy terms. In this section, the influence of heat transfer and internal irreversibilities on the distribution and magnitude of product exergy, exergy destruction, and exergy loss is examined. Additionally, the implications of these results for system performance are discussed, providing a comprehensive understanding of the thermodynamic behavior observed during the experiments.

3. Results and Discussion

3.1. Turbine Heat Transfer Estimation Under Steady Flow

The heat transfer estimation results of the turbine under standard steady flow for different turbine inlet temperatures of TIT= 400 °C and 600 °C are plotted in power-based diagrams in Figure 6. Both diagrams also include the adiabatic measurements, which allow to quantify the heat loss in each diabatic test compared to adiabatic data. A line was fitted through the maximum ICP operating points for each speed line ranging from 85 k rpm up to 240 k rpm to calculate the turbine heat transfer using the introduced power-based method. As shown in Figure 6, higher TITs result in greater turbine heat loss, primarily due to the higher temperature gradient being the key factor in the heat flow. The turbine heat flows for TIT= 400 °C and 600 °C are calculated to be ${\dot{Q}}_{T,400}=1.1\mathrm{k}\mathrm{W}$ and ${\dot{Q}}_{T,600}=2.2\mathrm{k}\mathrm{W}$ respectively. This indicates that the heat flow increases twofold as the inlet temperature rises from 400 °C to 600 °C. Furthermore, the turbine’s pure aerodynamic power can be calculated and corrected using Equation (7), represented by the green-lined graphs in Figure 6. At this stage, the corrected power of the turbine is no longer influenced by heat transfer effects.

3.2. Turbine Heat Transfer Estimation Under Pulsating Flow

This section presents the results of heat transfer estimation for the turbine under pulsating flow to further investigate the turbine’s aerothermodynamic performance under real engine operation. Figure 7 illustrates a comparison of heat flow results at a turbine inlet temperature (TIT) of 400 °C between steady and pulsating flows across different pulse frequencies. The findings indicate that pulsating flow significantly increases the heat flow of the turbine from 1.1 kW under steady flow conditions to 1.7 kW under pulsating flow at a pulse frequency of 16.5 Hz, representing a 54.5% increase, and further to 1.8 kW at a pulse frequency of 33.3 Hz, marking an overall increase of 63.6% from the steady flow. The increase in heat transfer rate under pulsating flow can be explained by the fact that the pulsations intensify flow turbulence and frequently disrupt the thermal boundary layer, both of which enhance convective heat transfer. Moreover, the fluctuating temperature and velocity profiles in pulsating flow create steeper thermal gradients, leading to more efficient heat exchange. The results demonstrate that pulsating flow significantly enhances heat transfer in the turbine, highlighting its relevance to the overall aerothermodynamic performance under real engine conditions. Additionally, these findings provide a solid foundation for the exergy-based analysis, which is presented in the subsequent section.

3.3. Exergy-Based Analysis of the Turbine

Based on the heat transfer estimations presented in the previous sections, this part of the study focuses on the exergy-based analysis of the turbine under both steady and pulsating flow conditions. The heat flow results obtained under different test conditions serve as the basis for evaluating the exergy performance of the turbine. By incorporating these heat transfer calculations, the exergy loss and exergy destruction of the turbine are further analyzed to provide a more comprehensive understanding of its aerothermodynamic performance under realistic engine operation scenarios. Figure 8 depicts the normalized exergy budget of the turbocharger turbine across various turbocharger speeds under steady flow at various operating points, comparing adiabatic conditions with turbine inlet temperatures (TIT) of 400 °C and 600 °C. The exergy budgets include rate of product exergy (${\dot{E}}_P$), exergy destruction (${\dot{E}}_D$), and exergy loss due to heat transfer (${\dot{E}}_L$), presented as percentages relative to the total fuel exergy (available exergy). This approach clarifies the contribution of each component to the overall exergy balance. It is evident that the heat transfer exergy loss increases as the turbine inlet temperature rises, which is attributed to the higher heat transfer rate calculated using the power-based approach described in Section 3.2. On the other hand, exergy destruction at each turbocharger speed is highest in the adiabatic case and decreases as the turbine inlet temperature (TIT) increases. This is because the exergy destruction rate is directly proportional to the mass flow rate, which is the primary cause of flow friction, leading to increased exergy destruction. In the adiabatic scenario, lower operating temperatures reduce the contribution of specific enthalpy differences to turbine power generation. As a result, mass flow becomes the dominant factor in turbine power production. Consequently, higher mass flow rates are required in adiabatic conditions to achieve the same turbine power output as in diabatic scenarios. However, the increased mass flow also intensifies flow friction, resulting in higher exergy destruction rates under adiabatic conditions compared to diabatic ones. This trend is similarly observed when comparing turbine inlet temperatures (TIT) of 400 °C and 600 °C, where lower TIT leads to similar effects on flow friction and exergy destruction. Additionally, higher turbine speeds at any scenario (adiabatic, TIT of 400 °C and 600 °C) lead to increased gas mass flow, resulting in elevated exergy destruction rates.

Figure 9 further investigates the impact of pulsating flow on the exergy budget of the turbocharger turbine under both adiabatic and diabatic conditions at a turbine inlet temperature (TIT) of 400 °C. The analysis compares steady flow with pulsating flow at two distinct frequencies, 16.6 Hz and 33.3Hz, highlighting the effects of pulsating flow on the turbine’s aerothermodynamic performance. The results show that, in both adiabatic and diabatic cases, exergy destruction increases significantly under pulsating flow conditions (16.6 Hz and 33.3 Hz) compared to steady flow. This increase is attributed to pulsation-induced pressure and velocity fluctuations, which intensify flow friction and turbulence, leading to greater irreversibilities and elevated exergy destruction rates. The results show that, in both adiabatic and diabatic cases, exergy destruction increases significantly when pulsating flow is applied compared to steady flow. However, as the pulsation frequency increases, exergy destruction decreases slightly compared to lower pulse frequencies. This initial increase is attributed to pulsation-induced pressure and velocity fluctuations, which intensify flow friction and turbulence, leading to greater irreversibilities and elevated exergy destruction rates. The subsequent decrease in exergy destruction at higher pulsation frequencies is due to enhanced flow stabilization and the damping of pulsation effects, which promote quasi-steady behavior of the flow, thereby reducing flow friction and turbulence.

The significant increase in exergy destruction caused by pulsating flow leads to a reduction in heat transfer exergy loss. Although the turbine heat transfer rate rises under pulsating flow (as determined by the power-based approach), the corresponding heat transfer exergy loss decreases.

As the pulsation frequency increases, exergy destruction gradually decreases, and subsequently, the heat transfer exergy loss increases. This shift causes heat transfer exergy loss to become more dominant at higher pulsation frequencies. At these higher frequencies (representative of real engine operating conditions) the flow transitions toward quasi-steady behavior, further amplifying the effects of heat transfer on the overall exergy distribution. Consequently, standard turbocharger performance measurements that neglect the combined effects of heat transfer and pulsating flow may lead to significant inaccuracies, particularly under these conditions, as they fail to capture the dynamics of exergy losses and exergy destructions.

3.4. Impact Exergy-Based Aerothermodynamic Analysis on Engine Development Process

Engine development is heavily reliant on numerical methods, including 3D CFD for component and 1D powertrain simulation for system analysis, as simulation allows for much faster and more cost-effective design iteration than experimental testing. However, during the modeling process, many input parameters need to be provided by test bench measurements. In the case of the turbocharger within a 1D engine model, current practice is still to employ a heavily data-driven modeling approach based on turbocharger maps from hot gas measurements according to SAE J922 and SAE 1826 standards. These models are typically developed under the assumption of adiabatic conditions, which fail to account for the unavoidable aerothermodynamic effects of heat transfer that occur during actual operation.

Due to the limitations of this measurement approach and the inevitable errors in the aerothermodynamic representation of the turbocharger mainly caused by disregarding heat transfer within the turbocharger, heat loss to the environment and pulsation, more time-consuming steps are needed to arrive at a well-functioning model. Specifically, central output parameters of the turbocharger model within a 1D engine simulation, such as turbine outlet temperature, compressor outlet temperature, and turbocharger speed, have a very significant impact on engine operation and exhaust gas aftertreatment performance. The power-based approach has proven to reduce the simulation prediction error of these variables by a factor of 10 [29]. This significantly reduces the effort during the modeling process, such as the application of correction factors within common engine simulation tools or even the need for additional measurements, such as time-consuming adiabatic turbocharger testing.

The addition of an exergy-based aerothermodynamic evaluation of the turbocharger, as introduced in this paper, demonstrates its applicability under pulsating flow conditions and provides valuable insights into the thermodynamic behavior of the turbocharger while avoiding substantial additional measurement or computational efforts. Thus, this method can easily be incorporated into existing workflows. On the one hand, the results can be used to feed regular map-based turbocharger models with heat-transfer-corrected maps. Additionally, more sophisticated turbocharger maps, such as thermal lumped system approaches, can be parametrized based on the presented approach and thus provide much more accurate predictions even in transient operation.

4. Conclusions

This study provides a comprehensive experimental investigation into the aerothermodynamic performance of a turbocharger turbine under both steady and pulsating flow conditions, with a focus on the effects of heat transfer and pulsation across varying turbine inlet temperatures (TITs) and pulsation frequencies. By utilizing a power-based approach for estimating turbine heat transfer and conducting detailed exergy analyses, the findings highlight the significant impact of heat transfer and pulsation on turbine performance.

Heat transfer was found to increase significantly with higher TITs under steady flow, doubling from 1.1 kW at 400 °C to 2.2 kW at 600 °C. Pulsating flow further amplified heat transfer, with increases of up to 63.6% compared to steady flow, driven by intensified turbulence and disrupted thermal boundary layers.

Pulsating flow also caused a significant rise in exergy destruction compared to steady flow, attributed to pulsation-induced velocity and pressure fluctuations. However, at higher pulsation frequencies, exergy destruction decreased slightly due to enhanced flow stabilization and quasi-steady behavior, while heat transfer exergy loss became more dominant. These results demonstrate that at higher pulsation frequencies—representative of real engine conditions—the flow transitions toward quasi-steady behavior, reshaping the exergy distribution. The interplay between heat transfer and exergy destruction is critical, providing valuable insights for optimizing turbine performance under realistic operating conditions. Beyond the measurement results, the study demonstrates the value of exergy analysis as an advanced tool for evaluating turbocharger performance. Compared to conventional energy-based methods, exergy analysis provides a deeper understanding of the aerothermodynamic processes in turbochargers by accounting for irreversibilities and heat transfer effects. This approach enables more precise insights into turbine behavior and offers a robust framework for analyzing and interpreting turbocharger measurement data. By enhancing the understanding of these complex interactions, the exergy-based methodology establishes itself as a powerful tool for advancing the design and optimization of turbochargers and other turbomachinery systems. This study underscores the importance of integrating pulsating flow and heat transfer effects into testing and modeling methodologies to enhance performance prediction accuracy and turbine optimization. This study provides valuable insights into the turbine’s heat transfer and exergy dynamics, offering practical implications for the design and optimization of turbochargers and other turbomachinery applications. By advancing the understanding of these complex phenomena, the work contributes to the development of more efficient and sustainable technologies for internal combustion engines, hydrogen-powered systems, and a broader range of industrial and energy-sector applications.