Conjugate Heat Transfer Method Research Articles

Target temperature-based simulation method for predicting performance and designing aircraft thermal anti-icing systems

The prevention of ice build-up on aircraft surfaces is crucial for safe operations. Thermal ice protection systems, particularly electro-thermal systems, are commonly employed to mitigate ice formation. However, the weight of electric batteries used in these systems significantly impacts aircraft performance, necessitating the minimization of power load during design. Despite this requirement, effective anti-icing operation mandates a sufficient heat flux to maintain surface temperature above the freezing point and evaporate any runback water film. Previous research has utilized numerical simulation analysis to predict the performance of electro-thermal anti-icing systems. The conjugate heat transfer method has been commonly employed to predict temperature distribution on the protected surface. However, non-isothermal surfaces exhibit distinct local convective heat transfer coefficients that influence local thermal balance, unlike isothermal surfaces that adopt the loosely-coupled method for computational efficiency. In this study, we present a novel target temperature-based anti-icing simulation method that predicts the required heat flux for thermal ice protection systems without employing the conjugate heat transfer method. Our objective was to calculate the necessary heat flux to achieve the desired non-isothermal surface temperature for effective anti-icing. By eliminating the excessive iteration process associated with the coupling method for conjugate heat transfer, we have streamlined the simulation procedure. Through validation, target temperature-based anti-icing simulation method, when compared to the tight coupling method, demonstrated the ability to predict the same surface water flow rates while reducing computation time by up to 90 %. Furthermore, when applied to design problems, our method achieved approximately a 10 % reduction in the required heat capacity for anti-icing compared to experimental values. As a result, target temperature-based anti-icing simulation method offers a more efficient alternative to traditional conjugate heat transfer methods, providing valuable insights for both predicting anti-icing system performance and optimizing aircraft design.

Toward the Development of Low-NO Ammonia Cofiring Furnaces: Numerical Investigation into the Secondary Injection System Using the Conjugate Heat Transfer Method

Toward the Development of Low-NO Ammonia Cofiring Furnaces: Numerical Investigation into the Secondary Injection System Using the Conjugate Heat Transfer Method

In-flight anti-icing simulation of electrothermal ice protection systems with inhomogeneous thermal boundary condition

Conventional anti-icing computational solvers calculate the convective heat transfer coefficient using a homogeneous thermal boundary condition, assuming a constant temperature across the surface. However, this approach can lead to inaccuracies in regions with significant temperature variations. To address this limitation, the present study proposes a novel approach that utilizes an inhomogeneous thermal boundary condition, which updates the convective heat transfer coefficient based on the transient wall temperature distribution. We developed a unified finite volume framework that efficiently integrates various in-house solvers, including a compressible Navier-Stokes-Fourier (NSF) airflow solver, a Eulerian droplet impingement solver, a PDE-based ice solver, and a multilayer heat conduction solver. Thermal interaction between the different solvers was modeled using the conjugate heat transfer method. The effects of updating airflow on anti-icing results were investigated by comparing the results obtained by coupled and decoupled solvers. While the decoupled solver computes airflow once and remains unchanged, the coupled solver updates the airflow during the anti-icing simulation. Our findings show that the decoupled solver has the highest deviations from the coupled solver in evaporative anti-icing regimes, where dry regions form within the protection limits. Using coupled solvers in designing ice protection systems in evaporative regimes improves temperature prediction accuracy, enabling designers to reduce safety factors and save energy.

Study on effects of inlet nonuniformities on aerothermal performance of NGV pressure side with different film cooling designs

High pressure (HP) turbine works under nonuniform inlet conditions produced mainly by modern lean burn combustors. This article employed the conjugate heat transfer method to investigate the influences of nonuniform inflow conditions and film hole arrangements on the film coolant coverage and heat transfer characteristics. The researched region is on the pressure side (PS) of the nozzle guiding vane (NGV). A scaled-up model of the GE-E3 engine HP turbine stator vane was used and the film cooling performances of four different film hole arrangement schemes on the PS were discussed. In addition, the results of four nonuniform inflow conditions, including positive/negative swirl aligned with the stator vane leading edge (case PSW-LE and NSW-LE), and positive/negative swirl aligned with the stator vane mid passage (case PSW-PA and NSW-PA), were compared with the uniform inlet condition. The results indicate that the temperature distributions of stator vane PS are dominated by the film hole arrangements and the nonuniform inlet conditions. In the positive swirl (PSW) influenced region, film cooling effectiveness can be improved if the coolant orientation is consistent with the swirl direction. The film cooling effectiveness can be improved by 12%–20% under the Leading Edge (LE) clocking position and 45% under the Passage (PA) clocking position. In contrast, the negative swirl dominates the film cooling effectiveness distribution. Under the PA clocking position, the highest film cooling effectiveness can be enhanced by 45% compared with the LE. In contrast, the design of film holes has a weak contribution to the coolant outflow direction under the negative swirl (NSW) condition. However, the film holes with negative angles can enhance the cooling effectiveness behind the 13th row holes.

Numerical investigation on the effects of air-staged strategy and ammonia co-firing ratios on NO emission characteristics using the Conjugate heat transfer method

Ammonia co-firing is recognized as a promising approach within the realm of achieving carbon neutrality. This method not only effectively mitigates carbon emissions but also augments the stability of ammonia combustion. However, achieving low NO emissions in ammonia combustors remains a formidable challenge. The present study employed numerical simulations to assess the impact of an air-staged strategy and varying ammonia co-firing ratios on NO emissions within a 10-kW industrial ammonia co-firing furnace. To accurately represent the thermal conditions at the furnace walls, a Conjugate Heat Transfer (CHT) model encompassing both solid materials and reacting flow regions was utilized. Initially, the numerical results were compared with experimentally measured NO emissions, validating the accuracy of the customized solver. Subsequently, the effectiveness of the air-staged strategy under the parallel injection system was verified. This approach created a fuel-rich region near the burner primary nozzle, significantly reducing NO production. Under different ammonia co-firing ratios, with ammonia injection levels increasing from 0% to 100%, NO emissions at the furnace outlet displayed an initial increase, followed by a decrease, peaking at a co-firing ratio of 50%. Further analysis of the Rate of Production (ROP) of NO within the furnace revealed that at higher ammonia co-firing ratios, ammonia serves both as a reducing agent and as a fuel for heat release. These findings provide valuable insights for the development and application of ammonia-based industrial furnaces.

Creep behavior of different elliptical film cooling holes in complex temperature fields

This paper investigates the creep damage of film cooling holes with varying ellipticity within complex temperature fields. The temperature field, derived through the conjugate heat transfer method, serves as a boundary condition for crystal plastic finite element simulations. We discovered that film hole patterns with an ellipticity (λ) of ≤0.5 exhibit superior cooling effectiveness, particularly at a blowing ratio (B) of 1.0. For λ = 0.5, these holes demonstrate exceptional cooling effectiveness and mechanical properties. Reducing the ellipticity of film holes induces a shift in the high-stress region around the hole, subsequently diminishing stress concentration on the acute side of the hole. Moreover, the temperature difference between the edges on both sides of the hole perimeter and the upstream zone on the high-temperature surface for hole patterns with λ ≤ 0.5 introduces additional stress concentrations, with a significant temperature difference causing creep damage in this region.

Numerical simulations on the performance of transpiration cooling implemented with perforated flat plates

Transpiration cooling is an effective method of protecting high-temperature components. However, this technology is currently not applicable to turbine blades because conventional sintered porous materials cannot precisely control the geometric parameters of the cooling channels and coolant outlets. In this study, numerical simulations using the conjugate heat transfer method were conducted to study the effects of hole diameter, injection ratio, and mainstream Reynolds number on the cooling performance of perforated flat plates. A novel optimisation method for the overall transpiration cooling efficiency that reduces coolant consumption through a nonuniform coolant allocation strategy was proposed. The effects of different pore diameters (0.15 mm, 0.2 mm, 0.25 mm, 0.3 mm) on transpiration cooling were investigated numerically. The results revealed that the hole diameter had a marginal effect on the average cooling efficiency of transpiration cooling under the same coolant-injection ratio. With dense heat transfer occurring within the solid matrix, the influence of variations in the pore size was diminished. However, the nonuniformity of the cooling efficiency on the hot wall surface increased with increasing pore size. A double coolant chamber non-uniform injection was adopted for the 0.3 mm perforated plate. The results indicated that there is an optimum coolant allocation ratio for achieving the highest average cooling efficiency with a certain coolant.

Effects of thermal barrier coating thickness and surface roughness on cooling performance sensitivity of a turbine blade

In this study, the conjugate heat transfer method is used to research the impact of the thermal barrier coating thickness (0–300 μm) and surface roughness (Ra = 0–30 μm) on the cooling characteristics of the high-pressure turbine blade. A physical thin-walled structure is applied to simulate the TBC on the turbine blade surface. The results indicate that the temperature distribution on the coated metal surface is more uniform. With an increase in coating thickness, the heat flux of the blade surface decreases, reaching a maximum of 106W/m2 at the leading edge. Furthermore, leading-edge temperature is the most sensitive to changes in coating thickness, and the pressure surface is the least sensitive. The overall cooling effectiveness is less sensitive to changes in the roughness after coating. Increasing the surface roughness, the heat flux reduces at the leading edge and increases at other places. The range of the overall cooling effectiveness rate of the blade rises, and the sensitivity of the overall cooling effectiveness to the coating thickness increases. When Ra reaches 20 μm, the insulation effect with different coating thickness remains unaffected.

Conjugate Heat Transfer Evaluation of Turbine Blade Leading-Edge Swirl and Jet Impingement Cooling With Particulate Deposition

Abstract Internal cooling structures for gas turbine engines are becoming more complicated to push the hot gas temperature as high as possible, which, however, allows particulates drawn into the coolant air to be more readily to deposit within these passages and thus greatly affect their flow loss and thermal performance. In this study, internal swirl cooling and jet impingement cooling subjected to particulate deposition were evaluated and compared using a conjugate heat transfer method, with an emphasis on the thermal effects of the insulative deposits. To accomplish the goal, an unsteady conjugate mesh morphing simulation framework was developed and validated, which involved particle tracking in an unsteady fluid flow, particle–wall interaction modeling, conjugate mesh morphing of both fluid and solid domains, and a deposit identification method. The swirl and the jet impingement cooling configurations modeled the internal cooling passage for the leading-edge region of a turbine blade and were investigated in a dust-laden coolant environment at real engine conditions. Coupling effects between the dynamic deposition process and the unsteady flow inside the two cooling channels were examined and the insulative effects of the deposits were quantified by comparing the temperatures on the external and internal surfaces of the metal channel walls, as well as on the deposit layers. Results demonstrated the ability of the newly developed, unsteady conjugate simulation framework to identify the deposits from the original bare wall surface and to predict the insulation effects of the deposits in the dynamic deposition process. The dust almost covered the entire impingement channel, while deposits were only seen in the vicinity of the jets in the swirl channel. Despite this, a dramatical decrease of convection heat transfer was found in the swirl channel because the swirling flow was sensitive to the interruption of the deposits. In contrast, the deposits improved the heat transfer rate in the impingement channel. When the thermal effects of the deposit layer were taken into account, the wall temperatures of both two cooling geometries were substantially elevated, exceeding the allowable temperature of the metal material. Due to the denser deposit coverage, the impingement channel wall had a greater temperature increase than the swirl channel. In terms of flow loss, the presence of the deposits inhibited the swirl intensity by interrupting the swirling flow and thus reduced the friction loss, whereas the pressure loss was improved by the deposits in the impingement cooling.

Research on transient heat transfer of ball valves in high-pressure liquid hydrogen receiving stations

As one of the most important fluid control devices in the liquid hydrogen receiving station, the liquid hydrogen ball valve's performance directly affects the system's stability. Aiming at the problem of insufficient cold shrinkage compensation ability of ball valve under high-temperature difference and excessive flow rate during the working process, a high-pressure liquid hydrogen hollow ball valve with elastic compensation ability is designed. Based on the conjugate heat transfer method, the transient conjugate heat transfer and transient thermal stress analysis were carried out on the high-pressure hollow ball valve of the liquid hydrogen receiving station. The results show that the transient temperature of each part of the ball valve decreases under different flow rates, and the closer to the flow part of the medium, the faster the cooling. In the initial stage, the larger the flow rate of liquid hydrogen, the greater the heat flux density of the fluid-solid interface, but after a certain period, the large flow rate is cooled to a greater extent, the heat transfer is weakened, and the heat flux density is smaller. Under different flow rates, the transient thermal stress of the key components of the ball valve first increases sharply and then decreases. At large flow rates, the temperature change is more obvious, and the maximum stress of each component increases. The research results have guiding significance for designing and applying ball valves in high-pressure liquid hydrogen receiving stations.

A multiscale framework for unsteady conjugate heat transfer with turbulence resolving methods — With application to rotating cavities

Carrying out unsteady conjugate heat transfer (CHT) with turbulence resolving methods is challenging due to the significant disparity in both time and length-scales that appear in the problem. The solid domain initial transient needs to be accelerated to a steady state, but time-accuracy for the solid domain temperatures fluctuations must be maintained. Many current state-of-the-art methods aim to do this by accelerating the solid domain timescale until the simulation is temporally converged, before switching to a non-accelerated solid solution that is assumed to be correct. However, this paper demonstrates that these current time domain CHT methods still introduce a long-lasting error in the solid domain temperature.To meet this challenge, we present a new multiscale framework that enables the interaction of all timescales in the fluid and solid domains to be consistently captured, without corruption by mesh resolution effects or the solid initial transient. Monochromatic low frequency temperature fluctuations from large coherent structures in the fluid domain are coupled to a time-spectral solid domain solution with a harmonic balance interface condition. Broadband higher frequency temperature fluctuations from turbulence are captured locally on the wall using a wall transfer function approach, reformulated using recursive convolution to simplify its application.The framework is applied to the simulation of rotating cavities with various disk materials and heating configurations. Various aspects of the framework and unsteady conjugate heat transfer in general are illustrated — in particular that starting from a roughly correct time-average solution can still lead to a large initial transient once an unsteady wall temperature is introduced. Comparison of the simulations yields new insight into the effect that different industrially relevant choices for the cavity material can have, even at the same non-dimensional operating conditions.

Conjugate Heat Transfer Model for an Induction Motor and Its Adequate FEM Model

The primary objective of the research presented in this paper was to design a methodology for analyzing the thermal field of an induction motor that would be of higher fidelity but less time- and cost-consuming and that would deal with air-cooled induction motors of all sizes. The complexity of the simulation is increased by the geometric asymmetry and by the asymmetric character of flow cooling the motor casing caused by the fan’s rotation. This increases demand, especially on computational resources, as creating a simplified numerical model using symmetry boundary conditions is impossible. The new methodology uses the existing findings from many partial articles and literature, which are modified into more accurate relationships suitable for predicting the external thermal field of induction motors. That way, we do not have to solve the thermal field by the conjugate heat transfer method, and it is possible to assess temperature gradients over the entire range. Furthermore, a new relationship between shear strain rate and thermal contact conductivity has been discovered that allows solving heat transfer of fluid adjacent to the internal walls of an induction motor at any location. That approach has not yet been published in the literature, so it can be considered a new method to simplify heat transfer simulation. An experimentally validated new methodology of the induction motor was performed. The so-called digital twin will be used for the virtual optimization of the new designs concerning minimizing losses and maximizing efficiency.

Comparison of different CFD-FEM coupling methods in advanced structural fire analysis

The research approach of multi-physical field coupling can be used to analyze the structural fire resistance problem. In the process of numerical simulation, multiple coupling interfaces are involved. Regarding fluid-thermal-solid coupling, most of the previous numerical studies on structural fire resistance have used the adiabatic surface temperature (AST) parameters in order to accurately describe complex boundary conditions in fire analysis. This approach belongs to the iterative coupling form, and the other type of direct coupling form is rarely used. In this paper, the specific scenario of a steel column surrounded by fire source is selected as a typical case to explore the thermodynamic phenomena of the steel column. Based on the computational fluid dynamics (CFD) method, the fire model analysis in the fluid domain was first implemented to investigate the distribution laws of the spatial velocity and temperature fields. Then the fluid-thermal-solid coupling was realized via iterative coupling (Adiabatic Surface Temperature method, AST method) and direct coupling (Full Conjugate Heat Transfer method, FCHT method) respectively to obtain the steel column temperatures. The accuracy of these two coupling methodologies was verified by comparing their results with the experimental data, and the accuracy of AST method depends on the reasonable sampling of fire analysis results. Following this, structural model analysis was completed using the solid temperature as the boundary condition to achieve the solid thermal-mechanical coupling. The yield strength degradation of the steel column after heating was explored. Finally, the non-necessity of fluid-mechanical-solid coupling in structural fire resistance was discussed.

Flow and Conjugate Heat Transfer of Swirl Chamber With Micro-Ribs in Turbine Vane Leading Edge

Abstract Swirl cooling can provide effective protection for the turbine vane leading edge (LE). In this paper, a swirl cooling model for improving the turbine vane heat transfer is established. The model includes the high-temperature mainstream region, LE region, and swirl cooling region. The conjugate heat transfer (CHT) method is used to examine the influence of wall structures on swirl cooling. Then, the best surface structure in the studied range is selected to further analyze the impact of the coolant inlet mass flow. The results show that the circumferential micro-rib structure has a more excellent performance in both fluid flow and cooling performance. The hindering effect of the micro-ribs can effectively avoid the development of axial cross-flow, thus enhancing the heat transfer with a small friction loss increment and providing a lower surface temperature and more uniform temperature distribution. When the inlet mass flowrate improves, the thermal performance factor increases and the LE temperature decreases gradually. Under the same pumping power condition, the circumferential micro-ribs structure has higher heat transfer efficiency. This investigation can provide a new design for further improving the thermal performance of swirl cooling for turbine vanes.

Assessment of a Conjugate Heat Transfer Method on an Effusion Cooled Combustor Operated With a Swirl Stabilized Partially Premixed Flame

Abstract Computational fluid dynamics (CFD) plays a crucial role in the design of cooling systems in gas turbine combustors due to the difficulties and costs related to experimental measurements performed in pressurized reactive environments. Despite the massive advances in computational resources in the last years, reactive unsteady and multi-scale simulations of combustor real operating conditions are still computationally expensive. Modern combustors often employ cooling schemes based on effusion technique, which provides uniform protection of the liner from hot gases, combining the heat removal by means of heat sink effect with liner coverage and protection by film cooling. However, a large number of effusion holes results in a relevant increase of computational resources required to perform a CFD simulation capable of correctly predicting the thermal load on the metal walls within the combustor. Moreover, a multi-physics and multi-scale approach is mandatory to properly consider the different characteristic scales of the several heat transfer modes within combustion chambers to achieve a reliable prediction of aerothermal fields within the combustor and wall heat fluxes and temperatures. From this point of view, loosely coupled approaches permit a strong reduction of the calculation time, since each physics is solved through a dedicated solver optimized according to the considered heat transfer mechanism. The object of this work is to highlight the capabilities of a loosely coupled unsteady multi-physics tool (U-THERM3D) developed at the University of Florence within ansys fluent. The coupling strategy will be employed for the numerical analysis of the TECFLAM effusion cooled swirl burner, an academic test rig well representative of the working conditions of a partially premixed combustion chamber equipped with an effusion cooling system, developed by the collaboration of the Universities of Darmstadt, Heidelberg, Karlsruhe, and the DLR. The highly detailed numerical results obtained from the unsteady multi-physics and multi-scale simulation will be compared with experimental data to validate the numerical procedure.

Simulation on the effect of impinging distance for the aerodynamic and heat transfer characteristics of sweeping jet and film composite cooling

The influence of different impinging distances for sweeping jet cooling is investigated by employing the conjugate heat transfer method in a blade leading edge model with film holes. Three impinging distances (P/D = 3, 4, 5) are discussed and compared with the blowing ratio varying from 1.05 to 4.11. In addition, the SST k-ω turbulence model is validated by comparing the sweeping frequency and spanwise-averaged Nusselt number. Results indicate that the three impinging distance schemes obtain similar flow structures under identical blowing ratios. The total pressure loss coefficient is insensitive to the impinging distance and increases with the increasing blowing ratio. The Nusselt number and overall cooling effectiveness (OCE) are enhanced in response to the increased blowing ratio for all cooling schemes. A smaller impinging distance obtains a more considerable internal impingement cooling effectiveness, but the overall cooling effectiveness under each impinging distance is basically the same. Therefore, the results show that the sweeping jet and film composite cooling (SJF) can be applied to actual blades without considering the impinging distance.

Computational simulation of aircraft electrothermal de-icing using an unsteady formulation of phase change and runback water in a unified framework

Accurately predicting de-icing processes is essential to ensure the proper sizing and design of ice protection systems in aircraft icing. A unified framework was developed to simulate an unsteady electrothermal de-icing process, using an unsteady formulation to account for phase change and runback water. Two physically-motivated concepts were newly introduced to the icing model to accurately describe the unsteady electrothermal de-icing (ice accretion/melting) process. A conjugate heat transfer method was utilized to tightly couple the ice and conduction solvers. Sub-iterations were incorporated at every time step to ensure the convergence of temperature and heat flux at the interface. The unsteady de-icing framework consists of a compressible Navier-Stokes-Fourier airflow solver, Eulerian droplet impingement solver, unsteady ice accretion/melting solver, and heat conduction solver, which can handle multilayer composite materials. All solvers were formulated based on partial differential equations and developed in a unified finite volume framework, enabling the use of a single grid system and eliminating unnecessary grid generation for the ice layer. The results showed better agreement with experimental data compared to other results. The unified solver was used to analyze the unsteady electrothermal de-icing process by investigating the ice accretion, ice melting, runback water film, and freezing of water film in unprotected areas. Runback water film due to ice melting may exceed the impingement limits and freeze in unprotected areas, leading to ice ridge formation.

Thermal hydraulic simulation of the steam generator under fast transient events

A multidomain computational procedure was applied to model the RD-14M steam generator. It was based on the two-fluid Eulerian approach to model the water–steam flow, the blending method for interfacial force terms, the wall heat partition model (RPI) for wall boiling, and the conjugate heat transfer (CHT) method for thermal coupling between the primary and secondary circuits. The computational model of the overall steam generator is achieved by combining full 3D simulation in the riser and 0D modeling with ad hoc Dynamic Boundary Conditions (DBC) in separator/dryer, downcomer, and pre-heater regions. The implementation was carried out in the OpenFOAM(R) environment. Both steady state nominal conditions as well as transient events, such as loss of power supply and reactor shutdown, were studied. The results were compared with previous RELAP5 and full-3D models getting quite good agreement. The information obtained was very useful to understand the overall thermal-hydraulic behavior of steam generators but also local phenomena around the tubes and baffles inside the riser, which are unavailable in system-code models.

Heat transfer and flow structure characteristics of film-cooled leading edge model with sweeping and normal jets

The heat transfer and flow structure characteristics of a film-cooled leading edge model with sweeping and normal jets were numerically investigated using the conjugate heat transfer method. The leading edge model is a simplified obtuse body model that has three rows of traditional cylindrical film holes, each with three holes inclined at 25° with respect to the surface and three angles oriented at 0° and ± 30° with respect to the axial direction. A normal jet has one row of cylindrical impingement nozzles, and a sweeping jet has only one fluidic oscillator. Three blowing ratios (M = 1.05, 2.07, and 4.11) and three temperature ratios (TR = 0.5, 0.625, and 0.75) are considered in the study. The shear stress transport k–ω turbulence model and an extremely fine structured grid were validated and applied to all simulations. The results indicate that the total pressure loss coefficient and heat transfer performance increase internally and externally, respectively, with the blowing ratio. However, they are insensitive to the temperature ratio in all cooling configurations. The sweeping jet and film (SJF) composite cooling exhibits 1.6162, 2.1195, and 2.1766 times the total pressure loss coefficient of the normal jet and film composite cooling when the blowing ratio increases from 1.05 to 4.11. However, the SJF offers the advantages of uniform Nusselt number distribution on the impinging surface and high overall cooling effectiveness on the external surface.

Effects of lateral cooling hole configuration on a swirl-stabilized combustor

It is necessary to cool the combustor liner due to its harsh operating conditions. In the current study, wall temperatures of a swirling combustor with and without cooling holes are compared using a three-dimensional numerical simulation with conjugate heat transfer method. It is shown that the wall temperature can be reduced by 344–501 K by using cooling holes. Two lateral coolant injection designs are then proposed since the laterally injected coolant may interact with the swirling flow. Normal axial injection is also investigated to compare NOx emissions, cooling effectiveness and total pressure loss for various scenarios with different injection angles. The results show that when the incidence angle is 15°, NOx emissions remain low for all incidence configurations. When the lateral incidence is implemented, especially at small incidence angles such as 15° and 30°, the cooling effectiveness is maintained above 0.9. However, when the coolant incidence direction is opposite to the swirling flow and the incidence angle is 15° results in a high total pressure loss. At an incidence angle of 60°, the total pressure loss is about the same for all cases, at 3.2%.