Serpentine Nozzle Research Articles

Effects of cross-sectional shape on the low observability of double serpentine nozzles

When unmanned combat aerial vehicles (UCAVs) egress from the battlefield after attacking the target, the defensive radar systems detect signals reflected by the cavity structure of the nozzle and engine of the UCAVs, threatening their survivability. Infrared (IR) guided missiles can also threaten them by detecting the gaseous plume and hot engine parts. We present a comprehensive investigation of the effects of the cross-sectional shape of double serpentine nozzles on thrust, IR signature, and radar cross section (RCS), which are associated with propulsive performance and low observability. The fillet radius and cross-sectional shape of the nozzles were considered as the main design variables. The thermal flow field was analyzed using the compressible Navier-Stokes equations, while the IR signature was analyzed with the radiative heat transfer equation with a narrow band model. The RCS was calculated using a multi-level fast multipole method of full Maxwell's equations instead of the approximate methods often employed. The double serpentine (DS) nozzle with an elliptical cross-section showed high pressure recovery and a 9.66 % lower IR signature than the DS nozzle with a rectangular cross section. The maximum RCS and mean RCS were lowest for the DS nozzle with an elliptical cross section, with a maximum difference in maximum RCS of 383 % and mean RCS of 90 % compared with the DS nozzle with a rectangular cross section. The DS nozzle with an elliptical cross section distributes the current more evenly across the central part of the engine than the DS nozzle with a rectangular cross section. The DS nozzle with an elliptical cross-section showed excellent nozzle performance with a negligible difference in thrust. In addition, the results show that the cross-sectional shape of the nozzles has different levels of impact on thrust and pressure recovery (negligible), IR signature (limited), and RCS (significant).

Experimental investigation and numerical analysis on high-efficiency shock vectoring control serpentine nozzles

The high-efficiency Shock Vectoring Control Serpentine Nozzle (SVCSN) takes into account both thrust vectoring and infrared stealth, and significantly improves the comprehensive performance of the aero-engines through an additional auxiliary duct. In this paper, the schlieren photographs at the exit of the high-efficiency SVCSN and the wall static pressure distributions were obtained by experiments, and the numerical results were used to enrich the thrust vectoring characteristics. The effects of the auxiliary injection were analyzed first to reveal the advantages of the high-efficiency SVCSN compared to the conventional SVCSN. Then, the aerodynamic parameters and the structural parameters of the high-efficiency SVCSN were investigated, including the Nozzle Pressure Ratio (NPR), the Secondary flow Pressure Ratio (SPR), the secondary flow relative area and the secondary flow injection angle. Finally, the coupling performance of the high-efficiency SVCSN is studied by using the approximate modeling technology. Results show that the auxiliary injection increases the range between the two shock legs of the “λ” shock wave induced by the secondary flow, then causes the separation zone and high-pressure boss of the down wall to expand upstream, and finally results in a prominent increase in the thrust vectoring performance. The thrust vectoring angle and Vectoring Efficiency (VE) of the high-efficiency SVCSN are about 61.6% and 75.7%, respectively, higher than those of the conventional SVCSN at NPR = 6. The effects of the NPR and the SPR on the thrust vectoring performance of the high-efficiency SVCSN are coupled with each other. A larger NPR matched with a smaller SPR shows better thrust vectoring performance. The maximum fluctuations in thrust vectoring angle and VE caused by the NPR and SPR are about 22% and 64%. The VE decreases monotonously with the increase of the secondary flow relative area. Smaller secondary flow injection angle shows better thrust vector performance, and the thrust vectoring angle and VE of the secondary flow injection angle of 90° are about 20% higher than those of the secondary flow injection angle of 110° at NPR = 6. Therefore, the secondary flow relative area of 0.06 and the secondary flow injection angle of 90° are recommended.

Numerical investigation into the effects of aft deck angle on the flow characteristics of a serpentine nozzle

For modern military aero-engine, the serpentine nozzle with aft deck is deployed to meet the requirements of stealth and integrated design. Different from existing studies which emphasize the rectangular nozzles and corresponding infrared radiation impact, the effect of the aft deck angle on flow characteristics of serpentine nozzles with a focus on the internal flow, the shock system, the jet’s evolution, and the performance parameters are systematically investigated in this paper. This study is carried out through three-dimensional numerical simulations, which are validated by the experiment. The results show that the aft deck with different angles has a significant impact on the overall flow characteristics, such as the static pressure and the three-dimensional shock system, as a result of the asymmetry and the contraction/expansion effects on the jet. Specifically, upward-deflected aft decks lead to a re-compression effect and the variation of the internal static pressure value can be up to 7%, whereas for downward-deflected aft decks, the effect on the internal flow can be neglected in under-expansion conditions. In addition, the aft deck angle and the extent of boundary layer separation greatly affect the thrust performance and the vortex evolution, which determines the downstream evolution of the jet cross-section. Effective thrust coefficient is closely tied to the thrust vector angle, with the coefficient reaching its zenith when the thrust vector angle is closest to 0°. This study reinforces understanding of the interrelated problems and may facilitate the development of the optimal aft deck angle for various applications.

Influence of Double-Ducted Serpentine Nozzle Configurations on the Interaction Characteristics between the External and Nozzle Flow of Aircraft

To clarify the influence of the serpentine nozzle configurations on the flow characteristics and aerodynamic performance of aircraft, the flow features and aerodynamic performances of the double-ducted serpentine nozzles with different aspect ratios (AR), length–diameter ratios (LDR) and shielding ratios (SR) are numerically investigated. The results show that the asymmetric nozzle flow occurs due to the curved profile of serpentine nozzles, and a local accelerating effect exists at the S-bend, causing the increase in wall shear stress. The unilateral unsymmetrical expansion of the tail jet in the upward direction interacts with the separated external flow of the afterbody, forming an obvious cross-shock wave and shear layer structure. The surface pressure of the afterbody increases along the external flow direction, and decreases sharply in the separation point of the boundary layer. With the increase in AR and LDR, the local accelerating effect of the nozzle flow weakens, while with the increase in SR, the accelerating effect increases. The total pressure recovery coefficient, flow coefficient and axial thrust coefficient all decrease with the increase in AR, LDR, and SR. The thrust vector angle decreases with the increase in AR but is less affected by LDR and SR.

Experimental investigation on the effects of complex pressure gradients on the film cooling effectiveness of a serpentine nozzle

Serpentine nozzles more easily deform and damage due to high-temperature airflow because of their multi-bend channel configuration. Therefore, film cooling technologies should be applied to serpentine nozzles. Complex pressure gradients in serpentine nozzles lead to different film cooling characteristics from combustion chambers, turbine blades, and other exhaust systems. This study experimentally investigated the effects of complex pressure gradients and film hole inclination angles on a serpentine nozzle’s film cooling effectiveness (FCE) using pressure-sensitive paint (PSP). The flow mechanisms were obtained via numerical simulations. The experimental nozzle design needs to consider the needs of PSP observations and the normal flow of serpentine nozzles. However, the complex structure of serpentine nozzles makes those increasingly difficult. The studied pressure gradients include the pressure gradient mutation (PGM), strong adverse pressure gradient (SAPG), weak adverse pressure gradient (WAPG), and favorable pressure gradient (FPG). The results show that complex pressure gradients change the coolant coverage and adhesion and may induce a recirculation zone in the SAPG region. This affects the development of the vortex construction and leads to different FCE distributions. The FCE under the effects of the PGM is the largest, followed by the SAPG, WAPG, and FPG. A larger inclination angle weakens the coolant adhesion but may enhance its downstream and lateral flow treads. This is coupled with the effects of complex pressure gradients, where larger inclination angles bring better film cooling effects in some cases. After accounting for the four blowing ratios, the area-averaged FCEs under the effects of the SAPG, WAPG, and FPG are 28.9 %, 42.8 %, and 52.3 % lower than that under the PGM, respectively. The area-averaged FCEs under the conditions α = 45° and 60° are 6.6 % and 10 % lower than that under α = 30°.

Experimental Study on Infrared Radiation Characteristics and Matching Performance of Low-Observable Nozzles

Infrared stealth performance is one of the most crucial criteria for modern warplanes. The low-observable nozzle suppresses the infrared radiation by shielding the high-temperature engine components and enhancing the exhaust plume mixing with the atmosphere, thereby improving warplane survivability. Using a Fourier transform infrared spectrometer, the infrared radiation characteristics of two low-observable nozzles, including a two-dimensional nozzle and a serpentine nozzle, were measured in this paper. The nozzles were mounted on a micro-turbojet engine, and the variations of engine thrust, exhaust gas temperature, and fuel consumption rate were also measured to evaluate the matching performance of low-observable nozzles. The results show that the engine exhaust temperature rises after installing the low-observable nozzles. The two-dimensional nozzle has a maximum effect of 1.3% on the fuel consumption rate, and the serpentine nozzle has a maximum impact of 5%. The influence of low-observable nozzles on engine thrust is less than 1.9%. The infrared radiation intensity of the two-dimensional nozzle increases by 9% when the detection angle is 0° compared to the axisymmetric nozzle, while the serpentine nozzle decreases by 7%. When the detection angle is 90°, both low-observable nozzles achieve more than a 70% reduction in infrared radiation intensity.

Investigation on influence mechanism of length-to-diameter ratio on fluid-structure interaction characteristic of serpentine nozzle

Investigation on influence mechanism of length-to-diameter ratio on fluid-structure interaction characteristic of serpentine nozzle

Multi-objective optimization design of aerodynamic and infrared characteristics of multi-stream serpentine nozzle

A multi-objective optimization design of multi-stream serpentine nozzle was carried out to improve the aerodynamic performance and reduce the infrared radiation signal. A numerical simulation was carried out to investigate the effects of nozzle pressure ratio (NPR), Aspect ratio (AR) and Ratio of length and diameter (L/D). Computational fluid dynamics (CFD) simulation was employed to study the aerodynamic performance of the multi-stream serpentine nozzle, and the narrow-band method with discrete transfer method were used to calculate its infrared radiation intensity distribution characteristics. A 3-factor, 21-level orthogonal table was designed based on the orthogonal experimental method, and multi-stream serpentine nozzle with different geometrical parameter and operating conditions were designed to obtain the aerodynamic performance and infrared radiation intensity data of each experimental sample point. Radial Basis Function (RBF) neural network and Multi-Objective Particle Swarm Optimization algorithm were used to optimize the geometry and operating conditions with better aerodynamic performance and weaker infrared signal. The result shows that the Pareto solutions obtained by the optimization have good accuracy compared with the numerical simulation results, with an aerodynamic performance error of 0.02% and an infrared radiation intensity error of 0.24%.

Multi-Objective Bayesian Optimization Design of Elliptical Double Serpentine Nozzle

The use of traditional optimization methods in engineering design problems, specifically in aerodynamic and infrared stealth optimization for engine nozzles, requires a large number of objective function evaluations, therefore introducing a considerable challenge in terms of time constraints. In this paper, this limitation is addressed by using a sample-efficient multi-objective Bayesian optimization that takes Kriging as a surrogate model and Expected Hypervolume Improvement as the infill criterion. Using this approach, the probabilistic model is continuously established and updated, and the approximate Pareto front is obtained at a relatively small computational budget. The objective of this work is to evaluate the applicability of employing a multi-objective Bayesian optimization framework for the aerodynamic-infrared shape optimization of an elliptical double serpentine nozzle at 6 km flight condition, where the objective functions are evaluated by means of high-fidelity computational fluid dynamics and reversed Monte Carlo ray tracing simulations. We achieve good results in both infrared radiation signature reduction and aerodynamic performance improvement with a reasonable number of evaluations, indicating that the proposed method is effective and efficient for tackling the computationally intensive optimization challenges in the aircraft design.

Thermal–Solid Interaction Study of Serpentine Nozzle and Analysis on Structural Response Law

The serpentine nozzle effectively suppresses infrared radiation and radar signals from advanced aero-engine exhaust system. However, the extreme operating environment of thermal–solid interaction complicates the heat transfer of the flow inside the serpentine nozzle and the structural response of the nozzle itself. In this study, the internal flow heat transfer and the structural response of the serpentine nozzle were investigated numerically. Further, the parameter influence law of wall thickness was explored. The results show that the mechanism of the thermal-solid interaction is formed through the data transfer of the heat flux and the temperature at the interface between the flow field and structure field. The heat flux distribution of the nozzle under the bending configuration is non-uniform. The upper wall surface at the first bend and the lower wall surface at the second bend exhibit the highest heat flux. In the structural response, the temperature extremes appear on the upper wall at the first bend and the lower wall at the second bend. Subsequently, they shift to the inlet. The stress in the nozzle with a thickness of 3 mm first increases and then decreases, with a maximum stress of 139.43 MPa at t = 51.20 s. For nozzles of different thicknesses, the positions of the maximum stresses all appear at the outlet and the moments concentrate in approximately 50 s. However, with the increase in thickness, the maximum stress of nozzle increases continuously, and the maximum increases by 93% compared with the minimum.

Optimization and sensitivity analysis of double serpentine nozzles within confined layouts by response surface methodology

Optimization and sensitivity analysis of double serpentine nozzles within confined layouts by response surface methodology

Effect of inclination angle on the film cooling in a serpentine nozzle with strong adverse pressure gradient

The serpentine nozzle is widely used in military unmanned aerial vehicles to improve their viability. The film cooling technology should be used in the serpentine nozzle to cope with excessive thermal load. Strong adverse pressure gradient (APG) in the serpentine nozzle induces the recirculation zone near the upper wall downstream of the film hole, such that the effect of inclination angle on the film cooling characteristics is quite different from that in other studies. A numerical investigation was conducted to study the influence of the film hole inclination angle (α = 20°, 30°, 45°, 60°) on the film cooling characteristics in a serpentine nozzle with strong APG. Results show that the inclination angle changes the region of recirculation zone, then affects the development of counter rotating vortex pair and anti-counter rotating vortex pair (ACRVP), and finally results in different distributions of the film cooling effectiveness (FCE). For blowing ratio, M, = 0.5, 1, and 1.5, with the increase in the inclination angle, the recirculation zone expands, and the vorticity of the ACRVP increases. For M = 2, with the increase in the inclination angle, the recirculation zone first shrinks and then expands, and the vorticity of the ACRVP first decreases and then increases. Taking all the four blowing ratios into account, we find that the 30° inclination angle gives the best film cooling effect, and the area-average FCE under conditions α = 20°, α = 45°, and α = 60° is 7.5%, 5.6%, and 5.0%, respectively, lower than that under condition α = 30°. Therefore, the 30° inclination angle is the optimal choice for the film holes near the APG region of the serpentine nozzle.

The influence of the adverse pressure gradient on the flow characteristics of a serpentine nozzle with film cooling

With the increase of the turbine inlet temperature, the thermal load of serpentine nozzles increases greatly, leading to the stiffness degradation and structure deformation. Therefore, efficient cooling technologies are required. There are adverse pressure gradients (APGs) and strong swirl characteristics in the serpentine nozzle. Therefore, the film cooling design of serpentine nozzles faces greater difficulty than that of other exhaust systems. This paper aims to obtain the flow characteristics of serpentine nozzles with film cooling and to provide theoretical support for the film cooling design of serpentine nozzles. We obtained the influence of the APG and the favorable pressure gradient (FPG) on the flow characteristics of a serpentine nozzle with film cooling via the employment of numerical methods. The results show that the APG obstructs the flow of the cooling airflow, and causes a part of the cooling airflow to decelerate, to stagnate, and eventually to flow in the reverse direction, thus forming a recirculation zone. The counter rotating vortex pair (CRVP) induces the anti-counter rotating vortex pair (ACRVP) near the boundary layer of the wall, and the ACRVP develops rapidly in the recirculation zone. With the development of the ACRVP, the CRVP leaves the wall and gradually dissipates. As the blowing ratio increases, the recirculation zone moves downstream, and the recirculation zone first expands and then shrinks, such that the location where the ACRVP develops also moves downstream. There is no recirculation zone under the influence of the FPG, and the CRVP occupies the core of the cooling airflow along the flow direction.

Influences of geometric parameters on serpentine nozzles for turbofan

Serpentine nozzles possess excellent advantages in improving the stealth ability of aero-engine exhaust. For a real turbofan, the flow characteristics of the serpentine nozzle are evidently affected by the geometric parameters and the complex exhaust mixer. This is an issue that needs to be seriously considered. The aim of this paper is to investigate the influences of the critical geometric parameters on the serpentine nozzles for turbofan. The detailed flow field of the serpentine nozzle for a small-scale model is precisely measured. The influence of the ratio of axial length to inlet diameter on the flow field and on the aerodynamic performance of the serpentine nozzle is numerically explored. Results show that the pressure on the upper wall first drops rapidly and then ascends with the local minimum occurring at the first inflection. The relative error between the numerical prediction and the experimental data is less than 2%. The calculated distributions of the expansion-shock waves and the jet shear layers are highly consistent with the schlieren flow visualization data. Thus, the reliability of the numerical method is effectively confirmed. The internal flow and the external jet features of the serpentine nozzle are extremely non-uniform. Such poor uniformity is reflected in the phenomena including the existence of the local high-shear-stress regions and the high-velocity regions, the multiple bending of the limiting streamlines, as well as the velocity fluctuation of plume core. The aerodynamic performance of the serpentine nozzle first enhances greatly and then stays unchanged as the value of L/D rises. The vortex loss and the shock loss both reduce evidently owing to the flow separation and the disappearance of the shock wave during the rise of L/D from 2.2 to 2.4. The value of the discharge coefficient and the thrust coefficient increases by 1.5% and 2.1%, respectively. The length of the plume core is effectively shortened due to the disappearance of the shock wave inside the nozzle.

Optimization for aerodynamic performance of double serpentine nozzles with spanwise offsets using Taguchi-based CFD analysis

Serpentine nozzles are widely used in combat aircraft to realize strong stealth characteristics. Based on the layout characteristics within a confined space, a series of double serpentine nozzles with spanwise offsets are established. Using computational fluid dynamics and Taguchi method, the influence mechanisms of the Distribution of Area (DA), Distributions of Centerline for the first and second ‘S’ sections in the Vertical direction (DCV1 and DCV2), and Distribution of Centerline in the Spanwise direction (DCS) are analyzed. The impact of these factors on the total pressure recovery coefficient can be ranked as DA > DCV2 > DCS > DCV1, whereas their impacts on the discharge coefficient and axial thrust coefficient can be ranked as DCV2 > DCS > DA > DCV1. Considering the statistical significance of these factors, a nozzle in which DA changes rapidly at the exit and DCV1, DCV2, and DCS change rapidly at the entrance gives the best aerodynamic performance. Compared to the worst configuration, the total pressure recovery coefficient, discharge coefficient, and axial thrust coefficient are improved by 1.6%,3.5% and 3.6%, respectively. DA influences the gas flow acceleration in the entire serpentine channel, resulting in different wall shear stress and friction losses. The various centerline distributions influence the gas flow acceleration effects and form complex wave structures in the constant-area extension section, resulting in different local and friction losses.

Numerical Simulations on the Performance of Two-Dimensional Serpentine Nozzle: Effect of Cone Mixer Angle and Aft-Deck

The current study addresses the effect of different designs of the exhaust mixer and aft-deck on the performance of a two-dimensional convergent nozzle represented by the internal and external flows and heat transfer process. The effect of different exhaust mixer cone angles of 10°, 15°, and 20°, and different aft-deck lengths of 140 mm, 280 mm, and 420 mm on the nozzle performance was investigated. To address the effect of an aft-deck, the flow behavior of a nozzle with an aft-deck was compared to that of a nozzle without an aft-deck. Then, the effect of different aft-deck lengths and different aft-decks with rectangular and trapezoid shapes was investigated. The results demonstrated that increasing the mixer cone angle resulted in decreasing the high-temperature core flow and increasing the low-temperature bypass flow. Increasing the mixer cone angle resulted in reducing the velocity inside the nozzle and at the exhausted jet, which can reduce the noise generated by the engine. Furthermore, increasing the mixer cone angle decreased the internal temperature of the nozzle and, along with the exhausted jet, decreased the infrared radiation. The results also illustrated that the presence of the aft-deck resulted in decreasing the pressure, temperature, and velocity inside the nozzle. The aft-deck also decreased the length and size of the potential core. The aft-deck length had no clear effect on the internal flow. However, increasing the aft-deck length resulted in a decrease in the exhaust gas temperature, which can decrease the infrared radiation. On another hand, using trapezoid and triangle aft-deck can enhance the performance of the nozzle by decreasing the velocity and temperature inside the nozzle and at the exhausted jet.

Fluid-Structure Interaction Study of the Serpentine Nozzle for Turbofan

Serpentine nozzle can effectively suppress the infrared radiation signatures of the aero-engine exhaust system. However, it experiences the remarkable fluid-structure interaction (FSI) process at the work condition. In this paper, the deformation behavior of the serpentine nozzle and its flow characteristic were investigated numerically. Then, the influences of the wall thickness and the geometric configuration on the FSI effect were also explored. The results show that, the mechanism of the fluid-structure interaction is formed through the data transfer of the force and the displacement at the FSI interface. Under the FSI effect, there occur the ballon-like swellings at the second S passage, and the linear section bends upward along the Y direction. They induce the special flow features including the flow separation, the shock wave and the plume vector angle. As the value of the wall thickness increases from 3mm to 6mm, the maximum of the deformation displacement of the serpentine nozzle decreases 68.5mm. As compared to the uncoupled state, the variation of the axial thrust decreases from 2.70% to 0.70% at the coupled state. The circular-to-rectangular profile and the S-shaped passage enlarge the deformation behavior of the nozzle structure. The value of the axial thrust of the serpentine nozzle with 5mm wall thickness for the coupled state is lower 1.92% than these for the uncoupled state.

Investigation on the Film Cooling Characteristics of a Serpentine Nozzle Under the Influence of the Adverse Pressure Gradient

Investigation on the Film Cooling Characteristics of a Serpentine Nozzle Under the Influence of the Adverse Pressure Gradient

A computational study of two-dimensional serpentine nozzle performance with different annular mixer configurations

Serpentine nozzles are widely utilized in many types of military aircraft to maximize survivability due to their ability to suppress infrared radiation emitted from the engine exhaust system. An annular mixer is used in a serpentine nozzle to improve the performance of the nozzle by intensifying the mixing between the ambient air and exhausted gases. Therefore, this study aims to numerically investigate the performance of a two-dimensional single serpentine nozzle with different annular mixer configurations. The performance of the nozzle based on the internal flow behavior and the external jet of different models of an annular mixer is investigated. Herein, different models of annular mixers with different annular diameters of 320 and 340 mm, different annular lengths of 140 and 280 mm, and different mixer shapes are investigated. The simulations are conducted with a 3-dimensional model using commercial STAR CMM+ software. The results demonstrate that a smaller mixer diameter, indicating a higher bypass ratio nozzle, has a lower temperature inside the nozzle and at the external jet compared to a larger mixer diameter, indicating that a lower bypass ratio nozzle can improve the nozzle performance by reducing the infrared radiation. The smaller mixer length can decrease the temperature inside and outside the nozzle but increase the velocity outside the nozzle. Finally, the conical shape of the mixer can reduce the temperature inside the nozzle due to the reduction of the core flow rate but increases the temperature of the exhausted jet due to the lower expansion of flow inside the nozzle compared to the nozzle with a cylindrical shape. This study demonstrates that a mixer with a smaller diameter and shorter length with a cylindrical shape can provide better performance for a nozzle.

Experimental investigation of serpentine nozzles for turbofan

Serpentine nozzles are widely used in stealth bombers and unmanned aerial vehicles to significantly suppress the infrared radiation signatures and to acquire excellent stealth performance with the goal to improve the survivability on the battlefield. The flow characteristics of serpentine nozzles are complex and noticeably different from those of axisymmetric nozzles due to the geometric configuration. This paper aims to obtain the flow characteristics of both serpentine nozzles and axisymmetric nozzles and to compare them under various working conditions. We obtained the flow characteristics of serpentine nozzles and axisymmetric nozzles with the employment of a schlieren system, PSI electronic pressure scanning valves, a six-component force balance system and flowmeters. The results show that the static pressure distributions on the upper and down walls of serpentine nozzles are completely different from those of axisymmetric nozzles, which are mainly affected by the flow tube near the walls. The flow velocity increases and the static pressure drops when the flow tube contracts. The outcome is opposite once the flow tube expands. The nozzle configuration and the bypass flow pressure ratio have little influence on the schlieren photographs of the flow fields downstream of the nozzle exit, which are composed of expansion waves and shock waves alternately. The values of the flow coefficient and the thrust coefficient both decrease when the difference between the core flow pressure ratio and the bypass flow pressure ratio gets large. The configuration of the serpentine nozzle, especially the wall curvature, affects the values of its flow coefficient and thrust coefficient. The value of the flow coefficient for serpentine nozzle 2 is about 1.5% lower than that for serpentine nozzle 1, and the value of the thrust coefficient for serpentine nozzle 2 is about 0.5% lower than that for serpentine nozzle 1.