Jet Flow Field Research Articles

Numerical simulation of influence of jet flow parameters on cone-cylinder-flare configuration

Abstract Reaction control system technology is used to realize attitude control or trajectory change. The hot jet effect should be considered to get more accurate aerodynamic characteristics as the flight vehicle develops. The simulation for hot jet flow needs more calculation resources, so it is important to research the suitable similarity parameters of jet flow. Then, we can use cold jet flow to simulate hot jet flow. In this paper, the influence of jet flow parameters is numerically studied on cone-cylinder-flare configuration. The numerical simulation method for hot jet flow is established, containing finite volume method, multi-component three-dimensional Reynolds Navier-Stokes equation with source terms, multi-block patched grid technique, and fully implicit processing method. The numerical method is verified by using experimental reference results, and the grid independence is assured. The numerical results reveal that the cold jet flowfield under the same mass flow ratio is more similar to the hot jet flowfield than the cold jet flowfield under the total temperature of 293 K. The maximum amplification factor difference between cold and hot jet flow is reduced from 14.1% to 1.2%.

Numerical Study on the Operational Ventilation Patterns of Alternative Jet Fans in Curved Tunnels

In tunnel operation ventilation systems, the arrangement of jet fans plays a decisive role in ensuring ventilation efficiency. Curved tunnels, due to their unique radius of curvature, exhibit significant differences in fan installation parameters and jet flow field distribution compared to traditional straight-line tunnels. In order to investigate the distinct characteristics, this research utilized computational fluid dynamics (CFD) simulation methods to analyze the ventilation performance of both an innovative, adjustable jet fan system and conventional jet fans within the context of curved tunnel configurations. The findings reveal that by adjusting the horizontal deflection angle of the novel jet fan, the flow field distribution can be effectively optimized, and the jet effect can be enhanced, thereby improving ventilation efficiency. Compared to traditional jet fans, the novel fan demonstrates a significantly greater capability in flow field optimization, especially when its horizontal deflection angle is adjusted, showing a trend where the jet effect initially increases and then decreases, with the longitudinal impact range being adjustable within a range of 5 m to 25 m.

Optimization Study on Nozzle Selection Based on the Influence of Nozzle Parameters on Jet Flow Field Structure

Currently, the primary method for controlling red tides in the ocean involves spraying water solutions with special chemicals as solutes. High-pressure spraying results in the formation of typical jet structures. In this study, numerical simulation methods are employed to investigate the velocity variations, turbulent characteristics, and gas content distribution of jet flow fields under different initial jet flow pressures, cone angles, and nozzle diameters. Based on practical application scenarios, cluster analysis is used to explore the similarities and differences in jet equivalent diameters under different parameter conditions. The research findings indicate the following. (1) The difference of jet velocity distribution at the far field exit will be enlarged with the increase in the nozzle cone angle. When the nozzle cone angle is 4 mm, the velocity uniformity at the outlet is the best. (2) The TKE of the flow field has no consistent change law along the central axis. At the jet exit, the TKE shows an obvious multi-peak structure. (3) The gas content demonstrates a typical “double-valley” feature at the jet outlet cross-section. Increasing the initial pressure leads to a decrease in the gas content within the jet due to reduced entrainment, while the entrainment range remains largely constant. (4) Cluster analysis reveals that the similarity of jet flow width when it reaches the water surface is minimal compared to other operating conditions when the initial pressure is 0.36 MPa, the cone angle is 115°, and the nozzle diameter is 2 mm. All conditions can be categorized into two or three groups to ensure jet effectiveness. The study results provide scientific guidance for selecting spray devices for controlling red tides in the ocean.

Research on the jet active control mechanism of gas-liquid separation in helical-axial multiphase pumps

In the field of deep-water oil and gas extraction, the intermittent gas blocking phenomenon in helical-axial multiphase pumps leads to decreased pump performance and reliability, severely limiting their large-scale application and promotion in engineering projects. To address this challenge, this study is based on the principle of jet flow field control to flow separation, utilizing external energy for active intervention to suppress the separation phenomena and improve the hydraulic efficiency within the impeller flow channel. The research reveals that the jets achieved a reconstruction of the internal flow in the helical-axial gas-liquid mixed transport pumps. Using orthogonal experimental methods, a preliminary predictive analysis of the factors influencing the effectiveness of the jet system was conducted. The study explored the impact of jet parameters on enhancing the performance of helical-axial gas-liquid mixed transport pumps from the perspective of diminishing gas aggregation at the trailing edge of the rotor cascade and curtailing backflow conditions, and established a mathematical model for the head and efficiency of helical-axial multiphase pumps under jet active control. Research indicates that the jet velocity significantly impacts the efficiency enhancement of multiphase pumps, with an optimal jet speed coefficient, Cjet = 10, identified. Beyond this speed, the benefits brought by increased jet velocity do not compensate for the costs of introducing high-speed jets, and instead, may lead to a reduction in the efficiency of the pump. Jet flow field control methods alleviate the suction side gas aggregation downstream of the jet holes and in the flow domain traversed by the jets, effectively reducing the aggregation of gas phases in the rear channel of the rotor and suppressing backflow near the trailing edge of the rotor cascade. Jet control measures strengthen the working capacity of the blade in the flow direction beyond 0.35 times the length of the streamline, expanding the working range of the blade and enhancing the work efficiency of the multiphase mixed transport pump. Higher jet velocities result in more significant enhancements of blade working power, especially under conditions of high initial gas content, where the relative increase in blade load is more pronounced.

Simulation of flow field based on constrained fluid for electrolyte jet control

In previous studies, jets were controlled by adjusting parameters such as velocity, pressure, size and shape of nozzle, and temperature. In this study, a new method of controlling electrolyte jets was proposed by introducing a constrained fluid. To analyze the effects of the constrained fluid on the jet flow field, the initial jet velocity and velocity ratio of the flow field were examined. Simulation results showed that the proposed method can avoid stray deposition caused when the electrolyte is spread on the substrate surface. The electrolyte jet could be controlled by the constrained fluid, indicating the characteristic of cyclical fluctuation. The initial jet velocity and velocity ratio had different impacts on the flow field; the former mainly affected the velocity and pressure distribution. The relationship between the velocity of flow field and initial jet velocity was observed to be linear. However, the relationship between pressure of the flow field and initial jet velocity was quadratic. The velocity ratio had a significant impact on the state of electrolyte jet. At low initial jet velocities, the electrolyte jet was not continuous at different velocity ratios. When the initial jet velocity increased, cyclical fluctuations in the electrolyte jet weakened under high velocity ratios. The electrolyte jet diameter also decreased linearly as the velocity ratio increased. The velocity and pressure of the flow field were quadratically related to the velocity ratio. This indicates that the constrained fluid had a considerable impact on the flow field and state of the electrolyte jet. Moreover, the electrolyte jet could be controlled effectively by adjusting the initial jet velocity and velocity ratio to obtain a stable and small electrolyte jet diameter.

Numerical Simulation and Flow Field Analysis of Porous Water Jet Nozzle Based on Fluent

The water jet nozzle is a penetrating drilling tool, which sends the pumped water to the nozzle through a high-pressure hose. It can work in a variety of working environments. When it dredges the blockage in the pipeline, its structural parameters will affect the jet flow field in the pipeline. Taking the self-propelled water jet nozzle as the research object, SolidWorks was used to establish the nozzle model with different parameter structures. Based on Fluent, the k-ε turbulence model was used to simulate the jet of nozzles with different nozzle sizes and arrangements in the pipeline. The distribution of the jet flow field and the change in velocity and displacement of nozzles with different parameters in the pipeline were compared, and then computational fluid dynamics (CFD) were used to process the simulation data for further research. The results show that when the inclination angle of the rear nozzle is 35°, the attenuation of the front jet velocity and the fluctuation of the wall fluid velocity are the smallest. When the nozzle aperture is increased from 2 mm to 3.5 mm, the vortex area inside the pipe is reduced, and the velocity attenuation of the front jet is also reduced, with the velocity attenuation rate decreasing by about 10%. This study provides a reference for the design and parameter optimization of self-propelled water jet nozzles.

Study on the Influence of High-Altitude Helical Tunnel Curvature on Jet Fan Spatial Layout

During the operational ventilation process of high-altitude helical tunnels, the installation method of jet fans is a key factor in determining the ventilation efficiency of the tunnel. In this study, the CFD numerical simulation method is adopted to establish three-dimensional ventilation models of helical tunnels with different curvature radii. Through orthogonal experiments, the effects of tunnel curvature radius on the characteristics of the air jet flow field, under the coupled influences of factors such as lateral spacing of jet fans, vertical height of fans, longitudinal spacing, and lateral offset, are investigated. The results show that when R = 500 m, 600 m, 700 m, and 800 m, the longitudinal spacing has the most significant impact on ventilation efficiency, followed by vertical height, with lateral offset and fan spacing having the least impact. The optimal spacing and vertical height of the fan groups remain consistent under different curvature radii, at 1.25D (fan diameter) and 15 cm, respectively. The optimal longitudinal spacing of the fan groups is 90 m, 90 m, 135 m, and 90 m, respectively. Shifting the fan groups 0.25 to 0.75 m towards the inner side of the tunnel helix (for R < 700 m) can optimize the flow field distribution within the tunnel. Finally, expressions for the relationship between the helical radius and the lateral offset and longitudinal spacing of the fan groups are established for the optimal installation parameters of fan spatial positions under different helical tunnel radii.

Surrogate multi-objective optimization of missile RCS performance in hypersonic rarefied flow of the near space

This study focuses on optimizing the lateral jet efficiency of THAAD-like (Terminal High Altitude Area Defense) missiles operating under hypersonic rarefied flow conditions. We employ the DSMC-QK algorithm to simulate the three-dimensional lateral jet flow field, accounting for thermochemical non-equilibrium effects. The analysis investigates how the force/momentum amplification coefficient varies with the angle of attack, jet pressure ratio, jet Mach number, and jet gas composition. Subsequently, we develop an artificial neural network (ANN) proxy model using the pyrenn toolbox, achieving an average prediction error of 0.866% and a maximum error of 1.60%. Utilizing this ANN model, we perform single- and multi-objective optimizations with a genetic algorithm to determine the optimal jet parameters. The results reveal that in multi-objective optimization, the proportion of helium in the jet gas composition increases, leading to a slight reduction in the force amplification coefficient but a substantial 61.4% decrease in the mass flow rate. This demonstrates that a judicious selection of jet gas composition can significantly reduce mass flow while maintaining high jet efficiency, thus achieving efficient lateral jet control.

Contrail Polarization Scattering Characteristics Simulation Based on Jet Flow Field

Contrail Polarization Scattering Characteristics Simulation Based on Jet Flow Field

Numerical prediction of mean flow and acoustic field of a supersonic impinging jet

The three-dimensional turbulent mean flow and acoustic field of a supersonic jet impinging on a solid plate is studied computationally using the general purpose CFD code Ansys Fluent. A pressure-based coupled solver formulation with the second order weighted central-upwind spatial discretization is applied to compute transient solutions. Cold and hot jet thermal conditions are considered. Mean flow characteristics are investigated by a steady-state modeling approach. Acoustic radiation of impingement tones is simulated using a transient time-domain formulation. The effects of turbulence in steady-state are modeled by the SST k-ω turbulence model. The Wall-Modeled Large-Eddy Simulation (WMLES) model is applied to compute transient solutions. The near-wall mesh on the impingement plate is fine enough to resolve the viscosity-affected near-wall region all the way to the laminar sublayer. Nozzle-to-plate distance is parameterized in the model for automatic re-generation of the mesh and results. Steady-state predictions of hover lift loss and mean jet velocity distributions are compared with experimental data, and favorable agreement is reported. The transient solution reproduces the mechanism of impingement tone generation by the interaction of large scale vortical structures with the impingement plate. The acoustic near-field is directly resolved by Computational Aeroacoustics (CAA) to accurately propagate impingement tone waves to near-field microphone locations. Calculated impingement tone frequencies and sound pressure levels agree with experimental values.

Experimental study on the coupled flow field and thrust characteristics of tail cavity and jet

During the launch process of underwater vehicles, a tail cavity is formed at the bottom, which plays a crucial role in the engine ignition stage. The flow state within this tail cavity significantly impacts the engine's operational efficiency. Moreover, the evolution of the tail cavity and jet coupling, along with hydrodynamic characteristics, influences the motion attitude of the vehicle. This article delves into the effects of initial tail cavity length, Froude number, and pressure ratio on cavity morphology and hydrodynamic characteristics, utilizing water tunnel experiments to explore these dynamics at the vehicle's bottom. The experimental findings suggest that while the length of the initial tail cavity influences the jet's coupling mode, it does not significantly affect the cavity's ultimate morphological evolution. A larger initial cavity scale correlates with a lower initial pressure peak following nozzle activation; similarly, an increase in the Froude number leads to a decrease in the initial pressure peak. When the cavity morphology remains intact, the pressure pulsation amplitude and frequency are relatively low. In contrast, partially broken cavities and pulsating foam cavities differ in morphological structure and peak internal pressure oscillations, though their pressure pulsation frequencies are similar. During the initial phase of nozzle activation, the thrust produced by the nozzle plays a more significant role than the bottom thrust. Notably, in the initial phase of nozzle activation, the nozzle-generated thrust is more influential than the bottom thrust. The thrust pulsations from pulsating foam cavities are especially strong, with peak values surpassing the initial peak thrust. These insights offer a new insight on the dynamic behavior of underwater vehicles, crucial for refining engine startup strategies.

Experimental study on control of transverse jet mixing by arrayed plasma energy deposition

The efficient and prompt mixing of fuel is crucial in the operation of scramjet engines. This paper presents the findings from wind tunnel experiments that examined the influence of plasma energy deposition on transverse jets at a Mach number of 6.13. The study took into account various inlet flow total pressures and momentum flux ratios between the jet and the main flow. Utilizing a database containing time-resolved intensities from instantaneous schlieren images, we perform turbulence analysis employing various techniques such as the root mean square, fast Fourier transform, proper orthogonal decomposition, and the two-point correlation method. Specifically, we aim to compare and analyze the pulsation characteristics and spatial self-organization of the jet flow field, both with and without energy deposition control. The findings reveal that intermittent “hot bubbles” created by plasma energy deposition interact with the bow shock induced by the jet, resulting in the formation of an array of large-scale vortices. These vortices emerge as the dominant structures within the jet, effectively amplifying its pulsations. At low inlet flow pressures, energy deposition primarily disrupts the jet, causing large-scale vortices to propagate primarily within the jet plume region. However, at high inlet flow pressures, the impact of energy deposition extends to both the jet and the turbulent boundary layer, encompassing their respective disturbance ranges. Increasing the inlet flow pressure constraints the evolution of large-scale vortices, thus limiting the efficacy of energy deposition in governing the mixing process.

The influence of pulse frequency on the energy evolution law and rock-breaking effect of pulsed abrasive water jet

Compared to continuous abrasive jet and high-pressure water jet, pulsed abrasive water jet can intermittently generate high water hammer pressure and is commonly used in applications such as coal mining and petroleum engineering for rock-breaking purposes. Pulse frequency is one of the key factors affecting the evolution of abrasive acceleration and jet impact energy, thereby influencing the system's energy transfer efficiency and cutting ability. The equation of motion for abrasive acceleration is established based on the two-phase flow theory, and the variation law of abrasive velocity with pulse frequency is solved. Fluent-EDEM (Extended Discrete Element Method) was used to simulate the abrasive water jet flow field structure and abrasive acceleration process under different pulse frequency conditions, and the intrinsic influence mechanism of pulse frequency on impact energy was clarified. Combined with rock-breaking experiments using pulsed abrasive water jets, the following conclusions are drawn: as the pulse frequency increases, the inertia of the abrasive makes it unable to respond in a timely manner to the high pulsation frequency of water, resulting in a reduction in the exchange rate of intermittent energy and a gradual decrease in the maximum velocity of the abrasive. This trend is more pronounced at a higher pulse frequency. Within the same time period, the cumulative impact energy of the pulsed abrasive water jet decreases first and then increases with the increase in pulse frequency, indicating the existence of an optimal impact frequency that maximizes the cumulative impact energy of the pulsed abrasive water jet. Under fixed jet pressure conditions and the same erosion time, the pulsed abrasive water jet with a frequency of 30 Hz exhibits the best rock-breaking capability.

Numerical simulation of the underwater gun using gas-curtain launch

A novel gas-curtain launch technique is proposed to enhance the interior ballistic performance for underwater guns. The size of the initial gas curtain in front of the projectile is a critical factor in determining the subsequent behavior of the gunpowder gas jet flow field once the projectile leaves the muzzle. Hence, a validated two-dimensional unsteady multiphase model is built for the flow field at the muzzle of an underwater gas-curtain launch. The calculation involves determining the development of the initial gas curtain sizes for a 30 mm underwater gun, specifically focusing on the evolution of the precursor jet and gunpowder gas jet flow field. The results indicate that a double three-wave point structure forms within the bottle-shaped shock wave structure of the precursor jet when the initial gas curtain length equals the barrel. As the initial gas curtain size increases, the “bottle” structure elongates along the axial direction and compresses radially. After the projectile exits the muzzle, the gunpowder gas quickly expands toward the front, causing the collapse of the Mach disk of the precursor jet. The gunpowder gas jet then reforms a new bottle-shaped shock wave structure. A larger initial gas curtain can facilitate the expansion of the gunpowder gas, resulting in an increased size of the bottle, delayed formation, and weakened intensity of the Mach disk. Additionally, increasing the size of the initial gas curtain decreases the resistance experienced by the projectile outside the barrel. The initial gas curtain can also affect the cavitation bubble evolution process on the projectile sidewall, showing a growth-(attenuation)-stability trend.

Numerical study on transport and deposition characteristics of particles associated with heat setting process in opposed jet flow field

The transport and deposition of particles accompanying the heat setting process in the opposed jet air supply system have a significant impact on the equipment safety. This paper used the Realizable k–ε model to simulate the flow field distribution of the impinging jet and the Lagrange method to track the trajectory of particles, by considering factors, such as jet velocity (7–13 m/s), oven temperature (413–473 K), and particle size (1–30 μ m ) changes, the instantaneous force process of particles was analyzed and their deposition mechanism was revealed. The numerical results have been well validated, with the root mean square error of within 10%. The results indicate that the flow field form of the opposed jet significantly affects particle placement on the surface of the air duct, the maximum turbulent vortex structure appears at the inlet of the air duct on both sides of the protruding nozzle, enhancing the capture of particles. Under the influence of gravity, the lower surface of the air duct becomes the main deposition surface, this phenomenon becomes more pronounced as the particle size increases and the maximum deposition rate difference between the upper and lower layers is 37%. The number of particles deposited on the rear end of the air duct is greater than that on the front end, and the deposition rate decreases with the increase in jet velocity. In the initial stage, a temperature gradient appeared in the machine room, which provided upward lift for the particles, resulting in more small diameter particles ( d p < 10 μ m ) depositing on the upper surface of the air duct. The results can provide theoretical support for the fire prevention and pollutant purification of equipment, such as heat setting machines.

Progress of air flow field and fiber motion analysis in textile manufacturing process: a review

The control of air flow fields generated in the textile manufacturing process is important to fiber motion. With the expansion of textile applications and the challenges brought by carbon emissions, a series of fundamental research has been conducted on the control of various forms of air flow fields in textile processes. This paper reviews the research on air flow fields and fiber motion in textile processes over the past few decades, focusing on both experimental and numerical studies. The air flow field characteristics, fiber motion patterns, and corresponding control methods for vortex, jet and shear flow fields in the textile process are summarized. The results show that the air flow field and fiber motion are major factors affecting textile structure. These fundamental studies are of great significance in improving product quality, reducing energy consumption, and exploring novel applications.

Nonlinear modeling and parameter optimization of the pilot stage applied to the deflector-jet servovalve

Due to its good anti-pollution performance and high reliability, the deflector-jet servovalve is widely used in aerospace engineering. However, because the jet effects such as boundary expansion and adsorption are neglected, the model of the pilot stage applied to the deflector-jet servovalve is inaccurate, making it difficult to simulate the performance and optimize the parameters of the deflector-jet servovalve based on the model. Based on the structure of the jet flow field and the hydraulic resistance network bridge, an accurate nonlinear mathematical model of the pilot stage applied to the deflector-jet servovalve was developed, which considers the influence of the jet effect. Based on the new mathematical model, the structural parameters of the pilot stage were optimized with the maximum pressure, maximum flow, and maximum transmission power as the optimization objectives, respectively. Then the design criteria of the structural parameters were given based on the parameter optimization. Finally, the accuracy of the model was verified by three experiments. The comparison between experiments and this new model showed the maximum relative error of the flow between the model and experiment to be about 8.09%, which is more accurate than the traditional models.

Insights into unique in-situ self-adaptive sealing property of pressure-activated sealant in leaks: Experimental and numerical investigations on mechanism of liquid-to-solid transformation triggered by differential pressure

Pressure activated sealant (PAS) has been proven safety and efficiency for quick leak repairs in oil & gas production, due to the unique in-situ self-adaptive sealing property. However, its sealing mechanim of the liquid-to-solid transformation under leak pressures remains poorly understood to date. Elucidating the sealing mechanism of PAS is critical for designing and developing a new generation of wellbore sealing repair technology. In the present work, we conducted a pioneering investigtion that integrated experimental techniques with numerical simulations, to systematically explore the in-situ self-adaptive sealing performance of PAS in leaks. Firstly, latex deposition experiments were carried out to fabricate PAS from carboxylated acrylonitrile butadiene rubber latex (XNBRL), and then the physicochemical features of the XNBRL-based PAS, including chemical composition and microsctructure, were typically characterized using FTIR and SEM techniques. Subsequently, the micro-leak sealing capability of XNBRL-based PAS was evaluated under 20 MPa. The results showed that the fabriacted PAS is a type of multiphase fluid, wherein disperse phase are of regular spherical shape with an average size of 239.75 μm. The disperse phase are essentially compound droplets with material interfaces, exhibiting unique interfacial mechnical and chemical properties in the surrounding flow. PAS demonstrated excellent pressure-activated sealing performance towards crack and screw leaks, and solid barriers can be rapidly formed to fill micro-leaks in 500s under 16 MPa. Considering the microstructural and dynamic features of compound droplets, a mechanical-chemical coupling model was proposed to explain the activation and agglomeration process of liquid sealant at leak. In the jet flow field caused by differential pressures, the self-adaptive sealing process of PAS consists of four stages: (1) the impact deformation of compound droplets in jet flow, (2) compound droplets activated by breakup of hydrated membrane, (3) adhesion and agglomeration of activated compound droplets, and (4) self-adaptive solidification of deformed drolpets to fill and block leakages. Finally, three-dimensional (3D) numerical simulations were empolyed to investigate dynamic deformation of compound droplet in the pressure differential flow, to rationalize liquid-to-solid transformation of PAS. The numerical results showed that dynamic motion of compound droplet in jet flow field includes deformation of compound droplet, breakup of outer hydrated membrane, and collision of inner polymer core with wall. The hydrated membrane completely breaks up into ligaments in 0.8 ms, facilitating exposure of activated inner core and enables further chemical agglomeration, which agrees generally well with the experimental and model analyses.

Flow characteristics of two-dimensional impinging synthetic jets

We aimed to elucidate the behavior of impinging synthetic jets against the surface of a wall placed near the slot exit. Synthetic jets with various frequencies were used, and a rectangular body of finite length (target plate) was placed downstream of these jets. The flows were visualized by the smoke-wire method and numerical simulation, and the velocity distributions around the target plate were measured using a hot-wire anemometer. The flow fields of steady continuous jets and synthetic jets with unsteady characteristics were compared, and their flow characteristics were explored. We experimentally found that the flow field depends on the dimensionless target plate length and dimensionless frequency of the synthetic jet for a fixed distance from the slot to the target plate. Furthermore, at low frequencies, the behavior after impinging the target plate was similar to that observed for a continuous jet. Additionally, it has been confirmed that these results qualitatively agree with the numerical simulation results.

Sınırlandırılmış Çarpan İkiz Jetlerin Akış Yapısı ve Isı Transferi Karakteristikleri Üzerine Bir İnceleme

An investigation into the heat transfer performance and flow characteristics of circular twin jets was conducted using both numerical and experimental methods. The jets emanated from the lower surface and were confined to impinge perpendicularly on the upper surface. To simulate the bidimensional impinging twin jet flow field with powerful turbulence and heat transfer, Realizable k-ε and Standard k-ω turbulence models were employed. Reynolds numbers ranging from 30000 to 50000 were used in both simulations and experiments, with jet-to-jet spacing ranging from 0.5 to 2 and nozzles to target impingement plate spacing in the same range. Sub-atmospheric pressure regions were detected on the impingement surface in experimental measurements for spacing up to 1, whereas numerical results suggested that they could be found at all nozzle to target impingement plate spacings studied. A correlation was discovered between the peaks in coefficients of heat transfer on the target surface and the sub-atmospheric regions in pressure distributions.