Comparison of the efficiencies of spike and combined annular nozzles

The comparative efficiency of two layouts of self-adjusted annular nozzles operating over a wide flight altitude range is studied. One of the layouts is presented by the so-called spike nozzles (plane or antisymmetric, with a central body) having the property of self-adjustment when operating in different regions of the flight trajectory. The possibility of locating an annular plug nozzle or a conventional round nozzle in the base region of an axisymmetric spike is considered as a possible means for reducing its base losses. Two layouts of annular self-adjusted nozzles (in combination with internal nozzles or without them) are optimized for the mean thrust in operation in the launch and altitude flight regimes using the “classical” and “genetic” approaches. It is shown that optimal annular spike nozzles in combination with internal nozzles do not provide considerable advantages in the thrust compared with purely spiked optimal configurations. At the same time, an effective optimization of spike nozzles with account for the contribution made by the base thrust can ensure a comparatively low level of the losses.     

Contouring spike nozzles and determining the optimal direction of their primary flows

Problems related with the optimal contouring of two-dimensional and axisymmetric spike nozzles providing maximum thrust for given dimensions and external pressure are studied. The nozzles under consideration are self-adjustable which is ensured by the non-zero inclination of their primary supersonic flow to the plane (axis) of symmetry. Along with the optimal contouring of the spike, the optimal orientation of the “primary” nozzle producing the primary flow is obtained. In the exact formulation, its optimal inclination is determined by an exhaustive search for the configurations providing maximum thrust for a given spike length and various fixed inclinations of the primary nozzle. The spike and primary nozzle contours of these configurations are generally joined through a bend with the formation of an expansion fan in the flow around the bend. The efficiency of a simpler approximate method for contouring the spike and determining a near-optimal inclination of the primary nozzle is demonstrated. The method is based on passage to a modified formulation of the problem differing from the original one in that it is only the part of the spike extending beyond the primary nozzle edge that is preassigned rather than its entire length. In the modified formulation, there is no a bend in the flow around which an expansion fan could be formed, while the inclination of the primary nozzle is determined in the process of designing the unique optimal configuration.     

Calculating the Thrust Characteristics of Nozzles from Their Outlet Cross-Section Parameters

Within the framework of boundary-layer theory, simple formulas are presented for finding the viscous loss from the gas parameters in the nozzle outlet cross-section. The analysis is performed for ordinary Laval nozzles and spike nozzles. It is found that for nozzles with large expansion ratios the viscous loss is almost independent of the outlet cross-section parameters and is determined only by the parameter values on the nozzle contour. The effect of the longitudinal nozzle curvature on this loss is investigated. It is shown that the viscous losses calculated from the nozzle outlet parameters and by integrating along the nozzle contour with account for the longitudinal curvature fully coincide.     

On profiling supersonic nozzles to achieve uniform flow in the annular exit section

The problem of profiling supersonic nozzles with a central body in order to achieve uniform supersonic flow with Mach number M _e >1 in the annular exit section is studied. Equal lengths of the profiled inner (central body) and outer nozzle walls can be achieved by displacing downstream the initial bend in the inner contour, i.e., in the central body wall. A displacement of this kind was proposed and tested in [1, 2] for annular nozzles with circular exit sections.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 204–206, March–April, 1995.     

Numerical Investigation of the Flows in Cumulative Short-Plug Nozzles within the Framework of the Reynolds Equations

Numerical simulation is used to study the gasdynamics of annular cumulative nozzles. The class of nozzles considered includes those with a flat-ended plug and plugs of different length. The thrust performance of cumulative nozzles is determined over wide ranges of the nozzle pressure ratio and the specific heat ratio and the ranges on which the self-adjustment effect takes place are established. It is found that for low nozzle pressure ratios the cumulative nozzle with a flat-ended plug provides greater thrust than a finite-length plug nozzle optimal for operation in a vacuum.     

Contouring optimal three-dimensional nozzles

The contouring of near-optimal three-dimensional nozzles with subsonic flow regions is considered with reference to certain examples. The contouring is carried out in accordance with the earlier-developed direct optimization technique using the approximation of the surfaces of the objects under consideration by the Bernstein-Bézier polynomials and tested against both the solution of the optimization problem for the supersonic region of an axisymmetric convergent-divergent nozzle and the problem of contouring the supersonic region of a nozzle from the dense multi-nozzle maximum-thrust nozzle cluster. The problems of contouring three-dimensional transonic nozzles of an infrared stealth engine and the three-dimensional nozzle of a high-velocity ramjet are considered. The transonic nozzle optimization is realized within the framework of the Reynolds equations. A modified technique for describing the geometry under consideration using the inhomogeneous Bernstein-Bézier surfaces is proposed to more completely describe the set of the possible shapes.     

采用NND方法计算三维喷管气流场

本文运用NND显式差分格式,计算了三维喷管气流场。气流场计算的基本方程为一般贴体坐标系下三维守恒型的欧拉方程。采用了时间分裂法和Steger-Warming矢通量分裂技术。在喷管内沿周向的每个由轴线和壁面构成的子午面上根据泊松方程生成贴体网格。本文运用三维程序计算了轴对称JPL喷管,同时与实验结果和前人采用轴对称二维程序所计算的结果做了对比。最后,本文还计算了三维矢量喷管,计算结果与现有的实验结果一致。通过轴对称JPL喷管和三维矢量喷管的计算考核,表明建立的算法和编写的计算程序是正确的。文中提出了采用子午面形式的贴体网格时奇性轴的处理方法。计算结果表明在喷管壁面处,马赫数与压强的计算结果与实验值吻合较好,而在喷管轴线处,只有当网格较密时,才能得出与实验结果接近的计算结果。     

Liquid flow in a simplex swirl nozzle

Pressure-swirl nozzles are widely used in applications such as combustion, painting, air-conditioning, and fire suppression. Understanding the effects of nozzle geometry and inlet flow conditions on liquid film thickness, discharge coefficient and spray angle is very important in nozzle design. The nozzle-internal flow is two-phase with a secondary flow which makes its detailed analysis rather complex. In the current work, the flow field inside a pressure-swirl nozzle is studied theoretically. Using the integral momentum method, the growth of the boundary layer from the nozzle entry to the orifice exit is investigated and the velocity through the boundary layer and the main body of the swirling liquid is calculated. A numerical modeling and a series of experiments have also been performed to validate the theoretical results. The effect of various geometrical parameters is studied and results are compared for viscous and inviscid cases. In addition, the condition in which the centrifugal force of the swirling flow overcomes the viscous force and induces an air core is predicted. The theoretical analysis discussed in this paper provides better criteria for the design and the performance analysis of nozzles.     

A gas jet superposition model for CFD modeling of group-hole nozzle sprays

In the present study, a jet superposition modeling approach is explored to model group-hole nozzle sprays, in which multiple spray jets interact with each other. An equation to estimate the merged jet velocity from each of the individual jets was derived based on momentum conservation for equivalent gas jets. Diverging and converging group-hole nozzles were also considered. The model was implemented as a sub-grid-scale submodel in a Lagrangian Drop–Eulerian Gas CFD model for spray predictions. Spray tip penetration predicted using the present superposition model was validated against experimental results for parallel, diverging and converging group-hole nozzles as a function of the angle between the two holes at various injection and ambient pressures. The results show that spray tip penetration decreases as the group hole diverging or converging angle increases. However, the spray penetration of the converging group-hole nozzle arrangement is more sensitive to the angle between the two holes compared to diverging nozzle because the radial momentum component is converted to axial momentum during the jet–jet impingement process in the converging group-hole nozzle case. The modeling results also indicate that for converging group-hole nozzles the merged sprays become ellipsoidal in cross-section far downstream of the nozzle exit with larger converging angles, indicating increased air entrainment.     

Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

Origin of flow asymmetry in planar nozzles with separation

An experimental investigation was conducted to study the mechanisms that lead to the origin of flow asymmetry in overexpanded planar nozzles, especially at low nozzle pressure ratios. Three Mach 2 planar nozzles with different divergent wall angles but same area-ratio were tested. For all three nozzles, a large portion of the dimensional pressure rise data across the separation shock shows the nature of boundary layer to be in the laminar/transitional state. Depending upon the local flow conditions, the flow can, therefore, experience either an early or a delayed separation on either wall. This can result in a free or a restricted shock separation condition on either wall which can initiate the beginning of flow asymmetry in nozzles at low nozzle pressure ratio. However, a higher nozzle wall angle was observed to prevent initiation of such a flow asymmetry. The present tests, therefore, indicate that in addition to the state of the boundary layer along the nozzle wall, the proximity of the separated shear layer to the nozzle walls also seems to play a dominant role in initiating conditions that favor the origin of flow asymmetry in nozzles. A significant drop in the shock unsteadiness levels was also indicated by increasing the wall angle.     

Experimental study of heat transfer characteristics due to confined impinging two-dimensional jets

Experimental results are presented for characteristics of impingement heat transfer caused by three slot jets. Experimental values were obtained for the dimensionless distance H = 0.5−3, dimensionless pitch P = 6−16, and Reynolds number Re = 500−8000. For laminar impinging flow, they were compared with numerical results. For turbulent impinging flow, two peaks of the local Nusselt number were obtained behind the second nozzle. The position of the second peak approached the nozzle as the space between nozzle and impinged surface decreased. The average Nusselt number between the central and second nozzles was determined from the ratio P/H and the Reynolds number based on the pitch of the nozzles.     

The effect of nozzle layout on droplet ejection of a piezo-electrically actuated micro-atomizer

We study here effects of nozzle layout on the droplet ejection of a micro atomizer, which was fabricated with the arrayed nozzles by the MEMS technology and actuated by a piezoelectric disc. A theoretical model was first built for this piezoelectric-liquid-structure coupling system to characterize the acoustic wave propagation in the liquid chamber, which determined the droplet formation out of nozzles. The modal analysis was carried out numerically to predict resonant frequencies and simulate the corresponding pressure wave field. By comparing the amplitude contours of pressure wave on the liquid-solid interface at nozzle inlets with the designed nozzle layout, behaviors of the device under different vibration modes can be predicted. Experimentally, an impedance analyzer was used to measure the resonant frequencies of the system. Three types of atomizers with different nozzle layouts were fabricated for measuring the effect of nozzle distribution on the ejection performance. The visualization experiment of droplet generation was carried out and volume flow rates of these devices were measured. The good agreement between the experiment and the prediction proved that only the increase of nozzles may not enhance the droplet generation and a design of nozzle distribution from a viewpoint of frequency is necessary for a resonant related atomizer. The project supported by the National Natural Science Foundation of China (50405001).     

Laval nozzle flow calculation

The inverse problem of the theory of the Laval nozzle is considered, which leads to the Cauchy problem for the gasdynamic equations; the streamlines and the flow parameters are found from the known velocity distribution on the axis of symmetry.The inverse problem of Laval nozzle theory was considered in 1908 by Meyer [1], who expanded the velocity potential into a series in powers of the Cartesian coordinates and constructed the subsonic and supersonic solutions in the vicinity of the center of the nozzle. Taylor [2] used a similar method to construct a flowfield which is subsonic but has local supersonic zones in the vicinity of the minimal section. Frankl [3] and Fal'kovich [4] studied the flow in the vicinity of the nozzle center in the hodograph plane. Their solution, just as the Meyer solution, made it possible to obtain an idea of the structure of the transonic flow in the vicinity of the center of the nozzle.A large number of studies on transonic flow in the vicinity of the center of the nozzle have been made using the method of small perturbations. The approximate equation for the transonic velocity potential in the physical plane, obtained in [3–6], has been studied in detail for the plane and axisymmetric cases. In [7] Ryzhov used this equation to study the question of the formation of shock waves in the vicinity of the center of the nozzle, and conditions were formulated for the plane and axisymmetric cases under which the flow will not contain shock waves. However, none of the solutions listed above for the inverse problem of Laval nozzle theory makes it possible to calculate the flow in the subsonic and transonic parts of the nozzles with large gradients of the gasdynamic parameters along the normal to the axis of symmetry.Among the studies devoted to the numerical calculation of the flow in the subsonic portion of the Laval nozzle we should note the study of Alikhashkin et al., and the work of Favorskii [9], in which the method of integral relations was used to solve the direct problem for the plane and axisymmetric cases.The present paper provides a numerical solution of the inverse problem of Laval nozzle theory. A stable difference scheme is presented which permits analysis with a high degree of accuracy of the subsonic, transonic, and supersonic flow regions. The result of the calculations is a series of nozzles with rectilinear and curvilinear transition surfaces in which the flow is significantly different from the one-dimensional flow. The flowfield in the subsonic and transonic portions of the nozzles is studied. Several asymptotic solutions are obtained and a comparison is made of these solutions with the numerical solution.The author wishes to thank G. D. Vladimirov for compiling the large number of programs and carrying out the calculations on the M-20 computer.     

PIV Measurements in the Near and Intermediate Field Regions of Jets Issuing from Eight Different Nozzle Geometries

An experimental study was conducted to investigate the effect of nozzle geometry on the mixing characteristics and turbulent transport phenomena in turbulent jets. The nozzle geometry examined were round, square, cross, eight-corner star, six-lobe daisy, equilateral triangle as well as ellipse and rectangle each with aspect ratio of 2. The jets were produced from sharp linear contoured nozzles which may be considered intermediate to the more widely studied smooth contraction and orifice nozzles. A high resolution particle image velocimetry was used to conduct detailed velocity measurements in the near and intermediate regions. It was observed that the lengths of the potential cores and the growth rates of turbulence intensities on the jet centerline are comparable with those of the orifice jets. The results indicate that the decay and spreading rates are lower than reported for orifice jets but higher than results for smooth contoured jets. The jets issuing from the elliptic and rectangular nozzles have the best mixing performance while the least effective mixing was observed in the star jet. The distributions of the Reynolds stresses and turbulent diffusion clearly showed that turbulent transport phenomena are quite sensitive to nozzle geometry. Due to the specific shape of triangular and daisy jets, the profiles of mean velocity and turbulent quantities are close to each other in their minor and major planes while in the elliptic and rectangular jets are considerably different. They also exhibit more isotropic behavior compared to the elliptic and rectangular jets. In spite of significant effects of nozzle geometry on mean velocity and turbulent quantities, the integral length scales are independent of changes in nozzle geometry.     

Nozzle parameters affecting vortex tube energy separation performance

This experimental study reports the effect of nozzle parameters on the energy separation of the vortex tube. The results indicate that maximum energy separation is achieved with tangential nozzle orientation while the symmetry/asymmetry of nozzles has a minimal effect on the performance of the energy separation. For current selected conditions and parameters, the study shows that the optimum number of nozzles for maximum energy separation is around 4 nozzles.     

Experimental study on mixing enhancement in two dimensional supersonic flow

 Studies on mixing enhancement with two dimensional (2D) lobed nozzle have been conducted in a dual stream supersonic flow facility. The distributions of momentum flux, stagnation pressure and stagnation temperature across a plane at different axial distances from the nozzle exit were considered as a measure of mixing. The results indicated an enormous enhancement in mixing when 2D lobed nozzle was employed in comparison with conventional plain 2D nozzle. The enhanced mixing performance could be attributed to the large scale axial vortices observed in the flow-field of subsonic lobed nozzles by earlier investigators. Received: 27 December 1996 / Accepted: 21 August 1997     

SiC/(W,Ti)C梯度陶瓷喷嘴材料的制备及其冲蚀磨损机理研究

针对陶瓷喷嘴磨损特点,在喷嘴材料的设计和制造中提出运用梯度功能材料理论,通过控制陶瓷喷嘴材料的成分分布以实现其力学性能的合理梯度变化,将梯度陶瓷喷嘴材料制备过程中所产生的残余压应力引入喷嘴入口以提高喷嘴入口的力学性能,从而缓解喷嘴入口的高应力,提高其抗冲蚀磨损能力.采用热压烧结工艺制备SiC/(W,Ti)C梯度陶瓷喷嘴材料并分析其冲蚀磨损机理.结果表明,在相同冲蚀磨损条件下,梯度陶瓷喷嘴材料的抗冲蚀磨损性能较非梯度陶瓷喷嘴材料显著提高,这是由于梯度陶瓷喷嘴应力状态的改善及其力学性能提高的缘故.梯度陶瓷喷嘴材料的磨损机制为入口处呈现疲劳断裂、中间呈现微切削、出口处呈现疲劳断裂和脆性断裂特征.     

A numerical investigation of side‐loads resulting from rigid body motions of an overexpanded engine nozzle

A numerical model for fluid–structure interactions is presented. Its purpose, within the context of 2D overexpanded engine nozzles, is to improve understanding of interactions between side‐loads and rigid body rotations, and more generally of the underlying physics between a shock in motion and nozzle movements. The model is based on three different solvers, for fluid, structure and mesh deformation respectively, which are linked to a coupling scheme in a parallel environment. In particular it is shown that the nozzle has a natural torsional frequency for which the measured side‐loads are the greatest. This phenomenon is associated with a transversal wave in the flow between the two internal walls of the nozzle. For free coupling cases, our calculations go some way to explain how the mechanical energy is dissipated with a transfer of energy to the shock that encounters the largest motions to dissipate it. It has also been observed that the compression shock may adopt a quasi‐steady state response with regard to nozzle rotations at low frequencies, whereas this will no longer be the case at higher frequencies, where a phase shift may occur between side‐loads and rotational position. This study is aimed at enhancing the only current aeroelastic stability model for overexpanded nozzles (AIAA, 29th Joint Propulsion Conference and Exhibit, Monterey, CA, 28–30 June 1993). Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical investigation of shock starting of supersonic nozzles and comparison with experimental data

A numerical investigation was made of the interaction of a shock wave with a contracting and expanding channel in the process of shock starting of planar and axisymmetric supersonic nozzles. The calculated results are compared with experimental data. The justification is given for the use of a method based on integration of the one-dimensional nonstationary equations of motion of an inviscid gas with allowance for a variable specific heat in the calculation of the propagation of wave structure in the nozzle starting process. The influence of the shape of the entrance opening of the reflecting channel during the nozzle starting is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 120–127, January–February, 1980.