Flow structures of gaseous jets injected into water for underwater propulsion

Gaseous jets injected into water are typically found in underwater propulsion,and the flow is essentially unsteady and turbulent.Additionally,the high water-to-gas density ratio can result in complicated flow structures;hence measuring the flow structures numerically and experimentally remains a challenge.To investigate the performance of the underwater propulsion,this paper uses detailed Navier-Stokes flow computations to elucidate the gas-water interactions under the framework of the volume of fluid(VOF) model.Furthermore,these computations take the fluid compressibility,viscosity,and energy transfer into consideration.This paper compares the numerical results and experimental data,showing that phenomena including expansion,bulge,necking/breaking,and back-attack are highlighted in the jet process.The resulting analysis indicates that the pressure difference on the rear and front surfaces of the propulsion system can generate an additional thrust.The strong and oscillatory thrust of the underwater propulsion system is caused by the intermittent pulses of the back pressure and the nozzle exit pressure.As a result,the total thrust in underwater propulsion is not only determined by the nozzle geometry but also by the flow structures and associated pressure distributions.     

Optimal distribution of reliability for a large network based on connectivity

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms （GA）. Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.     

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.     

On the ratio of expectation crossings of random-excited dielectric elastomer balloon

The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter.The Mooney–Rivlin model is adopted to describe the constitutive relation while the random pressure is described by Gaussian white noise.Through a specific transformation,the stochastic differential equations for the total energy and phase are derived.With the application of the stochastic averaging,the system total energy is then approximated by a one-dimensional diffusion process.Solving the associated Fokker–Planck–Kolmogorov(FPK)equation yields the stationary probability density of the system total energy.The ratio of expectation crossings is then derived based on the joint stationary probability density of stretch ratio and its ratio of change.The efficacy and accuracy of the proposed procedure are verified by comparing with the results from Monte Carlo simulation(MCS).     

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed.Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model(DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density.The pressure propagation is slower in the direction of larger fracture density.     

AN EXACT SOLUTIN FOR INCOMPRESSIBLE FLOW THROUGH A TWO-DIMENSIONAL LAVAL NOZZLE

A careful examination of the variation of the velocity along the centerline and thecontour of a Laval nozzle in the physical plane shows that either the upper or the lower halfof the Laval nozzle assumes the same form of a slitted thick airfoil with tandem trailingedges.These two airfoils lie on different Riemann sheets in the hodograph plane.Theinterior of the airfoil is then mapped onto an infinite strip in the complex potential plane.Making use of these results,we obtained an exact solution for the incompressible potentialflow through a two-dimensional Laval nozzle.The solution is applicable for nozzles withany given contraction ratio n1 expansion ratio n2.and throat wall radius R.As examples ofthe method,various nozzle contours,the velocity distribution of the flow,and the locationsof the fluid particles at different time intervals are presented.     

EQUIVALENT MODEL OF EXPANSION OF CEMENT MORTAR UNDER SULPHATE EROSION

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is results indicate that the model perfectly describes performed. The numerical and experimental the expansion of the cement mortar.     

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.     

Analysis of non-symmetrical flapping airfoils

Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non- symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil＇s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interac- tions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter＇s wing.     

Aerodynamics of indirect thrust measurement by the impulse method

The aerodynamic aspects of indirect thrust measurement by the impulse method have been studied both experimentally and numerically. The underlying basic aerodynamic principle is outlined, the phenomena in subsonic, supersonic and arc-heated jets are explored, and factors affecting the accuracy of the method are studied and discussed. Results show that the impulse method is reliable for indirect thrust measurement if certain basic requirements are met, and a simple guideline for its proper application is given.     

Propulsive performance of a liquid kerosene/oxygen pulse detonation rocket engine

Thrust and specific impulse are two critical parameters to estimate the performance of rocket engine. Utilizing liquid kerosene as the fuel, oxygen as oxidizer and nitrogen as purge gas, a series of multi-cycle detonation experiments were conducted to systemically investigate the relationships among the operating frequency, fill fraction and performance parameters of the pulse detonation rocket engine (PDRE). The operating frequency of PDRE was up to 49 Hz. The mass flow of liquid kerosene was measured by orifice meter and the mass flow of oxygen was measured based on the method of gas collection. The detonation chamber pressure traces were recorded by dynamic piezoelectric pressure transducers. A dynamic piezoelectric thrust transducer was used to record the instantaneous thrust produced by PDRE. Average thrust and detonative mixture-based specific impulse of PDRE with different operation frequency were obtained by experiments. The experimental results indicate that in the practical operation, the operating frequency caused the change of fill fraction, which resulted in a thrust enhancement. Due to the effect of fill fraction, average thrust did not linearly increase as the frequency rises. Fill fraction has a significant influence on the specific impulse of PDRE. The detonative mixture-based specific impulse presented a second order exponential decay with fill fraction, and was correspondingly increased with the raise of the operating frequency. With the strategy of partial filling in detonation tube, the specific impulse can be remarkably enhanced.     

Experimental research on the rotating detonation in gaseous fuels�Coxygen mixtures

An experimental study on rotating detonation is presented in this paper. The study was focused on the possibility of using rotating detonation in a rocket engine. The research was divided into two parts: the first part was devoted to obtaining the initiation of rotating detonation in fuel–oxygen mixture; the second was aimed at determination of the range of propagation stability as a function of chamber pressure, composition, and geometry. Additionally, thrust and specific impulse were determined in the latter stage. In the paper, only rich mixture is described, because using such a composition in rocket combustion chambers maximizes the specific impulse and thrust. In the experiments, two kinds of geometry were examined: cylindrical and cylindrical-conic, the latter can be simulated by a simple aerospike nozzle. Methane, ethane, and propane were used as fuel. The pressure–time courses in the manifolds and in the chamber are presented. The thrust–time profile and detonation velocity calculated from measured pressure peaks are shown. To confirm the performance of a rocket engine with rotating detonation as a high energy gas generator, a model of a simple engine was designed, built, and tested. In the tests, the model of the engine was connected to the dump tank. This solution enables different environmental conditions from a range of flight from 16 km altitude to sea level to be simulated. The obtained specific impulse for pressure in the chamber of max. 1.2 bar and a small nozzle expansion ratio of about 3.5 was close to 1,500 m/s.     

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.     

Hysteresis phenomena in a plane rotatable nozzle

The flow in a rotatable nozzle is calculated within the framework of the Reynolds equations and the Spalart-Allmaras turbulence model on the pressure difference range 1.1 < π < 5 for four configurations of the nozzle with the area ratio ε = 1.52 and two angles of the nozzle axis rotation. The flow structure is determined and the thrust characteristics and the angles of the thrust vector rotation are obtained. It was found that in the overexpansion regime the flows in plane symmetric and rotatable nozzles involve hysteresis phenomena due the Coanda effect and the interaction between the boundary layer and a shock generated within the nozzle on its supersonic walls. The hysteresis phenomena detected provide an up-to-4% divergence in the thrust coefficient for the same problem parameters. The results of the numerical modeling are compared with the experimental data and the results of calculations in accordance with Sekundov’s model.     

Assessment of gas thermodynamic characteristics on fluidic thrust vectoring performance: Analytical,experimental and numerical study

The cross injection in a supersonic flow is an issue encountered in several aerodynamic applications such as fuel injection in scramjet combustor, missile control, drag reduction and thrust vector control. In a recent work, an analytical model has been presented to calculate the fluidic thrust vectoring performance for a supersonic axisymmetric nozzle. The model is able to take into account both the injected gas thermodynamic properties and the geometrical nozzle characteristics. The analytical model has been successfully validated following the cold air flow experimental analysis, in the case of fluidic thrust vectoring applied to conical nozzle. The aim of this work is to show how far the injected gas thermodynamic properties, different from that of the nozzle main flow, could influence the fluidic thrust vectorization parameters.In this work, the experimental performance of the fluidic thrust vectoring concept, using numbers of gases as injectant, has been qualitatively and quantitatively analyzed. Schlieren visualization, force balance and wall pressure measurements were used in the case of a truncated ideal contour nozzle. The experimental results are compared to the numerical and analytical findings.Performance analysis are conducted and basic conclusions are drawn in terms of thermodynamic gas properties effect on the fluidic thrust vector system. The primary effect was related to the gas molecular weight and its specific heat ratio product. It is observed that for fixed injection conditions, the vectoring angle is higher when the injected gas molecular weight and specific heat ratio product is less than that of the primary gas. For a given mission of the launcher, it can be concluded that the mass of the embedded gas, used for the fluidic vectorization system, can be significantly reduced, depending on its molecular weight and specific heat ratio.     

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.     

Freestream effects on base pressure development of an annular plug nozzle

An experimental investigation has been carried out to study the effect of freestream flow and cowl-length variation on (i) upstream flow interference effects and (ii) the base wake-closure nozzle pressure ratio. It is observed that for supersonic freestream Mach numbers the nozzle exhaust seems to only slightly influence the upstream interference effects for M = 1.2 but shows significant influence for M = 1.6. Increasing the cowl-length further reduces the upstream flow interference effects significantly. Further, the reduced momentum thrust from the inner nozzle in the presence of freestream for similar nozzle pressure ratio (relative to static tests) delays the downstream movement of the system of shocks on the plug surface. In the case of the plug truncated at 40% length, this delays the onset of base-wake closure and hence, increases the base-wake closure nozzle pressure ratio with increasing freestream Mach number. Increasing the cowl-length also helps to increase the base pressure thrust contribution at all operating conditions.     

Experimental and numerical investigations on PDE performance augmentation by means of an ejector

To improve the performance of pulse detonation engines, a 48 cm long cylindrical combustion chamber of 5cm internal diameter (i.d.) is fitted with an ejector of constant section. The role of the ejector is (i) to provide partial confinement of the detonation products escaping from the chamber and (ii) to suck in fresh air and then to increase the mass ejected compared to the ejection of burned gases alone.The combustion chamber is fully filled with a stoichiometric ethylene/oxygen mixture at ambient conditions. Three parameters of the ejector are varied: the i.d. D, the length L, and the position d relative to the thrust wall of the combustion chamber. For various configurations, the specific impulse (I _sp) is determined in single shot experiments. The maximum operating frequency (f _max) and the maximum thrust are then deduced. I _sp is measured by means of the ballistic pendulum method, and f _max is derived from the pressure signal recorded on the combustion chamber thrust wall.The addition of an ejector increases the specific impulse up to 60% in the best configuration tested, from 164s without ejector to 260s with ejector. The specific impulse can be represented by a single curve using suitable dimensionless parameters. The thrust results for the main ejector studied (D = 80mm) indicate an optimal (L, d) configuration that provides a 28% thrust gain. For the same ejector, f _max remains constant and equal to the frequency obtained without ejector in a large range of (L, d) values, before decreasing.Two-dimensional unsteady numerical computations agree reasonably with the experiments, slightly overestimating the experimental values. The results indicate that 80% of the I _sp gain comes from the action of the expanding detonation products on the annular end surface of the combustion chamber, governed by the tube wall thickness.This paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003 PACS 47.40.Rs     

喷管对脉冲爆轰发动机性能的影响

采用热力学循环分析方法, 从理论上推导了脉冲爆轰发动机(pulse detonationengine, PDE)不完全膨胀条件下的热效率公式, 并定量考察了不同燃烧室初始温度下热循环效率随出口压力比的变化, 研究表明气体膨胀越完全, 工质的热循环效率越高. 应用数值模拟方法分别研究了收缩-扩张喷管和扩张喷管, 比较了它们对PDE推力和比冲的影响, 考察了它们在PDE各个循环阶段的作用. 此外, 还分析了收缩-扩张喷管收缩段引起的反射激波的影响, 理论上反射激波会降低PDE热循环效率和比冲, 但当反射激波马赫数小于1.5时, 对PDE热循环效率的影响很小, 其正面作用占优.