Experimental investigation of forced flow regime transition in a dual bell nozzle by secondary fluidic injection

Experiments on an axisymmetric dual-bell nozzle were performed at EDITH nozzle test facility of CNRS in Orléans, France. The main purpose of the study was to explore the possibility of controlling the flow regime transition by a secondary fluidic injection in the dual bell nozzle. The main focus of the present paper is to investigate the impact of the secondary injection parameters on the flow regimes transition in such nozzles. Secondary injection has been found to effectively control the flow regime transition and consequently to increase the propulsive performance of the device. It has also been pointed out that even a very low injected secondary mass flow rate leads to the control of the transition and contributes to reducing the lateral loads which can exist, moreover, when transitions are operated without injection.     

Flow regime effects on non-cavitating injection nozzles over spray behavior

This paper deals with the influence of flow regime (laminar, transition or turbulent) on the internal flow behavior, and how it affects the spray development in diesel nozzles. In particular, the research described here aims at studying and quantifying the internal flow regime effects on the spray behavior. With this purpose, internal flow results, based on mass flow rate and momentum flux measurements performed on three different tapered nozzles and which helped to determine the flow regime, has been taken into account as a point of departure for the spray behavior analysis. Thus, in this work, spray macroscopic visualization tests have been performed and analyzed which clearly revealed a change in the behavior of the angle and penetration of the spray related to the change of the flow nature. Moreover, with all the experimental data available, it has been possible to relate macroscopic parameters of the spray with those describing the internal flow (momentum and effective velocity) or the geometry of the nozzle (length or diameter) through correlations.     

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.     

Loss of Specific Impulse Due to Friction in Spike Nozzles

The class of nozzles with a central body, so-called spike nozzles, is considered for axisymmetric and plane central body geometries. A method of constructing the nozzle contour is outlined. The boundary layer is calculated using a three-parameter turbulence model and the loss of specific impulse due to friction in both spike nozzles and a Laval nozzle with the same expansion ratio are determined. A comparative analysis of the calculation results obtained, which makes it possible to determine the advantages and limitations of the nozzles considered, is carried out.     

Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle

This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813–847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813–847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli’s function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli’s function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813–847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.     

Investigation of flows in hypersonic nozzles in the framework of simplified Navier-Stokes equations

Simplified Navier-Stokes equations have found application as an alternative to the complete Navier-Stokes equations for the simulation of viscous gas flows in regions of large dimensions, when there is a predominant direction of the flow [1–4]. In the present paper, flows in wind tunnel nozzles are investigated on the basis of this model. Flows in conical and profiled axisymmetric hypersonic nozzles are calculated in a wide range of Mach and Reynolds numbers. Good agreement with the experiment is obtained. The important role of viscous-inviscid interaction in nozzles for large hypersonic Mach numbers is shown. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–26, November–December, 1986. The representation of the nature of flows in hypersonic nozzles given here arose as a result of repeated discussions of the results of the calculations with my colleagues: V. N. Vetlutskii, V. L. Ganimedov, G. P. Klemenkov, Yu. G. Korobeinikov, and V. I. Pinchukov, for which the author is deeply grateful to them.     

Deformation boundaries of an axisymmetric cavity by gas jets

A method is proposed for calculating small deformations of the boundaries of an axisymmetric cavity with impinging gas jets. No constraints are imposed on the configuration and characteristics of the system of nozzles generating the jets. Numerical results are compared with data obtained by available semi-empirical methods and with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 80–86, September–October, 2008.     

Analysis of the thrust characteristics of jet nozzles designed by various methods

A comparative numerical analysis of the thrust characteristics of axisymmetric jet nozzles designed by various methods is carried out. “Extremal“ nozzles designed by variational methods in the absence/presence of internal shocks (I), so-called “truncated“ nozzles with a uniform characteristic (II), and nozzles designed by the method of conjugate circular arcs (III) are considered. A comparison is carried out for both perfect and real gases (in the latter case the boundary layer gas viscosity is taken into account). It is shown that extremal nozzles are the most efficient, while truncated nozzles are somewhat less so. The thrust characteristics of nozzles designed by the method of conjugate circular arcs for both inviscid and viscous flow are inferior to those of extremal nozzles by 0.7–1%. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-00891).     

Calculation of supersonic steady-state flow in axisymmetric nozzles with an upwind difference scheme

This paper is on the application of the upwind difference scheme proposed by the author^[1] to the calculation of supersonic steady-state flow in axisymmetric nozzles. The upwind scheme is conservative (or weakly conservative), it yields results approximating those from the characteristic relations, and it has corresponding boundary difference schemes. The entropy phenomenon in the calculation of shock reflection on boundaries with the shock-capturing method will be discussed and a correction of this phenomenon will be proposed. From numerical experiments on an arbitrary nozzle, it is seen that the upwind difference scheme, its corresponding boundary scheme, and the improved treatment of shock reflection work well for the calculation of supersonic steady-state flow in axisymmetric nozzles.     

Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow

A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.     

Profiling the Supersonic Part of a Plug Nozzle with a Nonuniform Transonic Flow

The effect of transonic flow nonuniformity on the profiling of optimal plug nozzles is studied in the inviscid gas approximation. Sonic and supersonic regions providing maximum thrust for given nozzle dimensions and a given outer pressure are designed for given subsonic contours and calculated nonuniform transonic flows. As in the case of uniform flow on a cylindrical sonic surface, the initial regions of the designed contours satisfy the condition that in these regions the flow Mach number is unity or near-unity. In all the examples calculated, the optimal plug nozzles produce a greater thrust than the optimal axisymmetric and annular nozzles with a near-axial flow for the same lengths and the same gas flow rates through the nozzle. It is established that contouring without regard for transonic flow nonuniformity can result in considerable thrust losses. However, these losses are due only to a decrease in the flow rate, while the specific thrust may even increase slightly.     

Temperature force of interaction between spherical particles

The force of interaction between small particles in a gas induced by a temperature difference between the particle surface and the gas far away from the particle is considered. The particle dimensions correspond to the free-molecular, transitional, and continuum heat transfer regimes. A Monte-Carlo numerical method of direct statistical simulation of the solution of the nonlinear Boltzmann equation and the results of asymptotic solutions are used. The force of interaction between two hot or cold spherical particles is investigated. The dependence of the temperature force on the particle size, i.e. on the flow regime (Knudsen number), and the distance between the particles is examined. Approximations for these dependences are constructed.     

Free and confined jets at low Reynolds numbers

Free jets, and jets with tubular confinements, are investigated in the jet Reynolds number regime 80 Re_j 1000 being of interest for micro-jet pumps, among other applications. For issuing the jets, conventional (single-hole) nozzles as well as dual-hole nozzles of a particular design are used. Both flow visualization and LDA measurement indicate that, in agreement with previous findings, the jets issuing from conventional nozzles remain laminar up to large distances from the orifice. Thus there is but little entrainment of ambient fluid, and the performance of conventional nozzles in micro-jet pumps is rather poor. The dual-hole nozzles, on the other hand, are found to enforce transition to turbulent flow near the orifices. As a result, the entrainment rate is considerably increased, and the performance of jet pumps is improved when the dual-hole nozzles are applied. The experimental data are found to be in fair agreement with predictions based on mass and momentum balances.     

Investigation of supersonic flows in conical nozzles

The article gives the results of an investigation of flows in supersonic axisymmetric conical nozzles with the presence of shock waves in the flow. The method of straight-through calculation [1] and the method of small perturbations [2] are used. An investigation is made of the effect of various geometric parameters and of the adiabatic index on the flow of a gas in conical nozzles. A comparison is made with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 101–107, May–June, 1974.In conclusion, the authors thank N. V. Drozdov for his participation in carrying out the calculations.     

Modeling of two-phase flow in porous media with heat generation

The main purpose of this work is investigation of coolability of a boiling debris bed. The main governing equations are derived using volume averaging technique. From this technique some specific interfacial areas between phases are appeared and proper relations for modeling these areas are proposed. Using these specific areas, a modification for the Tung/Dhir model in the annular flow regime is proposed. The proposed modification is validated and the agreements with experimental data are good. Finally, governing equations and relations are implemented in the THERMOUS program to model two-phase flow in the debris bed in the axisymmetric cylindrical coordinate. Two typical configurations including flat and mounted beds are considered and the main physical phenomena during boiling of water in the debris bed are studied. Comparing the results with the one-dimensional analysis shows higher specific power of the bed.     

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.     

A fast algorithm to solve viscous two-phase flow in an axisymmetric rocket nozzle

A numerically fast algorithm has been developed to solve the viscous two-phase flow in an axisymmetric rocket nozzle. A Eulerian–Eulerian approach is employed in the computation to couple the gas–particle flow. Turbulence closure is achieved using a Baldwin–Lomax model. The numerical procedure employs a multistage time-stepping Runge–Kutta scheme in conjunction with a finite volume method and is made computationally fast for the axisymmetric nozzle. The present numerical scheme is applied to compute the flow field inside JPL and AGARD nozzles. © 1998 John Wiley & Sons, Ltd.     

Optimal Profiling of the Supersonic Part of a Plug Nozzle Contour

The problem of the optimal profiling of the supersonic part of a plug nozzle contour is solved within the framework of the ideal (inviscid and non-heat-conducting) gas model. The contours obtained provide a thrust maximum for given uniform sonic flow in the radial critical section of the nozzle, given constraints on the nozzle dimensions, and a given outer pressure (counterpressure). The initial sonic regions of the optimal contours are profiled on the basis of the condition that there the flow Mach number is unity. Varying the initial sonic region length makes it possible to construct nozzles of different sizes. The possibilities of the computational programs developed are demonstrated with reference to the example of plug nozzles, optimal when operated in a vacuum. It is shown that low thrust losses are obtained even for moderate nozzle dimensions. In the examples calculated, the optimal plug nozzles provide a greater thrust than the optimal axisymmetric and two-dimensional nozzles with an axial sonic flow for the same lengths and gas flow rates.     

Mechanics of axisymmetric wavy surface adhesion: JKR–DMT transition solution

Recent work on the mechanics of detachment of a rigid sphere from an elastic axisymmetric wavy surface in the presence of JKR adhesion has shown that the presence of small-amplitude waviness introduces instabilities into the detachment process which dissipate mechanical energy. These instabilities result in interface toughening and strengthening; both the external work and peak force required for separation of a wavy interface are higher than those for a flat interface. In this paper, we summarize the key dimensionless parameters governing axisymmetric wavy surface adhesion in the JKR regime. We then proceed to derive a solution for the JKR–DMT adhesion transition for the axisymmetric wavy surface contact problem using a Maugis–Dugdale cohesive zone formulation. The phenomenon of interface toughening and strengthening due to the presence of surface waviness is seen to be restricted primarily to the JKR adhesion regime.     

On numerical modelling of embedded subsonic flow

An analytical model has been developed for computing embedded subsonic flow in rocket plumes from underexpanded axisymmetric supersonic nozzles. Numerical procedures based on the analysis have been incorporated in a simplified, non-reacting exhaust structure program and calculations for representative plume conditions performed. The technique is numerically stable and has provided satisfactory predictions of Mach–disc associated embedded subsonic flow.