Shock unsteadiness in a thrust optimized parabolic nozzle

This paper discusses the nature of shock unsteadiness, in an overexpanded thrust optimized parabolic nozzle, prevalent in various flow separation modes experienced during start up and shut down sequences. The results are based on simultaneously acquired data from real-time wall pressure measurements using Kulite pressure transducers, high-speed schlieren (2 kHz) of the exhaust flow-field and from strain-gauges installed on the nozzle bending tube. Shock unsteadiness in the separation region is seen to increase significantly just before the onset of each flow transition, even during steady nozzle operation. The intensity of this measure (rms level) is seen to be strongly influenced by relative locations of normal and overexpansion shock, the decrease in radial size of re-circulation zone in the back-flow region, and finally, the local nozzle wall contour. During restricted shock separation, the pressure fluctuations in separation region exhibit periodic characteristics rather than the usually observed characteristics of intermittent separation. The possible physical mechanisms responsible for the generation of flow unsteadiness in various separation modes are discussed. The results are from an experimental study conducted in P6.2 cold-gas subscale test facility using a thrust optimized parabolic nozzle of area-ratio 30.

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Wave pattern characteristics of a two-phase nozzle flow by shock propagation

In this paper, the wave pattern characteristics of shock-induced two-phase nozzle flows with the quiescent or moving dusty gas ahead of the incident-shock front has been investigated by using high-resolution numerical method. As compared with the corresponding results in single-phase nozzle flows of the pure gas, obvious differences between these two kinds of flows can be obtained. Received 14 June 1996 / Accepted 19 October 1996     

Flow-rate and thrust coefficients for two-layer flows in a convergent nozzle

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–189, January–February, 1990.     

Separated two-phase flow in a nozzle

This work was performed to extend and further test the method of handling separated two-phase flow by studying each phase separately and, particularly, by placing emphasis on the study of the gas phase with interface transport expressions showing the influence of the liquid phase on it. A one-dimensional flow model for accelerating flows was used in conjunction with experimental data to obtain the pressure distribution and velocity distribution in a converging nozzle for several values of flow quality and nozzle inlet stagnation pressure. The results tend to support the use of the model (which includes the assumption that the gas is in critical flow when the two-phase mixture is in critical flow) and give some insight regarding the nature of the liquid distribution near the nozzle throat.     

Nonequilibrium gas-condensate flow in a laval nozzle

A scheme is proposed which simplifies the algorithm and reduces the labor involved in solving the system of quasi-linear hyperbolic equations describing supersonic nonequilibrium two-phase flow in an axisymmetric nozzle.     

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.     

Cold-gas experiments to study the flow separation characteristics of a dual-bell nozzle during its transition modes

An experimental investigation has been carried out to study the effect of test environment on transition characteristics and the flow unsteadiness associated with the transition modes of a dual-bell nozzle. Cold-gas tests using gaseous nitrogen were carried out in (i) a horizontal test-rig with nozzle exhausting into atmospheric conditions and, (ii) a high altitude simulation chamber with nozzle operation under self-evacuation mode. Transient tests indicate that increasing δP ₀/δt (the rate of stagnation chamber pressure change) reduces the amplitude of pressure fluctuations of the separation shock at the wall inflection point. This is preferable from the viewpoint of lowering the possible risk of any structural failure during the transition mode. Sea-level tests show 15–17% decrease in the transition nozzle pressure ratio (NPR) during subsequent tests in a single run primarily due to frost formation in the nozzle extension up to the wall inflection location. Frost reduces the wall inflection angle and hence, the transition NPR. However, tests inside the altitude chamber show nearly constant NPR value during subsequent runs primarily due to decrease in back temperature with decrease in back pressure that prevents any frost formation.     

Unsteady flow with separation behind a shock wave diffracting over curved walls

The unsteady separation of the compressible flow field behind a diffracting shock wave was investigated along convex curved walls, using shock tube experimentation at large length and time scales, complemented by numerical computation. Tests were conducted at incident shock Mach numbers of $M_{\hbox {s}} =$ 1.5 and 1.6 over a 100 mm radius wall over a dimensionless time range up to $\tau \le $ 6.45. The development of the near wall flow at $M_{\hbox {s}} =$ 1.5 has been described in detail and is very similar to that observed for slightly lower $\tau $ ’s at $M_{\hbox {s}} =$ 1.6. Computations were performed at wall radii of 100 and 200 mm and for incident shock Mach numbers from 1.5 up to and including Mach 2.0. Comparing dimensionless times for different size walls shows that for a given value of $\tau $ the flow field is very similar for the various wall radii published to date and tested in this study. Previously published results that were examined alongside the results from this study had typical values of $1.6 < \tau < 3.2$ . At the later times presented here, flow features were observed that previously had only been observed at higher Mach numbers. The larger length scales allowed for a degree of Reynolds number independence in the results published here. The effect of turbulence on the numerical and experimental results could not be adequately examined due to limitations of the flow imaging system used and a number of questions remain unanswered.     

Asymptotic nature of hypersonic flow in a conical nozzle

This study investigates hypersonic flow in a conical nozzle at large distances from the throat with account for the interaction with the laminar boundary layer.A study of the asymptotic nature of the hypersonic flow of an ideal gas in an expanding nozzle whose wall was close to a kth-power parabola was made by Ladyzhenskii [1], who showed in particular that for 00)_0* the nonuniformity in the distribution of all the gasdynamic parameters in the flow is hydraulic in nature; in this case the maximal Mach number is determined from the boundary-layer joining condition at the nozzle centerline; 2) for Reynolds numbers much larger than (R₀)_0*, when most of the gas is concentrated near the outer edge of the potential core, the region of isentropic flow is bounded in the direction of the stream by the interaction of the compressed gas layers.The author wishes to thank V. N. Gusev and V. N. Zhigulev for helpful discussions of this study.     

Determination of specific thrust in unchoked regimes and design of a separationless convergent nozzle contour

The variation of the specific thrust R_Y on the angle of inclination of the wall is analyzed within the framework of the ideal gas model using the results of specific impulse and flow rate calculations for conical convergent nozzles. It is shown that in unchoked regimes nozzles with different have almost the same values of R_Y for both subcritical and supercritical pressure ratios _c. On the interval _C < 6 typical of convergent nozzles conical convergent nozzles with =30–90° have almost the same value of the specific thrust, maximal relative to the R_Y of nozzles with < 30°. In the presence of viscosity forces local boundary layer separation may occur in the neighborhood of the entrance section of the convergent nozzle. A method of constructing a separationless convergent nozzle contour with enhanced thrust is developed on the basis of a boundary layer separation criterion. The separationless contour is determined for given values of the flow rate, specific heat ratio, Reynolds number, wall temperature and initial boundary layer displacement thickness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–164, January–February, 1990.     

Experimental and computational studies focusing processes of shock waves reflected from parabolic reflectors

This paper describes experimental and numerical studies of the focusing process of shock waves reflected from various shapes of a parabolic reflector. The effect of incident shock strength on the focusing process was also investigated. Experiments were carried out in a conventional shock tube and a test gas was air for incident shock Mach numbers ranging from 1.1 to 2.0. In the experiments, the process of shock focusing was visualized by schlieren method. Numerical simulations were conducted for incident shock Mach numbers up to 3.0 by solving the two-dimensional unsteady Euler equations. The numerical results were compared with experiment for various parabolic reflector shapes and for various incident shock Mach numbers. Based on the experimental and computational results, the pattern of shock focusing and shock focusing mechanism are discussed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Simulating radiative shocks in nozzle shock tubes

We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1 ns. Later times are calculated with the CRASH code. CRASH solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The synthetic radiographs produced can be used for comparison with future nozzle experiments at high-energy-density laser facilities.     

Focusing of weak shock waves on a target in a parabolic chamber

Theoretical study of a weak shock focusing process in a confined chamber filled with liquid is presented. The chamber has a form of a thin cylinder with a parabolic cross-section, planar bottom and an arbitrary, although slowly varying, upper bounding surface. Analytical, numerical and experimental studies of weak shock wave focusing have been previously performed in the elliptic and ellipsoidal cases with a shock wave generated at one of the foci by means of an electric discharge or a microexplosion. In the present case a planar shock, perpendicular to the axis of the parabolic cross-section, sent in the inner of the chamber will converge at the focus after the reflection off the chamber wall, thus offering a different technical realization of the shock generation. The problem is solved within the frame of the geometrical acoustics approximation and a relation between the form of the upper bounding surface of the chamber and the pressure distribution behind the converging wavefront is obtained. It is shown that a desired pressure distribution may be obtained by an appropriate choice of the upper bounding surface.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

An experimental investigation of hypervelocity flow in a conical nozzle

The flow in a conical nozzle is examined experimentally for a range of hypervelocity conditions in a free-piston shock tunnel. The pitot pressure levels compare reasonably well with an inviscid numerical prediction which includes a correction for the growth of the nozzle wall boundary layer. The size of the nozzle wall boundary layer seems to be well predicted by semi-empirical expressions developed for perfect gas flows, as do data from other free-piston shock tunnels.     

Starting of an axisymmetric convergent-divergent nozzle in a hypersonic flow

The starting of an axisymmetric convergent-divergent nozzle, with the result that supersonic flow is formed within almost the entire channel, is modeled, as applied to the hypersonic aerodynamic setup of the Institute of Mechanics of Moscow State University. A successful starting is realized when the nozzle is thrown in a uniform supersonic air flow at a fairly high Mach number. The steady flow structure is studied. It is numerically shown that in the convergent section of the channel there arises an oblique shock wave whose interaction with the nozzle axis leads to the formation of a reflected shock and a curvilinear Mach disk with a region of unsteady subsonic flow in the vicinity of the throat. The mathematical model is based on the two-dimensional Euler equations for axisymmetric gas flows.