Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

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.     

Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle

The objective of this effort is to develop a computational methodology to capture the side load physics and to anchor the computed aerodynamic side loads with the available data by simulating the startup transient of a regeneratively cooled, high-aspect-ratio nozzle, hot-fired at sea level. The computational methodology is based on an unstructured-grid, pressure-based, reacting flow computational fluid dynamics and heat transfer formulation, and a transient inlet history based on an engine system simulation. Emphases were put on the effects of regenerative cooling on shock formation inside the nozzle, and ramp rate on side load reduction. The results show that three types of asymmetric shock physics incur strong side loads: the generation of combustion wave, shock transitions, and shock pulsations across the nozzle lip, albeit the combustion wave can be avoided with sparklers during hot-firing. Results from both regenerative cooled and adiabatic wall boundary conditions capture the early shock transitions with corresponding side loads matching the measured secondary side load. It is theorized that the first transition from free-shock separation to restricted-shock separation is caused by the Coanda effect. After which the regeneratively cooled wall enhances the Coanda effect such that the supersonic jet stays attached, while the hot adiabatic wall fights off the Coanda effect, and the supersonic jet becomes detached most of the time. As a result, the computed peak side load and dominant frequency due to shock pulsation across the nozzle lip associated with the regeneratively cooled wall boundary condition match those of the test, while those associated with the adiabatic wall boundary condition are much too low. Moreover, shorter ramp time results show that higher ramp rate has the potential in reducing the nozzle side loads.

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On the possibility of blowing a gas jet into a supersonic flow without formation of a three-dimensional boundary-layer separation zone

We consider the flow formed by the interaction of a supersonic flow and a transverse sonic or supersonic jet blown at right angles to the direction of the main flow through a nozzle whose exit section is in a flat wall. When a gas jet is blown through a circular opening [1] the pressure rises in front of the jet because of the stagnation of the oncoming flow. This leads to separation of the boundary layer formed on the wall in front of the blowing nozzle. The resulting three-dimensional separation zone leads to a sharp increase in the pressure and the heat fluxes to the wall in front of the blowing nozzle, which is undesirable in many modern applications. The aim of the present investigation was to find a shape of the exit section of the blowing nozzle for which there is no three-dimensional separation zone of the boundary layer in front of the blowing nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–165, May–June, 1979.     

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.     

Behaviour of a shock train under the influence of boundary-layer suction by a normal slot

The interaction of a shock train with a normal suction slot is presented. It was found that when the pressure in the suction slot is smaller or equal to the static pressure of the incoming supersonic flow, the pressure gradient across the primary shock is sufficient to push some part of the near wall boundary layer through the suction slot. Due to the suction stabilized primary shock foot, the back pressure of the shock train can be increased until the shock train gradually changes into a single normal shock. During the experiments, the total pressure and therewith the Reynolds number of the flow were varied. The structure and pressure recovery within the shock train is analysed by means of Schlieren images and wall pressure measurements. Because the boundary layer is most important for the formation of a shock train, it has been measured by a Pitot probe. Additionally, computational fluid dynamics is used to investigate the shock boundary-layer interaction. Based on the experimental and numerical results, a simplified flow model is derived which explains the phenomenology of the transition of a shock train into a single shock and derives distinct criteria to maintain a suction enhanced normal shock. This flow model also yields the required suction mass flow in order to obtain a single normal shock in a viscous nozzle flow. Furthermore, it allows computation of the total pressure losses across a normal shock under the influence of boundary-layer suction.     

Experimental study of boundary layer separation in truncated ideal contour nozzles

DLR Lampoldshausen carried out a cold flow test series to study the boundary layer separation and the related flow field in a truncated ideal contour nozzle. A special focus was set on low nozzle pressure ratios to identify the origin of a locally re-attached flow condition that was detected in previous test campaigns. A convex shaped Mach disc was found for nozzle pressure ratios less than 10 and a slight concave one for nozzle pressure ratios more than 20. Due to boundary layer transition at low nozzle pressure ratios the convex Mach disc is temporary tilted and redirects the flow towards the nozzle wall. A simple separation criterion for turbulent nozzle flows is presented that fits well for both cold and hot flows. It is shown that the oblique separation shock recompresses the flow to 90% of the ambience. The separation zone of the presented film cooled nozzle is compared with a conventional one around 40% longer. Furthermore a relation between shear layer shape and forced side loads is described.      

Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948): given the appropriately large exit pressure p _e(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes p _e(x). We solve this problem completely for a general class of de Laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible Euler system. The problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic–elliptic system. One of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted Hölder space with low regularities for a second order quasilinear elliptic equation with a free parameter (the position of the shock curve at one wall of the nozzle) and non-local terms involving the trace on the shock of the first order derivatives of the unknown function.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

Aeroelastic stability analysis of flexible overexpanded rocket nozzle

The aim of this paper is to present a new aeroelastic stability model taking into account the viscous effects for a supersonic nozzle flow in overexpanded regimes. This model is inspired by the Pekkari model which was developed initially for perfect fluid flow. The new model called the “Modified Pekkari Model” (MPM) considers a more realistic wall pressure profile for the case of a free shock separation inside the supersonic nozzle using the free interaction theory of Chapman. To reach this objective, a code for structure computation coupled with aerodynamic excitation effects is developed that allows the analysis of aeroelastic stability for the overexpanded nozzles. The main results are presented in a comparative manner using existing models (Pekkari model and its extended version) and the modified Pekkari model developed in this work.     

Investigations of gas and particle dynamics in first generation needle-free drug delivery devices

Abstract. Transdermal powdered drug delivery involves the propulsion of solid drug particles into the skin by means of high-speed gas-particle flow. The fluid dynamics of this technology have been investigated in devices consisting of a convergent-divergent nozzle located downstream of a bursting membrane, which serves both to initiate gas flow (functioning as the diaphragm of a shock tube) and to retain the drug particles before actuation. Pressure surveys of flow in devices with contoured nozzles of relatively low exit-to-throat area ratio and a conical nozzle of higher area ratio have indicated a starting process of approximately 200 s typical duration, followed by a quasi-steady supersonic flow. The velocity of drug particles exiting the contoured nozzles was measured at up to 1050 m/s, indicating that particle acceleration took place primarily in the quasi-steady flow. In the conical nozzle, which had larger exit area ratio, the quasi-steady nozzle flow was found to be overexpanded, resulting in a shock system within the nozzle. Particles were typically delivered by these nozzles at 400 m/s, suggesting that the starting process and the quasi-steady shock processed flow are both responsible for acceleration of the particle payload. The larger exit area of the conical nozzle tested enables drug delivery over a larger target disc, which may be advantageous. Received 12 March 2000 / Accepted 8 June 2000     

Unsteady Separated Two-Throat Nozzle Flows

A numerical study of a supersonic planar two-throat nozzle flow, using the Reynolds averaged Navier–Stokes equations, is presented. This nozzle flow can induce asymmetrical separation between the throats. The start-up processes are examined. Initial pressure ratio and increasing pressure time influence are investigated. The objective is to gain a better understanding of the mechanisms causing the asymmetry.     

Sonic annular jet in a counterstreaming supersonic flow

When sonic annular jets encounter a supersonic flow, two interaction regimes are possible with open or closed central separation regions. When the flow regimes change, there is an abrupt change in the separation of the shock wave from the nozzle and of the pressure in the central separation region, and hysteresis is also observed. The flow regimes with open central separation region are stationary and can be calculated numerically on the basis of Euler's equations fairly accurately.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–180, September–October, 1979.     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

Surface flow studies of restricted shock separation in a thrust optimized parabolic nozzle

In this paper, surface flow features such as length of separation region and separation bubble are studied during restricted shock separation condition in a thrust optimized parabolic nozzle. It is found that peaks in the variation of these surface flow features are directly related to beginning of conditions for flow transition suggesting changes in exhaust flow features which are responsible for initiating flow transitions in a nozzle. Results are obtained from surface oil tests performed during the shut down phase for a range of nozzle pressure ratio during which restricted shock separation condition is prevalent.     

Static pressure measurement along the centerline of an induced flow ejector

Conclusion The static pressure measuring system described in this paper is simple and does not disturb the flow perceptibly. Compared to wall pressure taps, the present measuring system has the advantage of being able to measure the static pressure at any section of the nozzle and to provide a continuous distribution, if necessary. An arrangement using a large number of wall pressure taps can be avoided.In addition, this system allows the internal static pressure of the flow to be measured, which is particularly interesting in the case of two coflowing streams inside an induced flow ejector. The primary jet can be investigated downstream of the primary nozzle exit plane. The static pressure at this exit plane, which is of great importance in numerical simulation of flows in ejectors, can be directly measured by means of this pressure probe (Lu 1986). This system also permits the detection of shock waves in the supersonic stream and gives accurate information about their location, their strength and the lengths of the disturbed areas. Hence, this system is useful for shock structure investigation, especially when flow visualization techniques are impossible to apply (non-transparent walls).However, the use of this measuring system is restricted to relatively short ejectors in order to limit the length of the capillary tube (less than 1.50 m in these experiments) and to minimize its oscillations in the flow.     

Transonic Shock Problem for the Euler System in a Nozzle

In this paper, we study the well-posedness problem on transonic shocks for steady ideal compressible flows through a two-dimensional slowly varying nozzle with an appropriately given pressure at the exit of the nozzle. This is motivated by the following transonic phenomena in a de Laval nozzle. Given an appropriately large receiver pressure P _r , if the upstream flow remains supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the flow is compressed and slowed down to subsonic speed, and the position and the strength of the shock front are automatically adjusted so that the end pressure at exit becomes P _r , as clearly stated by Courant and Friedrichs [Supersonic flow and shock waves, Interscience Publishers, New York, 1948 (see section 143 and 147)]. The transonic shock front is a free boundary dividing two regions of C ^2,α flow in the nozzle. The full Euler system is hyperbolic upstream where the flow is supersonic, and coupled hyperbolic-elliptic in the downstream region Ω₊ of the nozzle where the flow is subsonic. Based on Bernoulli’s law, we can reformulate the problem by decomposing the 3 × 3 Euler system into a weakly coupled second order elliptic equation for the density ρ with mixed boundary conditions, a 2 × 2 first order system on u ₂ with a value given at a point, and an algebraic equation on (ρ, u ₁, u ₂) along a streamline. In terms of this reformulation, we can show the uniqueness of such a transonic shock solution if it exists and the shock front goes through a fixed point. Furthermore, we prove that there is no such transonic shock solution for a class of nozzles with some large pressure given at the exit. This research was supported in part by the Zheng Ge Ru Foundation when Yin Huicheng was visiting The Institute of Mathematical Sciences, The Chinese University of Hong Kong. Xin is supported in part by Hong Kong RGC Earmarked Research Grants CUHK-4028/04P, CUHK-4040/06P, and Central Allocation Grant CA05-06.SC01. Yin is supported in part by NNSF of China and Doctoral Program of NEM of China.     

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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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.     

Numerical calculation of FSS/RSS transition in highly overexpanded rocket nozzle flows

Turbulent flow separation in over-expanded rocket nozzles is investigated numerically in a sub-scale parabolic nozzle fed with cold nitrogen. Depending upon the feeding to ambient pressure ratio either a free shock separation or a restricted shock separation is computed, with a significant hysteresis between these two flow regimes. This hysteresis was also found in experimental tests with the same nozzle geometry. The present study is mainly focused on the transition between the two shock separation patterns. The analysis of the numerical solutions aims to provide clues for the explanation of the hysteresis cycle.