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.     

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.      

Supersonic flow separation in planar nozzles

We present experimental results on separation of supersonic flow inside a convergent–divergent (CD) nozzle. The study is motivated by the occurrence of mixing enhancement outside CD nozzles operated at low pressure ratio. A novel apparatus allows investigation of many nozzle geometries with large optical access and measurement of wall and centerline pressures. The nozzle area ratio ranged from 1.0 to 1.6 and the pressure ratio ranged from 1.2 to 1.8. At the low end of these ranges, the shock is nearly straight. As the area ratio and pressure ratio increase, the shock acquires two lambda feet. Towards the high end of the ranges, one lambda foot is consistently larger than the other and flow separation occurs asymmetrically. Downstream of the shock, flow accelerates to supersonic speed and then recompresses. The shock is unsteady, however, there is no evidence of resonant tones. The separation shear layer on the side of the large lambda foot exhibits intense instability that grows into large eddies near the nozzle exit. Time-resolved wall pressure measurements indicate that the shock oscillates in a piston-like manner and most of the energy of the oscillations is at low frequency.      

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.     

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.     

Viscous simulation of shock reflection hysteresis in ideal and tapered overexpanded planar nozzles

While a CFD simulation of the flow in overexpanded planar nozzles shows, inside an ideal nozzle, the existence of a hysteresis process in the transition from regular to Mach and from Mach to regular reflections such a process does not appear in tapered nozzles. Previous simulations have dealt only with the flow outside the nozzle and thus concluded that the hysteresis phenomenon takes place outside the nozzle even when viscous effects were introduced. When including the geometry of the nozzle in the simulation it becomes evident that flow separation will occur before transition from regular to Mach reflection for all relevant flow Mach numbers. The simulation reveals complex changes in the flow structure as the ratio between the ambient and the stagnation pressures is increased and decreased. The pressure along the nozzle wall downstream of the separation point was found to be less than the ambient pressure with the effect being more pronounced in the case of the ideal nozzle. The present study complements a previous study that dealt only with flow separation in an ideal nozzle.     

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.     

Experimental analysis of unsteady separated flows in a supersonic planar nozzle

The unsteady aspects of shock-induced-separation patterns have been investigated inside a Mach 2 planar nozzle. The mean location of the shock can vary by changing, relatively to the nozzle throat, the height of the second throat which is positioned downstream of the square test section. This study focuses on the wall pressure fluctuations spectra and the unsteady behaviour of the shock. Symmetric shock configurations appear both for the largest openings of the second throat, and for the smallest openings. For an intermediate opening the shock system exhibits asymmetrical configurations. A coating with roughnesses sticked on the throat part of the nozzle in order to modify the state of the incoming boundary layers (from smooth to rought turbulent statement) is a driver for the asymmetry. The fluctuating displacements of the shock patterns were analysed by using an ultra fast shadowgraph visualization technique. A spectral analysis of the unsteady wall pressure measurements has revealed low frequency phenomena governed by large structure dynamics in the separated flows. Communicated by K. Takayama PACS 02.60.Cb; 05.10.Ln; 47.11.+j; 47.15.Cb; 47.40.Nm     

Shock pattern in the plume of rocket nozzles: needs for design consideration

For ideal nozzles, basically two different types of shock structures in the plume may appear for overexpanded flow conditions, a regular shock reflection or a Mach reflection at the nozzle centreline. Especially for rocket propulsion, other nozzle types besides the ideal nozzles are often used, including simple conical, thrust-optimized or parabolic contoured nozzles. Depending on the contour type, another shock structure may appear: the so-called cap-shock pattern. The exact knowledge of the plume pattern is of importance for mastering the engine operation featuring uncontrolled flow separation inside the nozzle, appearing during engine start-up and shut-down operation. As consequence of uncontrolled flow separation, lateral loads may be induced. The side-load character strongly depends on the nozzle design, and is a key feature for the nozzle’s mechanical structure layout. It is shown especially for the VULCAIN and VULCAIN 2 nozzle, how specific shock patterns evolve during transients, and how - by the nozzle design - undesired flow phenomena can be avoided.     

On the use of a two-layer model for large-eddy simulations of supersonic boundary layers with separation

The two-layer modeling approach has become one of the most promising and successful methodology for simulating turbulent boundary layers in the past ten years. In the present study, a mixed wall model for large-eddy simulations (LES) of high-speed flows is proposed which combine two approaches; the thin-Boundary Layer Equations (TBLE) model of Kawai and Larsson (1994) and the analytical wall-layer model of Duprat et al. (2011) for streamwise pressure gradients. The new hybrid model has been efficiently implemented into a three-dimensional compressible LES solver and validated against DNS of a spatially-evolving supersonic boundary layer (BL) under moderate and strong pressure gradients, before being employed for the prediction of nozzle flow separations at different flow conditions, ranging from weakly to highly over-expanded regimes. A good agreement is obtained in terms of mean and fluctuating quantities compared to the DNS results. Particularly, the current wall-modeled LES results are found to perfectly match the DNS data of supersonic BL with/out pressure gradient. It is also shown that the model can account for the effect of the large-scale turbulent motions of the outer layer, indicating a good interaction between the inner and the outer part of the wall layer. In terms of simulations costs and improvements of computing power, the obtained results highlight the capability of the current wall-modeling LES strategy in saving a considerable amount of computational time compared to the wall-resolved LES counterpart, allowing to push further the simulations limits. Furthermore, the application of these computationally low-costly LES simulations to nozzle flow separation allows to clearly identify the origin of the shock unsteadiness, and the existence of broadband and energetically-significant low-frequency oscillations (LFO) in the vicinity of the separation region.     

Parametric Study of Alternating Flow Patterns in Non-Reacting Multiple-Swirl Flows

Multiple nozzle combustors, under certain conditions, may result in flowfields that differ between nozzles in an alternating pattern. Previous work has provided some clues on the parameters which govern the appearance of this behavior, but there is a lack of systematic studies. A series of non-reacting simulations of adjacent swirling flows is used to investigate the effect of nozzle exit flare angle and swirl number on the presence of the alternating flow pattern. Two-nozzle simulations are shown to accurately predict if an asymmetric flow characteristic appears and are therefore used in the parametric investigation. Alternating flow patterns are predicted at nozzle exit flare angles of 105 degrees (for a swirl number of 0.79) and 120 degrees (for a swirl number of 0.69 and 0.79). Under conditions close to the stability boundary between symmetric and asymmetric flows, the nozzle exit flare and increased swirl number push the shear layers against the dome wall so that the flows between each nozzle are largely opposite in direction. An increase in nozzle exit flare above 120^° results in separated flows exiting from the inlet and a return to a symmetric flow state. This is consistent with a proposed physical mechanism based on hydrodynamic stability in turbulent opposed jets.     

Investigation on onset of shock-induced separation

A great number of experimental data indicating shock wave/boundary layer interactions in internal or external supersonic flows were reviewed to make clear the mechanism of the interaction and to decide the onset of shock-induced separation. The interesting conclusions were obtained for the considerably wide range of flow geometries that the onset of separation is independent of the flow geometries and the boundary layer Reynolds number. It is found that the pressure rise necessary to separate the boundary layer in supersonic external flows could be applied to such internal flows as overexpanded nozzles or diffusers. This is due to the fact that the separation phenomenon caused by shock wave/boundary layer interactions is processed through a supersonic deceleration. The shock-induced separation in almost all of interacting flow fields is governed by the concept of free interaction, and the onset of shock-induced separation is only a function of the Mach number just upstream of shock wave. However, physical scales of the produced separation are not independent of the downstream flow fields.     

Enhanced delayed DES of shock wave/boundary layer interaction in a planar transonic nozzle

An enhanced delayed detached eddy simulation of a shock wave/boundary layer interaction in an over-expanded planar transonic nozzle has been carried out to predict the fundamental features of shock low-frequency unsteadiness. The modification of the sub-grid length-scale proposed in Shur et al. (2015) has been implemented to attenuate some well-known problems of detached eddy simulation: the modeled-stress depletion in the switch region between RANS and LES and the consequent delay of transition to turbulence at the onset of separation. The comparison of the computational results with the experimental data shows that the enhanced DDES leads to significant improvements in the estimation of some flow features with respect to a different DDES version, even though some discrepancies are still observable in the distribution of the mean wall pressure, and additional work is needed to further improve the transition from modeled to resolved turbulence.     

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.     

Effect of the turbulent viscosity relaxation time on the modeling of nozzle and jet flows

Certain modifications of three-equation turbulence models are proposed. They are intended for increasing the accuracy of the calculations of turbulent flows in nozzles with boundary layer separation and in supersonic jets with complicated shock wave structures. Basing on the idea of the inclusion of flow prehistory in terms of an additional relaxation equation for nonequilibrium turbulent viscosity we propose three modifications of the k-ω-µ _t model based on the k-ω model and a version of the k- ?-µ _t turbulence model. In these modifications we introduce an additional dependence of the nonequilibrium turbulent viscosity relaxation time on different physical parameters which can be important near the point of boundary layer separation from the nozzle wall, such as viscous effects and effects of large gradients of the mean velocity and the kinetic energy of turbulence (turbulent pressure). The comparison of the results of the calculations with the experimental data shows that all the proposed versions of the three-equation models make it possible to improve the accuracy of the calculations of turbulent flows in nozzles and jets.     

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.     

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.     

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.     

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.