Subsonic and transonic flow field in two-dimensional de laval nozzles

This paper presents solutions of subsonic and transonic flow fields in two-dimensional De Laval nozzles with preassinged contraction ration ₁, expansion ration ₂, and throat wall radiusR _*. The effects of the contraction and the expansion angle on nozzle flow, the transformation of flow pattern of a De Laval nozzle in the throat region, and the conditions of occurrence and the governing parameters of the supersonic bubbles are discussed.     

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.     

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.     

Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH

Temporal sequences of planar laser-induced fluorescence (PLIF) images of several high-speed, transient flowfields created in a reflection-type shock tunnel facility were acquired. In each case, the test gas contained either nitric oxide or the hydroxyl radical, the fluorescent species. The processes of shock reflection from an endwall with a converging nozzle and of underexpanded free jet formation were examined. A comparison was also made between PLIF imaging and shadow photography. The investigation demonstrated some of the capabilities of PLIF imaging diagnostics in complex, transient, hypersonic flowfields, including those with combustion.Nomenclature A spontaneous emission rate - A _las cross sectional area of laser sheet - B laser absorption rate - C _opt constant dependent on optical arrangement, collection efficiency, etc. - D nozzle throat diameter - E _p laser pulse energy - f _J Boltzmann fraction of absorbing state - g spectral convolution of laser and absorption lineshapes - k Boltzmann constant - M _s incident shock Mach number - N noise, root-mean-square signal fluctuation - P static pressure - P ₁ initial pressure of test gas in shock tube - P _a free jet ambient pressure - P _s stagnation pressure - Q electronic quenching rate of excited state - S PLIF signal - t time between shock reflection and image acquisition - T static temperature - T _s stagnation temperature - _a mole fraction of absorbing species     

Separated nozzle flow

A separated turbulent flow in an axisymmetrical nozzle is studied numerically. Two configurations nozzle are investigated. The first one is the truncated ideal contour nozzle, DLR-TIC, is fed with nitrogen. The second configuration is called the thrust optimized contour nozzle or TOC type, ONERA-TOC, where the operating gas is a hot air. The classical pattern of a free shock separation is obtained for different values of the nozzle pressure ratio. The results are compared and validated using experimental data.     

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.      

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     

Turbulent flow in converging nozzles,part one: boundary layer solution

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.     

Shock and wave dynamics in cavitating compressible liquid flows in injection nozzles

Due to the exceptional high inlet pressures up to 2,000 bar flow dynamics and efficiency of modern injection systems are controlled by high frequency wave dynamics of the compressible liquid flow. Corresponding to alternating shock and expansion waves the liquid fluid evaporates and recondenses instantaneously. Here we present CFD simulations of the time accurate evolution of cavitating flows in 2-D plane and in six-hole injection nozzles with focus on the wave dynamics just after initialisation of the flow and within the time scale Δt ≤ 10^?4 s of pilot and multi-point injection. Due to shock reflections at the bottom of the sack hole the instantaneous maximum pressure increases more than three times higher as compared with the prescribed pressure at the nozzle inlet. For instance, in case of an inlet pressure of 600 bar the maximum pressure in the sack and therefore ahead of the nozzle bore holes reaches about 2,100 bar. It is quite reasonable that this amplification of the pressure affects the evolution of the convective flow and therefore the mass flow through the nozzle bore holes.     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Supersonic flow past a wedge on a flat plate. Laminar boundary layer separation and reattachment

Supersonic laminar flow past a two-dimensional “flat-plate/wedge“ configuration is numerically investigated. The pressures at the boundary layer separation and reattachment points are calculated over wide Mach and Reynolds number ranges. The minimum angles of the wedge surface inclination at which a return flow occurs are determined. The results are presented in the form of generalized Mach-number-dependences of the theoretical pressure on the wedge surface initiating boundary layer separation and the pressure at the boundary layer reattachment point.     

Supersonic two-dimensional flow in a forward separation zone

Supersonic separated flow past a spiked body with a plane cap on the end of the spike (a flat plate or a wedge) is studied. The cases of both symmetric and nonsymmetric flow, with a rotating or nonrotating spike, are considered. The flow pattern, visualized by means of a Toepler instrument and a laser knife, and the limiting streamline patterns are analyzed. The reasons for the initiation of self-oscillations in the flow between the cap and the body are determined. The flow patterns for a rotating and nonrotating spike are compared.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 1995.     

Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body

The flow with a free-stream Mach number M _∞ = 6 around a cylindrical body with a sharp spike is studied. The existence of a supersonic reverse flow for one of the phases of the pulsating flow regime is experimentally validated. A range of spike lengths is determined, which ensures a region of a supersonic reverse flow near the side surface of the spike. The time of existence of the supersonic reverse flow region is shown to be 0.15 of the period of pulsations if the spike length equals the model diameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 30–39, July–August, 2007.     

Flow instability and transient flow patterns inside intercrossed silicon microchannel array in a micro-timescale

The objective of this study is to visualize the transient flow patterns and heat transfer behaviors at low mass fluxes and high heat fluxes. The silicon chip consists of the intercrossed microchannel array with 10 triangular microchannels with the hydraulic diameter of 155.4 μm, and five transverse trapezoid microchannels, separating the triangular microchannels into six independent zones. The chip is horizontally positioned. Liquid acetone is used as the working fluid. Tests were performed in the range of mass flux 40–80 kg/m² s and heat flux 107–216 kW/m².     

Flow transition in dual bell nozzles

The dual bell nozzle is a concept of altitude adaptive nozzles. The flow adapts to the altitude by separation at the wall inflection at low altitude, and full flowing at high altitude. To understand the phenomenology of the flow by the transition from sea-level mode to high altitude mode, a series of tests have been made at the cold flow test bench P6.2 at DLR Lampoldshausen. A dual bell nozzle have been successively shorten and driven in the same conditions for each length. Hence it was possible to observe the flow in the vicinity of the wall inflection using Schlieren optics. Furthermore this study yields the influence of the length ratio between basis and extension on the transition conditions.

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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.     

Convergence properties of high-Reynolds-number separated flow calculations

The convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two-dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi-coarsening multigrid technique that has previously been found to be particularly advantageous for high-Reynolds-number (Re) flows with flow separation and with highly stretched surface-normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock-like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high-frequency fine-grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three-dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high-Re flow computations, since coarser grids may yield oscillation-free solutions that cannot be obtained on finer grids.