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.     

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.     

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.     

Near field shock structure of dual co-axial jets

Experimental results on the shock structure of dual co-axial jets are presented. The effects of the geometric parameters of the inner nozzle, jet static pressure ratio (ratio of the exit plane static pressures of the inner and outer nozzles) and the ratio of outer to inner nozzle throat area on the shock structure were studied. A superimposed outer and inner jet structure was observed in the schlieren photographs. The inner flow is compressed by the outer flow resulting in the formation of a Mach disc and an exit shock. A parameter incorporating the effect of Mach number of the inner nozzle and jet static pressure ratio was found to correlate the observations regarding the Mach disc location.     

Hyperbolic Approximation of the Navier-Stokes Equations for Viscous Mixed Flows

Simplified two-dimensional Navier-Stokes equations of the hyperbolic type are derived for viscous mixed (with transition through the sonic velocity) internal and external flows as a result of a special splitting of the pressure gradient in the predominant flow direction into hyperbolic and elliptic components. The application of these equations is illustrated with reference to the calculation of Laval nozzle flows and the problem of supersonic flow past blunt bodies. The hyperbolic approximation obtained adequately describes the interaction between the stream and surfaces for internal and external flows and can be used over a wide Mach number range at moderate and high Reynolds numbers. Examples of the calculation of viscous mixed flows in a Laval nozzle with large longitudinal throat curvature and in a shock layer in the neighborhood of a sphere and a large-aspect-ratio hemisphere-cylinder are given. The problem of determining the drag coefficient of cold and hot spheres is solved in a new formulation for supersonic air flow over a wide range of Reynolds numbers. In the case of low and moderate Reynolds numbers a drag reduction effect is detected when the surface of the sphere is cooled.     

Shock boundary layer interaction under the influence of a normal suction slot

The phenomenon of shock boundary layer interaction of a shock train under the influence of a normal suction slot is studied. In previous work, it was found that a normal, circumferential suction slot is sufficient to stabilize the primary shock of a shock train in as much as that the back pressure of the shock train can be increased until the shock train gradually changes into a single normal shock. Based on the experimental and numerical results, a flow model was derived which explains the transition of a shock train into a single shock under the influence of boundary layer suction. In this work, the normal shock boundary layer interaction model is validated against flow cases with different upstream Mach and Reynolds numbers. For that purpose three different nozzle flows are investigated at various total pressure levels. In a second step, the flow model is extended to the oblique shock case, correlating the suction mass flow with the total pressure distribution of the incoming boundary layer and the static pressure downstream of the oblique shock. Finally, the influence of the suction cavity pressure onto the shock boundary layer interaction is considered.     

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.     

Investigation of a compressible turbulent boundary layer in the presence of tangential blowing and a positive pressure gradient

The present study is devoted to the computational investigation of the compressible turbulent boundary layer and flow that are formed during tangential blowing of various gases in a thick boundary layer for large positive pressure gradients. Such flows occur in elements of the gas-dynamic channel of turbojet engines and liquid-fuel rocket engines, ejector pumps, and other technical devices. Using a numerical method we investigate the effect of various factors (the Mach number of blowing, the type of blown gas, and the intensity of variation of the pressure gradient) on the stability of the boundary layer up to its separation.     

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.     

Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.     

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.     

Boundary-layer separation on conical bodies

Some characteristics of the variation in the linear dimensions of the flow separation zones on conical bodies with expanding conical skirts and of variation of the pressure within these zones as a function of variation of the Mach number, Reynolds number, and intensity of the disturbance that causes the boundary layer separation are examined. Experiments were conducted in laminar, transitional, and turbulent flows in flow separation regions. The interaction of viscous and nearly inviscid flows is quite common. This phenomenon occurs in flow past a concave corner, when a compression shock impinges on a boundary layer, and in many other cases. The characteristics of this phenomenon in flow about two-dimensional bodies have been investigated experimentally in [1, 2] and other studies. Attempts have been made to analyze the interaction of compression shocks with the boundary layer theoretically. In “free” separated flows, when the points of separation and reattachment of the boundary layer are not fixed (for example, on a flat plate with a long wedge attached to it), theoretical studies are usually made within the framework of the boundary layer theory with use of the approximate integral methods [3, 4]. In this article we examine some results from studies of free separated flows on conical bodies with conical skirts in laminar, transitional, and turbulent flows (Fig. 1).     

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.     

Unsteadiness of the shock wave structure in attached and separated compression ramp flows

Wall pressure fluctuations have been measured upstream of the corner-line in several two dimensional, adiabatic, compression ramp flows. The nominal freestream Mach number was 3 and the Reynolds number, based on boundary layer thickness, was 1.4 million. The measurements show that the shockwave structure is unsteady in both separated and attached flows, resulting in a region in which the wall pressure signal is intermittent. Statistical properties of this intermittent region, and of the separated flow, are presented and correlated with results from other studies.     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

Statistical laws of the pressure fluctuations in a hypersonic turbulent boundary layer

The results of measuring the pressure fluctuations on the wall of the nozzle of a hypersonic wind tunnel beneath a developed turbulent boundary layer are presented for the Mach number M_∞ = 7.5. On the basis of a statistical analysis, it is shown that the action of the turbulent flow is dynamically similar to the propagation of a random sequence of wave packets with continuously distributed temporal and spatial scales. Low-frequency disturbances are associated with large-scale structures of long duration that propagate at a mean-statistical velocity similar in value to the outer flow velocity. The continuous generation of weakly-correlated small-scale disturbances ensuring the maintenance and development of turbulence occurs chiefly in the inner region of the boundary layer. Spectral estimates of the power generated by the turbulent flow in the wall region of the boundary layer are presented.     

Calculation of supersonic separation flow in circular nozzles with abrupt expansion

A study is made of the interaction of a circular supersonic jet with a turbulent layer of the near-wake kind formed behind a circular step on the end part of a nozzle with abrupt expansion. The flow in the viscous layer is calculated by the integral method, and in the inviscid flow by a through-computation method using a monotonic implicit difference scheme of first order of accuracy. The interaction between the inviscid and turbulent flows is determined by the displacement thickness of the viscous layer. The initial conditions for the flow in the layer are determined from the integral conditions of its matching to the isobaric mixing flow in the base region behind the step. The computed interaction flows are determined as a function of the length of the end part and the counter pressure simultaneously or separately by the boundary condition that the pressure at the end of the end part be equal to the pressure of the external medium and by a singular solution of the equations passing through a saddle singular point — the throat of the wake. In a conical nozzle with profiled attachments of different lengths, calculations were made of separation flows with open and closed base regions and with allowance for secondary separation. The obtained solutions are multivalued in a certain range of lengths of the end part and values of the counter pressure. The solutions realized in reality are selected by analyzing the regimes of operation of the nozzles, and the calculated regions of hysteresis and associated low-frequency nonstationary separation flows are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 120–128, July–August, 1979.We are grateful to M. Ya. Ivanov for consultation on the use of the program of [6] and to Z. A. Donskovaya for assistance in preparing the paper.     

A hybrid pressure–density‐based algorithm for the Euler equations at all Mach number regimes

In the present work, we propose a reformulation of the fluxes and interpolation calculations in the PISO method, a well‐known pressure‐correction solver. This new reformulation introduces the AUSM⁺ ? up flux definition as a replacement for the standard Rhie and Chow method of obtaining fluxes and central interpolation of pressure at the control volume faces. This algorithm tries to compatibilize the good efficiency of a pressure based method for low Mach number applications with the advantages of AUSM⁺ ? up at high Mach number flows. The algorithm is carefully validated using exact solutions. Results for subsonic, transonic and supersonic axisymmetric flows in a nozzle are presented and compared with exact analytical solutions. Further, we also present and discuss subsonic, transonic and supersonic results for the well known bump test‐case. The code is also benchmarked against a very tough test‐case for the supersonic and hypersonic flow over a cylinder. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

A procedure for the design of nozzles used for the production of turbulent liquid jets

Where turbulent liquid jets are used for cutting and mining purposes the pressure generated by impact must be maximized. Initial jet behaviour has an important influence on subsequent jet impact pressures at medium range. Nozzle wall boundary layer history has a strong influence on the initial jet, and certain boundary layer features can be linked to poor jet performance. The procedure outlined in this paper was developed to eliminate new nozzle designs or changes in operating conditions on the grounds of badly behaved nozzle boundary flow. The design procedure consists of a potential flow analysis and a boundary layer analysis coupled to empirical correlations for boundary layers in accelerated flows. The procedure is exemplified by application to the design of a nozzle to be used for the specific purpose of mining china clay.