Supersonic Region Research Articles

Resolvent-based study of compressibility effects on supersonic turbulent boundary layers

The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the freestream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.

Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

A quantification of penetration length of steam jet condensation in turbulent water flow in a vertical pipe

An experimental research is performed to investigate the penetration length of steam jet condensation in turbulent water flow in a vertical pipe. The penetration length of the condensing jet, with steam mass velocities ranging from subsonic to supersonic, was measured via utilizing a visualization window and a high-speed camera. At low steam flow rate a steam bubble plume forms, while at relatively high flow rate the bubbles in the plume coalesce and a steam jet is produced. Quantitative analyses of the interface behavior of the condensing jet are performed by exploring the transient and statistical characteristics of the jet penetration length. The waveforms of the transient jet penetration length exhibit that in the bubbling regime the period is approximately constant, while in the jetting regime the period varies a lot. The statistical analysis of the transient jet penetration length confirms that significant variations of the power distribution function (PDF) and power spectrum density (PSD) between the bubbling and jetting regimes occur at the transonic condition. The ratio of steam mass flux to critical steam mass flux at ambient pressure is found to have good linearity with the mean of the jet penetration length. And a linear correlation is fitted with a maximum absolute deviation of 5.5% between the measured and predicted values of mean of the jet penetration length. The relative unsteadiness of jet penetration length, defined as the ratio of the standard deviation to mean of transient penetration length, is approximately invariable in the bubbling and jetting regime. The bubbling regime contains more relative unsteadiness, while the jetting regime yield less relative unsteadiness. Because absolute instability exists in the subsonic region while no absolute instability occurs in the supersonic region, the transition from the bubbling to jetting regime occurs in the transonic region.

Experimental investigation on interfacial behavior and its associated pressure oscillation in steam jet condensation in subcooled water flow

An experimental study is performed to investigate mechanisms of the interfacial behavior and their associated pressure oscillations in steam jet condensation in subcooled water flow in a vertical pipe. The transient interfacial behavior of the condensing jet is first captured by a high speed camera, and then its parameters are quantitatively computed by using digital image processing technology. Pressure oscillations associated with jet interfacial evolutions are acquired by flush mounted pressure transducers with high frequency response on the wall. The interfacial behavior of the jet at two typical condensation regimes, i.e., bubbling regime and jetting regime, and their corresponding quantitative temporal and spatial evolutions of radial and axial interfaces and pressure oscillations are analyzed. With increase of steam mass flux, interfacial oscillations and pressure oscillations reach local maximum near the sonic point, and they remain almost unchanged after entering the supersonic region. Dominant frequencies of radial and axial interfacial oscillations and those of pressure oscillations are almost the same at subsonic and sonic conditions, while the dominant frequency disappears at supersonic conditions. Very strong correlations between interfacial oscillations and pressure oscillations are quantified through the oscillation intensity and correlation coefficient and also the power spectrum density, which confirms quantitatively that pressure oscillations are induced by interfacial oscillations of the jet.

Numerical Investigation of Jet Interactions for a Lateral Thrust Jet Controlled Interceptor Operating at Medium Altitudes

Lateral thrust jets exhibit better maneuverability performance than control surfaces such as conventional fins for attitude control or the orbital transfer of guided weapons. In the supersonic region, however, jet interaction phenomena occur due to the lateral thrust jet during flight and a complicated flow structure is exhibited by the interaction of the shock wave, boundary layer flow, and vortex flow. In particular, hit-to-kill interceptors require precise control and maneuvering; therefore, it is necessary to analyze the effect of the jet interaction flow. A number of conventional jet interaction analyses have been performed under low-altitude conditions; however, there are not many cases with respect to medium-altitude conditions. Unlike low-altitude conditions, jet interaction flows at medium-altitude conditions have different flow characteristics. In this study, a jet interaction flow analysis is performed on a lateral thrust jet controlled interceptor operating at medium altitudes. Based on the results, the characteristics of the flow structure and the changes in the aerodynamic coefficients are analyzed.

Boundary-Layer Development Downstream of Normal Shock in Transonic Intakes at Incidence

The flowfield around five transonic inlet lips at high incidence is investigated for a variety of flow conditions around a design point representative of high-incidence maneuvering. Changes to the operating point are simulated by varying the angle of incidence and the mass flow rate over the lip, which is intended to mimic the effect of an increase in engine flow. For these inflow conditions, the flow on the lip is characterized by a supersonic region, which is terminated by a near-normal shock wave. Of particular interest is the effect of the lip geometry and operating point on the boundary layer at the equivalent fan location. The parametric investigation revealed a significant effect of the lip shape on the position and severity of the shock-wave/boundary-layer interaction. From correlation studies, it appears that the extent of shock-induced separation is the main factor affecting the boundary-layer state downstream of the normal shock-wave/boundary-layer interaction. Somewhat surprisingly, this was found to be independent of shock strength.

Nacelle-airframe integration design method for blended-wing-body transport with podded engines

Strong shock waves and flow separation often occur during the integration of nacelle and airframe for blended-wing-bodies with podded engines. To address this problem, this paper presents an integration method with numerical simulations. The philosophy of channeling flow and avoiding the throat effect on the nacelle and airframe is established based on the analysis of flow interference in the initial configuration. A parametric integration design method is proposed from two-dimensional plane to three-dimensional space with control mechanisms and selection principles of the key parameters determined by their influences. Results show that strong shock waves and flow separation can be successfully eliminated under the influence of both the reshaped channel and decelerated inflow below the nacelle. Supersonic regions around the nacelle are effectively reduced, concentrating mainly on the lip position. Thus, a significant cruise drag reduction (8.7%) is achieved though the pressure drag of the nacelle increases.

Experimental investigation on interfacial oscillation of direct contact condensation of steam jet in water pipe flow

Interfacial oscillation associated with direct contact condensation of steam jet in water pipe flow is of high significance for industrial processes. In this paper, experimental study is conducted to reveal the mechanisms of the interfacial oscillation in steam jet condensation in subcooled water flow in a vertical pipe. The interfacial behavior of the jet plume is acquired by high speed camera, and the entire interface in both space and time simultaneously is quantitatively analyzed with digital image processing technology. Bubbling regime occurs at subsonic conditions, where an undulated bubble plume forms with one or more large bubbles falling off intermittently. Jetting regime happens at transonic or supersonic conditions, where a quasi-stable jet plume is observed with numerous uncondensed tiny bubbles continuously shedding off from the end of the jet plume. Distinct waveforms of the radial interface position in both space and time simultaneously are recognized for the two typical condensation regimes. The interfacial unsteadiness reaches a maximum near the sonic point and then drops in the supersonic region, which exhibits similar trend with pressure oscillation induced by condensing jet in a qualitative sense. The results confirm that the pressure oscillation is highly relevant to the motion of the jet interface and it should be induced by the interfacial oscillation. The spatial growth rate of the interface unsteadiness along the jet decreases steadily as steam mass flux increases from subsonic to sonic point and it almost does not vary in the supersonic region. The Kelvin-Helmholtz instability mechanism is more important near the nozzle exit, while in other region the Kelvin-Helmholtz instability is of the same importance as the Rayleigh-Taylor instability.

Characteristics of plasma flow profiles in a super-X-divertor-like configuration

Abstract Plasma flow patterns in a super-X-divertor-like configuration are investigated by using a one-dimensional plasma fluid model with the anisotropic-ion pressure (AIP model). The AIP model enables to treat supersonic plasma flows self-consistently by describing the parallel plasma momentum transport with a hyperbolic equation keeping the finite effect of the parallel viscosity. A supersonic plasma flow in the diverging-magnetic-field divertor region is generated due to the magnetic nozzle effect. It is found that the sonic-transition point has bifurcation characteristics. A numerical solution from the AIP model agrees well with an analytical one. The Braginskii’s plasma fluid model, on the other hand, creates various unphysical profiles in the supersonic plasma flow region for different boundary conditions of the plasma flow at the sheath entrance. It is also found that a particle source/sink in front of the target brings about generations of subsonic/supersonic plasma flow profiles. Moving the target position, it is found that a discontinuous change in the sonic-transition point and corresponding profile of plasma flow can happen due to the bifurcating characteristics of the sonic-transition point.

Numerical analysis of the aerodynamic performance & heat transfer of a transonic turbine with a partial squealer tip

The purpose of this study is to evaluate thermal load and aerodynamic performance by applying different shapes of tips depending on the velocity region in a transonic turbine where subsonic and supersonic regions coexist. The RS1S, which is the transonic turbine of SNECMA, is used. To understand the tendencies, geometries A, B and C were created by varying the length of the pressure surface rim and the suction surface rim, and they were compared with a flat tip, squealer tip, pressure surface rim and suction surface rim. RANS computational analysis was performed using the commercial code ANSYS CFX 18.0, and aerodynamic performance was evaluated by using the mass-averaged total pressure loss coefficient at the 133% Cax and the mass flow rate of tip leakage. Thermal load was also evaluated by using the area-averaged heat transfer coefficient at the tip. Although the mass flow rate of leakage was smallest with the squealer tip, geometry C, the 75% rim of the pressure surface and the suction surface showed the lowest total pressure loss coefficient, which was 6.5% lower than that of the flat tip. In addition, when only the suction surface rim was applied, the area-averaged heat transfer coefficient was 10% lower than that of the flat tip.

Characteristic path analysis of confinement influence on steady two-dimensional detonation propagation

Steady detonation in multi-dimensional flow is controlled by the chemical energy release that occurs in a subsonic elliptic flow region known as the detonation driving zone (DDZ). It is the region encompassing the detonation shock and sonic flow locus (in the frame of the detonation shock). A detonation that is strongly confined by material surrounding the explosive has the shock and sonic locus separated at the material interface. Information about the material boundary is traditionally believed to influence the DDZ structure via the subsonic flow on the boundary ahead of the sonic locus. A detonation that is weakly confined has the detonation shock and sonic locus intersecting at the material boundary. The sonic nature of the flow at the intersection point on the boundary is believed to isolate the DDZ structure from the material properties of the confinement. In this study, we examine the paths of characteristics propagating information about the confinement through the supersonic hyperbolic flow region that exists beyond the sonic locus, and determine whether these paths may impinge on the sonic locus and consequently influence the DDZ structure. Our configuration consists of a solid wall boundary deflected through a specified angle on detonation shock arrival, so that the streamline turning angle of the wall at the explosive edge is unambiguously defined. By varying the wall deflection angle from small through large values, we can systematically capture the evolution of the DDZ structure and the characteristic flow regions that influence its structure for strongly to weakly confined detonations. In all strong and weak confinement cases examined, we find that a subset of characteristics from the supersonic flow regions always impinge on the sonic locus. Limiting characteristics are identified that define the boundary between characteristics that impinge on the sonic surface and those that propagate information downstream of the sonic surface. In combination with an oblique-shock polar analysis, we show that the effects on the DDZ of characteristic impingement can be significant.

Smooth Transonic Flows of Meyer Type in De Laval Nozzles

A smooth transonic flow problem is formulated as follows: for a de Laval nozzle, one looks for a smooth transonic flow of Meyer type whose sonic points are all exceptional and whose flow angle at the inlet is prescribed. If such a flow exists, its sonic curve must be located at the throat of the nozzle and the nozzle should be suitably flat at its throat. The flow is governed by a quasilinear elliptic–hyperbolic mixed type equation and it is strongly degenerate at the sonic curve in the sense that all characteristics from the sonic points coincide with the sonic curve and never approach the supersonic region. For a suitably flat de Laval nozzle, the existence of a local subsonic–sonic flow in the convergent part and a local sonic–supersonic flow in the divergent part is proved by some elaborate elliptic and hyperbolic estimates. The precise asymptotic behavior of these two flows near the sonic state is shown and they can be connected to a smooth transonic flow whose acceleration is Lipschitz continuous. The flow is also shown to be unique by an elaborate energy estimate. Moreover, we give a set of infinitely long de Laval nozzles, such that each nozzle admits uniquely a global smooth transonic flow of Meyer type whose sonic points are all exceptional, while the same result does not hold for smooth transonic flows of Meyer type with nonexceptional points.

RANS/ILES Analysis of the Flow Pattern and the Acoustic Characteristics of a Supersonic Off-Design Jet at Large Nozzle Pressure Ratios

The outflow of a cold supersonic off-design jet with the nozzle pressure ratio of 21.8 is calculated using the high-resolution RANS/ILES method. For the nozzle under consideration and at the given nozzle pressure ratio the exit-to-ambient pressure ratio is 0.6. The jet is characterized by a long supersonic region with many “barrels.” The calculations are validated against the experimental data. The fluctuating and acoustic characteristics of the jet flow under consideration are compared with the characteristics of other supersonic jets. The geometric dimensions of the barrels and the acoustic properties of the jet are estimated from the known empirical relations for supersonic jets.

Sound radiation and transonic boundaries of a plate with an acoustic black hole.

The acoustic black hole (ABH) phenomenon has shown promise for noise and vibration control applications. In this paper, a two-dimensional (2-D) Daubechies wavelet (DW) model is established for the sound radiation prediction of plates embedded with a circular ABH indentation. ABH plates are shown to exhibit a reduced sound radiation efficiency as compared with their flat counterpart. Below the critical frequency, this is caused by the weakening of the structural stiffness due to the ABH indentation. Above the critical frequency, a subsonic region inside the ABH cell may appear, containing acoustically slow structural waves. This region, confined within a transonic boundary, is due to the ABH-specific phase velocity reduction of the bending waves. Drawing energy away from the supersonic region of the plate, this subsonic region warrants a reduced sound radiation to the far field. Numerical results on the investigated configuration show an increase in the sound radiation efficiency due to the added stiffness effect of damping layers. Sound radiation efficiency alongside the transonic boundary changes is scrutinized and quantified. Visualization of the supersonic acoustic intensity and radiation allows identifying the effective sound radiation regions of ABH plates and their relationship with the transonic boundaries at different frequencies.

Investigation of a highly underexpanded jet with real gas effects confined in a channel: flow field measurements

This article describes experiments to investigate the fluid-to-wall interaction downstream of a highly underexpanded jet, with a pressure ratio of 120, confined in a channel. Heat transfer induced by Joule-Thomson cooling, which is a real gas effect in such a configuration, has critical implications on the safety of pressurised gas components. This phenomenon is challenging to model numerically due to the requirement to implement a real gas equation of state, the large range of (subsonic and supersonic) velocities, the high turbulence levels and the near-wall behaviour. An experimental setup with simple geometry and boundary conditions, and with a wide optical access was designed and implemented. It consisted of a high-pressure gas reservoir at controlled temperature and pressure, discharging argon through a nozzle into a square channel. This facility was designed to allow for a steady-state expansion from over 120 bar to atmospheric pressure for over 1 min. The choice of fluid, pressure and temperature regulation system, and the implementation of a high pressure particle seeding system are discussed. The gas dynamics of this flow was then investigated by two separate optical techniques. Schlieren measurements were used to locate the position of the Mach disk, and planar particle image velocimetry (PIV) was used to measure the turbulent velocity field in the regions of lower velocity downstream. Mie scattering images also indicated the presence of a condensed argon phase in the supersonic region as expected from previous studies on nucleation. The observed location of the sharp interface at the Mach disk was found to be in excellent agreement with the Crist correlation. Rapid statistics were derived from the PIV measurements at 3 kHz. The recirculation zone was found to extend about 4 channel heights downstream, and in the region between 2 and 3 channel heights downstream, a continuous deceleration on the centerline velocity was observed in line with the narrowing of the recirculation zone. The first and second velocity moments as well as Reynold stresses were quantified, including pdf distributions. In addition, a sensitivity and repeatability analysis, an evaluation of the PIV random uncertainty, as well as an estimation of errors induced by particle inertia were performed to allow for a full quantitative comparison with numerical simulations.

Subsonic impulsively starting flow at a high angle of attack with shock wave and vortex interaction

Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently, a preliminary numerical study for subsonic starting flow at a high angle of attack displays an advance of stall around a Mach number of 0.5, when compared to other Mach numbers. To see what happens in this special case, we conduct here in this paper a further study for this case, to display and analyze the full flow structures. We find that for a Mach number around 0.5, a local supersonic flow region repeatedly splits and merges, and a pair of left-going and right-going unsteady shock waves are embedded inside the leading edge vortex once it is sufficiently grown up and detached from the leading edge. The flow evolution during the formation of shock waves is displayed in detail. The reason for the formation of these shock waves is explained here using the Laval nozzle flow theory. The existence of this shock pair inside the vortex, for a Mach number only close to 0.5, may help the growing of the trailing edge vortex responsible for the advance of stall observed previously.

Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach

Shock-dominated hypersonic laminar flows over a double cone are investigated using time accurate direct simulation Monte Carlo combined with the residuals algorithm for unit Reynolds numbers gradually increasing from 9.35 × 104 to 3.74 × 105 m−1 at a Mach number of about 16. The main flow features, such as the strong bow-shock, location of the separation shock, the triple point, and the entire laminar separated region, show a time-dependent behavior. Although the separation shock angle is found to be similar for all Re numbers, the effects of Reynolds number on the structure and extent of the separation region are profound. As the Reynolds number is increased, larger pressure values in the under-expanded jet region due to strong shock interactions form more prominent λ-shocklets in the supersonic region between two contact surfaces. Likewise, the surface parameters, especially on the second cone surface, show a strong dependence on the Reynolds number, with skin friction, pressure, and surface heating rates increasing and velocity slip and temperature jump values decreasing for increasing Re number. A Kelvin-Helmholtz instability arising at the shear layer results in an unsteady flow for the highest Reynolds number. These findings suggest that consideration of experimental measurement times is important when it comes to determining the steady state surface parameters even for a relatively simple double cone geometry at moderately large Reynolds numbers.

Unsteady surface pressures measured at a pitching Lambda wing with vortex dominated flow and transonic effects

In the Transonic Wind Tunnel Gottingen, pitch oscillations were performed with a Lambda wing to study unsteady pressure distributions of vortex dominated flow including transonic effects. The free stream Mach number was varied between 0.3 and 0.7. Small pitching amplitudes of $$0.08^{\circ }$$ – $$0.4^{\circ }$$ at excitation frequencies up to 40 Hz were used. In this paper, particularly the data of unsteady Pressure Sensitive Paint measurements and unsteady pressure sensors are analyzed. With increasing angle of attack, a suction peak and a shock occur near the leading edge. Then a shock-induced separation triggers the development of a vortex at the main wing. The unsteady pressures show: for lower angles of attack, the transonic influences are dominant. For higher angles of attack, the influence of the vortex becomes of similar magnitude and dominates the behavior of the pressure variations. The shock exhibits, with increasing angle of attack, an inverse motion. For angles of attack beyond the maximum lift, the unsteady pressure distributions and the lift show a significant phase lag, already at very low oscillation frequencies. Compared to subsonic cases, the supersonic region shifts the vortex induced pressures downstream.

Identification of temporal and spatial signatures of broadband shock-associated noise

Broadband shock-associated noise (BBSAN) is a particular high-frequency noise that is generated in imperfectly expanded jets. BBSAN results from the interaction of turbulent structures and the series of expansion and compression waves which appears downstream of the convergent nozzle exit of moderately under-expanded jets. This paper focuses on the impact of the pressure waves generated by BBSAN from a large eddy simulation of a non-screeching supersonic round jet in the near-field. The flow is under-expanded and is characterized by a high Reynolds number $$\mathrm{Re}_\mathrm{j} = 1.25\times 10^6$$ and a transonic Mach number $$M_\mathrm{j}=1.15$$ . It is shown that BBSAN propagates upstream outside the jet and enters the supersonic region leaving a characteristic pattern in the physical plane. This pattern, also called signature, travels upstream through the shock-cell system with a group velocity between the acoustic speed $$U_{\mathrm{c}}-a_\infty $$ and the sound speed $$a_\infty $$ in the frequency–wavenumber domain $$(U_\mathrm{c}$$ is the convective jet velocity). To investigate these characteristic patterns, the pressure signals in the jet and the near-field are decomposed into waves traveling downstream ( $$p^+$$ ) and waves traveling upstream ( $$p^-$$ ). A novel study based on a wavelet technique is finally applied on such signals in order to extract the BBSAN signatures generated by the most energetic events of the supersonic jet.

A Study on Efficiency Characteristics of Axial Counter Rotating Fan in Supersonic Region.

A Study on Efficiency Characteristics of Axial Counter Rotating Fan in Supersonic Region.