Weak Oblique Shock Wave Research Articles

Base Flow and Drag Characteristics of a Supersonic Vehicle with Cold and Hot Jet Flows of Nozzles

Base drag has a significant effect on the overall drag of a projectile in a supersonic flow. Herein, the base drag and flow characteristics of cold and hot gas flow in a supersonic flow are analyzed via numerical simulations. The hot gas flow is simulated using a chemical equilibrium application code based on hydrogen combustion. Two types of nozzle configurations, namely conical and contoured, are chosen for the simulation. The simulation results reveal that the change in base drag is 5–85% according to the injection gases. In the over-expanded and slightly under-expanded conditions, the base drag decreases in the hot gas flow, owing to the weak expansion fan caused by the high-temperature nozzle flow expansion, whereas in the highly under-expanded condition, the base drag decreases, owing to the strong shock wave near the base caused by the deflection of the recirculation region toward the body wall. In addition, the variations in base flow structures are observed differently compared with the cold flow; for example, a weak oblique shock wave at the nozzle exit, an increase in the distance between the shock wave and base, and deflection of the recirculation region based on the body wall are observed.

Development of unsteady background-oriented schlieren system in an indraft supersonic wind tunnel

To visualize the flow in the test section of an indraft supersonic wind tunnel in the University of Glasgow as long as possible, a background-oriented schlieren system was built up preliminarily. A MATLAB program based on a random dot algorithm developed in this study provides a fully customizable tool to generate background patterns with different sizes and dot densities. Background patterns produced by the in-house developed program then can be printed by a common ink-jet printer. To enhance the signal-noise ratio of the measurement system, white reflective film sheets, or semi-transparent paper can be employed. The correlation algorithm base on fast Fourier transform that is also applicable for PIV was chosen to process background oriented schlieren images. A validation test was performed to visualize the flow structure around a Pitot tube at M = 2.0. The experimental result proves that the BOS system established in this study is capable of visualizing the supersonic flow structure around the Pitot tube and sensitive enough to reveal weak density changes produced by the boundary layer, expansion waves, and weak oblique shock waves. Next, the current BOS system will be improved further by increasing the intensity of light sources to shorten the exposure time, using new cameras with better spatial resolution, and optimizing the background pattern.

Numerical investigations on detonations in a condensed-phase explosive and oblique shock waves in surrounding fluids

In this work, we studied detonation in condensed-phase explosives of PETN and the oblique shock waves in the surrounding fluid. The surrounding fluid was modeled as an ideal gas equation of state using the specific heat ratio as a parameter. Depending on the specific heat ratio, four types of flow structures were observed behind the oblique shock wave in the ideal gas. We measured the detonation/shock angles and the contact angle between the detonation products and the ideal gas. When the specific heat ratio was greater than the critical value, the oblique shock wave was detached from the detonation front at the PETN/ideal gas interface. When attached, three types of waves are observed, depending on the specific heat ratio: a strong oblique shock wave, strong and weak oblique shock waves which meet at the triple point as well as a weak oblique shock wave. To understand the properties of the flow near the detonation and the oblique shock waves, they were modeled as planar Chapman–Jouguet (CJ) detonation in PETN and as oblique shock waves in ideal gas. They were theoretically estimated as (1) Prandtl–Meyer expansion of the detonation products from the CJ state, and (2) oblique shock waves around a wedge using oblique shock theory or around a cone using the Taylor–Maccoll equation. From the flow models, we obtained a solution for the pressure equilibrium and parallel flows between the detonation products and ideal gas under the assumption that the wedge and cone angles correspond to the contact angle between them. For the attached cases, the solution was consistent with the simulated observations at the PETN/ideal gas interface. From the flow models, the maximum deflection angles for the detonation products and the ideal gas were obtained, and their magnitude correlations used to classify the four types of flow.

Aerodynamic actuation characteristics of radio-frequency discharge plasma and control of supersonic flow**Project supported by the National Natural Science Foundation of China (Grant Nos. 11472306, 51407197, and 51507187).

In this paper, aerodynamic actuation characteristics of radio-frequency (RF) discharge plasma are studied and a method is proposed for shock wave control based on RF discharge. Under the static condition, a RF diffuse glow discharge can be observed; under the supersonic inflow, the plasma is blown downstream but remains continuous and stable. Time-resolved schlieren is used for flow field visualization. It is found that RF discharge not only leads to continuous energy deposition on the electrode surface but also induces a compression wave. Under the supersonic inflow condition, a weak oblique shock wave is induced by discharge. Experimental results of the shock wave control indicate that the applied actuation can disperse the bottom structure of the ramp-induced oblique shock wave, which is also observed in the extracted shock wave structure after image processing. More importantly, this control effect can be maintained steadily due to the continuous high-frequency (MHz) discharge. Finally, correlations for schlieren images and numerical simulations are employed to further explore the flow control mechanism. It is observed that the vortex in the boundary layer increases after the application of actuation, meaning that the boundary layer in the downstream of the actuation position is thickened. This is equivalent to covering a layer of low-density smooth wall around the compression corner and on the ramp surface, thereby weakening the compressibility at the compression corner. Our results demonstrate the ability of RF plasma aerodynamic actuation to control the supersonic airflow.

Intensification of shock-induced combustion by electric-discharge-excited oxygen molecules: numerical study

Mechanisms of combustion enhancement in a supersonic H2–O2 reactive flow behind an oblique shock wave front are investigated when vibrational and electronic states of O2 molecule are excited by an electric discharge. The analysis is carried out on the base of updated thermally nonequilibrium kinetic model for the H2–O2 mixture combustion. The presence of vibrationally and electronically excited O2 molecules in the discharge-activated oxygen flow allows to intensify the chain mechanism and to shorten significantly the induction zone length at shock-induced combustion. It makes possible, for example, to ignite the atmospheric pressure H2–O2 mixture at the distance shorter than 1 m behind the weak oblique shock wave at a small energy Es = 1.2 × 10–2 J · cm–3 input to O2 molecules. At higher pressure it is needed to put greater specific energy into the gas in order to ignite the mixture at appropriate distances. It is shown that excitation of O2 molecules by electric discharge is much more effective for accelerating the hydrogen–oxygen mixture combustion than mere heating the gas.

Design of a Near-Isentropic Supersonic Inlet Using Active Control

At wo-dimensional Mach 2.2 internal compression with 97% total pressure recovery has been designed using viscid-inviscid computational tools. Losses are minimized by careful boundary-layer management combined with shape design for weak shocks. The resulting has reduced stability to unstart in the face of atmospheric and engine-borne disturbances, necessitating the use of an active stabilization bleed system that recovers the disturbance-rejection capabilities required of modern inlets. Atmospheric disturbances that the may en- counter during supersonic flight are characterized. Two separate physical mechanisms for unstart are identified, and active control algorithms to prevent these forms of unstart are designed and demonstrated using one- and two-dimensional unsteady Euler simulations. The resulting actively stabilized can withstand flight velocity, temperature, and angle-of-attack perturbations consistent with atmospheric flight. N acts as an interface between the freestream and an air- craft propulsion system. The flow is decelerated to a Mach number required at the compressor face, and energy is recovered in the form of increased pressure. Although it is theoretically possible to design an to achieve virtually isentropic compression of the supersonic flow to sonic conditions, in practice this may be impos- sible to realize due to flow disturbances and geometric variations in the inlet. Because shock waves contribute to loss in pressure recov- ery, a more realistic design is one that can achieve near-isentropic internal compression with a number of weak oblique shock waves and a weak terminal normal shock just behind the throat to decel- erate the flow to subsonic conditions. Such a design is shown in Fig. 1. The potential payoff of such a high-recovery is significant. In the case of a typical 100,000-lb (45,300 kg) supersonic aircraft, such as the quiet supersonic platform, improving the recovery to 97% in cruise could increase the range by approximately 500 n miles. 1 In addition, because most supersonic inlets require bleed on the order of 8% of the flow to stabilize the terminal shock and control boundary-layer separation for the worst-case atmospheric disturbances, the reduced bleed requirement of the present design, primarily due to the weaker shock waves, may lead to additional gains at the system level. The price of achieving high recovery is reduced stability to flow disturbances. These include atmospheric disturbances entering the and engine-borne disturbances traveling upstream from the compressor face. These disturbances can cause a normal shock blowout event known as inlet 2 Inlet unstart results in a severe increase in drag due to flow spillage and formation of a strong shock wave at the lip. In addition, the accompanying decrease in mass flow through the may also result in engine surge. We can define the unstart tolerance of the as the magnitude of the disturbance that can be tolerated without unstart. The tradeoff between stability and pressure recovery is primarily a conse- quence of the strength of the terminal normal shock. 3 Thus, an

A Study on the Aerodynamic Noise of a Supersonic Exhaust Nozzle of Slotted Tube

The objective of this study is to experimentally investigate the noise propagating characteristics, the noise reduction mechanism and the performance of a slotted tube attached at the exit plane of a circular convergent nozzle. The experiment is performed through the systematic change of the jet pressure ratio and the slot length under the condition of two kinds of open area ratios, 25% and 51%. The open area ratio calculated by the tube length equivalent for the slot length is defined as the ratio of the total slot area to the surface area of a slotted tube. The experimental results for the near and far field sound, the visualization of jet structures and the static pressure distributions in the jet passing through a slotted tube are presented and explained in comparison with those for a simple tube. The propagating characteristics of supersonic jet noises from the slotted tube is closely connected with the slot length rather than the open area ratio, and its propagating pattern is similar to the simple tube. It is shown that the slotted tube has a good performance to suppress the shock-associated noise as well as the turbulent mixing noise in the range of a limited jet pressure and slot dimension. The considerable suppression of the shock‘associated noise is mainly due to the pressure relief caused by the high-speed jets passing through the slots on the tube. Both the strength of shock waves and the interval between them in a jet plume are decreased by the pressure relief. Moreover, the pressure relief is divided into the gradual and the sudden relief depending upon the open area ratio of the slotted tube. Consequently, the shock waves in a jet plume are also changed by the type of pressure relief. The gradual pressure relief caused by the slotted tube with the open area ratio 25% generates the weak oblique shock waves. On the contrary, the weak normal shock waves appear due to the sudden pressure relief caused by the slotted tube with the open area ratio 51%.

Gasdynamic enhancement of nonpremixed combustion

To promote efficient performance of very high speed air-breathing propulsion systems, the combustor Mach number must be of the order of six for a flight Mach number of 18. Because of this high gas speed through the combustor, mixing rates of hydrogen fuel with air must be very rapid in order to allow a combustor of reasonable length. It is proposed to enhance the rate of mixing and combustion of hydrogen and air, and thereby reduce combustor length, through the introduction of streamwise vorticity generated by the interaction of a weak oblique shock wave with the density gradient between air and a cylindrical jet of hydrogen. Because of the high Mach number flow in the combustor, the oblique shock traverses the jet at a small angle with respect to the free stream direction, and the principle of slender body theory allows one conceptually to replace the three-dimensional steady flow with a two-dimensional unsteady flow. As a consequence, two-dimensional time-dependent computational studies and an extensive experimental shock tube investigation were employed to assess mixing rates for the steady flow in the combustor. The results indicated that under realistic conditions, adequate mixing could be accomplished within 1 ms, a rate that was technologically interesting. Encouraged by these experiments, a “practical” injector, utilizing shock-enhanced mixing, was designed for a combustor having a free stream Mach number of 6.0. A detailed aerodynamic and mixing investigation was carried out in the Mach 6 High Reynolds Number Tunnel at the NASA-Langley Research Center. The results confirmed both the details and the overall effectiveness of the shock-enhanced mixing concept.

Comment on 'Approximate formula of weak oblique shock wave angle'

Comment on 'Approximate formula of weak oblique shock wave angle'

Approximate formula of weak oblique shock wave angle

Approximate formula of weak oblique shock wave angle

Spatial Stability of the Slab Jet. II. Numerical Simulations

view Abstract Citations (72) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spatial Stability of the Slab Jet. II. Numerical Simulations Norman, Michael L. ; Hardee, Philip E. Abstract Results of numerical simulations of a supersonic slab jet wiggled at different frequencies are presented and compared with the linearized spatial stability analysis performed in Paper I. Slabs with different densities and Mach numbers have been simulated. In general, results from the numerical simulations compare favorably with predictions of the linearized analysis. In all simulations the slab jet is disrupted by sinusoidal oscillation at or near the resonant wavelength of the fundamental sinusoidal mode, independent of the driving frequency. The jet then propagates behind a jet front and forms a lobe, and the jet flaps within the growing lobe. The sinusoidal oscillation approaches a wavelength corresponding to the driving frequency except when the driving frequency is much less than or significantly exceeds the resonant frequency. In addition to sinusoidal oscillation, the simulations also show weak oblique shock waves which cross the jet channel at about the Mach angle. These oblique shock waves can be identified with the first and second sinusoidal reflection modes predicted by the linearized analysis. Publication: The Astrophysical Journal Pub Date: November 1988 DOI: 10.1086/166819 Bibcode: 1988ApJ...334...80N Keywords: GALAXIES: JETS; HYDROMAGNETICS full text sources ADS | data products SIMBAD (6) NED (6) Related Materials (1) Part 1: 1988ApJ...334...70H

Interaction between a weak oblique shock wave and a turbulent boundary layer in purely supersonic flow

The paper deals with the interaction of a weak oblique shock and a turbulent boundary layer at a flat plate at purely supersonic speeds. Except for a small region where nonlinear transonic effects are of importance analytical expressions for the pressure- and skin friction distributions are derived.

Experimental Results for Waveriders in Certain Off-Design Conditions

SummaryFor caret waveriders at the design condition the attached shock wave in the plane of the leading edges may correspond to either a strong or a weak oblique shock wave when viewed normal to the edges. In cases when the design shock wave corresponds to the strong oblique shock the off-design behaviour of the wing is not completely understood. In this note some measured results are analysed in an attempt to understand this off-design behaviour.

The non-linear refraction of shock waves by upstream disturbances in steady supersonic flow

The general problem studied is the propagation of an oblique shock wave through a two-dimensional, steady, non-uniform oncoming flow. A higher-order theory is developed to treat the refraction of the incident oblique shock wave by irrotational or rotational disturbances of arbitrary amplitude provided the flow is supersonic behind the shock. A unique feature of the analysis is the formulation of the flow equations on the downstream side of the shock wave. It is shown that the cumulative effect of the downstream wave interactions on the propagation of the shock wave can be accounted for exactly by a single parameter Φ, the local ratio of the pressure gradients along the Mach wave characteristic directions at the rear of the shock front. The general shock refraction problem is then reduced to a single non-linear differential equation for the local shock turning angle θ as a function of upstream conditions and an unknown wave interaction parameter Φ. To lowest order in the expansion variable θΦ, this equation is equivalent to Whitham's (1958) approximate characteristic rule for the propagation of shock waves in non-uniform flow. While some further insight into the accuracy of Whitham's rule does emerge, the theory is not a selfcontained rational approach, since some knowledge of the wave interaction parameter Φ must be assumed. Analytical and numerical solutions to the basic shock refraction relation are presented for a broad range of flows in which the principal interaction occurs with disturbances generated upstream of the shock. These solutions include the passage of a weak oblique shock wave through: a supersonic shear layer, a converging or diverging flow, a pure pressure disturbance, Prandtl–-Meyer expansions of the same and opposite family, an isentropic non-simple wave region, and a constant pressure rotational flow. The comparison between analytic and numerical results is very satisfactory.