Sharp Flat Plate Research Articles

Shock-induced leading-edge separation in hypersonic flows

We investigate the leading-edge separation, also called negligible boundary-layer thickness separation, induced by an impinging shock on a sharp flat plate. The canonical impinging shock wave/boundary-layer interaction configuration consisting of a wedge and a plate wall, placed in hypersonic free stream, is used for the investigations. We first construct a theoretical model for the leading-edge separated flow field (LESF) which predicts separation bubble geometry and surface pressure distribution as a function of three parameters: free-stream Mach number, wedge angle and the reattached flow turning angle. Markedly different predictions of the separated flow field are obtained for an oblique and a near normal reattachment on the plate surface. Experiments in a shock tunnel at a nominal Mach $6$ flow, with an impinging shock generated by a wedge of angle $26.6^{\circ }$ , are used to validate the model. Schlieren flow visualization using a high-speed camera and surface pressure measurements using fast response piezoelectric sensors are the diagnostics employed. For a range of shock impingement locations, the LESFs are observed to be geometrically similar and in good agreement with the LESF model. When the impingement location gets closer to the leading edge, it is observed from experiments that the flow field is no longer geometrically similar, and the separation angle increases as the impingement gets closer to the leading edge beyond the range of similarity. The work thereby offers an elaborate description of the leading-edge separated flow when shock impingement occurs near the plate leading edge.

Experimental investigations on the sharp leading-edge separation over a flat plate at zero incidence using particle image velocimetry

Leading-edge separated flow field over a sharp flat plate is experimentally investigated in Reynolds numbers ranging from 6.2 × 103 to 4.1 × 104, using particle image velocimetry (PIV) and its statistics. It was observed that the average reattachment length is nearly independent of Reynolds number and the small secondary bubble observed near the leading edge was found to shrink with increasing Reynolds number. The wall-normal profiles of the statistical values of kinematic quantities such as the velocity components and their fluctuations scaled well with average reattachment length lR and freestream velocity U∞. Their magnitudes compare well with previous investigations even though the current triangular shaped sharp leading edge is different from previous flat-faced or semi-circular ones. The shear layer was observed to exhibit 2 different linear growth rates over 2 distinct regions. Instantaneous PIV realizations demonstrate unsteady nature of the separation bubble, whose origins in the upstream portion of the bubble are analysed. Bimodal nature of the probability density function (PDF) of fluctuating streamwise velocity at around x/lR = 0.08–0.15 indicates successive generation and passage of vortices in the region, which subsequently interact and evolve into multiscale turbulent field exhibiting nearly Gaussian PDF. Shedding of vortices with wide range of scales are apparent in most of the instantaneous realizations. Proper Orthogonal Decomposition (POD) of the velocity fluctuation magnitude field revealed that the flow structures of the dominant modes and their relative energies are independent of Reynolds number. In each of the dominant modes (first 3 modes), the length scales corresponding to the large scale structures and their spacing are the same for all Reynolds numbers, suggesting that their Strouhal number (observed to be ~ 0.09–0.2 at Reynolds number of 6.2 × 103) of unsteadiness should also be independent of Reynolds number. A single large structure- comparable in size to lR—was apparent well before reattachment in a few instantaneous realizations, as compared to multiple small-scale structures visible in most realizations; at Reynolds number of 6.2 × 103, realizations with such large-scale structures occurred approximately after every 20–30 realizations, corresponding to non-dimensional frequency of 0.4–0.6, which is identified to be the “regular shedding”. It was possible to reconstruct the large-scale structure during the instances from just the first 3 POD modes, indicating that the Strouhal number of regular shedding too is independent of Reynolds number.Graphic abstract

Effect of Görtler-like vortices of various intensity on heat transfer in supersonic compression corner flows

Experiments on heat transfer over Mach 8, 15° compression corner flow affected by Görtler-like reattachment vortices of controllable intensity are carried out in the shock wind tunnel UT-1 M (TsAGI). Experiments cover two Reynolds numbers Re∞,L=(1.75±0.08) × 105 and Re∞,L=(3.90±0.15) × 105 based on the sharp flat plate length at which the reattachment flow is close to laminar or beginning transitional, respectively. The effect of streamwise vortices of different intensity on spanwise variations of the heat flux and its spanwise-averaged level at the reattachment region is investigated. The intensity of the vortices is varied by accurate controlling the height of a spanwise rake of cylindrical pins (seeding elements) placed on the plate ahead of the separation bubble.

Influence of Mach number and static pressure on plasma flow control of supersonic and rarefied flows around a sharp flat plate

This paper presents an experimental investigation, carried out at the Icare Laboratory by the FAST team, focusing on plasma flow control in supersonic and rarefied regime. The study analyzes how the Mach number as well as the ambient pressure modify the repercussions of the plasma actuator on the shock wave. It follows previous experiments performed in the MARHy (ex–SR3) wind tunnel with a Mach 2 flow interacting with a sharp flat plate, where modifications induced by a plasma actuator were observed. The flat plate was equipped with a plasma actuator composed of two aluminum electrodes. The upstream one was biased with a negative DC potential and thus, created a glow discharge type plasma. Experimental measurements showed that the boundary layer thickness and the shock wave angle increased when the discharge was ignited. The current work was performed with two nozzles generating Mach 4 flows but at two different static pressures: 8 and 71 Pa. These nozzles were chosen to study independently the impact of the Mach number and the impact of the pressure on the flow behavior. In the range of the discharge current considered in this experimental work, it was observed that the shock wave angle increased with the discharge current of $$+15\%$$ for the Mach 2 flow but the increase rate doubled to $$+28\%$$ for the Mach 4 flow at the same static pressure, showing that the discharge effect is even more significant when boosting the flow speed. When studying the effect of the discharge on the Mach 4 flow at higher static pressure, it was observed that the topology of the plasma changed drastically and the increase in the shock wave angle with the discharge current of $$+21 \%$$ .

Numerical Simulation and Analysis of Supersonic flow over a flat plate

Two dimensional supersonic flows over a sharp flat plate at zero incidence has been investigated numerically. A fictitious curvature is formed due to the development of a boundary layer at the leading edge of the plate. The pressure along the entire surface and at the trailing edge has been computed over a wide range of Mach numbers and two different temperatures. The temperature variation due to dissipation of kinetic energy within the boundary layer has been analysed numerically. Keywords: Computational Fluid Dynamics, Supersonic Flow, Flat Plate, Numerical Investigation.

Laminar-turbulent flow over wedges mounted on sharp and blunt plates

The flow pattern and the heat transfer on sharp and blunt flat plates near a wedge in a Mach 6 stream are experimentally investigated for two Reynolds numbers corresponding to the laminar and transitional states of the undisturbed boundary layer ahead of the wedge. It is shown that, as in a two-dimensional flow, plate bluntness leads to the attenuation of the heat transfer in the boundary layer/shock wave interference zone. However, when a certain threshold value of the bluntness is exceeded, a further increase in the bluntness has almost no effect on the heat transfer. For the first time, an experiment conducted in an intermittent (blow-down) wind tunnel has been based on the comprehensive use of panoramic (global) techniques for measuring the heat transfer and pressure coefficients and a method for visualizing the surface friction employing the luminescence effect after UV irradiation.

The influence of rotational and vibrational energy relaxation on boundary-layer stability

We investigate the influence of rotational and vibrational energy relaxation on the stability of laminar boundary layers in supersonic flows by numerically solving the linearized equations of motion for a flow in thermal non-equilibrium. We model air as a mixture of nitrogen, oxygen and carbon dioxide, and derive accurate models for the relaxation rates from published experimental data in the field of physical chemistry. The influence of rotational relaxation is to dampen high-frequency instabilities, consistent with the well known damping effect of rotational relaxation on acoustical waves. The influence of rotational relaxation can be modelled with acceptable accuracy through the use of the bulk-viscosity approximation when the bulk viscosity is computed with a formula described herein. Vibrational relaxation affects the growth of disturbances by changing the characteristics of the laminar mean flow. The influence is strongest when the flow field contains a region at, or near, stagnation conditions, followed by a rapid expansion, such as inside wind tunnels and around bodies with a blunt leading edge, whereby the rapid expansion causes the internal energy to freeze in a distribution out of equilibrium. For flows at Mach 4.5 and stagnation temperature of 1000 K, the total amplification exhibited by boundary-layer disturbances over a sharp flat plate in wind-tunnel flows can reach a value that is fifty times as high as the value computed under the assumption of thermal equilibrium. The difference in amplification can be twice as high in the case of a blunt flat plate at atmospheric flight conditions.

Boundary layer receptivity to free-stream sound on parabolic bodies

We use a numerical approach to study the receptivity of the boundary layer flow over a slender body with a leading edge of finite radius of curvature to small streamwise velocity fluctuations of a given frequency. The body of interest is a parabola in order to exclude jumps in curvature, which are known sites of receptivity and which occur on elliptic leading edges matched to finite-thickness at plates. The infinitesimally thin flat plate is the limiting solution for the parabola as the nose radius of curvature goes to zero. The formulation of the problem allows the two-dimensional unsteady Navier–Stokes equations in stream function and vorticity form to be converted to two steady systems of equations describing the basic (nonlinear) flow and the perturbation (linear) flow. The results for the basic flow are in excellent agreement with those in the literature. As expected, the perturbation flow was found to be a combination of an unsteady Stokes flow and Orr–Sommerfeld modes. To separate these, the unsteady Stokes flow was solved separately and subtracted from the total perturbation flow. We found agreement with the streamwise wavelengths and locations of Branches I and II of the linear stability neutral growth curve for Tollmien–Schlichting waves. The results showed an increase in the leading-edge receptivity with decreasing nose radius, with the maximum occurring for an infinitely sharp flat plate. The receptivity coefficient was also found to increase with angle of attack. These results were in qualitative agreement with the asymptotic analysis of Hammerton & Kerschen (1992). Good quantitative agreement was also found with the recent numerical results of Fuciarelli (1997), and the experimental results of Saric, Wei & Rasmussen (1994).

燃焼・圧力駆動衝撃風胴と二，三の平板熱伝達実験

A combustion and/or pressure-driven shock tunnel with a conical nozzle is constructed. The tailoring Mach number MST of the combustion tumel is from 6.7 to 7.4. The heat transfer rate of sharp leading edge flat plates with a backward facing step in hypersonic flow of Mach number M∞=7.05 and 11.1 are measured by use of the pressure tunnel, and it is shown that the magnitude and the location of the peak heat transfer rate at reattachment region behind the step seem to be affected by the magnitude of M∞. The measured heat transfer rate of a sharp flat plate with angle of attack in M∞=11.1 hypersonic flow from the conical nozzle of the pressure tunnel is in qualitatively proper agreement with the author's analytical result. The behavior of the heat transfer rate near the sharp leading edge of anat plate in M∞=11.1·high stagnation temperature To=7, 900K flow measured by using the combustion tunnel shows tolerable agreement with the existing measured results at lower To in the strong viscous interactlon region.

The Slip-Dominated Merged Layer Regime for Newtonian Hypersonic Flow Past a Flat Plate

The rarefied uniform hypersonic flow past the leading edge of a sharp flat plate at zero angle of attack is analyzed on the basis of a continuum model consisting of the Navier–Stokes equations and the velocity-slip and temperature-jump plate boundary conditions. The model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and first and second viscosity coefficients varying as a power of the absolute temperature. For this flow, it is taken that the Newtonian parameter, $\varepsilon = ( {\gamma - 1} )/( {\gamma + 1} )$, goes to zero, and that the freestream Mach number, $M = ( \rho _\infty u_\infty ^2 /\gamma p_\infty )^{1/2} $, the stagnation temperature parameter, $\theta _S = \{ 1 + \varepsilon )/( 1 - \varepsilon )\}\varepsilon M^2 $, and the free-stream Reynolds number (based on the characteristic axial length from the leading edge), $R_L = \rho _\infty u_\infty L/\mu _\infty $, go to infinity.For the viscosity-temperature exponent, $\omega $, satisfying $1...

Electron-density and electron-temperature measurements in boundary layers

Thin-wire Langmuir probes haye been used to measure the electron-density and electrontemperature distributions in the nozzle-wall boundary layer of a hypersonic shock tunnel and in the boundary layer of a sharp flat plate located on the nozzle centerline. Experiments were performed in a nozzle-wall boundary layer, with nitrogen as the test gas, in order to obtain a comparison between the results obtained with voltage-swept probes aligned with the flow and constant bias-voltage probes perpendicular to the flow direction. These measurements were performed in the boundary-layer flow because that is the flow environment in which the const ant-volt age probes were to be used in flight applications. Only voltage-swept probes aligned with the flow were used in the flat-plate experiments which were performed in preparation for antenna admittance measurements to be made in the future. These experiments were conducted in a test gas composed of argon plus 0.12% nitrogen. The flow conditions for both experiments were such that free-molecular flow theories could be used to infer ion densities from the ion-current portion of the probe characteristics. Electron temperatures measured in these boundary layers were found to be substantially greater than the calculated heavy-particle translational temperature at the boundary-layer edge. For the flat-plate experiments, the .electron temperature remained relatively constant through the boundary layer and along the plate. However, the electron temperature in the nozzle-wall boundary layer decreased from the outer-flow value as the wall was approached. The positive iondensity distributions obtained in this latter boundary layer using the two probing techniques (aligned with and perpendicular to the flow) were found to be in good agreement. In addition, the calculated boundary-layer thickness was found to approximate the distance from the wall at which the measured electron density approached a constant value.

Experimental Model for High-Speed Rarefied Flow over a Sharp Flat Plate

A flow field survey has been made of the shock layer development on a flat plate, at M = 6, from just upstream of the leading edge to downstream of the merged layer. The electron beam fluorescence technique has been used to measure density profiles from which a comprehensive description of the flow field is constructed. Close to the leading edge the flow is near free molecular and can be described in terms of two effective mean free paths, as proposed by Hamel and Cooper. The results suggest that continuum flow is not established for a distance approximately four times the mean free path for the collision of a free stream molecule with a body molecule. An upstream disturbance occurs a few free stream static mean free paths ahead of the leading edge, although this was aerodynamically sharp.

Leading edge flow by the Monte Carlo direct simulation technique

The flow near the leading edge of a sharp flat plate is studied by means of a Monte Carlo molecular simulation. This technique consists of following, by digital computation, the motion of a representative set of molecules flowing past the body while collisions are computed by statistical sampling. Flowfield properties and plate surface fluxes are presented for a monatomic gas for several molecular models: hard spheres and point centers of inverse power repulsion. The gas-surface interaction law used was a prescribed mixture of diffuse and specular reflection. Mach number was varied from 5.5 to 29.2 and both insulated and cooled plates were studied. Plate length relative to the freestream mean free path was varied from 10 to 88. For the longer plates the flow over much of the plate is that for a semiinfinite plate. Comparisons are made between these results and experimental data.

Laminar Reynolds analogy factor on a sharp flat plate at Mach 10.4

Values measured on sharp flat plate in 10.4 Mach boundary layer induced pressure gradient, discussing effects of wall pressure and temperature gradients

Hypersonic interactions near sharp leading edges.

Abstract : Numerical solutions of a set of parabolic equations, uniformly valid throughout the entire continuum flow domain, were obtained for the axi-symmetric flow over slender sharp nose cones at zero angle of attack, the hypersonic interference flow between two finite length flat plates and the flow over a sharp flat plate of finite span. The regions of interest are the leading edge merged layer and the initial portion of the strong interaction flow. The analysis represents an extension of the theory first used successfully for the flow over two-dimensional sharp flat plates. Merged layer interference, the merging of streams at different pressures in the wake of the channel geometry, the three-dimensional flow and shock structure, as well as the significant differences between two-dimensional, and axi-symmetric or three-dimensional flow fields are discussed. Comparisons with available experimental data are good, as evidenced by surface pressure and heat transfer results, for the flow over cones. (Author)

Surface measurements on sharp flat plates and wedges in low-density hypersonic flow.

Abstract : Measurements of surface pressure, skin friction, and heat transfer are presented for sharp flat plates at zero angle of attack and at large and small wedge angles in a hypersonic flow. These data largely span the transition from continuum to near-free-molecule flow. The magnitude of slip velocity and energy jump at the surface are inferred from the data. The inferred slip velocity compares favorably with independent measurements by other investigators of slip velocity obtained with pitot probes. The data are compared with relevant theories ranging from the continuum to the free-molecule flow regimes and are used to check the validity of Reynolds analogy. The flat plate data at zero angle of attack are in good agreement with continuum theory when the appropriate Chapman-Rubesin constant is used, and the data are in reasonable agreement with available theories in the viscous layer regime. Heat transfer data are presented which completely define the transition to the free-molecule limit. The data obtained at large wedge angles agree reasonably with viscous shock layer theory which spans the transition from continuum to near-free-molecule flow. Discrepancies appear to be traceable to assumptions in the theory regarding Prandtl number, the Chapman-Rubesin constant, and boundary-layer displacement effects. Data obtained at small wedge angles compare favorably with theory in the continuum limit. Low-density departures of pressure from continuum theory are predicted reasonably by a momentum integral theory. (Author)

A theoretical model for the sharp flat plate in rarefied hypersonic flow.

Rarefied hypersonic flow model for sharp flat plate in strong interaction regimes, discussing inviscid and viscous shock and merged layers subregimes

1516. Low density high temperature gas dynamics: J J Smolderen,Rep AFOSR-68-0463; AD-666474, Oct 1967, 16 pages ( Sci Tech Aerospace Reps, 6 (11), 1686, N68-21323)

Abstract : Surface pressures on a flat plate with sharp leading edge were measured in a M = 1.5 monatomic gas flow. The results were in essential agreement with those recorded for a diatomic gas, but differed quantitatively from a recent theory based on a discrete ordinate solution of the BGK equation. The modulated hot-wire probe was proven conclusively to provide a measurement of local mass flux in a hypersonic flow. Surveys performed in a low density free jet showed very clearly the initial disturbance produced by the thick surrounding shock structure. The upstream influence of a sharp flat plate was measured with the modulated hot wire probe. The disturbance field was symmetrical about the leading edge and extended upstream for approximately three mean-free-paths based on a body-free stream collision. Thermographic phosphors were determined to exhibit a sensitivity of 8% change in output light intensity per deg C and to have an equivalent noise figure of 0.1C; thus they will be suitable for measuring local surface temperature at sharp leading edges. (Author)

An experimental model for the sharp flat plate in rarefied hypersonic flow.

An experimental model for the sharp flat plate in rarefied hypersonic flow.

Heat-transfer measurements with a catalytic flat plate in dissociated oxygen.

Heat-transfer measurements are presented which were obtained with catalytic and noncatalytic surfaces on a sharp flat plate. The experiments were made in a shock-tube flow of argon and dissociated oxygen, and are intended to provide a check on existing laminar boundary-layer theories. The design of the experiment is described, and the instrumentation and surface-conditioning requirements are discussed. Typical experimental data are presented to demonstrate the effects of shock-wave attenuation and other gasdynamic transients, and to show that these effects are negligible. The data obtained with the noncatalytic surface are compared with existing theories to demonstrate the importance of Prandtl number effects and variations in the p/j, product through the boundary layer. An approximate relation, based on an extension of Crocco's laminar boundary-layer theory, is given which accounts for these quantities and for surface recombination. It is found to be in good agreement with the data obtained with both the noncatalytic and the catalytic surfaces. The data obtained with both surfaces are used to infer the ambient atom concentration, as in diagnostic applications, and the inferred concentrations agree with those predicted using equilibrium theory with typical uncertainties of 5%.