Flat Plate In Supersonic Flow Research Articles

Transition induced by an egg-crate roughness on a flat plate in supersonic flow

Hot-wire measurements in a Mach 3.5 quiet tunnel were made in the wake of a roughness patch on a flat plate. These measurements were used to determine mode shapes and frequencies of the dominant instabilities leading to boundary-layer transition. The egg-crate roughness pattern is an analytic function described by a sinusoidal equation, similar to an array of discrete elements that are positioned in a spanwise and streamwise grid, but containing both protuberances and dimples. This is an intermediate configuration towards understanding the underlying physics of a pseudorandom distributed roughness, and ultimately, the underlying physics of roughness-induced boundary-layer transition. The roughness pattern had a wavelength of 6.25 mm, with a nominal amplitude of 272 ${\rm \mu}{\rm m}$ (0.49 times the boundary layer thickness at the first row of protuberances). The roughness was positioned near the leading edge of the flat plate and contained 3.5 wavelengths in the streamwise direction and 7.5 wavelengths in the spanwise direction. The dominant instability was centred near 74 kHz at a free stream unit Reynolds number of $12.9\times 10^{6}\,{\rm m}^{-1}$ and resembled an antisymmetric mode downstream of each of the protuberances in the roughness patch. Computations using linear stability analysis based on the plane-marching parabolized stability equations (PSE) showed limited agreement with measurements when comparing the growth of the wake instability. Better agreement with the measurements was observed when considering the modification of first mode waves by the egg-crate roughness patch and the solution of the three-dimensional harmonic linearized Navier–Stokes equations was used as the in-flow to the PSE. The agreement confirms the significance of disturbance growth both upstream of and above a finite length roughness patch and the effect on the growth of instabilities in the wake.

Fluid–structure interaction study of the splitter plate in a TBCC exhaust system during mode transition phase

Splitter plate plays an important role in a turbine-based combined-cycle (TBCC) exhaust system during the mode transition phase when turbojet engine and ramjet engine operate simultaneously. Dissimilar pressure distribution on both sides of the plate has a potential origin in the aeroelastic coupling, which is an interesting topic while few research works have devoted to that aspect. To better understand the aeroelastic behavior of the plate and the corresponding dynamic flow features, an integrated fluid–structure interaction simulation is conducted under one particular operation condition during mode transition phase in the TBCC exhaust system. A finite-volume-based CFD solver FLUENT is adopted to solve the unsteady Reynolds average Navier–Stokes equations. ABAQUS, a finite-element-method-based CSD solver, is employed to compute the plate elastic deformation. A two-way interaction between the fluid and the structure is accomplished by the mesh-based parallel-code coupling interface (MpCCI) in a loosely-coupled manner. The accuracy of the coupling procedure is validated for the flutter of a flat plate in supersonic flow. Then, features of steady flow field of the TBCC exhaust system are discussed, followed by the investigation of the aeroelastic phenomenon of the splitter plate and the evolution process of the flow field pattern. Finally, performances variation of the exhaust system is obtained and discussed. The results show that the plate vibrates with decaying amplitude and reaches a dynamic stable state eventually. The thrust, lift and pitch moment of the TBCC exhaust system are increased by 0.68%, 2.82% and 5.86%, respectively, compared with the corresponding values in steady state which does not take into account the fluid–structure interaction effects. The analysis reveals the importance of considering the fluid–structure interaction effects in designing the splitter plate in the TBCC exhaust system and demonstrates the availability of the present coupled CFD/CSD method as a tool to predict the aeroelastic phenomenon in the TBCC exhaust system.

Aeroelastic response of rocket nozzles to asymmetric thrust loading

The aeroelastic response of rocket nozzles subjected to combined axial thrust and side loads is investigated using a particular computational technique. The technique uses two-way “loose” coupling between an accurate flow solver and an accurate structural-dynamics solver to accurately capture the behavior of the internal flow, the behavior of the nozzle wall, and the interactions between the fluid-dynamic and structural-dynamic phenomena. It is shown that the technique captures the fluid-dynamic phenomena that are known to contribute to nozzle side loads, including the asymmetry in the propagation of the initial blast wave, the asymmetry in the separation lines, the pressure pulsations at the separation lines, the transition of separated flow patterns, and various flow instabilities. It is also shown that the computational technique couples the fluid-dynamic and the structural-dynamic solutions with an accuracy and a resolution that are sufficient for accurate prediction of the aeroelastic response modes in the system. The fluid-dynamics solver is validated for shock-induced flow separations in a sub-scale J-2S nozzle, while the structural-dynamic solver is validated for a typical dynamic response in a rocket nozzle. The two-way loose coupling methodology is validated for the flutter of a flat plate in supersonic flow, and the validation results are discussed and assessed with respect to the fitness of the computational technique for the prediction of the aeroelastic response of typical actual nozzle configurations. Finally, the side loads are computed for a J-2S nozzle with rigid walls and with flexible walls, and the results for the two types of walls are analyzed and compared. It is found that allowing aeroelastic coupling significantly affects the response of the nozzle and the predicted side loads. It is speculated that the computational technique investigated in this work combines all the elements required to accurately predict and simulate the aeroelastic response of a rocket nozzle to non-symmetric thrust, and that such a technique can be used to study and investigate side load phenomena in rocket nozzles in detail and also as a design tool for rocket nozzles. The technique is also speculated to be effective and appropriate for other fluid–structure interaction problems within an appropriate range of aeroelastic regimes.

Improvements in Modeling 90-degree Bleed Holes for Supersonic Inlets

The modeling of porous bleed regions as boundary conditions in computational fluid dynamics (CFD) simulations of supersonic inlet flows has been improved through a scaling of sonic flow coefficient data for 90-degree bleed holes. The scaling removed the Mach number as a factor in computing the sonic flow coefficient and allowed the data to be fitted with a quadratic equation with the only factor being the ratio of the plenum static pressure to the surface static pressure. This simplified the implementation of the bleed model into the Wind-US CFD flow solver by no longer requiring the evaluation of the flow properties at the edge of the boundary layer. The quadratic equation can be extrapolated to allow the modeling of small amounts of blowing, which can exist when recirculation of the bleed flow occurs within the bleed region. The improved accuracy of the bleed model was demonstrated through CFD simulations of bleed regions on a flat plate in supersonic flow with and without an impinging oblique shock. The bleed model demonstrated good agreement with experimental data and three-dimensional CFD simulations of bleed holes.

Improvements in Modeling 90-degree Bleed Holes for Supersonic Inlets

The modeling of porous bleed regions as boundary conditions in computational fluid dynamics (CFD) simulations of supersonic inlet flows has been improved through a scaling of sonic flow coefficient data for 90deg bleed holes. The scaling removed the Mach number as a factor in computing the sonic flow coefficient and allowed the data to be fitted with a quadratic equation, with the only factor being the ratio of the plenum static pressure to the surface static pressure. The implementation of the bleed model into the Wind-US CFD flow solver was simplified by no longer requiring the evaluation of the flow properties at the boundary-layer edge. The quadratic equation can be extrapolated to allow the modeling of small amounts of blowing, which can exist when recirculation of the bleed flow occurs within the bleed region. The improved accuracy of the bleed model was demonstrated through CFD simulations of bleed regions on a flat plate in supersonic flow with and without an impinging oblique shock. The bleed model demonstrated good agreement with experimental data and three-dimensional CFD simulations of bleed holes.

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

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

Shock wave interaction with a viscous wake in supersonic flow

A theoretical investigation of the breakdown of the viscous wake downstream of a flat plate in supersonic flow is performed in this paper based on the large Reynolds number ($Re \to \infty $) asymptotic analysis of the Navier–Stokes equations. The breakdown is provoked by an oblique shock wave impinging on the wake a small distance $l_s$ downstream of the plate trailing edge. Two flow regimes are considered. In the first $l_s$ is assumed to be an $O(Re^{-3/8})$ quantity in which case the shock impinges on the wake within the region of viscous–inviscid interaction that is known to occupy a vicinity of the trailing edge with longitudinal extent of $O(Re^{-3/8})$. Under these conditions the interaction process may be described by the equations of the triple-deck theory. To obtain a numerical solution of these equations we used a rapid matrix Thomas technique in conjunction with Newton iterations. The results of the calculations not only predict the wake breakdown near the shock location but also reveal a hysteresis behaviour of the flow as the shock is moved downstream, giving rise to three solution branches. The second part of the paper is concerned with the flow regime when the shock interacts with the wake further downstream of the trailing edge triple-deck region: $l_s \gg Re^{-3/8}$. In this case the fluid motion proves to be inviscid to leading order not only in the upper deck of the interaction region but also everywhere inside the wake. Due to this simplification the interaction problem can be reduced to a single integro-differential equation governing the pressure distribution along the interaction region. With known pressure the Bernoulli equation may be used to find the velocity field. The Bernoulli equation also allows us to formulate a simple criterion which may be used to predict the onset of wake breakdown. We found that viscosity becomes important again in a smaller vicinity of the breakdown point where the flow reversal takes place. It is remarkable that the viscous–inviscid interaction problem governing the flow in this vicinity admits an analytical solution.

Entropy-layer instabilities over a blunted flat plate in supersonic flow

Entropy-layer instabilities in the supersonic flow over a blunted flat plate with a nose radius of Rn=2.5 mm at a Mach number M=2.5 and a unit Reynolds number Re/l=9.9×106/m are investigated. A type of entropy-layer instability most amplified at zero wave angle is found. Its streamwise wave number and the wall-normal phase distribution of the numerically obtained density eigenfunctions agree with flow-field visualization using the Schlieren technique. The frequencies of this entropy-layer instability made nondimensional on the basis of an appropriate entropy-layer length scale matches documented experimental observations at a blunted cone.

Unsteady boundary layer with self-induced pressure near rapidly heated segment of flat plate in supersonic flow

Unsteady boundary layer with self-induced pressure near rapidly heated segment of flat plate in supersonic flow

Effect of Reynolds Number on Laminar Separation of a Supersonic Stream

Accurate numerical solutions for both interacting boundary-layer and asymptotic triple-deck equations are presented for a closed separation region generated by a compression wedge on a flat plate in supersonic flow. Interacting boundary-layer solutions were obtained for a range of Reynolds numbers from Re-lQ (where experimental verification is obtained) to Re10 (where agreement with triple-deck solutions is reached). These results provide insight into the development of the separating flow structure as the shear-layer thickness collapses with increasing Reynolds number. It is shown that the triple-deck model identifies the dominant length scales and important correlation parameters, and that the interacting boundary-layer model correctly approaches a triple-deck solution in the limit /fe-~oo, while producing accurate results at finite Reynolds number.

Flowfield in the vicinity of cylindrical protuberances on a flat plate in supersonic flow.

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Heat transfer caused by combustion on a flat plate in supersonic flow.

Abstract : A theoretical and experimental investigation was undertaken of heat transfer effects at the surface of a flat plate on which combustion is occurring in a supersonic air stream. A simplified theoretical model is developed which leads to expressions for the heat transfer coefficient and heat transfer rate at the surface. The experimental technique used to obtain heat transfer parameters is described. The experimental tests were conducted at Mach number 3.1 using the pyrophoric fuel triethylaluminum. A comparison between the theoretical and experimental results indicates that the former yields order-of-magnitude estimates of the heat transfer coefficient and rate which are satisfactory for purposes of engineering design. The theory is then used to obtain estimates of heat transfer parameters at the surface of a cone-shaped interceptor executing a coast trajectory. The results are shown to be well correlated by an empirical expression similar to that encountered in the literature for turbulent non- reacting flow over flat plates having both constant and variable surface temperatures.

Supersonic combustion of storable liquid fuels in mach 3.0 to 5.0 air streams

Supersonic combustion of reactive aluminum alkyl fuels has been experimentally demonstrated in two-dimensional ducted combustors and adjacent to a flat plate. Fuel was injected from the combustor walls through multiple orifices and ignited spontaneously. Stable supersonic heat release was maintained as evidenced by schlieren and direct motion pictures of the flow field and deduced from static and pitot pressure measurements in the combustion zone. zone. The results from the ducted combustor tests were correlated with simple theoretical models thus enabling a reasonable determination of combustion efficiency to be made. A theoretical model of constant-pressure heat release on a flat plate in supersonic flow is postulated. Normal force, coefficients and specific impulse values are tabulated for a variety of flight Mach Numbers and altitudes. Additional refinements in this theoretical model were required to adequately describe the experimental results. In a test simulating Mach 5 flight at 66,000-feet altitude, a side force specific impulse of 1350 sec was measured at equivalence ratio of one. Combustion was only partially completed 12 in. downstream of fuel injection. Based on the theoretical model an additional 12 in. of combustor length and 36 in. of expansion length would be required to obtain, the estimated theoretical impulse of 5760 sec. The interaction of a vaporizing liquid droplet with a supersonic stream is considered. Additional refinements were made in the existing theories on droplet trajectory to include the influences of a separated zone and the normal component of velocity of the external stream. Calculations of the trajectory and evaporation of the estimated mean droplet size based on the modified technic were in general agreement with the observed fame zone and deduced combustion efficiency.

Measurements of Turbulent Friction on a Smooth Flat Plate in Supersonic Flow

Direct measurements of supersonic local skin friction, using the floating-element technique, are presented for Mach Numbers from 2.0 to 4.5 and Reynolds Numbers from 3 X 10^5 to 9 X 10^6. Turbulent flow and transition are emphasized, although some measurements in the laminar regime are included. The observed effect of compressibility is to reduce the magnitude of turbulent skin friction by a factor of two at a Mach Number of 4.5 and a Reynolds number of about 10^7. The boundary-layer momentum-integral equation for constant pressure is verified within a few per cent by two experimental methods. Typical static pressure measurements are presented to show that transition can be detected by observing disturbances in pressure associated with changes in displacement thickness of the boundary layer. It is found that the turbulent boundary layer cannot be defined experimentally for values of u_1 θ/v_1 less than about 2,000, where θ is the momentum thickness. For larger values of u_1 θ/v_1, there is a unique relationship between local friction coefficient and momentum-thickness Reynolds Number at a fixed Mach Number. The Appendix compares the present measurements at M = 2.5 with experimental data from other sources.

A Temperature-Sensitive Phosphor Used to Measure Surface Temperatures in Aerodynamics

A thin sheet of a temperature-sensitive phosphor has been used to show the distribution of temperature on the surface of a flat plate in supersonic flow. Calibration of the phosphor is described, and a photograph is shown. Use of a photomultiplier tube permits one to determine the temperature as a function of time, from which recovery temperatures and heat transfer coefficients may be deduced.