Perpendicular Flat Plate Research Articles

Numerical Studies on Heat Transfer of Supersonic Combustion-Gas Jet Impingement on Perpendicular Flat Plate

This paper numerically investigates the heat transfer characteristics of supersonic high-temperature combustion-gas jet impinging to a perpendicular flat plate. First, the numerical method is validated using an experimental case and meanwhile different turbulence models are evaluated for heat transfer prediction. Then, the effects of multi-species, nozzle-to-plate distance, and nozzle pressure ratio on wall heat transfer are studied through a series of numerical experiments. Comparison of different turbulence models indicates that the variations of turbulent viscosity across the detached normal shock wave differ among the studied three models. Furthermore, if the real multi-species of combustion-gas are mixed as a single species with the same thermal-physical properties, the pressure and heat flux distributions are identical with the results of combustion-gas. Finally, when there is no stagnation bubble in the jet flow field, the heat flux on the flat plate produces a local minimum at the stagnation point for short nozzle-to-plate distance, while a local maximum appears at the stagnation point for large nozzle-to-plate distance. When the stagnation bubble exists, the other maximum of heat flux is produced at the edge of bubble.

Effects of bevelled nozzles on standoff shocks in supersonic impinging jets

Abstract Moderately under-expanded jets issuing from a circular baseline and two bevelled circular nozzles impinging upon a perpendicular flat plate were experimentally studied. The effects of nozzle-pressure-ratio and separation distance variations on the standoff shock formations were investigated with schlieren visualizations and a visual hull based three-dimensional (3D) shock reconstruction technique to provide deeper insights into their 3D features. Across all flow configurations arising from the different combinations of these parameters, results indicated that the bevelled nozzles are effective in introducing asymmetry to the standoff shock geometries. Depending on the exact flow configuration, standoff shock locations may also undergo significant upstream displacements. In particular, the single-bevelled nozzle produces highly unsteady standoff shocks with asymmetric oscillation amplitudes along both side of the nozzle lip regions. Changes to the standoff shock key characteristics were observed to be sensitive towards the jet shock structures and reflection point modified by the bevelled nozzle exits. In particular, the strength and relative position of the reflection point are identified as the major contributing factors influencing the upstream static pressure distribution of the standoff shock, hence leading to the observed changes in the standoff shock behaviour.

Hybrid LES-RANS simulations of a jet impinging on a flat plate

In this paper, we explore the use of a second-order unstructured-grid, finite-volume code for direct noise prediction. We consider a Mach 1.5 jet impinging on a perpendicular flat plate. Hybrid LES-RANS simulations are used to calculate directly both the flow field and the radiated sound. The ANSYS Fluent commercial code is utilized for the calculations. The acoustic field is obtained directly from the simulations and is compared with the integral approach of Ffowcs-Williams–Hawkings. Results indicate the existence of a preferred radiation angle. The spectrum obtained is in good agreement with observations. This points out to the possibility of handling the effects of complicated geometries on noise radiation by using unstructured second-order codes.

Sensitivity analysis of a streamwise corner flow

The stability of the flow formed by the intersection of two perpendicular flat plates is revisited through a study of the sensitivity to base-flow variations. After a brief presentation of the asymptotic regime, sensitivity functions underlying corner mode (concentrated close to the intersection) and Tollmien–Schlichting modes, with different obliqueness angles, are computed. Taking this into consideration, associated mechanisms as well as active regions are identified, which further confirm the sensitivity area of the corner mode along the intersection of two flat plates. Furthermore, the concept of ΔU-pseudospectra indicates that under a small base-flow modification, a certain range of frequencies underlying the corner mode could become unstable. Then, an optimization technique tracking the worst-case scenario, i.e., the deviation leading to a maximum temporal amplification rate, shows that a small variation in the reference field in the area of uncertainty leads to a significant decrease in the critical Reynolds number as observed in experiments. A hypothesis based on the onset of an inflectional mechanism is thus proposed to explain the experimental results.

3. Setting up of three-dimensional endplate effect on the starting wake of a perpendicular flat plate

3. Setting up of three-dimensional endplate effect on the starting wake of a perpendicular flat plate

Flow resolution and domain influence in rarefied hypersonic blunt-body flows

The study assesses the effects of the upstream domain size and grid resolution upon flow properties and body aerodynamics computed for rarefied flows over cold blunt bodies with a direct simulation Monte Carlo (DSMC) particle method. Empirical correlations are suggested for aerodynamic coefficients for two-dimensional flows past a perpendicular flat plate. Free-stream parameters which were varied in the study include the Mach number, Knudsen number, surface temperature, and intermolecular potential. Insufficient grid resolution leads to overprediction of aerodynamic heating and forces in the DSMC method. Solution accuracy correlates well with the Reynolds number defined at the wall temperature and the stagnation mean free path relative to the cell dimension. Insufficient upstream domain size in the DSMC method leads to overprediction of heating and drag. Errors in aerodynamic coefficients correlate well with the distance ahead of the body where flow temperature reaches half of its peak value. Simulation of a hard-sphere gas is more sensitive to grid resolution, while simulation of a Maxwell gas is more sensitive to upstream domain size.

Breakdown of steady axisymmetric flow in the shock layer formed when a supersonic underexpanded jet interacts with a perpendicular flat plate

The process accompanying the deceleration of a supersonic jet striking a perpendicular barrier are investigated.

Efficient real gas upwinded Navier-Stokes computations of high speedflows

An efficient method to account for the chemically frozen thermodynamic and transport properties of air in three-dimensional Navier-Stokes calculations has been demonstrated. This approach uses an explicitly specified equation of state (EOS) so that the fluid pressure, temperature, and transport properties are directly related to the flow variables. The method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code. The flexibility of the EOS approach is shown by its implementation into a high-order total variation diminishing upwinding scheme as well as a standard central-differencing scheme. The EOS approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central-differencing schemes.

Impingement of Under-Expanded Jets on a Flat Plate

When an under-expanded sonic jet impinges on a perpendicular flat plate, a shock wave forms just in front of the plate and some interesting phenomena can occur in the flow field between the shock and the plate. In this paper, experimental and numerical results on the flow pattern of this impinging jet are presented. In the experiments the flow field was visualized using shadow-photography and Mach-Zehnder interferometry. In the numerical calculations, the two-step Lax-Wendroff scheme was applied, assuming inviscid, axially symmetric flow. Some of the pressure distributions on the plate show that the maximum pressure does not occur at the center of the plate and that a region of reversed flow exists near the center of the plate.

Thermal expansion tensor measurement by holographic interferometry

The displacement on a plane, originated by a temperature increase of three perpendicular flat plates, is measured by means of a double exposure hologram. These displacements allow us to calculate the thermal expansion tensor of an anisotropic material.

The effect of member spacing upon the base pressure distributions recorded on perpendicular flat plates

The experimental results presented in this note have provided a comparison between the flow induced pressure distributions associated with non-connecting perpendicular flat plates and similar configurations composed of circular cylinders and square section bars.

On the flow pattern when an underexpanded jet impinges on a flat plate.

Impingement of an axially-symmetric, underexpanded sonic jet on a perpendicular flat plate is studied using flow visualization and a numerical technique. The numerical results which are obtained by a two-step Lax-Wendroff scheme under the assumption of inviscid flow are in good agreement with the experimental results. It is found that the maximum pressure is not always at the center on the plate, and that there may be a reverse flow in the central area on the plate.

Free convection near a corner formed by two vertical plates embedded in porous medium

The analysis of free convection heat transfer near a corner formed by two mutually perpendicular flat plates embedded in porous medium is presented. It is found that local similarity solution exists for the case of constant wall temperature. Solutions are obtained by selecting a stream function to satisfy the continuity equation, the energy equation and the asymptotic boundary conditions at infinity. The problem is solved by finite difference method. Velocity profiles and heat transfer characteristics are also presented.

The Occurrence of Stagnation Bubbles in Supersonic Jet Impingement Flows

SummaryThis paper reports an experimental investigation into the stagnation bubbles found in the shock layers of some supersonic jets impinging on perpendicular flat plates at small nozzle-to-plate distances. The experiments used twelve contoured nozzles within the Mach number range 1.42 to 2.83. Surface pressures were measured on the plate and free-jet pitot pressure distributions were obtained at the level of the centre of the plate shock. Schlieren pictures were taken of both impinging and free jets. It was found that the bubbles result from the interaction of the plate shock with very weak shock waves which are produced in the jet either by small imperfections in the nozzle wall or by slight inaccuracies in the design or production of the nozzle contour. The bubbles can be eliminated by suitable improvements to the nozzle. Other anomalous flows produced by shock interactions are described and explanations offered. It is shown that the bubbles sometimes encountered at close plate spacings with conical nozzles are also due to shock waves. However, for wide-angled nozzles, internal shocks can be an inherent part of the flow from the nozzle and the bubbles which they produce are thus an inherent part of the impingement flow. From physical arguments concerning the main factors involved in producing a bubble, a parameter is constructed whose values are shown to be a good criterion for whether a bubble occurs or not.

The Three-Shock Confluence Problem for Normally Impinging, Overexpanded Jets

SummaryIn this paper, a systematic study of the triple shock confluence point is presented for the case of an overexpanded jet which impinges on a perpendicular flat plate at small displacements from the nozzle. The jet is uniform upstream of the free jet shock wave. Non-homentropic effects are taken into account and lead to modifications to the accepted flow patterns at a triple point for the case of strong incident shock waves. Where more than one thermodynamically possible solution to the triple point equations exists, the alternative solutions are re-examined, taking non-homentropic effects into consideration. Some discussion of the possibility of infinite shock curvatures is also included. Qualitative flow patterns of the impinging flow are constructed, based on the triple point solutions and the known boundary conditions. The interesting cases where the tail shock flow is supersonic are given particular attention and two possible flow patterns are distinguished. Finally, some experimental evidence in the form of schlieren pictures is presented. Although not conclusive, this evidence supports the theory.

Compressible corner flow

The viscous compressible flow in the vicinity of a right-angle corner, formed by the intersection of two perpendicular flat plates and aligned with the free stream, is investigated. In the absence of viscous-inviscid interactions and imbedded shock waves, a theory is developed that is valid throughout the subsonic and supersonic Mach number range. Within this limitation and the additional assumptions of unit Prandtl number and a linear viscosity-temperature law, a consistent set of governing equations and boundary conditions is derived. The method of matched asymptotic expansions is applied in order to distinguish the relevant regions in the flow field.In the corner region the Crocco integral is shown to apply, even for a three-dimensional flow field. The equations governing the flow in the corner layer consist of four coupled nonlinear elliptic partial differential equations of the Poisson variety. Since they do not lend themselves to analytic solution, numerical methods are employed. Two such methods used here are the Gauss-Seidel explicit technique and the alternating direction implicit method. The merits of both techniques are discussed with regard to convergence rate, accuracy and stability. The calculations show that in cases where the Gauss-Seidel method fails to give converged solutions, owing to instability, the alternating direction implicit method does provide converged solutions. However, in cases where both methods are convergent, there is no appreciable difference in convergence rates. The numerical calculations were done on a CDC 6600 computer.Results of calculations are presented for representative compressible-flow conditions. The extent of the corner disturbance is controlled by the Mach number and wall temperature ratio in a manner analogous to the two-dimensional boundary layer. A swirling motion is noted in the corner layer which is influenced to a great extent by the asymptotic cross-flow profiles. The skin-friction coefficient is shown to increase monotonically from zero at the corner point to its asymptotic two-dimensional value. For cold wall cases, this value is approached more rapidly. The asymptotic analysis indicates that for even colder wall cases, not considered here, an overshoot is possible.