Kung Ming Chung

Investigation on Transonic Convex-Corner Flows

An experimental investigation was conducted to study the transonic flow past convex corners. The mean surface pressure indicated strong inviscid-viscous interactions, and the interaction region increased with the freestream Mach number and the convex-corner angle. Unsteadiness of the interaction was characterized by an intermittent region and a local peak pressure fluctuation. The peak pressure fluctuations and the tentative boundary between the attached and separated flows could be scaled with the convex-corner angle and a second-order freestream Mach number (M 2 ∞η)

Characteristics of Transonic Rectangular Cavity Flows

Experiments are performed to study the characteristics of rectangular cavity e ows. Mean and e uctuating surfacepressurein a Mach-1.28 turbulente owpastrectangularcavitiesareobtained. Thecavity length-to-depth ratio L/D varies from 2.43 to 43.00, and the length-to-width ratio L/W is 0.5, 1.0, and 2.0. The effect of cavity depth is studied, in which L/W or both L/D and L/W are held constant. The results indicate that L/D is the most important parameter in determining the characteristics inside the cavity and in its vicinity. The effect of L/W is signie cant only at the aft half of the cavity. Lower static pressure aft of the front face and higher static pressure at the aft half of the cavity are observed with decreasing depth-to-incoming boundary-layer thickness D/±0 at constant L/W. At constantL/D and L/W, the results show an opposite trend. The amplitude of surfacepressure e uctuation decreases at larger L/D. The parameter L/W mainly affects the peak surface pressure e uctuation ahead of the rear face.

Downstream influence scaling of turbulent flow past expansion corners

Previous studies of the high-speed viscous inviscid interaction between a turbulent boundary layer and an expansion at a convex corner have noted that surface pressure decreases toward the downstream inviscid value yielded by a Prandtl-Meyer expansion. A downstream influence on the corner is presently identified which is based on the mean surface pressure distribution; a scaling law is proposed for this distance.

Transition of subsonic and transonic expansion-corner flows

A naturally developed turbulent boundary layer past convex corners was studied. Attention is on the transition of subsonic and transonic expansion flows. Convex-corner angle α ranges from 5 to 20 deg, and freestream Mach numbers M∞ are 0.33, 0.64, and 0.83. Reynolds numbers based on the incoming boundary-layer thickness Re 60 are 10.0, 14.9, and 16.8 × 10 4 , respectively. Transition of subsonic and transonic expansion-corner flow is observed at M 2 ∞ α = 6.14. The sudden expansion near the corner is also scaled with this parameter at M∞ = 0.64 and 0.83, but not for M∞ = 0.33

Characteristics of Compressible Rectangular Cavity Flows

Experiments are performed to study the effect of cavity geometry and Mach number on the characteristics of compressible rectangular cavity flows. The study indicates that the corresponding length-to-depth ratio for the open- and transitional-type cavities increases with higher freestream Mach number. The depth-to-incoming boundary-layer thickness ratio is another important parameter to define the type of the cavity flow. The upstream influence region is minimized with the presence of a cavity, and larger downstream influence region is observed for the transitional-closed- and closed-type cavities. The distributions of surface pressure fluctuations show similar trend as those of static pressure distributions. The amplitude of surface pressure fluctuations increases toward the rear face for an open-type cavity, whereas a minor peak near the middle of the cavity floor is observed for a closed-type cavity. A transitional-type cavity induces more intense surface pressure fluctuations at the cavity floor. Higher levels of pressure fluctuations near the rear face are observed at higher Mach numbers for the transitional-and open-type cavities

Flow Similarity in Compressible Convex-Corner Flows

T HE Prandtl-Meyer expansion is well-known in supersonic convex-corner flows. It is also possible to formulate an interaction law in an explicit form that would relate the displacement effect of the boundary layer to the pressure induced in the inviscid part of subsonicflows. In the literature, studies that attributed theflow properties near the corner to the viscous-invisvid interaction at the transonic flow regime are scarce [1]. For a laminar boundary layer, an analysis by Ruban and Turkyilmaz [2] indicated that the displacement effect near the corner point is primarily due to the inviscid part. The flow is governed by the main part of the boundary layer and the potential flow region outside the boundary layer (inviscid-inviscid interaction). However, a subsequent study by Ruban et al. [3] highlighted the contribution of viscous-inviscid interaction, in which the displacement thickness near the corner is affected by the overlapping region that lies between the viscous sublayer and main part of the boundary layer. For a turbulent boundary layer, Chung [4] indicated that there would be a mild initial expansion, followed by a strong expansion near the corner apex and then downstream recompression for a compressible convex-corner flow. AtM 0:64 and 0.83, the flow is expanded from subsonic to transonic speed when the similarity parameter M 6:14. Note that the convex-corner angle ranges from 5 to 17 deg. A small separation bubble might also be born at the formation of ah normal shock wave [5]. With an increasing convexcorner angle atM 0:83, there is a slight upstreammovement of the separation position and a downstreammovement of the reattachment position. The shock-induced separated region at M 8:95 is expanded and also induces intense surface-pressure fluctuations, which are associated with the intermittent nature of the surface pressure signals or shock-excursion phenomena. The amplitude of peak surface-pressure fluctuations could also be scaledwithM [6]. In Chung’s study [4], it is known that M cannot be used as a similarity parameter for the test cases at M 0:34. However, it is also known that there exists a relationship (i.e., the Prandtl-Glauert rule) [7] between the minimum pressure coefficients for the incompressible airfoil Q2 Cp;ic and compressible airfoil Cp;c, where Cp;c Cp;ic= 1 M p . According to the hypothesis that small streamline deflections produce proportionally small changes in Mach number and pressure, a hodograph solution for compressible flow past a corner was given by Verhoff et al. [8]. The viscous sublayer is relatively unimportant when the Reynolds number is sufficiently large. In terms of the stream function , the hodograph equation for compressible corner flows is given as follows:

Damping of surface pressure fluctuations in hypersonic turbulent flow past expansion corners

Surface pressure fluctuations of Mach 8 turbulent flow past a 2.5- and a 4.25-deg expansion corner maintained a Gaussian distribution but were severely attenuated by the expansion process. The pressure fluctuations did not recover to those of an equilibrium turbulent flow even though the mean pressures reached downstream inviscid values in four to six boundary-layer thicknesses. The fluctuations were convected with a velocity comparable to that on a flat plate, and they maintained their identities longer for the stronger expansion. The damping of pressure fluctuations at hypersonic Mach numbers, even by small corner angles, may be exploited in fatigue design.

Tunnel Background Noise on Compressible Convex-Corner Flows

The perforated test section walls of a transonic wind tunnel are responsible for generating edgetones, thus contributing significantly to the overall noise level and possibly invalidating the measurements of surface pressure fluctuations. In the present study, the wind tunnel was assembled with perforated top/bottom walls, solid side walls, and four perforated walls. The focus was to investigate the effects of tunnel background noise on compressible convex-corner flows, which correspond to the upper control surface of an aircraft wing. External acoustic disturbance has a minor effect on the mean surface pressure distributions, including flow expansion and recompression near the corner. Higher peak pressure fluctuations, which are associated with shock excursion phenomena, are observed with more intense tunnel background noise, particularly for the flow with initial separated boundary layers.

An experimental study of a cold-wall hypersonic boundary layer

The boundary layer that developed on a one-meter long flat plate at a nominal Mach number of 8 and a Reynolds number of 10.2 million per meter was studied using a shock tunnel. The wall-to-stagnation temperature ratio was 0.35. The turbulent velocity profiles possessed very small wake components. The small wake component is characteristic of low Reynolds number flows and may indicate that a turbulent boundary layer was not fully developed. The magnitude of the surface pressure fluctuations in the turbulent part of the flow was found to be in agreement with semi-empirical predictions. These fluctuations were larger than those obtained at lower supersonic Mach numbers and indicated that pressure fluctuations may not be neglected at hypersonic Mach numbers. The fluctuations also possessed a convection velocity that increased with transducer spacing and followed the trend of previous investigations.

Transonic Cavity-Convex Corner Interactions

An experimental study was conducted to investigate the transonic convex-corner flows with and without the presence of an upstream cavity. Measurements were made to investigate the geometric effect and the spacing of a cavity on attached and separated convex-corner flows. The upstream expansion and downstream initial recompression are strongly affected by the upstream cavity, which includes the delay on the transition of subsonic and transonic expansion flows, the initial boundary-layer separation, the characteristics of separated flow, and the intensity of surface pressure fluctuations