Investigation of mach number effects on flow over a flat plate at Reynolds number of 1.0 × 104 by Schlieren visualization

Author(s):  
Kensuke Kusama ◽  
Takayuki Nagata ◽  
Masayuki Anyoji ◽  
Taku Nonomura ◽  
Keisuke Asai
Author(s):  
Shane Colón ◽  
Mark Ricklick ◽  
Doug Nagy ◽  
Amy Lafleur

Abstract Thermal barrier coatings (TBC) found on turbine blades are a key element in the performance and reliability of modern gas turbines. TBC reduces the heat transfer into turbine blades by introducing an additional surface thermal resistance; consequently allowing for higher gas temperatures. During the service life of the blades, the TBC surface may be damaged due to manufacturing imperfections, handling damage, service spalling, or service impact damage, producing chips in the coating. While an increase in aerofoil temperature is expected, it is unknown to what degree the blade will be affected and what parameters of the chip shape affect this result. During routine inspections, the severity of the chipping will often fall to the discretion of the inspecting engineer. Without a quantitative understanding of the flow and heat transfer around these chips, there is potential for premature removal or possible blade failure if left to operate. The goal of this preliminary study is to identify the major driving parameters that lead to the increase in metal temperature when TBC is damaged, such that more quantitative estimates of blade life and refurbishing needs can be made. A two-dimensional computational Conjugate Heat Transfer model was developed; fully resolving the hot gas path and TBC, bond-coat, and super alloy solids. Representative convective conditions were applied to the cold side to emulate the characteristics of a cooled turbine blade. The hot gas path properties included an inlet temperature of 1600 K with varying Mach numbers of 0.30, 0.59, and 0.80 and Reynolds number of 5.1×105, 7.0×105, and 9.0×105 as referenced from the leading edge of the model. The cold side was given a coolant temperature of 750 K and a heat transfer coefficient of 1500 W/m2*K. The assigned thermal conductivities of the TBC, bond-coat, and metal alloys were 0.7 W/m*K, 7.0 W/m*K, and 11.0 W/m*K, respectively, and layer thicknesses of 0.50 mm, 0.25 mm, and 1.50 mm, respectively. A flat plate model without the presence of the chip was first evaluated to provide a basis of validation by comparison to existing correlations. Comparing heat transfer coefficients, the flat plate model matched within uncertainty to the Chilton-Colburn analogy. In addition, flat plate results captured the boundary layer thickness when compared with Prandtl’s 1/7th power-law. A chip was then introduced into the model, varying the chip width and the edge geometry. The most sensitive driving parameters were identified to be the chip width and Mach number. In cases where the chip width reached 16 times the TBC thickness, temperatures increased by almost 30% when compared to the undamaged equivalents. Additionally, increasing the Mach number of the incoming flow also increased metal temperatures. While the Reynolds number based on the leading edge of the model was deemed negligible, the Reynolds number based on the chip width was found to have a noticeable impact on the blade temperature. In conclusion, this study found that chip edge geometry was a negligible factor, while the Mach number, chip width, and Reynolds number based on the chip width had a significant effect on the total metal temperature.


1973 ◽  
Vol 60 (2) ◽  
pp. 257-271 ◽  
Author(s):  
G. T. Coleman ◽  
C. Osborne ◽  
J. L. Stollery

A hypersonic gun tunnel has been used to measure the heat transfer to a sharpedged flat plate inclined at various incidences to generate local Mach numbers from 3 to 9. The measurements have been compared with a number of theoretical estimates by plotting the Stanton number against the energy-thickness Reynolds number. The prediction giving the most reasonable agreement throughout the above Mach number range is that due to Fernholz (1971).The values of the skin-friction coefficient derived from velocity profiles and Preston tube data are also given.


1968 ◽  
Vol 90 (4) ◽  
pp. 596-600 ◽  
Author(s):  
A. L. Laganelli ◽  
J. P. Hartnett

Heat transfer results are reported for a transpiration cooled porous flat plate placed in a stream of air and in a stream of CO2. The tests were performed at a Mach number of 1.96 over a range of effective length Reynolds number, from 5 million to 9.1 million, when CO2 was used as the free stream gas. A Mach number of 2.53 for an effective length Reynolds number range of 5.3 million to 8.3 million was characteristic when the free stream gas was air. The heat transfer data were normalized and presented as the ratio of the Stanton number to the no-blowing Stanton value (St/St0) as a function of the dimensionless transpiration rate F/St0. The recovery factor data were also normalized and presented as the ratio of r/r0 as a function of the transpiration rate F. The results for both the air and the CO2 free stream flows showed a reduction in heat transfer with increasing transpiration rate, using air and CO2 as the injectant gases. The measured recovery factor and the normalized recovery factor also decreased with increasing transpiration for the reported gas combinations. It was found that Rubesin’s air theory adequately predicts all of the heat transfer results including those obtained in CO2 atmospheres within the reported Mach number range. Also, the empirical theories which predict recovery factor results for air free streams can be used for air or CO2 injection into a CO2 free stream gas.


1960 ◽  
Vol 9 (2) ◽  
pp. 257-299 ◽  
Author(s):  
John Laufer ◽  
Thomas Vrebalovich

Self-excited oscillations have been discovered experimentally in a supersonic laminar boundary layer along a flat plate. By the use of appropriate measuring techniques, the damping and amplification of the oscillations are studied and the stability limits determined at free-stream Mach numbers 1·6 and 2·2. The wave-like nature of the oscillations is demonstrated and their wave velocities are measured using a specially designed ‘disturbance generator’. It is shown empirically that the stability limits expressed in terms of the boundary-layer-thickness Reynolds number are independent of the Mach number and dependent only on the oscillation frequency. The main effect of compressibility is an increase in wave velocity with Mach number. This has the consequence that the disturbances, although possessing the same dimensionless amplification coefficient as in the incompressible case, have less time (per unit distance) to grow in amplitude. Thus, the adiabatic compressible boundary layer is shown to be more stable than the incompressible one. In general, the experiments confirm the basic assumptions and predictions of the existing stability theory and also suggest the desirability of improvement in the theory in certain phases of the problem. Finally, on the basis of these results a rough estimate of the transition Reynolds number is made in the compressible flow range.


Author(s):  
J. Lepicovsky ◽  
T. J. Bencic

Application of thin-film thermocouples and temperature sensitive paint to surface temperature and heat transfer rate measurement on a flat plate with internal cooling is described in this paper. The test arrangement was designed to model flow and heat transfer conditions in terms of gas (external) and coolant (internal) Reynolds numbers that are typical for cooled turbine components. The test article is geometrically simple; however, from the heat transfer point of view it represents a fairly complex case. For both flows, internal and external, the hydrodynamic boundary layers start well ahead of the thermal boundary layers. The thermally active surface is preceded by an adiabatic starting length. Also, the heat transfer occurs under nonisothermal wall conditions and nonuniform heat flux conditions. The heat transfer experiments were carried out for a range of Mach number and Reynolds number on the gas side from 0.17 to 0.53 and from 135 000 to 580 000, respectively. On the coolant side, the corresponding ranges were from 0.3 to 0.52 for the flow Mach number, and from 20 000 to 65 000 for the Reynolds number. Measured bulk heat transfer rates demonstrated expected trends as functions of external (gas) and internal (coolant) Reynolds numbers. Local heat transfer rates measured along the mid-span line behaved as expected in relation to the internal (coolant) Reynolds number. However, they seem to be insensitive to changes in the external (gas) Reynolds number — at least for the particular test arrangement. Local heat transfer rates, however, strongly depend on the location with respect to the width of the cooling passage. These results were not expected; they may be caused by three dimensional nature of heat convection and conduction in this test arrangement.


1967 ◽  
Vol 18 (3) ◽  
pp. 237-258 ◽  
Author(s):  
Bryan E. Richards

SummaryAn experimental investigation of natural transition and turbulent boundary layers on a cold flat plate in hypersonic flow was carried out in the Imperial College Gun Tunnel. Studies were also made of the effects of both two- and three-dimensional roughness elements including vortex generators.Results indicate that the Reynolds number based on the end of transition consists of two separate parts. These are the Reynolds numbers based respectively on the position of the apparent origin of the transition region behaviour, Ri, and on the length of the transition region measured from this origin. Ri is shown to be independent of unit Reynolds number for a sharp leading-edge model, and by correlations of other published data to vary little with Mach number. This origin is perhaps the most relevant point when comparisons are made between experiment and classical stability theory. The variation of the heat transfer rate during the transition region is compared with findings at low speed and shown to be similar to that expected from the turbulent spot concept of Emmons. The measured variation of the length of the transition region (x) from this origin gives an explanation for the unit Reynolds number effect on transition, and the rapid increase of transition Reynolds number with Mach number in hypersonic flow. The effect of bluntness on these factors is discussed.The virtual origin of the turbulent boundary layer is shown to lie close to the measured beginning of transition. At these high Mach number and low wall temperature conditions experimental values of heat transfer and values of skin friction coefficient derived from the estimated momentum thickness growth in the turbulent region are found to be appreciably higher than predictions by present theories.Roughness trips were found to bring the whole transition region forward. Only small differences in the measured boundary layer thickness, shape and heat transfer rates in the turbulent region (referenced to the estimated virtual origin in each case) were found after natural and forced transition. The transition point locations on a flat plate with either spherical roughness elements or vortex generators were found to agree with values predicted by the method of Potter and Whitfield as modified by Luxton to account for the effects of heat transfer.


Author(s):  
Yuan Hu ◽  
Quanhua Sun ◽  
Jing Fan

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum/particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.


Author(s):  
Marion Mack ◽  
Roland Brachmanski ◽  
Reinhard Niehuis

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.


Author(s):  
E. Valenti ◽  
J. Halama ◽  
R. De´nos ◽  
T. Arts

This paper presents steady and unsteady pressure measurements at three span locations (15, 50 and 85%) on the rotor surface of a transonic turbine stage. The data are compared with the results of a 3D unsteady Euler stage calculation. The overall agreement between the measurements and the prediction is satisfactory. The effects of pressure ratio and Reynolds number are discussed. The rotor time-averaged Mach number distribution is very sensitive to the pressure ratio of the stage since the incidence of the flow changes as well as the rotor exit Mach number. The time-resolved pressure field is dominated by the vane trailing edge shock waves. The incidence and intensity of the shock strongly varies from hub to tip due to the radial equilibrium of the flow at the vane exit. The decrease of the pressure ratio attenuates significantly the amplitude of the fluctuations. An increase of the pressure ratio has less significant effect since the change in the vane exit Mach number is small. The effect of the Reynolds number is weak for both the time-averaged and the time-resolved rotor static pressure at mid-span, while it causes an increase of the pressure amplitudes at the two other spans.


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