High-Speed Subsonic Compressible Lubrication

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Florence Dupuy ◽  
Benyebka Bou-Saïd ◽  
John Tichy
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Mach Number ◽  
Compressible Flow ◽  
High Speed ◽  
Transfer Number ◽  
Flow Equations ◽  
Foil Bearings ◽  
Basic Studies ◽  
Bearing Number

The present study extends the scope of compressible lubrication theory (CLT) by considering a more complete formulation of compressible flow in a thin film. A one-dimensional (1D) approximation is obtained, which is common in basic studies of compressible flow. A dimensionless formulation of the thin film compressible flow equations (continuity, momentum, energy, and perfect gas) is derived. There are three dimensionless governing parameters, the Mach number M, the compressibility or bearing number Λ, and a heat transfer number H (a sort of inverse Péclet number). The classical theory assumes isothermal conditions (a consequence of a large heat transfer number) and implicitly assumes low Mach number conditions. It turns out that neither of these conditions are met in high-speed applications such as foil bearings. Results are calculated by varying M and H in a parametric fashion. We find that the influence of Mach number is small (at least up to M = 0.5) but the influence of heat transfer is large: the classical predicted results are in error by a factor of four or so. The improved theory predicts much greater load than the traditional. This means that high-speed air bearing design based on CLT would function satisfactorily, as born out by their successful application; however, such bearings would be significantly over-designed.

scholarly journals Computing multi-mode shock-induced compressible turbulent mixing at late times

2015 ◽  
Vol 779 ◽  
pp. 411-431 ◽  
Author(s):  
T. Oggian ◽  
D. Drikakis ◽  
D. L. Youngs ◽  
R. J. R. Williams
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Suitable Model ◽  
Late Time ◽  
Flow Equations ◽  
Multi Mode

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

scholarly journals The effect of core size on the speed of compressible hollow vortex streets

2017 ◽  
Vol 836 ◽  
pp. 797-827 ◽  
Author(s):  
Darren G. Crowdy ◽  
Vikas S. Krishnamurthy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Vortex Core ◽  
Perturbation Expansion ◽  
Core Size ◽  
Flow Equations ◽  
Stable Case ◽  
First Order ◽  
Aspect Ratios ◽  
Vortex Streets

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Mach-number perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai–Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky–Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down.

Temperature measurements in a hypersonic gun tunnel using heat-transfer methods

1967 ◽  
Vol 27 (3) ◽  
pp. 503-512 ◽  
Author(s):  
B. E. Edney
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Mach Number ◽  
Heat Losses ◽  
Transfer Rates ◽  
Gun Barrel ◽  
Compression Cycle ◽  
Initial Shock ◽  
Working Section ◽  
Good Agreement

The theory of Fay & Riddell (1958) is used to calculate stagnation temperatures from stagnation-point heat-transfer rates measured in the working section of a hypersonic gun tunnel at a Mach number of 9·8. Measurements using both thin-film gauges and calorimeters are described. The temperatures measured using this technique are found to be lower than predicted by Lemcke (1962) from measurements of shock strengths and final pressures in the gun barrel. This discrepancy is attributed to heat losses in the barrel during the initial shock compression cycle. A simple theory is developed to take into account these losses. There is good agreement between this theory and the experimental results.

High Effectiveness, Low Pressure Drop Recuperator for High Speed and Power Oil-Free Turbogenerator

2015 ◽  
Author(s):  
José Luis Córdova ◽  
James F. Walton ◽  
Hooshang Heshmat
Keyword(s):  
Heat Transfer ◽  
System Integration ◽  
High Speed ◽  
Point Of View ◽  
Operating Conditions ◽  
Specific Power ◽  
Foil Bearings ◽  
Mass Flow Rates ◽  
Manufacturing Technologies ◽  
Cycle Efficiency

Development of a compact radial recuperator prototype for a previously demonstrated 8 kW turboalternator has been completed. Its novel geometry has resulted in measured heat transfer effectiveness that surpasses 90% at the operating conditions of the engine, with acceptable pressure penalty (< 35 kPa) that can be easily accommodated by the compressor. Unrecuperated, the oil-free, high-speed micro-turboalternator, operating at 180,000 rpm and featuring compliant-foil bearings, presented a thermal (or cycle) efficiency of 12%. With the recuperator, thermal efficiency of approximately 30% is possible. The recuperator configuration is unique from both a geometric and a heat transfer point of view. Its radial (axisymmetric) configuration allows for compact system integration, concentric to the existing engine/combustor hardware assembly. While the addition of the recuperator prototype has increased the overall weight of the system, and hence reduced its specific power from the previously reported 1.6 kW/kg (1 hp/lbm) to approximately 0.9 kW/kg, the unprecedented gain in efficiency by such a compact device justifies its implementation. Furthermore, it is anticipated that continuing prototype refinement, along with the use of novel manufacturing technologies and materials (e.g. 3D printing and ceramics) will result in a significant increase in power density. Performance characterization has been performed for mass flow rates up to 0.08 kg/s and gas inlet temperatures up to 925 K, which are representative of meso-scale turbine engines. Scalability of the device has also been evaluated, down to a 1 kW engine, and up to MW order.

scholarly journals An Experimental Study to Compare the Naphthalene Sublimation With the Liquid Crystal Technique in Compressible Flow

1995 ◽  
Author(s):  
M. Häring ◽  
A. Hoffs ◽  
A. Bolcs ◽  
B. Weigand
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Mach Number ◽  
Transfer Coefficient ◽  
Compressible Flow ◽  
Test Facility ◽  
Number Range ◽  
Naphthalene Sublimation ◽  
Sublimation Technique

The naphthalene sublimation and the liquid crystal technique are two methods being used for measurements of the heat transfer coefficient on turbine airfoils. In this paper the results obtained with the two methods for the same compressible flow conditions are compared. The measurements were performed in a free jet test facility on a flat plate and a cylinder. The free stream Mach number ranged from M=0.4 to 0.8. The naphthalene sublimation technique was applied to obtain the local Nusselt number, based on the Sherwood number, applying a new analogy function (Häring, Weigand (1995)). These results were compared with measurements on the same test arrangement using the transient liquid crystal technique. A good agreement between the two measurement techniques and correlations was found for the entire Mach number range. An application of both techniques on a turbine airfoil confirmed this observation. The sublimation technique was also applied to measure the local heat transfer coefficient on a turbine vane at exit Mach numbers up to M=0.9 and exit Reynolds numbers up to Re=1.8e6. The experimental results were compared with the two dimensional boundary layer code TEXSTAN (Crawford, 1986).

scholarly journals An Ultra-Fast TSP on a CNT Heating Layer for Unsteady Temperature and Heat Flux Measurements in Subsonic Flows

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 657
Author(s):  
Martin Bitter ◽  
Michael Hilfer ◽  
Tobias Schubert ◽  
Christian Klein ◽  
Reinhard Niehuis
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Surface Temperature ◽  
Flat Plate ◽  
High Speed ◽  
Ambient Pressure ◽  
Frame Rate ◽  
Temperature Fields ◽  
Test Case ◽  
Unsteady Temperature

In this paper, the authors demonstrate the application of a modified Ru(phen)-based temperature-sensitive paint which was originally developed for the evaluation of unsteady aero-thermodynamic phenomena in high Mach number but short duration experiments. In the present work, the modified TSP with a temperature sensitivity of up to −5.6%/K was applied in a low Mach number long-duration test case in a low-pressure environment. For the demonstration of the paint’s performance, a flat plate with a mounted cylinder was set up in the High-Speed Cascade Wind Tunnel (HGK). The test case was designed to generate vortex shedding frequencies up to 4300 Hz which were sampled using a high-speed camera at 40 kHz frame rate to resolve unsteady surface temperature fields for potential heat-transfer estimations. The experiments were carried out at reduced ambient pressure of p∞ = 13.8 kPa for three inflow Mach numbers being Ma∞=[0.3;0.5;0.7]. In order to enable the resolution of very low temperature fluctuations down to the noise floor of 10−5 K with high spatial and temporal resolution, the flat plate model was equipped with a sprayable carbon nanotube (CNT) heating layer. This constellation, together with the thermal sensors incorporated in the model, allowed for the calculation of a quasi-heat-transfer coefficient from the surface temperature fields. Besides the results of the experiments, the paper highlights the properties of the modified TSP as well as the methodology.

An appraisal of ‘flat plate’ closure for the approximate solution of boundary layer problems

1987 ◽  
Vol 91 (908) ◽  
pp. 373-389
Author(s):  
D. I. A. Poll ◽  
C. M. Hellon
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Flat Plate ◽  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Similarity Solutions ◽  
Laminar Flows ◽  
Reynolds Analogy

SummaryThe usefulness of zero pressure gradient, flat plate closure relations in providing approximate solutions for the boundary layer momentum and energy integral equations is examined. Expressions are obtained for skin friction, surface heat transfer rate and local Reynolds analogy factor under general compressible flow conditions. For laminar flows the predictions are compared with well known similarity solutions, with some exact solutions for non-similar flows and with experimental heat transfer data for high speed flow over a blunt cone. Consideration is also given to situations in which the surface temperature is a function of position. For turbulent flow situations comparisons are made with experimental data obtained from two-dimensional and axi-symmetric tests. Conditions vary from low Mach number incompressible flows through to high Mach number compressible flows with highly cooled walls. Some comparisons are also made with other prediction techniques.

Turbine Blade Tip Heat Transfer in Low Speed and High Speed Flows

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Andrew P. S. Wheeler ◽  
Nicholas R. Atkins ◽  
Li He
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Coefficient ◽  
Mach Number ◽  
Transfer Coefficient ◽  
High Speed ◽  
Low Speed ◽  
Blade Tip ◽  
The Heat Transfer Coefficient ◽  
Recovery Temperature

In this paper, high and low speed tip flows are investigated for a high-pressure turbine blade. Previous experimental data are used to validate a computational fluid dynamics (CFD) code, which is then used to study the tip heat transfer in high and low speed cascades. The results show that at engine representative Mach numbers, the tip flow is predominantly transonic. Thus, compared with the low speed tip flow, the heat transfer is affected by reductions in both the heat-transfer coefficient and the recovery temperature. The high Mach numbers in the tip region (M>1.5) lead to large local variations in recovery temperature. Significant changes in the heat-transfer coefficient are also observed. These are due to changes in the structure of the tip flow at high speed. At high speeds, the pressure side corner separation bubble reattachment occurs through supersonic acceleration, which halves the length of the bubble when the tip-gap exit Mach number is increased from 0.1 to 1.0. In addition, shock/boundary-layer interactions within the tip gap lead to large changes in the tip boundary-layer thickness. These effects give rise to significant differences in the heat-transfer coefficient within the tip region compared with the low speed tip flow. Compared with the low speed tip flow, the high speed tip flow is much less dominated by turbulent dissipation and is thus less sensitive to the choice of turbulence model. These results clearly demonstrate that blade tip heat transfer is a strong function of Mach number, an important implication when considering the use of low speed experimental testing and associated CFD validation in engine blade tip design.

Sign in / Sign up

Export Citation Format

Share Document