Extended Reynolds analogy for the rarefied Rayleigh problem: Similarity parameters

The local heat transfer from a plane rotating disc enclosed in a casing has been studied experimentally. The disc of 800 mm diameter can be run up to 2000 min−1 at axial distances between disc and casing varied between 5 and 55 mm. Centrifugal or alternatively centripetal flow of cooling air at rates up to ṁ = 1 kg/s can be applied, both with or without an inlet swirl. With the disc rotating in a closed casing (ṁ = 0 kg/s) the influence of the characteristic dimensionless groups on the local heat transfer has been investigated. At a fixed radius, a variation of the local Reynolds Number by either speed or density results in corresponding changes of the heat transfer. However, with a variation of the radius different heat transfer-Re relations are found. In fact, the temperature distribution in the gas caused by the heat flux results in an additional influence of free convection, to be expressed by a Grashof Number. This is confirmed by a comparison of the experimental results with calculations based on Reynolds Analogy and measured friction coefficients. The discrepancies found can be explained only, if in addition to the limitations of the analogy, the influence of free convection is taken into account. Additional results of ongoing experiments concerning the influence of the geometry of the cavity between disc and casing, of the coolant flow rate and of the swirl are presented.

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Swirl Flow Investigations on the Enhancement of Heat Transfer Processes in Cyclone Cooling Ducts

Volume 4: Heat Transfer, Parts A and B ◽

10.1115/gt2012-69395 ◽

2012 ◽

Cited By ~ 1

Author(s):

Florian Wassermann ◽

Sven Grundmann ◽

Michael Kloss ◽

Heinz-Peter Schiffer

Keyword(s):

Heat Transfer ◽

Mass Transfer ◽

Complex Structure ◽

Three Dimensional ◽

Swirl Flow ◽

Flow Structures ◽

Stable Complex ◽

Reynolds Analogy ◽

Transfer Processes ◽

Cooling Ducts

Cyclone cooling is a promising method to enhance heat-transfer processes in future internal turbine-blade leading-edge cooling-ducts. The basic component of such cooling channels is the swirl generator, which induces a swirling movement of the coolant. The angular momentum generates stable, complex and three-dimensional flow structures of helical shape with alternating axial flow directions. Full three-dimensional and three-component velocity measurements using magnetic resonance velocimetry (3D3C-MRV) were conducted, with the aim to understand the complex structure of pipe flows with strong swirl. In order to mimic the effect of different installation concepts of the cyclone-cooling ducts an idealized bend-duct swirl-tube configuration with variable exit orifices has been investigated. Pronounced helical flow structures and distinct velocity zones could be found in this swirl flow. One substantial result is the identification of stationary helix-shaped streaks of high axial velocity in the direct vicinity of the wall. These findings are in good agreement with mass-transfer measurements that also show helix-shaped structures with increased mass transfer at the inner surface of the tube. According to the Reynolds analogy between heat and mass transfer, augmented heat-transfer processes in these areas are to be expected.

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Assessment of turbulence models using DNS data of compressible plane free shear layer flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.919 ◽

2021 ◽

Vol 931 ◽

Author(s):

D. Li ◽

J. Komperda ◽

A. Peyvan ◽

Z. Ghiasi ◽

F. Mashayek

Keyword(s):

Shear Layer ◽

Compressible Flows ◽

Eddy Viscosity ◽

Turbulence Models ◽

Correlation Coefficients ◽

Free Shear Layer ◽

Smagorinsky Model ◽

Reynolds Analogy ◽

Velocity Fluctuations ◽

Scale Similarity

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

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A Numerical Model for Stirling Cycle Machines

Journal of Engineering for Power ◽

10.1115/1.3230337 ◽

1980 ◽

Vol 102 (4) ◽

pp. 756-761 ◽

Cited By ~ 2

Author(s):

D. M. Berchowitz ◽

I. Urieli ◽

C. J. Rallis

Keyword(s):

Integral Equation ◽

Differential Forms ◽

Local Heat Transfer ◽

Viscous Friction ◽

Local Heat ◽

Momentum Equation ◽

Transfer Coefficients ◽

Reynolds Analogy ◽

Stirling Cycle ◽

Heat Transfer Coefficients

The further development of a model to accurately simulate the performance and detailed behavior of Stirling cycle machines is described. The transport equation set (which describe the working gas) is derived in both the so-called integral and differential forms. Only the integral equation set is solved for the simulation. The differential equation set is used to investigate the structure of individual terms in the integral equation set. This procedure allows these terms to be more accurately understood and, hence, modeled. The energy equation includes kinetic energy and dissipation terms while the momentum equation includes the effects of working gas acceleration and viscous friction. Heat leakage and longitudinal conduction in the machine walls are accounted for and due regard is taken of the working gas instantaneous properties. The Reynolds analogy is used to calculate the local heat transfer coefficients.

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Effects of a Realistically Rough Surface on Vane Heat Transfer Including the Influence of Turbulence Condition and Reynolds Number

Journal of Turbomachinery ◽

10.1115/1.4003026 ◽

2011 ◽

Vol 134 (2) ◽

Cited By ~ 2

Author(s):

E. L. Erickson ◽

F. E. Ames ◽

J. P. Bons

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Rough Surface ◽

Reynolds Numbers ◽

Suction Surface ◽

Average Roughness ◽

Surface Distribution ◽

Reynolds Analogy ◽

Pressure Surface ◽

Early Transition

Heat transfer distributions are experimentally acquired and reported for a vane with both a smooth and a realistically rough surface. Surface heat transfer is investigated over a range of turbulence levels (low (0.7%), grid (8.5%), aerocombustor (13.5%), and aerocombustor with decay (9.5%)) and a range of chord Reynolds numbers (ReC=500,000, 1,000,000, and 2,000,000). The realistically rough surface distribution was generated by Brigham Young University’s accelerated deposition facility. The surface is intended to represent a TBC surface that has accumulated 7500 h of operation with particulate deposition due to a mainstream concentration of 0.02 ppmw. The realistically rough surface was scaled by 11 times for consistency with the vane geometry and cast using a high thermal conductivity epoxy (k=2.1 W/m/K) to comply with the vane geometry. The surface was applied over the foil heater covering the vane pressure surface and about 10% of the suction surface. The 958×573 roughness array generated by Brigham Young on a 9.5×5.7 mm2 region was averaged to a 320×191 array for fabrication. The calculated surface roughness parameters of this scaled and averaged array included the maximum roughness, Rt=1.99 mm, the average roughness, Ra=0.25 mm, and the average forward facing angle, αf=3.974 deg. The peak to valley roughness, Rz, was determined to be 0.784 mm. The sand grain roughness of the surface (kS=0.466 mm) was estimated using a correlation offered by Bons (2005, “A Critical Assessment of Reynolds Analogy for Turbine Flows,” ASME J. Turbomach., 127, pp. 472–485). Based on estimates of skin friction coefficient using a turbulence correlation with the vane chord Reynolds numbers representative values for the surface’s roughness Reynolds number are 23, 43, and 80 for the three exit condition Reynolds numbers tested. Smooth vane heat transfer distributions exhibited significant laminar region augmentation with the elevated turbulence levels. Turbulence also caused early transition on the pressure surface for the higher Reynolds numbers. The rough surface had no significant effect on heat transfer in the laminar regions but caused early transition on the pressure surface in every case.

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Free-Stream Turbulence From a Circular Wall Jet on a Flat Plate Heat Transfer and Boundary Layer Flow

Journal of Turbomachinery ◽

10.1115/1.3262240 ◽

1989 ◽

Vol 111 (1) ◽

pp. 78-86 ◽

Cited By ~ 17

Author(s):

R. MacMullin ◽

W. Elrod ◽

R. Rivir

Keyword(s):

Heat Transfer ◽

Turbulence Intensity ◽

Free Stream ◽

Flow Characteristics ◽

Surface Profile ◽

Constant Heat Flux ◽

Length Scale ◽

Wall Jet ◽

Reynolds Analogy ◽

Free Stream Turbulence

The effects of the longitudinal turbulence intensity parameter of free-stream turbulence (FST) on heat transfer were studied using the aggressive flow characteristics of a circular tangential wall jet over a constant heat flux surface. Profile measurements of velocity, temperature, integral length scale, and spectra were obtained at downstream locations (2 to 20 x/D) and turbulence intensities (7 to 18 percent). The results indicated that the Stanton number (St) and friction factor (Cf) increased with increasing turbulence intensity. The Reynolds analogy factor (2St/Cf) increased up to turbulence intensities of 12 percent, then became constant, and decreased after 15 percent. This factor was also found to be dependent on the Reynolds number (Rex) and plate configuration. The influence of length scale, as found by previous researchers, was inconclusive at the conditions tested.

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Prediction of compressible turbulent boundary layer via a symmetry-based length model

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.710 ◽

2018 ◽

Vol 857 ◽

pp. 449-468 ◽

Cited By ~ 2

Author(s):

Zhen-Su She ◽

Hong-Yue Zou ◽

Meng-Juan Xiao ◽

Xi Chen ◽

Fazle Hussain

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Layer Structure ◽

Analytic Form ◽

Algebraic Model ◽

Length Function ◽

Turbulent Heat Transfer ◽

Turbulent Heat ◽

Reynolds Analogy ◽

The Mean

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL) – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes, thus achieving a Mach number ($Ma$) invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of$Ma$from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin–Lomax and Spalart–Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our$Ma$-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.

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