High Rotation Numbers Research Articles

Rib-Spacing Effect on Heat Transfer in Rectangular Channels at High Rotation Numbers

This study experimentally determined the effects of rib spacing on heat transfer in a rotating 1:4 AR channel with a sharp-bend entrance. The leading and trailing walls used 45 deg angled ribs. The rib-height-to-hydraulic-diam ratio e/D h was 0.078. The rib-pitch-to-rib-height ratios P/e studied were P/e = 2.5, 5, and 10. Each ratio was tested at five Reynolds numbers up to 40,000. For each Reynolds number, experiments were conducted at five rotational speeds up to 400 rpm. Results showed that the sharp-bend entrance has a significant effect on the first-pass heat transfer enhancement. In the second pass, the rib spacing and rotation effect are reduced. The P/e = 10 case had the highest heat transfer enhancement, based on the total area, and the P/e = 2.5 had the highest heat transfer enhancement, based on the projected area. The current study has extended the range of the rotation number Ro and local buoyancy parameter Bo x for a ribbed 1:4 AR channel up to 0.65 and 1.5, respectively. Correlations for predicting heat transfer enhancement due to rotation in the ribbed 1:4 AR channel, based on the extended range of the rotation number and buoyancy parameter, are presented in the paper.

New Analysis of the ν3 fundamental band of HDCO: Positions and intensities

Using high-resolution Fourier transform spectra of mono deuterated formaldehyde (HDCO) recorded in the 5.8-μm spectral range at Giessen (Germany), we carried out an extensive analysis of the strong ν 3 fundamental band (carbonyl stretching mode) at 1724.2676 cm −1, starting from results of a previous analysis [J.W.C. Johns, A.R.W. McKellar, J. Mol. Spectrosc. 64 (1977) 327–339]. For this hybrid band (with both A- and B-type transitions) the analysis was pursued up to high rotational quantum numbers. In this way, it was possible to evidence a resonance which perturbs the ν 3 lines for high K a values which is due to the existence of the 2 ν 5 and ν 5 + ν 6 dark bands in the same spectral region. In addition a local resonance is perturbing the 3 1 levels in K a ′ = 8 which is due to a crossing with the 4 1 energy levels in K a = 11. The model used to calculate the energy levels accounts for the observed A- type, B- type C-type Coriolis (and/or) Fermi resonances which couple the 3 1 and the 5 16 1, 5 2, and 4 1 energy levels. However the 4 1 state is also involved in strong vibration–rotation interactions coupling the {5 1,6 1,4 1} system of resonation states of HDCO [A. Perrin, J.M. Flaud, L. Margulès, J. Demaison, H. Mäder, S. Wörmke, J. Mol. Spectrosc. 216 (2002) 214–224]. Therefore the final energy levels calculation was performed for the {5 1,6 1,4 1,3 1,5 2,5 16 1} resonating states and in this way it was possible to reproduce the observed line positions, within their experimental uncertainties. The present work also led to the determination of the intensity ratio of the B- to A-type components of the ν 3 band I A/ I B ∼24 band from spectral fittings performed in several parts of the observed spectrum. Finally, using the 5.8 μm band intensity available in the literature we generated, for the first time, a list of line parameters (positions and intensities) for the 5.8 μm region of HDCO.

Dynamic Contact Angle of Spreading Thin Film on a Rotating Disk

The effect of dynamic contact angle on fingering instability during spin coating is investigated by flow visualization experiment. A modified rotational Bond number, which demonstrates the dynamic contact angle of fluid front that affects the dimensionless critical radius, is proposed in this work. For high rotational Bond number, the variation in dimensionless critical radius is not linearly proportional to the rotational Reynolds number because of the variation in critical contact angle if the relaxation time is fixed at zero. By modifying the rotational Bond number with the change in critical contact angle, the dimensionless critical radius becomes a function of the modified rotational Bond number.

Heat transfer in rotating scale-roughened trapezoidal duct at high rotation numbers

An experimental study of heat transfer in a radially rotating trapezoidal duct with two bevel walls roughened by deepened scales is performed with cooling applications to gas turbine rotor blades. Laboratory scale heat transfer data along the centerlines of two scale-roughened walls is generated within the parametric ranges of 7500 ⩽ Re ⩽ 15,000, 0 ⩽ Ro ⩽ 1.8 and 0.13 ⩽ Δ ρ/ ρ ⩽ 0.42. No previous study has examined the heat transfer in a rotating scale-roughened channel and the present Ro range extends considerably from other researches to date. A selection of experimental data illustrates the individual and interactive impacts of Re, Ro and buoyancy number ( Bu) on local heat transfer through which the manners of isolated and synergetic influences of Coriolis force and rotating buoyancy on heat transfer are examined. Local Nusselt number ratios between rotating and static channels on the stable (leading) and unstable (trailing) scale-roughened surfaces with Ro varying from 0.1 to 1.8 fall in the ranges of 0.8–2 and 1.1–2.5, respectively. Rotating buoyancy effects are weakened as Ro increases that impair local heat transfer for the present test configurations. Empirical heat transfer correlations for developed flow regions on two scale-roughened surfaces are derived that permit the evaluation of interactive and individual effects of Re, Ro and Bu on local heat transfer.

Heat Transfer in a Two-Pass Rectangular Channel (AR=1:4) Under High Rotation Numbers

This paper experimentally investigated the rotational effects on heat transfer in a two-pass rectangular channel (AR=1:4), which is applicable to the channel near the leading edge of the gas turbine blade. The test channel has radially outward flow in the first passage through a redirected sharp-bend entrance and radially inward flow in the second passage after a 180deg sharp turn. In the first passage, rotation effects on heat transfer are reduced by the redirected sharp-bend entrance. In the second passage, under rotating conditions, both leading and trailing surfaces experienced heat transfer enhancements above the stationary case. Rotation greatly increased heat transfer enhancement in the tip region up to a maximum Nu ratio (Nu∕Nus) of 2.4. The objective of the current study is to perform an extended parametric study of the low rotation number (0–0.3) and low buoyancy parameter (0–0.2) achieved previously. By varying the Reynolds numbers (10,000–40,000), the rotational speeds (0–400rpm), and the density ratios (inlet density ratio=0.10–0.16), the increased range of the rotation number and buoyancy parameter reached in this study are 0–0.67 and 0–2.0, respectively. The higher rotation number and buoyancy parameter have been correlated very well to predict the rotational heat transfer in the two-pass, 1:4 aspect ratio flow channel.

Heat Transfer in Trailing Edge, Wedge-Shaped Cooling Channels Under High Rotation Numbers

Heat transfer coefficients are experimentally measured in a rotating cooling channel used to model an internal cooling passage near the trailing edge of a gas turbine blade. The regionally averaged heat transfer coefficients are measured in a wedge-shaped cooling channel (Dh=2.22cm, Ac=7.62cm2). The Reynolds number of the coolant varies from 10,000 to 40,000. By varying the rotational speed of the channel, the rotation number and buoyancy parameter range from 0 to 1.0 and 0 to 3.5, respectively. Significant variation of the heat transfer coefficients in both the spanwise and streamwise directions is apparent. Spanwise variation is the result of the wedge-shaped design, and streamwise variation is the result of the sharp entrance into the channel and the 180deg turn at the outlet of the channel. With the channel rotating at 135° with respect to the direction of rotation, the heat transfer coefficients are enhanced on every surface of the channel. Both the nondimensional rotation number and buoyancy parameter have proven to be excellent parameters to quantify the effect of rotation over the extended ranges achieved in this study.

Heat transfer of rotating rectangular duct with compound scaled roughness and V-ribs at high rotation numbers

Local heat transfer measurements for a radially rotating rectangular channel fitted with the compound roughness of staggered V-ribs and deepened scales on two opposite wide walls are performed at the parametric conditions of 10000 ⩽ Re ⩽ 24000 , 0 ⩽ Ro ⩽ 1 and 0.137 ⩽ Δ ρ / ρ ⩽ 0.274 . Heat transfer augmentations achieved by using this compound surface roughness at selected locations along the span and centerline of the leading and trailing walls of the rotating duct are 2.8–5 and 5–7.8 times of the Dittus–Boelter values respectively. No previous attempt has examined the heat transfer performances for such compound surface roughness in the rotating channel with cooling applications to gas turbine rotor blades. A selection of experimental data illustrates the HTE effectiveness with the individual and interdependent Re, Ro and buoyancy number ( Bu) effects on heat transfer revealed. Empirical equations that calculate the averaged Nusselt numbers ( Nu) over leading and trailing surfaces in the periodically developed flow region are derived to correlate all the heat transfer data generated by present study and permit the evaluation of interdependent and individual effects of Re, Ro and Bu on heat transfer.

Heat Transfer at High Rotation Numbers in a Two-Pass 4:1 Aspect Ratio Rectangular Channel With 45deg Skewed Ribs

Heat transfer measurements are reported for a rotating 4:1 aspect ratio (AR) coolant passage with ribs skewed 45deg to the flow. The study covers Reynolds number (Re) in the range of 10,000–70,000, rotation number (Ro) in the range of 0–0.6, and density ratios (DR) between 0.1 and 0.2. These measurements are done in a rotating heat transfer rig utilizing segmented copper pieces that are individually heated, and thermocouples with slip rings providing the interface between the stationary and rotating frames. The results are compared with the published data obtained in a square channel with similar dimensionless rib-geometry parameters, and with the results obtained for a 4:1 AR smooth channel. As in a 1:1 AR channel, rotation enhances the heat transfer on the destabilized walls (inlet-trailing wall and outlet-leading wall), and decreases the heat transfer ratio on the stabilized walls (inlet-leading wall and outlet-trailing wall). However, the rotation-induced enhancement/degradation for the 4:1 rectangular channel is much weaker than that in the square ribbed channel, especially in the inlet (the first passage). The results on the inlet-leading wall are in contrast to that in the smooth channel with the same AR, where rotation causes heat transfer to increase along the inlet-leading wall at lower Reynolds number (Re=10,000 and 20,000). Higher DR is observed to enhance the heat transfer on both ribbed walls in the inlet (the first passage) and the outlet (the second passage), but the DR effects are considerably weaker than those in a ribbed square channel. Measurements have also been parameterized with respect to the buoyancy parameter and results show the same general trends as those with respect to the rotation number. In addition, pressure drop measurements have been made and the thermal performance factor results are presented.

High resolution vacuum ultraviolet emission spectrum of D2: The B′Σu+1→XΣg+1 band system

In this work, we have extended our previous high resolution study of the vacuum ultraviolet emission spectrum of the D2 molecule [M. Roudjane, et al. J. Chem. Phys. 125, 214305 (2006)] up to 124.2 nm in order to investigate the B' 1Sigmau+-->X 1Sigmag+ band system. The analysis of the spectrum has been carried out by means of a complex spectrum visual identification code IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656, (1993)] and supported by theoretical calculations using ab initio data [L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); G. Staszewska and L. Wolniewicz, J. Mol. Spectrosc. 212, 208 (2002); L. Wolniewicz and G. Staszewska, 220, 45 (2003)] which provided level energies and transition probabilities. More than 1480 new emission lines have been observed and 109 bands belonging to the B' 1Sigmau+-->X 1Sigmag+ system have been identified between 84.1 and 121.6 nm. Except for the upsilon'-0 bands that were reported in absorption [I. Dabrowski and G. Herzberg, Can. J. Phys. 52, 1110 (1974)], all the upsilon'-upsilon" bands are reported here for the first time. The analysis led to the determination of 111 rovibronic energy levels in the B' 1Sigmau+ state, of which 31 with higher rotational numbers J are new. Observed perturbations are accounted for through a set of coupled equations involving the four excited electronic states B 1Sigmau+, B' 1Sigmau+, C 1Piu, and D 1Piu and including nonadiabatic couplings. The solution of this set provides the percent contribution of these four states to each of the observed rovibronic level.

Effect of Coriolis and centrifugal forces on turbulence and transport at high rotation and density ratios in a rib-roughened channel

Prediction of three-dimensional flow field and heat transfer in a two pass rib-roughened square internal cooling channel of turbine blades with rounded staggered ribs rotating at high rotation and density ratios is the main focus of this study. Rotation, buoyancy, ribs, and geometry affect the flow within these channels. The full two-pass channel with bend and with rounded staggered ribs with fillets ( e / D h = 0.1 and P / e = 10 ) as tested by Wagner et al. [J.H. Wagner, B.V. Johnson, R.A. Graziani, F.C. Yeh, Heat transfer in rotating serpentine passages with trips normal to the flow, ASME J. Turbomach. 114 (1992) 847–857] is investigated. Reynolds stress model (RSM) turbulence model is used for this study. To resolve the near wall viscosity-affected region, enhanced wall treatment approach is employed. RSM model was validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with higher rotational numbers (0.24, 0.475, 0.74 and 1) and higher density ratios (0.13, 0.23, and 0.3). Particular attention is given to how secondary flow, Reynolds stresses, turbulence intensity, and heat transfer are affected by Coriolis and buoyancy/centrifugal forces, caused by high levels of rotation and density ratios. A linear correlation for 4-side-average Nusselt number as a function of rotation number is derived.

Prediction of flow and heat transfer in narrow rotating rectangular channels using Reynolds stress model

A computational study is performed on three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with aspect ratio (AR) of 10:1, oriented 120° from the direction of rotation. The Focus is on high rotation and high-density ratios effects on the heat transfer characteristics of the 120° orientation. The Reynolds stress model (RSM), which accounts for rotational effects are used to compute the turbulent flow and heat transfer in the rotating channel. The effects of rotation and coolant-to-wall density ratio on the fluid flow and heat transfer characteristics is reported on a range of rotation numbers and density ratios (0 < Ro < 0.25 and 0.07 < Δρ/ρ < 0.4). The computational results are in good agreement with experimental data within ±15%. The results show that the density ratio, rotation number and channel orientation significantly affect the flow field and heat transfer characteristics in the rotating rectangular channel. Flow reversal occurs at high rotation number and density ratio.

Internal Cooling in 4:1 AR Passages at High Rotation Numbers

Heat transfer and pressure drop measurements are reported for a rotating 4:1 aspect ratio (AR) smooth two-pass coolant passage for Reynolds number in the range of 10,000–150,000, rotation number in the range of 0–0.6, and density ratios in the range of 0.1–0.2. The measurements are performed for both 90deg and 45deg orientations of the coolant passage relative to the rotational axis. A large-scale rotating heat transfer rig is utilized, with the test section consisting of segmented foil-heated elements and thermocouples. Results for the 4:1 AR indicate that beyond specific Ro values (different values for the inlet and outlet passages), the expected trends of heat transfer enhancement on the destabilized surface and degradation on the stabilized surface are arrested or reversed. Unlike the 1:1 AR, the inlet-leading surface for the 4:1 AR shows enhancement with Ro at low Re (less than 20,000) and shows the expected degradation only at high Re. Increasing the density ratio enhances the heat transfer on all walls. Orientation of the coolant passage relative to the rotational axis has an important effect, with the 45deg orientation reducing the heat transfer on the destabilized surface and enhancing it on the stabilized surface.

Contribution of the polarizability anisotropy to Rayleigh scattering

A calculation from first principles of the differential cross section for Rayleigh scattering shows that the contribution of polarizability anisotropy found in the literature is valid only in the high rotational quantum number limit of the vector coupling coefficients, that is, in the high‐temperature or classical limit. The additional term in the total Rayleigh scattering cross section arising from the polarizability anisotropy is about four times smaller than what is called the King factor in the literature. These errors, resulting from ignoring the constraints imposed by the conservation of angular momentum, can lead to significant corrections in estimating populations from stratospheric and mesospheric measurements.

High rotation number heat transfer of a 45° rib-roughened rectangular duct with two channel orientations

An experimental study of heat transfer in a radially rotating rectangular channel of aspect ratio 1/2 with two opposite walls roughened by 45° staggered ribs is performed. Heat transfer distributions along centerlines of two rib-roughened surfaces are measured for the radially outward airflow at test conditions of Reynolds number ( Re), rotation number ( Ro) and density ratio (Δ ρ/ ρ) in the ranges of 5000–15,000, 0–2 and 0.07–0.28. The rotating test rig permits the generation of heat transfer data with Ro considerably higher than previous data ranges. A selection of experimental data illustrates the individual and interactive influences of Re, Ro and buoyancy number ( Bu) on local heat transfer with two channel orientations of 0° and 45°. With Ro varying from 0.1 to 2, heat transfer ratios between rotating and static channels on the stable and unstable rib-roughened surfaces with 0° (45°) of channel orientation are in the ranges of 0.5–1.42 (0.5–1.49) and 1.08–2.73 (1.06–2.21) respectively. A set of heat transfer correlations for the test geometry with channel orientations of 0° is derived to evaluate the local Nusselt number ( Nu) in the periodically developed region with Re, Ro and Bu as the controlling flow parameters.

Asymptotic energy levels of a rigid asymmetric top†

The spectra of larger molecules are often observed to high rotational quantum numbers, and the asymptotic behaviour of the rotational energy levels is of interest. This paper is mainly concerned with the lowest-energy levels for high values of J. These tend to occur in oblate-type doublets, for which E. K. Gora gave an energy-level formula in 1965 that seems to be little known among pure rotational spectroscopists. In particular, the mean energies and splittings of these doublets are discussed and a new derivation of Gora's formula is described.

Heat Transfer in Channels in Parallel-Mode Rotation at High Rotation Numbers

This study attempts to understand one of the most fundamental and challenging problems in fluid flow and heat transfer for rotating machines. The study focuses on electric generators for high energy density applications, which employ rotating cooling channels so that materials do not fail under high temperature and high stress environment. Prediction of fluid flow and heat transfer inside internal cooling channels that rotate at high rotation number and high wall heat flux is the main focus of this study. Rotation, buoyancy, and boundary conditions affect the flow inside these channels. A fully computational approach is employed in this study. Reynolds stress turbulence model with enhanced near-wall treatment is validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with high rotation number (as much as 0.35) and high wall heat flux. Particular attention is given to how turbulence intensity, Reynolds stresses, and transport are affected by Coriolis and buoyancy/centrifugal forces caused by high levels of rotation number and wall heat flux. Variations of flow total pressure along the rotating channel are also predicted. The results obtained are explained in view of physical interpretation of Coriolis and centrifugal forces.

Turbulent Heat Transfer in Ribbed Coolant Passages of Different Aspect Ratios: Parametric Effects

Abstract Turbulent flow and heat transfer in rotating ribbed ducts of different aspect ratios (AR) are studied numerically using an unsteady Reynolds averaged Navier–Stokes procedure. Results for three ARs (1:1, 1:4, and 4:1) and staggered ribs with constant pitch (P∕e=10) in the periodically developed region are presented and compared. To achieve periodic flow behavior in successive inter-rib modules calculations are performed in a computational domain that extends to two or three inter-rib modules. The computations are carried out for an extended parameter set with a Reynolds number range of 25,000–150,000, density ratio range of 0–0.5, and rotation number range of 0–0.50. Under rotational conditions, the highest heat transfer along the leading and side walls are obtained with the 4:1 AR, while the 1:4 AR has the highest trailing wall Nu ratio and the lowest leading wall Nu ratio. The 1:4 AR duct shows flow reversal near the leading wall (leading to low Nu) at high rotation numbers and density ratios. For certain critical parameter values (low Re, high Ro, and/or DR), the leading wall flow is expected to become nearly stagnant, due to the action of centrifugal buoyancy, leading to conduction-limited heat transfer. The 4:1 AR duct shows evidence of multiple rolls in the secondary flow that direct the core flow to both the leading and trailing surfaces which reduces the difference between the leading and trailing wall heat transfer relative to the other two AR ducts.

Heat Transfer in a Radially Rotating Square-Sectioned Duct With Two Opposite Walls Roughened by 45Deg Staggered Ribs at High Rotation Numbers

This paper describes an experimental study of heat transfer in a radially rotating square duct with two opposite walls roughened by 45deg staggered ribs. Air coolant flows radially outward in the test channel with experiments to be undertaken that match the actual engine conditions. Laboratory-scale heat transfer measurements along centerlines of two rib-roughened surfaces are performed with Reynolds number (Re), rotation number (Ro), and density ratio (Δρ∕ρ) in the ranges of 7500–15,000, 0–1.8, and 0.076–0.294. The experimental rig permits the heat transfer study with the rotation number considerably higher than those studied in other researches to date. The rotational influences on cooling performance of the rib-roughened channel due to Coriolis forces and rotating buoyancy are studied. A selection of experimental data illustrates the individual and interactive impacts of Re, Ro, and buoyancy number on local heat transfer. A number of experimental-based observations reveal that the Coriolis force and rotating buoyancy interact to modify heat transfer even if the rib induced secondary flows persist in the rotating channel. Local heat transfer ratios between rotating and static channels along the centerlines of stable and unstable rib-roughened surfaces with Ro varying from 0.1 to 1.8 are in the ranges of 0.6–1.6 and 1–2.2, respectively. Empirical correlations for periodic flow regions are developed to permit the evaluation of interactive and individual effects of ribflows, convective inertial force, Coriolis force, and rotating buoyancy on heat transfer.

Analysis of kinetic energy release distributions by the maximum entropy method

Energy is not always fully randomized in an activated molecule because of the existence of dynamical constraints. An analysis of kinetic energy release distributions (KERDs) of dissociation fragments by the maximum entropy method (MEM) provides information on the efficiency of the energy flow between the reaction coordinate and the remaining degrees of freedom during the fragmentation. For example, for barrierless cleavages, large translational energy releases are disfavoured while energy channeling into the rotational and vibrational degrees of freedom of the pair of fragments is increased with respect to a purely statistical partitioning. Hydrogen atom loss reactions provide an exception to this propensity rule. An ergodicity index, F, can be derived. It represents an upper bound to the ratio between two volumes of phase space: that effectively explored during the reaction and that in principle available at the internal energy E. The function F( E) has been found to initially decrease and to level off at high internal energies. For an atom loss reaction, the orbiting transition state version of phase space theory (OTST) is especially valid for low internal energies, low total angular momentum, large reduced mass of the pair of fragments, large rotational constant of the fragment ion, and large polarizability of the released atom. For barrierless dissociations, the major constraint that results from conservation of angular momentum is a propensity to confine the translational motion to a two-dimensional space. For high rotational quantum numbers, the influence of conservation of angular momentum cannot be separated from effects resulting from the curvature of the reaction path. The nonlinear relationship between the average translational energy 〈 ɛ〉 and the internal energy E is determined by the density of vibrational–rotational states of the pair of fragments and also by non-statistical effects related to the incompleteness of phase space exploration. The MEM analysis of experimental KERDs suggests that many simple reactions can be described by the reaction path Hamiltonian (RPH) model and provides a criterion for the validity of this method. Chemically oriented problems can also be solved by this approach. A few examples are discussed: determination of branching ratios between competitive channels, reactions involving a reverse activation barrier, nonadiabatic mechanisms, and isolated state decay.

Effect of Coriolis and Centrifugal Forces at High Rotation and Density Ratios

Numerical simulation of fluid flow and heat transfer of high rotation and density ratio flow in internal cooling channels of turbine blades with smooth walls is the main focus of this study. The flow in these channels is affected by rotation, buoyancy, bends, and boundary conditions. On the basis of comparison between two-equation (k−e and k−ω) and Reynolds-stress (RSM) turbulence models, it is concluded that the two-equation turbulence models cannot predict heat transfer correctly, whereas RSM showed improved prediction. Thus RSM model was validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with high rotation numbers (as much as 1.29) and high-density ratios (up to 0.4) not studied previously. Particular attention was given to how Reynolds stresses, turbulence intensity, and transport are affected by coriolis and buoyancy/centrifugal forces caused by high levels of rotation and density ratio. The results obtained are explained in view of physical interpretation of Coriolis and centrifugal forces. It has been concluded that the heat-transfer rate can be enhanced rapidly by increasing rotation number to values that are comparable to the enhancement caused by introduction of ribs inside internal cooling channels. It is possible to derive linear correlation for the increase in Nusselt number as a function of rotation number. Increasing density ratios at high rotation number does not necessarily cause an increase in Nusselt number. The increasing thermal boundary-layer thickness near walls is the possible reason for this behavior of Nusselt number.