An Analytical Modeling of the Central Core Flow in a Rotor-Stator System With Several Preswirl Conditions

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Roger Debuchy ◽  
Fadi Abdel Nour ◽  
Gérard Bois
Keyword(s):  
Boundary Layers ◽  
Solid Body ◽  
Total Pressure ◽  
Static Pressure ◽  
Rotating Disk ◽  
Central Core ◽  
Swirl Ratio ◽  
The Core ◽  
Flow Features ◽  
Analytical Relations

In the most part of an enclosed rotor-stator system with separated boundary layers, the flow structure is characterized by a central core rotating as a solid body with a constant core-swirl ratio. This behavior is not always observed in an isolated rotor-stator cavity, i.e., without any centripetal or centrifugal throughflow, opened to the atmosphere at the periphery: Recent works have brought to evidence an increasing level of the core-swirl ratio from the periphery to the axis, as in the case of a rotor-stator with superposed centripetal flow. The present work is based on an asymptotical approach in order to provide a better understanding of this process. Assuming that the boundary layers behave as on a single rotating disk in a stationary fluid on the rotor side, and on a stationary disk in a rotating fluid on the stator side, new analytical relations are obtained for the core-swirl ratio, the static pressure on the stator, and also the total pressure at midheight of the cavity. An experimental study is performed: Detailed measurements provide data for several values of the significant dimensionless parameters: 1.14≤10−6×Re≤1.96, 0.05≤G≤0.10, and 0.07≤104×Ek≤2.65. The analysis of the results shows a good agreement between the theoretical solution and the experimental results. The analytical model can be used to provide a better understanding of the flow features. In addition, radial distributions of both core-swirl ratio, dimensionless static pressure on the stator, as well as dimensionless total pressure at midheight of the cavity, which are of interest to the designers, can be computed with an acceptable accuracy knowing the levels of the preswirl coefficient Kp and the solid body rotation swirl coefficient KB.

Influence of Peripheral Opening on the Central Core Flow Behaviour in a Rotor-Stator System

2009 ◽  
Author(s):  
Fadi Abdel Nour ◽  
Roger Debuchy ◽  
Ge´rard Bois ◽  
Hassan Naji
Keyword(s):  
Static Pressure ◽  
Radial Flow ◽  
Numerical Study ◽  
Outer Region ◽  
Experimental Tests ◽  
Flow Property ◽  
Computation Method ◽  
Swirl Ratio ◽  
Rotating Disc ◽  
The Core

This work relates to an experimental, theoretical and numerical study of a turbulent flow with separated boundary layers between a rotating disc (rotor) and a stationary one (stator) without any superposed radial flow. The originality of this study is that the pre-swirl ratio at the periphery of the cavity (Kp) is lower than the core swirl ratio (KB) corresponding to the solid body rotation, as predicted by Batchelor in the case of infinite discs: this is what the authors call a rotor-stator system with low pre-swirl ratio. Under these conditions, recent works have shown that the core swirl ratio (K) is a decreasing function of the radius, at least in the peripheral region. This behaviour has rather been observed in the cavities with superposed centripetal radial flow. In the present paper, this flow property is explained starting from an asymptotic approach which leads to step-by-step analytical computation method of the radial distribution of the core swirl ratio (K) and of the static pressure on the stator side p*. The validation of the theory is based both on experimental and numerical results. The experimental tests are carried out in a rotor-stator cavity for different values of the pre-swirl ratio, which is done by geometrical changes of the periphery of the system. The experimental data mostly include the velocity measurements and the turbulent correlations by hot-wire anemometry in interstice between the discs, as well as the static pressure measurements on the stator side. Comparisons with predictions from the CFD code Fluent are also provided. The numerical simulations are performed using the two-equation k – ω SST turbulence model, assuming a 2D-axisymmetric steady flow, in a domain corresponding to the inter-disks spacing and the peripheral outer region of the cavity. Computed and experimental values are in good agreement with the theoretical results.

scholarly journals Flow Distortion into the Core Engine for an Installed Variable Pitch Fan in Reverse Thrust Mode

2021 ◽  
pp. 1-30
Author(s):  
David John Rajendran ◽  
Vassilios Pachidis
Keyword(s):  
Total Pressure ◽  
Reverse Flow ◽  
Flow Distortion ◽  
Engine Operation ◽  
Variable Pitch ◽  
The Core ◽  
Aircraft Landing ◽  
Swirl Angle ◽  
Flow Features ◽  
Reverse Thrust

Abstract The flow distortion at core engine entry for a Variable Pitch Fan (VPF) in reverse thrust mode is described from a realistic flowfield obtained using an integrated airframe-engine-VPF research model. 3D RANS solutions are generated for the complete aircraft landing run from 140 to 20 knots at different VPF settings. The internal reverse thrust flowfield is characterized by nozzle lip separation, pylon wake and recirculation of flow turned back from the VPF. A portion of the reverse flow turns 180° with separation at the splitter edge to feed the core engine. The core feed flow exhibits circumferential and radial non-uniformities that depend on the reverse flow development at different landing speeds. The temporal dependence of the distorted flow features is also explored by an URANS analysis. Total pressure and swirl angle distortion descriptors, and total pressure loss are described for the core feed flow at different VPF settings and landing speeds. It is observed that the radial intensity of total pressure distortion is critical to core engine operation, while the circumferential intensity is within acceptable limits. Therefore, the baseline sharp splitter edge is replaced by two larger rounded splitter edges of radii, ∼0.1x and ∼0.2x times the core duct height. This was found to reduce the radial intensity of total pressure distortion to acceptable levels. The description of the installed core feed flow distortion, as in this study, is necessary to ascertain stable core engine operation, which powers the VPF in reverse thrust mode.

Influence of a Weak Superposed Centripetal Flow in a Rotor-Stator System for Several Pre-Swirl Ratio

2011 ◽  
Author(s):  
Fadi Abdel Nour ◽  
Roger Debuchy ◽  
Ge´rard Bois
Keyword(s):  
Boundary Layers ◽  
Flow Behavior ◽  
Central Core ◽  
Major Influence ◽  
Swirl Ratio ◽  
Mean Velocity ◽  
Core Flow ◽  
Dimensionless Coefficient ◽  
Gap Ratio ◽  
High Reynolds

The present study is devoted to the influence of a superposed centripetal flow q in a rotor-stator cavity with a peripheral opening. In the literature, previous works have already shown that a weak radial inflow has no major influence near the periphery of the cavity, whereas the flow behavior is strongly modified when approaching the axis [1–2]. The challenge of this work is to give a better understanding of this phenomenon. Attention is focused on a rotor-stator system characterized by a small gap ratio G and high Reynolds number Re, so that the flow is divided into two boundary layers separated by a core region, according to the classification by Daily and Nece [3]. Until now, numerous authors obtained analytical solutions for the central core flow behavior: following the analysis performed by Schlichting [4], and assuming that the evolution of the velocity in the Ekman boundary layer corresponds to a 1/7 power law, Poncet et al. [2] proposed an analytical law predicting the evolution of the core swirl ratio K versus a local dimensionless coefficient of flow rate Cqr. Debuchy et al. [5] improved this last solution by taking into account the radial exchange of fluid outside the boundary layers. This last approach was used by Abdel Nour et al. [6] in a rotor-stator cavity without any superposed flow (isolated cavity). They obtained an original analytical law, different from the classical similitary solution proposed by Batchelor [7] in the case of infinite disc, convenient for a cavity with peripheral opening and small pre-swirl ratio. In this paper, the authors present an original analytical law in order to model the central core flow behavior in a rotor-stator cavity subjected to a very weak inflow rate (q → 0). The validity of the solution is tested with the help of: • a new set of experimental data including the radial and tangential mean velocity measured by hot-wire anemometry, • experimental results from the literature.

Numerical investigations on the effect of volute casing treatment for performance augmentation in a centrifugal fan

2021 ◽  
pp. 095440622110341
Author(s):  
Manjunath L Nilugal ◽  
K Vasudeva Karanth ◽  
Madhwesh N
Keyword(s):  
Total Pressure ◽  
Static Pressure ◽  
Numerical Study ◽  
Pressure Coefficient ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Centrifugal Fan ◽  
Casing Treatment ◽  
Sliding Mesh ◽  
Optimum Configuration

This article presents the effect of volute chamfering on the performance of a forward swept centrifugal fan. The numerical analysis is performed to obtain the performance parameters such as static pressure rise coefficient and total pressure coefficient for various flow coefficients. The chamfer ratio for the volute is optimized parametrically by providing a chamfer on either side of the volute. The influence of the chamfer ratio on the three dimensional flow domain was investigated numerically. The simulation is carried out using Re-Normalisation Group (RNG) k-[Formula: see text] turbulence model. The transient simulation of the fan system is done using standard sliding mesh method available in Fluent. It is found from the analysis that, configuration with chamfer ratio of 4.4 is found be the optimum configuration in terms of better performance characteristics. On an average, this optimum configuration provides improvement of about 6.3% in static pressure rise coefficient when compared to the base model. This optimized chamfer configuration also gives a higher total pressure coefficient of about 3% validating the augmentation in static pressure rise coefficient with respect to the base model. Hence, this numerical study establishes the effectiveness of optimally providing volute chamfer on the overall performance improvement of forward bladed centrifugal fan.

Effect of the turning angle on the flow and performance characteristics of long S-shaped circular diffusers

2003 ◽  
Vol 217 (1) ◽  
pp. 29-41 ◽  
Author(s):  
R B Anand ◽  
L Rai ◽  
S N Singh
Keyword(s):  
Total Pressure ◽  
Static Pressure ◽  
Area Ratio ◽  
Secondary Flows ◽  
Performance Characteristics ◽  
Pressure Recovery ◽  
Recovery Coefficient ◽  
Turning Angle ◽  
And Performance ◽  
Pressure Recovery Coefficient

The effect of the turning angle on the flow and performance characteristics of long S-shaped circular diffusers (length-inlet diameter ratio, L/Di = 11:4) having an area ratio of 1.9 and centre-line length of 600 mm has been established. The experiments are carried out for three S-shaped circular diffusers having angles of turn of 15°/15°, 22.5°/22.5° and 30°/30°. Velocity, static pressure and total pressure distributions at different planes along the length of the diffusers are measured using a five-hole impact probe. The turbulence intensity distribution at the same planes is also measured using a normal hot-wire probe. The static pressure recovery coefficients for 15°/15°, 22.5°/22.5° and 30°/30° diffusers are evaluated as 0.45, 0.40 and 0.35 respectively, whereas the ideal static pressure recovery coefficient is 0.72. The low performance is attributed to the generation of secondary flows due to geometrical curvature and additional losses as a result of the high surface roughness (~0.5 mm) of the diffusers. The pressure recovery coefficient of these circular test diffusers is comparatively lower than that of an S-shaped rectangular diffuser of nearly the same area ratio, even with a larger turning angle (90°/90°), i.e. 0.53. The total pressure loss coefficient for all the diffusers is nearly the same and seems to be independent of the angle of turn. The flow distribution is more uniform at the exit for the higher angle of turn diffusers.

Preston-Static Tubes for the Measurement of Wall Shear Stress

1994 ◽  
Vol 116 (3) ◽  
pp. 645-649 ◽  
Author(s):  
Josef Daniel Ackerman ◽  
Louis Wong ◽  
C. Ross Ethier ◽  
D. Grant Allen ◽  
Jan K. Spelt
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Convenient Method ◽  
Pipe Flow ◽  
Total Pressure ◽  
Static Pressure ◽  
Shear Stresses ◽  
Streamline Curvature ◽  
Syringe Needle ◽  
Wall Shear

We present a Preston tube device that combines both total and static pressure readings for the measurement of wall shear stress. As such, the device facilitates the measurement of wall shear stress under conditions where there is streamline curvature and/or over surfaces on which it is difficult to either manufacture an array of static-pressure taps or to position a single tap. Our “Preston-static” device is easily and conveniently constructed from commercially available regular and side-bored syringe needles. The pressure difference between the total pressure measured in the regular syringe needle and the static pressure measured in the side-bored one is used to determine the wall shear stress. Wall shear stresses measured in pipe flow were consistent with independently determined values and values obtained using a conventional Preston tube. These results indicate that Preston-static tubes provide a reliable and convenient method of measuring wall shear stress.

The density variation of the earth's central core*

1942 ◽  
Vol 32 (1) ◽  
pp. 19-29
Author(s):  
K. E. Bullen
Keyword(s):  
Pure Iron ◽  
Outer Boundary ◽  
Density Variation ◽  
Central Core ◽  
Good Precision ◽  
Wide Margin ◽  
The Core ◽  
The Earth ◽  
The Mean ◽  
Published Paper

ABSTRACT A detailed analysis of the problem of the earth's density variation has been extended to the earth's central core. It is shown that in the region between the outer boundary of the core and a distance of about 1400 km. from the earth's center the density ranges from 9.4 gm/cm.3 to 11.5 gm/cm.3 within an uncertainty which, if certain general assumptions are true, does not exceed 3 per cent. The density and pressure figures are, moreover, compatible with the existence of fairly pure iron in this part of the earth. The result for the earth's outer mantle as given in a previously published paper, together with those in the present paper, are found to give with good precision the density distribution in a region occupying 99 per cent of the earth's volume. Values of the density within 1400 km. of the earth's center are subject, however, to a wide margin of uncertainty, and there appears to be no means of resolving this uncertainty for the present. The most that can be said is that the mean density in the latter region is greater than 12.3 gm/cm.3 and may quite possibly be several gm/cm.3 in excess of this figure. In the present paper figures are also included for the variation of gravity and the distribution of pressure within the central core. The gravity results are shown to be subject to an appreciable uncertainty except within about 1000 km. of the outer boundary of the core, but the pressure results are expected to be closely accurate at all depths.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

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