Three-dimensional effects on the transfer function of a rectangular-section body in turbulent flow

2019 ◽  
Vol 872 ◽  
pp. 348-366 ◽  
Author(s):  
Yang Yang ◽  
Mingshui Li ◽  
Haili Liao
Keyword(s):  
Transfer Function ◽  
Turbulent Flow ◽  
Transfer Functions ◽  
Coherence Function ◽  
Three Dimensional ◽  
Accurate Estimation ◽  
Rectangular Section ◽  
Dimensional Effects ◽  
Aspect Ratios ◽  
Strip Theory

This paper investigates the influence of three-dimensional effects on the transfer function of a rectangular-section body in turbulent flow. The dimensionless factor $\unicode[STIX]{x1D713}$, as derived by Li et al. (J. Fluid Mech., vol. 847, 2018, pp. 768–785), is adapted to evaluate this influence. The calculation of $\unicode[STIX]{x1D713}$ requires the spanwise influence term. For this purpose, an adapted form of the lift coherence function is derived, enabling the use of the measured lift coherence for the estimation of the spanwise influence term. Three rectangular models with different cross-sections (chord-to-depth ratios of 3, 5 and 10) are chosen for testing, and a NACA 0015 airfoil model is tested for comparison. Using the measured spanwise influence terms, the dimensionless factors of these models are then numerically calculated under different ratios of the turbulent integral scale to the chord $\unicode[STIX]{x1D6FE}$ and aspect ratios $\unicode[STIX]{x1D703}$. It is shown that the dimensionless factors of the rectangular models increase as $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D703}$ increase, which are similar to the dimensionless factor of the airfoil model. If $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D703}$ have suitable values, the strip theory could be applicable to the rectangular-section body. It is also found that the dimensionless factors of all the rectangular models are larger than the dimensionless factor of the airfoil model under the same parameters. The smaller the chord-to-depth ratio is, the larger the dimensionless factor is. Using the strip theory to calculate the lift response of the rectangular-section body may provide more accurate estimation. Additionally, the one-wavenumber transfer functions of these models are determined under the consideration of the three-dimensional effects. The results show that the experimental transfer functions of the rectangular models cannot be captured by the Sears function. They are larger than the Sears function at lower frequencies, while falling at a faster rate as the frequency increases. For bluff bodies with separated flow, the modified transfer function presented here appears to be an appropriate approach.

Three-Dimensional Aerodynamic Characteristics of Oscillating Supersonic and Transonic Annular Cascades

1982 ◽  
Author(s):  
M. Namba ◽  
A. Ishikawa
Keyword(s):  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Aerodynamic Forces ◽  
Numerical Work ◽  
Dimensional Effects ◽  
Mathematical Expressions ◽  
Strip Theory ◽  
Clear Insight ◽  
Theory Approximation ◽  
Insight Into

A lifting surface theory is developed for unsteady three-dimensional flow in rotating subsonic, transonic and supersonic annular cascades with fluctuating blade loadings. Application of a finite radial eigenfunction series approximation not only affords a clear insight into the three-dimensional structures of acoustic fields but also provides mathematical expressions advantageous to numerical work. The theory is applied to oscillating blades. Numerical examples are presented to demonstrate three-dimensional effects on aerodynamic characteristics. Three-dimensional effects in supersonic cascades are generally small and strip theory predicts local aerodynamic forces as well as total aerodynamic forces with good accuracy. In transonic flow, however, the strip theory approximation breaks down near the sonic span station and three-dimensional effects are of primary importance.

Dynamic Observer Method Based on Modified Green’s Functions for Robust and More Stable Inverse Algorithms

2008 ◽  
Author(s):  
Priscila F. B. Sousa ◽  
Ana P. Fernandes ◽  
Vale´rio Luiz Borges ◽  
George S. Dulikravich ◽  
Gilmar Guimara˜es
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Green's Functions ◽  
Transfer Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Original Method ◽  
Identification Algorithm ◽  
Transfer Function Model ◽  
Function Model

This work presents a modified procedure to use the concept of dynamic observers based on Green’s functions to solve inverse problems. The original method can be divided in two distinct steps: i) obtaining a transfer function model GH and; ii) obtaining heat transfer functions GQ and GN and building an identification algorithm. The transfer function model, GH, is obtained from the equivalent dynamic systems theory using Green’s functions. The modification presented here proposes two different improvements in the original technique: i) A different method of obtaining the transfer function model, GH, using analytical functions instead of numerical procedures, and ii) Definition of a new concept of GH to allow the use of more than one response temperature. Obtaining the heat transfer functions represents an important role in the observer method and is crucial to allow the technique to be directly applied to two or three-dimensional heat conduction problems. The idea of defining the new GH function is to improve the robustness and stability of the algorithm. A new dynamic equivalent system for the thermal model is then defined in order to allow the use of two or more temperature measurements. Heat transfer function, GH can be obtained numerically or analytically using Green’s function method. The great advantage of deriving GH analytically is to simplify the procedure and minimize the estimative errors.

Spectral analysis and coherence of aerodynamic lift on rectangular cylinders in turbulent flow

2017 ◽  
Vol 830 ◽  
pp. 408-438 ◽  
Author(s):  
Shaopeng Li ◽  
Mingshui Li
Keyword(s):  
Turbulent Flow ◽  
Closed Form ◽  
Vertical Velocity ◽  
Lift Force ◽  
Three Dimensional ◽  
Experimental Investigations ◽  
Velocity Fluctuations ◽  
Dimensional Effects ◽  
Decay Parameters ◽  
Rectangular Cylinders

The goal of the present work is to derive the closed-form expressions of coherence and admittances to describe the spatial distribution of lift on rectangular cylinders in turbulent flow, which can be used to investigate the three-dimensional effects of turbulence. The coherence of the three-dimensional aerodynamic admittance (3D AAF), which takes into full account the spanwise variations in the vertical velocity fluctuations, is introduced to assess the validity of the strip assumption. A theoretical coherence model expressed in a double-exponential form is derived starting from the two-wavenumber spectral tensor of the lift on a thin aerofoil in Fourier space, providing us with explicit insight into the coherence of the lift force. Notably, it is an intrinsic property that the lift force on the structure is more strongly correlated than the oncoming flow and 3D AAF. This coherence model is extended to rectangular cylinders by the introduction of three floating parameters into the decay parameters of the 3D AAF. Based on theoretical and experimental investigations, it is shown that the three-dimensional effects of turbulence grow more prominent as the difference between the decay parameters of the 3D AAF and vertical velocity fluctuations decreases. A generalized approach for rapidly deriving the closed-form expressions of the admittances is proposed to study the unsteady behaviour of the lift force and the distortion of the free stream passing through the rectangular cylinders.

Three-Dimensional Aerodynamic Characteristics of Oscillating Supersonic and Transonic Annular Cascades

1983 ◽  
Vol 105 (1) ◽  
pp. 138-146 ◽  
Author(s):  
M. Namba ◽  
A. Ishikawa
Keyword(s):  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Aerodynamic Forces ◽  
Numerical Work ◽  
Dimensional Effects ◽  
Mathematical Expressions ◽  
Strip Theory ◽  
Clear Insight ◽  
Theory Approximation ◽  
Insight Into

A lifting surface theory is developed for unsteady three-dimensional flow in rotating subsonic, transonic and supersonic annular cascades with fluctuating blade loadings. Application of a finite radial eigenfunction series approximation not only affords a clear insight into the three-dimensional structures of acoustic fields but also provides mathematical expressions advantageous to numerical work. The theory is applied to oscillating blades. Numerical examples are presented to demonstrate three-dimensional effects on aerodynamic characteristics. Three-dimensional effects in supersonic cascades are generally small and strip theory predicts local aerodynamic forces as well as total aerodynamic forces with good accuracy. In transonic flow, however, the strip theory approximation breaks down near the sonic span station and three-dimensional effects are of primary importance.

scholarly journals Experimental Investigations of Three-Dimensional Effects on Cavitating Hydrofoils

1961 ◽  
Vol 5 (03) ◽  
pp. 22-43
Author(s):  
R. W. Kermeen
Keyword(s):  
Aspect Ratio ◽  
High Speed ◽  
Three Dimensional ◽  
Cavitating Flow ◽  
Experimental Investigations ◽  
Water Tunnel ◽  
Pitching Moment ◽  
Two Dimensional ◽  
Dimensional Effects ◽  
Aspect Ratios

An investigation in the high-speed water tunnel of the hydsrodynamic characteristics of a family of three-dimensional sharp-edged hydrofoils is described. Four rectangular plan-form, 6-deg wedge profiles with aspect ratios of 4.0, 2.0, 1.0 and 0.5 were tested over a range of cavitation numbers from noncavitating to fully cavitating flow. The effects of aspect ratio on the flow and cavity configurations and on the lift, drag and pitching moment are discussed. Where data were available the results have been compared with the two-dimensional case.

A Unified Transfer Function (UTF) Approach for the Modeling and Stability Analysis of Long Slender Bars in 3-D Turning Operations

1993 ◽  
Vol 115 (2) ◽  
pp. 193-204 ◽  
Author(s):  
I. N. Tansel
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Transfer Functions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Tool Geometry ◽  
Turning Operations ◽  
Chip Area ◽  
The Stability ◽  
Unique Relationship

A new approach is introduced to model 3-D turning operations that are used for the stability analysis of long slender bars. This approach utilizes the unique relationship between externally created feed direction tool displacements (input) and the resultant thrust direction workpiece vibrations (output) to estimate stability limits in three-dimensional turning operations from the data of a single dynamic cutting test. In this paper, this unique relationship is referred to as the “Unified Transfer Function ” (UTF) and its expressions are derived from conventional cutting and structural dynamics transfer functions. For the stability analysis, the uncut chip area variations of oblique cutting are represented by a linear model having different coefficients at different depths of cuts. These coefficients are found by using a tool geometry simulation program. An iterative procedure is developed for the stability analysis. The proposed approach considers in-process structural and cutting dynamics and can be automatically implemented without any input from the operator for the traverse turning of a long slender bar. Experimental studies have validated the proposed modeling and stability analysis techniques. The UTFs can also be used to monitor machine tool structure, tool wear, and the machinability of the material.

Rotordynamic Analysis of a Large Industrial Turbo-Compressor Including Finite Element Substructure Modeling

2006 ◽  
Author(s):  
J. Jeffrey Moore ◽  
Giuseppe Vannini ◽  
Massimo Camatti ◽  
Paolo Bianchi
Keyword(s):  
Finite Element ◽  
Transfer Function ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Coupled Model ◽  
Element Model ◽  
7Th Edition ◽  
Curve Fit ◽  
Turbo Compressor ◽  
Fully Coupled

A rotordynamic analysis of a large turbo-compressor that models both the casing and supports along with the rotor-bearing system was performed. A three-dimensional (3-D) finite element model of the casing captures the intricate details of the casing and support structure. Two approaches are presented, including development of transfer functions of the casing and foundation, as well as a fully coupled rotor-casing-foundation model. The effect of bearing support compliance is captured, as well as the influence of casing modes on the rotor response. The first approach generates frequency response functions (FRF’s) from the finite element case model at the bearing support locations. A high-order polynomial in numerator-denominator transfer function format is generated from a curve-fit of the FRF. These transfer functions are then incorporated into the rotordynamics model. The second approach is a fully coupled rotor and casing model that is solved together. An unbalance response calculation is performed in both cases to predict the resulting rotor critical speeds and response of the casing modes. The effect of the compressor case and supports caused the second critical speed to drop to a value close to the operating speed and not compliant with API 617 7th edition requirements. A combination of rotor, journal bearing, casing, and support modifications resulted in a satisfactory and API compliant solution. The results of the fully coupled model validated the transfer function approach.

Study of Flame Transfer Function With Three Dimensional Calculations

2003 ◽  
Author(s):  
M. Zhu ◽  
A. P. Dowling ◽  
K. N. C. Bray
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Low Frequency ◽  
Systematic Investigation ◽  
Flow Properties ◽  
Low Frequency Oscillation ◽  
Local Flow ◽  
Shape Factors ◽  
Annular Combustor

Combustors with fuel-spray atomisers are particularly susceptible to a low-frequency oscillation at idle and sub-idle conditions. For aero-engine combustors, the frequency of this oscillation is typically in the range 70–120Hz and is commonly called ‘rumble’. The mechanism involves interaction between the plenum around the burner and the combustion chamber. In our previous work, the CFD calculation has been conducted in an idealised 2D axisymmetric annular combustor to calculate unsteady combustion flow at idle conditions. In this work, in order to investigate the effects of asymmetrical geometry and flow distributions on the transfer functions of flame and shape factors, the CFD code has been extended to fully three-dimensional geometries. The results are compared with those from 2D calculations. Though the differences of the distribution local flow properties are evident, the integrated results for the 3D flow are broadly similar to those obtained in 2D. One substantial difference arises due to the more accurate modelling of the downstream contraction near the combustor exit, which is treated as a smooth contraction in our 3D calculations and as an abrupt change in the simplified 2D geometry. The gradual downstream contraction not only accelerates the fluid near the combustor exit but also unifies the flow properties. As the consequence, we can see that, near the exit, the phase of the flame transfer function increases rapidly, and the shape factors tend toward unity. This work is a further development of our systematic investigation into the ‘rumble’ phenomenon, and gives encouragement that much of the essential physics can be captured in a quasi-one-dimensional model.

Hydroelastic Instability of Low Aspect Ratio Control Surfaces

2004 ◽  
Vol 126 (1) ◽  
pp. 84-89 ◽  
Author(s):  
Michael E. McCormick ◽  
Luca Caracoglia
Keyword(s):  
Aspect Ratio ◽  
Special Class ◽  
Three Dimensional ◽  
Added Mass ◽  
Experimental Results ◽  
Low Aspect Ratio ◽  
Dimensional Effects ◽  
Aspect Ratios ◽  
Modified Equations ◽  
Control Surfaces

As the operational speeds of surface ships and submarines increase, so does the probability that unwanted vibrations caused by the hydroelastic instability (flutter) of the special class of hydrofoils called control surfaces. These include rudders and diving planes. By nature, these are thick symmetric hydrofoils having low aspect ratios. The 3-D tip effects become more pronounced as the aspect ratio decreases. In the present study, the added-mass and circulation terms of the 2-D flutter equations are modified to include three-dimensional effects. The modifications are performed by introducing quasi-steady coefficients to each term. The results predicted by the modified equations are found to compare well with experimental results on a towed rectangular foil having an aspect ratio of one.

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