Blade Forces Research Articles

Modeling of 3-D losses and deviations in a throughflow analysis tool

This contribution is dedicated to the modeling of the end-wall flows in a throughflow model for turbomachinery applications. The throughflow model is based on the Euler or Navier-Stokes equations solved by a Finite-Volume technique. Two approaches are presented for the end-wall modeling. The first one is based on an inviscid formulation with dedicated 3-D distributions of loss coefficient and deviation in the end-wall regions. The second approach is directly based on a viscous formulation with no-slip boundary condition along the annular end-walls and blade force modification in the region close to the end-walls. The throughflow results are compared to a series of 3-D Navier-Stokes calculations averaged in the circumferential direction. These 3-D calculations were performed on the three rotors of a low pressure axial compressor, for a series of tip clearance values.

Actuator surface hybrid model

A hybrid model has been developed in order to represent the flow downstream a wind turbine rotor. The blades are replaced by their mean surfaces and a "pressure jump" boundary condition is applied here. The hybrid model combines CFD solver with a blade element method (BEM). The solving method is iterative: at the beginning of iteration a BEM determines the pressure discontinuities along the blade span, using the rotor inflow and the aerodynamic properties of blade sections. Then the CFD solver applies this pressure discontinuity in order to model the blade forces and the wake downstream the rotor. At the end of iteration the obtained rotor inflow, the wake development and the residuals are compared with those obtained from previous iteration. If the required precision is attained, the calculation stops. The solution is obtained after thousands of iterations, depending on the number of nodes, residuals etc. The approach of replacing blades by pressure discontinuity surfaces is validated by comparison the wakes in the cases of flat plate and the S809 airfoil. Finally, the proposed hybrid model is used to calculate the performance of NREL Phase VI wind turbine and the results obtained are satisfactory.

Axial turbomachine modelling with a 1D axisymmetric approach: Application to gas cooled nuclear reactor

This work concerns the design and safety analysis of direct cycle gas cooled reactor. The estimation of compressor and turbine performances in transient operations is of high importance for the designer. The first goal of this study is to provide a description of compressor behaviour in unstable conditions with a better understanding than the models based on performance maps (“traditional” 0D approach). A supplementary objective is to provide a coherent description of the turbine behaviour. The turbomachine modelling approach consists in the solution of 1D axisymmetric Navier–Stokes equations on an axial grid inside the turbomachine: mass, axial momentum, circumferential momentum and total-enthalpy balances are written. Blade forces are taken into account by using compressor or turbine blade cascade steady correlations. A particular effort has been developed to generate or test correlations in low mass flow and negative mass flow regimes, based on experimental data. The model is tested on open literature cases of the gas turbine aircraft community. For compressor and turbine, steady situations are fairly described, especially for medium and high mass flow rate. The dynamic behaviour of compressor is also quite well described, even in unstable operation (surge): qualitative tendencies (role of plenum volume and role of throttle) and some quantitative characteristics (frequency) are in a good agreement with experimental data. The application to transient simulations of gas cooled nuclear reactors is concentrated on the hypothetical 10 in. break accident. The results point out the importance of the location of the pipe rupture in a hypothetical break event. In some detailed cases, compressor surge and back flow through the circuit can occur. In order to be used in a design phase, a simplified model of surge has also been developed. This simplified model is applied to the gas fast reactor (GFR) and compared quite favourably with 1D axisymmetric simulation results.

Simulations of the Fluid Flow around a Rotating Vertical Axis Wind Turbine

Numerical simulations of the fluid flow around a small rotating vertical axis wind turbine are performed using a time accurate Reynolds Averaged Navier Stokes (RANS) solver. A moving mesh technique is applied for the simulation of the rotating wind turbine. The RANS equations are then formulated in ALE. All computations are performed assuming 2D incompressible fully turbulent flow. Turbulence is modelled by the SST k/ω model of Menter. Blade forces and torque are obtained from the solution of the RANS equations by integrating the pressure and shear stress over the blade surface. The expected wind turbine output is determined at given rotational speeds. The resulting power coefficients are compared to that obtained by applying a multiple stream tube theory.

A fluid dynamic investigation of the Big Blade and Macon oar blade designs in rowing propulsion

The purpose of this investigation was to examine the fluid dynamic characteristics of the two most commonly used oar blades: the Big Blade and the Macon. Scaled models of each blade, as well as a flat Big Blade, were tested in a water flume using a quasi-static method similar to that used in swimming and kayaking research. Measurement of the normal and tangential blade forces enabled lift and drag forces generated by the oar blades to be calculated over the full range of sweep angles observed during a rowing stroke. Lift and drag force coefficients were then calculated and compared between blades. The results showed that the Big Blade and Macon oar blades exhibited very similar characteristics. Hydraulic blade efficiency was not therefore found to be the reason for claims that the Big Blade could elicit a 2% improvement in performance over the Macon. The Big Blade was also shown to have similar characteristics to the flat plate when the angle of attack was below 90°, despite significant increases in the lift coefficient when the angle of attack increased above 90°. This result suggests that the Big Blade design may not be completely optimized over the whole stroke.

直線運動機構の手漕ぎボートのオール運動装置への応用

The Peaucelier Mechanism, that is one of straight-line motion mechanisms, and a parallel crank mechanism were combined, and the combined device was utilized in an oar motion mechanism of rowing boat for the aim of increasing the power of the oar blade. The comparison between the power of the oar blade of the conventional device and that of the improved device was discussed by obtaining force and velocity of the oar blade. It was found by the calculation that the improved device creates greater power of the oar almost around all range of oar angle, especially in the narrower angle or in the wider angle, than the conventional oar motion mechanisms. It is considered that the rowing angle of oar will be designed narrower, as possible, than 107 degrees.

くさび刃による板紙の切断特性

In this paper, we gives a describe of the pushing shear process on a kraft paperboard. The cutting line force of a center bevel blade on the kraft paperboard was measured using a load cell and its cutting deformation was observed using a CCD camera to reveal the basic effects of the tip angle and tip thickness of the blade on the surface failures of the kraft paperboard. A deformation flow in the side view of the kraft paperboard was observed with respect to the indentation depth of the blade by varying the tip angle and tip thickness of the blade. From the experiment, the following results were obtained. 1) There are certain critical values of the tip angle αC and the tip thickness wC at which the inflection load response disappears and also the surface failures are restricted. 2) After the time when the surface layer of the kraft paperboard is cut off, lateral shear flow occurs in an in-plane layer of a laminated structure. The deformation flow and its resistance are strongly affected by the delamination and raised upper layer.

A Numerical Tool for the Design/Analysis of Dual-Cavitating Propellers

The motivation of this work is to develop a numerical tool to explore a new propeller design with dual-cavitating characteristics, i.e., one that is capable of operating efficiently at low speeds in subcavitating (fully wetted) mode and at high speeds in the supercavitating mode. To compute the hydrodynamic performance, a three-dimensional (3D) potential-based boundary element method (BEM) is presented. The BEM is able to predict complex cavitation patterns and blade forces on fully submerged and partially submerged propellers in subcavitating, partially cavitating, fully cavitating, and ventilated conditions. To study the hydroelastic characteristic of potential designs, the 3D BEM is coupled with a 3D finite element method (FEM) to compute the blade stresses, deflections, and dynamic characteristics. An overview of the formulation for both the BEM and FEM is presented. The numerical predictions are compared to experimental measurements for the well-known Newton Rader (NR) three-bladed propeller series with varying pitch and blade area ratios. Comparison of the performance of the Newton Rader blade section to conventional blade sections is presented.

Axial flow fan broad-band noise and prediction

Two prediction methods for broad-band noise of low-pressure axial fans are investigated. Emphasis is put on the interaction noise due to ingested turbulence. The numerical large eddy simulation (LES) is applied to predict the unsteady blade forces due to grid generated highly turbulent inflow; the blade forces are then fed into an analytical two-dimensional acoustic ducted source model. A simple semi-empirical noise prediction model (SEM) is utilized for indicative comparison. Finally, to obtain a database for detailed verification, the turbulence statistics for a variety of different inflow configurations are determined experimentally using hot wire anemometry and a correlation analysis. In the limits of the necessary assumptions the SEM predicts the noise spectra and the overall sound power surprisingly well without any further tuning of parameters; the influence of the fan operating point and the nature of the inflow is obtained. Naturally, the predicted spectra appear unrealistically “smooth”, since the empirical input data are averaged and modeled in the frequency domain. By way of contrast the LES yields the fluctuating forces on the blades in the time domain. Details of the source characteristics and their origin are obtained rather clearly. The predicted effects of the ingested turbulence on the fluctuating blade forces and the fan noise compare favorably with experiments. However, the choice of the numerical grid size determines the maximal resolvable frequency and the computational cost. As contrasted with the SEM, the cost for the LES-based method are immense.

Large Eddy Simulation of Acoustical Sources in a Low Pressure Axial-Flow Fan Encountering Highly Turbulent Inflow

A large eddy simulation (LES) was applied to predict the unsteady flow in a low-speed axial-flow fan assembly subjected to a highly “turbulent” inflow that is generated by a turbulence grid placed upstream of the impeller. The dynamic Smagorinsky model (DSM) was used as the subgrid scale (SGS) model. A streamwise-upwind finite element method (FEM) with second-order accuracy in both time and space was applied as the discretization method together with a multi-frame of reference dynamic overset grid in order to take into account the effects of the blade-wake interactions. Based on a simple algebraic acoustical model for axial flow fans, the radiated sound power was also predicted by using the computed fluctuations in the blade force. The predicted turbulence intensity and its length scale downstream of the turbulence grid quantitatively agree with the experimental data measured by a hot-wire anemometry. The response of the blade to the inflow turbulence is also well predicted by the present LES in terms of the surface pressure fluctuations near the leading edge of the blade and the resulting sound power level. However, as soon as the effects of the turbulent boundary layer on the blades become important, the prediction tends to become inaccurate.

A potential flow 2-D vortex panel model: Applications to vertical axis straight blade tidal turbine

A potential flow 2-D vortex panel model (VPM2D) for unsteady hydrodynamics calculation of the vertical axis straight blade variable pitch turbine was given for tidal streams energy conversion. Numerical results of predicted instantaneous blade forces and wake flow of the rotor showed good agreement with the test data. The model was also compared with the previous classic free vortex model (V-DART) and vortex method combined with finite element analysis (FEVDTM). It showed that the present model was much better than the former, less complex than the latter and suitable for designing and optimization of the vertical axis straight blade turbine.

Unsteady Aerodynamic Blade Excitation at the Stability Limit and During Rotating Stall in an Axial Compressor

The stable operating range of axial compressors is limited by the onset of rotating stall and surge. These flow conditions endanger the reliability of operation and definitely have to be avoided in compressors of gas turbines. However, there is still a need to improve the physical understanding of these flow phenomena to prevent them while utilizing the maximum available working potential of the compressor. This paper discusses detailed experimental investigations of the rotating stall onset with the main emphasis on the aerodynamic blade excitation in the Dresden four-stage low-speed research compressor. The stall inception, which is triggered by modal waves, as well as the main flow features during rotating stall operation are discussed. To investigate the unsteady pressure distributions, both the rotor and the stator blades of the first stage were equipped with piezoresistive pressure transducers. Based on these measurements the unsteady blade pressure forces are calculated. Time-resolved results at the stability limit as well as during rotating stall are presented. For all operating conditions rotor–stator interactions play an important role on the blade force excitation. Furthermore the role of the inertia driven momentum exchange at the stall cell boundaries on the aerodynamic blade force excitation is pointed out.

Numerical prediction of vortex shedding noise radiated by a centrifugal impeller

Numerical prediction of fan noise is very difficult work because of the restriction of the computer technology. The fluctuating blade force caused by the vortex shedding from a centrifugal impeller is a main noise source but no paper has been published so far to predict this kind of noise. Vortex flow models to predict low-pressure axial flow fans were developed by several researchers since 1964. In this paper a study of numerical prediction of vortex shedding noise radiated by a commercial centrifugal impeller is reported, which is based on a vortex flow model developed by Lee in 1993. Three main research works are carried out by the authors. First, using FLUENT software a numerical simulation of 3D turbulent flow field of the impeller in order to predict the aerodynamic performance is completed and well validated by the experiment. Then, the velocity profile near the wall at the trailing edge of the blade is analyzed in detail to determine the boundary layer thickness both on the pressure and suction sides. Finally, the total SPL of the noise is predicted and the results agree with the experimental data within 3 dB near the design operation.

Analysis of Model Rotor Blade Pressures During Parallel Interaction with Twin Vortices

This paper presents and provides analysis of unsteady surface pressures measured on a model rotor blade as the blade experienced near parallel blade vortex interaction with a twin vortex system. To provide a basis for analysis, the vortex system was characterized by hot-wire measurements made in the interaction plane but in the absence of the rotor. The unsteady pressure response resulting from a single vortex interaction is then presented to provide a frame of reference for the twin vortex results. A series of twin vortex interaction cases are then presented and analyzed. It is shown that the unsteady blade pressures and forces are very sensitive to the inclination angle and separation distance of the vortex pair. When the vortex cores lie almost parallel to the blade chord, the interaction is characterized by a two-stage response associated with the sequential passage of the two cores. Conversely, when the cores lie on a plane that is almost perpendicular to the blade chord, the response is similar to that of a single vortex interaction. In all cases, the normal force response is consistent with the distribution of vertical velocity in the flow field of the vortex system. The pitching moment response, on the other hand, depends on the localized suction associated with the vortex cores as they traverse the blade chord.

Unsteady Wake Alignment for Propellers in Nonaxisymmetric Flows

A low-order boundary element method is applied to predict the trailing wake geometries shedding from hydrofoil and marine propellers in steady and unsteady flows, as well as the vortex motions of the classical lifting line problem with elliptic loading distribution. In order to prevent the numerical instability near the vortex roll-up region, a tip vortex with finite core size is introduced at the end of the vortex line (or at the tip of the wake sheet in the case of a three-dimensional problem), and the induced velocities are evaluated at the displaced control points instead of the actual control points on the vortex (or wake) panels. Green's integral equation with boundary conditions is formulated based on the perturbation potential and solved for the potentials on the lifting bodies and the tip vortex surface. The three-component velocities on the tip vortex surface are computed by numerically differentiating the solution potentials, and the induced velocities on the wake surface are directly determined from the integral equation derived from analytical differentiation of Green's integral equation. The new geometries of the vortex line or the trailing wake as well as the location of the tip vortex core center are then determined by aligning them to the flow so that the force-free condition is satisfied on the wake. The method is applied for the two-dimensional and three-dimensional problems, and validated with experiments and other numerical methods in terms of tip vortex trajectory and blade forces.

A BEM for the modeling of unsteady propeller sheet cavitation inside of a cavitation tunnel

A boundary element method is applied to predict the unsteady cavitating performance of marine propellers subject to a non-axisymmetric inflow with the complete tunnel wall effect. The tunnel and propeller problem is solved directly to predict the fully unsteady performance of the cavitating propeller. The cavitation on blade and wake surface is determined by applying the dynamic and the kinematic boundary conditions on the cavity surface. The potential on the cavity surface is known from the dynamic boundary condition and the relation between cavitation number and cavity velocity. Once the boundary value problem is solved for the unknowns- the potentials on the wetted blade surface and the normal derivative of potentials on the cavity surface – the new cavity shape is adjusted by using the normal derivative of the potential. The potential on the new cavity surface is determined by using the kinematic boundary condition on the cavity. The procedure is repeated until the cavity shape converges and the pressure on the cavity becomes constant. To validate the present method, the effects of the number of blade panels and the dimensions of the tunnel walls on blade forces are presented. The predicted cavity patterns are compared with those observed from experiment.

Untersuchung einer Axialturbinen-Stufe mit tangential gekrümmten Leitschaufeln - Teil I: Strömungsstruktur im Leitradkanal

By tangential curvature of the stacking line of the blade profiles guide vanes can be designed, which have on both ends an obtuse angle between suction side and sidewall. This configuration, according to literature, is capable of reducing the secondary loss. This type of vanes, because of the resulting radial components of the blade force, effects a radial displacement of the meridional stream-lines, a modification of the pressure distributions on the profiles and different flow outlet angles. Three-dimensional numerical simulations with the Navier-Stokes-solver Numeca have been made for a single stage axial turbine with different types of tangentially curved guide vanes. The effects of the blade curvature on the flow field and the blade forces have been investigated systematically and in detail.

Research on the Mechanism of Fan Blade Shape Effect on its Noise

The fan blade configuration affects its efficiency and sound pressure level—(SPL). This paper analyzes the fan blade noise components and studies the aerodynamic characteristics of fan blades. The bar theory and moving soundfield characteristics are used in the theoretical analysis. Nonlinear aerodynamics theory is used to analyze the blade force. A mathematical model of fan blade noise is developed and simulated by the precision Gauss-Legendre method. The model simulation and the experiment results are analyzed in the frequency domain. The simulation results are in reasonable agreement with the measured data. Our model and the Fukano model are compared for different rotational speeds of the fan. This paper then studies the change of SPL when the blade parameters (number of blades, rotation speed of fan, chord of fan, and blade profile etc.) vary. The major factors affecting the fan noise are analyzed. Our model is derived from the viewpoint of blade design, so the result can be used to study the aerodynamic characteristics of fan blades quantitatively. The study is considered as a prerequisite to designing fans of high quality, since it provides a theoretical basis for noise prediction and noise control.

Rotor-Stator Interactions in a Four-Stage Low-Speed Axial Compressor—Part II: Unsteady Aerodynamic Forces of Rotor and Stator Blades

This two-part paper presents detailed experimental investigations of unsteady aerodynamic blade row interactions in the four-stage low-speed research compressor of Dresden. In Part I of the paper the unsteady profile pressure distributions for the nominal setup of the compressor are discussed. Furthermore the effect of blade row clocking on the unsteady profile pressures is investigated. Part II deals with the unsteady aerodynamic blade forces, which are determined from the measured profile pressure distributions. A method to calculate the aerodynamic blade forces on the basis of the experimental data is presented. The resulting aerodynamic blade forces are discussed for the rotor and stator blade rows of the first stage and the third stage of the compressor. Different operating points between design point and stability limit of the compressor were chosen to investigate the influence of loading on the aerodynamic force excitation. The time traces and the frequency contents of the unsteady aerodynamic blade force are discussed. Strong periodic influences of the incoming wakes and of potential effects of downstream blade rows can be observed. The amplitude and shape of the unsteady aerodynamic blade force depend on the interaction of the superimposed influences of the blade rows.

Rotor-Stator Interactions in a Four-Stage Low-Speed Axial Compressor—Part I: Unsteady Profile Pressures and the Effect of Clocking

This two-part paper presents detailed experimental investigations of unsteady aerodynamic blade row interactions in the four-stage Low-Speed Research Compressor of Dresden. In part I of the paper the unsteady profile pressure distributions for the nominal setup of the compressor are discussed. Furthermore, the effect of blade row clocking on the unsteady profile pressures is investigated. Part II deals with the unsteady aerodynamic blade forces, which are calculated from the measured profile pressure distributions. The unsteady pressure distributions were analyzed in the first, a middle and the last compressor stage both on the rotor and stator blades. The measurements were carried out on pressure side and suction side at midspan. Several operating points were investigated. A complex behavior of the unsteady profile pressures can be observed, resulting from the superimposed influences of the wakes and the potential effects of several up- and downstream blade rows of the four-stage compressor. The profile pressure changes nearly simultaneously along the blade chord if a disturbance arrives at the leading edge or the trailing edge of the blade. Thus the unsteady profile pressure distribution is nearly independent of the convective wake propagation within the blade passage. A phase shift of the reaction of the blade to the disturbance on the pressure and suction side is observed. In addition, clocking investigations were carried out to distinguish between the different periodic influences from the surrounding blade rows. For this reason the unsteady profile pressure distribution on rotor 3 was measured, while stators 1–4 were separately traversed stepwise in the circumferential direction. Thus the wake and potential effects of the up- and downstream blade rows on the unsteady profile pressure could clearly be distinguished and quantified.