Tip Running Clearances Effects on Tip Vortices Induced Axial Compressor Rotor Flutter

2011 ◽  
Author(s):  
Caetano Peng
Keyword(s):  
Steady State ◽  
Leading Edge ◽  
Steady State Solution ◽  
Tip Vortices ◽  
Flutter Instability ◽  
Compressor Rotor ◽  
Stator Vane ◽  
Blade Tip ◽  
Variable Stator ◽  
Large Rotor

The present study aimed at investigating numerically the effects of large blade tip running clearances on flutter stability of axial core multi-stage compressor rotor. During this study, the influences of aerodynamic boundary conditions, variable stator vane incidence and tip running clearances of upstream and downstream rotors on aerodynamic compressor flow and rotor flutter stability are thoroughly investigated. The simulations were carried out using an in-house 3-D aeroelasticity code. The steady-state-solution computations are performed on single-blade-passage-one-bladerow, stage-blocks and whole compressor models. These analyses included rotor blade models with nominal tip running clearances and artificially large tip clearances. Moreover, the effects of the variable stator vane incidences are assessed by performing steady-state-solution computations for nominal vane schedules and extreme vane malschedule. The first four flap and torsion vibration modes from finite element analyses are included in the unsteady flow computations and assessed for flutter stability. The results from the numerical investigations showed that the compressors with large rotor tip running clearances are susceptible to rotor tip flow induced flutter instability. The aerodynamic losses on the rotor with large tip clearances increase with other rotors having also large tip gaps. For the aerodynamic boundary conditions considered here, the simulations predicted flutter instability for the first flap vibration mode. The flutter instability predicted on the rotors with large tip clearances is driven by oscillating tip vortices on blade suction surface close to the blade tip leading edge. The flow in the rotor tip gap is mostly stalled and tip vortices oscillations are close to blade tip leading edge. The strength of these oscillating vortices appears to increase with increase in variable stator vane malschedule or negative incidence. Small changes in aerodynamic conditions can offset these instabilities. These studies indicate that the main ingredients for the occurrence of these phenomena are likely to be excessively large rotor tip running clearances combined with significant changes in flow incidence.

The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

Numerical Simulation of Effects of Tip Geometry on the Performance of an Axial Compressor

2012 ◽  
Author(s):  
Hongwei Ma ◽  
Jun Zhang
Keyword(s):  
Mass Flow ◽  
Tangential Force ◽  
Axial Compressor ◽  
Pressure Rise ◽  
Leading Edge ◽  
Suction Side ◽  
Leakage Flow ◽  
Base Line ◽  
Compressor Rotor ◽  
Blade Tip

The purpose of this paper is to investigate numerically the effects of the tip geometry on the performance of an axial compressor rotor. There are three case studies which are compared with the base line tip geometry. 1) baseline (flat tip); 2) Cavity (tip with a cavity); 3) SSQA (suction side squealer tip) and 4) SSQB (modified suction side squealer tip). The case of SSQB is a combination of suction side squealer tip and the cavity tip. From leading edge to 10% chord, the tip has a cavity. From 10% chord to trailing edge, the tip has a suction side squealer. The numerical results of 2) show that the cavity tip leads to lower leakage mass flow and greater loss in tip gap and the rotor passage. The loading near the blade tip is lower than the baseline, thus the tangential force of the blade is lower. It leads to lower pressure rise than the baseline. The performance of the compressor for the tip with cavity is worse than the baseline. The results of 3) show that the higher curvature of the suction side squealer increases the loading of the blade and the tangential blade force. With the suction side squealer tip, the leakage flow experiences two vena contractor thus the mass of the leakage flow is reduced which is benefit for the performance of the compressor. The loss in the tip gap is lower than baseline. The performance is better than the baseline with greater pressure rise of the rotor, smaller leakage mass flow and lower averaged loss. For the case the SSQB, the leakage mass flow is lower than the SSQA and the loss in the tip gap and the rotor passage is greater than SSQA. The performance of the case of the SSQB is worse than the case of SSQA.

Experimental and Numerical Investigation of Effect of Center Offset Degree on Compressor Stability With Circumferential Grooved Casing Treatment

2016 ◽  
Author(s):  
HaoGuang Zhang ◽  
Feng Tan ◽  
YanHui Wu ◽  
WuLi Chu ◽  
Wei Wang ◽  
...  
Keyword(s):  
Axial Compressor ◽  
Leading Edge ◽  
Groove Depth ◽  
Tip Clearance ◽  
Central Difference ◽  
Stall Margin ◽  
Casing Treatment ◽  
Compressor Rotor ◽  
Stall Margin Improvement ◽  
Blade Tip

For compressor blade tip stall, one effective way of extending stable operating range is with the application of circumferential grooved casing treatment and its validity was proved by a lot of experimental and numerical investigations. The emphases of most circumferential grooved investigations are focused on the influence of groove depth and groove number on compressor stability, and there is few investigations dealt with the center offset degree of circumferential grooves casing treatment. Hence, an axial compressor rotor with casing treatment (CT) was investigated with experimental and numerical methods to explore the effect of center offset degree on compressor stability and performance. In the work reported here, The center offset degree is defined as the ratio of the central difference between rotor tip axial chord and CT to the axial chord length of rotor tip. When the center of CT is located within the upstream direction of the center of rotor tip axial chord, the value of center offset degree is positive. The experimental and numerical results show that stall margin improvement gained with CT is reduced as the value of center offset degree varies from 0 to 0.33 or −0.33, and the CT with −0.33 center offset degree achieves the lowest value of stall margin improvement at 53% and 73% design rotational speed. The detailed analysis of the flow-field in compressor tip indicates that there is not positive effect made by grooves on leading edge of rotor blade tip when the value of center offset degree is −0.33. As the mass flow of compressor reduces further, tip clearance leakage flow results in the outlet blockage due to the absence of the positive action of grooves near blade tip tail when the value of center offset degree is 0.33. Blockage does not appear in rotor tip passage owing to utilizing the function of all grooves with CT of 0 center offset degree.

Effects of Thermal Contact Resistance on Transient Thermoelastic Contacts for an Elastic Foundation

2005 ◽  
Vol 72 (6) ◽  
pp. 972-977 ◽  
Author(s):  
Yong Hoon Jang
Keyword(s):  
Steady State ◽  
Contact Resistance ◽  
Thermal Contact Resistance ◽  
Normal Load ◽  
Thermal Contact ◽  
Leading Edge ◽  
Transient Behavior ◽  
Steady State Solution ◽  
State Solution ◽  
Winkler Foundation

The paper presents a numerical solution to the problem of a hot rigid indenter sliding over a thermoelastic Winkler foundation with a thermal contact resistance at constant speed. It is shown analytically that no steady-state solution can exist for sufficiently high temperature or sufficiently small normal load or speed, regardless of the thermal contact resistance. However, the steady-state solution may exist in the same situation if the thermal contact resistance is considered. This means that the effect of the large values of temperature difference and small value of force or velocity which occur at no steady state can be lessened due to the thermal contact resistance. When there is no steady state, the predicted transient behavior involves regions of transient stationary contact interspersed with regions of separation regardless of the thermal contact resistance. Initially, the system typically exhibits a small number of relatively large contact and separation regions, but after the initial transient, the trailing edge of the contact area is only established and the leading edge loses contact, reducing the total extent of contact considerably. As time progresses, larger and larger numbers of small contact areas are established, until eventually the accuracy of the algorithm is limited by the discretization used.

The improvement of transonic compressor performance by the self-circulating casing treatment

2020 ◽  
pp. 095440622094226
Author(s):  
Song Yan ◽  
Wuli Chu
Keyword(s):  
Flow Field ◽  
Axial Flow ◽  
Leading Edge ◽  
Tip Clearance ◽  
The Self ◽  
Casing Treatment ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Blade Tip ◽  
Stability Effect

The performance curve of the compressor is limited by the surge boundary, so it is of great significance to increase the stable working range of the compressor. The self-circulating casing treatment is an effective way to improve the stable working range of the compressor. In this paper, the study of the influence of the injector position of the self-circulating casing treatment on the transonic axial flow compressor rotor performance is carried out by using the numerical simulation. The influence mechanism of the injector position on the enhancing stability effect of the self-circulating casing treatment is revealed. It is found that the self-circulating casing treatment can reduce the blade tip blockage by restraining the blade tip clearance leakage flow and changing the trajectory of the tip clearance leakage vortex, thus delaying the deterioration of the rotor tip flow field and improving the rotor stability. When the injector position of the self-circulating casing treatment moves from the upstream of the leading edge of the blade tip to the trailing edge of the blade tip, the enhancing stability effect of the self-circulating casing treatment increases first and then decreases. But the high-velocity jet from the injector of the self-circulating casing treatment aggravates the mixing loss of the rotor tip flow field, so that the rotor efficiency slightly decreases after using the self-circulating casing treatment.

Unsteady and Three-Dimensional Flow Mechanism of Spike-Type Stall Inception in an Axial Flow Compressor Rotor

2011 ◽  
Author(s):  
Hiroaki Kikuta ◽  
Ken-ichiro Iwakiri ◽  
Masato Furukawa ◽  
Kazutoyo Yamada ◽  
Satoshi Gunjishima ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Axial Flow ◽  
Leading Edge ◽  
Three Dimensional Flow ◽  
Stall Inception ◽  
Dimensional Flow ◽  
Compressor Rotor ◽  
Pressure Distributions ◽  
Blade Tip ◽  
Flow Compressor

The unsteady behaviors and three-dimensional flow structure of the spike-type stall inception in an axial flow compressor rotor have been investigated by experimental and numerical analyses. In order to capture the transient phenomena of spike-type stall inception experimentally, “SFMT (Simultaneous Field Measurement Technique)”, by which instantaneous pressure distributions on the casing wall were acquired, was developed. By applying this technique, the unsteady flow pattern on the casing wall was extracted for each phase of development process of the stall inception. The details of three-dimensional flow structure in the stall inception process were revealed by the numerical analysis using a detached-eddy simulation (DES). At the stall inception, the characteristic patterns of the casing wall pressure distributions are observed in the experimental results: the low pressure regions moving in the circumferential direction and the variations of the low pressure regions at the leading edge. Considering the results of DES, these patterns are made by the vortices fragmented from the deformed tip leakage vortex or the tornado-type separation vortex and also are made by the tornado-type separation vortex itself, as well. The vortical flow structures have been elucidated. These vortices actually result from the leading edge separation at the blade tip. Therefore, it has been found that spike-type stall inception is dominated by the leading edge separation at the rotor blade tip.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

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