Tip Passage Research Articles

Flow Mechanism Study on the Effect of Controllable Speed Casing With Different Axial Starting Points on Transonic Compressor Rotor Stability

Abstract The controllable speed casing represents an exploring approach to casing technology, designed to enhance the adaptability of casing in compressors under variable working conditions. This paper developed a numerical study into the effects of the axial starting point of the rotatable ring in the controllable speed casing on stability enhancement and performance. Additionally, the study sought to unveil the action mechanism of the rotating casing on various flow elements within the tip passage. The findings indicated that the optimal axial starting point for achieving the most pronounced stability enhancement effect in each rotating speed of the rotatable ring was located at the tip leading edge. In terms of the flow mechanism, the rotation of the rotatable ring was found to enhance the throughflow of the mainstream and the tip vortex, while exacerbating the backflow of the tip leakage flow, which occurred at middle and rear of the tip clearance and had not evolved into tip vortex.

Stability enhancement using a new combined casing treatment strategy in an ultra-highly loaded transonic compressor rotor

Low-reaction compressors are promising for achieving high loads but face severe flow instability challenges. This study investigates a low-reaction transonic compressor rotor using casing treatment technologies to control unstable flow dynamics precisely. First, a design integrating self-recirculating and circumferential groove casing treatments near the leading edge is implemented. This design enhances flow capacity at the tip passage inlet. However, it causes a “stall transposition” phenomenon. The unstable flow structures shift from shock-tip leakage vortex interactions at the front to corner separation at the rear. Consequently, the stall mechanism transitions from an end-wall stall to a blade stall. To address this issue, a new casing treatment layout is proposed. Grooves are added after the mid-chord of the initial front casing configuration. This adaptation suppresses emerging unstable flow structures and extends the stall margin by approximately 12.07 %. Detailed flow field analysis shows that the rear grooves effectively reduced the trailing edge separation vortex. They also limit downstream corner separation and mitigate disturbances from tip leakage flows in the rear of the passage.

Effect of non-uniform circumferential spallation of seal coating on the aerodynamic performance in a transonic axial rotor: A steady numerical simulation

Seal coating is a critical component of a compressor, and its function is to minimize the blade tip clearance and prevent fluid leakage. Non-axisymmetric spallation of the seal coating can compromise its effectiveness and reduce the compressor's efficiency. In this study, a numerical simulation was performed on a transonic axial rotor to study the effect of non-axisymmetric spallation of seal coating on the aerodynamic performance. Circumferential deep grooves were used to represent the irregular peeling of the seal coating in the full-annulus grids CFD simulation. Results show that as the circumferential length of spallation of seal coating increases, the total pressure ratio and isentropic efficiency decrease, and the surge margin decreases at first but then increases. After seal coating spallation, the flow loss changes near the suction surface and the tip passage. The flow loss changes on the suction surface relate to the interaction between the leading-edge shock/passage shock and the boundary layer. At the tip passage, the tip leakage flow and secondary flow induced low-velocity region and the effect of spallation on blockage dominate the flow loss and instability. The change in surge margin is contributed to the amount of and the chordwise variation of tip leakage flow, and the surge margin drops to the minimum when the spallation length is 9 passages where a “double-twist” flow behavior of TLF occurs substantially.

Influence of the ending position of controllable speed casing on a transonic compressor rotor tip leakage flow

Abstract The controllable speed casing is a novel casing treatment approach that makes partial casing rotate at adjustable and proper speed to achieve stability expansion. Structural parameters of casing treatment are found to influence the effect of stability expansion by many studies. In this paper, the effect of the ending position of the rotatable ring in controllable speed casing on the tip leakage flow and the stability expansion was studied numerically. The results show that when the rotatable ring rotates at 30 % and 50 % rotor design speed, the controllable speed casing achieves the stability expansion of the compressor rotor no matter where the ending position is. The upstream movement of the ending position decreases the axial pressure gradient in the middle and rear of the tip passage. It pushes the shock wave downstream, which reduces blockage region at tip leading edge. The upstream movement of the ending position contributes to an approximately linear increase in the stable operating margin.

Flow instability control of an ultra-highly loaded transonic compressor rotor using self-excited casing bleed

Flow instability is a common issue encountered by high-speed compressors when they operate outside of their optimal range, especially in highly loaded compressors. This study investigates the potential of an unsteady passive flow control technique, self-excited bleed (SEB), which involves casing modification, to improve the base flow and stability characteristics of an ultra-highly loaded low reaction transonic compressor rotor. Through transient computational fluid dynamics simulations, we demonstrate that SEB can extend the rotor's operating range by up to 14.07%. The physical mechanism underlying this stability enhancement is the suppression of the shock-induced breakdown of the tip leakage vortex (TLV) near the blade leading edge and the attenuation of the double leakage flow by SEB. The unsteady excitation of the bleed effect dominates the tip flow and eliminates the spontaneous closed-loop feedback process based on the dynamic interaction between the TLV breakdown, the tip secondary vortex, and the blade loading. Time-resolved tip-region flow patterns elucidate the self-organization and reconstruction of this feedback mechanism. Frequency spectral analysis further reveals that the self-induced oscillation frequency of the tip leakage flow formed during the feedback process disappears, and the bleed excitation frequency replaces it as the main frequency of the tip flow field. However, increasing the bleed flow rate causes the boundary layer on the suction surface to migrate radially outward, resulting in increased flow blockage at the rear of the tip passage. These two influences of SEB are quantified by a blockage factor, and determining the optimal bleed flow rate requires a trade-off between beneficial and detrimental impacts.

Mechanism Underlying the Effect of Self-Circulating Casings with Different Circumferential Coverage Ratios on the Aerodynamic Performance of a Transonic Centrifugal Compressor

The aim of this research was to explore the mechanisms underlying the effect of self-circulating casing treatment with different circumferential coverage ratios on the aerodynamic performance of a transonic centrifugal compressor. A three-dimensional unsteady numerical simulation was carried out on a Krain impeller. The circumferential coverage ratios of the self-circulating casings were set to 36%, 54%, 72% and 90%, respectively. The numerical results showed that the Stall Margin Improvement (SMI) increased with the increase in circumferential coverage ratios. The self-circulating casing with a 90% circumferential coverage ratio exhibited the highest SMI at 20.22%. Internal flow field analysis showed that the self-circulating casing treatment improved the compressor stability by sucking the low-speed flow in the blade tip passage and restraining the leakage vortexes breaking, which caused flow blockage. The compressor performance was improved at most of the operating points, and the improvement increased with increase in circumferential coverage ratio. The improvement in compressor performance was mainly attributed to reduction in the area of the high relative total pressure loss in the blade tip passage and significant decrease in the flow loss by the self-circulating casings.

Mechanisms of oscillating suction in controlling the tip leakage flow in a high-load compressor cascade

To control tip leakage flow and reduce related loss in axial-flow compressors, the oscillating suction scheme was introduced in a high-load compressor cascade with a tip clearance, and its flow control mechanisms on the tip leakage flow were studied numerically. It is found that the flow control effect of oscillating suction is the best when the unsteady excitation frequency is equal or harmonic to the feature frequency of the flow field related to the flow separation. The loss of the cascade controlled by the oscillating suction with a reduced frequency of 0.39 and excitation amplitude of 10 kPa was reduced by about 3.4% compared with the steady suction scheme, and about 11.14% less than that of the non-suction scheme. Oscillating suction discretized the concentrated tip leakage vortex into a series of scale-reduced vortex structures by the periodic unsteady excitation, which can be identified by the analysis using proper orthogonal decomposition (POD). The feature frequencies became consistent with the oscillating excitation frequency or its multiple, and the fluctuation generated by the tip leakage flow was enhanced. The energy proportion of high-order POD modes was increased by oscillating excitation, which indicated the vortex structures with weak fluctuation intensity were more active. The mixing and energy exchange among the mainstream, separated flow, endwall secondary flow, and tip leakage flow were enhanced, so that a better flow control effect could be achieved. Furthermore, flow capacity of tip passage was modified, the overall aerodynamic performance of the compressor cascade was improved thereby.

Mechanism of affecting the performance and internal flow field of an axial flow subsonic compressor with self-recirculation casing treatment

This investigation aims to understand the mechanisms of affecting the axial flow compressor performance and internal flow field with the application of self-recirculation casing treatment. Besides, the potentiality of further enhancing the compressor performance and stability by optimizing the geometric structure of self-recirculation casing treatment is discussed in detail. The results show that self-recirculation casing treatment generates about 7.06, 7.89% stall margin improvements in the experiment and full-annulus unsteady calculation, respectively. Moreover, the compressor total pressure and isentropic efficiency are improved among most of operating points, and the experimental and calculated compressor peak efficiencies are increased by 0.7% and 0.6%, respectively. The comparisons between baseline shroud and self-recirculation casing treatment show that the flow conditions of the compressor rotor inlet upstream are improved well with self-recirculation casing treatment, and the degree of the pressure enhancement in the blade top passage for self-recirculation casing treatment is higher than that for baseline. Further, self-recirculation casing treatment can restrain the leading edge-spilled flows made by the blade tip clearance leakage flows and weaken the blade tip passage blockage. Hence, the flow loss near the rotor top passage is reduced after the application of self-recirculation casing treatment. The rotor performance and stability for self-recirculation casing treatment are greater than those for baseline. The flow-field analyses also indicate that the adverse effects caused by the clearance leakage flows of the blades tip rear are greater than those made by the clearance leakage flows of the blades leading edge. When one injecting part of self-recirculation casing treatment is aligned with the inlet of one blade tip passage, the flow-field quality in the passage is not the best among all the passages between two adjacent injecting parts of self-recirculation casing treatment. Further, the flow-field analyses also indicate that the effect of the relative position between the blade and self-recirculation casing treatment on the flows in the self-recirculation casing treatment may be ignored during the optimization of the recirculating loop configuration.

Effect of inverse blade angle slots on a transonic rotor performance and stability

The aim of the paper is to explore the effects of inverse blade angle slots CT (IBSCT) on the NASA Rotor 67 stability and performance at 100% design speed. Considering the compromise between the stall margin improvement (SMI) and efficiency loss for the rotor, three kinds of IBSCT were design and researched in this investigation. The unsteady calculated results show that the slots with 100% axial coverage rate (IBSCT1), the slots with 100% axial coverage rate and 60 degrees radial skewed angle (IBSCT2) and the slots with 40% axial coverage rate and 60 degrees radial skewed angle (IBSCT3) can generate about 20.65% SMI with 0.766% peak efficiency loss (PEL), 24.28% SMI with 0.755% PEL and 17.61% SMI with −0.011% PEL respectively. Moreover, the flow field analyses show that the adverse flows made by the low energy tip clearance leakage flow (TLF) near the rotor tip leading edge passage play the key role in making the rotor with smooth wall stall, and the adverse flows are resulted from the interaction between the rotor tip passage shock wave and the TLF. When IBSCT1 was applied, the adverse flows were well restrained. However, the interaction between the passage mainstreams and the flows formed inside the slots makes extra flow losses, which make the rotor efficiency decrease at some operating points. Hence, the rotor stability was improved with the peak efficiency drop. Due to the deflection of some angle along the radial direction for the slots, IBSCT2 generates more useful injected flows inside the slots than IBSCT1. Due to the decrease of axial coverage rate for the slots, the injected flows formed inside the slots for IBSCT3 are less useful than those for IBSCT2 and IBSCT1, but IBSCT3 generates smaller flow losses in the rotor tip passage than IBSCT2 and IBSCT1.

Mechanism of affecting the axial rotor stability and performance with center offset degrees of axial skewed slots

A subsonic axial rotor with axial skewed slot casing treatment (ASSCT) was investigated with experimental and numerical methods to explore the effects of the center offset degree (Cod) on the rotor stability and performance. Cod is defined as the ratio of the central difference between the rotor tip section and ASSCT to the rotor tip axial chord length. The Cod values are selected as 1.16, 0.608, 0, and −0.36, respectively. When the ASSCT is located upstream, the value of the Cod is positive. The experimental and unsteady calculated results show that the stall margin improvement (SMI) and peak efficiency loss (PEL) are reduced when the slots move to the rotor upstream or downstream. The slots with 0 Cod (ASSCT1) achieve 50% SMI with 8.67% PEL. The slots with 0.608 Cod (ASSCT2) gain 48.5% SMI with 2.12% PEL. The slots with 1.16 Cod (ASSCT3) and −0.36 Cod (ASSCT4) gain −3.41%, 20.1% SMI, respectively. Considering the compromise between the SMI and PEL for the rotor, ASSCT5 was designed by changing the slot number of ASSCT2 from 180 to 90. The unsteady calculated result shows that ASSCT5 can gain 22.28% SMI and 0.485% PEL. The detailed analysis of the flow field in the compressor tip passage indicates that there are adverse effects made by the slots on the flow field near the rotor blade tip leading edge for ASSCT3. Moreover, the ability of reducing the range of low-velocity zones for ASSCT4 is much lower than that for ASSCT1 or ASSCT2, and ASSCT1 generates bigger flow losses in the rotor tip passage than ASSCT2. The positive effects and flow losses made by the slots with 0.608 Cod both become smaller with the slot number decreasing from 180 to 90.

Flow mechanism of affecting an axial flow compressor performance and stability with cross-blade slot casing treatments

The objective of this study is to evaluate the effect of cross-blade slot casing treatment on the stability and performance of an axial flow compressor rotor. The experimental and unsteady calculated results both show that cross-blade slot casing treatment can generate about 22% stall margin improvement, and the compressor peak efficiency is reduced by about 13%. The detailed flow-field analyses indicate that the sucked and injected flow caused by the slots of cross-blade slot casing treatment can restrain the rotor tip passage blockage, which is made by the low energy tip clearance leakage vortex. When cross-blade slot casing treatment is applied, not only the rotor wheel flange work becomes lower in most of the rotor blade span, but also the flow loss in the blade tip passage becomes fairly large due to the strong interaction between the mainstream and the injected flows made by the slots. As a result, the compressor total pressure ratio and efficiency for cross-blade slot casing treatment are reduced obviously. Three kinds of new cross-blade slot casing treatment were designed according to the previous successful experience and investigated in this paper. The numerical results show that the new three cross-blade slot casing treatments both generate about 54% stall margin improvement at the cost of minor peak efficiency. For one new cross-blade slot casing treatment (CSCT2), the compressor peak efficiency is reduced by about 0.3%. The low energy TLV, which is present for cross-blade slot casing treatment, is removed by the strong sucked flow made by CSCT2. Moreover, the interaction between the mainstream and the injected flows caused by CSCT2 becomes weak obviously, and the corresponding flow loss is reduced greatly. Hence, the compressor stability and performance with CSCT2 are higher than those with cross-blade slot casing treatment.

Experimental study on axially non-uniform clearances in a linear turbine cascade with a cavity squealer tip

The effects of axially non-uniform clearances on the tip leakage flow and aerodynamic performance in a linear turbine cascade with a cavity squealer tip were investigated in this study with the objective of improving the flow loss and tip flow field structure. A calibrated five-hole probe was used for the measurement of three-dimensional flows downstream of the cascade. The method of oil-flow visualization was used to show the endwall flow field structure. The distribution of endwall static pressure was measured particularly by using the special moveable endwall. The axially non-uniform clearance, as a novel strategy that has a non-negligible influence on tip clearance flow and clearance leakage loss, may become a potential technology for improving aerodynamic performance in turbine cascades. By using the expanding clearance, the flow loss at the outlet is reduced effectively and an apparent improvement of aerodynamic performance in the turbine cascade is gained. Under the tip clearances of 0.75% H and 2% H, the maximum reduction of overall total pressure loss coefficient at the outlet is separately about 2.3% and 3.5% compared with the uniform clearance. The shrinkage of the buffer zone is considered to be able to weaken the interaction of the tip leakage vortex and passage vortex and thus reduce the loss of passage vortex. For the shrinking clearance, a noticeable decline in the aerodynamic performance of turbine cascade with cavity squealer tip is exhibited at both on and off design conditions in contrast to the uniform clearance. In addition, the effects of axially non-uniform clearances on the aerodynamic performance at off-design conditions have been investigated.

Mesoscopic physical removal of material using sliding nano-diamond contacts

Wear mechanisms including fracture and plastic deformation at the nanoscale are central to understand sliding contacts. Recently, the combination of tip-induced material erosion with the sensing capability of secondary imaging modes of AFM, has enabled a slice-and-view tomographic technique named AFM tomography or Scalpel SPM. However, the elusive laws governing nanoscale wear and the large quantity of atoms involved in the tip-sample contact, require a dedicated mesoscale description to understand and model the tip-induced material removal. Here, we study nanosized sliding contacts made of diamond in the regime whereby thousands of nm3 are removed. We explore the fundamentals of high-pressure tip-induced material removal for various materials. Changes in the load force are systematically combined with AFM and SEM to increase the understanding and the process controllability. The nonlinear variation of the removal rate with the load force is interpreted as a combination of two contact regimes each dominating in a particular force range. By using the gradual transition between the two regimes, (1) the experimental rate of material eroded on each tip passage is modeled, (2) a controllable removal rate below 5 nm/scan for all the materials is demonstrated, thus opening to future development of 3D tomographic AFM.

Experiment study of the winglet-cavity tip on the aerodynamic performance in a turbine cascade

The effects of a novel winglet-cavity tip on the flow field and aerodynamic performance of a turbine blade with tip clearance have been investigated in a low-speed wind tunnel. A calibrated five-hole probe is used for the measurement of three-dimensional flows downstream of the cascade. The method of oil-flow visualization is used to show the endwall flow field structure. The distribution of endwall static pressure is measured particularly by using the special moveable endwall. The downstream results show that, compared with the flat tip and cavity tip, the winglet-cavity tip reduces aerodynamic loss in the region of tip leakage vortex and passage vortex effectively and gives a 8.5% reduction of total pressure losses at a tip clearance of τ/ H = 1.0%. Meanwhile, a more uniform flow angle is obtained with the winglet-cavity tip. Thus, the winglet-cavity tip provides better aerodynamic performance. It was found that more endwall flow enters the cavity from the front of suction side gap, combines with the flow entering the tip from the pressure side, and then separates upon the cavity. This reduces the loss of passage vortex. The endwall static pressure indicates that the winglet-cavity tip reduces the driving pressure difference and weakens the tip leakage flow. With the tip clearance increasing, the leakage flow is significantly enhanced. This strengthens the interaction between the tip leakage vortex and the passage vortex. With respect to the flat tip and cavity tip, the winglet-cavity tip obtains the lowest total pressure loss at all tested tip clearances.

Unsteady Wet Steam Flow Field Measurements in the Last Stage of Low Pressure Steam Turbine

Modern steam turbines need to operate efficiently and safely over a wide range of operating conditions. This paper presents a unique unprecedented set of time-resolved steam flowfield measurements from the exit of the last two stages of a low pressure (LP) steam turbine under various volumetric massflow conditions. The measurements were performed in the steam turbine test facility in Hitachi city in Japan. A newly developed fast response probe equipped with a heated tip to operate in wet steam flows was used. The probe tip is heated through an active control system using a miniature high-power cartridge heater developed in-house. Three different operating points (OPs), including two reduced massflow conditions, are compared and a detailed analysis of the unsteady flow structures under various blade loads and wetness mass fractions is presented. The measurements show that at the exit of the second to last stage the flow field is highly three dimensional. The measurements also show that the secondary flow structures at the tip region (shroud leakage and tip passage vortices) are the predominant sources of unsteadiness at 85% span. The high massflow operating condition exhibits the highest level of periodical total pressure fluctuation compared to the reduced massflow conditions at the inlet of the last stage. In contrast at the exit of the last stage, the reduced massflow operating condition exhibits the largest aerodynamic losses near the tip. This is due to the onset of the ventilation process at the exit of the LP steam turbine. This phenomenon results in three times larger levels of relative total pressure unsteadiness at 93% span, compared to the high massflow condition. This implies that at low volumetric flow conditions the blades will be subjected to higher dynamic load fluctuations at the tip region.

Effect of winglet geometry arrangement and incidence on tip clearance control in a compressor cascade

An experimental study is conducted to investigate the influences of blade tip winglet on the flow field of a compressor cascade. The tests are performed in a low speed linear cascade with stationary endwall, with three blade tip configurations, including the baseline tip, the suction-side winglet tip and the pressure-side winglet tip. The flowfield downstream of the cascade is measured using five-hole probe, from which the three-dimensional velocity field, vorticity field and pressure field are obtained. Static pressure measurements are made on the endwall above the blade row using pressure taps embedded in the plywood endwall. All measurements are made at both design and off-design conditions for tip clearance level of about 2 percent of the blade chord. The results revealed the incidence variation significantly affects the secondary flow and the associated loss field downstream of the cascade, where the tip leakage vortex and passage vortex exist as the major contributors on the field. The winglet geometry arrangements can change the trajectory of the tip leakage vortex. The suction-side winglet tip blade provides a lower overall total pressure loss coefficient when compared to the baseline tip blade and pressure-side winglet tip blade at all incidence angles.

Ultrasound-guided pleural puncture in supine or recumbent lateral position: feasibility study

Background: The aim of this study is to evaluate feasibility, safety and efficacy of accessing the pleural space with the patient supine or in lateral recumbent position, under constant ultrasonic guidance along the costophrenic sinus.
 Methods: All patients with pleural effusion, referred to thoracentesis or pleural drainage from February 2010 to January 2011 in two institutions, were drained either supine or in lateral recumbent position through an echomonitored cannulation of the costophrenic sinus. The technique is described in detail and an analysis of safety and feasibility is carried out.
 Results: One hundred and one thoracenteses were performed on 76 patients and 30 pigtail catheters were inserted in 30 patients (for a total of 131 pleural procedures in 106 patients enrolled). The feasibility of the procedures was 100% and in every case it was possible to follow real time needle tip passage in the pleural space. Ninety eight thoracenteses (97%) and all catheter drainages were successfully completed. Four thoracenteses were stopped because of the appearance of complications while no pigtail drainage procedure was stopped. After 24 hour follow up, one chest pain syndrome (1.3% of completed thoracenteses) and two pneumothoraces (1.4%) occurred. The mean acquisition time of pleural space was 76 ± 9 seconds for thoracentesis and 185 ± 46 seconds for drainage insertion (p < 0.05).
 Conclusions: This study highlights the safety and efficacy of this technique of real time echo-monitored pleural space puncture, that offers a more comfortable patient position, an easier approach for the operator, a very low rate of complications with short acquisition time of pleural space.

Ultrasound-guided pleural puncture in supine or recumbent lateral position - feasibility study

BackgroundThe aim of this study is to evaluate feasibility, safety and efficacy of accessing the pleural space with the patient supine or in lateral recumbent position, under constant ultrasonic guidance along the costophrenic sinus.MethodsAll patients with pleural effusion, referred to thoracentesis or pleural drainage from February 2010 to January 2011 in two institutions, were drained either supine or in lateral recumbent position through an echomonitored cannulation of the costophrenic sinus. The technique is described in detail and an analysis of safety and feasibility is carried out.ResultsOne hundred and one thoracenteses were performed on 76 patients and 30 pigtail catheters were inserted in 30 patients (for a total of 131 pleural procedures in 106 patients enrolled). The feasibility of the procedures was 100% and in every case it was possible to follow real time needle tip passage in the pleural space.Ninety eight thoracenteses (97%) and all catheter drainages were successfully completed. Four thoracenteses were stopped because of the appearance of complications while no pigtail drainage procedure was stopped. After 24 hour follow up, one chest pain syndrome (1.3% of completed thoracenteses) and two pneumothoraces (1.4%) occurred. The mean acquisition time of pleural space was 76 ± 9 seconds for thoracentesis and 185 ± 46 seconds for drainage insertion (p < 0.05).ConclusionsThis study highlights the safety and efficacy of this technique of real time echo-monitored pleural space puncture, that offers a more comfortable patient position, an easier approach for the operator, a very low rate of complications with short acquisition time of pleural space.

Numerical Sensitivity Analysis of Axial Flow Fan 3D Aerodynamics under Off Design Conditions

Compressor is a crucial component of an engine. Flow through the compressor is intricate and sensitive to the reference frame, geometry of the blade, tip clearance, stator, staging etc. Compressor, though designed for a particular environment, is also expected to show its performance under off design conditions like accelerating flight, landing, take off, climbing etc. The flow in third dimension leads to many complications and ambiguity. Tip aerodynamics, passage flow, and vortex aerodynamics play crucial role in describing the flow through the upper half of the blade and in the tip region, whereas flow over blade surface, trailing edge and the hub will guide the aerodynamic behavior of the rotor blade. This exercise is done for off design environment to study the aforesaid flow characteristics and is carried on an axial flow fan. The performance variation of fan flow under varying flow conditions is analyzed.

Reduction of Tip Clearance Losses in an Unshrouded Turbine by Rotor Casing Contouring

Tip leakage flow is responsible for a number of aerodynamic losses in turbines, and the mixing of tip leakage flow with the passage secondaryflowcauses significant losses. This paperpresents a numerical investigation of the effect of three types of casing contouring: 1) step, 2) trench, and 3) arc casings on aerodynamic performance of anunshrouded turbine rotor at design and off-design incidences, in an attempt to seek an optimal casing contour with the objective both of avoiding direct tip leakage in the tip clearance, and of efficiently using the interaction between the tip leakage vortex and passage vortex inside rotor passage, and then to reduce the total losses in turbines. The results show that the reduction in tip leakage losses obtained by the optimized casing contour significantly overrides the losses caused by the step in theflowpath. Introduction of casing step thickens the inlet boundary layer, which increases the strength of the tip passage vortex and hence suppresses the evolution of the tip leakage vortex. Step and trench casings provide the largest efficiency increase when the inlet flow direction is normal to the casing step while arc casing achieves the best performance improvement at the design incidence.