Linear Turbine Research Articles

Comparison between linear and quadratic power take off for a single chamber land-fixed oscillating water column (OWC)

This study examines the influence of turbine response type on the performance of a land-fixed Oscillating Water Column (OWC) under second-order Stokes waves of varying heights. Numerical modelling techniques, including the Finite Element Method, incompressible Reynolds-Averaged Navier–Stokes (RANS) equations with the Shear-Stress Transport (SST) k-ω turbulence model, and an Arbitrary Lagrangian–Eulerian (ALE) scheme, were employed to gain insights into OWC behaviour. The linear turbine consistently displayed reduced efficiency with increasing wave height, maintaining a stable peak non-dimensional wave number (kh). Conversely, the quadratic turbine exhibited peak efficiency within a narrower wave height range, strongly influenced by wave height. Non-dimensional volume flow rate, non-dimensional chamber pressure, chamber volume, and maximum force on the front wall remained unaffected by changes in wave height for the linear turbine. In contrast, the quadratic turbine was notably impacted by variations in wave height. Moreover, the quadratic turbine revealed stronger odd-numbered higher-order harmonic components in both force and pressure due to its non-linear response. Notably, both linear and quadratic response types exhibited sloshing at similar wave numbers, suggesting minimal influence of turbine response on sloshing behaviour. Finally, the derived non-dimensional turbine coefficients proved both turbines could scale OWC models with negligible scaling effects from the turbine.

Experimental Study on the Endwall Aerothermal Performance of Turbine Cascades in a Novel Transient Test Facility

Abstract Linear turbine cascades have been widely used to conduct fundamental and applied investigations, but only a few transient test facilities with the linear turbine cascade are available in the open literature. A novel transient test facility was presented in this paper, including detailed design and structure, and various experimental measurements (aerodynamic and thermodynamic) were conducted to verify the transient test facility’s capability. This test facility mainly includes a main air supply line (bypass line and test line), a coolant supply line, a test section, and a control system (heater and various valves). The linear cascade holds up six equally spaced cascade profiles, forming five completed cascade passages, and the center passage is used for aerodynamic and thermodynamic measurements. The aerodynamic loss and heat transfer performance were measured at various flow conditions (incidence angle, Ma, and blowing ratio (BR)). The endwall heat transfer coefficient and film cooling effectiveness were estimated by adopting a dual linear regression technique. Results indicate that the mianstream pressure and temperature present a desired step change, and remain relatively steady in the test window. The magnitudes of endwall heat transfer significantly increase as the Maex increases from 0.2 to 0.5, but the thermal load distributions remain the same. The BR is a key parameter for endwall film cooling performance, and the optimal film cooling coverage is acquired at the critical value of BR. Both insufficient and excessive coolant flowrate can result in undesirable endwall film cooling coverage, and may cause unnecessary consumption of the coolant flow.

Experimental study of flow control on tip leakage flow in variable geometry linear turbine cascades with different pivot layouts

Variable geometry turbines are essential for adjusting operational conditions in industrial gas turbines and variable cycle engines. These adjustments necessitate partial gaps at both ends of the variable guide vanes to alter the turning angle, consequently introducing an aerodynamic performance penalty. Moreover, the pivot layout profoundly influences aerodynamic losses. Research on turbine cascades that considers various partial gap layouts is limited, particularly in terms of experimental studies, which are rarely conducted. This study aims to diminish aerodynamic losses and augment the efficiency of gas turbines by examining the impact of pivot layouts on partial gap clearance and secondary flow. It further investigates the effectiveness of flow control strategies at the blade tip across different pivot configurations within a variable geometry turbine cascade, utilizing pneumatic probe scanning and surface oil flow visualization techniques. The results reveal that employing a cavity at the tip can significantly reduce aerodynamic losses in schemes both with and without a pivot, achieving maximum loss reductions of 15.8% and 3.7%, respectively. Additionally, a narrower squealer width can further decrease these losses. However, with a pivot located at the tip, the resulting separation flow and wake vortex become predominant sources of losses. The presence of the pivot weakens the tip leakage flow rate and the intensity of the tip leakage vortex (TLV), thus diminishing the effectiveness of cavity tip flow control. The cavity moderates TLV and enhances the interaction between TLV and the wake vortex, leading to increased aerodynamic losses.

Modelling of linear large-capacity wind turbines with application to distributed control in wind farms

ABSTRACT Due to the widespread penetration of wind energy, large-capacity wind turbines (WTs) are becoming more conspicuous. In this paper, a linear control-oriented large-capacity wind turbine (WT) model is redesigned based on the 15 MW WT in openFAST. Compared with the original model, the redesigned model is more efficient and conducive to the design of linear controllers. To verify the validity of the redesigned WT model, we design a distributed control scheme with deloading operation of the wind farm (WF) to fairly share the load. Simulations are performed to verify the effectiveness of the application in the WF.

Generalized predictive control application scheme for nonlinear hydro-turbine regulation system: Based on a precise novel control structure

Generalized predictive control (GPC), which has excellent control performance and robustness, is only applicable to the control object that can be expressed in the transfer function and is difficult to be directly applied to the hydraulic turbine regulation system (HTRS) that contain extremely complex nonlinearity. Therefore, considering the practical application of GPC in a hydropower station containing the Francis turbine, the double models, real-time feedback linearization module, and a nonlinear characteristic compensator are designed, and a generalized predictive control strategy combining these modules (GPC-DM-RFLM-NCC) is proposed. Firstly, the salp swarm algorithm (SSA) is improved based on the chaotic mapping and Levy flight, an accurate nonlinear hydraulic turbine model is constructed based on the backpropagation neural network (BPNN) and improved SSA (ISSA), and an HTRS simulation platform with nonlinear characteristics is built by combining modules such as water diversion system, servo system, and generator. Then, the irrationality of the commonly used linear hydraulic turbine models in HTRS dynamic process simulation is verified through quantitative calculation. Furthermore, by combining the real-time feedback linearization method and ISSA-based nonlinear characteristic compensator, the GPC-DM-RFLM-NCC is proposed. Finally, the HTRS simulation platform, which consists of GPC, double models, real-time feedback linearization module, and nonlinear characteristic compensator, is built, and the applicability, reliability, and excellent robustness of the proposed GPC-DM-RFLM-NCC are verified by the real data of a hydropower station.

Experimental investigation of secondary flow losses in a variable geometry linear turbine cascade with winglet tip

Variable geometry turbines (VGT) hold a crucial role in gas turbines and variable cycle engines (VCE) by allowing adjustments to different operational conditions. In order to realize the adjustable function of the VGT stator blade, there will be partial gap structure at both ends of the stator blade, which will lead to partial leakage flow and serious secondary flow loss at the blade end that cannot be ignored, especially in a large angle adjustment range. At present, there are few researches on turbine cascades considering the real partial gap structure and winglet tip, and the numerical simulation calculation is mainly used, while the in-depth study using wind tunnel test is rarely seen. Therefore, this study attempts to analyze the internal flow characteristics of variable geometry turbine cascade by using five-hole pneumatic probe scanning and surface oil flow visualization, and discusses the mechanism of controlling partial clearance leakage flow and reducing secondary flow loss in the cascade by using winglet tip flow control technology. The winglet offset distance and the change of the relationship between the pivot and the clearance position on the flow field and flow loss is studied experimentally for the first time. The results show that the influence mechanism of winglet tip applied in VGT partial gap is quite different from that of typical blade tip clearance application, and more consideration should be given to the influence of pivot structure. Reasonable parameter selection can achieve a maximum loss reduction of 13.4 % and 20.2 % with and without pivot, respectively, while the unreasonable flow control scheme may lead to the loss or even increase with pivot. The interaction between the new secondary flow structure induced by pivot in the gap and other gap leakage flows is analyzed to explore the new mechanism of using winglet tip to reduce the loss of gap leakage flow.

Experimental Investigation of Additional Loss Associated With Incoming Wakes in Low-Pressure Turbine Cascades

Abstract The present paper aims to experimentally investigate the influence of wake-passing frequency, Reynolds number, and suction surface diffusion rate on the additional loss due to incoming wakes to the profile loss in the low-pressure turbine (LPT) cascades and discuss a design guide for reducing the additional loss. Using a moving-bar mechanism, the unsteady effects of incoming wakes were measured in a low-speed linear turbine cascade facility. The wake-passing frequency was varied by adjusting the moving-bar speed. The different airfoils with different surface velocity distributions were tested to examine the effect of suction surface diffusion rate. For each test case in an unsteady flow condition, the additional loss due to incoming wakes was derived by subtracting the profile loss from the measured total pressure loss across the cascade. Here, the profile loss was estimated by using the friction drag force, which was calculated by the measured surface velocity distribution, and the pressure drag force, which was calculated by the measured surface pressure distribution and the predicted base pressure. The resultant additional loss includes all kinds of losses associated with incoming wakes, such as mixing loss of incoming wakes enhanced in the blade passage and unsteady interaction loss between incoming wakes and surface boundary layers. It was demonstrated that in an unsteady flow condition, a substantial performance improvement was obtained in the entire Reynolds number range by applying the surface velocity distribution with no laminar separation to a low-solidity blade row.

Effect of Plasma Actuator Layout on the Passage Vortex Reduction in a Linear Turbine Cascade for a Wide Range of Reynolds Numbers

This study examined how various plasma actuator (PA) configurations affect the passage vortex (PV) reduction in a linear turbine cascade (LTC) utilizing dielectric barrier discharge PAs. The experiments were carried out under three specific layout conditions: axial placement of the PA, slanted placement at the blade inlet, and slanted placement inside the blade. Particle image velocimetry was employed to measure the velocity distribution of the secondary flow at the LTC exit, followed by an analysis of the streamline patterns, turbulence intensity distribution, and vorticity distribution. At a Reynolds number of 3.7 × 104, the PA with an oblique orientation at the blade inlet provided the most effective PV suppression. The average value of the secondary flow velocity and the peak vorticity value at the LTC exit decreased by 59.0% and 68.8%, respectively, compared to the no-control case. Furthermore, the wind tunnel blower’s rotation speed was modified, adjustments were made to the LTC’s mainstream velocity, and the Reynolds number transitioned from 1.0 × 104 to 9.9 × 104, approximately 10 times. When the slanted PA was used at the blade inlet, the PV suppression effect was the highest. The peak vorticity value owing to the PV at the LTC exit decreased by 62.9% at the lowest Reynolds number of 1.0 × 104. The Reynolds number increased with a higher mainstream velocity and decreased flow induced by the PA, consequently reducing the PV suppression effect. However, the drive of the PA was effective even under the most severe conditions (9.9 × 104), and the peak vorticity value was reduced by 20.2%.

Profile Loss Prediction for Organic Rankine Cycle Turbines: An Experimental Case Study

The results of profile loss measurements, including trailing edge flow details, are presented for the flow of an organic vapor through a linear turbine cascade. The so-called VKI-I blade profile from the open literature was chosen for the cascade, and the working fluid was NOVEC 649. Pitot probes and hot-wire anemometry were employed to measure the flow field up and downstream of the cascade. Details of the unsteady flow caused by the trailing edge of the blades and the turbulent spectrum were investigated using hot-wire anemometry. The new organic vapor flow results were compared with the literature data obtained for air and with the prediction of conventional literature loss models. It was found that, under certain thermodynamic conditions, specific traditional loss models can reasonably predict organic Rankine cycle (ORC) turbines’ profile loss. Still, significant deviations between the loss models and the experimental data can also occur.

Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

Design and experimental analysis of a linear hydrokinetic turbine

The generation of electricity from free-flowing water is an important renewable energy source. In this paper, we introduce a new turbine concept based on a vertical axis turbine with two extraction planes and a rectangular harvest area suitable for rivers or ocean currents. Using numerical simulations, we show that the extension of the classic vertical axis turbine by linear sections can significantly improve efficiency, with gains of up to 12% in the case of the Reference Model 2 turbine, a benchmark prototype used for comparison. Based on the findings, a prototype is designed and built with a focus on optimizing the blade pitch using computational fluid dynamics simulations. The prototype is subsequently evaluated through performance measurements on a test boat. Our results show that the Linear Turbine has the potential to significantly improve the efficiency of kinetic energy converters for free-flowing water, with an efficiency of around 42% achieved in our small prototype. Key features of the turbine include its ability to generate electricity from rivers and ocean currents with minimal impact on the natural environment, its high potential efficiency, vertical construction, and linear working range. The design of the turbine is complex, but its potential applications include use in small-scale systems and as a environmental alternative to traditional hydroelectric dams. Further investigations are needed to focus on economic design and to validate improved designs with 3D fluid simulations.

Flutter Measurement of a Linear Turbine Blade Cascade with an Angular Position Deviation of One Blade

Abstract Experimental flutter testing of high-aspect ratio rotor blades is a mainstay of turbomachinery research. However, rotor blades are never identical, and geometrical errors between actual and nominal geometries exist due to limited machining precision or assembly imperfection. The paper presents the initial phase of the controlled flutter research of a linear turbine blade cascade with a geometric deviation in one blade position. A subsonic wind tunnel with four flexibly mounted blades in an otherwise rigid blade cascade is employed at one angle of incidence and three low reduced frequencies. Measurements are performed with an angular position deviation (±1.5°) of one blade in pure bending and torsion modes. A tangible effect of one blade’s slight incidence angle offset on the vibrating blade cascade aerodynamic stability is demonstrated, and this research effort opens the door to a more extensive testing campaign.

Experimental investigation of subsonic and transonic flows through a linear turbine cascade

Experimental investigations of high subsonic and transonic flows through a linear cascade consists of VKI LS-59 blades have been carried out. Emphasis was put on analysis of the flow characteristics at the cascade exit. Experiments reported the static pressure measurements on blade surface, flow field survey downstream the cascade by means of Particle Image Velocimetry (PIV) and visualization by means of the Schlieren method. The turbulent intensity measurements have been performed at the cascade inlet to provide inlet conditions for numerical studies. The measurements have been carried out at two isentropic Mach numbers: M2,is=0.777 (high subsonic) and M2,is=0.975 (transonic). The corresponding Reynolds numbers based on the chord length and isentropic downstream velocity were equal to Re2,is=6.21⋅105 and Re2,is=6.82⋅105, respectively. The numerical simulations with Transition SST model have been performed to complement experiments and to verify applicability of data for testing and development of turbulence models. The RANS-based transition model reproduced correct isentropic Mach number profiles on the blade surface but underpredicted the turbulent mixing in the wake flow.

Turbulence anisotropy analysis at the middle section of a highly loaded 3D linear turbine cascade using Large Eddy Simulation

This study analyzes the flow over a three-dimensional linear low-pressure turbine cascade blade using large eddy simulation at Re = 90,000. The computational model consists of one blade passage with periodic boundaries and synthetic turbulence is generated at the inlet of the domain. Various flow metrics, including isentropic Mach number distribution at mid-span and wake total pressure losses are compared with available experimental data and found to be in good agreement. A more detailed analysis of the turbulence with particular attention to the separation bubble region is subsequently presented. The analysis revealed that the turbulence is in a nearly two-component state very close to the wall region and gradually follows a certain anisotropy trajectory, as the distance from the wall increases. Even in the free-stream region no fully isotropic state is reached, due to large acceleration and flow turning. The results give a new insight into the state of turbulence within the separation region on the blade suction side and emphasize the deficiencies of the Reynolds-averaged Navier Stokes (RANS) turbulence models in reproducing the turbulence anisotropy. This insight is of relevance for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separation region.

Vortex structure for reducing tip leakage flow of linear turbine cascade using dielectric barrier discharge plasma actuator

An axial-flow turbine is one of the main components of aircraft jet engines. It is important to suppress the leakage flow at the blade tip to improve the aerodynamic performance of the turbine blades. To achieve this, a unique ring-type plasma actuator was developed as an active flow control device. This plasma actuator consists of a high-frequency−high-voltage electrode installed in the outer casing of the turbine rotor. The metallic turbine rotor blades act as the grounded electrode. Dielectric barrier discharge (DBD) plasma is generated between the outer casing and tip of the turbine blade; this plasma interrupts the leakage flow. In this study, the effect of the plasma actuator in reducing the tip leakage flow of a linear turbine cascade was demonstrated using particle image velocimetry (PIV) to obtain velocity measurements at two planes, namely, the blade mid-passage and blade exit. The turbulence intensity and vorticity were also analyzed. The blade mid-passage measurements showed that the low-velocity region caused by the tip leakage flow was reduced by the plasma actuator and the blade exit measurements clarified the vortex structure. The operation of the plasma actuator successfully reduced or eradicated the tip leakage vortex. Contrarily, the passage vortex at the tip side became clearer and stronger. The plasma actuator reduced the tip leakage vortex even when the Reynolds number was changed.

Experimental and Numerical Investigations for Dual−Cavity Tip Aerodynamic Performance in the Linear Turbine Cascade

Experimental and numerical studies of a linear high-loaded turbine cascade with a dual−cavity tip structure are presented in this paper. The experimental conditions contained an increase in the outlet Mach number from 0.42 to 0.92, a change in the incidence angle from −15° to 15° and an increase in the relative clearance size from 0.36% to 1.4%. The ability of the dual−cavity tip to control leakage losses and vortices is assessed using the total pressure coefficient and the Q-criterion. This research indicates that the leakage vortex interacts strongly with the passage vortex, and the change in working conditions affects the balance between the two vortices and thus the flow field structure. The experimental and numerical results prove that the dual−cavity tip can reduce losses in all operating conditions, with the best control effect reduced by 0.025 in a large clearance size condition. In addition, the leakage control effect of the blade tip structure is more influenced by the incoming flow angle and clearance size than the Mach number.

Experimental Subsonic Flutter of a Linear Turbine Blade Cascade With Various Mode Shapes and Chordwise Torsion Axis Locations

Abstract Axial flow turbomachinery is susceptible to self-excited vibrations known as flutter, primarily affecting high-aspect ratio rotor blades. Experimental studies of blade flutter are essential to understanding the phenomenon. The existing research has shown that the most critical factor in determining the aerodynamic stability of the blade is the mode shape. In this work, measurements of subsonic flutter of a linear turbine blade cascade with various mode shapes and torsion axis locations in a chordwise direction are carried out. The cascade consists of eight blades representing the reduced tip sections of the last stage blade of the steam turbine rotor, and central four flexibly mounted blades are forced to vibrate in pure bending and pure torsion modes and a combined motion. Both the traveling wave mode approach and the influence coefficient method are tested. The results show that the pure torsion mode is insensitive to increasing reduced frequency and is aerodynamically unstable for each positive angle of incidence tested, while pure bending and combined modes become less stable with the increased angle of incidence. In addition, high sensitivity of blade behavior to changes in torsion axis position and phase shift between bending and torsion motions is demonstrated.

Numerical Investigations on Effect of Inflow Parameters on Development of Secondary Flow Field for Linear Low-Pressure Turbine Cascade

Abstract Endwall flows contribute the most crucial role in loss generation for axial flow turbine and compressor blades. These losses lead to modifying the blade loading and overall performance in terms of stable operating range. The present study aimed to determine the endwall flow streams in a low-speed low-pressure linear turbine cascade vane using a numerical approach. The study includes two sections. The first section includes an attempt to understand different secondary flow streams available at the endwall. The location of the horseshoe vortex and subsequent vortex patterns are identified in the section. The selection of a suitable turbulence model among shear stress transport (SST) k–ω and SST γ–θ to identify endwall flow streams is studied prior to the section. The steady-state numerical study is performed using Reynolds Averaged Navier–Stokes equations closed by the SST γ–θ turbulence model. The computational results are validated with experimental results available in the literature and are found to be in good agreement. The study is extended for different inflow conditions in a later section. The second section includes the effect of flow incidence and turbulence intensity on the endwall secondary flow field. Four different inflow incidences are considered for the study. The inlet turbulence intensities are varied by 1% and 10% for each case. The results revealed different secondary flow patterns at an endwall and found the change in behavior with inflow conditions. SST γ–θ turbulence model with lower turbulence intensity is more suitable to identify such flow behavior.

Theoretically based correction to model test results of OWC wave energy converters to account for air compressibility effect

The oscillating-water-column (OWC) wave energy converter with air turbine has been object of extensive development. The spring-like effect of air compressibility in the chamber is related to the density–pressure relationship. It is known to significantly affect the power performance of the full-sized converter, and is rarely accounted for in model testing. A method is presented to correct results from physical model testing for effects of air compressibility. It combines linear theory in the frequency domain and hydrodynamic coefficients, together with air thermodynamics. A new concept of linear turbine simulator aerodynamically equivalent to the orifice simulator is introduced in the theory. Corrections for non-linear real-fluid effects may be accounted for from comparisons with data from wave tank testing. The method was validated in a case study involving published data from OWC model testing with regular waves of different periods and amplitudes in a wave flume. Theoretically based corrections were found to well predict the air compressibility effects upon power performance. Air compressibility may negatively or positively affect power conversion depending on whether the wave period is larger or smaller than a critical value accurately predicted by the theory.

Novel wave-shaped tip-shroud contours towards reducing turbine leakage loss

For axial turbines, tip leakage vortex and passage vortex flow are responsible for a large part of the aerodynamic loss. To pursue higher turbine efficiency, many methods are undertaken to eliminate the tip leakage loss. In this work, by experimental and numerical methods, novel wave-shaped tip-shroud contours on the unshrouded turbine cascade were proposed. In a low-speed large-scale linear turbine cascade facility, a traditional flat tip was first conducted to comprehensively validate the numerical tool, especially the inlet conditions and the total pressure loss due to the tip leakage loss. The numerical settings were kept the same as the experimental facility. It achieved a satisfactory agreement between the CFD and experiments. It was found that in a flat tip case, a large, integral tip leakage vortex structure was identified and responded to the aerodynamic loss within the tip leakage core. Then a series of novel wave-shaped tip-shroud contours were considered in the current turbine cascade. The overtip flow exited the suction side tip gap, and the peak mass flow rate was concentrated around the troughs of the wave tip. Several small-sized, but stronger-vorticity-magnitude vortex structures were identified. By breaking down a large, integral vortex structure into several smaller-scale vortices, the vortex evolution was beneficial for the turbine efficiency. Although a slight enhancement of passage vortex was identified, the overall loss reduction of 3.0% was achieved by reducing the tip leakage loss, which dominated the loss contribution. According to the real working condition, axial displacement for the blade was considered. Within the current scope, the maximum reduction of tip leakage loss coefficient was reduced by 14.6% compared to the flat tip case. It was mainly contributed by the smaller contraction coefficient within the tip gap, which reduced the overtip leakage mass flow. Meanwhile, the vena contracta within the tip gap was altered, as well as static pressure distribution on the tip surface. As a result, the minimum static pressure was re-distributed at the throat of the tip gap. It was proven that this novel wave-shaped tip-shroud contour was an efficient way to improve the aerodynamic performance at a larger tip gap.