Three-dimensional Unsteady Navier-Stokes Equations Research Articles

Numerical research on the resonance frequency characteristics of the Sparkjet actuator using modal analysis

In this study, the resonance frequency characteristics of the SparkJet actuator are examined through numerical investigation using modal analysis. First, an eigenvalue problem is established to compute the resonance frequencies of the SparkJet actuator, considering its configuration, boundary conditions and internal physical phenomena. To validate the eigenvalue problem, computational fluid dynamics (CFD) simulation is conducted utilizing unsteady three-dimensional Navier-Stokes equations with plasma energy source term, assuming local thermal equilibrium (LTE). Subsequently, the resonance frequencies are obtained by performing fast Fourier transform (FFT) on the thrust and average pressure data obtained from the CFD. In our investigation of the resonance frequency characteristics, eigenmode decomposition on the pressure contour obtained from the CFD is conducted utilizing the eigenfunctions obtained from the eigenvalue problem and their orthogonality. The eigenmode decomposition enables us to quantitatively evaluate the contribution of each eigenfunction to the thrust. Comparisons between the frequencies corresponding to the eigenfunctions significantly influencing on the thrust and the resonance frequencies obtained by FFT reveal a maximum error of 5.29 % and an average error of 2.35 % Moreover, when the taper angle is relatively large (approximately 45∘ or more), eigenfunctions significantly influencing on the thrust can be categorized into two distinct geometric patterns. These physically represent the waves that propagate and reflect in the streamwise or radial direction within the SparkJet actuator. This observation implies that the complex interactions of shock waves within the SparkJet actuator can be reduced to a few waves with simple physical interpretations. This may potentially aid in analyzing the physical phenomena within the SparkJet actuator.

Taylor–Couette flow and heat transfer in an elliptical enclosure with a rotating inner cylinder

We numerically investigate Taylor–Couette flows within a system consisting of an elliptical outer cylinder and a rotating inner circular cylinder, with particular emphasis on the behavior of Taylor cells. The three-dimensional unsteady Navier–Stokes equations are solved under the assumption of axial periodicity. Also, a scalar transport equation is solved for the heat transfer. Our methodology employs a Fourier-spectral meshless discretization technique, which interpolates variables at scattered points using polyharmonic splines and appended polynomials. A pressure-projection algorithm achieves the time advancement of the flow equations. We present findings for an elliptical enclosure with an aspect ratio of two, examining a range of Reynolds numbers (Re) from subcritical to 300. Our analysis includes streamlines, axial velocity contours, pressure, vorticity, and temperature profiles. The results indicate that the flow remains steady up to Re≈300 before transitioning to an unsteady state at Re≈350.

Study of the blood flow structure in personalized models of graft branch from the femoral artery

The paper presents the methodology and results of calculating the pulsating flow of blood-mimicking fluid in three personalized models of proximal anastomosis of the femo-ral artery after femoral popliteal bypass surgery performed using synthetic grafts. Per-sonalized models were built based on computed tomography data and ultrasound meas-urements of blood flow velocity in the common femoral artery and in the graft. The char-acteristics of the pulsating flow of blood-mimicking fluid were calculated by numerically solving the three-dimensional unsteady Navier-Stokes equations. Comparison of the calculated velocity field obtained for one of the personalized models with clinical meas-urement data using ultrasonic high-speed vector imaging (applying the V Flow technol-ogy implemented in the Mindray scanner) showed satisfactory agreement of the results. A comparative analysis of the flow structure in two personalized models built for the sec-ond patient one and seven months after surgery is given. It was established that the nar-rowing of the flow sections of the vascular bed, detected after seven months, due to the growth of neointima in the common femoral artery (immediately before the anastomosis) and in the initial section of the graft, led to a significant increase in gradients of the ve-locity field and the time-averaged wall shear stress (TAWSS) in the area of the anastomo-sis; at the same time, the value of the oscillatory shear index (OSI) on the wall throughout the entire anastomosis area decreased. It was also revealed that at a distance of several calibers from the anastomosis, a single-vortex, weakly swirling flow is formed in the graft, the direction of swirl in which is determined by the individual geometry of the anastomo-sis area.

Novel computational fluid dynamics-finite element analysis solution for the study of flexible material wave energy converters

The use of flexible materials for primary mover and power takeoff of wave energy converters (WECs) has attracted considerable attention in recent years, owing to their potential to enhance the reliability, survivability, and wave energy conversion efficiency. Although some reduced order models have been used to study the fluid–structure interaction (FSI) responses of flexible wave energy converters (fWECs), they are somehow inappropriate due to their limited accuracy and applicability span. To gain a deeper understanding of the physical mechanisms in fWECs, a high-fidelity approach is required. In this work, we build up a fluid–structure interaction analysis framework based on computational fluid dynamics and a finite element analysis method. The incompressible viscous flow is resolved by solving three-dimensional unsteady Navier–Stokes equations with a finite volume approach. The structure dynamics are solved by a finite element method, taking the nonlinear behavior of flexible material into consideration. A strong coupling strategy is utilized to enhance the numerical stability and convergence of the iterative process. We demonstrate the present FSI tool is able to provide rich flow field information and structural response details, such as the velocity, pressure, and structural stress distribution. This is illustrated through several case studies, including two types of fWECs. The unsteady wave–structure-interaction and the associated nonlinear phenomena are also accurately captured by this tool.

Flow structures and heat transfer characteristics in a vaneless counter-rotating turbine cavity with different cooling inflows

The cooling air is used in the gas turbine to prevent the hot gas ingress and overheating of turbine disks. In this paper, the flow structures and heat transfer characteristics of vaneless counter-rotating turbine (VCRT) with different types of cooling inflows are numerically analyzed. The three-dimensional unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with a Shear Stress Transport (SST) turbulence model are adopted. The results reveal that the inertia force, rotating effect and mainstream dominate the flow fields in VCRT cavity. The axial cooling inflow promotes the heat transfer characteristic in low pressure rotor (LPR) disk meanwhile the radial cooling inflow improves the heat transfer performance in high pressure rotor (HPR) disk. The vortexes interaction, viscous dissipation and heat transportation result in the decrease of heat transfer characteristic in the high radius region of rotor disk. The combined cooling inflow is adopted to solve the problem. It is the combination of radial cooling inlet and high position cooling inlet. The cooling air injected axially from the high position cooling inlet moves outward along the HPR disk which enhances the heat transfer characteristic. It is found that the Nusselt number and the amount of cooling air is not the simple linear relationship. The Nusselt number in HPR disk no longer increases if the high position cooling flow rate exceeds the threshold value. Compared with other types of cooling inflows, the needed amount of cooling air reduces when the combined cooling inflow is adopted. There is an optimum combined cooling flow rate which obtains the excellent heat transfer characteristics in the HPR disk.

Numerical investigation of flow around two cylinders in tandem above a scoured bed

Flow mechanisms around two cylinders in tandem arrangement above a scoured bed have been investigated using the three-dimensional unsteady Navier–Stokes equations with the Spalart–Allmaras improved delayed detached-eddy simulation model. A turbulent inlet boundary layer generation method is adopted to obtain more realistic inlet boundary conditions. First, uniform flow over a single cylinder at Re = 3900 and flow over a single cylinder above scoured beds at Re = 6000 were simulated to validate the numerical model, boundary layer generation method, and mesh density effect. Second, two cylinders in the tandem arrangement above scoured beds with six different pitch ratios L/D are investigated numerically in terms of instantaneous vortex characteristics, the hydrodynamic force, and time-averaged flow fields. The simulation results in scoured beds are compared with simulations under the near flat wall and wall-free conditions. The major findings can be summarized as follows. (1) When L/D≤2.0, the wake of two tandem cylinders is dominated by the intermittent shedding, and the downstream sand dune in the scoured bed hinders the Kármán vortex formation at the rear of the downstream cylinder. Lift force fluctuations of the two cylinders have small amplitudes, and their spectra show a multi-peak distribution and no dominant peak frequency in the spectrum of the upstream cylinder. A squarish cavity-like recirculation zone is formed between two cylinders at L/D=2.0. (2) When L/D≥3.0, the periodic vortex shedding is evident in the wake of the upstream cylinder, and the small sand berm between two cylinders has an impact on the bottom shear layer of the upstream cylinder. The downstream cylinder is periodically impacted by the vortices shed from the upstream cylinder. Lift force spectra of the upstream and downstream cylinders have the same peak frequency. (3) Due to the influence of scoured bed and the inlet boundary layer, the time-averaged lift coefficient of the upstream cylinder remains negative when L/D≥1.5, and the critical spacing for drag inversion is relatively smaller compared with under wall-free conditions. The negative pressure coefficient values of the upstream cylinder are smaller than the values in near flat wall and wall-free conditions.

Three-dimensional sweeping motion effects on hovering dragonflies

This paper describes numerical simulations of the typical hovering mode of dragonfly wings with different sweeping motions. The simulation process involves solving the three-dimensional unsteady Navier–Stokes equations and exploring the effects of the sweeping motion on aerodynamic performance. Various parameters related to the three-dimensional sweeping motion are studied, including the sweeping amplitude, phase difference between flapping and sweeping motions, asymmetry of sweeping amplitudes of the forewing and hindwing, and frequency of sweeping motion. The results show that as the sweeping amplitude of the forewing and hindwing increases from 0 to 35°, the time-averaged lift and the lift efficiency increase by ∼4 times and ∼3.6 times respectively, while the power consumption first decreases and then increases. Moreover, increasing the sweeping amplitude delays the shedding of the trailing edge vortex. A phase difference of ∼60° between flapping and sweeping maximizes efficiency and the change in phase difference can lead to vertical forces in opposite directions on the forewing and hindwing. Accordingly, the flow field interference between the two wings will be more serious. Greater symmetry between the sweeping amplitudes of the two wings leads to better lift performance. There is an optimal sweeping frequency which is also the same as the flapping motion, representing an elliptical trajectory that can make lift ∼0.75 times higher. The optimal combination of various sweeping motion parameters may contribute to better aerodynamic performance in the hovering state. This research provides theoretical guidance for the design of dragonfly-like aircraft with multiple degrees of freedom.

Influence of tunnel slope on movement characteristics of thermal smoke in a moving subway train fire

In this study, the three-dimensional unsteady Navier-Stokes equation and fully buoyant corrected Renormalization-group (RNG) k-ε turbulence model were employed to investigate the influence of tunnel slopes on the temperature distribution characteristics of a subway train moving with a fire source. The sliding grid technology was used to simulate the relative movement between the subway train and tunnel, and its reliability was verified by moving train fire experiments. It was found that the slipstream primarily determines the movement of the smoke when the subway train carries fire in transit. After the train stops, the residual slipstream drives the smoke downstream of the fire source. As the slipstream is attenuated, the smoke eventually flows backward. The influence of the tunnel slope on the temperature distribution law is mainly exhibited after the train stops. With the increase of the tunnel slope, the time elapses before the smoke counterflow increases, while the upstream temperature decreases. It was found that when the tunnel slope increased from −3% to 1%, the counterflow of smoke was delayed by 86 s.

Effects of Bent Outlet on Characteristics of a Fluidic Oscillator with and without External Flow

A fluidic oscillator with a bent outlet nozzle was investigated to find the effects of the bending angle on the characteristics of the oscillator with and without external flow. Unsteady aerodynamic analyses were performed on the internal flow of the oscillator with two feedback channels and the interaction between oscillator jets and external flow on a NACA0015 airfoil. The analyses were performed using three-dimensional unsteady Reynolds-averaged Navier-Stokes equations with a shear stress transport turbulence model. The bending angle was tested in a range of 0–40°. The results suggest that the jet frequency increases with the bending angle for high mass flow rates, but at a bending angle of 40°, the oscillation of the jet disappears. The pressure drop through the oscillator increases with the bending angle for positive bending angles. The external flow generally suppresses the jet oscillation, and the effect of external flow on the frequency increases as the bending angle increases. The effect of external flow on the peak velocity ratio at the exit is dominant in the cases where the jet oscillation disappears.

Flow control using fluidic oscillators on an airfoil with a flap

This study numerically evaluates the performance of flow control using fluidic oscillators on the NACA 0015 airfoil with a flap at different flap angles and different pitch angles of the oscillators. An inline array of fluidic oscillators is located just in front of the flap. Aerodynamic analysis was carried out using three-dimensional unsteady Reynolds-averaged Navier-Stokes equations in a computational domain that consists of the external domain around the airfoil and the internal domains in three fluidic oscillators. Flap angles of 20°, 40°, and 60° were tested with a fixed angle of attack of 8°. For each flap angle, the effects of the pitch angle of the oscillators on the aerodynamic performance were evaluated in a range of 60° to the negative value of the corresponding flap angle. It was found in this work that the oscillator jets parallel to the flap showed the best performance, which was achieved by using negative pitch angles and also bending the outlets of the oscillators. The results indicate that the aerodynamic performance varies significantly with the flap and pitch angles.

Experimental and numerical study on flow characteristics and heat transfer of an oscillating jet in a channel

A fluidic oscillator can produce self-induced and self-sustaining oscillating jet by fluid supply without moving parts. This device has attracted research interest in heat and mass transfer enhancement in recent years. In the current study, a double-feedback fluidic oscillator was numerically investigated based on three-dimensional unsteady Reynolds-averaged Navier-Stokes equations (3D-URANS) while the operating fluid is an incompressible flow. Then, the results were validated with experimental data by two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) and thermographic phosphor thermometry (TPT) for the velocity and temperature field, respectively. A grid sensitivity study was done by comparison of instantaneous and time-averaged flow fields. Additionally, the proper orthogonal decomposition (POD) method was used to find the phase information of the oscillating jet, and fast Fourier transform (FFT) analysis was used to find the frequency of the oscillating jet to validate the numerical results. The effect of the working fluid was also studied. Finally, in order to determine the effect of the Reynolds number on heat transfer enhancement, the Q-criterion was calculated to provide detailed insight into the oscillating mechanism. The results show that the non-dimensional frequency of oscillation is independent of either the working fluid or mass flow rate. Additionally, for a given fluid, increasing Re causes strong vortices and increases the frequency of oscillation. However, the convection heat transfer did not change significantly when varying the mass flow rate because the convection velocity of vortices increases as the mass flow rate is enhanced. A comparison with a free jet reveals that the oscillating jet in a channel is useful in terms of covering a larger area.

Cavitation Characteristics and Hydrodynamic Radial Forces of a Reversible Pump–Turbine at Pump Mode

As the most critical part of a hydropower station, reversible pump–turbines (RPTs) are facing the trend of high parameterization (e.g., high head and high rotation speed) with the rapid development of hydropower, which may cause more detrimental cavitation-induced hydrodynamic forces. Considering that cavitation occurs more easily under pump mode than turbine mode for the RPT, the characteristics and generation mechanism of the hydrodynamic radial force induced by cavitation of a RPT model at pump mode are investigated by computational fluid dynamics and experimental methods. Combined with the shear stress transport (SST) turbulence model, the three-dimensional (3D) unsteady Reynolds-averaged Navier-Stokes (URANS) equations are solved to calculate the cavitation flow of the RPT at various cavitation states. The blade loading and the pressure pulsations of the pressure/suction surfaces of the blade are monitored from the inlet to the outlet. Results show that with the development of cavitation, increasing cavitation bubbles covering the blade surfaces lead to the decrease of the blade loading, weaken the regularity of the pressure fluctuation, and increase the amplitude of the pressure pulsation, especially the suction surface. Furthermore, the characteristics of hydrodynamic radial forces under various cavitation states are discussed, and it is found that the values of the hydrodynamic radial forces become larger and the alternating hydrodynamic radial forces are more remarkable with the development of cavitation. Meanwhile, the symmetry of the radial force of the impeller presents a slight change due to the rotor–stator interaction between impeller and guide vanes and the symmetrical structure of the guide vanes. Then, to explore the generation mechanism of the hydrodynamic radial forces, the frequency spectrum of the pressure pulsation and hydrodynamic radial forces are analyzed comparatively. It is found that the hydrodynamic radial forces are affected by the rotor–stator interaction in the initial stage of cavitation, whereas the influence of the pressure distribution of suction surface of the blade increases with the development of cavitation.

A parallel non-nested two-level domain decomposition method for simulating blood flows in cerebral artery of stroke patient.

Numerical simulation of blood flows in patient-specific arteries can be useful for the understanding of vascular diseases, as well as for surgery planning. In this paper, we simulate blood flows in the full cerebral artery of stroke patients. To accurately resolve the flow in this rather complex geometry with stenosis is challenging and it is also important to obtain the results in a short amount of computing time so that the simulation can be used in pre- and/or post-surgery planning. For this purpose, we introduce a highly scalable, parallel non-nested two-level domain decomposition method for the three-dimensional unsteady incompressible Navier-Stokes equations with an impedance outlet boundary condition. The problem is discretized with a stabilized finite element method on unstructured meshes in space and a fully implicit method in time, and the large nonlinear systems are solved by a preconditioned parallel Newton-Krylov method with a two-level Schwarz method. The key component of the method is a non-nested coarse problem solved using a subset of processor cores and its solution is interpolated to the fine space using radial basis functions. To validate and verify the proposed algorithm and its highly parallel implementation, we consider a case with available clinical data and show that the computed result matches with the measured data. Further numerical experiments indicate that the proposed method works well for realistic geometry and parameters of a full size cerebral artery of an adult stroke patient on a supercomputers with thousands of processor cores.

Numerical simulation of dynamic multi-body separation flowfields

In this paper, three-dimensional unsteady Navier-Stokes equations coupled with six-degree-of-freedom equations are solved numerically to simulate the process of multi-body separation in the condition of high speed and high altitude. Overset grids are adopted to deal with the relative motion between two different parts. In order to study the security of separating process, the trajectories and attitudes of different parts are calculated and the characteristics of flow field during separation are analyzed carefully. Different initial angles of attack are considered during the simulation and its influence on the separation process is analyzed. The result shows that the initial angle of attack has significant impact on the flow field. Large angle of attack would cause shock/shock interactions between the two parts, threatening the safety of the separating process.

The effect of pulsating parameters on the spatiotemporal variation of flow and heat transfer characteristics in a ribbed channel of a gas turbine blade with the pulsating inlet flow

This paper presents an investigation on the cooling performance in a ribbed channel with the pulsating inlet flow. The flow structures and heat transfer characteristics are simulated by solving the three-dimensional Unsteady Reynolds-Averaged Navier-Stokes equations (U-RANS) and the Shear Stress Transport (SST) turbulence model coupled with the γ-Reθ transition. The influence of pulsating parameters in terms of pulsating amplitudes and frequencies on the cooling performance are evaluated at the Reynold number of 10000. The results obtained show that the coolant velocity variation corresponds to the inlet velocity variation, almost the sinusoidal curve shape. The heat transfer performance influenced by the turbulence intensity is also the sinusoidal curve shape and increases with increasing pulsating amplitudes and frequencies. The pressure loss penalty related to the flow characteristics is also the sinusoidal curve shape while the thermal performance indexes at four time frames (1T/4, 2T/4, 3T/4 and 4T/4) show the 90-degree phase difference with the sinusoidal curve. Additionally, the thermal performance increases with increasing pulsating amplitudes and frequencies.

Numerical Investigation on Flapping Aerodynamic Performance of Dragonfly Wings in Crosswind

Numerical simulations are performed to investigate the influence of crosswind on the aerodynamic characteristics of rigid dragonfly-like flapping wings through the solution of the three-dimensional unsteady Navier-Stokes equations. The aerodynamic forces, the moments, and the flow structures of four dragonfly wings are examined when the sideslip angleϑbetween the crosswind and the flight direction varied from 0oto 90o. The stability of the dragonfly model in crosswind is analyzed. The results show that the sideslip angleϑhas a little effect on the total time-average lift force but significant influence on the total time-average thrust force, lateral force, and three-direction torques. An increase in the sideslip angle gives rise to a larger total time-average lateral force and yaw moment. These may accelerate the lateral skewing of the dragonfly, and the increased rolling and pitching moments will further aggravate the instability of the dragonfly model. The vorticities and reattached flow on the wings move laterally to one side due to the crosswind, and the pressure on wing surfaces is no longer symmetrical and hence, the balance between the aerodynamic forces of the wings on two sides is broken. The effects of the sideslip angleϑon each dragonfly wing are different, e.g.,ϑhas a greater effect on the aerodynamic forces of the hind wings than those of the fore wings. When sensing a crosswind, it is optimal to control the two hind wings of the bionic dragonfly-like micro aerial vehicles.

Evolution of the flow structures in an elevated jet in crossflow

The characteristic flow features of an elevated square jet in crossflow (EJICF) are studied numerically using large eddy simulation. The effect of jet to crossflow velocity ratio, also called velocity ratio (VR), on the flow field of an elevated jet in crossflow (EJICF) is investigated. All the computations are carried out at a Reynolds number (Re) of 20 000, based on the outer width of the stack (d) and free stream crossflow velocity (U∞), for four different velocity ratios (VR), namely, 0.5, 1.0, 1.5 and 2.0. The stack used in this study has an aspect ratio h/d = 7. The shear-improved Smagorinsky model has been used to account for the subgrid scale stress while solving the filtered three-dimensional unsteady Navier-Stokes equations. The modes of shedding in the stack wake are analyzed using both instantaneous and phase-averaged data. It is found that at a low jet to crossflow velocity ratio (VR = 0.5), the stack wake exhibits two different modes of shedding, symmetric and antisymmetric, similar to the wake of a wall mounted finite-size cylinder. At higher velocity ratios (VR ≥ 1), the stack wake shows the presence of only antisymmetric modes of shedding. It is also found that velocity ratio (VR) has a profound effect on the source of vorticity of the jet shear layer structures near the upwind side. At VR = 0.5, the upstream sides of the jet shear layer structures are found to draw their vortices from the outer surface of the stack boundary layer. At higher VR, they seem to be fed by the vorticity of the boundary layer developed on the inner wall surface of the stack. Both jet vortices and stack wake vortices are found to be present in the jet wake, and the shedding frequency of both the jet wake and the stack wake is found to be same. The spatial evolution of the counter-rotating vortex pair in the case of an EJICF is found to be similar to that of a JICF.

Numerical simulation of forced circular jets: Effect of flapping perturbation

The forcing in round jets has large scale effects on the development and characteristics of the flow field such as the entrainment, spreading rate, and mixing of the flow. In the present work, an active control technique called the large scale flapping perturbation is studied for influencing the evolution of the circular jet. Direct numerical simulation of incompressible, spatially developing circular jets at a Reynolds number of 1000 is reported. The flow field has been explored by solving three-dimensional unsteady Navier-Stokes equations using second order spatial and temporal discretization. Among the considered variables (apart from the excitation amplitude), the perturbation frequency is the most important controlling parameter. For a circular jet at an excitation frequency of 0.1, there is evidence of a Y-shaped bifurcation on the bifurcating plane, while no bifurcation is observed on the other orthogonal plane. With an increase in the excitation frequency to 0.3, the circular jet issued from the orifice divides itself into three parts and a ψ-shaped bifurcation is obtained on the bifurcating plane. The development of the ψ-shaped bifurcation may be due to the interaction of the consecutive vortex ring and the formation of elongated vortices. However, with further increase in the excitation frequency, the spreading rate becomes weaker with the evidence of formation of the ψ-shaped bifurcation.

Tidal current energy potential assessment in the Avilés Port using a three-dimensional CFD method

Tidal energy is considered as an energy resource of maximum interest in both technical and research fields due to its largely unexploited energy potential. The use of hydrokinetic microturbines is now an attractive option with reduced environmental impact. The first step to evaluate the feasibility of a hydrokinetic microturbines installation is to perform a study of the velocity field characteristics and therefore the energy potential available. Up to now, different numerical models, of one, two and three spatial dimensions have been applied to evaluate the tidal potential in large areas. Due to the high computational resources needed, they include simplifications, like avoiding a precise study of the velocity in the vertical dimension, resulting in incomplete estimations of the available kinetic energy. To complete these estimations, the research presented sets out a methodology to evaluate the current effects, velocity profiles and the energy potential derived from tide movements in an estuary or port by solving the full Navier–Stokes equations. It also considers the water–air interface in the numerical scheme. The methodology is based, firstly, on the definition of a three-dimensional geometrical model of the geographical area of study, and then, the complete model is meshed with finite volumes, where the full three-dimensional Unsteady Navier–Stokes equations are solved. The methodology was applied and validated with a three-dimensional water–air numerical model of the port of Aviles (Spain). In conclusion, water surface elevations, averaged speed cycles, velocity profiles as a function of depth and tidal power and energy data have been obtained without the usual simplifications, which will mean an evaluation more accurate when assessing the implementation of a power generation system.

Effects of endwall profiling near the blade leading edge on the sealing effectiveness of turbine rim seal

Endwall profiling designed to reduce secondary flow loss may change the local pressure distribution which has an impact on the sealing effectiveness of a rim seal. This paper presents a numerical comparison of the sealing effectiveness of the rim seal and the aerodynamic performance of the blade with five different endwall profiling near the blade leading edge. Three-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) equations coupled with a fully developed shear stress transport (SST) turbulent model are utilized to investigate the sealing effectiveness and the flow characteristics of turbine rim seal. The numerical method for the pressure field and sealing performance of turbine rim seal is validated on the basis of published experimental data. The total-to-static efficiency of the blade and the minimum sealing rates of the rim seal with five endwall profiling near blade leading edge are compared. The baseline, convex and concave cases are selected to investigate the transient variation of the sealing effectiveness and the flow field in the disc cavity. In comparison with baseline case, the convex endwall makes the high pressure area move forward, increases the mainstream circumferential pressure fluctuation, and reduces the sealing effectiveness. The concave endwall reduces the local pressure and the mainstream circumferential pressure fluctuation, and increases the sealing effectiveness. However, the concave endwall profiling enhances the vortex in the blade passage and increases the secondary flow loss. The flow field near the rim seal with different endwall profiling is illustrated and analyzed.