Reθ Transition Model Research Articles

A novel multi-fidelity optimization framework for high-altitude propellers

A novel optimization methodology is presented for optimizing high-altitude propellers operating in the lower stratosphere. The proposed methodology combines a Bayesian optimization approach for most design variables and Vortex Theory for the optimization of twist distribution and rotational velocity. For the Bayesian optimization part of the problem, a multi-fidelity approach is employed with three levels of modeling fidelity. The considered fidelity levels, from lower to higher, are: Vortex Theory, and 3D Reynolds-Averaged Navier-Stokes (RANS) with the use of γ−Reθ transition model, converged with first-order upwind, and second-order upwind for the momentum equations. Additionally, the optimization problem involves two objectives: maximizing the cruise efficiency and minimizing the total volume of the propeller. To enhance the performance of multi-fidelity, multi-objective (MFMO) acquisition functions, a novel algorithm is proposed. The proposed optimization methodology demonstrates its effectiveness in generating several high-performing propeller designs and proves to be more efficient than an equivalent problem formulation relying solely on Bayesian optimization. Post-processing of optimization data reveals new design variable bounds that correspond to more efficient blade shapes. These findings provide insights into some important geometric features of high-altitude propellers and establish guidelines for future optimization efforts within the specified thrust and power consumption ranges. Finally, simulations of the best-performing designs across a range of advance ratios and altitudes confirm their high performance in various operating conditions.

Characteristics of Laminar Separation Bubble With Varying Leading-Edge Shapes and Deflections of the Trailing-Edge Flap

Abstract A series of implicit large eddy simulations (ILES) is carried out to examine the characteristics of a leading edge (LE) separation bubble. The test case comprises a flat plate with an elliptic leading edge (ELE), which is equipped with a trailing edge flap. Simulations are carried out (a) at three different flap angles (20 deg, 30 deg, 90 deg) and (b) using two different geometries of ELE where the ratio of the semimajor to semiminor axis is set to either 2:1 or 4:1. The flap is modeled using the immersed boundary method, which is computationally economical as it avoids regenerating the grid for varying flap angles. The results show that (a) the flow separates at lower flap deflection angles with a decrease in the aspect ratio of the ELE from 4:1 to 2:1 (b) an increase in the flap angle promotes separation at the LE due to an increase in the blockage in the bottom passage and a subsequent increase in the flow incidence at the leading edge. Simulations are also carried out using the γ−Reθ transition model and comparisons are drawn against ILES and experiments. Although the qualitative trends predicted using both ILES and Reynolds-Averaged Navier–Stokes (RANS) agree with the experiments, both approaches predict relatively shorter separation bubbles. This is attributed to the excess flow blockage in experiments due to the support plates, which are not modeled in the simulations. Nevertheless, the results demonstrate the superior accuracy of ILES over the RANS model.

Flows past airfoils for the low-Reynolds number conditions of flying in Martian atmosphere

Fixed-wing aircraft with potential for long-duration flight and efficient manoeuvrability is expected to be the next frontier of Mars surface exploration. However, the feasibility of such an aircraft demands for wing airfoil suitable for low Reynolds flight conditions. In this framework, the paper deals with the computational study of two wing sections specifically designed for Mars exploration aircraft. Two-dimensional steady Reynolds-averaged Navier–Stokes simulations, using the computational fluid dynamics tool SU2 with the γ−Reθ transition model and the XFoil panel flow solver, are performed to address airfoils’ aerodynamics. Computational tools are validated by simulating flow past the Eppler 387 airfoil at Re∞=60×103, and comparing the results with experimental data collected in wind tunnel experiments. Aerodynamic performances of optimal wing sections are investigated at Re∞=3.4×104 by considering pressure coefficients and skin friction coefficients. The application of a literature-based correlation, specifically tailored to identify transition and reattachment locations, is extended to separation point detection. Computational Fluid Dynamics analysis conducted on the studied airfoils revealed that separation occurs within the laminar regime. Additionally, examination of turbulent shear stresses highlighted the role of airfoil curvature in counterbalancing the suction defect produced by the laminar separation bubble. This curvature-induced effect was found to play a crucial role in optimizing airfoil efficiency.

Numerical study of scale effects on the open water performance of a rim-driven thruster

This paper presents the study of scale effects on the open water performance of a rim-driven thruster (RDT) based on Computational Fluid Dynamics (CFD) simulations. For marine propellers, the effects of viscosity are often significant when there is a dramatic change in Reynolds number, which occurs when the results from model scale tests are extrapolated to propellers at full scale. Reynolds-Averaged Navier–Stokes (RANS) simulations with the Moving Reference Frame (MRF) approach are carried out in ANSYS Fluent for the RDTs under different working conditions. Considering the potential transitional flow on the propeller at model scale, the γ−Reθ transition model is adopted which can better resolve the boundary layer and yield more accurate results for transitional flows. From the simulations, it is observed that the duct and rim are more affected by the scale effects than the propeller. When the Reynolds number increases, there is a small amount of increment in the total thrust coefficient but a significant decrease in the total torque coefficient, resulting in a substantial improvement in hydrodynamic efficiency of the full scale RDT compared to the model scale.

Numerical investigation of the effect of dielectric barrier discharge plasma actuator-induced momentum jet parameters on flow control of an oscillating wind turbine airfoil

Wind turbine blades that undergo pitch-oscillating motion exhibit dynamic stall behavior, deteriorating their aerodynamic performance. In this regard, dielectric barrier discharge (DBD) plasma actuators are promising tools for controlling flow by inducing momentum jet flow. Four key parameters typically determine the momentum jet: length, power, angle, and injection location. This paper presents a numerical study that investigates the effect of these parameters on flow control around an SG6042 wind turbine airfoil at a Reynolds number of Rec=1.35×105. For this sake, the study considers various numbers of actuators, force directions, and installation locations. This study utilizes two-dimensional, unsteady Reynolds-averaged Navier–Stokes equations with the γ–Reθ transition model. The results demonstrate the significant effects of momentum jet parameters on flow control. As the location of single-DBD moves closer to the leading edge, its effectiveness on the low-pressure vortex growth increases, resulting in a smaller vortex and a lower drag coefficient. Furthermore, an increase in the power and length of the jet leads to effective flow control. Vortices on the airfoil's suction surface are recognized as influential factors in the aerodynamic performance. As a result, the co-flow actuator significantly improves the performance of the airfoil by inducing the momentum jet in this region. Flow control is augmented when the actuator is installed at a location with a near-surface jet angle. The leading edge case with a co-flow single-DBD achieves the best control performance. In this instance, the dynamic stall occurs approximately 5% later than in the case of the clean configuration.

Repair Parameter Design of Outer Reinforcement Layers of Offshore Wind Turbine Blade Spar Cap Based on Structural and Aerodynamic Analysis

The influence of the outer reinforcement layers on the repair structure and aerodynamic performance was studied. Firstly, a continuous damage mechanics model was established, and the 3D Hashin criterion and cohesive zone material model were used to analyze the damage repair model. The failure load deviation was 5.5%. Secondly, on the basis of the γ−Reθ transition model and SST–ω turbulence model, the aerodynamic analysis model of DU300 airfoil was established. The numerical simulation results showed that the lift coefficient and pressure distribution at the angle of attack of 10° and 15° were deviated from the experimental values by 2%. Furthermore, 27 structural repair models, nine 2D aerodynamic repair models, and a 3D full-scale blade model were designed. It was found that, when the repair length accounted for 60% of the total model length, the failure load increased by 22%, but the aerodynamic power with the repair length of 10 m was decreased by 0.137%. When the repair area was large and the repair height was from 4 mm to 6 mm, the failure load was greatly increased by about 30%, and the aerodynamic pressure distribution and static pressure field fluctuated significantly. The results show that the structural and aerodynamic characteristics were closely related to the repair parameters.

Uncertainty quantification study of the aerodynamic performance of high-altitude propellers

Performance evaluations for propellers operating at high altitudes are subject to increased uncertainty due to scarce experimental or flight data and difficulties in modeling low Reynolds number flows. For this reason, the Polynomial Chaos Expansion (PCE) method is used in this paper to assess the performance uncertainty of propellers operating at high altitudes. Aleatoric (i.e. linked to the geometry or operating conditions) and epistemic (i.e. linked to the mathematical model describing the flow) uncertainty variables are included in this study to estimate the total uncertainty related to performance predictions made by two physical models, namely 3D RANS with the use of γ−Reθ transition model and Blade Element Momentum Theory (BEMT). In order to validate the proposed method, multipoint uncertainty quantification (UQ) studies are performed for two benchmark propeller geometries under various operating conditions for which experimental data are available. The UQ method is further illustrated on a propeller operating at high altitude. The efficacy of UQ with Computational Fluid Dynamics (CFD) and BEMT is compared and the most influential uncertain variables are found using Sobol's total order indices. As a result of the CFD-based uncertainty quantification studies, two major uncertain variables are identified, providing a direction for more computationally affordable UQ studies.

Investigation and Design of the Transonic Laminar Flow Characteristics in a Laminar Aircraft

Reducing drag is critical to aircraft design. In recent years, laminar technology has become one of the most important feasible technologies for civil aircraft drag reduction design under many design constraints. However, various factors have a certain impact on the laminar flow characteristics in the state of transonic flight. Therefore, it is necessary to deeply understand the specific effects of various flight parameters on the characteristics of laminar flow. In this paper, a parameter sensitivity analysis for a central experimental wing in a special layout aircraft was carried out to investigate its transonic laminar characteristics. Then, the airfoil of the central experimental wing of the aircraft was designed for real flight. The RANS (Reynold-averaged Navier–Stokes) method combined with the γ−Reθ transition model based on local variables was used. The computational approach was validated by the wind tunnel tests and analyzed by the grid independence analysis. The sensitivity mainly focuses on the transition location and the length of the laminar flow zone of the central experiment under different boundary conditions. The transonic transition was affected by a variety of interacting factors that include FSTI (free stream turbulence intensity), pressure gradient, Re (Reynolds number), Ma (Mach number) and α (angle of attack, degree). The essence of the transition is the disruption of flow stability caused by the increase in flow entropy. Among these factors, FSTI directly affects global flow stability, and the pressure gradient affects local flow stability. Ma and α can indirectly affect the flow stability by changing the pressure gradient. Re can control the boundary layer properties to change the flow stability, whereas its effect is easily determined by the pressure gradient. Finally, the improved design of the airfoil with the central experimental wing was conducted. The design of weak shock wave and aerodynamic load on the rear part of the airfoil can improve the aerodynamic characteristics (CL, lift coefficient, increases by 0.28) of the airfoil, which can reduce the load burden on the outboard wing without affecting the laminar flow characteristics of the airfoil. In the next step, cross-flow instability will be considered.

Predicting transition with wall-distance-free SST k-[formula omitted] model

Unlike the correlation-based γ–Reθ transition model, an exceptionally simplified approach is applied to extend the wall-distance-free (WDF) model toward transition predictions. An anisotropic stress-intensity parameter as a function of eddy-to-laminar viscosity ratio is introduced, preserving the “flow-structure-adaptive” characteristic. The prospective parameter is included with the constitutive relation for the eddy-viscosity. The proposed formulation is intrinsically plausible, having a dramatic influence on the prediction of bypass, separation-induced and natural transitions. The newly devised transitional WDF (TWDF) model is further modified to compute separation-induced transition over a low-Reynolds number (LRN) airfoil. The curiosity toward airfoil performance at an LRN has been executed with growing attention to marine autonomous systems. An extra viscous-production term Pklim is added to the turbulent kinetic energy (k) equation to ascertain proper development of k at the viscous sublayer region. Reliance on this Pklim is likely to be suitable for forecasting separation-induced transition over an LRN airfoil. Results illustrate that the TWDF model sustains decent agreement with the four-equation γ–Reθ transition model.

Estimation of Discretization Uncertainty Using the γ−Reθ Transition Model for Transitional Flows on 6:1 Spheroid

Abstract This paper aims to estimate the surface mesh size related discretization uncertainties using the γ−Reθ transition model combined with the shear stress transport (SST) k–ω turbulence model. For comparison, this work employs an available experimental study performed with a 6:1 prolate spheroid. The grid convergence index (GCI) study is performed for axial force, surface skin friction, and pressure coefficients with three levels of meshes. The transition model estimates the axial force coefficients (CX), approximately half of which are obtained using fully turbulent calculations with higher GCI values. The GCI values around the axial force coefficients for the level-2 mesh are less than 1% based on fully turbulent calculations. However, with the transition model, these values for the same mesh level increase to 10%. While the GCI values of surface pressure coefficients are very small based on both fully turbulent and transition model calculations, these coefficients show differences at the trailing part of the spheroid. Significant differences are also observed in the surface friction coefficients. While the model captures drastic changes in terms of transition in the surface friction coefficients at the suction side of the spheroid, such drastic change is not observed in fully turbulent calculations. On the other hand, there is no sign of any transition phenomenon at the pressure side, contrary to the observations of experimental measurements. The transition model is not able to estimate the transition front geometry correctly. The GCI values of the surface friction coefficients increase dramatically, up to 765% around the transition regions.

Effects of transition turbulence modeling on the hydrodynamic performance prediction of a rim-driven thruster under different duct designs

The rim-driven thruster (RDT) is an innovative marine propulsion device. During the design process, scale models of RDTs are frequently used and also smaller sized units used in Underwater Remotely Operated Vehicles (ROVs) or Autonomous Underwater Vehicles (AUVs) are often likely to operate under conditions where the boundary layer on the surface of the propeller makes a transition from a laminar to a turbulent regime. Accurately resolving this transitional boundary layer can help improve the performance prediction of RDTs. Studies addressing this are scarce and hence the present work investigates the influence of transition turbulence modeling on the hydrodynamic performance prediction of an RDT with different duct configurations by means of computational fluid dynamics (CFD). The turbulence models employed in this study are the two-equation SST k−ω model and the four-equation γ−Reθ transition model. For this purpose, three duct designs are considered, notably two modified 19A and 37 ducts, and one symmetric duct design often seen in RDT designs. Numerical calculations are performed using ANSYS Fluent 19.1 whilst a verification and validation study is firstly carried out to ensure the accuracy of the numerical model. The results demonstrate that the γ−Reθ transition model can better capture the transitional flow on the blade’s surface, and substantial discrepancies are observed between both turbulence models with regard to the streamline patterns near the blades on the one hand and skin friction profiles on the other. The torque calculated using the transition model better fits the experimental data, suggesting that it is more suitable to estimate the RDT performance. Three RDT duct designs are simulated which enable different ways to guide the incoming flow and it is shown that they have an important influence on the propeller performance. The results of the open water performance of the three different duct profiles are presented and compared, along with detailed analyses of the flow fields.

Improved Prediction of Sheet Cavitation Inception Using Bridged Transition Sensitive Turbulence Model and Cavitation Model

Sheet cavitation inception can be influenced by laminar boundary layer flow separation under Reynolds numbers regimes with transitional flow. The lack of accurate prediction of laminar separation may lead to massive over-prediction of sheet cavitation under certain circumstances, including model scale hydrofoils and marine propellers operating at relatively low Reynolds number. For non-cavitating flows, the local correlation based transition model, γ−Reθ transition model, has been found to provide predictions of laminar separation and resulting boundary layer transition. In the present study, the predicted laminar separation using γ−Reθ transition model is bridged with a cavitation mass transfer model to improve sheet cavitation predictions on hydrofoils and model scale marine propellers. The bridged model is developed and applied to study laminar separation and sheet cavitation predictions on the NACA16012 hydrofoil under different Reynolds numbers and angles of attack. As a reference case, the open case of the PPTC VP1304 model scale marine propeller tested on an inclined shaft is studied. Lastly as an application case, the predictions of cavitation on a commercial marine propeller from Kongsberg is presented for model scale conditions. Simulations using the bridged model and the standard unbridged approach with k−ωSST turbulence model are performed using the open-source package OpenFOAM, both using the Schnerr–Sauer cavitation mass transfer model, and the respective results are compared with available experimental results. The predictions using the bridged model agree well compared to experimental measurements and show significant improvements compared to the unbridged approach.

Conjugate Heat Transfer Simulation and Entropy Generation Analysis of Gas Turbine Blades

Abstract Reynolds-averaged Navier–Stokes (RANS) model-based conjugate heat transfer (CHT) method is so far popularly used in simulations and designs of internally cooled gas turbine blades. One of the important factors influencing the RANS-based CHT method's prediction accuracy is the choice of turbulence models for different fluid regions because the blade passage flow and internal cooling have considerably different flow features. However, most studies in the open literature adopted the same turbulence models in the blade passage flow and internal cooling. Another important issue is the comprehensive evaluation of the losses caused by the flow and heat transfer for both fluid and solid regions. In this study, a RANS-based CHT solver suitable for subsonic/transonic flows was developed based on OpenFOAM and then validated and used to explore suitable RANS turbulence model combinations for internally cooled gas turbine blades. Entropy generation, being able to weigh the losses caused by both flow friction and heat transfer, was used in the analyses of two vanes with smooth and ribbed cooling ducts to reveal the loss mechanisms. Findings indicate that the combination of the k–ω SST–γ–Reθ transition model for passage flow and the standard k–ε model for internal cooling provided the best agreement with measurement data. The relative error of vane surface dimensionless temperature was less than 3%. The variations of entropy generation with different internal cooling inlet velocities and temperatures indicate that reducing entropy generation was contradictory with enhancing heat transfer performance. This study, which provides a reliable computing tool and a comprehensive performance parameter, has an important application value for the design of advanced internally cooled gas turbine blades.

Circulation dynamics of small-amplitude pitching airfoil undergoing laminar-to-turbulent transition

This study is motivated by the non-linear behavior of the lift response of a pitching airfoil with a small amplitude and frequency where a linear behavior is expected. The validated γ−Reθ transition model coupled with k−ωSST (shear stress transport) turbulence model was utilized to solve the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for a harmonically pitching NACA 0012 at Reynolds numbers 75×103, 200×103 and reduced frequencies 0.05−0.3. First, the numerical setup was validated against experimental results for a pitching airfoil undergoing laminar-to-turbulent transition. Then, the circulation dynamics were investigated following an exact derivation of the Kutta condition. Unlike the classical Kutta condition which assumes a vanishing pressure loading at the sharp trailing-edge, it is shown that the transition induces non-linearity in the lift dynamics by creating a significant pressure variation across the boundary layer in the vicinity of the trailing-edge, affecting the development of the bound circulation around the airfoil. Moreover, the effects of reduced frequency, pitching amplitude and Reynolds number on the circulation dynamics were studied in both frequency and time domains. The results shed light on the further enhancement of potential flow-based solutions to capture non-linearity in the lift dynamics due to transition.

Aerodynamic performance and transition prediction of low-speed fixed-wing unmanned aerial vehicles in full configuration based on improved γ − Reθ model

A transition prediction method based on the coupled Michel transition Criterion and γ−Reθ transition model has been proposed for aerodynamic analysis of low-speed fixed-wing UAVs. Firstly the Michel transition criterion is utilized to estimate the transition momentum thickness Reynolds number R˜eθt. Then an empirical relation is used to obtain the critical momentum thickness Reynolds number Reθc and the length of the transition region Flength. Finally, the improved transition model is coupled with Reynolds Averaged Navier-Stokes (RANS) equations to conduct the aerodynamic analysis based on FLUENT platform. The method is validated through the cases of SD7032 airfoil and FX 63-137 wing, which prove that the new method can improve the stability and convergence of the original γ−Reθ transition model in FLUENT. Comparison study of the new method and S-A fully turbulent model is implemented to analyze aerodynamic characteristic of a low speed UAV. The results show that the maximum lift-to-drag ratio is about 17.1 and 15.6 by transition model and S-A model, respectively. Compared to S-A model, the computed lift coefficient with transition model is basically similar, but the drag coefficient is less by 15%. The results demonstrate that the improved transition model can predict transition phenomenon well.

A two-equation local-correlation-based laminar-turbulent transition modeling scheme for external aerodynamics

A local-correlation-based laminar-turbulent transition model has been developed for external aerodynamic problems and coupled with the Spalart-Allmaras (S−A) turbulence model. This laminar-turbulent transition modeling scheme is then termed as the γ−SA model. It has been validated against a series of two- and three-dimensional test cases with a relatively wide range of Reynolds numbers and free-stream turbulence intensity levels. Results show that the γ−SA model can give accurate transition-onset-location predictions, as well as more accurate predictions on the force coefficients than the underlying S−A turbulence model at various angles of attack. Comparison with the classic SST−γ−Reθ transition model shows that the γ−SA model can achieve comparable results, with the expect of less time or memory consumption, as the γ−SA model has two equations fewer than the former one. With a newly proposed local-farfield mixed turbulence intensity strategy, the turbulence intensity on the inlet or farfield boundary can be conveniently set directly with the value tested for the wind tunnel or the value as expected, while achieving local turbulence intensity variation. Moreover, the γ−SA model employs only local variables, which makes it totally modern-CFD-compatible and very appropriate for large-scale parallel running using unstructured grids. In the future, it can be modified into a robust and efficient DES-type model with the consideration of transition process.

Rotor–Stator Interactions in a 2.5-Stage Axial Compressor—Part II: Impact of Aerodynamic Modeling on Forced Response

Abstract The main objective of this study is the validation of numerical forced response predictions through experimental blade vibration measurements for higher order modes of a blade-integrated disk (blisk). To this end, a linearized and a nonlinear frequency domain CFD methods are used, as well as a tip timing measurement system. The focus is on the blade excitation by downstream vanes, in particular, because this study shows that the correct prediction of acoustic modes is of key importance in this case. The analysis of these modes is presented, both experimentally and numerically, in Part I of this publication. The grid independence study for the aerodynamic work on the blade surface conducted in this part shows a possible prediction uncertainty of more than 100% when a coarse grid is chosen. For the validation of the numerical setup, a study was performed using different turbulence and transition models. The results are compared to the measured performance map, to a 2D field traverse conducted with a pneumatic probe, and to data gained by unsteady pressure sensors mounted in the casing of the compressor. Flow features relevant for the prediction of blade stresses are best represented using the SST turbulence model in combination with the γ–ReΘ transition model. Nonlinear simulations with this setup are able to predict the blade stresses due to downstream excitation with an average difference of 23% compared to tip timing measurements. Single row linearized CFD methods have shown to be incapable of making a correct stress prediction when acoustic modes form a major part of the exciting mechanisms. In summary, this two-part publication proves the importance of acoustic rotor–stator interactions for blade vibrational stresses excited by downstream vanes in a state-of-the-art high-pressure compressor.

A numerical study on the interaction between forward and aft propellers of hybrid CRP pod propulsion systems

This paper presents a numerical study on the interaction between the forward and aft propellers of hybrid CRP pod propulsion systems (CRP-POD) in open water with a focus on both global quantities, that is, thrust and torque, and flow details, such as vortical structure, slipstream evolution, and lateral load on the pod unit. Improved delayed detached eddy simulation (IDDES) method is adopted and combined with the γ−Reθ transition model. The open-water characteristics of CRP-POD obtained by CFD are in satisfactory agreement with model test data. Two sets of CRP-PODs with different propeller geometries are considered. It is found independently of propeller geometry that (i) in terms of thrust and torque, the forward propeller is slightly affected by the aft propeller, while it has a large effect on the aft propeller; (ii) the wake of the forward propeller is accelerated in the axial direction and weakened in the tangential direction by the aft propeller; and (iii) the time-averaged lateral force on the pod unit is reduced remarkably by the propeller-propeller interaction. However, the vortex interaction between the forward and aft propellers depends significantly on the propeller geometry. In the case when the tip vortices shed by the forward and aft propellers can directly collide with each other, the vortical structure in the wake becomes unstable and rapidly breaks down.

Effects of boundary layer transition on the aerodynamic analysis of high-lift systems

Transition to turbulence is known as a factor that impacts the performance of high-lift devices, but only a few numerical results that include transition are available in the literature. We use the Langtry-Menter γ−Reθ transition model to study the influence of transition to turbulence in global aerodynamic coefficients and flow topology in three-dimensional high-lift configurations. The influence of turbulence inflow variables is also addressed. Numerical results are compared with previous results obtained with the Shear Stress Transport (SST) turbulence model, which does not account for transition effects. The numerical simulations are performed using configuration “one” from the 1st AIAA CFD High-Lift Prediction Workshop. Experimental data from the NASA Langley 14 by 22-ft Subsonic Wind Tunnel provide the global aerodynamic information for the verification of our numerical results. It is observed that the inclusion of transition to turbulence impacts the flow topology, as well as the aerodynamic coefficients.

Relevance of transition turbulent model for hydrodynamic characteristics of low Reynolds number propeller

The propeller of an Autonomous Underwater Vehicle (AUV) operates at low Reynolds number in laminar to turbulent transition region. The performance of these propellers can be calculated accurately using RANSE solver with γ − Reθ transition model. In this study, the global and local hydrodynamic characteristics of open and ducted propeller are investigated using the γ − Reθ transition model. The capability of the γ − Reθ transition model to capture laminar to turbulent transition on the surface of the open propeller is demonstrated by comparison with published experimental results. The application of transition model for the propeller Ka-4-70 inside the duct 19A shows that the centrifugal forces are dominant at low Reynolds number and the flow is mainly directed in the radial direction. The transition model is able to predict complex flow physics such as leading-edge separation, tip leakage vortex, and the separation bubble on outer surface of the duct. The accurate prediction of these flow phenomenon can lead to correct calculation of global hydrodynamic forces and moments acting on the propeller at low Reynolds number.