Unsteady RANS Research Articles

Numerical Investigations on Gas Ingestion Mechanism Based on Flow Instabilities in Rim Seal and Cooling Characteristics of Endwall in a 1.5-Stage Axial Turbine

Abstract The sealant flow and rim seal at the periphery of cavities formed between rotor and stator disks prevent the high-temperature gas from ingesting into disk cavities and reduce the use of secondary air bleeding from a compressor. The unsteady sealing performance of rim seal and the cooling characteristics of sealant flow on endwall of a 1.5-stage axial turbine are studied by solving the three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) equations via shear stress transfer (SST) turbulence model. Besides, mass transfer analogy is introduced to predict the sealant distribution which makes the numerical sealing effectiveness in front and aft cavities agree well with experimental data. The accuracy of the numerical method is verified. The sealing effectiveness in cavities and the flow field in rim seal clearance are analyzed, and the film cooling performance on endwall is explored. The results show that, compared with Φ0=0.0170, the area-averaged sealing effectiveness εc on stator face is increased by 19.05% when Φ0=0.500 in the front cavity, and compared with Φ0=0.0042, the area-averaged sealing effectiveness εc on stator face is increased by 9.82% when Φ0=0.096 in the aft cavity. The nonaxisymmetric pressure on the endwall near rim seal and Kelvin Helmholtz unstable vortices arise due to the circumferential velocity difference between main flow and cavity flow. The flow field in the rim seal clearance is jointly affected by these two factors. The flow pattern in the front rim seal clearance is mainly affected by unstable vortex while the flow pattern in the aft rim seal clearance depends on the circumferential pressure distribution. According to FFT, the most significant frequency of flow field variety is about 1200 Hz and 400 Hz (corresponding to two and six blades passing periods) in front and aft rim seals, respectively. The time-averaged cooling effectiveness increases with the increase of sealant flow on endwall and decreases gradually in the axial direction. The unsteady flow behavior of cooling effectiveness on endwall is also discussed in detail.

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.

Dynamic performance of a fluidic diode subjected to periodic flow

This paper presents the dynamic behavior of a fluidic diode (FD) subjected to periodic flow (oscillatory flow). This study captures the transient performance of the FD, which a steady-state flow analysis cannot predict, helping in better prediction of the performance and in designing an efficient model for the real sea flow profile. The FD offers variable resistance to the flow depending on its geometrical shape. Its performance is given by diodicity, which is a ratio of pressure drop in reverse to forward flow. It is used with the turbine to improve flow rectification. The numerical model is solved for three-dimensional unsteady Reynolds-Averaged Navier Stokes equations using ANSYS Fluent 16.1. The article presents the FD's detailed transient flow behavior and performance with the turbine. The FD operating in oscillatory flow performed better than in a steady flow because of the dynamic nature of the fluid. The analytical study shows that the performance of FD with turbine performed better at lower flow-coefficient.

Numerical study of the effect of geometric scaling of a fluidic oscillator on the heat transfer and frequency of impinging sweeping jet

In this research, the effects of a new approach of geometric scaling on the heat transfer rate of a hot plate impinged by a sweeping jet were investigated numerically. In this approach, the throat of the fluidic oscillator is constant while the geometry is scaled. Ansys Fluent 2020R2 was used to solve unsteady Reynolds-averaged Navier–Stokes (URANS) equations with a k-ω SST turbulence model inside and outside the fluidic oscillator with four scaling factors of 0.33, 0.5, 1, and 1.3 at three distance to throat diameter ratios of 4.5, 5.5, and 7.5 to analyze their effects on the heat transfer rate. The results indicated that the frequency of the sweeping jet increases by decreasing the scale factor due to shrinking the separation bubble, which increases the heat transfer rate of the hot plate. The maximum Nusselt number occurred for the scale factor of 0.33, which was 13% higher than that for the baseline geometry. Furthermore, the effect of changing the Reynolds number on the frequency of the self-sustained oscillating jet was numerically studied for the different scaled geometries to obtain a new general definition for the Strouhal number. The formation of the oscillating jet was correlated with the evolution of the separation bubble in the mixing chamber, and an appropriate length scale associated with the oscillation frequency was determined. An in-depth study demonstrated that the Strouhal number based on the new definition remained constant for the various scaled geometries.

CFD analysis of the WindEEE dome produced downburst-like winds

Thunderstorm is a severe phenomenon which can produce downburst winds capable for causing significant damage or even the collapse of low-rise structures. Experimental tests and numerical simulations are widely used by the Wind Engineering (WE) community for gaining increased understanding of complex winds like downbursts. In this paper, the accuracy of the Unsteady Reynolds-averaged Navier-Stokes (URANS) and Scale-Adaptive Simulation (SAS) to reproduce a vertical downburst wind - previously tested in the WindEEE Dome wind-simulator facility - was investigated. CFD results were first validated with the experiments and then used to study the dynamics of the phenomenon. The most suitable CFD setting (i.e. SAS case based on the k-ω SST turbulence model) was able to reproduce the development of the primary vortex ring, shedding of secondary rings induced by Kelvin-Helmholtz (KH) instabilities and the periodic detachments of smaller secondary vortices ahead the primary vortex. The superposition of these three contributions has shown to determine the temporal variation of the characteristic nose-shaped vertical profile which was found in the experiments. The performed simulations were also compared to field measurements from the NIMROD project showing a high level of agreement.

Numerical studies on wake and turbulence characteristics of aquaculture nets

This paper aims to understand the drag coefficient discrepancy between the equivalent-twine and twisted-twine nets based on their wake and turbulence characteristics. To that end, we conduct unsteady Reynolds-averaged Navier-Stokes (URANS) and the second-moment (Reynolds stress, RSM) simulations at a Reynolds number,Re=4.5×103, based on the effective diameter of the net twine, which corresponds to the subcritical flow regime. Then, the vortex structures and the turbulence statistics are assessed at AOA=90°. The results highlight that the wake interactions for the twisted-twine net are relatively strong compared to the equivalent-twine net, due to the disturbance of the helixes on the twisted twines. In comparison to the classical Karman vortex, the overall vortex shedding of these two nets is well organized. Symmetric vortices form behind the equivalent-twine net, while single vortices form behind the twisted-twine net. Moreover, the Reynolds normal and shear stresses show symmetric and anti-symmetric profiles. The addition of helixes to smooth circular cylinders changes the flow development, leading to a decrease of turbulence kinetic energy. With this understanding, engineers need to be carefully select the net type for preliminary design of marine aquaculture cages to avoid over- or underestimation of the drag forces.

Influence of Purge Flow Injection on the Performance of an Axial Turbine With Three-Dimensional Airfoils and Non-Axisymmetric Endwall Contouring

Abstract In this paper, we present the evaluation of the aerodynamic robustness to rim seal purge flow of an optimized 1.5-stage axial turbine configuration with a bowed stator profile and endwall contouring. Performance maps obtained by experiments and numerical simulations show that the efficiency benefit gained by this optimized configuration is partially reduced, but not eliminated, by the injection of purge flow through the cavity downstream of the first stator. Measurements with five-hole probes and hot-wire probes, as well as unsteady RANS simulations, give detailed insights into the physical effects of the purge flow inside the rotor passage. There, when no purge flow is injected, the optimized configuration diminishes the formation of loss-inducing secondary flow structures near the hub and the casing. When purge flow is injected, however, new strong secondary flow structures are induced near the hub. These vortices generate additional losses and thereby partially negate the efficiency benefits gained by the optimization. From the data, we found that this influence of the purge flow is limited to the lower half of the channel height. The data also show that the optimized configuration is able to reduce the vorticity near the casing regardless of the purge flow injection, which in turn leads to an efficiency increase in this area. Together, these effects lead to a reduction of the previously gained efficiency benefit by the optimized configuration when it is subjected to purge flow injection. However, compared to a baseline configuration with cylindrical endwalls also subject to purge flow injection, the overall efficiency is still increased by 0.38%.

Numerical Investigation of Vortex Shedding from a 5:1 Rectangular Cylinder at Different Angles of Attack

Although flow around a 5:1 rectangular cylinder at small angles of attack (AoA) has been extensively studied, when the AoA becomes larger, the research is rare. Therefore, this study performs Unsteady Reynolds-Averaged Navier-Stokes simulations (URANS) using the k-ω SST turbulence model for unsteady flow around a two-dimensional 5:1 rectangular cylinder at different AoAs up to 45°. A strong dependence of the flow characteristics on AoA is observed through the analysis of the time-averaged lift coefficient, drag coefficient, and Strouhal number. The peak of lift and drag coefficient is observed to be correlated, respectively, to the leading- and trailing-edge vortex based on the analysis of the flow. The x′-directional length of the main recirculation bubble on the top side and the distance from the bubble center to the leading edge of the cylinder both reach the maximum when α = 15°. In addition, the standard deviation σx′ of the time-averaged velocity U¯x′ along the cylinder shows a trend of increasing at first and then decreasing, and that σy′ also shows the same trend at α = 20°~45°; it fluctuates within a range of 0.05~0.2 at α = 0°~20°. Finally, two principal modes of vortex shedding are observed with α = 15° being their turning point, (i) “1 + 1” mode: in one vortex shedding period, two major vortices shed off from the top and bottom sides of the cylinder at α ≤ 15°; (ii) “2 + 2” mode, four vortices shed off from the top and bottom sides of the cylinder at α > 15° in one vortex shedding period.

Numerical study of higher-harmonic wave loads and runup on monopiles with and without ice-breaking cones based on a phase-inversion method

Ice-breaking cones are commonly used in the design of marine structures in cold regions. This study investigates the effects of higher-harmonic wave loads and wave runup on a 5-MW offshore wind turbine with and without ice-breaking cones under extreme wave conditions on the Liaodong Peninsula in China. Two ice-breaking cones (upward-downward and inverted types) are considered. The numerical model adopts a two-phase flow by solving unsteady Reynolds-averaged Navier-Stokes (URANS) equations using the volume of fluid (VOF) method. A phase decomposition method through a ‘Stokes-like’ formulation was adopted to obtain the parameters for each harmonics. The presence of the conical part is seen to increase the second-harmonic wave loads by up to 40%, but it has only limited influence on the fourth and fifth harmonics. The upward-downward-type ice-breaking cone increases the third harmonic, while the inverted-type ice-breaking cone decreases the third harmonic. Due to the phase difference between the first-harmonic and higher harmonics, the largest wave runup occurs at 0°, and 135° is the location with the smallest wave runup. This is because at the 135-degree location, the linear component is positive but the other nonlinear components are negative. For the 0-degree location, all harmonics are positive. By contrast, the inverted type has little effect. The high harmonic wave runup of the minimum point is backwards compared with that of the monopile, and most nonlinear wave runups are different upstream of the monopile.

Three dimensional unsteady analysis of a miniaturized pressure probe for turbocharger applications

Downsizing and turbocharging are nowadays widely spread techniques in automotive small-size internal combustion engines aimed at reducing the specific fuel consumption without affecting the power output. Due to the device small dimensions and to the high temperature of the exhaust-gases feeding the turbine, a relevant amount of heat is customarily exchanged between the turbine and the compressor so that a classical adiabatic approach could lead to an inaccurate estimation of the performance. This paper preliminary investigates the feasibility of an experimental procedure aimed at computing the exchanged work as variation of the angular momentum via a three-hole probe located at the impeller outlet. Because of the very reduced machine dimensions, torque measurements could be difficult, as the intrusive nature of the measurement could significantly affect the accuracy of the collected data. For this reason, the influence of the probe finite-size onto the flow field is numerically analysed solving the Unsteady Reynolds-Averaged Navier Stokes equations with and without the probe installed at the diffuser inlet. The equations are closed via the k − ω SST turbulence model, while a density-based commercial CFD package is used to integrate the governing equation. Finally, the pressure distribution in the azimuthal direction is analysed to assess the probe intrusive effects which, in the proposed case, result in a 0.47% (resp. 0.69%) difference in the specific work when a miniaturized probe with a diameter of 1mm (resp. 1.5 mm) is employed.

Application of an overset grid method for the performance analysis of flapping airfoils

With the growing importance of renewable energy, the interest in energy-harvesting technologies based on flow-induced vibrations of airfoils has been rekindled in the past few years. Compared to conventional turbines, these devices are centrifugal stress-free and hence they are structurally more robust. They are also environmentally friendly due to the relatively low speeds, thus reducing the impact on flying animals. In order to numerically investigate these types of devices, mesh motion techniques must be used so that the computational grid can adapt to the time-varying shape of the domain and boundaries, thus preserving its robustness and quality. During the last years, many different dynamic mesh approaches have been developed to better predict the behaviour of a flow interacting with solid moving bodies. The aim of the present work is to apply and validate the overset grid method offered by the OpenFOAM software. In this type of mesh, one or more grid blocks are allowed to overlap with other sets of cells to solve the fluid domain with moving bodies, thus showing many potential advantages compared to the other existing dynamic mesh approaches. In the first part of this work, a numerical investigation of the flow over a stationary SD 7003 airfoil at low Reynolds number has been performed using an unsteady RANS approach. The computed results have then been compared to experimental and high-fidelity computational data available from the literature in order to validate the presented model in terms of numerical domain configuration, mesh refinement, and turbulence modelling. Subsequently, unsteady RANS simulations have been performed on the SD 7003 and NACA 0012 airfoils for two different amplitudes of flapping motion, i.e., 30° and 45°. Finally, the results obtained with the OpenFOAM overset grid solver have been compared with the numerical and experimental benchmarks presented by Kurtulus, showing an excellent agreement with both computed and measured data.

Unsteady Numerical Investigation on the Sealing Effectiveness and Flow Field in Different Rim Seal Geometries

A rim seal is often used to prevent the ingress of high-temperature gas into the turbine disk cavity and protect the turbine disk from damage. Based on the overlapping rim seal (Seal-A), this paper proposes two more composite sealing structures (Seal-B and Seal-C) to show the effects of a deep cavity in the static disk and a modified platform in the rotating disk. Three-dimensional unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transfer (SST) k-ω turbulence model were used to reveal the flow field characteristics and the sealing efficiency. The results show that the rotor–stator interaction plays a dominant role in the sealing outlet pressure, and the sealing efficiency in the outflow area obtained by the transient calculation is lower than that of the steady-state calculation. The rise in the cooling air flow enhances the reverse vortex in the sealing cavity, and the disk cavity’s sealing efficiency is also improved. When the cooling air flow ratio increases from 0.6% to 1.8%, the sealing efficiency at the high radius increases by 30%. The shape of the deep cavity produces a new return vortex at the lower part of the sealing cavity, which improves the sealing efficiency. The shark nose platform in Seal-C aggravates the gas ingress at the sealing outlet but improves the sealing efficiency at the sealing cavity. In general, compared with Seal-A, the sealing efficiency of Seal-B and Seal-C is increased by 13.5% and 10%, respectively, at a cooling air flow ratio of 0.6%.

Finite Element Numerical Simulation of Local Scour of a Three-Dimensional Cylinder under Steady Flow

Pile safety has received increasing attention in marine engineering, especially in the field of local scour. In this paper, a finite element numerical model is established for local scour around a cylinder in steady currents. The flow is described by unsteady Reynolds–averaged Navier–Stokes equations with a traditional turbulent closure model. The proposed scour model takes bed load into account. The Exner equation is solved to determine the bed variation and the moving mesh approach is used to capture the evolution of the bed. When the resulting slope exceeds the angle of repose, a novel sand-slide model based on Rodrigues' rotation formula is used to prevent simulation distortion. All the equations are discretized by the two-step Taylor–Galerkin algorithm, and the resulting approach is fast to implement with second-order accuracy in space. The numerical results are found to be in good agreement with the experimental data.

Experimental verification and numerical simulation of a vortex flowmeter at low Reynolds numbers

This study presents experimental verification and numerical simulations of a vortex flow meter in the Reynolds number range between 8300 and 50,000. A custom-designed bluff body with a wedge back shape was used in the flowmeter. A shedding frequency of the flowmeter was measured in an air duct using a hot-film probe. To evaluate the accuracy of the flowmeter, a measurement uncertainty analysis was performed. Numerical simulations of the vortex flowmeter were performed with the open source code OpenFOAM. Transient simulations of periodic vortex shedding behind the bluff body were performed using different simulation methods depending on the pipe Reynolds number, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Unsteady Reynolds Averaged Navier Stokes (URANS) method. The simulated vortex shedding frequencies matched the experimental data very well. Experiments and simulations demonstrated a clear linear dependence of the shedding frequency on the volumetric flow rate over the entire range of Reynolds numbers. In addition, numerical simulations were used to study the main mechanisms of vortex formation and shedding behind the considered bluff body.

Effect of micro-cylinder as a passive controller on the Darrieus wind turbine performance

Vertical Axis Wind Turbines are more suitable for urban areas than Horizontal Axis Wind Turbines because they operate at lower wind speeds, and produce less noise, and are less expensive. In this study, the Darrieus turbine (three blades) is chosen as one of the (VAWTs) based on the NACA 0018 airfoil. The aerodynamic analyses are carried out by ANSYS Fluent software based on finite volumes method and the unsteady Reynolds averaged Navier–Stokes (URANS) equations with Shear Stress Transport (k-ω SST) turbulence model. The target of this work is to improve the performance of the Darrieus turbine by installing a micro-cylinder in various positions and various diameters. Three different micro-cylinder diameters are examined with a ratio of the micro-cylinder diameter to the chord (d/c = 0.029, 0.05, 0.065). It has been observed, the micro-cylinder improves the turbine performance in two cases: (1) The micro-cylinder diameter is smaller where the average power coefficient (CP-avg) increased by 9.5% compared to the conventional turbine at MC1 (d/c = 0.029). (2) By installing the micro-cylinder on the front of the blade leading edge where the average power coefficient (CP-avg) increased about 14.1% compared to the conventional turbine at the location (MC8). On the contrary, if the micro-cylinder diameter has lager diameter or located on the suction side or down towards the pressure side of the blade leading edge, the turbine performance decreases.

CFD investigation on the hydrodynamic loads and motions when ship maneuvers in regular and irregular waves

To explore and predict the ship maneuverability in the regular and irregular waves, the zigzag tests, the turning tests, and the course-keeping tests for the model-scale S175 containership under various wave conditions are simulated. The simulations are performed using a structured overset Unsteady Reynolds Averaged Navier-Stokes (URANS) solver with a moving grid. A body force method is adopted to predict the propeller forces. The simulation results are validated by the free-running experiments with satisfactory accuracy, which indicates that the present simulation strategy is effective and reliable. The hydrodynamic loads on the hull and the rudder together with the ship motion characteristics during the maneuvers in waves are obtained. It is concluded that the ship motions and hydrodynamic loads increase with the increase of the wavelength when the wave height is kept constant. The variation trends and magnitudes for low-frequency components of the self-propulsion factors in waves are similar to those in the calm water condition except obvious high-frequency fluctuations due to the wave effect. For the zigzag tests under the long-crested and short-crested irregular waves, the time histories of the yaw and rudder angle are similar. For the turning tests, the amplitude of roll motion in waves is much larger compared with that of the zigzag tests under the same wave condition, and the drift of the trajectory due to the wave is obvious. The current course keeping simulation can be an alternative tool to predict course keeping maneuvers in waves. Furthermore, flow visualizations are presented for providing a better understanding of the wave effect on free-running ship maneuvers.

The Effects of Meridian Surface Shape on the Pressure Pulsation of a Multi-Stage Electric Submersible Pump

The influence mechanism of the internal pressure fluctuation propagation law of multi-stage submersible electric pump (ESP) is still unclear, which has been a major problem restricting the stable exploitation of deep-sea oil and gas. In order to investigate the effect of different meridian profiles on the pressure pulsation characteristics of three-stage submersible electric pumps, the unsteady Reynolds-averaged Navier–Stokes (URANS) method is used to numerically investigate it. The results show that the lower the pressure pulsation amplitude in the pump caused by the meridional shape that is more in line with the flow law, has a positive effect on the operation stability. The change of the shape of the meridian greatly affects the pressure pulsation law in the secondary and final pumps. The rotor–stator interaction causes the pressure pulsation amplitude of the monitoring point in the middle of the pump chamber to reach a peak value. By using continuous wavelet transform analysis, it is found that the regularity of 1–2 times frequency conversion is complicated due to multiple pulsation sources and low frequency propagation coupling between stages. At 3–6 times frequency, it is basically close to the pulsation rule of the blade frequency. The above research provides a basis for improving the operation stability of the ESP.

Viscous effects on the added mass and damping forces during free heave decay of a floating cylinder with a hemispherical bottom

This paper presents an analysis of viscous effects on the added mass and damping forces during free heave decay of a cylinder with a hemispherical bottom. Results from unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and linear potential-flow solutions are compared. Expressions for the cycle-averaged viscous added mass and damping coefficients are derived based on first-order Fourier analysis of the URANS results. Viscous effects are extracted by comparing the URANS results and linear potential-flow solutions, as nonlinear potential-flow effects in this case are demonstrated to be negligible. It is observed that viscous effects on the added mass coefficient are minor during heave decay, such that the linear potential-flow model can predict the value of the added mass coefficient to within 5% deviations. In contrast, the viscous damping coefficient exhibits strong cycle-dependent variations. A parametric study of the effects of initial displacement, cylinder diameter and draft shows that viscous damping forces can play an important role when the cylinder has a relatively small diameter and large draft. Further, the damping coefficient is transformed to the nondimensional drag force coefficient, and its dependence on the Reynolds number Re is investigated, for Keulegan–Carpenter numbers in the range KC= 1.5–2.5. It is found that the drag force coefficient is likely to be unrelated to Re and KC during the first cycle. From the second cycle to the fourth cycle, the drag force coefficient rapidly decreases with increasing Re, up to Re≈3×105.

Numerical investigation on the aerodynamic efficiency of bio-inspired corrugated and cambered airfoils in ground effect

This research numerically investigates the flapping motion effect on the flow around two subsonic airfoils near a ground wall. Thus far, the aerodynamic efficiency of the dragonfly-inspired flapping airfoil has not been challenged by an asymmetric cambered airfoil considering the ground effect phenomenon, especially in the MAV flight range. The analysis is carried out on the basis of an unsteady Reynolds-averaged Navier-stokes (URANS) simulation, whereby the Transition SST turbulence model simulates the flow characteristics. Dragonfly-inspired and NACA4412 airfoils are selected in this research to assess the geometry effect on aerodynamic efficiency. Moreover, the impacts of Reynolds number (Re), Strouhal number (St), and average ground clearance of the flapping airfoil are investigated. The results indicate a direct relationship between the airfoil’s aerodynamic performance (C_l/C_d) and the ground effect. The C_l/C_d increases by reducing the airfoil and ground distance, especially at h_{0}=c. At Re=5times 10^4, by increasing the St from 0.2 to 0.6, the values of C_l/C_d decrease from 10.34 to 2.1 and 3.22 to 1.8 for NACA4412 and dragonfly airfoils, respectively. As a result, the C_l/C_d of the NACA4412 airfoil is better than that of the dragonfly airfoil, especially at low oscillation frequency. The efficiency difference between the two airfoils at St=0.6 is approximately 14%, indicating that the C_l/C_d difference decreases substantially with increasing frequency. For Re=5times 10^3, the results show the dragonfly airfoil to have better C_l/C_d in all frequencies than the NACA4412 airfoil.

CFD Body Force Propeller Model with Blade Rotational Effect

The purpose of this study is to consider propeller geometry and blade rotation in the propeller model in a CFD code. To predict propeller performance, a body force propeller model was developed based on blade element theory and coupled with URANS (unsteady Reynolds-averaged Navier–Stokes) solver CFDSHIP-IOWA V4.5 both implicitly and interactively. The model was executed inside the flow solver every inner iteration. The grid points inside each 2D blade geometry were identified by a numerical search algorithm. To calculate the lift coefficient, the total flow velocities at 25% foil chord length were obtained using the inverse distance weighting interpolation from the RANS solution. The body forces were distributed linearly along the chord length with the maximal value located at the leading edge and zero at the trailing edge. The main achievements are: (1) for a KP505 propeller in an open water condition, the error of the thrust coefficient generally is around or less than 3%, which is a better prediction than the previous model. (2) For a behind-hull condition, the error is about 1%. (3) For an E1619 propeller in an open water condition, the error is around 6%. (4) The blade-to-blade effect and unsteady flow field between blades are sufficiently resolved by the model.