Explicit Algebraic Stress Model Research Articles

Influence Evaluation of Open Propellers with Boss Cap Fins: Case Studies on Types B4-70 and Ka4-70

Numerical analysis of fins effect on propeller performance was conducted, specifically using the B4-70 and Ka4-70 propellers. The study investigated different types of fins, including bare fins and PBCF (Propeller Boss Cap Fins) using computational fluid dynamics (CFD) simulations. The explicit algebraic stress model (EASM) based on Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence modeling was employed to determine the optimal results. The main objective of this research was to enhance energy efficiency in ships by examining various open propeller configurations. The CFD simulation results for open propellers B4-70 and Ka4-70, with the addition of boss cap fins, revealed interesting phenomena. When the open propellers B4-70 and Ka4-70 were equipped with PBCF, they would experience an increase in efficiency (η0). This was because the performance of the fins functioned optimally when the advance ratio (J) is high, as evident from the high velocity values. Thus, with higher velocity and lower pressure in the boss cap region at high J values, there was an elevation in thrust force due to the reduction of hub vortex. In the case of open propeller B4-70 with added PBCF, there was an increase in the efficiency value (η0) ranging from 3% to 5% when J varied from 0 to 0.7. Similarly, for propeller Ka4-70 with the addition of PBCF, there was an increase in the efficiency value (η0) ranging from 1% to 3% when J varied from 0 to 0.7. Notably, the use of an Energy-Saving Device (ESD) in the form of PBCF can increase the efficiency of ship propeller, as reported in this paper. Consequently, these findings affirmed the reliability of the overall calculations using the CFD approach.

Hydrodynamic Performance Analysis of Camber Ratio Variations on B-series Propeller Types

The hydrodynamic performance of the B-series propeller can be determined by calculating the polynomial equation published by MARIN. Furthermore, analysis and evaluation of B-series propeller modifications can be done by varying the camber ratio of the foil. The camber ratio affects the lift force on the propeller foil, directly affecting the propeller thrust and torque. Numerical calculations were carried out using Computational Fluids Dynamics (CFD), based on Reynolds Averaged Navier Stokes Equations (RANSE) and turbulence model in the form of explicit algebraic stress models (EASM). The overall results of this study show an increase in efficiency of 4.182 on the foil with a camber ratio of 2.2% when compared to the foil camber ratio of 0%.

Characteristics Investigations of Ducted Ka4-70 Series Propeller with Boss Cap Fins Using Numerical and Experimental Method

Unconventional system that are generally adopted for ship propulsion are Ducted Propellers. These devices have recently been studied with medium-fidelity computational fluid dynamics code (based on the potential flow hypothesis) with promising results. Numerical and experimental comparison of ducted propeller with PBCF, case studies with Propeller Ka4-70 used combination ducted and PBCF Divergent. The study was done numerically using computational fluid dynamics (CFD) approach. The solver is based on the Reynolds-Averaged Navier-Stokes (RANS) solutions and turbulence modelling explicit algebraic stress model (EASM). The test data was obtained from CFD simulations consisting of the open propeller and combination Nozzle plus PBCF, but the experiment was done to Nozzle and PBCF only. All measurements were carried out from J = 0 to J = 1.0 with speeds from 0 m/s to 2.445 m/s. The results of the comparative investigation cases between numerical and experiment analysis from Ka4-70 propellers with Nozzle 19A and PBCF Divergent appears that between CFD and experiments, several phenomena are seen. (i) the Ka4-70 propeller without Nozzle 19A and PBCF divergent experienced large pressure at low-speed J = 0.1 to high-speed J = 0.7, but Ka4-70 propeller with Nozzle and PBCF divergent reach highest pressure at J = 0.1 to J = 0.5; (ii) the Ka4-70 propeller without 19A nozzle and PBCF divergent increases the flow velocity at the boss cap fins but does not increase the axial induce velocity, while Ka4-70 propeller using nozzle and PBCF divergent increases the axial induce velocity of the blade, but does not increase the flow velocity of the boss cap fins; (iii) Ka4-70 propeller without Nozzle and PBCF value increase of propeller η0 to 12% when ESD added in the form of Nozzle and PBCF when J is high, from J = 0.7 to J = 1.0. ; (iv) Ka4-70 propellers with Nozzle 19A and PBCF Divergent has very similar η0 from J=0 to J=1.0. CFD approach are still appropriate to be relied upon for the overall simulation.

Improvement of the algebraic stress model for separated flows based on field inversion and machine learning

Due to the difficulties of precisely calculating the turbulence intensity within the separated shear layer using traditional turbulent models, computing strongly separated flows is a key task of considerable interest. In this paper, the Reynolds stress functional expression is improved toward an explicit algebraic stress model for separated flows that are similar to hump flows using a data-driven framework of field inversion and machine learning that can take model consistency into account during the model correction process. The iterative Kalman filter algorithm is utilized to address the inversion problem, and the inversion results are used as training data for correction models that are trained using random forest regression. For model verification and validation, we employ both the curved backward-facing step and bump cases. The findings indicate that the inversion produces favorable outcomes, and the enhanced model developed utilizing the inversion data exhibits good generalizability.

Numerical and Experimental Investigations into the Characteristics of Wageningen B4-70 Series of Propeller with Boss Cap Fins

Applying propeller boss cap fins (PBCF) in open B-series has been studied. PBCF is able to decrease the wake effect behind the propeller which can influence the propeller’s thrust and torque. Open propeller using PBCF is analyzed using computational fluid dynamics (CFD) which generate convergent result compared to experimental data. The solver is based on the Reynolds Averaged Navier Stokes Equation (RANSE) solutions and turbulence modeling explicit algebraic stress model (EASM). The test data was obtained from CFD simulations consisting of the open propeller and PBCF despite the experiment was done to PBCF only. All measurements were carried out from J = 0 to J = 1.0 with speeds from 0 m/s to 2.445 m/s.The results of the investigation on the B4-70 propeller with Boss cap fins convergent showed thought-provoking phenomena both on CFD and experimental work. Test results at The B4-70 Propeller without using PBCF high Pressure at J = 0.1 - 0.9, but with boss cap fins can reduce pressure at high-speed J = 0.9, so further research is needed to low-speed J = 0.1 - 0.5; Then visualization of velocity on propeller B4-70 without PBCF shows an increase in flow velocity in the boss cap fins when J = 0 to J = 0.9. The induced axial velocity in the blade propeller is the same and propeller B4-70 with PBCF decreases in speed in the boss cap fins when J = 0 to J = 0.9. However, the induce axial velocity in the blade propeller is the same. Convergent PBCF can reduce the return flow velocity in the boss cap propeller area, inversely proportional to the open propeller. Comparison of open propeller and PBCF shows that using PBCF there is an increase in the KT value at high speed of 10% to24% and a decrease in the 10KQ value on PBCF from J = 0.8 to J = 1.0 of 7% to 14%, but η_0 value at J = 0.8 to J = 1.0 increased by 3% to 8%. This Explained that the use of PBCF when the higher the value of J, greater the increase in η_0 value. Mainly, B4-70 propeller with PBCF with a converging boss cap shape with 15-degree slope exhibits increased efficiency.

A study into the effect of tip clearance on the performance of b-series and kaplan-series ducted propellers

A study into the effect of tip clearance on ducted propellers was carried out. Two series of propellers, namely B-series and Kaplan-series, were used. The gap between tip of propeller and ducted was varied from 2mm to 5mm. The study was conducted numerically using computational fluid dynamics (CFD) approach. The solver is based on the Reynolds-Averaged Navier-Stokes (RANS) solutions and two turbulence modelling, i.e. k-ω SST by Menter and explicit algebraic stress model (EASM), were applied in order to find out the optimum results. This paper objective to discuss energy efficiency on ships by investigating variations of propeller tip clearances. Overall results showed that EASM demonstrated better score (particularly in term of thrust and efficiency) than the k-ω SST. The highest thrust, torque and efficiency were achieved at 3mm tip clearance for both series. Moreover, Kaplan-series showed better results than the B-series propeller indicating that the use of ducted propeller using Kaplan-series is more appropriate.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Assessment of Two Streamline Curvature Correction Methods for an Elliptic Blending Turbulence Model

Using two different methods, a previously developed elliptic blending model (the original STT k-ω-φ-α model) is modified for sensitization to streamline curvature. One method involves modifying the dissipation term in the turbulent dissipation equation, while the other constructs a new formulation for the turbulent kinetic energy production term based on an explicit algebraic stress model. The capabilities of the proposed models are evaluated by applying them to three flows with curved surfaces; namely, the two-dimensional (2D) infinite serpentine passage flow, the 2D U-turn duct flow, and the 2D periodic hill flow. The STT k-ω model with rotation and curvature correction (the STT k-ω-CC model) is also used for comparison. The computed results are compared with the relevant direct numerical simulation, experimental, and large eddy simulation data from the literature. It is found that the two proposed models significantly improve upon the original STT k-ω-φ-α model. Compared with the STT k-ω-CC model, the two proposed models produce better results in the 2D infinite serpentine passage flow and the 2D periodic hill flow. The proposed models are similarly competitive with the STT k-ω-CC model in the 2D U-turn duct flow.

Topology optimisation of turbulent flow using data-driven modelling

Fluid topology optimisation has become a popular approach for optimisation of geometries in aero-thermal applications. However, one of the main limitations of current approaches considering turbulent flow is the fidelity of the Reynolds Averaged Navier–Stokes models employed. In response, this paper shows the development of the first data-driven fluid topology optimisation technique based on the continuous adjoint method. The technique first extracts data from a high fidelity simulation of a standard topology-optimised geometry. These data are fed through a symbolic regression-based machine learning algorithm called gene expression programming, to learn an explicit model for the anisotropy tensor. The novel aspect of the work is the derivation of the adjoint form of the generalised explicit algebraic stress model such that the developed turbulence model can be inserted directly into the primal and adjoint system of equations. This allows a second, data-driven optimisation to be performed. Finally, a high fidelity simulation of the resulting geometry is also conducted to allow comparison against the standard geometry. The method is first applied to the back-facing step to verify the approach and then to a 2D u-bend configuration. The data-driven optimisation was able to find geometries exhibiting significant reductions in pressure loss when compared with results from the standard optimisation.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

Improving LES with OpenFOAM by minimising numerical dissipation and use of explicit algebraic SGS stress model

ABSTRACTThere is a rapidly growing interest in using general-purpose CFD codes based on second-order finite volume methods for Large-Eddy Simulation (LES) in a wide range of applications, and in many cases involving wall-bounded flows. However, such codes are strongly affected by numerical dissipation and the accuracy obtained for typical LES resolutions is often poor. In the present study, we approach the problem of improving the LES capability of such codes by reduction of the numerical dissipation and use of an anisotropy-capturing subgrid-scale (SGS) stress model. The latter is of special importance for wall-resolved LES with resolutions where the SGS anisotropy can be substantial. Here we use the Explicit Algebraic (EA) SGS model [Marstorp L, Brethouwer G, Grundestam O, et al. Explicit algebraic subgrid stress models with application to rotating channel flow. J Fluid Mech. 2009;639:403–432], and comparisons are made for channel flow at friction Reynolds numbers up to 934 with the dynamic Smagorinsky model. The numerical dissipation is reduced by using an OpenFOAM based custom-built flow solver that modifies the Rhie and Chow interpolation and allows to control and minimise its effects without causing numerical instability (in viscous, fully turbulent flows). Different resolutions were used and large improvements of the LES accuracy were demonstrated for skin friction, mean velocity and other flow statistics by use of the new solver in combination with the EA SGS model. By reducing the numerical dissipation and using the EA SGS model the resolution requirements for wall-resolved LES can be significantly reduced.

DES-based computation of the flow around the DARPA suboff

Flow modelling is a key issue not only for the correct prediction of hull-propeller interactions, manoeuvring characteristics and the flow field in the stern region of any marine vehicle, but also for the correct estimation of the fuel consumption. The paper describes a thorough investigation of the hydrodynamic performances of the DARPA suboff hull. The flow is numerically simulated by integrating in time the unsteady Navier-Stokes equations in which closure to the turbulence is achieved by means of a modified detached eddy simulation (DES hereafter) technique. The solver used for the purpose is the ISIS-CFD, part of the Numeca FineTM/Marine suite, which employs the finite volume of fluid technique. A comparative analysis between the numerical solutions based on the DES and explicit algebraic stress model (EASM hereafter) are provided in an attempt to sustain the choice for the turbulence model in the present study. Extensive parallel computations are carried out on 120 processors for which comparisons with the experimental data prove the accuracy of the chosen investigation methodology. A grid convergence test is performed for verification and validation purposes.

Design of the centrifugal fan of a belt-driven starter generator with reduced flow noise

Large eddy simulations based on the explicit algebraic subgrid-scale stress model were carried out to predict the flow-induced noise generated on the centrifugal fan of a belt-driven starter generator using Lighthill's analogy and the method of Ffowcs Williams and Hawkings. The surrounding air was approximated by an ideal gas at fixed room temperature (Tin = 300 K), and the rotating velocity of the fan was considered to be 6000 rpm. The blade array angles were designed using the modulation method, and a large blade curvature was adopted. We identified several centrifugal fan design parameters that could minimize the flow-induced noise while also minimizing fan efficiency losses. Three design parameters: the top serrated edge (θt), the step leading edge (0.52 Hb) and the tail edge (db and rb), played a critical role in preventing vortex generation and collision, significantly weakening the surface pressure fluctuations on the blade. The maximum sound pressure level at 800 Hz at a specific location was reduced by 5.5 dB (at the top serrated edge) and 6.8 dB (at the step leading edge) relative to the baseline case. The sound power, calculated over a hemisphere surface of 950 mm, was reduced by 77.3% (at the top serrated edge) and 61.0% (at the step leading edge) relative to the baseline whereas the mass flow rates were reduced by 5.2% and 10.6%, respectively. Experiments were performed using the optimally designed fan in a semi-anechoic chamber. The predicted sound pressure level and frequency were in good agreement with the experimentally measured values.

Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot

Machine learning was applied to large-eddy simulation (LES) data to develop nonlinear turbulence stress and heat flux closures with increased prediction accuracy for trailing-edge cooling slot cases. The LES data were generated for a thick and a thin trailing-edge slot and shown to agree well with experimental data, thus providing suitable training data for model development. A gene expression programming (GEP) based algorithm was used to symbolically regress novel nonlinear explicit algebraic stress models and heat-flux closures based on either the gradient diffusion or the generalized gradient diffusion approaches. Steady Reynolds-averaged Navier–Stokes (RANS) calculations were then conducted with the new explicit algebraic stress models. The best overall agreement with LES data was found when selecting the near wall region, where high levels of anisotropy exist, as training region, and using the mean squared error of the anisotropy tensor as cost function. For the thin lip geometry, the adiabatic wall effectiveness was predicted in good agreement with the LES and experimental data when combining the GEP-trained model with the standard eddy-diffusivity model. Crucially, the same model combination also produced significant improvement in the predictive accuracy of adiabatic wall effectiveness for different blowing ratios (BRs), despite not having seen those in the training process. For the thick lip case, the match with reference values deteriorated due to the presence of large-scale, relative to slot height, vortex shedding. A GEP-trained scalar flux model, in conjunction with a trained RANS model, was found to significantly improve the prediction of the adiabatic wall effectiveness.

Bubble induced turbulence model improved by direct numerical simulation of bubbly flow

Direct numerical simulations (DNS) provide a description of turbulent flow fields at every point in space and time. Since every statistical quantity can be computed, this data should be useful for the development of closure models. In this paper, models for bubbly turbulent flows, in a two-fluid framework, are investigated using DNS data. A front tracking method is employed to simulate turbulent flow with deformable bubbles in a vertical channel. Quantities such as void fraction, average velocities, velocity fluctuations, and turbulence statistics are computed and presented. After processing the DNS data, the turbulence kinetic energy and dissipation equations, based on the k-ε model and explicit algebraic stress model (EASM), are analyzed. The model for bubble-induced turbulence, represented by source terms in the k and ε equations, is re-evaluated using coefficients derived from the DNS results. This work is a first step to show what can be done by using the DNS data to evaluate turbulence closure models. More simulations should be conducted in future works to further improve such models.

Assessment of hybrid RANS-LES formulations for flow simulation around the Ahmed body

This paper presents an investigation of RANS and DES models for the Ahmed body with 25° and 35° slant angles. The Reynolds number, based on the height of the model and the upstream velocity, is 7.68× 105. Two RANS (Reynolds Averaged Navier–Stokes) models are used: the k−ω SST of Menter and the EARSM (Explicit Algebraic Stress Model), based on the k−ω model. Two hybrid RANS-LES (Large Eddy Simulation) models are used: a DES (Detached Eddy Simulation) and an IDDES (Improved Delay Detached Eddy Simulation). These hybrid models are also based on the k−ω model. The flow for the slant angle 35° is well predicted by all turbulence models with a slight advantage for the IDDES model. For the flow with the slant angle 25°, only the IDDES hybrid RANS-LES model predicts the recirculation bubble on the slant. It is concluded that the IDDES model is the only turbulence model that gives good agreements with the experimental data.

New explicit algebraic stress model for three‐dimensional turbulent flows

AbstractAn explicit algebraic turbulent‐stress model is built in the framework of so‐called Rodi's weak‐equilibrium approximation, which, taking into account the known model representations for the pressure‐strain‐rate correlation and turbulence‐dissipation rate, reduces the differential equations for the Reynolds‐tensor components to a system of quasi‐linear algebraic equations for the five independent components of the anisotropy tensor B. We propose an original method for solving this quasi‐linear system. The tensor in question B is sought in the form of an expansion in a tensorial basis formed from the mean strain and rotation rate tensors which contains only five elements. The expansion's coefficients are functions of five simultaneous invariants of these tensors. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling and experimental investigation of micromixing of single-feed semi-batch precipitation in a liquid–liquid stirred reactor

A finite-mode probability density function (FM-PDF) model is adopted to simulate the semi-batch precipitation process of barium sulfate from aqueous solutions of barium chloride and sodium sulfate in the presence of kerosene drops in a turbulent liquid–liquid stirred reactor driven by a Rushton turbine. The turbulent kerosene–water flow field is calculated with an anisotropic two-phase explicit algebraic stress model (EASM) and the standard k–ε model based on an Eulerian–Eulerian approach using in-house codes. The flow predictions are validated against macromixing homogenization curves measured from tracer mixing experiments. The particle size distribution has been calculated by solving five moments of the particle size distribution coupled with both nucleation and growth kinetics. The effects of impeller speed and inert dispersed oil volume fraction have been investigated. Agreement between micromixing model predictions and experimental data is satisfactory, which suggests that the time-dependent finite-mode probability density function model is a feasible approach for numerical prediction of the fast precipitation process in turbulent two-phase stirred reactors.

Numerical Simulation of Airfoil Flow at High Angle of Attack

A NACA 4412 airfoil tested in wind tunnel at flow conditions close to maximum lift is used for testing the accuracy of various turbulence models. What makes this test case unique is the appearance of a stable separation vortex on the upper surface of the airfoil, near the trailing edge. The linear k-ω turbulence model, a non-linear Explicit Algebraic Stress Model and a modified version of the algebraic Baldwin-Lomax model are tested using the same grid and input file. It is found that the tested turbulence models capture the physics of unsteady separated flow. However, the size and shape of the predicted separation vortex are different for each tested turbulence model. Also, good agreement between computational and experimental surface pressures is observed. The results support the view that such a simple configuration is appropriate to be used as benchmark for validating turbulence and LES models.

RANS Modeling of Accelerating Boundary Layers

Abstract A numerical investigation of accelerated boundary layers (BL) has been performed using linear and nonlinear eddy viscosity models (EVM). The acceleration parameters (KS) investigated the range between 1.5 × 10−6 and 3.0 × 10−6. The one-equation (k-l), Spalart Allmaras (SA), and the two-equation Menter Shear Stress Transport (SST) and Chien models in their standard forms are found to be insensitive to acceleration. Nevertheless, proposed modifications for the SA, Chien, and the k-l models significantly improved predictions. The major improvement was achieved by modifying the damping functions in these models and also an analogous source term, E, for the Chien model. Encouraging agreement with measurements is found using the Launder Sharma (LS), cubic and explicit algebraic stress models (EASM) in their standard forms. The cubic model best predicted the turbulence quantities. Investigations confirm that it is practical for Reynolds-Average Navier–Stokes (RANS) models to capture reversion from the turbulent to laminar state albeit for equilibrium sink type flows.