Algebraic Stress Model Research Articles

Numerical Analysis into the Improvement Performance of Ducted Propeller by using Fins: Case Studies on Types B4-70 and Ka4-70

Numerical analysis was conducted to assess the impact of fins on the B4-70 and Ka4-70 propeller performance. The study explored different fin variations, specifically bare fins, Propeller Boss Cap Fins (PBCF), and propeller nozzles, using computational fluid dynamics (CFD) simulations. To obtain the best results, the researchers utilized the explicit algebraic stress model (EASM) based on Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence modelling. The primary goal of this study was to improve the energy efficiency of ships by examining various propeller configurations, both open and ducted. The overall conclusions indicated that the B4-70 PBCF convergent and Ka4-70 PBCF divergent with the addition of nozzle 19A exhibited the highest efficiency based on the EASM analysis. The CFD simulation results for both B4-70 and Ka4-70 propellers, utilizing a nozzle 19A with added boss cap fins, revealed several noteworthy phenomena. Firstly, for the B4-70 propeller, efficiency (η0) at J = 0.6 to J = 0.8 showed an increase of 1% to 2%. Secondly, concerning the Ka4-70 propeller, efficiency (η0) at J = 0.6 to J = 0.8 increased by 2% to 10%. These findings clearly demonstrate that the use of an ESD, such as the nozzle 19A with added boss cap fins, enhances the propulsion performance of the ship. It is evident that the CFD approach remains suitable and reliable for overall simulations.

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.

A simple analytical model for turbulent kinetic energy dissipation for self-similar round turbulent jets

This work presents a simple analytical model for the streamwise and radial variations of turbulent kinetic energy dissipation in an incompressible round turbulent jet. The key assumptions in the model are: similarity in the axial velocity profile with a Gaussian shape, axisymmetric flow and the dominance of radial derivatives of the mean velocity over axial direction derivatives (similar to boundary layer theory). Initially, a simplified eddy-viscosity relation for turbulent stresses is derived using the algebraic stress model by Gatski & Speziale (J. Fluid Mech., vol. 254, 1993, pp. 59–78). Subsequently, with this eddy-viscosity relation, the relation for variations of turbulent kinetic energy dissipation is formulated using the conservation of turbulent kinetic energy. To extract the necessary constants of the model, experimental velocity statistics for round jets are obtained through particle image velocimetry measurements. The experimental results of the mean entrainment coefficient for turbulent jets are also analysed. When comparing the radial variation of turbulent kinetic energy dissipation from the model with experimental results at Reynolds number $1.4\times 10^5$ and numerical results at Reynolds number $1200$ from the available literature, we observe a maximum error of $10\,\%$ and $15\,\%$ , respectively. Finally, using the validated model, we analyse the impact of mean velocity evolution parameters on the behaviour of turbulent kinetic energy dissipation and discuss its potential significance in future studies.

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.

Numerical simulation study of offshore heavy oil desanding by hydrocyclones

Sand production often occurs in offshore heavy oil production. Sand particles enter offshore platform processing systems with heavy oil, easily causing pipeline sand deposition, valve and separator erosion and blockage, and pump and other equipment wear and damage, resulting in various oilfield production safety risks. Due to the high viscosity of heavy oil, it exerts a strong viscous drag on sand particles. They easily adhere to heavy oil and move with its flow, which also leads to the extremely difficult separation of heavy oil and sand. Due to the desanding difficulty of highly viscous oil, this work proposes a desanding scheme combining water blending for viscosity reduction with hydrocyclone separation and focuses on hydrocyclone separation in the heavy oil desanding process. Based on algebraic slip mixture, Reynolds stress and discrete-phase models, the hydrocyclone desanding characteristics of heavy oil with the water cut were studied by computational fluid dynamics (CFD) numerical simulations. Flow field, sand removal rate (SSR) and pressure drop differences under different oil viscosities, oil contents and hydrocyclone geometries were studied via single-factor sensitivity analysis, and the essence of these differences was comprehensively analysed. Through high-precision response surface prediction model establishment, the influence of the interaction between hydrocyclone structures on the pressure drop was analysed, and the influence of the pairwise interaction between the main hydrocyclone structures on the hydrocyclone pressure drop is mutual inhibition. The hydrocyclone structure is optimized with pressure drop minimization as the objective, and the pressure drop of the optimized hydrocyclone is 23.3% lower than that at the lowest pressure in response surface experiments, indicating that the optimization effect of the response surface method (RSM) is extremely significant. Moreover, the research methods and conclusions in this work provide a basis for subsequent experimental prototype development and experimental verification steps.

Explicit algebraic relation for calculating Reynolds normal stresses in flows dominated by bubble-induced turbulence

Two new algebraic turbulence models for flows dominated by bubble-induced turbulence (BIT) are presented. The first model, referred to as the algebraic Reynolds normal stress model, is derived from a differential Reynolds stress model for bubbly flows. The second model utilizes one two-equation turbulence model to achieve algebraic expressions for $k$ and $ϵ$ in the BIT dominated cases. If both models are combined, it results in a purely algebraic, explicit relation for the Reynolds normal stresses.

A Novel Algebraic Stress Model with Machine-Learning-Assisted Parameterization

Reynolds-stress closure modeling is critical to Reynolds-averaged Navier-Stokes (RANS) analysis, and it remains a challenging issue in reducing both structural and parametric inaccuracies. This study first proposes a novel algebraic stress model named as tensorial quadratic eddy-viscosity model (TQEVM), in which nonlinear terms improve previous model-form failure due to neglection of nonlocal effects. Then a data-driven regression model based on a fully-connected deep neural network is designed to determine the TQEVM coefficients. The well-trained data-driven model using high-fidelity direct numerical simulation (DNS) data successfully learned the underlying input-output relationships, further obtaining spatial-dependent optimal values of these coefficients. Finally, detailed validations are made in wall-bounded flows where nonlocal effects are expected to be significant. Comparative results indicate that TQEVM provides improvements both for the stress-strain misalignment and stress anisotropy, which are clear advantages over linear and quadratic eddy-viscosity models. TQEVM extends to the scope of resolution to the wall distance y + ≈ 9 as well as provides a realizable solution. RANS simulations with TQEVM are also carried out and the obtained mean-flow quantities of interest agree well with DNS. This work, therefore, results in a high-fidelity representation of Reynolds stresses and contributes to further understanding of machine-learning-assisted turbulence modeling and regression analysis.

Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.

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.

Central-upwind scheme for 2D turbulent shallow flows using high-resolution meshes with scalable wall functions

In this paper, the Reynolds-averaged Navier Stokes equations supplemented by the algebraic stress model are solved using the central-upwind scheme for simulating 2D turbulent shallow flows. The model is of spatially and temporally second-order accurate. To increase the accuracy, high-resolution meshes up to 3.4 million cells (6.8 million edges) are used. Consequently, a strategy combining the hydrostatic and topography reconstructions and the scalable wall functions – is proposed to accurately simulate wet–dry phenomena near the interfaces (moving boundary geometries) thus ensuring a proper calculation for the turbulence properties. This strategy has been proven to be accurate and to not deteriorate the results for such very fine meshes thus giving flexibility to users in generating meshes.