Reynolds-averaged Navier-Stokes Solver Research Articles

A three-dimensional inverse method based on moving no-slip boundary for profiled end wall design

How to utilize existing flow control mechanisms to make profiled end wall design more flexible, efficient, and physical is a meaningful challenge. This study presents a three-dimensional inverse method for profiled end wall design to achieve the application of flow control mechanisms. The predetermined pressure distribution on the end wall is reached by modifying the end wall geometry during flow field calculation. A motion velocity model is derived from the normal momentum equation of the moving no-slip boundary to modify the end wall geometry. A Reynolds-Averaged Navier-Stokes (RANS) solver based on the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is adopted to simulate the flow field. Based on the mechanism understanding obtained through numerical optimization results, this study adopts the inverse method to redesign an optimized end wall in a compressor cascade. The results indicate that the redesigned end wall exhibits better loss reduction, reducing the overall total pressure loss by 5.5%, whereas the optimized end wall reduces it by 3%. The inverse method allows the imposition of desired influences on the end wall flow without constructing a database, making it highly flexible, efficient, and physical.

Effects of a long-drive shaft on flow field around a high-speed boat propeller in Thailand using CFD

The Long-Tail Boat (LTB) is a high-speed boat in Thailand. The propulsive system has a long-drive shaft that holds the propeller on the end of the shaft. It is used under inclined shaft conditions because of shallow water draft. Thus, the fluid flow into the propeller blade area is unsteady due to the cross-flow component. Therefore, the long-drive shaft is an important parameter in generating the flow field before entering the propeller blades, which affects propeller efficiency. This paper presents a numerical analysis of the flow field around a long-drive shaft and propeller blade areas in a full-scale propeller size using the Reynolds-Averaged Navier-Stokes (RANS) solver. The unsteady propeller performance is carried out by considering inclined flow conditions. In addition, the computational results of fluid flow in terms of the pressure distributions and wake fields around a long-drive shaft and propeller are investigated, which influence the propeller performance and the generating drag forces by a long-drive shaft. The results can be applied to modify the long-drive shaft of boats. Highlights The Long-Tail Boat (LTB) is a local vessel in Thailand that has a high speed Computational fluid dynamics (CFD) code ANSYS Fluent to study the effect of a long-drive shaft propeller with inclined shaft angles The long-drive shaft should be designed in suitable for operating the inclined shaft conditions because it will directly affect the propeller efficiency

Updating Turbomachinery Aerodynamics Teaching on an Undergraduate Course Using Three-Dimensional Design Tools

Abstract This paper outlines the update of a turbomachinery course to cover three-dimensional (3D) aerodynamics using a Reynolds-Averaged Navier Stokes solver. Prior to the activities outlined in this paper, the course was taught in a conventional way with a series of lectures and a timed, written, open book examination in a formal exam setting. Students were equipped with a calculator and set of notes including correlations from Howell and Soderberg. The students had around 1 h to answer the turbomachinery question, which was revealed to them only when they opened the paper at the start of the exam. This limited the depth of any aerodynamic problem they could get through and so they were restricted to simple design or analysis exercises. The genesis of the course update was the release in 2017 of “MULTALL OPEN” (Denton, J. D., 2017, “Multall: An Open Source, Computational Fluid Dynamics Based, Turbomachinery Design System,” ASME J. Turbomach., 139(12), p. 121001), a freely available turbomachinery design system, and this was adopted as the course software—although other software choices were considered. Students now produce two turbomachinery designs during the course. These are both based on the J85 turbojet—largely to keep cycle calculations to a minimum but it was also important to ensure that students recognize that they were completing a real engineering task. The first task was a 3D aerodynamic design of multistage turbine, which includes compressible flow, tip clearance, and stacking techniques such as lean or sweep. The second task was a midspan (two-dimensional) compressor design. The exact cycle conditions were varied each year to explore design scenarios such as an increase in firing temperature. Assessment was by means of a short report where the best students report on their design choices, provide critical analysis of the design using appropriate postprocessing techniques, and compare their designs to the state of the art in the wider literature. As well as describing the successes and challenges of the update to 3D design methods the paper provides some guidance for educators thinking about adopting a similar approach.

Rheology-based wall function approach for wall-bounded turbulent flows of Herschel–Bulkley fluids

Modeling fully developed turbulent flow for Herschel–Bulkley (HB) fluids in pipes is a long-standing challenge. Existing semi-empirical, theoretical, and numerical methods are either inconsistent with experimental data or are validated for low Reynolds numbers. This study focuses on validating a novel approach using rheology-based wall functions within Reynolds-averaged Navier–Stokes solvers. Simulations of wall shear stress and velocity profiles were conducted across a wide range of Reynolds numbers using a single-phase HB fluid, with measurements taken both upstream and downstream of a 90° pipe bend. Two turbulence closure models, the k–ε model and the Reynolds stress model, were employed with the wall function implemented as a specified shear boundary condition. Results demonstrate significant improvements over the Newtonian-based models, such as standard wall function by Launder–Spalding or with available semi-empirical models, achieving strong statistical correlations and minimal deviation (from the experimental findings) at high Reynolds numbers. The study also examines the utility of the wall viscosity Reynolds number and assesses the reliability of semi-empirical models for HB fluids. These findings offer valuable insights for enhancing modeling accuracy in complex fluid flow scenarios, with potential applications spanning industries like mining, chemical processing, petroleum transportation, and sanitation systems, providing practical alternatives to costly experimental procedures in pipe systems.

Improvement of the efficiency for rim-driven thrusters through acceleration of gap flow

Efficiency optimization of the rim-driven thruster (RDT) has emerged as a prominent research topic in recent years. In this work, the Reynolds-averaged Navier-Stokes (RANS) solver is employed for simulating open water performance of RDTs, aiming at improving the efficiency of RDTs. Specifically, a series of RDTs are obtained by modifying the Ka4-70 propeller with a 19A duct, and their thrust and torque components, as well as efficiency and gap flow, are thoroughly examined. The investigation commences by exploring the impact of different rim sizes on RDT efficiency. A comparison is conducted between the open water performance of RDTs and the ducted propeller. Subsequently, a case with relatively high efficiency is identified, serving as a basis for the development of a series of modified RDTs equipped with acceleration devices. These devices facilitate accelerated axial flow in the gap, thereby enhancing the thrust generated by the duct, while simultaneously reducing the torque exerted on the rim through accelerated circumferential gap flow. Comparative analysis reveals that the improved RDTs can achieve an open water efficiency increase of up to 10.9% when the advance coefficient is set to 0.6, resulting in an efficiency value of 0.519. The findings presented in this paper introduce a novel direction for optimizing the efficiency of RDTs, contributing to the advancement of this field of study.

Performance improvement of horizontal axis wind turbines using curved gurney flap: 3D numerical investigation

The impact of curved Gurney flaps on the performance of a 660 kW V47 horizontal axis wind turbine (HAWT) is analyzed in this study. The trailing edge of the turbine blades is passively modified by curved flaps. The continuity and momentum equations are solved using a Reynolds-averaged Navier-Stokes solver and Shear-Stress-Transport turbulent model. The effect of the direction and radius of curved flaps on the aerodynamic performance of the wind turbine (torque and power generation, flow separation, and thrust loads) is examined. The study examines how the curved flap’s performance on HAWT is affected by the blade pitch angle ([Formula: see text]) and wind speed ([Formula: see text]). According to the results, curve flaps have a positive impact on the output torque at lower pitch angles ([Formula: see text]). The average torque increase for [Formula: see text] and [Formula: see text] is 3.7% for curve flaps, while it is only 2.9% for flat flaps. This conclusion is not valid for higher pitch angles ([Formula: see text]) where the flap disrupts the aerodynamic performance. Further, the use of curve flaps with the radius of [Formula: see text] (inward-type) can improve the torque produced (up to [Formula: see text]) compared to other curved flaps and even flat flaps, especially around the nominal operating point. This conclusion is valid for [Formula: see text], while for higher pitch angles, the flat Gurney flap has better performance generally.

A Computational Study to Predict the Seakeeping Performance of a Surfaced Submarine in Irregular Waves

Abstract In general, submarines are designed to optimize operation below the water surface because they spend most of their time underwater. On the other hand, the performance in the free surface condition is also important because submarines face a variety of scenarios to complete operational missions, and the free surface condition is unavoidable for port departure and arrival. In the case of a submarine, the numerical accuracy of the potential theory for seakeeping analysis is excellent in submerged conditions, but it is poor in free surface conditions because of nonlinear effects near the free surface area. In this study, star-ccm+ was used as a Reynolds-averaged Navier–Stokes (RANS) solver to estimate the seakeeping performance of a Canadian Victoria Class submarine in irregular waves. The results were compared with those of model tests from a published paper. In addition, the potential theory code was also used to assess the seakeeping performance and compare it with computational fluid dynamics (CFD) results. From the calculation results, the motion responses in irregular waves using CFD showed similar trends to the experimental results. In contrast, motion responses from potential code showed significantly larger values than the experimental results. In conclusion, CFD simulations with irregular waves can be a good solution to predict the seakeeping performance of submarines in free surface conditions.

Three-Dimensional Optimization of Blade Lean and Sweep for an Axial Compressor to Improve the Engine Performance

Nowadays, optimization methods have been considered as a practical tool to improve the performance of turbo-machines. For this purpose, the numerical study of the aerodynamic flow of the NASA Rotor-67 axial compressor has been investigated, and the results of this three-dimensional simulation show good agreement with experimental data. Then, the blade stacking line is changed using lean and sweep for Rotor-67 to improve the compressor performance. The third-order polynomial is selected to generate the lean and sweep changes from the hub to the shroud. The compressor flow field is solved by a Reynolds averaged Navier-Stokes solver. The genetic algorithm, coupled with the artificial neural networks, is implemented to find the optimum values for blade lean and sweep. Considering the three objective functions of pressure ratio, mass flow rate, and isentropic efficiency, the optimized rotor is obtained using the optimization algorithm. Two geometries are obtained using the optimization algorithm. The results of the optimized compressor include improving the isentropic efficiency, pressure ratio, and mass flow equal to 0.57%, 0.93%, and 1.8%, respectively. After compressor optimization, the effect of the changes in the compressor performance parameters is studied on a single spool turbojet engine. The engine is modeled by analyzing the Brayton thermodynamic cycle of the assumed turbojet engine under design point operating conditions. Results show that for the best test case, the engine with the optimized rotor, the thrust, and SFC are improved by 1.86% and 0.21%, respectively.

Data-driven turbulence anisotropy in film and effusion cooling flows

Film and effusion cooling flows contain complex flow that classical Reynolds-averaged Navier–Stokes (RANS) models struggle to capture. A tensor-basis neural network is employed to provide an anisotropic model that can reproduce the Reynolds stress fields of large-eddy simulations (LES). High-quality LES datasets are used to train, validate, and test a neural network model. A priori results show the model can reproduce the Reynolds stress field on a cooling case not present in the model's training. The neural networks are employed directly into RANS solver, augmenting a k-ω shear stress transport (SST) model, with conditioning applied. The model provided improvements to Reynolds stress, velocity, and temperature fields in cases not used to train the model, including a multi-hole case that differs from the single-hole geometry used to train the case. Underpredictions of the turbulent kinetic energy field, modeled with the SST transport equation, were found to lead to underpredictions in the neural network produced Reynolds stresses. Correcting this with the LES, resolved turbulent kinetic energy provided further agreement. The method found significant improvements to the surface cooling results that advance the current state-of-the-art in RANS modeling of film and effusion cooling flows.

Turbulence Modeling via Data Assimilation and Machine Learning for Separated Flows over Airfoils

Reynolds-averaged Navier–Stokes (RANS) models, which are known for their efficiency and robustness, are widely used in engineering applications. However, RANS models do not provide satisfactory predictive accuracy in many engineering-relevant flows with separation. Aiming at the difficulties of turbulence modeling for separated flows at high Reynolds number, this paper constructs turbulence models using data assimilation technique and deep neural network (DNN). Due to the uncertainty of traditional turbulence models, the parameters of Spalart–Allmaras (SA) turbulence model are optimized with experimental data to provide high-fidelity flowfields. Then DNN model maps the mean flow variables to eddy viscosity and replaces the SA model to be embedded within a RANS solver by iterative mode. Different from many existing studies, this DNN model does not depend on traditional turbulence models during the simulation process. This approach is applied to turbulent attached and separated flows and can significantly improve the accuracy for new flow conditions and airfoil shapes. Results show that the mean relative error of lift coefficient above the stall decreases by over 57% for all the airfoils.

Numerical simulation of KVLCC2 self-propulsion with ducted propeller in head waves

In order to meet the Energy Efficiency Design Index (EEDI) requirements, consideration of reducing added power in waves is important for large tankers operating in ocean environments. In this study, the Reynolds-averaged Navier-Stokes (RANS) solver is employed in Computational Fluid Dynamics (CFD) method to simulate the self-propulsion of KVLCC2 model with a ducted KP458 propeller in head waves, especially for comparison with the non-ducted cases. Two methods are adopted for simulating the ducted propeller: the discretized propeller method and the improved body force ducted propeller method. The latter method incorporates an improved principle of momentum conservation to solve the advance speed of the ducted virtual disk precisely in real time, resulting in similar accuracy and higher efficiency compared to the former method. For some wavelengths, the ducted cases display higher propulsive efficiency and lower power than the non-ducted cases, especially under very short wavelength condition, where negative thrust deduction fraction is observed in the ducted case. With the increase of wave height, the effect of the duct becomes more pronounced, resulting in an increase in propulsive efficiency and a reduction in power, both of which can exceed 10%. Moreover, this research carefully analyzes the added values of self-propulsion factors in head waves, as well as flow fields, providing useful insights to inform the application of ducted propellers in ultra-large ocean-going tankers.

Numerical simulations of cavitating water jet by an improved cavitation model of compressible mixture flow with an emphasis on phase change effects

Focusing on cavitation phenomena caused by high-speed submerged water jets, this paper presents an improved cavitation model for a compressible fluid mixture based on a concise estimation of fluid compressibility that considers phase change effects. The homogeneous two-phase flow assumption is adopted, and the gas phase is assumed to consist of vapor and non-condensable components. Equations of state for a pure liquid and an ideal gas are employed to evaluate the compressibility of the liquid and non-condensable components, and the compressibility of the vapor is treated semi-empirically as a constant. The model is embedded in an unsteady Reynolds-averaged Navier–Stokes solver, with the realizable k-ε model employed to evaluate the eddy viscosity. The turbulent cavitating flow caused by an impulsively started submerged water jet is treated. The pattern of periodic cavitation cloud shedding is acceptably captured, and the mass flow rate coefficient and its fluctuation frequency evaluated by simulations agree with the experimental results well. The validity of the proposed method is confirmed. The results reveal that cavitation occurs when pin/Pin reaches 0.65 and fluid flow begins to pulsate. In the well-developed stage, the leading cavitation cloud and a subsequent cloud are successively shed downstream, and this process is repeated. The subsequent cloud catches the leading cloud, and they coalesce in the range x/d≈ 2–3. The pressure fluctuations concentrate in the range of x/d≈2–5 corresponding to the periodic shedding of cavitation clouds. The mass flow rate coefficient pulsates from 0.59–0.66 under the effect of cavitation.

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Currently, the aviation industry is facing an oil and energy crisis and is contributing much more greenhouse gas emissions to the environment. Aircraft design approaches, such as aerodynamic shape optimization, new configuration concepts, and active control technology, have been the primary and effective means of achieving goals concerning fuel burn, noise, and emissions. For now, the design problems of relaxed static stability (RSS, an active control technique) and truss-braced wing (TBW) configurations with high-fidelity aerodynamic shape optimization methods have been investigated widely to promote aerodynamic performance. Nevertheless, they are studied almost always separately, and the combination of exploration and refined design is rarely presented. Therefore, the purposes of this work are to evaluate the benefits of RSS on a full TBW wing–body–tail configuration under various flight conditions and the effects on multi-components and to further explore the potential and analyze the aerodynamic features with the combination of shape optimization and RSS. To address these issues, on the one hand, a range of seven static stability margins are adopted to evaluate its effects with a high-fidelity Reynolds-averaged Navier–Stokes solver. On the other hand, seven cases of drag minimization multipoint aerodynamic design optimization are performed, which are with 600 shape variables and 13 twist variables, subject to lift coefficient, trim, and thickness constraints. The results indicate that with RSS only, the initial configuration has a 2.39% drag reduction under cruise conditions and a 3.01% and a 5.24% drag reduction under two off-design conditions. Additionally, the effects on the multi-components are observed and analyzed. Moreover, all of the optimized configurations with RSS have 2.13%, 2.42%, and 2.12% drag reductions under cruise conditions, drag divergence conditions, and near-buffet-onset conditions, respectively. The most promising optimized configuration has a lift-to-drag ratio of 24.48 with an aerodynamic efficiency of 17.14. The evaluations with a series of off-design points also present high-level aerodynamic efficiency.

Adjoint-based robust optimization design of laminar flow airfoil under flight condition uncertainties

Due to the high sensitivity of laminar wings to uncertain factors, although there have been a lot of engineering application attempts, so far laminar flow technology has not been effectively applied to the wings of large passenger aircraft. To address this issue, we develop an adjoint-based robust optimization design framework. The framework mainly includes a Reynolds-Averaged Navier-Stokes solver coupled with the simplified eN method, coupled adjoint equations considering the transition, a gradient-enhanced polynomial chaos expansion, and a statistical moment gradient solver. The robust optimization designs of laminar airfoils subject to uncertainties in flight conditions for subsonic and transonic conditions are performed and compared with the results with deterministic optimization. The results show that the robust design can improve the ability of the laminar airfoil to resist the uncertain disturbance of flight conditions and reduce the mean and standard deviation by reasonably balancing the deterministic and uncertain performance. The mean and standard deviation of the drag coefficient can be reduced by 28%-36% and 20%-71%. Meanwhile, a longer and more stable laminar flow region can be obtained. In contrast, the deterministic design may lead to a large decrease in the robustness of performance. The successful results demonstrate the effectiveness of the established robust design method for laminar airfoils, and could be applied and extended for future laminar flow wings design. Although the present framework is verified by 2D optimization examples, it has the potential to be applied to quasi-3D and 3D laminar wings, as well as actual large passenger aircraft design.

Resistance reduction optimization of an amphibious transport vehicle

The resistance reduction optimal design of amphibious vehicles is essential to improve efficiency and reduce energy consumption. In this paper, the hydrodynamic characteristics of an amphibious transport vehicle are investigated by Computational Fluid Dynamics (CFD) method based on the Reynolds-averaged Navier-Stokes (RANS) solver. A set of towing tests are conducted to verify grid independence and computational accuracy. Four typical shape control parameters are selected as optimal design variables and the independent effects of each variable are analyzed. The sample set is obtained using Latin Hypercube Sampling (LHS), and corresponding three-dimensional models are generated based on the parameters of each sample point. CFD calculations are then used to obtain the resistance characteristics of the models. The Kriging method is utilized to establish an approximate model, and the credibility of the model is verified. The Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is used to find a global optimal solution or set based on approximate models. Two optimized configurations, Opt1 and Opt2, are obtained, corresponding to single- and multi-objective optimization results, respectively. At the design speed of the amphibious transport vehicle, Opt1 has the highest resistance reduction rate of 12.7907% under the full load condition, while Opt2 has resistance reduction rates of 11.0863% and 8.5293% with and without load, respectively.

Hybrid Laminar Flow Control Optimizations for Infinite Swept Wings

Maintaining the laminar flow on surfaces through active control is a significantly promising technique for reducing fuel burn and alleviating environmental concerns in commercial aviation. However, there is a lack of systematic parameter studies for the hybrid laminar flow control (HLFC) together with natural laminar flow (NLF). To address this need, we optimize the infinite swept wings with different sweep angles and at various conditions, including different Mach numbers, Reynolds numbers, and lift coefficients. The Reynolds-averaged Navier-Stokes (RANS) solver coupled with the linear stability theory is applied for the laminar-turbulent transition prediction, and the traditional optimization method based on evolutionary algorithms is applied for laminar flow wing optimization. The optimization results found that HLFC is required when the NLF fails at a larger sweep angle (35°) and Reynolds number ( 20 × 10 6 ). The lower pressure peak with boundary-layer suction is found to delay the transition of the regional aviation condition. Besides, the pressure distribution of HLFC is similar to NLF results at the lower Reynolds number ( 10 × 10 6 ) or sweep angle (25°), i.e., a gentle negative pressure gradient near the leading edge and a small favorable pressure gradient behind it. Clarifying the characteristics of laminar flow wings will advance the application of the laminar flow technique within its field.

Adjoint high-dimensional aircraft shape optimization using a CAD-ROM parameterization

A gradient-based aeroelastic shape optimization framework making use of a reduced order model to substitute a parameterization based on computer-aided design software is presented. This parameterization concept is not novel in principle, but it is embedded here in a complex high-fidelity optimization process and proven for a high-dimensional design space. The design software is used initially to generate a parametric model of a three-dimensional transport aircraft configuration. To streamline the actual optimization process, the computer-aided design model is replaced with a parametric reduced order model based on proper orthogonal decomposition that is capable of predicting discrete surface displacement fields as a function of the design parameters. During the optimization, surface displacements are computed according to the current design parameters and applied on the baseline shape. In every optimization step, the aircraft's steady-state equilibrium of forces and moments are satisfied by a trimming algorithm and the Reynolds-averaged Navier–Stokes solver TAU is coupled with a linear structural finite-element method model. Gradients are computed analytically using geometric sensitivities provided by the reduced order model and by applying the adjoint method to the flow solver and the mesh deformation tool. The workflow is embedded within FlowSimulator, a multiphysics environment for high performance computing. The optimization process is demonstrated for a high-dimensional wing parameterization with 126 degrees of freedom. The aircraft cruise drag could be significantly reduced by 6% on a series of three continuously refined meshes for the aerodynamic analysis. For an accurate representation of the optimal shape by the computer-aided design software after the optimization, the approximation error introduced by the reduced order modelling approach must be sufficiently small. Therefore, the accuracy of the predictions was analyzed. The results identify the main source of the geometric error and quantify their effect on the drag reduction gained by the optimization. We dedicate this article to the memory of our colleague and friend Arno Ronzheimer, whose devotion to CAD modeling was unsurpassed.

Towards the effects of load condition on ship manoeuvrability by a system simulation method with hydrodynamic derivatives from RANS computations

The effects of load condition on ship manoeuvrability are investigated by means of system simulation method. To this end, a MMG-type mathematical manoeuvring model is applied to simulate the standard turning and zigzag rudder manoeuvres for a KVLCC2 ship model in six load conditions (two drafts × three trims). In order to determine the needed hydrodynamic derivatives, the forces and moments on the hull in a range of combined static drift and circle motions are computed by using the own expanded RANS (Reynolds-Averaged Navier-Stokes) solver on OpenFOAM. However, the coefficients of hydrodynamic interaction among hull, propeller and rudder are obtained from available experiments. The computed surge forces, sway forces and yaw moments agree fairly well with the experimental data, suggesting a promising prospect for the used RANS solver in the application of ship manoeuvring prediction. By regressing the hydrodynamic forces and moments, the hydrodynamic derivatives are obtained. Turning and zigzag rudder manoeuvres are simulated by solving ship motion equations in line with the acquired derivatives and coefficients. Comparing the simulated results between the full and ballast load condition without trim, a small draft (i.e. the ballast load condition) improves turning performance, but weaken course stability. For the three full load conditions or ballast load conditions, trim by bow improves turning ability, but deteriorates yaw-checking ability. The simulated results for two load conditions show satisfactory agreement with available experimental data, which suggests that the present procedure for ship manoeuvring prediction is effective. The course stability indexes are analysed as well. The load condition will affect significantly the manoeuvrability of a ship, at least for KVLCC2. It may be quite necessary to evaluate the manoeuvrability of a ship in different load conditions at the initial design stage.

Numerical study of periodic flame flashback in a cavity-based scramjet combustor

The periodic flame flashback phenomenon in an ethylene-fueled cavity-based scramjet combustor was numerically investigated by a three-dimensional unsteady Reynolds-averaged Navier–Stokes solver with two-step kinetics. The air inflow stagnation temperature is 1225 K, and its Mach number is 2.6. Spectral analyses revealed the combustion oscillations with flame flashbacks maintained in the separated scramjet mode with the establishment/vanishment of flow separation near the fuel injector, differing from previous studies of flame flashbacks connected to the ramjet/scramjet mode transitions. A mechanism with four evolution stages was proposed to elucidate the flow-flame interaction. In stage I, a rapid flame flashback upstream and shock-train extension were caused by the high-temperature induced auto-ignition tendency of well-mixed unburned gas in the near-sidewall low-speed region. In stage II, the combustion-induced back pressure and shock train gradually achieved an aerodynamic balance. The combustion flow barely changed in stage III. Meanwhile, a simplified model suggested that the gradual temperature rises occurring upstream of the cavity and away from the sidewall were caused by spanwise heat conduction. The higher temperatures would cause upstream flame propagation with enhanced heat release due to auto-ignition. However, the enhanced heat release occurred mostly in the subsonic flow, resulting in pressure decreases according to one-dimensional flow equations. A smaller near-sidewall separation was produced by the lower back-pressures, which prompted the rapid flame recession downstream in stage IV. Moreover, a simplified flame-spreading model was proposed to illuminate the flame propagation nature. The comparison of flame speeds with theoretical estimations indicated that the current flame was in the regime of turbulent flame propagation, rather than the C–J detonation or deflagration speculated in previous studies.

Prediction of biological development effects on drag forces of ceramic hull coating using Reynolds-averaged Navier–Stokes-based solver

Ships in service feature surfaces that exhibit biofouling, which alters the hydrodynamics of the vessels, thus affecting their normal displacement and significantly increasing their fuel consumption. The application of three types of ceramic coatings as ecological, effective and durable alternatives to commercial silicone-based marine coatings is investigated in this study. Three different ceramic glazes and two control commercial paints are analysed in an actual environment during 20 months of exposure to simulate the navigation conditions such that growth and roughness data can be obtained and then applied to computational fluid dynamics (CFD) software using an open-source Reynolds-averaged Navier–Stokes solver. The CFD results are validated under smooth hull conditions with a full-scale Kriso Container Ship (KCS) model and with different levels of hull roughness. The developed approach shows that the drag in hulls coated with conventional paint is 19% greater than that in hulls with ceramic coating.