Non-dimensional Wall Distance Research Articles

Best modeling practice for self-propulsion simulation of ship model in calm water

This paper presents the development of best Reynolds-Averaged Navier–Stokes modeling practices for simulations of propeller–hull interaction in calm water using Star-CCM+. Extensive convergence studies were carried out to examine effects of various propeller modeling methods and parameters, such as non-dimensional wall distance, grid resolution/distribution, and turbulence model. Bare-hull resistance and propeller open-water performance were first examined. For propeller–hull interaction, a simplified body-force method and a detailed propeller modeling method were applied to predict the wake fraction and propeller performance behind the hull. The difference in accuracy of the two methods was quantified, and the best modeling practices were recommended based on the convergence studies. Validation studies were carried out for the Korea Research Institute of Ships and Ocean Engineering Container Ship model. The pseudo-effective wake fraction determined from computational fluid dynamics simulations was introduced and compared with the experimental effective wake fraction.

Wall-resolved versus wall-modeled LES of the flow field and surface forced convective heat transfer for a low-rise building

Large eddy simulation (LES) is widely used to investigate the aerodynamics and convective heat transfer (CHT) at the surfaces of sharp-edged bluff bodies for a wide range of Reynolds (Re) numbers. Due to the heavy computational costs associated with implicit filtering in LES at high Reynolds number flows (Re ≥ 105), wall-modeled (WM) rather than wall-resolved (WR) LES is often adopted. However, the performance of LES-WM for such applications has not yet been systematically investigated. Therefore, this study evaluates the performance of LES-WM and LES-WR for the flow and thermal field at the facades of a low-rise building immersed in an atmospheric boundary layer. Four grids are constructed for LES-WM, each employing different resolution at the building surfaces reaching maximum non-dimensional wall distance y+ = 43, 57, 70, and 95. In addition, the performance of two wall functions, namely the Werner and Wengle and the enhanced wall function is investigated. The results show that the use of LES-WM can result in significant deviations in the predicted near-facade flow pattern and the surface convective heat transfer coefficient (CHTC). Grid resolution significantly impacts the CHTC results and deviations go up to 88% (at the base of the windward facade). Considerable deviations among the employed wall functions are apparent only on the finest grid. In this case, the implementation of the enhanced wall function indicates better performance compared to the non-blended law of the wall (combined with the Werner and Wengle) for CHTC in the regions of the leeward facade where the flow remains attached to the wall. The deviation of the enhanced wall function for surface-averaged CHTC is found to be 10.8% against the wall-resolved LES results, while for the non-blended law of the wall this is 19.2%.

A parametric study for a flettner rotor in standalone condition using CFD

In this study, the performance prediction and parametric study of a Flettner rotor in standalone condition was conducted based on a computational fluid dynamics (CFD) approach. A method for predicting the rotor performance based on steady RANS simulation was established, and the present method was validated with a reference rotor model in which wind tunnel test results were published. The CFD results depending on the turbulence models including k-omega shear stress transport (SST), k-epsilon, Spallart-Almaras and Reynolds stress model, and the non-dimensional wall distance (y+) as well as boundary conditions were compared with the experimental results. A model scale condition with a similar rotor diameter was considered to apply the CFD analysis method to the target rotor dimension. The CFD results based on the Reynolds number (Re) and y + values were compared in the model scale. In addition, a comparative analysis was performed on the model and prototype size under the same Re condition. Consequently, an appropriate condition for the CFD analysis was proposed and the lift, drag, torque and energy efficiency of the target rotor design were predicted. Based on this, parametric investigations for the rotor aspect ratios from 4 to 6 and the diameter ratio of the disk and rotor cylinder from 1.5 to 8 were conducted. The effect of aspect ratio was examined by varying the rotor diameter while maintaining the height. Furthermore, the torque components generated by the rotor cylinder and disk owing to the aerodynamic load were analyzed.

Three-Dimensional Simulation of Highly Unsteady and Isothermal Flow in Centrifugal Pumps for the Local Loss Analysis Including a Wall Function for Entropy Production

Abstract A local loss analysis (LLA) based on entropy production is presented for the numerical three-dimensional (3D) simulation of isothermal centrifugal pump flow. A finite volume method and a statistical turbulence model are employed. Wall functions for direct and turbulent entropy production in isothermal flow are derived, implemented in a node-centered finite volume scheme as a postprocessing procedure, and validated on an attached channel flow as well as on separated flow in an asymmetric diffuser. The integrity of the entropy wall function is demonstrated by a loss balance for a wide range of boundary layer resolution in terms of nondimensional wall distance y+≈1 to ≈200. Remaining differences to the total pressure loss are traced back to the particular turbulent wall function for the flow solution within the finite volume solver and vanish toward a wall resolution of the viscous sublayer, i.e., y+≈1. LLA together with the new entropy wall function is applied to highly unsteady isothermal flow in a single-blade pump as well as to part-load operation of a conventional multiblade pump which reveals distinctive flow structures that are associated with entropy production. By these examples, it is demonstrated how efficiency characteristics of centrifugal pumps can be attributed to local loss production in particular flow regions.

Computational and Experimental Study on Pressure Drop in a Fluidised Bed with Different Air Distributor Designs

Fluidised bed combustion (FBC) has been recognised as a suitable technology for converting a wide variety of fuels into energy. In a fluidised bed, the air is passed through a bed of granular solids resting on a distributor plate. Distributor plate plays an essential role as it determines the gas-solid movement and mixing pattern in a fluidised bed. It is believed that the effect of distributor configurations such as variation of free area ratio and air inclination angle through the distributor will affect the operational pressure drop of the fluidised bed. This paper presents an investigation on pressure drop in fluidised bed without the presence of inert materials using different air distributor designs; conventional perforated plate, multi-nozzles, and two newly proposed slotted distributors (45° and 90° inclined slotted distributors). A 3-dimensional Computational Fluid Dynamics (CFD) model is developed and compared with the experimental results. The flow model is based on the incompressible isothermal RNG k-epsilon turbulent model. In the present study, systematic grid-refinement is conducted to make sure that the simulation results are independent of the computational grid size. The non-dimensional wall distance, is examined as a key factor to verify the grid independence by comparing results obtained at different grid resolutions. The multi-nozzles distributor yields higher distributor pressure drop with the averaged maximum value of 749 Pa followed by perforated, 45° and 90° inclined distributors where the maximum pressure drop recorded to be about one-fourth of the value of the multi-nozzles pressure drop. The maximum pressure drop was associated with the higher kinetic head of the inlet air due to the restricted and minimum number of distributor openings and low free area ratio. The results suggested that low-pressure drop operation in a fluidised bed can be achieved with the increase of open area ratio of the distributor.

Unsteady aerodynamics computation and investigation of magnus effect on computed trajectory of spinning projectile from subsonic to supersonic speeds

AbstractThis paper describes the extensive numerical investigation carried out on a 203-mm spin-stabilised projectile to study the effects of Magnus force at high angles of attack on the stability and flight-trajectory parameters, for further validation and incorporation in a 6-DOF trajectory solver for flight-stability analysis. Magnus force typically influences the course of flight by causing the projectile to drift from its intended path in addition to generation of inbuilt dynamic instabilities in pitch and yaw orientation and is a function of AoA and spin rate. This study is a consolidation of the authors’ previous research on the same caliber projectile but with time-accurate analysis. It has been found that typically, the Magnus force and moment calculation requires time-accurate Navier Stokes equations to be solved numerically for accurate prediction(1,2). Hence, to complete the extraction of static and dynamic coefficients derivatives, unstructured time-accurate CFD analysis on multiple configurations, ranging from subsonic to supersonic Mach regimes, has been evaluated using Large Eddy Simulation (LES) and found to be suitable for capturing the desired effects. However, the LES simulation requires non-dimensional wall distance (y+) of the order of 0.5 – 1, with LES_IQ > 75% thus, is computationally-intensive. In addition, to cover the entire flight envelope from Charge 1 (249 m/s) to Charge 7 (595 m/s), at spin rate from 500 rad/s to 750 rad/s, 30 cases have been evaluated to generate the time-accurate coefficient library for integration with 6-DOF solver analysis. The results obtained have been compared with the available experimental data and found to be in reasonable agreement. The results of 6-DOF solver, incorporating the extracted coefficients, were compared with firing-table results, which further validated the computational methodology. This study provides an insight on how opposite flow interacts with the attached boundary layer due to spin rate and generates a turbulent interacting flow with variation in vortical structures for Q-Criterion vortex-flow visualization.

Effect of grid sensitivity on the performance of wall adapting SGS models for LES of swirling and separating–reattaching flows

The present study assesses the performance of the Wall Adapting SGS models along with the Dynamic Smagorinsky model for flows involving separation, reattachment and swirl. Due to the simple geometry and wide application in a variety of engineering systems, the Backward-Facing Step (BFS) geometry and Confined Swirling Flow (CSF) geometry are invoked in the present case. The calculation of the SGS stresses employs three models, namely, the Dynamic Smagorinsky model, the Wall Adapting Local Eddy viscosity (WALE) model and the Dynamic WALE model. For studying the effect of the grid sensitivity, the simulations are performed over two sets of grids with different resolutions based on the non-dimensional wall distance parameter ( y+ ). Grids corresponding to y+= 70 and y+= 20 are employed for the subsonic flow over the BFS while grids corresponding to y+= 40 and y+= 20 are employed for supersonic flow over the BFS and for confined swirling flow geometry. The validation against the experimental results includes the mean flow fields and the turbulent stresses obtained for each case. The results reveal that for the fine grid (y+= 20), the near wall eddy viscosity profile for the WALE model is better than both the Dynamic WALE and the Dynamic Smagorinsky model. The difference between the predictions of the coarse and fine grids for Dynamic Smagorinsky and the WALE model is high whereas, the Dynamic WALE model is almost insensitive to the grid resolutions considered for the present case. The mean velocity and pressure values as well as the turbulent quantities predicted by the Dynamic WALE model are closest to the experimental values for all the cases.

Methodology of Turbulence Parameter Correction in Water-Lubricated Thrust Bearings

Oil-lubricated bearings are widely used in high-speed rotating machines such as those found in automotive industries and aerospace. However, environmental issues and risk-averse operations are resulting in the removal of oil and the replacement of all sealed oil bearings with reliable water-lubricated bearings. The low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. This requires finer meshes for finite element modeling when compared to oil-lubricated bearings as the low-viscosity fluid produces a very thin lubricant film. Analyzing water-lubricated bearings can also produce convergence and accuracy issues in traditional oil-based analysis codes. Fitting the velocity profile with experiments having a nondimensional wall distance y+ in a certain range results in Ng-optimized Reichardt's constants k and δ+. The definition of y+ can be used to approximate the first layer thickness calculated for a uniform mesh. On the condition that the y+ is fixed to that of a standard oil bearing for which an oil-bearing code was validated, the number of elements across the film thickness and coefficients used in the eddy-viscosity equation can be adjusted to allow for convergence with other fluids other than that which the traditional oil-bearing code was designed for. This study proposed a new methodology to preserve the y+ value to make water-lubricated thrust bearing models valid. A method for determining the required number of cross-film elements in water-lubricated bearings was found. The results of this study could aid in improving future designs and models of water-lubricated bearings.

A unified wall function for compressible turbulence modelling

ABSTRACTTurbulence modelling near the wall often requires a high mesh density clustered around the wall and the first cells adjacent to the wall to be placed in the viscous sublayer. As a result, the numerical stability is constrained by the smallest cell size and hence requires high computational overhead. In the present study, a unified wall function is developed which is valid for viscous sublayer, buffer sublayer and inertial sublayer, as well as including effects of compressibility, heat transfer and pressure gradient. The resulting wall function applies to compressible turbulence modelling for both isothermal and adiabatic wall boundary conditions with the non-zero pressure gradient. Two simple wall function algorithms are implemented for practical computation of isothermal and adiabatic wall boundary conditions. The numerical results show that the wall function evaluates the wall shear stress and turbulent quantities of wall adjacent cells at wide range of non-dimensional wall distance and alleviate the number and size of cells required.

Using forward end-sweep to reduce transonic cantilevered stator losses to improve compressor performance

ABSTRACTThe complicated flows in a transonic cantilevered stator would cause serious aerodynamic losses and reducing these losses would contribute much to improving the overall aerodynamic performance of a compressor. The paper conducts an overview study of the potential aerodynamic losses in a transonic cantilevered stator and presents a systematic numerical study for the effects of forward end sweep on reducing aerodynamic losses. A 2-D stator blade is used to throw light upon the physical mechanism of the forward end sweep on reducing the losses. At the casing region, forward end sweep has led to a redistribution of the blade load along the chordwise direction, higher in the front part and lower in the rear part. This result leads to a lower pressure gradient from the 30% chord location to the trailing edge and can be beneficial for the reduction of the corner separation. At the hub region, on one aspect, forward end sweep reduces both the peak Mach number and the size of the high-Ma region of the blade suction surface, thus decreasing the shock loss near the hub. On the other aspect, it also reduces the peak load and the strength of the leakage vortex, therefore alleviating the flow blockages. Simultaneously, the forward end sweep is applied to a commercial and high-performance multistage compressor to further validate its feasibility. When the technique is applied to the transonic first four stator rows, an improvement of adiabatic efficiency is achieved by ∼ 0.85% and the compressor stable operating range is slightly increased. The results suggest that the forward end-swept transonic cantilevered stators have a significant potential for reducing the stator losses. They would provide guidelines to advance the cantilevered stator design and further improve the compressor aerodynamic performance.Abbreviations: h, stagnation enthalpy; , stagnation pressure; p, static pressure; U, blade rotational speed at tip; V, velocity; , non-dimensional wall distance; , total pressure loss coefficient; , flow coefficient (Vx/U); , stage load coefficient (Δh/U2); , adiabatic efficiency; , total pressure ratio; in, inlet; out, outlet; LE/TE, leading/trailing edge; PS/SS, pressure/suction surface

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

ABSTRACTWe developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier–Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y+ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y+ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.

Analysis of free-surface effects on swimming by the application of the computational fluid dynamics method

In this study, free-surface effects on swimming are investigated by the application of the computational fluid dynamics method for the first time. The major goal of this study is to represent a new methodology to numerically investigate free-surface effects on swimming. Utilizing a two-dimensional solver with steady flow conditions, the numerical results for swimming at a fully submerged level are validated with the data presented by previous researchers. The validity of the results is also examined through the study of mesh independency and the control of a critical turbulence feature, entitled as non-dimensional wall distance (y+). Finally, for the analysis of swimming at the free-surface level, a two-dimensional time-dependent solver with a well-known multiphase mathematical model is implemented to simultaneously investigate two-phase flow interactions and wave propagation in the proximity of the swimmer’s body. The development of different flow topology features, including major vortex cores and secondary recirculation zones as well as turbulence mixing and flow updraft and downdraft, are investigated and used to compare free-surface swimming against fully submerged cases. While the drag coefficient continuously decreases for higher advance velocities for a fully submerged case, a gradual augmentation is observed for the drag coefficient at a free-surface swimming level. The obtained results suggest that while the proportion of wave drag is ignorable at low swimming speeds below 1 m/s, in the case of higher speeds, its amount enhances significantly and constitutes about 15% of the total drag. Moreover, the proposed methodology is demonstrated to be efficient in the simulation of flow characteristics and phase interactions in swimming at the free-surface level.

Differing development of the velocity profiles of three-dimensional turbulent boundary layers

i x,z d •• Reynolds number based on boundarylayer thickness, = U^d/v • main-flow component of mean velocity in x direction : friction velocity, = VTV//O = freestream velocity at the edge of the boundary layer = scaling velocities of the wake function, Eqs. (7) and (12) = differences of the scaling velocities of the wake function, Eqs. (7) and (12) = nondimensional velocity component in x direction, = U/UTX • crossflow component of mean velocity in z direction = nondimensional velocity component in z direction, = W/UTZ nondimensional, characteristic quantity, = RedwK = y + K § = local coordinate aligned with the free streamline = local coordinate normal to the wall = nondimensional wall distance, = yuT/v local coordinate normal to the free streamline = angle of the free streamline = cross flow angle = angle of the wall shear stress = boundary-layer thickness = nondimensional wall distance, =y/d -von Karman constant, =0.41 = kinematic viscosity = fluid density = wall shear stress = wake function, Eq. (9) = model function, Eq. (10) = nondimensional friction velocity, = UT/

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.

Developing turbulent boundary layers with system rotation

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

Behavior of a Spark-induced Bubble between Parallel Walls

The knowledge of the behavior of a cavitation bubble in a narrow space, such as a cylinder liner, is still very scanty. In this study, the behavior of a spark-induced bubble between parallel walls is photographed by a high-speed camera, and the generated impulsive pressure waves are detected by piezo-type transducers. The experiment is carried out by changing the distance between the walls and the location of the bubble formation, and it is made clear that when the non-dimensional wall distance is small, the collapsing bubble becomes gourd shaped and at the final stage of the collapse, the bubble is broken down into two small bubbles, and their sizes depend on the initial bubble location. Moreover, such behavior of the bubble is simulated by the numerical method of Plesset-Chapman.