Normal Velocity Gradient Research Articles

Effect of near-wall distance on velocity slip and temperature jump conditions in hypersonic rarefied gas flows

In nonequilibrium slip and jump conditions, normal gas velocity and temperature gradients are used to calculate the gas slip velocity and temperature at the surface, respectively. Gökçen et al. (Computational fluid dynamics near the continuum limit, AIAA Paper No. 87-1115, 1987, and Gökçen and MacCormack, Nonequilibrium effects for hypersonic transitional flows using continuum approach, AIAA Paper No. 89-0461, 1989) stated that the tangential velocity and temperature of the gas molecules before a collision with the surface could be interpreted as the macroscopic tangential velocity and temperature of the gas molecules at the so-called near-wall distances auλ and aTλT away from the surface, respectively. The coefficients au and aT are the order of unity. In the present work, new forms of the slip and jump conditions are proposed by modifying the Gökçen slip and jump conditions to include the coefficients (au, aT). Numerical investigations are comprehensively conducted to determine the numerically proper values (au, aT) for the hypersonic rarefied gas flows. Cases such as the circular cylinder in cross-flow and sharp and blunted leading edge wedge are considered in the present work, with nitrogen as the working gas. The simulation results show the significant effects of the coefficients (au, aT) on the accuracy of the slip velocity and surface gas temperature predictions, and the values of au = 1.2 and aT = 1.1 show good agreement with the direct simulation Monte Carlo data.

Influence of initial permeability on seepage behavior of the lubricant stored in hydrogel surface

This paper studied the unsteady seepage characteristics of lubricant stored in hydrogel under different initial permeability. Results show that the distribution of the permeability is determined by the deformation of hydrogel. The normal velocity and normal pressure gradient on the hydrogel surface have diffusion, fluctuation and stabilization processes. The normal pressure gradient is the internal cause that drives the change of the velocity. With the increase of the initial permeability, the seepage velocity increases significantly. Higher initial permeability leads to a higher exudation rate of hydrogel at the initial stage of loading, but the exudation is unsustainable. Considering the instantaneous seepage rate of the lubricant and the long-term lubrication, it is necessary to reasonably design the initial permeability.

Extension of the boundary integral method for different boundary conditions in steady-state Stokes flows

PurposeThe boundary integral method (BIM) provides unparalleled computational efficiency for solving problems wherever it is applicable. For Stokes flows, the BIM in its current form can only be applied to a limited class of problems that generally comprises boundaries with either specified velocity or stress. This study aims to radically extend the applicability by developing a general method within the BIM framework that can handle periodic, symmetry, zero normal-velocity gradient and the specified pressure boundary conditions. This study is limited in scope to steady-state flows.Design/methodology/approachThe proposed method introduces a set of points near the boundary for the symmetry, zero normal-velocity gradient and specified pressure boundary conditions. The formulation for the first two boundary conditions use a spatial discretization procedure within the BIM framework to arrive at a set of equations for the unknowns. The specified pressure boundary condition warrants the decomposition of the unknown traction term into simpler components before the discretization procedure can be executed. Though the new methodology is illustrated in detail for two-dimensional rectangular domains, it can be generalized to more complex three-dimensional cases. This will be the subject for future investigations.FindingsThe current endeavor has successfully demonstrated the incorporation of the above boundary conditions through simple Stokes flow problems like plane channel flow, flow through ribbed duct and plane wall jet. The predicted results matched adequately with either analytical solutions or with available literature data.Originality/valueTo the best of the author’s knowledge, this is the first time that the exit boundary conditions like zero normal-velocity gradient and specified pressure have been formulated within the BIM for Stokes flows. These boundary conditions are extremely powerful and the current research initiative has the potential to dramatically increase the range of applicability of the BIM for Stokes flow simulations.

Experimental and numerical studies on the air-injection drag reduction of the ship model

Experimental and numerical studies on the air-injection drag reduction (AIDR) of the ship model are conducted. For the experiments, the ship model and air-injection device are specially designed and the AIDR of the ship model is investigated considering one draft and three speeds. Then, considering two ship speeds, the AIDR of the ship model is simulated using two numerical models, namely the Euler-Euler two-fluid model and VOF model. It is found that for the surface ship there are still three drag reduction regions. Microbubble drag reduction (MBDR) is dominant for low air flow rates and air layer drag reduction (ALDR) is dominant for high air flow rates, and the transitional region exists for the medium air flow rates. For MBDR, the mechanism is related to the reduction of both effective dynamic viscosity and normal velocity gradient. Bubble size is the key influencing factor. Smaller bubbles are more favorable for drag reduction. Large millimeter bubbles can increase drag, which is owing to the extra turbulence viscosity. For ALDR, the mechanism is mainly owing to the loss of wet surface area and the key influencing factor is the air cover area. In general, ships with higher speed are more favorable for AIDR.

Experimental and numerical studies of turbulent flows over two-dimensional and three-dimensional rough surfaces under an adverse pressure gradient

The effects of surface roughness and other surface topographical feature on turbulent boundary layer (TBL) development have been widely explored, especially for flow cases with a constant streamwise pressure gradient distribution. In the case where the TBL is exposed to the action of an adverse pressure gradient (APG), flow separation is expected to occur and the classical mechanisms responsible for energy transport between the inner and outer part of the TBL are invalid. The combined effect of roughness and APG on the TBL is not easy to predict, especially due to the lack of databases containing relevant research data. The main aims of the present study were to conduct experimental investigations and to perform large eddy simulations to determine the effects of different surface topographies (two-dimensional (2D) and three-dimensional (3D)) on turbulent flow development over a smooth wall under a strong APG downstream of the corrugation. The investigation was performed with a fixed value of the Reynolds number Reθ = 4900. In particular, the differences in the production and dynamics of near-wall vortical structures under different corrugation geometries were studied. It was found that the higher amplitude of 2D wavy surface the greater production of turbulence and the earlier separation of the TBL. The response of the TBL differed according to the 3D topography, where it was characterized by a greater streamwise velocity deficit, lower growth of all components of the velocity fluctuations, and a smaller increase in the normal velocity gradient relative to the 2D case with comparable amplitude. The results also demonstrated that the 3D case generated smaller and less energetic structures on the flat plate downstream of the corrugation compared with the 2D case.

Improved wall model treatment for aerodynamic flows in LBM

The article deals with an improved treatment of wall models for the simulation of turbulent flows in the framework of Immersed Wall Boundaries on Cartesian grids. The emphasis is put on the implementation in a Lattice-Boltzmann Method solver without loss of generality, since the proposed approach can be used in Navier–Stokes-based solvers in a straightforward way. The proposed improved wall model implementation relies on the combination of several key elements, namely i) the removal of grid points too close to the solid surface and ii) an original computation of wall normal velocity gradient and iii) the interpolation scheme. The new method is successfully assessed considering URANS simulations focusing on steady solutions of the Zero Pressure Gradient turbulent flat plate boundary layer and the turbulent flow around a NACA0012 airfoil at several angles of attack.

Coupling of turbulence wall models and immersed boundaries on Cartesian grids

An improved coupling of immersed boundary method and turbulence wall models on Cartesian grids is proposed, for producing smooth wall surface pressure and skin friction at high Reynolds numbers. Spurious oscillations are frequently observed on these quantities with most immersed boundary wall modeling methods, especially for the skin friction which is found to be very sensitive to the solid surface's position and orientation against the Cartesian grids. The problem originates from the irregularity of the wall distance on the stair-step grid boundaries where the immersed boundary conditions are applied. To reduce this directional error, several modifications are presented to enhance the near wall solution. First, the commonly used interpolation for the flow velocity is replaced by one for the friction velocity, which has much less variation near wall. The concept of using a fictitious point to retrieve flow fields in the wall normal direction is abandoned and the interpolation is performed in the wall parallel plane with existing fluid points. Secondly, the velocity gradients at the approximated boundary are computed with advanced schemes and the normal gradient of the tangential velocity is reconstructed from the wall laws. To further protect the near wall solution, the normal velocity gradient and the working viscosity from the Spalart-Allmaras turbulence model are enforced by their theoretical solutions in the interior fluid close to the wall. Additionally, various post-processing algorithms for reconstructing wall surface quantities and force integrations are investigated. Other related factors are also discussed for their effects on the results. The validity of present method has been demonstrated through numerical benchmark tests on a flat plate at zero pressure gradient, both aligned and inclined with respect to the grid, as well as aerodynamic cases of NACA 23012 airfoil and NASA trap wing.

Breakup process of liquid jet in gas film

In order to study the breakup process of liquid jet in gas film, the backlit photography technique and the VOF TO DPM method are used for experimental and simulation research respectively. Water and air are used as simulant media. Grid adaptive technology is used to refine the gas-liquid interface grid and improve the capture accuracy of the gas-liquid interface. The results show that there are two main breakup processes of liquid jet in gas film: column breakup and surface breakup. The local high-pressure zone in front of the liquid jet makes the jet have a large normal velocity gradient, which causes R-T instability. The surface wave that is generated by the R-T instability is mainly responsible for the liquid column breakup. When the thin liquid film reaches a column breakup point, the airflow penetrating the trough of the surface wave causes the jet column to break. The tangential velocity gradient is generated when the gas film bypasses the liquid jet surface, which causes K-H instability. The K-H surface waves cause ligaments and droplets to strip from the surface of the liquid jet. The local momentum ratio has an important influence on the breakup process of the liquid jet in gas film. When the local momentum ratio is low, the breakup of liquid jet is dominated by the K-H instability. As the local momentum ratio increases, the breakup of liquid jet is gradually dominated by R-T instability. The local momentum ratio plays an important role in the distribution range of the liquid jet in gas film. When the local momentum ratio is low, the ligaments and droplets caused by the liquid jet are mainly distributed within the range of gas film. As the local momentum ratio increases, part of the ligaments and droplets escape from the range of the gas film. The liquid jet penetrates the gas film when the local momentum ratio is greater than 0.74. The breakup length and the penetration depth are both affected by the local momentum ratio. The breakup length increases with the local momentum ratio increasing. The penetration depth also increases with the local momentum ratio, and the penetration depth increases significantly when the liquid jet penetrates the gas film.

A model to include turbulence-turbulence interaction in the prediction of trailing edge far field noise for high angles of attack or slightly separated flow

The most dominant noise source of modern wind turbines is considered to be trailing edge (TE) noise. TE noise increases with increasing angle of attack of the flow. For wind turbine development it is hence crucial to predict TE noise for high angles of attack up to slightly separated flow. It results from wall pressure fluctuations induced by turbulent vortices in the boundary layer. The source term for the pressure fluctuations consists of two terms, the interaction of the mean shear with the turbulence and the turbulence-turbulence interaction (TTI). TTI is neglected in the commonly used TE noise prediction model by Blake, resulting in a strong dependency of the model on the wall normal mean velocity gradient. With increasing angle of attack this wall normal gradient of the boundary layer diminishes. Hence the TTI of the source equation has to be taken into account in order to achieve reliable predictions towards higher angles of attack. Here a new simplified-analytical model including the TTI, based on the model deduction by Blake, is presented and compared to experimental data. It is found that the prediction quality for high angles of attack and slight TE separation can be improved with the new model.

Numerical research on the turbulent drag reduction mechanism of a transverse groove structure on an airfoil blade

The optimization of the airfoil has a significant impact on the reduction of energy consumption for a rotary machine. In this paper, ANSYS Fluent is used to study the influence of different groove structure sizes on the turbulence drag of NACA0012 airfoil blades, and the drag reduction mechanism is analyzed. The results show that the groove structure can significantly reduce the drag during the working speed of the fan. The optimal groove size is s = 0.1 mm and the drag is reduced by 9.65%. The secondary vortices reduce the normal velocity gradient at the top of the groove structure, resulting in a reduction in viscous drag. However, as the groove size increases, the drag reduction effect decreases, and even the drag increases. The overall shear stress of the airfoil surface with the transverse groove structure is smaller than the original airfoil, and the velocity gradient of the airfoil surface is reduced. The two sides work together to reduce the turbulence drag of the airfoil. Besides, the spacing between the grooves increases the shear stress in some areas, but reduces the mutual interference of the vortices, so there is an optimum value for the groove spacing.

Modelling Approach and Challenges in Simulating Dross Formation in Ductile Iron Castings

Dross is one of the most challenging quality issues in high integrity ductile iron castings. The formation of dross is linked to the applied metallurgy, metal treatment, process control and gating/rigging design. One of the primary concerns in this regard is entrainment of air into the melt during filling of the casting. Today, avoiding and controlling dross relies on the practical experience and process know-how of foundry experts. A quantitative understanding of the formation mechanisms or the prediction of final amounts and locations of dross in castings is not available. In this paper a computational model is developed for predicting the formation, motion and final location of dross inclusions during pouring of ductile iron castings. The focus is on the important mechanism of dross generation due to air entrainment during filling of the mold. The model predicts the local air entrainment rate as a function of the turbulent kinetic energy of the liquid metal and the normal velocity gradient of the metal at the liquid metal-air interface. The dross inclusions resulting from the exposure to the entrained air are transported with the melt flow under the combined influences of drag and buoyancy, and captured by the solidifying casting structure. The model is implemented in a commercial casting simulation software code. Ductile iron casting experiments are conducted to validate the model using castings having a variety of gating systems, section thicknesses, and surface orientations. Dross is measured by serial sectioning of the solidified castings. Good agreement between measured and predicted dross amounts and locations is obtained. The results reveal how gating system design affects dross formation. Clean ductile iron castings can be obtained by minimizing air entrainment during pouring. The present model allows foundries to evaluate different gating designs and pouring parameters before the first casting is poured. The paper also discusses open issues and practical challenges in quantifying the amounts of dross as a function of the entire processing route of a casting.

Modelling of air entrainment during pouring of metal castings

Air entrainment during mould filling is major source of oxide inclusions in metal castings. A model is developed to predict the location and rate of air entrainment as part of a standard mould filling simulation. The local air entrainment rate is calculated as a function of the turbulent kinetic energy and the magnitude of the normal velocity gradient of the liquid metal at the liquid–air interface. The model is validated through comparisons with experimental air entrainment measurements for a plunging water jet. It is then applied to study the effect of gating system design and pouring parameters on air entrainment in steel casting. Air entrainment is found to be reduced for a metal stream from the ladle that is centred above the pouring cup or the use of an offset step pouring basin, low head heights, high flow rates, a pressurised gating system and bottom ingates.

Research on Drag Reduction Performance of Bionic Shark Gill Jet Surface

According to the problem of bionic shark gill jet can reduce friction on shark surface, a model of bionic jet surface was established based on shark surface was analyzed by measurements, and its numerical simulation was processed by using RNG k-ε turbulence model. The results show that: the gill jet can reduce frictional resistance on shark surface, and the best drag reduction can be got when the speed of main field is 5m/s, furthermore the maximum drag reduction rate can be up to 17.15%. The pressure of jet hole upstream is reduced which due to the barrier to the facing fluid by the jet, so that the pressure resistance of jet surface is reduced as well. Besides, jet fluid is blocked in the boundary layer by mainstream fluid, which caused the fluid velocity of jet hole downstream is reduced, the thickness of boundary layer is increased, and the normal velocity gradient of wall is reduced, so as to achieve the effect of drag reduction.

Slip flow over micron-sized spherical particles at intermediate Reynolds numbers

A numerical investigation has been performed to identify the rarefaction effects on the flow structure of an isolated micron-sized spherical particle. An isothermal sphere in the slip flow regime 10−3 ≤ Kn ≤ 10−1 at intermediate Reynolds numbers (1 ≤ Re ≤ 50) is considered. The Navier-Stokes equations are solved by a control volume technique in conjunction with the velocity slip boundary condition. It was found that the wake region can shrink considerably as the Knudsen number increases. Furthermore, the skin friction and pressure drag coefficients decrease as the Knudsen number increases due to the reduction in normal velocity gradients and shrinkage of the wake region, respectively. Engineering correlations for predicting the total drag coefficient in the slip flow regime are presented.

Numerical simulation on ship bubbly wake

Based on a volume of fluid two-phase model imbedded in the general computational fluid dynamics code FLUENT6.3.26, the viscous flow with free surface around a model-scaled KRISO container ship (KCS) was first numerically simulated. Then with a rigid-lid-free-surface method, the underwater flow field was computed based on the mixture multiphase model to simulate the bubbly wake around the KCS hull. The realizable k-ɛ two-equation turbulence model and Reynolds stress model were used to analyze the effects of turbulence model on the ship bubbly wake. The air entrainment model, which is relative to the normal velocity gradient of the free surface, and the solving method were verified by the qualitatively reasonable computed results.

Study on turbulence features near an oscillating curved wall

In pursuit of possibly true turbulent characters and for exploring a change in turbulence structures near an oscillating flexible wall-curved surface, a sinusoidal oscillation mode was forced to a curved wall, whose vibrations disturbed the flow with an interacting effort between the fluid and the structure. The methodology used was the Large Eddy Simulation (LES) with fluid-structure interaction. The oscillating configuration was on a Fourier sinusoidal mode from the measurements of a Francis hydro turbine blade vibration. The effects of the vibration on the skin friction coefficient, vortices, turbulent coherent structures, and other statistical quantities were studied. The results showed that the streamwise velocity gradient along the normal direction and the normal velocity gradient along the spanwise direction were considerably increased within the viscous sublayer because of the oscillating wall, which additionally caused the low speed streaks to stay away from the wall and the high-momentum flows to be toward the wall. As a result, the streamwise vortices were much more elongated along the downstream to get an energy balance, and the wall skin friction coefficient or the wall friction velocity rose up.

Magnetic fluid in a time-dependent gap Hele–Shaw cell

The traditional Saffman–Taylor problem addresses the flow of non-magnetic fluids in a fixed gap Hele–Shaw cell. Under such circumstances interfacial singularities arise if the surface tension between the fluids is zero. In this work, we study a variant of this interesting hydrodynamic situation and consider the flow of a magnetic fluid in a Hele–Shaw cell with a time-dependent gap spacing. We focus on the zero surface tension limit and investigate the possibility of controlling interfacial singularities with an appropriate magnetic field. Our analytical mode-coupling approach shows evidence that the action of an azimuthal magnetic field and plus the inclusion of stresses originated from normal velocity gradients conspire to singularity inhibition.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Reducing turbidity and coagulant residue in treated water through optimization of rapid mix conditions

This study reports basic research on the effectiveness of raising the rapid agitation strength (velocity gradient, or GR value) in improving the treatment efficacy of coagulation and sedimentation. Coagulation and sedimentation treatment with a normal velocity gradient of 100-200 s-1 reduces turbidity to less than 1 mg/L but leaves a significant amount of coagulant residue and thus does not reduce the suction time index (STI) to a desirable level. By contrast, higher GR values yield improvements in the turbidity of the treated water, as well as marked improvements in the STI. Good coagulation and sedimentation treatment is also related to reductions in filtration head loss.

A micro-electro-mechanical-system-based thermal shear-stress sensor with self-frequency compensation

By applying the micro-electro-mechanical-system (MEMS) fabrication technology, we developed a micro-thermal sensor to measure surface shear stress. The heat transfer from a polysilicon heater depends on the normal velocity gradient and thus provides the surface shear stress. However, the sensitivity of the shear-stress measurements in air is less than desirable due to the low heat capacity of air. A unique feature of this micro-sensor is that the heating element, a film 1 µm thick, is separated from the substrate by a vacuum cavity 2 µm thick. The vacuum cavity prevents the conduction of heat to the substrate and therefore improves the sensitivity by an order of magnitude. Owing to the low thermal inertia of the miniature sensing element, this shear-stress micro-sensor can provide instantaneous measurements of small-scale turbulence. Furthermore, MEMS technology allows us make multiple sensors on a single chip so that we can perform distributed measurements. In this study, we use multiple polysilicon sensor elements to improve the dynamic performance of the sensor itself. It is demonstrated that the frequency-response range of a constant-current sensor can be extended from the order of 100 Hz to 100 kHz.