Pressure fields in the airflow over wind-generated surface waves

The quantification of pressure fields in the airflow over water waves is fundamental for understanding the coupling of the atmosphere and the ocean. The relationship between the pressure field, and the water surface slope and velocity, are crucial in setting the fluxes of momentum and energy. However, quantifying these fluxes is hampered by difficulties in measuring pressure fields at the wavy air-water interface. Here we utilise results from laboratory experiments of wind-driven surface waves. The data consist of particle image velocimetry of the airflow combined with laser-induced fluorescence of the water surface. These data were then used to develop a pressure field reconstruction technique based on solving a pressure Poisson equation in the airflow above water waves. The results allow for independent quantification of both the viscous stress and pressure-induced form drag components of the momentum flux. Comparison of these with an independent bulk estimate of the total momentum flux (based on law-of-the-wall theory) shows that the momentum budget is closed to within approximately 5%. In the partitioning of the momentum flux between viscous and pressure drag components, we find a greater influence of form drag at high wind speeds and wave slopes. An analysis of the various approximations and assumptions made in the pressure reconstruction, along with the corresponding sources of error, is also presented.

Transport of solute and solvent driven by lubrication pressure through non-deformable permeable membranes

A discrete-forcing immersed boundary method with permeable membranes is developed to investigate the effect of lubrication on the permeations of solute and solvent through membrane. The permeation models are incorporated into the discretisation at the fluid cells including the membrane, and discretised equations for the pressure Poisson equation and convection–diffusion equation for the solute are represented with the discontinuities at the membrane. The validity of the proposed method is established by the convergence of the numerical results of the permeate fluxes (solute and solvent) to higher-order analytical models in a lubrication-dominated flow field. As a model of the mass exchange between inside and outside of a biological cell flowing in a capillary, a circular membrane is placed between parallel flat plates, and the effect of lubrication is investigated by varying the distance between the membrane and the walls. The pressure discontinuity near the wall is larger than that at the stagnation point, which is a highlighted effect of lubrication. In the case of a small gap, the solute transport is dominated by convection inside the circular membrane and by diffusion outside. Through the time variation of the concentration in the circular membrane, lubrication is shown to enhance mass transport from/to inside and outside the membrane.

Pressure Stabilization Strategies for a LES Filtering Reduced Order Model

We present a stabilized POD–Galerkin reduced order method (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. In both steps of the EF algorithm, velocity and pressure fields are approximated using different POD basis and coefficients. To achieve pressure stabilization, we consider and compare two strategies: the pressure Poisson equation and the supremizer enrichment of the velocity space. We show that the evolve and filtered velocity spaces have to be enriched with the supremizer solutions related to both evolve and filter pressure fields in order to obtain stable and accurate solutions with the supremizer enrichment method. We test our ROM approach on a 2D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. We find that both stabilization strategies produce comparable errors in the reconstruction of the lift and drag coefficients, with the pressure Poisson equation method being more computationally efficient.

Ultrasonic velocity profiler applied to explore viscosity–pressure fields and their coupling in inelastic shear-thinning vortex streets

A method for simultaneous estimation of viscosity and pressure fields in inelastic shear-thinning fluids is developed by means of ultrasound velocity profiling technique (UVP). In the method, equation of continuity, rheological model and pressure Poisson equation are incorporated as data processing sequences for measured velocity distributions. The proposed method is applied to study the vortex street structure formed behind a circular cylinder, which shows viscosity–pressure coupling due to shear-thinning property of fluid. For demonstration, aqueous solution of CMC (carboxy methyl cellulose) of weight concentration of 0.1% is chosen as the working fluid with shear-thinning property. An alternating staggered pattern of low-pressure spots is successfully reconstructed for zero-shear-based Reynolds number, Re = 50–300. We have found that increasing Re resulted in decrease in vortex shedding Strouhal number because of vortex sustainability supported by shear-thinning property. Graphical abstract

Improved ISPH method for natural convection from heated T-open pipe of Al2O3-water nanofluid in a cavity: Buongiorno’s two-phase model

The unsteady natural convection of Al2O3-water nanofluid form heated open T-pipe inside a cavity has been investigated by ISPH method using non-homogenous two-phase Buongiorno's model. Different lengths and heights of T-pipe shape are considered. The side walls of the cavity are kept at cool temperature Tc and the horizontal walls are thermally insulated. The Lagrangian description of the controlling governing equations is discretized and solved using improved ISPH method. In this study, ISPH method is improved using kernel renormalization function for boundary treatment plus modification in the source term of pressure Poisson equation (PPE). The source term of PPE contains the velocity divergence plus density invariance multiply by relaxation coefficient. The calculations are performed for variable lengths of T-open pipe (0.2 ? Lb ? 0.6variable widths of T-open pipe (0.02 ?Wb?0.16), (0.02? Wt? 0.16) and variable concentration of nanoparticles volume fraction (1% ?.?avg ? 10). The obtained results showed that the maximum values of the stream function are reduced by 80.8% when ?avg is increased from 1% to 10%. Additionally, as lengths and widths of the T-pipe are raised, the average Nusselt numbers at the vertical walls are enhanced.

Fast-Projection Methods for the Incompressible Navier–Stokes Equations

An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations.

Unsteady 2D and 3D Navier-Stokes Solver with Application of Multigrid Scheme to Pressure Poisson Fractional Step on Arbitrary Unstructured Grids in Various Applications with Emphasis on Ship Motion

A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various applications, especially around a marine vessel. The Navier-Stokes solver is based on the fractional steps method coupled with a finite volume scheme and collocated grids by which velocity components and pressure fields are defined at the center of the control volume. However, the fluxes are defined at the midpoint on their corresponding cell faces. On the other hand, the CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) scheme is applied to capture the free surface. In the presented fractional step method, the pressure Poisson equation suffers from poor convergence rate by simple iterative methods like Successive Overrelaxation (SOR), especially in simulating complex geometrics like a ship with appendages. Therefore, to accelerate the convergence rate, an agglomeration multigrid method is applied on arbitrary moving mesh for solving pressure Poisson equation with two well-known cycles, V and W. In order to maintain accuracy, the geometry details should not change in grid coarsening procedure. Therefore, the boundary faces are assumed to be fixed in all grids level. This assumption requires nonstandard cells in coarsening procedures. To investigate the performance of the applied algorithm, various flows including one and two-phase flows are studied in two and three dimensions. It is found that the multigrid method can speed up the convergence rate of fractional step twofold. In most cases (not all), W cycle displays better performance. It is also concluded that the efficiency of the cycle depends on the number of meshes and complexity of the problem and this is mainly due to the data transferring between grids. Therefore, the type of cycle should be selected judiciously and carefully, while considering the mesh size and flow properties.