Hybrid Boundary Condition Research Articles

Study of implicit CFD modeling of riblets on wind turbine airfoil in transitional flow

The study introduces a novel hybrid boundary condition, derived from existing literature, crafted for predicting the impact of riblets on airfoils in transitional flow. In contrast to models tailored for fully turbulent flow, the hybrid approach successfully captures the operational dynamics of riblets, as demonstrated through meticulous testing. The boundary condition integrates slip length and a modified specific dissipation rate (ω) boundary to encompass the entire riblet regime. Adjusting the model to match measured drag behavior enables predictions of riblet effects at higher Reynolds numbers pertinent to wind turbine blades. Validation reveals the model’s proficiency in capturing the order of magnitude in drag reduction and aligns the change in drag in the correct direction for diverse riblet heights, yet highlights discrepancies in replicating absolute drag reduction values, particularly at smaller angles of attack. This underscores the imperative for further refinement and tuning, necessitating additional experimental data at higher Reynolds numbers and across various angles of attack to ensure the model’s robust applicability across a broader spectrum of conditions.

Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives

In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.

Real-time thermal error prediction and compensation of ball screw feed systems via model order reduction and hybrid boundary condition update

Thermal deformation of a ball screw is a quasi-static process and incurs positioning error. To obtain a rapid prediction model to compensate for this deformation error, a reduced-order finite element (FE) model is required. For updating the boundary conditions (BCs) of such a reduced-order model (ROM), a hybrid BC update process composed of the response surface method (RSM) and 3-point temperature measurement is devised in this paper. We develop an adaptive reduced-order model (AROM) for real-time prediction and compensation of the error in a time-varying environment under any operating conditions. This system solves not only the heat generation rate (HGR) and nut movement effects on the lubricant temperature variation, but also the convective heat transfer coefficient (CHTC) and thermal resistance (TR) effects at joint interfaces. High prediction accuracy has been verified via a test-bed with a precision linear scale. An AROM server application is also proposed for a thermal error free smart factory.

Numerical Investigation of Transitional Characteristics for Natural-Convection Flow in Open-Ended Inclined Channel Heated From Below

Abstract This report presents an investigation of the characteristics for transitional natural-convection flow in an open-ended inclined channel heated from below in the air under uniform heat flux intensity and non-Boussinesq condition. The investigated range of modified Rayleigh number and inclination is from 5.93 × 106 to 1.45 × 109 and 30–90 deg to the horizontal, respectively. Fine-resolution implicit large Eddy simulation is performed to solve the compressible governing equations using the modified preconditioned all-speed Roe scheme, hybrid boundary condition, and dual-time-stepping technique. The Nusselt number based on the maximum wall-temperature differs significantly while based on averaged wall-temperature is closer to the previously proposed laminar correlations. Transition is found to be pronounced at a lower angle of inclination (30 deg) for the considered heat flux intensity. The absolute magnitude of the critical length for the start and end of the transition when converted to nondimensional parameters is found to be higher compared to similar data for natural convection flow over a flat plate in water but the ratio of the end to start of the transition is found to be comparable. Single-roll longitudinal vortices periodically placed in spanwise direction exists in the transition region whose wavelength is found to be higher than those reported for channel flow under the isothermal condition and flow over a flat plate in water. Correlations for Nusselt number, critical aspect ratio, and vortex wavelength to the modified Rayleigh number are presented.

Atomistic simulations of long-chain polyethylene melts flowing past gold surfaces: structure and wall-slip

ABSTRACT The current article presents results from MD simulations of high molar mass polyethylene melts with the scope to investigate the structure and dynamics at the polymer/solid interphase, and to assess their dependence on strong Couette flows. The density profiles are decomposed into the contributions of specific types of segments such as tails, loops and trains in order to arrive at a detailed description of the structure under various flow conditions. The size and orientation of chain segments is quantified to assess the reorganisation of the chains at the interface leading to possible shear-thinning effects. The segmental velocity profiles and the layer- and direction-resolved mean square displacement of the chain segments are extracted from the simulations so as to compute the effective shear rate, slippage, and the emergence of possible interfacial failure mechanisms. Through representative snapshots of chain trajectories we unveil the dominant mechanisms dictating the chain reorganisation in the interfaces and the overall adsorption–desorption processes. Our findings suggest the manifestation of a hybrid boundary condition attributed mainly to interfacial failure and partly to cohesive failure.

Towards Lattice-Boltzmann modelling of unconfined gas mixing in anaerobic digestion

A novel Lattice-Boltzmann model to simulate gas mixing in anaerobic digestion is developed and described. For the first time, Euler–Lagrange multiphase, non-Newtonian and turbulence modelling are applied jontly with a novel hybrid boundary condition. The model is validated in a laboratory-scale framework and flow patterns are assessed through Particle Imaging Velocimetry (PIV) and innovative Positron-Emission Particle Tracking (PEPT). The model is shown to reproduce the experimental flow patterns with fidelity in both qualitative and quantitative terms.The model opens up a new approach to computational modelling of the complex multiphase flow in anaerobic digesters and offers specific advantages, such as computational efficiency, over an analogous Euler-Lagrange finite-volume computational fluid dynamics approach.

Finite element time domain modeling of controlled-source electromagnetic data with a hybrid boundary condition

We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.

Tetraquark and Pentaquark Systems in Lattice QCD

Motivated by the recent experimental discoveries of multi-quark candidates, e.g., the $\Theta^+(1540)$, we study multi-quark systems in lattice QCD. First, we perform accurate mass measurements of low-lying 5Q states with $J=1/2$ and I=0 in both positive- and negative-parity channels in anisotropic lattice QCD. The lowest positive-parity 5Q state is found to have a large mass of about 2.24GeV after the chiral extrapolation. To single out the compact 5Q state from $NK$ scattering states, we develop a new method with the hybrid-boundary condition (HBC), and find no evidence of the compact 5Q state below 1.75GeV in the negative-parity channel. Second, we perform the first study of the multi-quark potential in lattice QCD to clarify the inter-quark interaction in multi-quark systems. The 5Q potential $V_{\rm 5Q}$ for the QQ-${\rm \bar{Q}}$-QQ system is found to be well described by the ``OGE Coulomb plus multi-Y Ansatz": the sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term based on the flux-tube picture. The 4Q potential $V_{\rm 4Q}$ for the QQ-${\rm \bar{Q}\bar{Q}}$ system is also described by the OGE Coulomb plus multi-Y Ansatz, when QQ and $\rm \bar Q \bar Q$ are well separated. The 4Q system is described as a "two-meson" state with disconnected flux tubes, when the nearest quark and antiquark pair is spatially close. We observe a lattice-QCD evidence for the ``flip-flop'', i.e., the flux-tube recombination between the connected 4Q state and the ``two-meson'' state. On the confinement mechanism, the lattice QCD results indicate the flux-tube-type linear confinement in multi-quark hadrons.

Compressible direct numerical simulation with a hybrid boundary condition of transitional phenomena in natural convection

We investigate the phenomena involved in the transition from laminar to turbulent flow in natural convection through a channel using compressible direct numerical simulation (DNS). The Roe numerical scheme with preconditioning and dual time stepping is employed to handle slow natural convection flows with large temperature differences and variable densities. A hybrid boundary condition that combines absorbing and non-reflecting boundary conditions is applied at the inlet and outlet, which does not require a priori knowledge of the flow rate. No empirically derived turbulence parameters are required in the DNS code. The numerical predictions are qualitatively consistent with published experimental data and the transition point can be accurately captured. Our results show that the transitional phenomena can be naturally induced by the interactions between the buoyancy force and shear stress without prescribing any fluctuations at the inlet. We submit that the numerical scheme and model configuration developed in this study has the potential to be a benchmark case for evaluating the accuracy of other turbulence models.

An investigation of natural convection in parallel square plates with a heated top surface by a hybrid boundary condition

Natural convection in parallel squares plats with a heated top surface is investigated numerically. For solving a problem induced by different directions between the thermal diffusion and main flow streams, a hybrid boundary condition composed of the absorbing boundary condition and local one-dimensional inviscid relations (LODI) method is then adopted in artificial buffer zones. Methods of the Roe scheme, preconditioning and dual time stepping matching the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) are used to solve low speed compressible flows caused by natural convection. The results show that the hybrid boundary condition successfully prevents the rebound of heat energy from the artificial buffer zone back to the domain. The area-averaged Nusselt numbers of this study are slightly larger than those of existing experimental results, and the averaged deviation is about 10%.

Hybrid boundary condition combined with data assimilation for simulations of free surface flows using lattice Boltzmann method

In this paper, we combine the single-phase lattice Boltzmann method (LBM) including the hybrid boundary condition with the assimilation of experimental data into a simulation. This combination improves the accuracy of numerical simulations of violent free surface flows performed using the LBM. An unknown wall effect parameter used in the hybrid boundary condition is determined through iterative calculations to minimize the objective function that measures the discrepancy between the simulation and measurement. The present method is applied to a dam failure problem involving a very large deformation of a free surface. We confirm that the method proposed in this study can optimally incorporate the hybrid boundary condition into the LBM without ad hoc specification of the wall effect parameter.

Modelling of electrification in steady state and transient regimes

Abstract A microscopic model of electrification phenomena in steady state and transient regimes has been developed. The model has been applied for analysis of experimental data failing to be explained in the frame of classical macroscopic approach. Various boundary conditions have been studied regarding the possibility of experiential data fitting. The hybrid boundary condition has been suggested for explaining steady state and transient experiments. The proposed boundary condition can be related to the coexistence of two reactions on the active surface. The first reaction runs under the diffusion control (fast reaction) and the second one is limited by the kinetics (slow reaction).

Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in (1+1)-Dimensional Spacetime

The Casimir energy of massive scalar field with hybrid (Dirichlet–Neumann) boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures.

Tetra-Quark Resonances in Lattice QCD

We study qq qq-type four-quark (4Q) systems in SU(3)c anisotropic quenched lattice QCD, using the O(a)-improved Wilson (clover) fermion at β= 5.75 on 123 ×96 with renormalized anisotropy as/at = 4. For comparison, we first investigate the lowest qq scalar meson from the connected diagram and find its large mass of about 1.32 GeV after chiral extrapolation, and thus the lowest qq scalar meson corresponds to f0(1370). We investigate the lowest 4Q state in the spatially periodic boundary condition, and find that it is just a two-pion scattering state, as is expected. To examine spatially-localized 4Q resonances, we use the Hybrid Boundary Condition (HBC) method, where anti-periodic and periodic boundary conditions are imposed on quarks and antiquarks, respectively. By applying HBC on a finite-volume lattice, the threshold of the two-meson scattering state is raised up, while the mass of a compact 4Q resonance is almost unchanged. In HBC, the lowest 4Q state appears slightly below the two-meson threshold. To clarify the nature of the 4Q system, we apply the Maximum Entropy Method (MEM) for the 4Q correlator and obtain the spectral function of the 4Q system. From the combination analysis of MEM with HBC, we finally conclude that the 4Q system appears as a two-pion scattering state and there is no spatially-localized 4Q resonance in the quark-mass region of ms ≪ mq ≪ 2ms.

Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part II: Formulation of 3-D case and hybrid PFFEM

The hybrid power flow analysis (PFA) is an analytic method proposed for the effective prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the PFA algorithm and statistical energy analysis (SEA) coupling concepts. This paper presents the hybrid boundary condition on 3-D case for hybrid PFA in addition to 1-D and 2-D cases which are derived in the other companion paper, and formulates the hybrid power flow finite-element method (PFFEM) including coupling loss factor (CLF) of SEA to extend the application area of hybrid PFA to built-up structures. To verify the derived boundary condition and hybrid PFFEM, numerical analyses were successfully performed for various analytic models and reverberance factors.

Spin3/2pentaquarks in anisotropic lattice QCD

A high-precision mass measurement for the pentaquark (5Q) Theta^+ in J^P=3/2^{\pm} channel is performed in anisotropic quenched lattice QCD using a large number of gauge configurations as N_{conf}=1000. We employ the standard Wilson gauge action at beta=5.75 and the O(a) improved Wilson (clover) quark action with kappa=0.1210(0.0010)0.1240 on a 12^3 \times 96 lattice with the renormalized anisotropy as a_s/a_t = 4. The Rarita-Schwinger formalism is adopted for the interpolating fields. Several types of the interpolating fields with isospin I=0 are examined such as (a) the NK^*-type, (b) the (color-)twisted NK^*-type, (c) a diquark-type. The chiral extrapolation leads to only massive states, i.e., m_{5Q} \simeq 2.1-2.2 GeV in J^P=3/2^- channel, and m_{5Q} = 2.4-2.6 GeV in J^P=3/2^+ channel. The analysis with the hybrid boundary condition(HBC) is performed to investigate whether these states are compact 5Q resonances or not. No low-lying compact 5Q resonance states are found below 2.1GeV.

Penta-quark in Anisotropic Lattice QCD

Penta-quark (5Q) baryons are studied using anisotropic lattice QCD for high-precision measurement of temporal correlators. A non-NK-type interpolating field is employed to study the 5Q states with J^P=1/2^{\pm} and I=0. In J^P=1/2^+ channel, the lowest-lying state is found at m_{5Q} \simeq 2.25 GeV, which is too massive to be identified as the Theta^+(1540). In J^P=1/2^- channel, the lowest-lying state is found at m_{5Q} \simeq 1.75 GeV. To distinguish a compact 5Q resonance state from an NK scattering state, a new method with ``hybrid boundary condition (HBC)'' is proposed. As a result of the HBC analysis, the observed state in the negative-parity channel turns out to be an $NK$ scattering state.

Pentaquark baryon in anisotropic lattice QCD

The penta-quark(5Q) baryon is studied in anisotropic quenched lattice QCD with renormalized anisotropy a_s/a_t=4 for a high-precision mass measurement. The standard Wilson action at beta=5.75 and the O(a) improved Wilson quark action with kappa=0.1210(0.0010)0.1240 are employed on a 12^3 \times 96 lattice. Contribution of excited states is suppressed by using a smeared source. We investigate both the positive- and negative-parity 5Q baryons with I=0 and spin J=1/2 using a non-NK-type interpolating field. After chiral extrapolation, the lowest positive-parity state is found to have a mass, m_{Theta}=2.25 GeV, which is much heavier than the experimentally observed Theta^+(1540). The lowest negative-parity 5Q appears at m_{Theta}=1.75 GeV, which is near the s-wave NK threshold. To distinguish spatially-localized 5Q resonances from NK scattering states, we propose a new general method imposing a ``Hybrid Boundary Condition (HBC)'', where the NK threshold is artificially raised without affecting compact five-quark states. The study using the HBC method shows that the negative-parity state observed on the lattice is not a compact 5Q but an s-wave NK-scattering state.

A hybrid boundary condition for robust particle swarm optimization

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. However, it has been observed that there is a great variation in its performance due to the dimensionality of the problem and the location of the global optimum with respect to the boundaries of the search space. The present paper attempts to resolve this problem by proposing a simple hybrid "damping" boundary condition that combines the characteristics offered by the existing "absorbing" and "reflecting" boundaries. Simulation results on microwave image reconstruction have shown that with the proposed "damping" boundary condition, a much robust and consistent optimization performance can be obtained for PSO regardless of the dimensionality and location of the global optimum solution.

Boundary Effects for Macroscopic Patterns in Nematic Thin Layers under a Hybrid Boundary Condition

Macroscopic director patterns in the phase ordering process and equilibrium state of nematic liquid crystals under a hybrid boundary conditions are numerically studied. A new cell-dynamics model for nematic liquid crystals including anisotropic elastic constants is used. Competition between bulk and surface elastic energies yields periodic modulated equilibrium structures. String-like deformation between boojums is found when uniaxial anisotropy is present on a boundary.