Navier-Stokes Algorithm Research Articles

Research on snow prevention in the bogie region based on active blowing method

To reduce excessive snow accumulation on bogie surfaces during high-speed train operations in cold regions, two active blowing schemes are designed in this study based on the shape of the bogie cavity and the relative position of the brake caliper. The unsteady Reynolds-averaged Navier–Stokes algorithm coupled with a discrete phase model was used to calculate the airflow and snow flow under the train. Moreover, the algorithm is employed to explore the impact of active blowing on the flow field characteristics and snow accumulation in the bogie region. Results show that active blowing changes the upward airflow in the bogie region, causing air at the bottom of the train to flow outwards, carrying off numerous snow particles from the bogie region. Active blowing accelerates the surface friction velocity on the bogie, increases the shear force on snow particles, and effectively reduces the snow accumulation on the bogie surface. The foregoing observation indicates that active blowing has considerable potential for snow accumulation prevention.

Diffusion simulation and risk assessment model establishment of chlorine gas leakage based on terrain conditions

This study researches the impact of terrain factors on chlorine gas diffusion processes based on SLAB model. Simulating the law of wind speed changing with altitude by calculating the real-time speed with vertical height combing actual terrain data, and integrating the influence of terrain on wind speed by using Reynolds Average Navier-Stokes (RANS) algorithm, K-turbulence model, and standard wall functions, then plotting the gas diffusion range in the map with terrain data according to the Gaussian-Cruger projection algorithm and dividing the hazardous areas according to the public exposure guidelines (PEG). The accidental chlorine gas releases near Lishan Mountain, Xi'an City, were simulated by the improved SLAB model. The results show that there are obvious differences analyzing contrastively the endpoint distance and area of chlorine gas dispersion under real terrain condition and ideal condition at different times; it can be found that the endpoint distance of the real terrain conditions is 1.34km shorter than that of the ideal conditions at 300s with terrain factors, and also the thermal area is 3,768,026m2 less than that of the ideal conditions. In addition, it can predict the specific number of casualties within different levels of harm at 2min after chlorine gas dispersion, and casualties are constantly changing over time. The fusion of terrain factors can be used to optimize the SLAB model, which is expected to provide an important reference for effective rescue.

Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation

The discrete adjoint of an incompressible Navier-Stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular Couette flows. The forward Navier-Stokes model is based on the fractional-step algorithm in curvilinear coordinates on a structured grid [1], which has been widely adopted in direct numerical simulations of transitional and turbulent flows. The discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization, and expressions are derived that relate the discrete adjoint variables to their continuous counterpart. The key ingredients of the forward algorithm can be retained in the adjoint, including the computation of the cell geometry, the approximate factorization method, and the parallelization strategy. The accuracy, efficiency, and stability of the adjoint solver are also commensurate with the forward model. In addition, a novel symmetric projector is proposed to guarantee that the outcome of the adjoint algorithm is divergence free. The implementation of the algorithm in double precision satisfies the forward-adjoint relation up to eight significant figures, and further validation is performed using circular Couette flow. The forward and adjoint growth rates of instability modes from linear theory are accurately reproduced. In addition, an adjoint-variational data-assimilation algorithm (4DVar) is adopted to reconstruct the initial condition of circular Couette flows from limited measurements, obtained from an independent simulation. When the flow is comprised of saturated wavy vortices, wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time. For the more challenging turbulent case, coarse-grained velocity data are used to estimate the initial condition.

Advanced Tsunami Numerical Simulations and Energy Considerations by use of 3D–2D Coupled Models: The October 11, 1918, Mona Passage Tsunami

The most recent tsunami observed along the coast of the island of Puerto Rico occurred on October 11, 1918, after a magnitude 7.2 earthquake in the Mona Passage. The earthquake was responsible for initiating a tsunami that mostly affected the northwestern coast of the island. Runup values from a post-tsunami survey indicated the waves reached up to 6 m. A controversy regarding the source of the tsunami has resulted in several numerical simulations involving either fault rupture or a submarine landslide as the most probable cause of the tsunami. Here we follow up on previous simulations of the tsunami from a submarine landslide source off the western coast of Puerto Rico as initiated by the earthquake. Improvements on our previous study include: (1) higher-resolution bathymetry; (2) a 3D–2D coupled numerical model specifically developed for the tsunami; (3) use of the non-hydrostatic numerical model NEOWAVE (non-hydrostatic evolution of ocean WAVE) featuring two-way nesting capabilities; and (4) comprehensive energy analysis to determine the time of full tsunami wave development. The three-dimensional Navier–Stokes model tsunami solution using the Navier–Stokes algorithm with multiple interfaces for two fluids (water and landslide) was used to determine the initial wave characteristic generated by the submarine landslide. Use of NEOWAVE enabled us to solve for coastal inundation, wave propagation, and detailed runup. Our results were in agreement with previous work in which a submarine landslide is favored as the most probable source of the tsunami, and improvement in the resolution of the bathymetry yielded inundation of the coastal areas that compare well with values from a post-tsunami survey. Our unique energy analysis indicates that most of the wave energy is isolated in the wave generation region, particularly at depths near the landslide, and once the initial wave propagates from the generation region its energy begins to stabilize.

Numerical Investigation of Instabilities in Free Shear Layer Produced by NS-DBD Actuator

A numerical investigation of the effects of nanosecond barrier discharge on the stability of a two-dimensional free shear layer is performed. The computations are carried out using a compressible Navier-Stokes algorithm coupled with a thermodynamic model of the discharge. The results show that significant increases in the shear layer’s momentum thickness and Reynolds stresses occur due to actuation. Dependence on both frequency and amplitude of actuation are considered, and a comparison is made of the computed growth rates with those predicted by linear stability theory. Amplitude and frequency ranges for the efficient promotion of shear-layer instabilities are identified. Keywords—NS-DBD, plasma, actuator, flow control, instability, shear layer

Unsteady compressible flow simulation around low-aspect-ratio rectangular flat wings

Unsteady compressible flow solutions around a sharp-edged rectangular flat wing of an aspect ratio of 1.0 are obtained using a parallel Reynolds-averaged Navier–Stokes algorithm. The simulated cases are obtained for Mach numbers of 0.42–0.87 and Reynolds numbers of the order of 200 000–300 000 in the transitional flow regime up to an angle of attack of 15°. A Degani–Schiff modification for the Baldwin–Lomax turbulence model is used to distinguish between the boundary layers and the primary and secondary vortices over the flat plate. Unsteady vortex shedding frequencies and Strouhal number variation with the angle of attack are obtained by using the fast Fourier transform. The flow around the low-aspect-ratio rectangular flat wing is strongly dominated by the leading- and side-edge vortices and flow separations. The numerical results are compared with the prior experimental data acquired at the von Karman Institute that shows a mix of laminar/transitional flow. In the simulations, top surface pressures of the rectangular flat wing are well predicted except in the leading-edge region. Time-mean averaged surface flow topologies are also found to be in good agreement with the experiment. Complex flow structures, including the primary and secondary separation bubbles and the footprints of the primary and secondary vortex cores, are well captured through the use of the modified algebraic turbulence model.

Optimal frequency for flow energy harvesting of a flapping foil

Inspired by the correlation between the propulsion efficiency of a flapping foil propeller and stability of the wake behind it (which leads to the optimal Strouhal number for propulsion), we numerically simulated a heaving/pitching foil in energy harvesting regime, and investigated the relation between wake stability and the energy harvesting efficiency. The base flow is computed using a Navier–Stokes algorithm and the stability analysis is performed via the Orr–Sommerfeld equation. The wake is found to be convectively unstable and the frequency of the most unstable modefwis determined. The case whenfw~fcoincides with maximum energy harvesting efficiency of the system (fis the frequency of foil oscillation), suggesting that flow energy extraction is closely related to efficient evolution of the wake. This occurs at a frequency off~ 0.15 (fis normalized by the chord length and the flow speed), under the constraint that there is significant vortex shedding from the leading edge at sufficiently large effective angles of attack. Indeed, this ‘foil–wake resonance’ is usually associated with multi-vortex shedding from the leading edge. Furthermore, detailed examination of energy extractions from the heaving and the pitching motions indicates that near the optimal performance point the average energy extraction from the pitching motion is close to zero. This suggests the feasibility of achieving high-efficient energy harvesting through a simple fully passive system we proposed earlier in which no activation is needed.

Reflections on the evolution of implicit Navier–Stokes algorithms

This article gives a historical perspective on the evolution of implicit algorithms for the Navier–Stokes equations that utilize time or Newton linearizations and various forms of approximate factorization including alternating-direction, lower/upper, and symmetric relaxation schemes. A theme of the paper is how progress in implicit Navier–Stokes algorithms has been influenced and enabled by the introduction of characteristic-based upwind approximations, unstructured-grid discretizations, parallelization, and by advances in computer performance and architecture. Historical examples of runtime, problem size, and estimated cost are given for actual and hypothetical Navier–Stokes flow cases from the past 40 years.

Combined Analysis of Thruster Plume Behavior in Rarefied Region by Preconditioned Navier-Stokes and DSMC Methods

(Received August 11th, 2008) Satellite attitude is usually controlled by plume exhaust from thrusters into the vacuum of space. To study the plume effects in the highly rarefied region, the Direct Simulation Monte Carlo (DSMC) method is usually used, because the plume flow field contains the entire range of flow regime from the near-continuum near the nozzle exit through the transitional state to free molecular state at the far field region from the nozzle. The purpose of this study is to investigate the behavior of a small monopropellant thruster plume in the vacuum region numerically by using the DSMC method. To obtain more accurate results, the preconditioned Navier-Stokes algorithm is introduced to calculate continuum flow fields inside the thruster to predict nozzle exit properties, which are used for inlet conditions of DSMC method. As a result, the plume characteristics in the highly rarefied flow, such as strong nonequilibrium near nozzle exit, large back flow region, etc., are investigated.

Dust Effect on the Performance of Wind Turbine Airfoils

The full two-dimensional Navier-Stokes algorithm and the SST k-? turbulence model were used to investigate incom-pressible viscous flow past the wind turbine two-dimensional airfoil under clean and roughness surface conditions. The NACA 63-430 airfoil is chosen to be the subject, which is widely used in wind turbine airfoil and generally located at mid-span of the blade with thickness to chord length ratio of about 0.3. The numerical simulation of the airfoil under clean surface condition has been done. As a result, the numerical results had a good consistency with the experimental data. The wind turbine blade surface dust accumulation according to the operational periods in natural environment has been taken into consideration. Then, the lift coefficients and the drag coefficients of NACA 63-430 airfoil have been computed under different roughness heights, different roughness areas and different roughness locations. The role that roughness plays in promoting premature transition to turbulence and flow separation has been verified by the numeri-cal results. The trends of the lift coefficients and the drag coefficients with the roughness height and roughness area increasing have been obtained. What’s more, the critical values of roughness height, roughness area, and roughness location have been proposed. Furthermore, the performance of the airfoil under different operational periods has been simulated, and an advice for the period of cleaning wind turbine blades is proposed. As a result, the numerical simula-tion method has been verified to be economically available for investigation of the dust effect on wind turbine airfoils.

Simulation of 3-D Nonequilibrium Seeded Airflow in the NASA Ames MHD Channel

The 3-D nonequilibrium seeded airflow in the NASA Ames experimental magnetohydrodynamics channel has been numerically simulated. The channel contains a nozzle section, a center section, and an accelerator section in which magnetic and electric fields can be imposed on the flow. In recent tests, velocity increases of up to 40% have been achieved in the accelerator section. The flow in the channel is numerically computed using a 3-D parabolized Navier-Stokes algorithm that has been developed to efficiently compute magnetohydrodynamics flows in the low magnetic Reynolds number regime. The magnetohydrodynamics effects are modeled by introducing source terms into the parabolized Navier-Stokes equations, which can then be solved in a very efficient manner. The algorithm has been extended in the present study to account for nonequilibrium seeded airflows. The electrical conductivity of the flow is determined using the program of Park. The new algorithm has been used to compute two test cases that match the experimental conditions. In both cases, magnetic and electric fields are applied to the seeded flow. The computed results are in good agreement with the experimental data.

Hybrid Simulation Approach for Cavity Flows: Blending, Algorithm, and Boundary Treatment Issues

The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the difficulty of formulating a single set of closure coefficients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modifications to common second-order accurate Reynolds averaged Navier-Stokes algorithms are proposed to enhance the capturing of large eddy motions

Numerical prediction of unsteady vortex shedding for large leading-edge roughness

A full two-dimensional Navier–Stokes algorithm is used to investigate unsteady, incompressible viscous flow past an airfoil leading edge with surface roughness that is characteristic of ice accretion. The roughness is added to the surface through the use of a Prandtl transposition and can generate both small-scale and large-scale roughness. The focus of the study is a detailed flow analysis of the unsteady velocity fluctuations and vortex shedding induced by the surface roughness. The results of this study are compared to experimental data on roughness-induced transition for the same roughness geometry. A comparison is made between “fluctuation intensity” values from the current algorithm to experimentally determined turbulence intensity values. The effects of the roughness Reynolds number, Re k , are investigated and compared to experimental values of the critical roughness Reynolds number. The authors speculate that there may be a possible correlation between unsteady roughness-induced vortex shedding and the onset of experimentally measured transitional flow downstream of large-scale roughness.

Evaluation of one‐ and two‐equation low‐Re turbulence models. Part I—Axisymmetric separating and swirling flows

AbstractThis first segment of the two‐part paper systematically examines several turbulence models in the context of three flows, namely a simple flat‐plate turbulent boundary layer, an axisymmetric separating flow, and a swirling flow. The test cases are chosen on the basis of availability of high‐quality and detailed experimental data. The tested turbulence models are integrated to solid surfaces and consist of: Rodi's two‐layer k–ε model, Chien's low‐Reynolds number k–ε model, Wilcox's k–ω model, Menter's two‐equation shear‐stress‐transport model, and the one‐equation model of Spalart and Allmaras. The objective of the study is to establish the prediction accuracy of these turbulence models with respect to axisymmetric separating flows, and flows of high streamline curvature. At the same time, the study establishes the minimum spatial resolution requirements for each of these turbulence closures, and identifies the proper low‐Mach‐number preconditioning and artificial diffusion settings of a Reynolds‐averaged Navier–Stokes algorithm for optimum rate of convergence and minimum adverse impact on prediction accuracy. Copyright © 2003 John Wiley & Sons, Ltd.

Evaluation of one‐ and two‐equation low‐Re turbulence models. Part II—Vortex‐generator jet and diffusing S‐duct flows

AbstractThis second segment of the two‐part paper systematically examines several turbulence models in the context of two flows, namely a vortex flow created by an inclined jet in crossflow, and the flow field in a diffusing S‐shaped duct. The test cases are chosen on the basis of availability of high‐quality and detailed experimental data. The tested turbulence models are integrated to solid surfaces and consist of: Rodi's two‐layer k–ε model, Wilcox's k–ω model, Menter's two‐equation shear–stress‐transport model, and the one‐equation model of Spalart and Allmaras. The objective of the study is to establish the prediction accuracy of these turbulence models with respect to three‐dimensional separated flows with streamline curvature. At the same time, the study establishes the minimum spatial resolution requirements for each of these turbulence closures, and identifies the proper low‐Mach‐number preconditioning and artificial diffusion settings of a Reynolds‐averaged Navier–Stokes algorithm for optimum rate of convergence and minimum adverse impact on prediction accuracy. Copyright © 2003 John Wiley & Sons, Ltd.

Hybrid Simulation Approach for Cavity Flows: Blending, Algorithm, and Boundary Treatment Issues

The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the difficulty of formulating a single set of closure coefficients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modifications to common second-order accurate Reynolds averaged Navier-Stokes algorithms are proposed to enhance the capturing of large eddy motions

Effects of Surface Ice Roughness on Dynamic Stall

A two-dimensional Navier-Stokes algorithm is used to investigate unsteady, incompressible viscous flow past an airfoil leading edge with surface roughness that is characteristic of early-growth ice accretion. The roughness is added to the surface through the use of a Prandtl transposition and can generate both small-scale and large-scale roughness geometries. The algorithm is used to simulate steady or unsteady flow at constant angle of attack or pitch up corresponding to dynamic-stall conditions. Investigations of the dynamic stall show that some types of surface roughness can significantly alter the unsteady flow separation pattern and the formation of the dynamic-stall vortex. This includes both small-scale and large-scale roughness

Slow dynamics by molecular dynamics

We learned early in the computer study of the H-function with particle dynamics that the velocity distribution reaches a local equilibrium (Maxwellian) distribution fast, within a few mean collision times, but that the subsequent structural rearrangement of the particles can be quite slow, particularly if a highly correlated event of many degrees of freedom is involved. During that process potential energy is slowly converted into kinetic energy to reach overall equilibrium. To study processes that are so unlikely that they do not occur within long computer runs (typically less than 10 −8 s of real time) we developed a rare event algorithm. In that calculation the particles are brought adiabatically, that is so slowly that the system is at equilibrium in the presence of the external force at every step, to the rare event configuration (the activated state) and the work to do that is determined. The probability of the event is then calculated by standard reaction rate theory by also determining the transmission coefficient through releasing the constraint near the activated state and observing how often the system goes to the new state relative to how often it falls back to the initial state. The problem with that calculation besides the assumption of adiabaticity is that one needs a model for the activated state, which is often hard to guess. Simulated annealing might aid in the search for an activated state. The other possibility is to speed up particle dynamics and that can be done by direct simulation Monte Carlo, a stochastic particle solution of the Boltzmann equation for a perfect gas. That approach can be extended to higher densities, but the stochastic approach cannot account for the structural features of the medium. However, systems can be followed up to 10 −5 s . We have been able to follow, for example, droplet formation and coalescence by this method. To study even larger systems we have embedded this particle algorithm into a continuum Navier–Stokes algorithm to study the onset of hydrodynamic instabilities. However, the approach cannot deal with the protein folding problem, because the structural aspects dominate the process. One would have to embed molecular dynamics into a continuum, a much more computer intensive problem, in order to even treat water, for example, as a continuum beyond a few molecular layers around a biological molecule.

An overview and generalization of implicit Navier–Stokes algorithms and approximate factorization

A theme of linearization and approximate factorization provides the context for a retrospective overview of the development and evolution of implicit numerical methods for the compressible and incompressible Euler and Navier–Stokes algorithms. This topic was chosen for this special volume commemorating the recent retirements of R.M. Beam and R.F. Warming. A generalized treatment of approximate factorization schemes is given, based on an operator notation for the spatial approximation. The generalization focuses on the implicit structure of Euler and Navier–Stokes algorithms as nonlinear systems of partial differential equations, with details of the spatial approximation left to operator definitions. This provides a unified context for discussing noniterative and iterative time-linearized schemes, and Newton iteration for unsteady nonlinear schemes. The factorizations include alternating direction implicit, LU and line relaxation schemes with either upwind or centered spatial approximations for both compressible and incompressible flows. The noniterative schemes are best suited for steady flows, while the iterative schemes are well suited for either steady or unsteady flows. This generalization serves to unify a large number of schemes developed over the past 30 years.

Parabolized Navier-Stokes Algorithm for Solving Supersonic Flows with Upstream Influences

A new parabolized Navier ‐Stokes (PNS) algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects. Innovative techniques are used to automatically detect and measure the extent of the embedded regions. Within the embedded regions, the PNS equations are globally iterated to duplicate the results that would be obtained with the complete Navier ‐Stokes (NS) equations. Once an embedded region is computed, the algorithm returns to the standard space-marching PNS mode until the next embedded region is encountered. This procedure has been successfully incorporated into NASA’ s upwind PNS code and it has been validated by its application to several two-dimensional test cases. All of these test cases include embedded regions that produce signie cant upstream effects. The present numerical results arein excellent agreement with previous NS computations and experimental data. In addition, these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach.