scholarly journals Diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations

2017 ◽  
Vol 836 ◽  
pp. 324-351 ◽  
Author(s):  
Xiaodong Cai ◽  
Ralf Deiterding ◽  
Jianhan Liang ◽  
Mingbo Sun ◽  
Yasser Mahmoudi
Keyword(s):  
Adaptive Mesh Refinement ◽  
Stokes Equations ◽  
Detonation Front ◽  
Navier Stokes ◽  
Oxygen Mixture ◽  
Small Scale ◽  
Helmholtz Instability ◽  
Navier Stokes Equations ◽  
Subsequent Formation ◽  
Jet Initiation

In the present work, the role of diffusion and mixing in hot jet initiation and detonation propagation in a supersonic combustible hydrogen–oxygen mixture is investigated in a two-dimensional channel. A second-order accurate finite volume method solver combined with an adaptive mesh refinement method is deployed for both the reactive Euler and Navier–Stokes equations in combination with a one-step and two-species reaction model. The results show that the small-scale vortices resulting from the Kelvin–Helmholtz instability enhance the reactant consumption in the inviscid result through the mixing. However, the suppression of the growth of the Kelvin–Helmholtz instability and the subsequent formation of small-scale vortices imposed by the diffusion in the viscous case can result in the reduction of the mixing rate, hence slowing the consumption of the reactant. After full initiation in the whole channel, the mixing becomes insufficient to facilitate the reactant consumption. This applies to both the inviscid and viscous cases and is due to the absence of the unburned reactant far away from the detonation front. Nonetheless, the stronger diffusion effect in the Navier–Stokes results can contribute more significantly to the reactant consumption closely behind the detonation front. However, further downstream the mixing is expected to be stronger, which eventually results in a stronger viscous detonation than the corresponding inviscid one. At high grid resolutions it is vital to correctly consider physical viscosity to suppress intrinsic instabilities in the detonation front, which can also result in the generation of less triple points even with a larger overdrive degree. Numerical viscosity was minimized to such an extent that inviscid results remained intrinsically unstable while asymptotically converged results were only obtained when the Navier–Stokes model was applied, indicating that solving the reactive Navier–Stokes equations is expected to give more correct descriptions of detonations.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

scholarly journals Aerodynamic Dissipation

1958 ◽  
Vol 8 ◽  
pp. 966-974
Author(s):  
H. E. Petschek
Keyword(s):  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Mean Free Path ◽  
Navier Stokes ◽  
Small Scale ◽  
Minimum Length ◽  
Ionized Gas ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Rate Of Dissipation

Analyses of aerodynamic dissipation in ordinary un-ionized gases are all based upon the Navier-Stokes equations. These equations relate the rate of dissipation to the local gradients in velocity and temperature through the viscosity and heat conduction coefficients. Although it is true that in many flow situations the magnitude of the total dissipation in the gas does not depend on the magnitude of the viscosity coefficient, this coefficient does determine the minimum scale of variations observed in the gas and the form of the Navier-Stokes equations determines the type of phenomena which are observed on a small scale. In order to discuss dissipation in an ionized gas in the presence of a magnetic field, it is therefore necessary to re-examine the derivation of the basic flow equations. This paper attempts to do this for a case of a completely ionized gas and demonstrates that the basic microscopic dissipation mechanism is appreciably different. For example, it is shown that the minimum length in which the properties of the flow field can change noticeably is appreciably less than one mean free path.

Navier–Stokes solutions of unsteady separation induced by a vortex

2002 ◽  
Vol 465 ◽  
pp. 99-130 ◽  
Author(s):  
A. V. OBABKO ◽  
K. W. CASSEL
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Scale Interaction

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

Heat Transfer Generated by the Interaction of Single and Multiple Tandem Jets in Crossflow

2010 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Cooling Power ◽  
Small Scale ◽  
Fluid Composition ◽  
Navier Stokes Equations ◽  
The Impact

“Twin jets in Crossflow” is a common configuration that finds application in several large and/or small scale industrial fields. The interest in such a configuration is further enhanced by its dependence in several parameters, that may be geometric, dynamic, thermal, or relative to the handled fluid composition. We propose to focus in the present work on the effect of the number of the emitted jets on the generated heat transfer, in presence of an unchanged uniform crossflow. To reach this goal, single, double and triple jet configurations were simulated, based upon the resolution of the Navier Stokes equations by means of the RSM (Reynolds Stress Model) second order turbulent closure model, together with a non uniform grid system particularly tightened near the emitting nozzles. After validation, we tried to find out the impact of the number of the handled jets on their cooling “power” by tracking the temperature distribution of the resulting flowfield. Since in practically all applications we are in need of higher efficiencies and then of higher operating temperatures, we are constantly concerned about not going beyond the shielding material melting temperature. If the use of cooling jets proves to be efficient, this may bring a significant progress in the technological field.

scholarly journals COMPARISON OF DIFFERENT METHODS FOR GENERATION AND ABSORPTION OF WATER WAVES

2019 ◽  
Vol 18 (1) ◽  
pp. 71 ◽  
Author(s):  
J. M. P. Conde
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Numerical Models ◽  
Experimental Studies ◽  
Wave Generation ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Wave Absorption ◽  
Water Level Rise

The knowledge of water wave characteristics (generation, propagation, transformation and breaking) is fundamental for hydrodynamic studies and the design of ocean, coastal and port structures. In addition to the small-scale experimental studies, the use of numerical models is also a very important tool in hydrodynamic studies. To have reliable numerical results a proper validation is required. The main objective of this paper is to compare different methods of wave generation and wave absorption in a numerical flume, and to find what is the most suited to simulate non-breaking regular wave propagation in a two-dimensional flume in deep water condition. The numerical simulations were made using the OpenFOAM® software package. Two solvers, waves2Foam and IHFoam/OlaFlow, the utility GroovyBC and a mesh stretching technique are compared. These numerical codes solve the transient Navier-Stokes equations and use a VoF (Volume of Fluid) method to identify the free surface. A solution dependence study with the methods of wave generation and wave absorption is presented. The results are also compared with the theoretical wave and experimental data. The results show that the different methods of generation produce waves similar to the theoretical and the experimental ones, only slightly differences were visible. The three method of wave dissipation considered produce very different results: IHFoam/OlaFlow is not able to dissipate the wave tested; the mesh stretching technique is able to dissipate the waves but produces a water level rise; the waves2Foam solver is able to dissipate properly the wave tested.

scholarly journals Direct control of the small-scale energy balance in two-dimensional fluid dynamics

2015 ◽  
Vol 782 ◽  
pp. 240-259 ◽  
Author(s):  
Jason Frank ◽  
Benedict Leimkuhler ◽  
Keith W. Myerscough
Keyword(s):  
Fluid Dynamics ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
High Fidelity Simulation ◽  
Two Dimensional ◽  
Feedback Controls ◽  
Navier Stokes Equations ◽  
Direct Modification ◽  
Pseudo Spectral

We explore the direct modification of the pseudo-spectral truncation of two-dimensional, incompressible fluid dynamics to maintain a prescribed kinetic energy spectrum. The method provides a means of simulating fluid states with defined spectral properties, for the purpose of matching simulation statistics to given information, arising from observations, theoretical prediction or high-fidelity simulation. In the scheme outlined here, Nosé–Hoover thermostats, commonly used in molecular dynamics, are introduced as feedback controls applied to energy shells of the Fourier-discretized Navier–Stokes equations. As we demonstrate in numerical experiments, the dynamical properties (quantified using autocorrelation functions) are only modestly perturbed by our device, while ensemble dispersion is significantly enhanced compared with simulations of a corresponding truncation incorporating hyperviscosity.

Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Nagendra Dittakavi ◽  
Aditya Chunekar ◽  
Steven Frankel
Keyword(s):  
Large Eddy Simulation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Vapor Cavity ◽  
Eddy Simulation ◽  
Downstream Region ◽  
Large Eddy ◽  
Venturi Nozzle

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the AUSM+-up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

scholarly journals EULER EQUATIONS WITH SEVERAL INDEPENDENT PRESSURE LAWS AND ENTROPY SATISFYING EXPLICIT PROJECTION SCHEMES

2006 ◽  
Vol 16 (09) ◽  
pp. 1469-1504 ◽  
Author(s):  
CHRISTOPHE CHALONS ◽  
FRÉDÉRIC COQUEL
Keyword(s):  
Stokes Equations ◽  
Scale Effects ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Small Scale ◽  
Stability Estimates ◽  
Jump Conditions ◽  
Riemann Solutions ◽  
Navier Stokes Equations

This work aims at numerically approximating the entropy weak solutions of Euler-like systems asymptotically recovered from the multi-pressure Navier–Stokes equations in the regime of an infinite Reynolds number. The nonconservation form of the limit PDE model makes the shock solutions to be sensitive with respect to the underlying small scales. Here we propose to model these small scale effects via a set of generalized jump conditions expressed in terms of the independent internal energies. The interest in considering internal energies stems from the presence of solely first-order nonconservative products by contrast to other variables. These nonconservative products are defined in the now classical sense proposed by Dal Maso, LeFloch and Murat. We show how to enforce the generalized jump conditions at the discrete level with a fairly simple numerical procedure. This method is proved to satisfy a full set of stability estimates and to produce approximate solutions in good agreement with exact Riemann solutions.

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