Pressure and Temperature Effects on Particle Deposition in an Impinging Flow

2017 ◽  
Author(s):  
Ryan K. Lundgreen
Keyword(s):  
Reynolds Number ◽  
Particle Deposition ◽  
Stokes Equations ◽  
Focal Point ◽  
Three Dimensional ◽  
Stokes Number ◽  
Particle Impact ◽  
Internal Cooling ◽  
Particle Reynolds Number ◽  
Impinging Flow

Particle deposition is a significant problem in gas turbine engines. Internal cooling passages are of particular interest because deposition build up is observed at far lower temperatures than it is for external flows. Computational fluid dynamics were employed to investigate how changes in the particle Reynolds number affected deposition in an impinging flow. Three-dimensional, steady Reynolds-Averaged Navier-Stokes equations were solved for a single impinging jet that had a jet to wall spacing of H/D = 2. Pressure ratios of 1.015 and 1.03 were considered at three different discharge pressures, 0.1, 1 , and 3 MPa. Three different flow temperatures were also considered, 300, 700, and 1000 K. Five different particle diameters ranging from 0.5 – 10 μm were tracked in each solution. The aerodynamic lensing focal point of the particle tracks, particle impact velocities, particle impact angles, and particle impact locations were all characterized well by the effective Stokes number. The effective Stokes number adjusts the Stokes number by the non-Stokes drag correction factor, which is a function of the particle Reynolds number.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Motion of Descending Solid Particles and Local Flow Around the Particles in Downward Turbulent Water Duct Flow (Keynote)

2011 ◽  
Author(s):  
Yoshimichi Hagiwara ◽  
Hideto Fujii ◽  
Katsutoshi Sakurai ◽  
Takashi Kuroda ◽  
Atsuhide Kitagawa
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
High Speed ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Solid Particles ◽  
Duct Flow ◽  
Local Flow ◽  
Particle Reynolds Number ◽  
Turbulent Water

The Stokes number, the ratio of the particle time scale to flow time scale, is a promising quantity for estimating changes in statistics of turbulence due to particles. First, we explored the Stokes numbers in some recent studies. Secondly, we discussed the results of our direct numerical simulation for turbulent flow with a high-density particle in a vertical duct. In the discussion, we defined the particle Reynolds number from the mean fluid velocity in the near-particle region at any time. We evaluated a new local Stokes number for the particle. It is found that the Stokes number is effective for the prediction of the distance between the particle center and one wall. Finally, we carried out experiments for turbulent water flow with aluminum balls of 1 mm in diameter in a vertical channel. The motions of aluminum balls and tracer particles in the flow were captured with a high-speed video camera. We found that the experimental results for the time changes in the wall-normal distance of the ball and the particle Reynolds number for the ball are similar to the predicted results.

Numerical Three-Dimensional Pressure Patterns in a Recess of a Turbulent and Compressible Hybrid Journal Bearing

2003 ◽  
Vol 125 (2) ◽  
pp. 301-308 ◽  
Author(s):  
Mathieu Helene ◽  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Wire Mesh ◽  
Primary Concern ◽  
Reference Parameters ◽  
Exit Mach Number

The present work investigates the flow in the feeding recess of a hybrid journal bearing. Numerical integration of the complete Navier-Stokes equations was performed with an appropriate turbulence model. Of primary concern is the pressure field on the rotating journal surface that is commonly known as the recess pressure pattern. The goal of the work is to determine the influences of fluid compressibility, operating conditions and recess geometry. Reference parameters selected for this study comprise feeding Reynolds number Rea of 2.105, sliding Reynolds number Rec of 5.103 and recess depth over film thickness ratio e/H of 2.2. Compressibility was considered first. Three values of the axial exit Mach number were selected for computation, namely 0.2, 0.45, and 0.7. As no significant variation was found, the Mach number was fixed at 0.45 in subsequent studies concerning other parameters:     Feeding Reynolds number, Rea       2.104,2.105,4.105     Recess depth, e/H           0, 2.2, 8     Feedhole axis inclination        90°, 135°, 165°     Feedhole location (Figs. 1(a) and 13)   centered, downstream offset. As each parameter is varied, wire mesh plot of pressure and its sectional profiles are examined and effects of varying various parameters are discussed in reference to flow processes as they may affect the support characteristics of the hybrid journal bearing.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening

2006 ◽  
Vol 128 (4) ◽  
pp. 573-578 ◽  
Author(s):  
Andrew L. Hazel ◽  
Matthias Heil
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Elastic Tube ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Steady Propagation

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

scholarly journals Estimating intermittency in three-dimensional Navier–Stokes turbulence

2009 ◽  
Vol 625 ◽  
pp. 125-133 ◽  
Author(s):  
J. D. GIBBON
Keyword(s):  
Reynolds Number ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Space Time ◽  
Navier Stokes ◽  
Local Velocity ◽  
Vortex Sheets ◽  
Navier Stokes Equations ◽  
Local Number

The issue of why computational resolution in Navier–Stokes turbulence is hard to achieve is addressed. Under the assumption that the three-dimensional Navier–Stokes equations have a global attractor it is nevertheless shown that solutions can potentially behave differently in two distinct regions of space–time $\mathbb{S}$± where $\mathbb{S}$− is comprised of a union of disjoint space–time ‘anomalies’. If $\mathbb{S}$− is non-empty it is dominated by large values of |∇ω|, which is consistent with the formation of vortex sheets or tightly coiled filaments. The local number of degrees of freedom ± needed to resolve the regions in $\mathbb{S}$± satisfies $\mathcal{N}^{\pm}(\bx,\,t)\lessgtr 3\sqrt{2}\,\mathcal{R}_{u}^{3},$, where u = uL/ν is a Reynolds number dependent on the local velocity field u(x, t).

Transport of Heavy Particles in a Three-Dimensional Mixing Layer

1998 ◽  
Vol 120 (3) ◽  
pp. 613-620 ◽  
Author(s):  
Qunzhen Wang ◽  
Kyle D. Squires
Keyword(s):  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Stokes Number ◽  
Experimental Measurements ◽  
Initial Field ◽  
Heavy Particles ◽  
Velocity Statistics

Particle transport in a three-dimensional, temporally evolving mixing layer has been calculated using large eddy simulation of the incompressible Navier-Stokes equations. The initial fluid velocity field was obtained from a separate simulation of fully developed turbulent channel flow. The momentum thickness Reynolds number ranged from 710 in the initial field to 4460 at the end of the calculation. Following a short development period, the layer evolves nearly self-similarly. Fluid velocity statistics are in good agreement with both the direct numerical simulation results of Rogers and Moser (1994) and experimental measurements of Bell and Mehta (1990). Particles were treated in a Lagrangian manner by solving the equation of motion for an ensemble of 20,000 particles. The particles have the same material properties as in the experiments of Hishida et al. (1992), i.e., glass beads with diameters of 42, 72, and 135 μm. Particle motion is governed by drag and gravity, particle-particle collisions are neglected, and the coupling is from fluid to particles only. In general, the mean and fluctuating particle velocities are in reasonable agreement with the experimental measurements of Hishida et al. (1992). Consistent with previous studies, the Stokes number (St) corresponding to maximum dispersion increases as the flow evolves when defined using a fixed fluid timescale. Definition of the Stokes number using the time-dependent vorticity thickness, however, shows a maximum in dispersion throughout the simulation for St ≈ 1.

scholarly journals Effect of Side Wind on a Simplified Car Model: Experimental and Numerical Analysis

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Emmanuel Guilmineau ◽  
Francis Chometon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Data ◽  
Numerical Results ◽  
Separated Flows ◽  
Wind Gust ◽  
Bluff Bodies ◽  
Test Model ◽  
Steady Flows

A prior analysis of the effect of steady cross wind on full size cars or models must be conducted when dealing with transient cross wind gust effects on automobiles. The experimental and numerical tests presented in this paper are performed on the Willy square-back test model. This model is realistic compared with a van-type vehicle; its plane underbody surface is parallel to the ground, and separations are limited to the base for moderated yaw angles. Experiments were carried out in the semi-open test section at the Conservatoire National des Arts et Métiers, and computations were performed at the Ecole Centrale de Nantes (ECN). The ISIS-CFD flow solver, developed by the CFD Department of the Fluid Mechanics Laboratory of ECN, used the incompressible unsteady Reynolds-averaged Navier–Stokes equations. In this paper, the results of experiments obtained at a Reynolds number of 0.9×106 are compared with numerical data at the same Reynolds number for steady flows. In both the experiments and numerical results, the yaw angle varies from 0 deg to 30 deg. The comparison between experimental and numerical results obtained for aerodynamic forces, wall pressures, and total pressure maps shows that the unsteady ISIS-CFD solver correctly reflects the physics of steady three-dimensional separated flows around bluff bodies. This encouraging result allows us to move to a second step dealing with the analysis of unsteady separated flows around the Willy model.

Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers

1996 ◽  
Vol 306 ◽  
pp. 293-323 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Large Reynolds Number ◽  
Kolmogorov Flow ◽  
Turbulence Decay ◽  
High Reynolds

High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.

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