Computer Methods for Simulation of Multidimensional, Nonlinear, Subsonic, Incompressible Flow

1972 ◽  
Vol 94 (4) ◽  
pp. 337-346 ◽  
Author(s):  
Douglas G. Fox ◽  
J. W. Deardorff
Keyword(s):  
Reynolds Numbers ◽  
Conditional Stability ◽  
Flow Simulations ◽  
Computer Methods ◽  
Current State ◽  
Wide Range ◽  
Dependent Variables ◽  
Two Dimensional Flow ◽  
High Reynolds ◽  
Types Of Information

This review attempts to summarize the current state of fluid flow simulations with particular regard to numerical discretization techniques, treatment of large Reynolds numbers, and past and future accomplishments of the simulation methodology. Three alternative mathematical representations of the flow are presented and compared for an idealized two-dimensional flow, namely, use of the velocity and pressure as dependent variables (primitive equation), use of vorticity and stream function as dependent variables, and expansion of either of these in a truncated set of orthogonal eigenfunctions of the boundary-value problem (whose coefficients become the dependent variables). Various classes of finite-difference algorithms are discussed with regard to their conditional stability as well as their ability to preserve invariants of the continuous equations. Methods of removing aliasing of high-frequency solutions are discussed. Parameterization and other techniques for dealing with the high-Reynolds-number regime in which solutions exhibit a wide range of scales are considered in depth. We conclude that certain types of information can be better obtained by numerical simulation than by other techniques.

scholarly journals On the Scope of Lagrangian Vortex Methods for Two-Dimensional Flow Simulations and the POD Technique Application for Data Storing and Analyzing

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 118
Author(s):  
Kseniia Kuzmina ◽  
Ilia Marchevsky ◽  
Irina Soldatova ◽  
Yulia Izmailova
Keyword(s):  
Flow Simulation ◽  
Internal Flow ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Vortex Methods ◽  
Flow Simulations ◽  
Additional Information ◽  
Two Dimensional Flow ◽  
Different Shapes ◽  
Problem Formulations

The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods—the Viscous Vortex Domain method—is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers 104 and 105, the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.

Entry Length Requirements for Two- and Three-Dimensional Laminar Couette–Poiseuille Flows

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Bayode E. Owolabi ◽  
David J. C. Dennis ◽  
Robert J. Poole
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Channel Height ◽  
Development Length ◽  
Square Duct ◽  
Entry Length ◽  
Wide Range ◽  
High Reynolds ◽  
Pressure Driven Flow ◽  
Poiseuille Flows

In this study, we examine the development length requirements for laminar Couette–Poiseuille flows in a two-dimensional (2D) channel as well as in the three-dimensional (3D) case of flow through a square duct, using a combination of numerical and experimental approaches. The parameter space investigated covers wall to bulk velocity ratios, r, spanning from 0 (purely pressure-driven flow) to 2 (purely wall driven-flow; 4 in the case of a square duct) and a wide range of Reynolds numbers (Re). The results indicate an increase in the development length (L) with r. Consistent with the findings of Durst et al. (2005, “The Development Lengths of Laminar Pipe and Channel Flows,” ASME J. Fluids Eng., 127(6), pp. 1154–1160), L was observed to be of the order of the channel height in the limit as Re→0, irrespective of the condition at the inlet. This, however, changes at high Reynolds numbers, with L increasing linearly with Re. In all the cases considered, a uniform velocity profile at the inlet was found to result in longer entry lengths than in a flow developing from a parabolic inlet profile. We show that this inlet effect becomes less important as the limit of purely wall-driven flow is approached. Finally, we develop correlations for predicting L in these flows and, for the first time, also present laser Doppler velocimetry (LDV) measurements of the developing as well as fully-developed velocity profiles, and observe good agreement between experiment, analytical solution, and numerical simulation results in the 3D case.

Supercritical Reynolds number simulation for two-dimensional flow over circular cylinders

1975 ◽  
Vol 70 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Edmond Szechenyi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Practical Significance ◽  
Circular Cylinders ◽  
Wind Tunnels ◽  
Bluff Bodies ◽  
Wide Range ◽  
Two Dimensional Flow ◽  
Different Diameters

In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number.This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn.

Heat Transfer Coefficient Distribution of W and Broken W Turbulators At High Reynolds Numbers

2021 ◽  
pp. 1-29
Author(s):  
Sam Ghazi-Hesami ◽  
Dylan Wise ◽  
Keith Taylor ◽  
Étienne Robert ◽  
Peter Ireland
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Thermal Performance ◽  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
Smooth Channel ◽  
Wide Range ◽  
High Reynolds

Abstract An experimental and numerical study of the convective heat transfer enhancement provided by two rib families (W and Broken W) is presented, covering Reynolds numbers (Re) between 300,000 to 900,000 in a straight channel with a rectangular cross section (AR=1.29). These high Reynolds numbers were selected for the current study since most data in the available literature typically pertain to investigations at lower Reynolds numbers. The objective of this study is to assess the local heat transfer coefficient (HTC) enhancement (compared with a smooth channel) and the overall thermal performance, taking into account the effect of increased roughness on the friction factor, of a group of W shaped turbulators over a wide range of Reynolds numbers. Furthermore, the effects of increasing the rib spacing on the thermal performance of the Broken W configuration are presented and discussed. The numerical results are compared against heat transfer measurements obtained using the Transient Liquid Crystal (TLC) method. The research shows that for the Broken W turbulators, increasing the Reynolds number is associated with an overall decrease of the thermal performance while the thermal performance of the W configuration is relatively insensitive to Reynolds number. Nevertheless, the Broken W configuration delivers higher thermal performance and heat transfer compared with the W configuration for the range of Re investigated. The Broken W configuration with a pitch spacing of 10 times the rib height was shown to provide the optimal thermal performance in the configurations investigated here.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Experimental evidence for the theory of local isotropy

1948 ◽  
Vol 44 (4) ◽  
pp. 560-565 ◽  
Author(s):  
A. A. Townsend ◽  
Geoffrey Taylor
Keyword(s):  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Local Isotropy ◽  
High Reynolds Numbers ◽  
Wide Range ◽  
Skewness Factor ◽  
High Reynolds ◽  
Image Position

Some new measurements of isotropic turbulence produced behind a biplane grid have been made at high Reynolds numbers, and these results are compared with the predictions of the theory of local isotropy developed by A. N. Kolmogoroff. The transverse double-velocity correlation has been measured at mesh Reynolds numbers up to 3·2 × 105, and the observed form agrees well with the predicted form. Measurements of the skewness factor of velocity differences over finite intervals have also been made, and the factor is nearly constant and equal to −0·38, if the interval is small compared with the integral scale. The invariance of dimensionless functions of the velocity derivatives has been confirmed for the flattening factor of ∂u/∂x, namely,which is nearly constant over a wide range of conditions. It is concluded that the theory of local isotropy is substantially correct for isotropic turbulence of high Reynolds number.

On Pressure-Velocity Correlation of Steady and Oscillating Flows in Regenerators Made of Wire Screens

1999 ◽  
Vol 121 (1) ◽  
pp. 52-56 ◽  
Author(s):  
Chin-Tsau Hsu ◽  
Huili Fu ◽  
Ping Cheng
Keyword(s):  
Pressure Drop ◽  
Reynolds Numbers ◽  
Steady Flows ◽  
Oscillating Flows ◽  
Velocity Correlation ◽  
Boundary Layer Effect ◽  
Wide Range ◽  
Layer Effect ◽  
High Reynolds ◽  
Very High

A facility capable of generating steady and oscillating flows was constructed and experiments were conducted to investigate the pressure-drop characteristics of regenerators packed with wire screens. Both the velocity and pressure-drop across the regenerator were measured. To accurately determine the correlation between pressure-drop and velocity, the experiments covered a wide range from very low to very high Reynolds numbers, Reh. The steady flow results reveal that a three-term correlation with a term proportional to Reh−1/2 in addition to the Darcy-Forchheimer two-term correlation will fit best to the data. This Reh−1/2 term accounts for the boundary layer effect at intermediate Reynolds number. The results also show that the correlation for oscillating flows coincides with that for steady flows in 1 < Reh < 2000. This suggests that the oscillating flows in the regenerators behave as quasi-steady at the frequency range of less than 4.0 Hz, which is the maximum operable oscillating flow frequency of the facility.

The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 2 The influence of stratification

2012 ◽  
Vol 708 ◽  
pp. 45-70 ◽  
Author(s):  
A. Mashayek ◽  
W. R. Peltier
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Instability ◽  
Developed Turbulence ◽  
Wide Range ◽  
Stratified Shear Flow ◽  
High Reynolds ◽  
The Individual ◽  
Secondary Instabilities ◽  
Alternate Routes

AbstractThe linear stability analyses described in Mashayek & Peltier (J. Fluid Mech., vol. 708, 2012, 5–44, hereafter MP1) are extended herein in an investigation of the influence of stratification on the evolution of secondary instabilities to which an evolving Kelvin–Helmholtz (KH) wave is susceptible in an initially unstable parallel stratified shear layer. We show that over a wide range of background stratification levels, the braid shear instability has a higher probability of emerging at early stages of the flow evolution while the secondary convective instability (SCI), which occurs in the eyelids of the individual Kelvin ‘cats eyes’, will remain a relevant and dominant instability at high Reynolds numbers. The evolution of both modes is greatly influenced by the background stratification. Various other three-dimensional secondary instabilities are found to exist over a wide range of stratification levels. In particular, the stagnation point instability (SPI), which was discussed in detail in MP1, may be of great potential importance providing alternate routes for transition of an initially two-dimensional KH wave into fully developed turbulence. The energetics of the secondary instabilities revealed by our simulations are analysed in detail and the preturbulent mixing properties are studied.

1999 Turbomachinery Committee Best Paper Award: Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines— Part II: Experimental and Theoretical Analysis

1999 ◽  
Vol 122 (3) ◽  
pp. 406-414 ◽  
Author(s):  
Bernhard Ku¨sters ◽  
Heinz-Adolf Schreiber ◽  
Ulf Ko¨ller ◽  
Reinhard Mo¨nig
Keyword(s):  
Boundary Layer ◽  
Gas Turbines ◽  
Total Pressure ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Surface Boundary ◽  
Heavy Duty ◽  
High Reynolds Numbers ◽  
Wide Range ◽  
High Reynolds

In Part I of this paper a family of numerically optimized subsonic compressor airfoils for heavy-duty gas turbines, covering a wide range of flow properties, is presented. The objective of the optimization was to create profiles with a wide low loss incidence range. Therefore, design point and off-design performance had to be considered in an objective function. The special flow conditions in large-scale gas turbines have been taken into account by performing the numerical optimization procedure at high Reynolds numbers and high turbulence levels. The objective of Part II is to examine some of the characteristics describing the new airfoils, as well as to prove the reliability of the design process and the flow solver applied. Therefore, some characteristic members of the new airfoil series have been extensively investigated in the cascade wind tunnel of DLR cologne. Experimental and numerical results show profile Mach number distributions, total pressure losses, flow turning, and static pressure rise for the entire incidence range. The design goal with low losses and especially a wide operating range could be confirmed, as well as a mild stall behavior. Boundary layer development, particularly near stall condition, is discussed using surface flow visualization and the results of boundary layer calculations. An additional experimental study, using liquid crystal coating, provides necessary information on suction surface boundary-layer transition at high Reynolds numbers. Finally, results of Navier–Stokes simulations are presented that enlighten the total pressure loss development and flow turning behavior, especially at high incidence in relation to the results of the design tool. [S0889-504X(00)02602-7]

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