scholarly journals 3D Laser Anemometry in a Rotating Cooling Channel

1998 ◽  
Author(s):  
Y. Servouze
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Static Mode ◽  
Jet Engine ◽  
Laser Anemometry ◽  
Axial Velocity Profile ◽  
Laser Anemometer ◽  
First Results ◽  
The Subject

The flow in rotating cooling passages of jet engine turbine rotors is considered. Contrary to thermal data which have been obtained by a lot of people, velocity field data are very few. Nevertheless, in order to validate Navier-Stokes calculations, these two types of data are necessary. In such a flow with complexe secondary structures, 3D laser anemometer is the most suitable tool but its implementation on this application was a challenge. Measurements were made first in static mode at Reynolds numbers of 5,000 and 25,000. The same model sections were then explored during rotation at a Reynolds number of 5,000 and a Rossby number of 0.33. Some results were obtained a Reynolds number of 25,000 and a Rossby numbers of 0.033 and 0.066. The distortion of the axial velocity profile resulting from the Coriolis acceleration appears clearly when comparing the results obtained in the sections of the centrifugal arm. In the transverse plane, the two other velocity components show the secondary flow structures with two contrarotating vortices. The results obtained in the centripetal arm show that the flow depends on the 180 deg straight-corner turn located upstream. These measurements confirm the assumptions made on the organisation of this type of flow, and the simulation results obtained at ONERA with the MATHILDA code and also by other teams who have published papers on the subject. The first results obtained during this experimental work demonstrate the validity of the 3D laser anemometry in such a case. They show also some insufficiencies due to an application deemed difficult.

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Investigating Gas Turbine Internal Cooling Using Supercritical CO2 at High Reynolds Numbers for Direct Fired Cycle Applications

2021 ◽  
Author(s):  
Matthew Searle ◽  
Arnab Roy ◽  
James Black ◽  
Doug Straub ◽  
Sridharan Ramesh
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Cfd Simulation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Process Conditions ◽  
Internal Cooling ◽  
Air Breathing

Abstract In this paper, experimental and numerical investigations of three variants of internal cooling configurations — dimples only, ribs only and ribs with dimples have been explored at process conditions (96°C and 207bar) with sCO2 as the coolant. The designs were chosen based on a review of advanced internal cooling features typically used for air-breathing gas turbines. The experimental study described in this paper utilizes additively manufactured square channels with the cooling features over a range of Reynolds number from 80,000 to 250,000. Nusselt number is calculated in the experiments utilizing the Wilson Plot method and three heat transfer characteristics — augmentation in Nusselt number, friction factor and overall Thermal Performance Factor (TPF) are reported. To explore the effect of surface roughness introduced due to additive manufacturing, two baseline channel flow cases are considered — a conventional smooth tube and an additively manufactured square tube. A companion computational fluid dynamics (CFD) simulation is also performed for the corresponding cooling configurations reported in the experiments using the Reynolds Averaged Navier Stokes (RANS) based turbulence model. Both experimental and computational results show increasing Nusselt number augmentation as higher Reynolds numbers are approached, whereas prior work on internal cooling of air-breathing gas turbines predict a decay in the heat transfer enhancement as Reynolds number increases. Comparing cooling features, it is observed that the “ribs only” and “ribs with dimples” configurations exhibit higher Nusselt number augmentation at all Reynolds numbers compared to the “dimples only” and the “no features” configurations. However, the frictional losses are almost an order of magnitude higher in presence of ribs.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

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.

Prediction of Unsteady Loading on a Circular Cylinder in High Reynolds Number Flows Using Large Eddy Simulation

2005 ◽  
Author(s):  
Sung-Eun Kim ◽  
L. Srinivasa Mohan
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Turbulent Viscosity ◽  
Reynolds Numbers ◽  
Unstructured Meshes ◽  
Navier Stokes ◽  
Step Method ◽  
Fractional Step Method ◽  
Eddy Simulation ◽  
Large Eddy

Large eddy simulations were carried out for the flow around a hydrodynamically smooth, fixed circular cylinder at two Reynolds numbers, one at a subcritical Reynolds number (Re = 1.4 × 105) and the other at a supercritical Reynolds number (Re = 1.0 × 106). The computations were made using a parallelized finite-volume Navier-Stokes solver based on a multidimensional linear reconstruction scheme that allows use of unstructured meshes. Central differencing was used for discretization of both convection and diffusion terms. Time-advancement scheme, based on an implicit, non-iterative fractional-step method, was adopted in conjunction with a three-level, backward second-order temporal discretization. Subgrid-scale turbulent viscosity was modeled by a dynamic Smagorinsky model adapted to arbitrary unstructured meshes with the aid of a test-filter applicable to arbitrary unstructured meshes. The present LES results closely reproduced the flow features observed in experiments at both Reynolds numbers. The time-averaged mean drag coefficient, root-mean-square force coefficients and the frequency content of fluctuating forces (vortex-shedding frequency) are predicted with a commendable accuracy.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Downstream decay of fully developed Dean flow

2015 ◽  
Vol 777 ◽  
pp. 219-244 ◽  
Author(s):  
Jesse T. Ault ◽  
Kevin K. Chen ◽  
Howard A. Stone
Keyword(s):  
Reynolds Number ◽  
Linear Dependence ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Curvature Radius ◽  
Navier Stokes Equations ◽  
Curved Pipe ◽  
Dean Flow ◽  
Junction Flow

Direct numerical simulations were used to investigate the downstream decay of fully developed flow in a $180^{\circ }$ curved pipe that exits into a straight outlet. The flow is studied for a range of Reynolds numbers and pipe-to-curvature radius ratios. Velocity, pressure and vorticity fields are calculated to visualize the downstream decay process. Transition ‘decay’ lengths are calculated using the norm of the velocity perturbation from the Hagen–Poiseuille velocity profile, the wall-averaged shear stress, the integral of the magnitude of the vorticity, and the maximum value of the $Q$-criterion on a cross-section. Transition lengths to the fully developed Poiseuille distribution are found to have a linear dependence on the Reynolds number with no noticeable dependence on the pipe-to-curvature radius ratio, despite the flow’s dependence on both parameters. This linear dependence of Reynolds number on the transition length is explained by linearizing the Navier–Stokes equations about the Poiseuille flow, using the form of the fully developed Dean flow as an initial condition, and using appropriate scaling arguments. We extend our results by comparing this flow recovery downstream of a curved pipe to the flow recovery in the downstream outlets of a T-junction flow. Specifically, we compare the transition lengths between these flows and document how the transition lengths depend on the Reynolds number.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

scholarly journals Prediction of the Propeller Performance at Different Reynolds Number Regimes with RANS

2021 ◽  
Vol 9 (10) ◽  
pp. 1115
Author(s):  
João Baltazar ◽  
Douwe Rijpkema ◽  
José Falcão de Campos
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Scale Effects ◽  
Open Water ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transition Model ◽  
Sst Turbulence Model ◽  
Propeller Performance ◽  
Selection Of

In this study, a Reynolds averaged Navier-Stokes solver is used for prediction of the propeller performance in open-water conditions at different Reynolds numbers ranging from 104 to 107. The k−ω SST turbulence model and the γ−R˜eθt correlation-based transition model are utilised and results compared for a conventional marine propeller. First, the selection of the turbulence inlet quantities for different flow regimes is discussed. Then, an analysis of the iterative and discretisation errors is made. This work is followed by an investigation of the predicted propeller flow at variable Reynolds numbers. Finally, the propeller scale-effects and the influence of the turbulence and transition models on the performance prediction are discussed. The variation of the flow regime showed an increase in thrust and decrease in torque for increasing Reynolds number. From the comparison between the turbulence model and the transition model, different flow solutions are obtained for the Reynolds numbers between 105 and 106, affecting the scale-effects prediction.

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