Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

2002 ◽  
Author(s):  
Vladimir Kriventsev ◽  
Hiroyuki Ohshima ◽  
Akira Yamaguchi ◽  
Hisashi Ninokata
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Axial Velocity ◽  
Complex Geometry ◽  
Turbulent Viscosity ◽  
Secondary Flows ◽  
Turbulence Structure ◽  
Empirical Parameter ◽  
Rod Bundle ◽  
Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. Ensemble-averaged Navier-Stokes, or Reynolds, equations are considered to be sufficient and practical enough to describe the turbulent flow in complex geometry of rod bundle array. We suggest the turbulence is a process of developing of external perturbations due to wall roughness, inlet conditions and other factors. We also assume that real flows are always affected by perturbations of any possible scale lower than the size of the channel. Thus, turbulence can be modeled in the form of internal or “turbulent” viscosity. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. From analysis of dimensions, some physical explanations of Reynolds number are possible. We can define the local turbulent Reynolds number in two ways: i) simply as Re = ul/v, where u is a local velocity deformation within the local scale l and v is total accumulated molecular and turbulent viscosity of all scales lower then 1. ii) Re = K/W, where K is kinetic energy and W is work of friction/dissipation forces. Both definitions above have been implemented in the calculation of samples of basic fully-developed turbulent flows in straight channels such as a circular tube and annular channel. MSV has been also applied to prediction of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. It is known that the nature of these turbulence-driven motions is originated in anisotropy of turbulence structure. Due to the lack of experimental data up to date, numerical analysis seems to be the only way to estimate intensity of the secondary flows in hexagonal fuel assemblies of fast breeder reactors (FBR). Since MSV can naturally predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re = 8170), while for higher Reynolds number (Re = 160,100) the intensity of secondary flow is as negligible as 0.2%.

Influence of Inlet Velocity Condition on Unsteady Flow Characteristics in Piping With a Short-Elbow at High Reynolds Number Condition

2014 ◽  
Author(s):  
Ayako Ono ◽  
Masaaki Tanaka ◽  
Jun Kobayashi ◽  
Hideki Kamide
Keyword(s):  
Reynolds Number ◽  
Flow Separation ◽  
Velocity Fluctuation ◽  
Complex Geometry ◽  
Perforated Plate ◽  
Secondary Flows ◽  
Curvature Radius ◽  
Mean Velocity ◽  
Inlet Velocity ◽  
Velocity Condition

In design of the Japan Sodium-cooled Fast Reactor (JSFR), mean velocity of the coolant is approximately 9 m/s in the primary hot leg (H/L) piping which diameter is 1.27 m. The Reynolds number in the H/L piping reaches 4.2×107. Moreover, a short-elbow which has Rc/D = 1.0 (Rc: Curvature radius, D: Pipe diameter) is used in the hot leg piping in order to achieve compact plant layout and reduce plant construction cost. In the H/L piping, flow-induced vibration (FIV) is concerned due to excitation force which is caused by pressure fluctuation on the wall closely related with the velocity fluctuation in the short-elbow. In the previous study, relation between the flow separation and the pressure fluctuations in the short-elbow was revealed under the specific inlet condition with flat distribution of time-averaged axial velocity and relatively weak velocity fluctuation intensity in the pipe. However, the inlet velocity condition of the H/L in a reactor may have ununiformed profile with highly turbulent due to the complex geometry in reactor vessel (R/V). In this study, the influence of the inlet velocity condition on unsteady characteristics of velocity in the short-elbow was studied. Although the flow around the inlet of the H/L in R/V could not simulate completely, inlet velocity conditions were controlled by installing the perforated plate with plugging the flow-holes appropriately. Then expected flow patterns were made at 2D upstream position from the elbow inlet in the experiments. It was revealed that the inlet velocity profiles affected circumferential secondary flow and the secondary flows affected an area of flow separation at the elbow, by local velocity measurement by the PIV (particle image velocimetry). And it was found that the low frequent turbulence in the upstream piping remained downstream of the elbow though their intensity was attenuated.

On the definition of the secondary flow in three-dimensional cascades

2009 ◽  
Vol 223 (6) ◽  
pp. 667-676 ◽  
Author(s):  
G Persico ◽  
P Gaetani ◽  
V Dossena ◽  
G D'Ippolito ◽  
C Osnaghi
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Secondary Flow ◽  
Boundary Layers ◽  
Complex Geometry ◽  
Flow Direction ◽  
Flow Analysis ◽  
Secondary Flows ◽  
Streamwise Vorticity ◽  
Reference Flow

The present article proposes a novel methodology to evaluate secondary flows generated by the annulus boundary layers in complex cascades. Unlike two-dimensional (2D) linear cascades, where the reference flow is commonly defined as that measured at midspan, the problem of the reference flow definition for annular or complex 3D linear cascades does not have a general solution up to the present time. The proposed approach supports secondary flow analysis whenever exit streamwise vorticity produced by inlet endwall boundary layers is of interest. The idea is to compute the reference flow by applying slip boundary conditions at the endwalls in a viscous 3D numerical simulation, in which uniform total pressure is prescribed at the inlet. Thus the reference flow keeps the 3D nature of the actual flow except for the contribution of the endwall boundary layer vorticity. The resulting secondary field is then derived by projecting the 3D flow field (obtained from both an experiment and a fully viscous simulation) along the local reference flow direction; this approach can be proficiently applied to any complex geometry. This method allows the representation of secondary velocity vectors with a better estimation of the vortex extension, since it offers the opportunity to visualize also the region of the vortices, which can be approximated as a potential type. Furthermore, a proficient evaluation of the secondary vorticity and deviation angle effectively induced by the annulus boundary layer is possible. The approach was preliminarily verified against experimental data in linear cascades characterized by cylindrical blades, not reported for the sake of brevity, showing a very good agreement with the standard methodology based only on the experimental midspan flow field. This article presents secondary flows obtained by the application of the proposed methodology on two annular cascades with cylindrical and 3D-designed blades, stressing the differences with other definitions. Both numerical and experimental results are considered.

Turbulence Modeling of Axial Flow in a Bare Rod Bundle

1979 ◽  
Vol 101 (4) ◽  
pp. 628-634 ◽  
Author(s):  
J. G. Bartzis ◽  
N. E. Todreas
Keyword(s):  
Secondary Flow ◽  
Turbulent Flows ◽  
Axial Velocity ◽  
Nuclear Reactor ◽  
Turbulence Modeling ◽  
Three Dimensional ◽  
Axial Flow ◽  
Reynolds Stresses ◽  
Rod Bundle ◽  
Aspect Ratios

Temperature distribution within the rod bundle of a nuclear reactor is of major importance in nuclear reactor design. However temperature information presupposes knowledge of the hydrodynamic behavior of the coolant which is the most difficult part of the problem due to the complexity of the turbulence phenomena. In the present work a two equation turbulence model—a strong candidate for analyzing actual three dimensional turbulent flows—has been used to predict fully developed flow of infinite bare rod bundle of various aspect ratios (P/D). The model has been modified to take into account anisotropic effects of eddy viscosity. Secondary flow calculations have been also performed although the model seems to be too rough to predict the secondary flow correctly. Heat transfer calculations have been performed to confirm the importance of anisotropic viscosity in temperature predictions. Experimental measurements of the distribution of axial velocity, turbulent axial velocity, turbulent kinetic energy and radial Reynolds stresses were performed in the developing and fully developed regions. A two channel Laser Doppler Anemometer working in the reference mode with forward scattering was used to perform the measurements in a simulated interior subchannel of a triangular rod array with P/D = 1.124. Comparisons between the analytical results and the results of this experiment as well as other experimental data in rod bundle arrays available in the literature are presented. The predictions are in good agreement with the results for high Reynolds numbers.

scholarly journals Laminarisation of flow at low Reynolds number due to streamwise body force

2016 ◽  
Vol 809 ◽  
pp. 31-71 ◽  
Author(s):  
S. He ◽  
K. He ◽  
M. Seddighi
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Body Force ◽  
Turbulent Viscosity ◽  
The Body ◽  
Wall Turbulence ◽  
Turbulence Structure ◽  
Pressure Force ◽  
Conventional View ◽  
Ejections And Sweeps

It is well established that when a turbulent flow is subjected to a non-uniform body force, the turbulence may be significantly suppressed in comparison with that of the flow of the same flow rate and hence the flow is said to be laminarised. This is the situation in buoyancy-aided mixed convection when severe heat transfer deterioration may occur. Here we report results of direct numerical simulations of flow with a linear or a step-change profile of body force. In contrast to the conventional view, we show that applying a body force to a turbulent flow while keeping the pressure force unchanged causes little changes to the key characteristics of the turbulence. In particular, the mixing characteristics of the turbulence represented by the turbulent viscosity remain largely unaffected. The so-called flow laminarisation due to a body force is in effect a reduction in the apparent Reynolds number of the flow, based on an apparent friction velocity associated with only the pressure force of the flow (i.e. excluding the contribution of the body force). The new understanding allows the level of the flow ‘laminarisation’ and when the full laminarisation occurs to be readily predicted. In terms of the near-wall turbulence structure, the numbers of ejections and sweeps are little influenced by the imposition of the body force, whereas the strength of each event may be enhanced if the coverage of the body force extends significantly away from the wall. The streamwise turbulent stress is usually increased in accordance with the observation of more and stronger elongated streaks, but the wall-normal and the circumferential turbulent stresses are largely unchanged.

Heat/Mass Transfer Characteristics for Flow in a Corrugated Wall Channel

1977 ◽  
Vol 99 (2) ◽  
pp. 187-195 ◽  
Author(s):  
Leonardo Goldstein ◽  
E. M. Sparrow
Keyword(s):  
Mass Transfer ◽  
Reynolds Number ◽  
Secondary Flow ◽  
Low Reynolds Number ◽  
Secondary Flows ◽  
Turbulent Regime ◽  
Transfer Rates ◽  
Transfer Characteristics ◽  
Low Reynolds ◽  
Corrugated Wall

Experiments based on the naphthalene sublimation technique were carried out to determine the local and average transfer characteristics for flow in a corrugated wall channel. The range of the experiments encompassed the laminar, transition, and low-Reynolds-number turbulent regimes. Local mass transfer measurements were made both in the spanwise (i.e., cross stream) and streamwise directions, and overall transfer rates were also determined. The experiments demonstrated the existence of a variety of complex transfer processes and related fluid flow phenomena. These included secondary flows and associated spanwise mass transfer variations, suppression of the secondary flow by counteracting centrifugal forces, and destruction of the secondary flow by the onset of turbulence. Flow separation on the leeward facets of the corrugated wall caused a sharp decrease in the local transfer rates, but relatively high transfer rates were in evidence in the reattachment region. In the laminar range, the average transfer coefficients for the corrugated wall channel were only moderately larger than those for a parallel-plate channel. On the other hand, in the low-Reynolds-number turbulent regime, the wall corrugations were responsible for an increase of nearly a factor of three in the average coefficient compared with the smooth wall channel.

scholarly journals Hydrodynamic behavior of a bare rod bunle

1977 ◽  
Author(s):  
Ιωάννης Μπαρτζής
Keyword(s):  
Secondary Flow ◽  
Turbulent Flows ◽  
Axial Velocity ◽  
Nuclear Reactor ◽  
Three Dimensional ◽  
Hydrodynamic Behavior ◽  
Rod Bundle ◽  
Aspect Ratios ◽  
Strong Candidate ◽  
High Reynolds

Temperature distributions within the rod bundle of a nuclear reactor is of major importance in nuclear reactor design. However temperature information presupposes knowledge of the hydrodynamic behavior of the coolant which is the most difficult part of the problem due to complexity of the turbulence phenomena. In the present work a 2-equation turbulence model - a strong candidate for analyzing actual three dimensional turbulent flows - has been used to predict fully developed flow of infinite bare rod bundle of various aspect ratios (P/D). The model has been modified to take into account anisotropic effects of eddy viscosity. Secondary flow calculations have been also performed although the mo^el seems to be too rough to predict the secondary flow correctly. Heat Transfer calculations have been performed to confirm the importance of anisotropic viscosity in temperature predictions. All numerical calculations for flow and heat have been performed by two computer codes developed in the present work which were based on the TEACH code [71]· Also experimental measurements of the distribution of axial velocity, turbulent axial velocity, turbulent kinetic energy and radial Reynoldsstresses were performed in the developing and fully developed regions. A 2-channel Laser Doppler Anemometer working on the Reference mode with forward scattering was used to perform the measurements in a simulated interior subchannel of a triangular rod array with P/D=1.124. Comparisons between the analytical results and the results of this experiment as well as other experimental data in rod bundle array available in literature are presented. The predictions are in good agreement with the results for the high Reynolds numbers.

scholarly journals Coriolis and buoyancy effects on heat transfer in viewpoint of field synergy principle and secondary flow intensity for maximization of internal cooling

2021 ◽  
Author(s):  
Seyed Mostafa Hosseinalipour ◽  
Hamidreza Shahbazian ◽  
Bengt Sunden
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Secondary Flow ◽  
Rotation Number ◽  
Numerical Results ◽  
Secondary Flows ◽  
Internal Cooling ◽  
Field Synergy ◽  
Field Synergy Principle ◽  
Flow Intensity

AbstractThe present investigation emphases on rotation effects on internal cooling of gas turbine blades both numerically and experimentally. The primary motivation behind this work is to investigate the possibility of heat transfer enhancement by dean vortices generated by Coriolis force and U-bend with developing turbulent in the view point of the field synergy principle and secondary flow intensity analysis. A two-passage internal cooling channel model with a 180° U-turn at the hub section is used in the analysis. The flow is radially outward at the first passage of the square channel and then it will be inward at the second passage. The study covers a Reynolds number (Re) of 10,000, Rotation number (Ro) in the range of 0–0.25, and Density Ratios (DR) at the inlet between 0.1–1.5. The numerical results are compared to experimental data from a rotating facility. Results obtained with the basic RANS SST k-ω model are assessed completely as well. A field synergy principle analysis is consistent with the numerical results too. The results state that the secondary flows due to rotation can considerably improve the synergy between the velocity and temperature gradients up to 20%, which is the most fundamental reason why the rotation can enhance the heat transfer. In addition, the Reynolds number and centrifugal buoyancy variations are found to have no remarkable impact on increasing the synergy angle. Moreover, vortices induced by Rotation number and amplified by Reynolds number increase considerable secondary flow intensity which is exactly in compliance with Nusselt number enhancement.

Free-surface Taylor vortices

1994 ◽  
Vol 261 ◽  
pp. 169-198 ◽  
Author(s):  
F. J. Wang ◽  
G. A. Domoto
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Method ◽  
Secondary Flow ◽  
Stokes Equations ◽  
Hydrodynamic Instability ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Secondary Flows ◽  
Two Dimensional

The hydrodynamic instability of a viscous incompressible flow with a free surface is studied both numerically and experimentally. While the free-surface flow is basically two-dimensional at low Reynolds numbers, a three-dimensional secondary flow pattern similar to the Taylor vorticies between two concentric cylinders appears at higher rotational speeds. The secondary flow has periodic velocity components in the axial direction and is characterized by a distinct spatially periodic variation in surface height similar to a standing wave. A numerical method, using boundary-fitted coordinates and multigrid methods to solve the Navier–Stokes equations in primitive variables, is developed to treat two-dimensional free-surface flows. A similar numerical technique is applied to the linearized three-dimensional perturbation equations to treat the onset of secondary flows. Experimental measurements have been obtained using light sheet techniques to visualize the secondary flow near the free surface. Photographs of streak lines were taken and compared to the numerical calculations. It has been shown that the solution of the linearized equations contains most of the important features of the nonlinear secondary flows at Reynolds number higher than the critical value. The experimental results also show that the numerical method predicts well the onset of instability in terms of the critical wavenumber and Reynolds number.

Fundamental Analysis of the Secondary Flows and Jet-Wake in a Torque Converter Pump—Part II: Flow in a Curved Stationary Passage and Combined Flows

2005 ◽  
Vol 127 (1) ◽  
pp. 75-82 ◽  
Author(s):  
R. Flack ◽  
K. Brun
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Suction Side ◽  
Torque Converter ◽  
Secondary Flows ◽  
Wake Flow ◽  
Streamwise Vorticity ◽  
Shell Side ◽  
The Core ◽  
Vorticity Component

Previously, experimental results for the velocity field in a torque converter pump showed strong jet/wake characteristics including backflows and circulatory secondary flows. Navier-Stokes flow models were developed herein to independently analyze the pump pressure-to-suction side jet/wake flow, the core-to-shell side jet/wake flow, and the secondary flows. Two relatively simple models were employed: (i) a rotating two-dimensional straight-walled duct and (ii) a 180 deg flow bend. Parametric studies were undertaken to evaluate the effect that operating conditions and geometry had on the characteristics. Results from the model showed that the core side wake, which was due to flow separation caused by rapid radial flow turning, was primarily a function of the Reynolds number; increasing the Reynolds number increased the core-to-shell side jet/wake flow. The passage length (or curvature) strongly affected the core-to-shell jet/wake. Using the modified equations for the generation of streamwise vorticity and the results from the two-dimensional jet/wake model for the normal and binormal vorticity components, trends for the secondary flows in the torque converter pump were predicted. Predicted secondary flows in the torque converter pump circulated in the counterclockwise direction (positive streamwise vorticity) in the pump midplane and in the clockwise direction (negative streamwise vorticity) in the pump exit plane. These trends agreed with experimental observations. Both the Reynolds number and the modified Rossby number were seen to have a significant influence on the streamwise vorticity and, thus, on the magnitude of the secondary flow velocities. The pump midplane counter-clockwise secondary flow circulation was primarily caused by the interaction of the pressure-to-suction side jet/wake nonuniform flow (and the associated normal vorticity component) with the high radial/axial flow turning angle the flow underwent while passing through blade passage. Similarly, the pump exit plane clockwise secondary flow circulation was caused by the core-to-shell side jet/wake nonuniform flow (and the associated binormal vorticity component) being rotated about a fixed centerline (pump shaft). Thus, the pump streamwise vorticity, which was responsible for the generation circulatory secondary flows, was directly related to the pump jet/wake phenomena.

Effects of Freestream Turbulence Intensity, Turbulence Length Scale, and Exit Reynolds Number on Vane Endwall Secondary Flow and Heat Transfer in a Transonic Turbine Cascade

2020 ◽  
Author(s):  
Zhigang Li ◽  
Bo Bai ◽  
Luxuan Liu ◽  
Jun Li ◽  
Shuo Mao ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Secondary Flow ◽  
Turbulence Intensity ◽  
Thermal Load ◽  
Secondary Flows ◽  
Length Scale ◽  
Freestream Turbulence ◽  
Turbulence Length ◽  
Turbulence Length Scale

Abstract In gas turbine engines, the first-stage vanes usually suffer harsh incoming flow conditions from the combustor with high pressure, high temperature and high turbulence. The combustor-generated high freestream turbulence and strong secondary flows in a gas turbine vane passage have been reported to augment the endwall thermal load significantly. This paper presents a detailed numerical study on the effects of high freestream turbulence intensity, turbulence length scale, and exit Reynolds number on the endwall secondary flow pattern and heat transfer distribution of a transonic linear turbine vane passage at realistic engine Mach numbers, with a flat endwall no cooling. Numerical simulations were conducted at a range of different operation conditions: six freestream turbulence intensities (Tu = 1%, 5%, 10%, 13%, 16% and 20%), six turbulence length scales (normalized by the vane pitch of Λ/P = 0.01, 0.04, 0.07, 0.12, 0.24, 0.36), and three exit isentropic Mach number (Maex = 0.6, 0.85 and 1.02 corresponding exit Reynolds number Reex = 1.1 × 106, 1.7 × 106 and 2.2 × 106, respectively, based on the vane chord). Detailed comparisons were presented for endwall heat transfer coefficient distribution, endwall secondary flow field at different operation conditions, while paying special attention to the link between endwall thermal load patterns and the secondary flow structures. Results show that the freestream turbulence intensity and length scale have a significant influence on the endwall secondary flow field, but the influence of the exit Reynolds number is very weak. The Nusselt number patterns for the higher turbulence intensities (Tu = 16%, 20%) appear to be less affected by the endwall secondary flows than the lower turbulence cases. The thermal load distribution in the arc region around the vane leading edge and the banded region along the vane pressure side are influenced most strongly by the freestream turbulence intensity. In general, the higher freestream turbulence intensities make the vane endwall thermal load more uniform. The Nusselt number distribution is only weakly affected by the turbulence length scale when Λ/P is larger than 0.04. The heat transfer level appears to have a significant uniform augmentation over the whole endwall region with the increasing Maex. The endwall thermal load distribution is classified into four typical regions, and the effects of freestream turbulence, exit Reynolds number in each region were discussed in detail.

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