scholarly journals Prandtl’s Secondary Flows of the Second Kind. Problems of Description, Prediction, and Simulation

2021 ◽  
Vol 56 (4) ◽  
pp. 513-538
Author(s):  
N. V. Nikitin ◽  
N. V. Popelenskaya ◽  
A. Stroh
Keyword(s):  
Secondary Flow ◽  
Turbulent Flows ◽  
Longitudinal Component ◽  
Secondary Flows ◽  
Physical Mechanisms ◽  
Numerical Studies ◽  
Flow Formation ◽  
Active Research ◽  
Prediction And Simulation ◽  
Turbulent Pulsations

Abstract— The occurrence of turbulent pulsations in straight pipes of noncircular cross-section leads to the situation, when the average velocity field includes not only the longitudinal component but also transverse components that form a secondary flow. This hydrodynamic phenomenon discovered at the twenties of the last century (J. Nikuradse, L. Prandtl) has been the object of active research to the present day. The intensity of the turbulent secondary flows is not high; usually, it is not greater than 2–3% of the characteristic flow velocity. Nevertheless, their contribution to the processes of transverse transfer of momentum and heat is comparable to that of turbulent pulsations. In this paper, a review of experimental, theoretical, and numerical studies of secondary flows in straight pipes and channels is given. Emphasis is placed on the issues of revealing the physical mechanisms of secondary flow formation and developing the models of the apriori assessment of their forms. The specific features of the secondary flow development in open channels and channels with inhomogeneously rough walls are touched upon. The approaches of semiempirical simulation of turbulent flows in the presence of secondary flows are discussed.

scholarly journals Mechanism of formation of Prandtl’s secondary flows of the second kind

2019 ◽  
Vol 484 (4) ◽  
pp. 420-425
Author(s):  
N. V. Nikitin ◽  
V. O. Pimanov ◽  
N. V. Popelenskaya
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Physical Interpretation ◽  
Nonlinear Interaction ◽  
Longitudinal Component ◽  
Secondary Flows ◽  
Mechanism Of Formation ◽  
Longitudinal Vortices ◽  
Turbulent Pulsations

Turbulent flow in a tube of square cross section is investigated numerically. The concentrated longitudinal vortices responsible for the occurrence of secondary flows are studied. It is shown that the longitudinal vortices are formed as a result of nonlinear interaction of turbulent pulsations in which the pulsations of the longitudinal component of vorticity are specially adjusted in phase with the pulsations of the longitudinalvelocity component. A physical interpretation of this mechanism is given.

scholarly journals Modeling Inspiratory Flow in a Porcine Lung Airway

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Peshala P. T. Gamage ◽  
Fardin Khalili ◽  
M. D. Khurshidul Azad ◽  
Hansen A Mansy
Keyword(s):  
Secondary Flow ◽  
Turbulent Flows ◽  
Cross Sections ◽  
Animal Studies ◽  
Inspiratory Flow ◽  
Secondary Flows ◽  
Inlet Flow Rate ◽  
Simulation Results ◽  
Human Airways ◽  
Viscous Pressure

Inspiratory flow in a multigeneration pig lung airways was numerically studied at a steady inlet flow rate of 3.2 × 10−4 m3/s corresponding to a Reynolds number of 1150 in the trachea. The model was validated by comparing velocity distributions with previous measurements and simulations in simplified airway geometries. Simulation results provided detailed maps of the axial and secondary flow patterns at different cross sections of the airway tree. The vortex core regions in the airways were visualized using absolute helicity values and suggested the presence of secondary flow vortices where two counter-rotating vortices were observed at the main bifurcation and in many other bifurcations. Both laminar and turbulent flows were considered. Results showed that axial and secondary flows were comparable in the laminar and turbulent cases. Turbulent kinetic energy (TKE) vanished in the more distal airways, which indicates that the flow in these airways approaches laminar flow conditions. The simulation results suggested viscous pressure drop values comparable to earlier studies. The monopodial asymmetric nature of airway branching in pigs resulted in airflow patterns that are different from the less asymmetric human airways. The major daughters of the pig airways tended to have high airflow ratios, which may lead to different particle distribution and sound generation patterns. These differences need to be taken into consideration when interpreting the results of animal studies involving pigs before generalizing these results to humans.

Secondary motion of fully developed oscillatory flow in a curved pipe

1992 ◽  
Vol 237 ◽  
pp. 189-208 ◽  
Author(s):  
K. Sudo ◽  
M. Sumida ◽  
R. Yamane
Keyword(s):  
Laminar Flow ◽  
Flow Velocity ◽  
Secondary Flow ◽  
Flow Pattern ◽  
Velocity Component ◽  
Oscillatory Flow ◽  
Secondary Flows ◽  
Curved Pipe ◽  
Numerical Studies ◽  
Secondary Motion

Experimental and numerical studies were made of the secondary flow induced in fully developed oscillatory laminar flow in a curved circular pipe. Photographs of traces of nylon particles suspended in water were taken systematically with Womersley numbers α = 5.5 ∼ 28 and oscillatory Dean numbers D = 40 ∼ 500. The secondary flow velocity component and the location of the vortex eye were obtained from the photographs. The experimental results were checked with the numerical ones and the variations of the secondary flow pattern with the Dean and Womersley numbers were analysed based on both results. These results suggest that secondary flows can be classified into five patterns.

The production and diffusion of vorticity in duct flow

1964 ◽  
Vol 19 (3) ◽  
pp. 375-394 ◽  
Author(s):  
E. Brundrett ◽  
W. D. Baines
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Longitudinal Component ◽  
Secondary Flows ◽  
Duct Flow ◽  
Square Duct ◽  
Circular Pipes ◽  
Flow Circulation ◽  
Diffusion And Convection

Secondary flows in non-circular ducts are accompanied by a longitudinal component of vorticity. The equation of motion defining this component in a turbulent flow is composed of three terms giving the rates of production, diffusion and convection. Since the expression for production is the second derivative of Reynolds strees components, longitudinal vorticity cannot exist in laminar flow. For turbulent flow in a square duct the Reynolds stress tensor is examined in detail. Symmetry requirements alone provide relationships showing that the production is zero along all lines of symmetry. General characteristics of flow in circular pipes are sufficient to indicate where the production must be greatest. Experimental measurements verify this result and define the point density of production, diffusion and convection of vorticity. Data also indicate that the basic pattern of secondary flow is independent of Reynolds number, but that with increasing values of Reynolds number the flows penetrate the corners and approach the walls. A similar experimental investigation of a rectangular duct shows that the corner bisectors separate independent secondary flow circulation zones. Production of vorticity is again associated with the region near the bisector. However, there is some evidence that the secondary flow pattern is not so complex as inferred from the distortion of the main longitudinal flow.

scholarly journals A Review of Numerical Simulations of Secondary Flows in River Bends

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 884
Author(s):  
Rawaa Shaheed ◽  
Abdolmajid Mohammadian ◽  
Xiaohui Yan
Keyword(s):  
Numerical Modeling ◽  
Numerical Simulations ◽  
Secondary Flow ◽  
Cross Section ◽  
Turbulence Models ◽  
Main Flow ◽  
Secondary Flows ◽  
River Bends ◽  
River Cross Section ◽  
River Bend

River bends are one of the common elements in most natural rivers, and secondary flow is one of the most important flow features in the bends. The secondary flow is perpendicular to the main flow and has a helical path moving towards the outer bank at the upper part of the river cross-section, and towards the inner bank at the lower part of the river cross-section. The secondary flow causes a redistribution in the main flow. Accordingly, this redistribution and sediment transport by the secondary flow may lead to the formation of a typical pattern of river bend profile. It is important to study and understand the flow pattern in order to predict the profile and the position of the bend in the river. However, there are a lack of comprehensive reviews on the advances in numerical modeling of bend secondary flow in the literature. Therefore, this study comprehensively reviews the fundamentals of secondary flow, the governing equations and boundary conditions for numerical simulations, and previous numerical studies on river bend flows. Most importantly, it reviews various numerical simulation strategies and performance of various turbulence models in simulating the flow in river bends and concludes that the main problem is finding the appropriate model for each case of turbulent flow. The present review summarizes the recent advances in numerical modeling of secondary flow and points out the key challenges, which can provide useful information for future studies.

scholarly journals Incidence Angle and Pitch-Chord Effects on Secondary Flows Downstream of a Turbine Cascade

1992 ◽  
Author(s):  
A. Perdichizzi ◽  
V. Dossena
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Oil Flow ◽  
Secondary Velocity ◽  
Secondary Flow Field

This paper describes the results of an experimental investigation of the three-dimensional flow downstream of a linear turbine cascade at off-design conditions. The tests have been carried out for five incidence angles from −60 to +35 degrees, and for three pitch-chord ratios: s/c = 0.58,0.73,0.87. Data include blade pressure distributions, oil flow visualizations, and pressure probe measurements. The secondary flow field has been obtained by traversing a miniature five hole probe in a plane located at 50% of an axial chord downstream of the trailing edge. The distributions of local energy loss coefficients, together with vorticity and secondary velocity plots show in detail how much the secondary flow field is modified both by incidence and cascade solidity variations. The level of secondary vorticity and the intensity of the crossflow at the endwall have been found to be strictly related to the blade loading occurring in the blade entrance region. Heavy changes occur in the spanwise distributions of the pitch averaged loss and of the deviation angle, when incidence or pitch-chord ratio is varied.

scholarly journals The Design of an Improved Endwall Film-Cooling Configuration

1998 ◽  
Author(s):  
S. Friedrichs ◽  
H. P. Hodson ◽  
W. N. Dawes
Keyword(s):  
Secondary Flow ◽  
Film Cooling ◽  
Large Scale ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Aerodynamic Loss ◽  
Cooling Flow ◽  
High Static Pressure ◽  
Endwall Film Cooling ◽  
Aerodynamic Losses

The endwall film-cooling cooling configuration investigated by Friedrichs et al. (1996, 1997) had in principle sufficient cooling flow for the endwall, but in practice, the redistribution of this coolant by secondary flows left large endwall areas uncooled. This paper describes the attempt to improve upon this datum cooling configuration by redistributing the available coolant to provide a better coolant coverage on the endwall surface, whilst keeping the associated aerodynamic losses small. The design of the new, improved cooling configuration was based on the understanding of endwall film-cooling described by Friedrichs et al. (1996, 1997). Computational fluid dynamics were used to predict the basic flow and pressure field without coolant ejection. Using this as a basis, the above described understanding was used to place cooling holes so that they would provide the necessary cooling coverage at minimal aerodynamic penalty. The simple analytical modelling developed in Friedrichs et al. (1997) was then used to check that the coolant consumption and the increase in aerodynamic loss lay within the limits of the design goal. The improved cooling configuration was tested experimentally in a large scale, low speed linear cascade. An analysis of the results shows that the redesign of the cooling configuration has been successful in achieving an improved coolant coverage with lower aerodynamic losses, whilst using the same amount of coolant as in the datum cooling configuration. The improved cooling configuration has reconfirmed conclusions from Friedrichs et al. (1996, 1997); firstly, coolant ejection downstream of the three-dimensional separation lines on the endwall does not change the secondary flow structures; secondly, placement of holes in regions of high static pressure helps reduce the aerodynamic penalties of platform coolant ejection; finally, taking account of secondary flow can improve the design of endwall film-cooling configurations.

scholarly journals Secondary Flow Control in Low Aspect Ratio Vanes Using Splitters

2016 ◽  
Author(s):  
Christopher Clark ◽  
Graham Pullan ◽  
Eric Curtis ◽  
Frederic Goenaga
Keyword(s):  
Kinetic Energy ◽  
Aspect Ratio ◽  
Secondary Flow ◽  
Current Practice ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Secondary Flows ◽  
Optimization Approach ◽  
Flow Strength ◽  
Low Aspect Ratio

Low aspect ratio vanes, often the result of overall engine architecture constraints, create strong secondary flows and high endwall loss. In this paper, a splitter concept is demonstrated that reduces secondary flow strength and improves stage performance. An analytic conceptual study, corroborated by inviscid computations, shows that the total secondary kinetic energy of the secondary flow vortices is reduced when the number of passages is increased and, for a given number of vanes, when the inlet endwall boundary layer is evenly distributed between the passages. Viscous computations show that, for this to be achieved in a splitter configuration, the pressure-side leg of the low aspect ratio vane horseshoe vortex, must enter the adjacent passage (and not “jump” in front of the splitter leading edge). For a target turbine application, four vane designs were produced using a multi-objective optimization approach. These designs represent: current practice for a low aspect ratio vane; a design exempt from thickness constraints; and two designs incorporating splitter vanes. Each geometry is tested experimentally, as a sector, within a low-speed turbine stage. The vane designs with splitters geometries were found to reduce the measured secondary kinetic energy, by up to 85%, to a value similar to the design exempt from thickness constraints. The resulting flowfield was also more uniform in both the circumferential and radial directions. One splitter design was selected for a full annulus test where a mixed-out loss reduction, compared to the current practice design, of 15.3% was measured and the stage efficiency increased by 0.88%.

The Mechanics of the Secondary Flows of Viscoelastic Fluids in Non-Circular Straight Tubes and the Mean Transversal Field in Pulsating Flows

2000 ◽  
Author(s):  
Dennis A. Siginer ◽  
Mario F. Letelier
Keyword(s):  
Secondary Flow ◽  
Cross Sections ◽  
Viscoelastic Fluids ◽  
Secondary Flows ◽  
Novel Approach ◽  
Transversal Field ◽  
Time Domains ◽  
Viscoelastic Liquids ◽  
First Time ◽  
Secondary Flow Field

Abstract A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is summarized. The transversal field arises at the second order of the perturbation of the nonlinear constitutive structure, and is driven by first order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

Second Vane Total Pressure Loss Due to Endwall Iceform Contouring

2008 ◽  
Author(s):  
Ronald S. LaFleur
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Pressure Loss ◽  
Total Pressure ◽  
Aerodynamic Drag ◽  
Pressure Coefficient ◽  
Secondary Flows ◽  
Total Pressure Loss ◽  
Surface Shape ◽  
Exit Plane

The iceformation design method generates an endwall contour, altering the secondary flows that produce elevated endwall heat transfer load and total pressure losses. Iceformation is an analog to regions of metal melting where a hot fluid alters the isothermal surface shape of a part as it is maintained by a cooling fluid. The passage flow, heat transfer and geometry evolve together under the constraints of flow and thermal boundary conditions. The iceformation concept is not media dependent and can be used in analogous flows and materials to evolve novel boundary shapes. In the past, this method has been shown to reduce aerodynamic drag and total pressure loss in flows such as diffusers and cylinder/endwall junctures. A prior paper [1] showed that the Reynolds number matched iceform geometry had a 24% lower average endwall heat transfer than the rotationally symmetric endwall geometry of the Energy Efficiency Engine (E3). Comparisons were made between three endwall geometries: the ‘iceform’, the ‘E3’ and the ‘flat’ as a limiting case of the endwall design space. This paper adds to the iceformation design record by reporting the endwall aerodynamic performances. Second vane exit flow velocities and pressures were measured using an automated 2-D traverse of a 1.2 mm diameter five-hole probe. Exit plane maps for the three endwall geometries are presented showing the details of the total pressure coefficient contours and the velocity vectors. The formation of secondary flow vortices is shown in the exit plane and this results in an impact on exit plane total pressure loss distribution, off-design over- and under-turning of the exit flow. The exit plane contours are integrated to form overall measures of the total pressure loss. Relative to the E3 endwall, the iceform endwall has a slightly higher total pressure loss attributed to higher dissipation of the secondary flow within the passage. The iceform endwall has a closer-to-design exit flow pattern than the E3 endwall.

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