Cross-stream Plane Research Articles

Investigation of Discrete-Hole Film Cooling Parameters Using Curved-Plate Models

Computations have been conducted on curved, three-dimensional discrete-hole film cooling geometries that included the mainflow, injection hole, and supply plenum regions. Both convex and concave film cooling geometries were studied. The effects of several film cooling parameters have been investigated, including the effects of blowing ratio, injection angle, hole length, hole spacing, and hole staggering. The blowing ratio was varied from 0.5 to 1.5, the injection angle from 35 to 65 deg, the hole length from 1.75D to 6.0D, and the hole spacing from 2D to 3D. The staggered-hole arrangement considered included two rows. The computations were performed by solving the fully elliptic, three-dimensional Navier–Stokes equations over a body-fitted grid. Turbulence closure was achieved using a modified k–ε model in which algebraic relations were used for the turbulent viscosity and the turbulent Prandtl number. The results presented and discussed include plots of adiabatic effectiveness as well as plots of velocity contours and velocity vectors in cross-stream planes. The present study reveals that the blowing ratio, hole spacing, and hole staggering are among the most significant film cooling parameters. Furthermore: (1) The optimum blowing ratios for curved surfaces are higher than those for flat surfaces, (2) a reduction of hole spacing from 3D to 2D resulted in a very significant increase in adiabatic effectiveness, especially on the concave surface, (3) the increase in cooling effectiveness with decreasing hole spacing was found to be due to not only the increased coolant mass per unit area, but also the smaller jet penetration and the weaker counterrotating vortices, (4) for all practical purposes, the hole length was found to be a much less significant film cooling parameter.

Analysis of flow in the spiral casing using a streamline upwind Petrov Galerkin method

Numerical simulation of complex three-dimensional flow through the spiral casing has been accomplished using a finite element method. An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime. For spatial discretization, a streamline upwind Petrov Galerkin technique has been used. The velocity field and the pressure distribution inside the spiral casing corroborate the results available in literature. The flow structure reveals the fact that very strong secondary flow is evolved on the cross-stream planes. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of flow in the spiral casing using a streamline upwind Petrov Galerkin method

Numerical simulation of complex three-dimensional flow through the spiral casing has been accomplished using a finite element method. An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime. For spatial discretization, a streamline upwind Petrov Galerkin technique has been used. The velocity field and the pressure distribution inside the spiral casing corroborate the results available in literature. The flow structure reveals the fact that very strong secondary flow is evolved on the cross-stream planes. Copyright © 1999 John Wiley & Sons, Ltd.

On reduction of turbulent wall friction through spanwise wall oscillations

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier–Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations.

Turbulent Air Flow Measurement with the Aid of Three-Dimensional Particle Tracking Velocimetry in a Curved Square Duct.

A three-dimensional particle tracking velocimeter (3-D PTV) was successfully applied to turbulent air flow measurement in a strongly curved U-bend of square cross-section. He-filled bubbles, of which specific density was very close to that of air were employed as a flow tracer. Distributions of the mean velocities and Reynolds stresses were obtained at 90°downstream of the inlet to the curved section. The secondary flow as strong as 20% of the bulk mean velocity is observed in the cross-stream plane ; it results in a marked trough in the streamwise velocity at a distance of about 0.3 times the channel height from the inner wall. The present experimental result is mostly in good agreement with the LDV data of Chang et al. (1983). Moreover, turbulent statistics including all Reynolds stress components are obtained. The production mechanism of turbulent kinetic energy as well as the distributions of invariants for stress anisotropy tensor are discussed in detail.

Three-dimensional analysis of flow in the spiral casing of a reaction turbine using a differently weighted Petrov Galerkin method

A weighted residual based finite element method has been used to predict the flow structure and the head loss in the spiral casing of a reaction turbine. An explicit Eulerian velocity correction scheme has been employed to solve the complete Reynolds-averaged Navier-Stokes equations. A Differently Weighted Petrov Galerkin (DWPG) method has been used for spatial discretization. The simulation has been performed for high Reynolds numbers. The head loss in the spiral casing has been calculated for Re = 5 × 10 5 and Re = 10 6. The velocity field and the pressure distribution inside the spiral casing corroborate the trends available in literature. The velocity field reveals the existence of a free-vortex character of the global flow field. A strong secondary flow is evolved on the cross-stream plane due to the centrifugal forces which act at right angles to the main flow.

Numerical analysis of the flow and heat transfer characteristics for forced convection-radiation in entrance region of an internally finned tubes

The flow and heat transfer characteristics of combined forced convection and radiation in the entrance region of internally finned tubes are investigated numerically in this paper. The uniform flow is considered for an inlet flow condition. A three dimensional parabolic problem is solved by a marching-type procedure envolving a series of two dimensional elliptic problems in the cross-stream plane. The SIMPLER-algorithm and Raithby's pressure-velocity coupling method are employed to analyze the flow and heat transfer characteristics. For the calculation of radiative heat transfer, the P1-approximation and the weighted sum of gray gases method (WSGGM) are used. The effects of fin height, number of fins, optical thickness, reference temperature, and Planck number on the flow and heat transfer characteristics are examined. It was found that the effect of fin-height on the heat transfer characteristic is more dominant than that of number of fins. The present results show that the optimal non-dimensional fin height and number of fins are 0.4 and 16, respectively.

Flow Past Large Obstructions Between Corotating Disks in Fixed Cylindrical Enclosures

Numerical calculations have been performed for isothermal, laminar, three-dimensional flow past one or two fixed obstructions radially aligned and symmetrically located between a pair of disks corotating in a fixed cylindrical enclosure. The single-obstruction cases respectively model the influence on the flow of (a) a magnetic head arm support and (b) an air lock. The dual-obstruction cases model the simultaneous presence of these two objects. The air lock produces an interdisk cross-stream plane blockage of 62 percent while the two head arm supports produce blockages of 31 percent and 62 percent, respectively. For the cases with the air lock and arm support simultaneously present, the circumferential angle between them is fixed to 40 or 80 deg. Velocity, pressure, shear stress and the disk torque coefficient are predicted mostly for a Reynolds number (Re=ΩR22/v) corresponding to 10,000, approximately, where R2, Ω, and v are the disk radius, the disk angular velocity in rad/s, and the kinematic viscosity of air at 300 K, respectively. The calculations show that a large blockage significantly alters the interdisk flow characteristics by markedly raising the pressure ahead of an obstruction and accelerating the flow through the empty space around it. This induces a detached region of reversed flow ahead of the obstruction, quite distinct from that in its wake. The disk surface pressure distributions point to a potential source of dynamical instability in rotating disk flows with obstructions. By redefining the torque coefficient and Reynolds number to account for dual blockage effects the relationship between these two quantities generally follows the theoretical expression of Humphrey et al. (1992). It is shown that the bulk of the drag on an obstruction is form drag as opposed to friction drag.

Developing combined convection of non-Newtonian fluids in an eccentric annulus

Laminar combined convection of non-Newtonian fluids in vertical eccentric annuli, in which the inner and outer walls are held at different constant temperatures is considered and a new economical method of solution for the three-dimensional flow in the annulus is developed. Assuming that the ratio of the radial to the vertical scale, e, is small, as occurs frequently in many industrial applications, then the governing equations can be simplified by expanding all the variables in terms of e. This simplification gives rise to the presence of a dominant cross-stream plane in which all the physical quantities change more rapidly than in the vertical direction. The solution trechnique consists of marching in the vertical streamwise direction using a finite-difference scheme and solving the resulting equations at each streamwise step by a novel technique incorporating the Finite Element Method. The process is continued until the velocity, pressure and temperature fields are fully developed, and results are presented for a range of the governing non-dimensional parameters, namely the Grashof, Prandtl, Reynolds and Bingham numbers.

Trailing Vortex Wake Growth Characteristics of a High Aspect Ratio Rectangular Airfoil

The growth characteristics of trailing vortex wakes are investigated in a towing tank. The wakes from a lifting rectangular NACA 0012 airfoil with an aspect ratio of 8 are studied up to 1400 chords downstream. The circulation Reynolds number ranged from 4 x 10 3 to 4 x 10 4 . Digital particle image velocimetry is used to measure the velocity field in the cross-stream plane from which vorticity is calculated. The vortex pair is observed to be very stable and long-lived, showing little decay in the circulation of the individual vortices. The vorticity, however, diffuses over time within the cores of the vortices.

Trailing vortex wake growth characteristics of a high aspect ratio rectangular airfoil

The growth characteristics of trailing vortex wakes are investigated in a towing tank. The wakes from a lifting rectangular NACA 0012 airfoil with an aspect ratio of 8 are studied up to 1400 chords downstream. The circulation Reynolds number ranged from 4 x 10 3 to 4 x 10 4 . Digital particle image velocimetry is used to measure the velocity field in the cross-stream plane from which vorticity is calculated. The vortex pair is observed to be very stable and long-lived, showing little decay in the circulation of the individual vortices. The vorticity, however, diffuses over time within the cores of the vortices.

Experimental study of heat and momentum transfer in rotating channel flow

The enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolis instability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non-linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non-linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation.

Unsteady laminar flow between a pair of disks corotating in a fixed cylindrical enclosure

The unsteady streamlined motion of a constant property fluid in the unobstructed space between a pair of disks corotating at angular velocity Ω in a fixed cylindrical enclosure is investigated numerically. Two-dimensional (axisymmetric) and three-dimensional calculations are performed using a second-order accurate time-explicit algorithm. The flow configuration corresponds to that investigated experimentally by Schuler et al. [Phys. Fluids A 2, 1760 (1990)]. The steady flow solutions are characterized by a symmetrical pair of counter-rotating toroidal vortices in the cross-stream (r-z) plane. This secondary motion is driven by the radial imbalance between the outward-directed centrifugal force and the inward-directed pressure gradient force. Axisymmetric calculations predict a flow that is steady for Re<22 200, where Re is the Reynolds number based on the disk radius, the tip speed of the disks, and the kinematic viscosity of the fluid. Above this value the motion is unsteady periodic and, while the features of the cross-stream flow pattern are broadly preserved, the symmetry of the motion about the midplane is broken by alternating periodic crossings of the toroidal vortices. This instability is maintained through an interaction that arises between outward-directed fluid in the disk Ekman layers and inward-directed fluid in the return core flow. Three-dimensional calculations at Re=22 200 and 44 400 show that the toroidal vortices acquire a time-varying sinuous shape in the circumferential direction. These calculations reveal circumferentially periodic reversals of the axial velocity component in the cross-stream plane, including the detached shear layer separating the region of motion in solid-body rotation near the hub from the potential core, in agreement with the flow visualization observations of Humphrey and Gor [Phys. Fluids A 5, 2438 (1993)]. The wavelength of this oscillation is shown to be twice that of the circumferential velocity component which is responsible for the nodal distribution of axial vorticity. When plotted on the interdisk midplane, the axial component of vorticity manifests itself as an even integer number, 2n (n=1,2,...), of circumferentially periodic foci. Experiments show that the number of foci decreases in a stepwise manner with increasing Reynolds number. For the conditions of this study, the calculated dimensionless angular velocity of the foci, ΩF/Ω, ranges from 0.55 at Re=22 200 to 0.44 at Re=44 400. These values are close to the present experimental estimate ΩF/Ω=0.5.

Second-Order Closure Study of Open-Channel Flows

A complete second-order closure model of turbulence is used to predict the behavior of fully developed turbulent flows in open channels of both simple and compound cross sections. This level of closure entails the solution of seven differential transport equations for turbulence quantities and is found to reproduce fairly accurately the details of the turbulence-driven secondary motions that occur in the cross-stream planes. In particular, the number, location, and strength of the secondary-flow cells are well predicted, as is their effect on the bulk properties of the mean flow. Data from simple rectangular channels are used to check the model's sensitivity to the effects of a free surface, and data from compound channels, both symmetric and asymmetric, serve to validate the model for a range of parameters typical of those encountered in practice.

Flow structure in the wake of a wishbone vortex generator

The results of an experimental examination of the vortex structures shed from a low-profile «wishbone» generator are presented. The vortex generator height relative to the turbulent boundary layer was varied by testing two differently sized models. Measurements of the mean three-dimensional velocity held were conducted in cross-stream planes downstream of the vortex generators. In all cases a counter-rotating vortex pair was observed. Individual vortices were characterized by three descriptors derived from the velocity data: circulation, peak vorticity, and cross-stream location of peak vorticity. Measurements in the cross plane at two axial locations behind the smaller wishbone characterize the downstream development of the vortex pairs

Circular-to-rectangular transition duct flow without and with inlet swirl

Circular-to-rectangular transition ducts are used as exhaust system components of aircraft with rectangular exhaust nozzles. Often, the flow into these ducts includes a swirling velocity component remaining from the gas turbine engine. Previous transition duct studies involving detailed experimental measurements have not compared the flowfield without and with inlet swirl. The study reported in this article explored circular-to-rectangular transition duct flows without and with inlet swirl in order to document the effect of inlet swirl on the transition duct flowfield and to provide detailed duct flow data for comparison with numerical code predictions. A method was devised to develop a swirling, solid-body rotational flow with minimal associated disturbances. Coefficients based on velocities and total and static pressures measured in cross-stream planes at four axial locations within the transition duct, along with surface static pressure measurements and surface oil-film visualization, are presented and discussed for both nonswirling and swirling incoming flows. In both cases the inlet centerline Mach number was 0.35. The differences between flowfields for the two cases were striking. Two pairs of counterrotating side-wall vortices appeared in the duct flow without inlet swirl. These vortices were absent in the swirling incoming flow case.

Effect of bluff body wakes on skin friction and surface heat transfer in a turbulent boundary layer

Experiments were conducted in a turbulent boundary layer which interacts with the wake of a bluff body mounted upstream with its axis spanwise. Measurements reported here include surface shear stress and heat transfer rate. Wakes from both stationary and vertically-oscillating cylinders, with circular and square cross-sections and of different sizes, were considered. Measurements were also made with a 16 mm circular cylinder translated to different locations from the plane of the flat plate, and with a cylinder rotated (‘rolled‘) about the centerline of the plate to different angles in the cross-stream plane. The results show that the skin friction in the turbulent boundary layer decreases significantly in the presence of the wake from the stationary cylinder. The effect of the wake from an oscillating cylinder appears to be closely the same as deduced from a set of measurements with a cylinder fixed at different vertical positions. The streamwise distribution of skin friction shows the expected trend for the case of the translated cylinder in that the surface shear stress changes only when the cylinder is above the plane of the plate. The spanwise distribution of skin friction in the case of the rolled cylinder shows similarly significant changes on one side of the centre line as expected. The net effect of the wake on the Stanton number, on or off the axis of the plate, is always small: reduction due to decrease in mean velocity in the wake roughly balances the increase due to the wake turbulence.

Experimental observations of an unsteady detached shear layer in enclosed corotating disk flow

The flow in the unobstructed space between a pair of disks corotating at high speed in a fixed cylindrical enclosure can be divided into five regions amenable to theoretical analysis [C. A. Schuler, Ph.D. Thesis, University of California at Berkeley (1990); C. A. Schuler et al., Phys. Fluids A 2, 1760 (1990)]. One of these, region III in Fig. 2, is an axially-aligned detached shear layer predicted by the analysis to be located at rIII/R2≊Γ1/2 and of thickness δIII/R2≊(2 Re)−1/4, where R2 is the radius of the disks, Re is the Reynolds number based on R2 and the tip speed of rotation of the disks (ωR2), and Γ is an experimentally determined constant. Through viscous diffusion, the detached shear layer allows the transition that must take place between the bulk of the three-dimensional flow in the interdisk space (region II) and the two-dimensional flow in solid body rotation surrounding the hub that spins the disks (region IV). Present findings, based on flow visualization, confirm these hitherto untested theoretical expressions and reveal that beyond a critical value of the Reynolds number the detached shear layer oscillates in the cross-stream (r-z) plane of the flow. The unsteadiness appears to originate at the enclosure side wall where the disk Ekman layers collide as a result of being redirected from the radial into the axial direction. These observations agree with the direct numerical simulations of Schuler [Ph.D. Thesis, University of California at Berkeley (1990)] which also show that the onset of flow unsteadiness in the cross-stream plane coincides with the appearance of an integer number of circumferentially-periodic large-scale flow structures with large component of axial vorticity, of the type found by Hide and Titman [J. Fluid Mech. 29, 39 (1967)] in a similar flow configuration as of a critical value of the Reynolds number.

Effects of Adjacent Wall on Turbulent Jets 3rd Report, Three-Dimensional Wall Jet.

A three-dimensional turbulent jet discharging from a round nozzle along a flat plate has been studied experimentally. Measurements of the three components of mean and fluctuating velocities and the wall shear stress were obtained with a hot wire in various cross-stream planes. The estimation of the Reynolds stress balance was made with the help of the experimental results, and the role of the Reynolds stress to the jet diffusion was discussed. These results suggest that the jet behavior is explained well with the Reynolds stress distribution and that the pressure-strain correlation in the Reynolds stress balance is fairly approximated by the LRR's turbulence model.

Streamwise computation of three-dimensional incompressible potential flows

A new method for the computation of three-dimensional incompressible potential flows is presented. The dependent variables of this method are the Streamwise velocity along a set of chosen streamlines, and the coordinates of the chosen streamlines in the cross-stream plane. Since the method computes streamline coordinates directly, it can be easily used to generate boundary fitted grids for the computation of three-dimensional viscous flows. Sample computations are presented for (i) flow through a rectangular diffuser with an offset and with a change in the aspect ratio, and (ii) flow through a duct whose cross section changes from a square to a rhombus.