Large Separation Region Research Articles

Laser Velocimeter Measurements in the Pump of an Automotive Torque Converter: Part I—Average Measurements

A torque converter was tested for two turbine/pump rotational speed ratios, 0.065 and 0.800, and a laser velocimeter was used to measure three components of velocity within the pump. Shaft encoders were used to record the instantaneous pump angular position, which was correlated with the velocities. Average flow velocity profiles were obtained for the pump inlet, mid-, and exit planes. Large separation regions were seen in the mid- and exit planes of the pump for a speed ratio of 0.800. Strong counterclockwise secondary flows were observed in the midplane and strong clockwise secondary flows were seen in the exit plane of the pump for all conditions; vorticities were evaluated and are reported. Velocity data were also used to find the torque distribution. For both speed ratios the torque was approximately evenly distributed between the inlet and exit. Finally, slip factors were evaluated at the mid-and exit planes. At the midplane they were approximately the same as for conventional centrifugal pumps; however, at the exit plane the slip factors are larger than for centrifugal pumps.

Measurement of Hydrodynamic Sway Force Acting on Two-Dimensional Models of Small Ship

In the previous papers authors studied capsizing phenomena of a small pleasure boat in beam seas. Small ships, which usually have large breadth/draft ratio, are apt to sway with a large amplitude in waves and to drift at a high velocity in wind. It was clarified that the large lateral motion can lead to a large drag force and moment because their complicated under-water hull forms can easily make flow separation. In a heeled condition the rolling moment by the separated flow works asymmetrically to the direction of sway motion, being larger when the ship moves to the direction of heeling than to the other direction. This asymmetries helps to enlarge the heeling angle and finally to capsize.In this paper a large amplitude forced sway motion test was conducted to investigate the effect of hull forms to the non-linear sway force and moment. Three two-dimensional round-chine models with dead-rise angle of 10, 20, 30 degrees were used. Totally the test was carried out on nine hull forms, using the three round-chine models with/without hard-chine pieces and skegs. It is clarified that a conventional linear integral equation method can almost evaluate the acceleration component of sway force and moment, but cannot evaluate the damping component, because drag component occupies the main or non-negligible part of sway damping. It is also clarified that the rolling moment by the sway motion gets very asymmetric when flow separation occurs locally at the vicinity of the bottom center or of the chine. The asymmetry becomes small when the separated flow covers the whole bottom, which happens on the models with skeg or with large dead-rise angle.This paper also deals with the force and moment of drift motion at a constant speed. The characteristics of the heeling moment is similar to that of sway motion. The moment works to increase the heel angle when the ships moves to the direction of heeling. But, it becomes small if the model makes a large separation region.

Numerical prediction of transonic viscous separated flow past an airfoil

A method for the numerical treatment of transonic viscous flows past an airfoil has been developed allowing for calculation of both attached flows and flows with large separation regions including shock-induced separation. The method accounts for the entropy correction and the presence of vorticity behind the shock. The method is based on a zonal approach. The computation of the separated-flow regimes is provided by a quasi-simultaneous method of viscous—inviscid interaction. A computer code, called “VISTRAN,” is developed on the basis of this method and extensive comparisons of computed results with experimental data are made.

Viscous flow calculations in turbomachinery channels

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations in the presence of large separated regions. Turbulence effects are accounted for by the Chien low Reynolds number form of the K - e turbulence model and the Baldwin-Lomax algebraic expression for turbulent viscosity. The governing equations are written in conservative form and irnplicitly solved in fully coupled form using the approximate factorization technique. Preliminary tests were carried out in a laminar flow regime to check the accuracy and stability of the method in two-dimensional and cylindrical axisymmetric flow configurations. After testing in laminar and turbulent flow regimes and comparing the two turbulence models, the code was successfully applied to an actual gas turbine diffuser at low Mach numbers.

Temperature dependent phase separation in the Emery model

We report on calculations for the Emery model of the carriers in the copper oxygen planes of HTSC materials using the variational principle of Bogoljubov. A strong coupling ansatz optimized for small values of the ratio hopping constant to Coulomb correlation gives the lowest free energy in the neutral case and in the case of moderate doping. From the curves chemical potential vs. doping concentration large regions of thermodynamic instability and phase separation respectively are determined using a Maxwell construction. The temperature and parameter dependence of these coexistence regions with respect to para-, ferro- and antiferromagnetic order is given.

Numerical prediction of subsonic turbulent flows over slender bodiesat high incidence

The physical aspects governing accurate numerical simulation of turbulent flows having large regions of crossflow separation are re-examined. Time-accurate, three-dimensional fine-grid Navier-Stokes solutions were obtained for turbulent subsonic flows over a slender ogive-cylinder body of revolution at large angles of attack. These flowfields are complex and contain regions of crossflow separation and an organized leeward-side vortex structure. An algebraic eddy-viscosity turbulence model has been modified to correctly account for the effects of the vortices on the underlying viscous layers

Turbulence in a separated boundary layer

This paper presents and discusses the results of an extensive experimental investigation of a flat-plate turbulent boundary subjected to an adverse pressure gradient sufficiently strong to lead to the formation of a large separated region. The pressure gradient was produced by applying strong suction through a porous cylinder fitted with a rear flap and mounted above the boundary layer and with its axis in the spanwise direction. Attention is concentrated on the structure of the turbulent flow within the separated region and it is shown that many features are similar to those that occur in separated regions produced in a very dissimilar manner. These include the fact that structure parameters, like Reynolds stress ratios, respond markedly to the re-entrainment of turbulent fluid transported upstream from the reattachment region, the absence of any logarithmic region in the thin wall boundary layer beneath the recirculation zone and the lack of any effective viscous scaling in this wall region, and the presence of a significant low-frequency motion having timescales much longer than those of the large-eddy structures around reattachment.Similarities with boundary layers separating under the action of much weaker pressure gradients are also found, despite the fact that the nature of the flow around separation is quite different. These similarities and also some noticeable differences are discussed in the paper, which concludes with some inferences concerning the application of turbulence models to separated flows.

Acceleration of iterative algorithms for Euler equations of gasdynamics

of the grid size). The solution is considered converged when the maximum absolute residual is one order of magnitude smaller than the truncation error. The convergence history for the stream-function vorticity formulation is similar. The residual of the linear Poisson equation for the stream function is always of machine accuracy and the residual of the vorticity transport equation reduces quadratically; convergence is obtained after six iterations. For the biharmonic equation, convergence takes six iterations and is also quadratic. The solutions in terms of the wall skin-friction distribution are presented in Fig. 2. The results for the three formulations are in excellent agreement and correlate well with the skin-friction distribution presented by Briley. 8 Next, the model problem of a separated flow in a symmetrical diffuser, introduced by Inoue, 9 is examined. The diffuser problem is solved using the stream-function vorticity and the biharmonic formulation. The inlet and outlet boundary of the diffuser are at x = - 1.0 and x = 3.0, respectively. The shape factor of the diffuser wall A = -0.089. The centerline is located at.y = 1.0 and the Reynolds number based on this reference length and the free-stream velocity is R = 6250. The inflow conditions provide the initial conditions for the entire flowfield. Convergence is quadratic and machine zero is reached in 6-7 iterations. The solutions in terms of the wall skin-friction distribution are shown in Fig. 3. The results for the two formulations are in excellent agreement and correlate well with Inoue's results, except for the outflow conditions. In Fig. 3 the solution for the higher Reynolds number, R - 12500, with a larger separation region is also presented. The biharmonic equation is the most efficient of the three formulations in terms of CPU time and storage requirements. The biharmonic program is more than two-times faster and requires more than a factor two less memory than the streamfunction vorticity program. The primitive variable method is the slowest among the three formulations and it puts severe demands on the computer storage requirements. In this case the bandwidth is 0(67V) and this coupled with the increase in the number of variables results in more than a four-fold increase in storage and CPU time as compared to the biharmonic program. Conclusions Three formulations of the two-dimensional Navier-Stokes equations are solved numerically using Newton's method and a direct solution routine for banded matrices. The fully implicit solution techniques use second-order central differencing for all the terms and are shown to be reliable and to provide quadratic convergence. The biharmonic formulation is most efficient in terms of CPU time and memory without loss of accuracy. Finally, while it is well known that iterative methods (line overrelaxation or ADI) for biharmonic equations have very slow rates of convergence, the present study, using direct solvers, indicates that the biharmonic formulation is the most recommended.

Computing of separated flow using the space-marching conservative supra-characteristics method

Steady, hypersonic viscous flows over compression corners with streamwise separation have been computed using the space marching Conservative Supra-Characteristics Method (CSCM-S) of Lombard. The CSCM-S method permits stable space marching of the parabolized Navier-Stokes (PNS) equations through large separated flow regions. The present method has been used to compute surface pressure, heat transfer, and skin friction coefficients for two compression corner cases studied experimentally by Holden and Moselle. The computed results compare favorably with previous Navier-Stokes results and the experimental data. The present method has also been compared with the conventional Beam-Warming scheme for solving the PNS equations. Comparison are made for accuracy, computer time, and computer storage.

Computation of internal turbulent flow with a large separated flow region

AbstractAn implicit two‐equation turbulence solver, KEM. in generalized co‐ordinates, is used in conjunction with the three‐dimensional incompressible Navier–Stokes solver, INS3D, to calculate the internal flow in a channel and a channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the κ‐ε turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations is integrated using wall functions. The latter approach yields a faster convergence to the steady‐state solution than the former. For the case of channel flow, both the wall‐function and wall‐boundary‐condition approaches yield results in good agreement with the experimental data. The back‐step (sudden expansion) flow is calculated using the wall‐function approach. The predictions are in reasonable agreement with the experimental data.

Computation of turbulent supersonic flows around pointed bodies having crossflow separation

The numerical method developed by Schiff and Sturek (1980) on the basis of the thin-layer parabolized Navier-Stokes equations of Schiff and Steger (1980) is extended to the case of turbulent supersonic flows on pointed bodies at high angles of attack. The governing equations, the numerical scheme, and modifications to the algebraic eddy-viscosity turbulence model are described; and results for three cones and one ogive-cylinder body (obtained using grids of 50 nonuniformly spaced points in the radial direction between the body and the outer boundary) are presented graphically and compared with published experimental data. The grids employed are found to provide sufficient spatial resolution of the leeward-side vortices; when combined with the modified turbulence model, they are shown to permit accurate treatment of flows with large regions of crossflow separation.

Comparison of inviscid and viscous computations with an interferometrically measured transonic flow

In order to provide an experimental test case for use with the computer simulation of transonic flowfields, the transonic flow around a wedge profile in a wind tunnel has been measured using holographic interferometry. The quantitative detail provided by the interferogram is compared with the numerical predictions of a two dimensional inviscid time-marching method and a two dimensional Navier-Stokes solver. The a priori NavierStokes solution is in agreement with the experimental data. The predictions of the inviscid method can be made to agree with the measurements if the geometrical data used for the computations are modified to represent the presence of the large separated region observed experimentally.

Analysis of aerothermal loads on spherical dome protuberances

Hypersonic flow over spherical dome protuberances was investigated to determine increased pressure and heating loads to the surface. The configuration was mathematically modeled in a time-dependent three-dimensional analysis of the conservation of mass, momentum (Navier-Stokes), and energy equations. A boundary mapping technique was used to obtain a rectangular parallelepiped computational domain, a MacCormack explicit time-split predictor-corrector finite difference algorithm was used to obtain solutions. Results show local pressures and heating rates for domes one-half, one, and two boundary layer thicknesses high were increased by factors on the order of 1.4, 2, and 6, respectively. Flow over the lower dome was everywhere attached while flow over the intermediate dome had small windward and leeside separations. The higher dome had an unsteady windward separation region and a large leeside separation region. Trailing vortices form on all domes with intensity increasing with dome height. Discussion of applying the results to a thermally bowed thermal protection system are presented.

A time-dependent vortex-shedding model

A time-dependent vortex-shedding model has been developed. The application of the model to problems involving the reduction of large separated wake regions by introduction of vortices is straightforward. The model demonstrates the increase in the azimuthal velocity as a function of spatial and temporal location. For a given flow, this perturbation would be superimposed on the other velocity components.

Cavitation phenomena within regions of flow separation

The phenomenon of cavitation inception was studied on four axisymmetric bodies whose boundary layers underwent a laminar separation and subsequent turbulent reattachment. The non-cavitating flow was studied by holographic and schlieren flow-visualization techniques. Surface distributions on the mean and the fluctuating pressures were also measured. The conditions for cavitation inception and desinence were determined and holograms were recorded just prior to and at the onset of cavitation. The population of microbubbles and the subsequent development of visible cavitation was determined from the reconstructed image. In every case the appearance of visible cavitation was preceded by a cluster of microscopic bubbles in a small portion of the flow field providing clear evidence that cavitation is initiated from small nuclei. The inception zone was located within the turbulent shear layer downstream of transition and upstream of the reattachment region of the bodies with large separation regions. The location and the shape of this cavitation suggested a relation to the mixing-layer eddy structure. The inception region on the body with the smallest separation zone, a hemisphere-cylinder body, was located in the reattachment region, but the cavities were still detached from the surface. Instantaneous minimum-surface-pressure measurements do not account for observed cavitation-inception indices except for the hemisphere body, where the correlation is satisfactory. The rate of cavitation events was estimated from measurements of nuclei population, and fluctuating-pressure statistics in the portion of the flow susceptable to cavitation. It was demonstrated for the hemisphere body that at least one such cavitation event could occur every second. These findings are consistent with what is observed visually at the onset of cavitation and support the location of inception determined holographically.

Turbulent flow over large-amplitude wavy surfaces

The laser-Doppler velocimeter is used to measure the mean and the fluctuating velocity for turbulent flow over a solid sinusoidal wave surface having a wavelength λ of 50.8 mm and a wave amplitude of 5.08 mm. For this flow, a large separated region exists, extending from x/λ = 0.14 to 0.69. From the mean velocity measurements, the time-averaged streamlines and therefore the extent of the separated region are calculated. Three flow elements are identified: the separated region, an attached boundary layer, and a free shear layer formed by the detachment of the boundary layer from the wave surface. The characteristics of these flow elements are discussed in terms of the properties of the mean and fluctuating velocity fields.

Dynamic stability boundaries for a sinusoidal shallow arch under pulse loads

the position of shock Xs0 at zero turbulence level. The boundary-layer momentum thickness Reynolds number Re and boundary-layer displacement thickness <5* measured just before the shock are also shown in the figure. It is observed that an increase in Tu from 0.3 to 6% produces a shift in the shock position of 20%. Such a large change in the shock position cannot be explained solely in terms of the thickening of the boundary layer associated with the increase in freestream turbulence. First, the initial increase in d* followed by a decrease is not likely to produce such a large shift in the shock position in one direction. This is shown by the experiments performed by Delery3 on a similar model and at a constant freestream turbulence level. Second, Re does not increase continuously with the increase in Tu^, whereas the shock position shifts in only one direction with the increase in Tu^. Typically, Tu^ levels of 2.5 and 5.1% produce the same value of Re, whereas the shock positions for these two values of Re are not the same. It appears that the freestream turbulence has a direct effect on the shock interactions and, therefore, the shock position. Figure 3 shows the influence of Tu on the peak Mach number on the model Mpk. The influence of Tux on Mpk is larger at M pk ^1.3, a condition corresponding to significant shock-induced separation. This suggests that the freestream turbulence plays an important part in strong adverse pressure gradients where large regions of separation are present. The pressure distributions in the region of shock-induced separation for a constant value of Mpk = 1,44 and for various freestream turbulence levels Tu are shown in Fig. 4. The differences in Cp levels at the shock position are due to the differences in the freestream Mach numbers needed to achieve a constant value of Mpk. The shock position at this value of Mpk is typically 80% chord. Increase in Tux is shown to produce an increase in pressure recovery at the trailing edge of the motfel. Similar trends in Cp have been observed with the

Numerical solutions for high Reynolds number separated flow past a semi-infinite compression corner

The present paper addresses the high Reynolds number, two-dimensional, steady laminar flow separation phenomenon near an interior (concave) corner. A very fast Alternating Direction Implicit finite difference approach is used to solve the Interacting Boundary Layer approximation to the Navier Stokes equations in a conformal plane. Solutions are presented for corner angles up to 18° for Reynolds numbers (based on forebody length) up to 10 8. Convergence properties and accuracy levels are identified in order to provide reliability estimates of the results. Limitations to the numerical algorithm for large separation regions at high Reynolds numbers are identified.

Prediction of Hypersonic Laminar Boundary-Layer/Shock-Wave Interactions

UMERICAL solution of the compressible timedependent Navier-Stokes equations is one method of obtaining the theoretical solution of the interaction of an oblique shock wave and a laminar boundary layer. MacCormack1 and MacCormack and Baldwin2 used the method of MacCormack 3 to generate solutions for low supersonic Mach numbers. The purpose of this Synoptic is to ascertain the validity of the MacCormack algorithm for laminar boundary-layer/shock-wave interactions in the hypersonic regime. Results of several numerical solutions were compared with experimental data from the von Karman Facility (VKF) Hypersonic Wind Tunnel (B) and the Langley Research Center (LRC) Mach 8 Variable Density Tunnel. Agreement between the numerical solution and the data was generally satisfactory, although the extent of separation was under predicted in interactions with large separated regions. When applied to hypersonic interactions having large separated and recirculating regions, the method gave marginal performance. Lack of spatial resolution in the longitudinal direction is the suspected cause of the discrepancies. Contents The MacCormack method, which is an explicit, split, twostep algorithm, was used to solve the laminar, compressible, time-dependent Navier-Stokes equations expressed in conservative form. The equations, together with the details of the algorithm, are given by MacCormack. 2 Because of the difficulty in maintaining laminar flow throughout hypersonic boundary-layer/shock-wave interactions for strong shock waves and moderate-to-high Reynolds numbers, the incident shock angles (Fig. 1 for schematic) in this study are limited to a maximum of 16 deg and the Reynolds numbers to a maximum of 106/ft. The computed pressure ratio at the wall, pw/pw, is compared with measured data of an AEDC-VKF Tunnel B experiment in Fig. I.4 Agreement is excellent particularly near the peak pressure location where the correct shape is generated, and in the midrange where the correct pressure gradient is obtained. No evidence of separation was obvious from the data, and no separated region was predicted by the program.

Flow separation due to jet pluming.

D missile ascent rapidly decreasing ambient pressure causes the rocket exhaust plume diameter to equal and exceed the vehicle length. At sufficiently high altitudes, the plume interacts with the vehicle flowfield and produces a boundary-layer separation that can occur well forward of the vehicle base. Because this phenomenon significantly influences vehicle stability, heating, and stage separation, the conditions at which plume-induced flow separations can occur are naturally of interest. In a series of wind-tunnel experiments, large regions of plume-induced flow separation have been demonstrated by Falanga et al and by Vick et al using cold-flow jet simulation techniques. Since these available data indicate a considerable degree of configuration dependence, they cannot be used readily to predict flow-separation characteristics for arbitrary missile shapes. Furthermore, the adequacy of the jet simulation techniques used to simulate vehicle-plume interaction has not been demonstrated. Additional wind-tunnel tests now have been conducted in order to determine the plume-induced flow-separation pattern to be expected on several typical missile configurations. Furthermore, a flight program using one of the windtunnel configurations has served to check the validity of the jet simulation techniques. The results of these tests are reported in this note.