Normal Flat Plate Research Articles

Wake interference behind two flat plates normal to the flow: A finite-element study

A finite-element model of the Navier-Stokes equations is used for numerical simulation of flow past two normal flat plates arranged side by side at Reynolds number 80 and 160. The results from this simulation indicate that when the gap between the plates is twice the width of a single plate, the individual wakes of the plates behave independently, with the antiphase vortex shedding being dominant. At smaller gap sizes, the in-phase vortex shedding, with strong wake interaction, is favored. The gap flow in those cases becomes biased, with one of the wakes engulfing the other. The direction of the biased flow was found to be switching at irregular intervals, with the time histories of the indicative flow parameters and their power spectra resembling those of a chaotic system.

Performance of the tolerant tunnel for bluff body testing

A new passive form of low-boundary-correction wind tunnel test section is under development. In the version designed for testing two-dimensional bluff bodies the two boundaries opposite the model under test consists of arrays of evenly spaced airfoils at zero incidence. The spacing is selected so that the outer streamlines of the test section flow can pass into an outer plenum and return to the test section downstream, in such a way that the overall streamline pattern closely approximates the corresponding free-air pattern. The design is passive in that a fixed optimized boundary configuration is used for all sizes and shapes of test model. The theoretical background of the design is described, and experimental pressure distributions are presented for several sizes each of normal flat plates, circular cylinders, and circular cylinders with splitter plates, over a range of boundary airfoil spacings. It is shown that a single optimal spacing exists for which the pressure distributions for all sizes of each bluff body shape collapse onto or very close to appropriate reference curves representing unconfined flow conditions.

Steady two-dimensional flow through a row of normal flat plates

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

Spatial correlation measurement in turbulent flows using pulsed wire anemometry

Details of a new technique in pulsed wire anemometry, developed to allow measurement of two-point spatial velocity correlations in highly turbulent flows, are described. An outline of the interface devices necessary for linking two anemometers to a microcomputer is given and examples of the use of the technique are presented. Firstly, measurements of spatial correlations with and without time delay in the near wake of a nominally two-dimensional cylinder normal to a uniform stream confirmed the viability of the technique. Secondly, measurements in the highly turbulent, separated region behind a normal flat plate fitted with a downstream splitter plate are presented as a demonstration of the effectiveness of the technique in such ‘difficult’ flows. We believe that these are the first direct measurement of spatial correlation functions within a separated flow.

Studies in numerical computations of recirculating flows

AbstractThis paper considers the use of various finite differencing schemes for the computation of flows involving regions of recirculation. Standard first‐order hybrid schemes, vector (or skew) schemes and second‐order schemes are used to predict laminar flows in a channel containing a constriction and over a normal flat plate with a downstream splitter plate. In the former case the results are compared with those of other workers and with the implications of analytic theories for the viscous dominated flow around the sharp corner.Attention is concentrated on the effects of errors arising from the use of non‐uniform grids and it is shown that higher‐order differencing schemes are generally much less susceptible to these than the simpler schemes. The major conclusion is that for flows containing regions where pressure gradients largely balance the convective terms in the momentum equations, in addition to other regions where convection and diffusion balance, higher order differencing schemes are likely to be essential if accurate predictions are required on grids without excessive numbers of nodes. It is argued that similar conclusions must hold for high Reynolds number turbulent flows.

The feedback mechanism of supersonic edge and plate tones

Intense tones are generated when supersonic (choked) “2‐D” jets impinge on edges [Powell, Acoustica 3, 233–243 (1955)] or on normal flat plates [Krothapalli, AIAA J. 23, 1910–1915 (1985)] considered herein equivalent to a 180° edge. A feedback mechanism is now proposed: Puffing to alternating sides of the high‐impedance midplane, the jet generates essentially monopole radiation into half‐or quarter‐space, respectively. The resultant sound pressure p′ at the nozzle changes the (quasistatic) efflux angle by p′/ρjcj (Mj2−1)1/2/Mj (Mj is the jet Math number), as for choked jet screech. The induced jet sinuosity is amplified by flow instability until interacting with edge or plate. The phase criterion of I yields the principal frequencies: f = c0h′ N + p(1 + M̄con−1), N= integer, where h′ is the nozzle to effective source distance, c0 is the ambient sound speed, M̄con is the averaged instability convection Math number, and p = 1/4. Limited experimental data yield p≅0.25, N≅7 for edge tones; for plate tones 2 < N < 5, and p = 0 (sometimes, but M̄con , values are uncertain!). Again following I, the gain criterion yields sound intensity and lateral jet displacements consistent with experiment.

Mechanisms of sound‐producing instabilities of choked round jets impinging on small and large flat plates

At the 112th Meeting certain characteristics of the discrete tones emitted when a choked round jet impinges on a normal flat plate were reported [J. Acoust. Soc. Am. Suppl. 1 80, S9 (1986)]. These are now shown to be one of two classes, dependent on whether the plate is small or large. If small (≅ orifice diameter D), the action occurs when the stand‐off shock‐wave is in a pressure recovery region of the spatially periodic jet structure, as in a Hartmann resonator, and the frequency overlaps those of a Hartmann resonator, successively excited at high harmonics. If large (> 4D), feedback to the orifice occurs, with up to seven frequency jumps not correlated with the periodic jet structure: f = c0(h + h′) N(1 + Mcon−12), 1 ≲ N = integer; ≲ 8, where N ≅ h/D + 3/2 (2<N<8) for the principal frequencies, c0 is the ambient sound speed, h is the orifice‐plate distance, h″ is a constant ≅ 4D/5, and Mcon is the jet instability convection Mach number. These are almost independent of jet velocity and plate size, differing significantly in character from the subsonic case.

Sound producing instability of a choked jet impinging on a normal flat plate

An axially symmetric choked air jet expands to a supersonic condition and then contracts to approximate to the sonic exit condition. This “cell” structure is repetitive in the downstream direction until destroyed by dissipation. If a rigid flat plate is introduced normal to the jet axis, a strong transverse shock wave (“normal” or “stand‐off”) separates the supersonic jet flow from the locally subsonic divergent flow caused by the presence of the plate. If the plate is small, the flow is unstable and emits intense sound when the plate is positioned near where a cell junction would be. For larger plates, these positions for instability merge together. The frequency then drops steadily with increasing orifice‐to‐plate distance, but is interrupted by upward jumps, characteristic of acoustic feedback to the orifice. Phased Schlieren photographs make clear some of the main features of the highly nonlinear oscillations of the complex supersonic/subsonic flow: In particular, the stand‐off shock wave undergoes large amplitude nonlinear oscillations with consequent violent periodicity of the (mainly) subsonic flow.

Effects of droplet-size distribution and gas-phase flow separation upon inertia collection of droplets by bluff-bodies in gas—liquid mist flow

This paper describes a trajectory analysis of the inertia collection of monodisperse- and polydisperse-droplets by a normal flat plate and a circular cylinder in gas—liquid mist flow. taking into account the far-wake displacement effect of gas-phase flow. The effects of the far-upstream droplet-size distribution and the gas-phase flow separation upon the local collection efficiency and the velocities and size distribution of droplets on impringement are examined. On the basis of these results. a new equivalent diameter of polydisperse-droplets is proposed.

Wake interference of a row of normal flat plates arranged side by side in a uniform flow

The wake characteristic of groups of normal flat plates, consisting of two, three, or four plates placed side by side with slits in between, have been investigated experimentally. When the ratio of the slit width to the plate width (slit ratio) was small, the gap flows were observed to be biased either upward or downward in a stable way, leading to multiple, stable flow patterns for a single slit-ratio value. Some regularities were recognized in the gap-flow directions and the appearance of the flow patterns. The plates on the biased side showed high drag and regular vortex shedding, while those on the unbiased side showed the opposite. The origin of the biased flow has also been investigated with water-tank experiments, numerical calculations and wind-tunnel experiments. The-results showed that the origin of biasing is strongly related to the vortex shedding of each plate of a row.

On a potential flow theory for a bluff body in a parallel channel. 1st report Normal flat plate.

A theoretical study was made to predict the pressure coefficient and separation streamline for a bluff body in a parallel channel. A separated flow was formed with a source on a real axis in an upper half plane which was conformally mapped from a physical plane. An unknown parameter was to be determined by an empirically known back pressure coefficient. A comparison was made with discontinuous flow theory. Differences in the pressure cofficient between the present theory and discontinuous theory was very small except for a small blockage. Considerable difference in separation streamline was found for the case of a small blockage.

The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake

The Navier-Stokes equations are solved numerically for the steady separated flow past a normal flat plate for Reynolds numbers in the range 0.1 ≤ R ≤ 20. Eddy dimensions together with the position of the vortex centre are presented and compared with the few other estimates and predictions available. Streamlines and equivorticity lines are also given. The main result of interest is the extremely good comparison with experimental results over this range of Reynolds numbers. The method of solution is based on an artificial time-dependent procedure using a distorted time. Results are given only for the steady-state flow.

Large-Scale and Small-Scale Turbulence Structure in the Intermediate Wake of a Two-Dimensional Normal Plate

Turbulence structure in the intermediate wake of a normal flat plate was studied experimentally by a conditional-sampling technique. The measurements were made at a section 8.0 heights downstream of the front face of the plate. Velocity fluctuations were decomposed into those produced by large-scale structures and those associated with small-scale structures : the former fluctuations were again decomposed into the phase-averaged fundamental component and the deviation form it (large-scale deviation). Velocity vector fields, contours of streamlines, vorticity of the fundamental component, together with contours of intensity and correlation of the large-scale deviation velocity, were presented and discussed. Contours of intensity, correlation and turbulence intermittency of the small-scale fluctuations were also presented in and around the large-scale structures. Large Reynolds shear stress associated with the large-scale deviation velocity was suggested to be the result of a stretching of vortex filaments in the saddle-point flow region.

Characteristics of the Flow around a Bluff Body near a Plane Surface

The characteristics of the flow around a normal flat plate and a triangular cylinder near a plane surface has been investigated experimentally in the Reynolds number range of 102to 3×104. Frequency analysis of hot wire signal of the wake flow in a wind tunnel revealed that regular vortex shedding from the normal flat plate and the triangular cylinder was suppressed for spaces less than about 0.6 and 0.37 times the body width respectively. Investigation of the time-mean distance between two shear layers in the vortex formation region demonstrated that the suppression of vortex shedding for both configurations occurred for any space between the inner shear layer and the plane surface less than about 0.3 times the shear Iayer distance. Flow visualization experiments in a water tank revealed the structural differences of the wakes with and without vortex shedding.

Large-Scale and Small-Scale Turbulence Structure in the Intermediate Wake of a Two-Dimensional Normal Plate

Turbulence structure in the intermediate wake of a normal flat plate was studied experimentally by a conditional-sampling technique. The measurements were made at a section 8.0 heights downstream of the front face of the plate. Velocity fluctuations were decomposed into those produced by large-scale structures and those associated with small-scale structures: the former fluctuations were again decomposed into the phase-averaged fundamental component and the deviation from it (large-scale deviation). Velocity vector fields, contours of streamlines, vorticity of the fundamental components, together with contours of intensity and correlation of the large-scale deviation velocity, were presented and discussed. Contours of intensity, correlation and turbulence intermittency of the small-scale fluctuations were also presented in and around the large-scale structures. Large Reynolds shear stress associated with the large-scale deviation velocity was suggested to be a result of the stretching of vortex filaments in the saddle-point flow region.

The effect of strong three-dimensional disturbance on vortex shedding

This paper describes an experimental study of the fluid dynamics of a cross, formed by the intersection at right angles of two high aspect-ratio normal flat plates. It is found that in the immediate vicinity of the intersection, within two to three plate widths of the centre-line, periodic vortex shedding is completely suppressed with a fairly abrupt elevation of the base pressure in this region. Outboard of this primary interaction vortex shedding recommences within about three to four plate widths, with a constant Strouhal number across the span. It appears that in the inner part of the shedding region vortex formation is delayed so that vortex cores are initially inclined to the model, but that spanwise variations in convection velocity mean that this inclination is subsequently reduced further downstream. There is no correlation between adjacent, or opposite, arms of the intersection.

A Normal Flat Plate Close to a Large Plane Surface

SummaryThe flow around a normal flat plate close to a large plane surface has been investigated for a range of boundary-layer thickness on the plane surface of 0.72 to 2.53 times the plate height, h. As the gap between the plate and the plane surface is reduced below about 0.55h vortex shedding from the plate is inhibited by the presence of the plane surface. Boundary layer thickness has little effect on the gap at which this occurs, but does affect the strength and frequency of vortex shedding at greater gaps. As the gap between the plate lower edge and the plane surface is decreased towards the critical value of 0.55h, both vortex strength and Strouhal number are more significantly affected when the approaching boundary layer is thin. It is not clear whether this is a result of shear or increased turbulent intensity.

Numerical predictions of the laminar flow over a normal flat plate

AbstractFinite‐difference and finite‐element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half‐width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re = O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds‐number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier‐Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher‐order numerical methods, before the numerical accuracy of predictions of, for example, bluff‐body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in such situations.

一様流中に並列配置された垂直平板列の後流干渉

Experimental investigations have been made on the wake characteristics of groups of normal flat plates, consisting of two, three, or four plates placed side by side in a uniform flow with slits in between. When the ratio of the slit width to the plate width (slit ratio) was small, the gap flows were observed to be biassed either upward or downward in a stable way, leading to multiple, stable flow patterns for a single slit ratio value. Some regularities were found in the gap flow directions and the appearance of the flow patterns. The plate on the biassed side showed high drag and regular vortex shedding, while the plate on the unbiassed side showed the opposite. The variations with slit ratio of base pressure and STROUHAL number of individual plates showed similar tendencies when the neighboring gap flows were alike. In four-plate rows, the wake characteristics were compared with those of two dimensional perforated plates studied earlier by CASTRO.

Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag

The asymptotic theory for the laminar, incompressible, separating and reattaching flow past the bluff body is based on an extension of Kirchhoff's (1869) free-streamline solution. The flow field (only the upper half of which is discussed since we consider a symmetric body and flow) consists of two basic parts. The first is the flow on the body scalel*, which is described to leading order by the Kirchhoff solution with smooth inviscid separation, but with an$O(Re^{-\frac{1}{16}})$modification to explain fully the viscous separation (hereRe([Gt ] 1) is the Reynolds number). The influence of this$O(Re^{-\frac{1}{16}})$modification is determined for the circular cylinder. The second part is the large-scale flow, comprising mainly the eddy and the ultimate wake. The eddy has length scaleO(Rel*), widthO(Re½l*) and is of elliptical shape to keep the eddy pressure almost uniform. The ultimate wake is determined numerically and fixes the eddy length. The (asymptotically small) back pressure from the eddy acts (on the body scale) both in the free stream and in the eddy, and it has a marked effect at moderate Reynolds numbers; combined with the Kirchhoff solution, it predicts the pressure drag on a circular cylinder accurately, to within 10% whenRe= 5 and to within 4% whenRe= 50. Other predictions, for the eddy length and width, the front pressure and the eddy pressure, also show encouraging agreement with experiments and Navier-Stokes solutions at moderate Reynolds numbers (of about 30), both for the circular cylinder and the normal flat plate. Finally, an analysis in the appendix indicates that, in wind-tunnel experiments, the tunnel walls (even if widely spaced) can exert considerable influence on the eddy properties, eventually forcing an upper bound on the eddy width asReincreases instead of theO(l*Re½) growth appropriate to the unbounded flow situation.