Colloquium FLUID DYNAMICS 1 Institute of Thermomechanics AS CR, v.v.i., Prague, October 4-6, 1 p.1 REMARKS ABOUT THE CONTROL OF THE GRID GENERATED TURBULENCE DECAY Pavel Jonáš Institute of Thermomechanics Academy of Sciences CR, v.v.i., Praha Abstract The results of preliminary eperiments to slo don the decay of the grid generated turbulence are presented. The effects ere testing of a moderate mean velocity lateral gradient and of the distribution of velocity disturbances sources distribution. Introduction hen investigating the evolution of a to-dimensional boundary layer attached to a flat plate it is necessary to create a to-dimensional eternal homogeneous flo, parallel to the plate. The research of flo phenomena occurring in technological applications requires modelling of deterministic and random flo disturbances in the free stream. Special attention is paid to the effect of free stream turbulence on boundary layer laminar-turbulent transition, friction drag, flo separation and miscellaneous interactions of shear layers in different stages of evolution. Passive turbulence generators make a good approimation of homogeneous isotropic turbulence (screens, square mesh plane/ biplane grids) or some sort of un-isotropic turbulence (e.g. many fluttering small flags bounded to a grid). The evolution of turbulent kinetic energy in such flo is described by the equation ( ) Dk = P ε, k= δij i j, P= i j Sij, ε = νsijsij, Dt 1 i j 1 i j Sij = ; sij = j i j i hich implies the rate of change of turbulent kinetic energy equals to difference of the energy production P and to the dissipation ε. Folloing notation is applied: Cartesian coordinate system ith 1 as the main stream direction ( 1., 3), kinematic viscosity ν, Kronecker delta δ ij. The common feature of all above mentioned passive turbulence generators is a rather fast Figure 1: Eperimental arrangement control of grid turbulence by shear flo.
p. stream ise decay of turbulent fluctuations because there is no production mean velocity gradients are missing. Preliminary studies on a possibility to introduce some additional turbulence sources into a stea flo ere done formerly [1 and ]. The revised and supplemented results are presented in this paper. Control by a shear flo ith the aim to slo don the decay of the grid generated turbulence it as decided to produce a mean shear flo in the test section (.5.91.5m 3 ) of the close type ind-tunnel IT AS CR. A fine screen built in the form of the letter S across the channel is able to create the mean shear flo y d = > The arrangement is shon in the Figure 1. The location and the shape of the S-profile ere calculated after Elder [3] ith the regard to the ind-tunnel lay out and ith the pursuit of maimal mean velocity gradient [1]. Cartesian coordinate system (, y, z) is introduced as shon in the Figure 1 ith the origin at entry to the test section. After Elder [3] a linear mean velocity profile ( y ) can be modelled by means of a homogeneous screen ith cylindrical shape placed across the ind-tunnel channel. The generating lines are parallel to z-aes. The profile of the screen is described generally by the equation ( ) y L λ ( ) ( ) 3 5 =.915 π y L + π y L / B+ π ( y L) 5 / 6 +... π BE that is derived from formulas (7.1) and (7.3) presented in Elder (1959). Intervals of the variables /L and y/l are determined by the height of the channel L and from the magnitude of the S-shape deflection the location of maimum (/L) is placed at y/l = ±.94. Constants B and E describe changes in the tangential component and the normal one of momentum flo 1.15 1.1 y =.988 +.996 1.5 1.995 y =.466 +.9954.99.5.1 y.15 [m]..5 =.45m; Uo=m/s =1.5m; Uo=m/s =.45m; Uo=3m/s =1.5m; Uo=3m/s =.45m; Uo=m/s; GT Figure : Mean velocity dimensionless profiles.
Colloquium FLUID DYNAMICS 1 Institute of Thermomechanics AS CR, v.v.i., Prague, October 4-6, 1 p.3 through the screen. Having in mind the aim to reach maimum of d/ and comply ith the space limitations, the screen (CSN 1531, porosity 31%) as inserted upstream from the entry to the contraction nozzle and its shape as designed in form ( ) 3 5 y y y y =.33.875 + 1.4 + 5.7 L L L L The investigations of the modelled shear flo ere done by Pitot-static probes and by a single hot-ire CTA-anemometer. Presented results relate to the relative velocity = m/s (eceptionally 3 m/s) in the section.5 m donstream the entry of the orking section. The dimensionless profiles of the mean velocity in planes =.45 m (circles) and = 1.5 m (triangles) are shon in the Figure. Red symbols denote undisturbed flo donstream the shear generator at the section =.45 m (green at 1.5 m). The black circles describe results taken donstream the flags turbulence generator inserted beteen the shear generator and the cross section =.45 m. (The flags turbulence generator is a net of oscillating flags about..5 m, producing non-isotropic turbulence of intensity 14 percent at ~.4 m). Statistical estimates of the slopes of straight lines are.99 in case ithout turbulence generator and.47 donstream the flags generator. Apparently the increased turbulent diffusion results in the attenuation of the mean flo shear. 1.5E+5 1.E+5 7.5E+4 5.E+4 d = d >.5E+4.E+..5 1. 1.5. [m] Figure 3: Comparison of the natural turbulence level development (red symbols) ith turbulence development donstream of the shear generator. The course of natural turbulence level i.e. neither turbulence generator nor the shear generator ere inserted upstream the test section (red circles) and ith the shear generator inserted across the channel (blue circles) are shon in Figure 3. Obviously natural turbulence level, about.3 percent increases donstream up to about.4 percent in the case of grad =. Modelling the shear flo, the turbulence level increases about tice beteen =.6 m and 1.6 m up to about one percent at the end of the test section. Results on the grid turbulence decay, plotted in Figure 4, illustrate the effect of tested shear flo on turbulence amplification. The values corresponding to the uniform flo are marked by red symbols and the relevant data measured in the shear flo are marked by blue symbols. The distributions valid in the uniform flo demonstrate that the grid turbulence as in the developing state. Evidently the modelled shear flo contributes to turbulence production. The delayer decay (loer slope of blue lines) and at least suppressed decay (constant course) prove the stabilizing effect of shear flo.
p.4 As partial conclusion: modelling homogeneous shear flo (in z- direction) generates an additional turbulent energy supply into a dissipating turbulent flo e.g. grid turbulence. It induces the increase of turbulent intensity and the reducing the damping rate. 14 1 1 8 6 d d = > 4..5 1. 1.5. [m] GT 6/5 GT 6/5 GT 6/75 Figure 4: Decay of grid turbulence in the uniform flo (red symbols) and in the shear flo (blue symbols). 14 1 1 8 6 d d = > 4 Control by layout of disturbances sources..5 1. 1.5. [m] GT 6/5 GT 6/5 GT 6/75 Figure 4: Decay of grid turbulence in the uniform flo (red symbols) and in the shear flo (blue symbols). The principal idea of this preliminary stu [] as to reduce the decay of grid turbulence by means of a distribution of disturbances sources in the flo field. The sources distributed regularly donstream from a grid are producing turbulent kinetic energy that might compensate, to some etent, the dissipation losses. The tested eperimental set up in the close type indtunnel IT AS CR is shon in the Figure 5.
Colloquium FLUID DYNAMICS 1 Institute of Thermomechanics AS CR, v.v.i., Prague, October 4-6, 1 p.5 Due to the relatively short test section (1.5 m) the square mesh bi-plane grid (cylindrical rods: diameter = 1 mm, mesh = 5 mm) is fied perpendicularly to the tunnel ais.5 m upstream from the outset of the orking section, in the section = -.5 m. The fence channel (.8.8 1.5 m 3 ) is inserted in the test section, fastened to the grid and placed on the flat plate. The scheme of this set up is shon in Figure 5. The upper all and the side ones of the fence channel are created by the system of parallel square rods (11 mm ) ith the spacing 5 mm. The loer all constitutes the smooth flat plate ith an investigated boundary layer. The leading edge of the plate is identical ith the z-ais ( = ). This configuration as designated the fence generator of turbulence. The mean velocity as measured by means of a Pitot-static tube in the plane (, y) at a height y =.5 m. The single ire CTA-anemometer The turbulent fluctuations of the longitudinal velocity component ere measured in similar locations..5.4.3..1...5 1. 1.5 [m] o=1 m/s o= m/s o=3 m/s interpolation Figure 6: Distributions of turbulence intensity inside the fence channel donstream the grid 1/5.
p.6 The distribution of the mean velocity inside the fence channel as found out uniform in the limits of measuring accuracy for >.1 m. Note, the fence channel has no bottom from = -.5 m up to the leading edge of the plate. As follos from the distribution of turbulence intensity shon in Figure 6, the intensity of longitudinal fluctuations begun moderately gro from the distance ~.3 m. Turbulent disturbances generating due to the action of pickets represent production of additional turbulence. Thus turbulence production prevails the dissipation. It as found from eploratory measurements that the cross section of the fence channel and the spacing of the side fences control the ratio of production to dissipation. 3 1..5 1. 1.5 [m] GRID m/s o=1 m/s o= m/s o=3 m/s Figure 7: Decay of the longitudinal component of velocity fluctuations donstream of the grid 1/5 (rhombus) and inside the fence channel attached to the same grid. The comparison of to eamples of turbulence decay development is shon in Figure 7. The first eample (rhombus) is the decay donstream the isolated grid 1/5 (across the orking section,.5.9 m ) and the second ones are the decay measurements at different relative velocities inside the fence channel connected to the original grid. Dissipation prevails the production only on small piece of the channel length, say up to =.5m. Net the turbulence production predominate the dissipation. Interesting knoledge as also received from the measurement of the skeness factor Su and the flatness one Fu. Small negative values of Su indicate a turbulent transport of kinetic energy from the rod alls to the core of flo in the channel. The flatness Fu equals three ith a small scatter. The value of the longitudinal integral scale of generated turbulence as estimated beteen 16 mm up to 18 mm from the autocorrelation measurements ith using the Taylor s hypothesis. A similar method of inserting the net of singular turbulent disturbances sources as realized in the small high-speed ind tunnel (.1.1 m ) [4]. Sidealls of the orking section ere made from perforated plates (diameter of gaps mm; a checkerboard pattern ith mesh 3 mm). To-dimensional mean flo ith a long part of constant turbulence level as accomplished.
Colloquium FLUID DYNAMICS 1 Institute of Thermomechanics AS CR, v.v.i., Prague, October 4-6, 1 p.7 3 1..5 1. 1.5 [m] GRID m/s o=1 m/s o= m/s o=3 m/s Figure 7: Decay of the longitudinal component of velocity fluctuations donstream of the grid 1/5 (rhombus) and inside the fence channel attached to the same grid. Conclusions To methods of the grid generated turbulence control ere checked out namely the modelling of the lateral gradient of the longitudinal velocity and the distribution of disturbances sources in the flo field. Modelling homogeneous shear flo (in z- direction) generates an additional turbulent energy supply into a dissipating turbulent flo e.g. grid turbulence. It induces the increase of turbulent intensity and the reduction in the damping rate. The sources of the flo disturbances (jet/ake) distributed regularly donstream from a grid are producing turbulent kinetic energy that can compensate, to some etent, the dissipation losses. The accomplishment equilibrium beteen turbulence production and dissipation in a given part of the orking section depends on the possibility to match up the dimensions of ind-tunnel lay out ith the selected equilibrium region. After the received eperiences this represents laborious hard task. Acknoledgements This ork has been supported by the Czech Science Foundation, the project GA11/8/111 and GAP11/1/171 and ith the institutional support, projects AVZ76514. References [1] Jonáš, P. and Řehák, V. Preliminary measurement of the shear flo effect on grid turbulence development (In Czech). Inst. of Thermomechanics CSAV, 1975, Rep. Z-468/75, 4p. [] Řehák, V. and Jonáš, P., A short remark to generating nearly stea turbulence level in a ind tunnel flo, contribution EUROMECH 65, Liblice Castle, September 1975.
p.8 [3] Elder, J.., Stea flo through non-uniforms gauges of arbitrary shape. J. Fluid Mech., Vol. 5, 1959, 355-368. [4] Jonáš, P., Modelling of a quasi to-dimensional flo in small high-speed ind tunnel IT (In Czech). Inst. of Thermomechanics CSAV, 197, Rep. Z-385/7, 6p.