ACCEPTED AS SATISFACTORY: REGULATION FOR PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN ENGINEERING (MECHANICAL ENGINEERING), BUET, DHAKA. Mean properties of the flow at the trailing edge and in the wake downstream of the trailing edge were experimentally determined. Within the wake, near the trailing edge of the plate, there was a transverse velocity gradient.
Abdul Halim for their constructive criticism and valuable suggestions that certainly increased the quality of the work. Many thanks go to the employees of the various SUET workshops for their help in preparing the experimental setup. Enlarged boundary layer velocity profile at the wall of the test section (ReQe=2.01X103) Enlarged boundary layer velocity profile at the wall of the test section (R ~ =1.90x103).
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Hall and HisloP[S] investigated the velocity and temperature distributions in the turbulent wake behind a heated body of revolution. They also found that the experimental values of the average velocities fit satisfactorily with the empirical equation given by Schlichting [7Jin cf. Swain (9) also obtained such an expression for the velocity profile in an axially symmetric track in a similar manner.
The dimensionless velocity defect profile was obtained experimentally by Rehichardt.[10] in the wake behind a heated wire at a distance of X=100ro. is the radius of the wire) of it. The measurements were also made by Fage and Falkner [11Jin the wake behind a heated prismatic rod at a distance of X = 72 ro from it. Goldstein's attempt [12J and other students. van Taylor to apply the vorticity transfer theory to determine the velocity profile in an axially symmetric wake. did not lead to results consistent with experimental data. To find the shape of the velocity profile in a two-dimensional wake Schlichting [7J uSBd mOm antum equation of.
The author defined the velocity profile in the usual functional form U-u = (U-uc) f ("
Recent Approach
Average static pressure in wake behind the body depends on the size of the body. If the thickness of the body is large, the pressure gradient cannot be ignored. The flow both at the trailing edge of the plate and at the downstream of the plate will be tested experimentally.
The mean velocity and pressure in the wake must be measured for different initial conditions at different locations from the trailing edge of the plate. The general solution of the nonlinear Navier-Stokes equations is not available. To apply Navier-Stokes equations to practical cases, hypotheses and empirical assumptions must be introduced to obtain a closed set of equations with time-averaged dependence - bulge variables. Imagining that the flow past an obstacle produces a completely separated, stagnant region of width 2g • Then 2PU29 represents the net momentum defect per time and depth unit. where, g is called the pulse thickness of the wake.
The momentum thickness is related to the drag coefficient of the obstacle producing the wake. where 01 is the resistance per unit depth and L is the characteristic height of the obstacle. The resistance, °1, produces the momentum flux,M. The momentum integral equation for the drag on the obstacle with a pressure gradient is given by. 3.2.8) But according to the definition of drag coefficient.
3.2.8) But according to the definition of drag coefficient
The plates were made in such a way that they fit tightly in the center of the working section. The first channel (45.7 cm x 45.7 cm x 96.5 cm) was made of wood, and the boards were placed at the mid-height of the cross section of this channel. Sufficient holes were provided in the bottom of the plexiglass channels along the center line to insert the pitot-static tube.
There was also one hole at a distance of 15 cm from the inlet of the second channel, halfway up the side wall, for inserting the pitot-static tube into the channel. The outside diameter at the end of the pitot tube was 0.159 cm. • The pitot-static tube was connected to an inclined strain gauge. To prevent vibration of the sensor, the pitot-static tube was supported by a copper rod with a diameter of 0.635 cm.
For the calibration of the wind tunnel, the speed and pressure in the test section were measured. The velocity profile is flat across the test section, except for a small boundary layer at the top and bottom walls of the test section.
CHARACTERISTICS QF THE VELOCITY PROFILE IN THE TEST SECTION CALIBRATIONS
The velocity distribution is also symmetrical about the center line as shown in fig. The area under the velocity profile was calculated and from there the average velocity over the test section was determined. The Reynolds number of the flow is calculated on the basis of the average velocity and the width of the test section, such calibrations were performed for flows with Reynolds numbers used in this study.
The thickness of the boundary layer is obtained by measuring the distance Y from the wall, for which u/U=0.99. The wall moment thickness is calculated using eqn. 3.2~5) • Calculated values of various flow parameters for ~est section are given below in table 4.1. The two sets of experimental points show a negligible difference as shown in Fig~4.5_ This implies that there is a negligible pressure gradient in the axial direction within the test section.
A thin layer of varnish was allowed to grow down through the Plexiglas channel. The pressure gauge reading was fairly stable except for a narrow area near the wall where it fluctuated. Similar readings were taken at the trailing edge of the p12te and at different Reynolds numbers.
The room temperature and pressure were taken at the beginning and at the end of each experiment. The uncertainty in the measurements of the maan velocity and pressure is affected by the variation in the fluid's specific gravity (in strain gauge) which is associated with the variation in the ambient temperature and pressure, the accuracy of the angle of inclination of the static pitot tube to the mean flow direction, and the accuracy of the the measurements of the depth sounder reading.
CHAPTER - V
RESULTS AND DISCUSSION 5.1 General
- Half width and center-line velocity
Dimensionless half-width (2~/CdmL) of the wakes are plotted against axial distances, which are shown in Figs. The axial variation of the wake half-width near the trailing edge of the plate deviates from semi-empirical results, but it agrees with empirical results after xjCdm L;50. It should also be noted that the effect of the initial state only exists up to a certain axial distance, and then the current forgets its state of origin.
Near the trailing edge of the plate- I' the velocity increase in the centerline8 of the track is greater than that of Chevray and Kovasznay[ ~ and Korst and Chow [22]. For all calculations, Korst and Chow 122] used a flat velocity profile at the beginning of the trace. No similarity of mean velocity is observed near the trailing edge of the plate.
Deviation of the experimental results from the semi-empirical equation (3.2.11) can be expressed in rms ~ error. The flow is not self-preserving in the range of axial distance covered in this study, as the smallest rms error is of the order of 0.058, which is considered high for self-preserving. The Diag coefficient is also calculated using equation (3.2.10) near the rear edge of the plate taking into account the effect of the pressure.
The initial boundary layer is identified as turbulent based on experimental velocity values that fit the universal turbulent boundary layer velocity profile. The uniform flow surrounding the trace is limited by the wall of the test section. This indicates that the development of wakes in the middle of the test section does not affect the average parameter in the wall boundary layer within the axial distance covered in the experiment.
The shape factor of the wake decreases with increasing Reynrild's number and with the axial distance from the trailing edge, but it decreases with decreasing plate thickness. The decrease of the shape factor to unity is 'an indication of self-preservation of flow. The velocity distribution near the flat plate is unstable due to the presence of high velocity gradient in the axial direction, and it gradually decreases to make the flow self-sustaining.
The rate of increase of centerline velocity is fast in the near region of the wake and becomes slow as the axial distance increases. Abr'amovich, JI G.N., The 'theory of turbulent M.I.T.Press; MQssachusetts Institute of M.I.T.Press; MQssachusetts Institute of Cambridge, Massachusetts.
OF THE TEST0'010'0
XIS FIG.5_9 VARIATION OF SHAPE
APPENDIX - I UfJCERTAINTY ANALYSIS
If the sensing point of the pitot-static tube is deviated by an angle APPENDIX - II
