In most experiments this parameter was varied from 4 to about 50. Measurements along the axis of symmetry in the flow show that there is a relatively short region of stagnant fluid just in front of the body. Most of the disturbance is found from many existence. Although the radial gradients in the flow increase with N, they are found to be much smaller than would be expected in a flow with thin flow payers. A physical model of the flow with flows and pressures consistent with these results is discussed.
3): . where: *. and star quantities represent dimensional quantities. The non-dimensional parameters appearing in the equations are In the experiments described here, and in other experiments referred to later, Laboratory conditions. Yonas (Ref. 2) measured the drag of spheres and of a flat disk in the same liquid sodium tunnel.
In the GALCIT facility, Ahlstrom (Ref. 10) has measured the magnetic field disturbances produced in front of a semi-infinite Rankine body, and Suzuki (~ e f, 4) has measured the resistance of a semi-infinite Rankine body. The experiments described here were carried out to provide a description of the fluid movements using velocity measurements. These were performed using electrically isolated hot film sensors in the flow in front of a semi-infinite Rankine body.
DESCRIPTION OF EXPERIMENTS 2.1 The Mercury Tow Tank
The only important difference between calibration runs and data runs was the presence of the magnetic field during the latter. When measurements were made with the sensor mounted at the top of the tank, the sensor was calibrated using the increasing shear flow produced in the mercury by the drive shaft as it entered from below. The velocity profile of this flow was measured and found to be quite flat at the sensor level (see Fig. 5).
When data runs were made with the sensor mounted in this manner and placed within one body radius of the tow tank centerline, the drift shaft stops were set so that the stagnation point of the Rankine body was 0.5'@ from the sensor at the end of each run . It is Tfilm8 the temperature of the platinum film at r = '~i~m' which is known and kept constant. The velocity measured by the sensor, the velocity of the displacement flow and the velocity of the drive axis were used to calculate a normalized velocity, u, so that u = 8 in the undisturbed displacement flow and u = 1 at the body stagnation point.
It is a normalized form of velocity perturbation caused by a moving body for measurements made with a sensor mounted on top of the towing tank. When runs were made with the sensor mounted on top of the drag tank, the relative position of the sensor and the body was determined using the drive shaft speed and. Most of the data was obtained using a sensor mounted on the tow tank, these estimates show.
In a way, the flow in the tow tank was never steady because the model was always approaching the free surface at the top of the tank.
DISCUSSION OF RESULTS
The results of the experiments are presented in terms of the normalized error of the velocity in the fzeestream, so that the above-mentioned velocity is U = 1 - u. The effects of Joule dissipation on the pressure and velocity in the flow can be considered by referring again to Bernoulli's foot (Eq. 4.1) - The stagnation pressure a Po = p +(U2) decreases on all flows that have passed through the non-zero flow den- regions. Since the stagnation pressure can only decrease and the amount of Joule dissipation that occurs along different flows varies, radial and axial stagnation pressure gradients appear in the flow. In axial positions in front of the body, the stagnation pressure drops from P 1 at r = 0 to lower values at r > 0, in the region where the flow-.
As shown by Tamada (Ref. 7), far downstream of the body where the flow again becomes uniform in the sense that v = 0, there can be no radial static pressure gradient and the axial velocity must be directly related to the stagnation pressure Due to of the loss in stagnation pressure due to the flow along streamlines that have experienced Joule dissipation, the axial velocities near the body are lower than those in the flow far from the body. Because of the stagnation pressure variations in the flow, the velocity measurements cannot be used directly to determine static pressures. This is especially true over the front of the body near r = where I the stagnation pressure must be close to its minimum value. Measurements of static pressures and stagnation pressures over the surface of a sphere in aligned-field MHD flow, for 1.5 < N < 40, are made.
The resulting net pressure force on the face of the sphere rises only up to about CD = 0.5 at N -- 12, and then drops to zero as N is further increased, due to the effect of the increasingly large contribution of the negative pressure. These results are cited to demonstrate the possible effects of the stagnation pressure losses due to Joule dissipation in such flows, and to introduce a discussion of whether such an effect may occur in the flow considered here. Although at low N there are certainly areas of negative pressure on the front of the body (as there are for N = O), these measurements are.
Therefore, the downstream measurements are not complete enough to allow calculation of the drag using the downstream wake profile and a momentum balance, such a calculation would be difficult in any case, since the flow in this region may vary more. or less continuously from the hull to the draw tank walls. Changes in the magnetic field caused temperature changes of up to 2o0c due to heating of the magnet. However, the most meaningful indication of the average uncertainty in the parameter X(PQ) is that given by the scatter in the calibration curve.
Values of the P& from the calibration curves were used to calculate the normalized velocities. The velocity profile of the displacement flow could have peaked near the axis of the tow tank if the mercury had been allowed to rise through the edge magnetic field near the top of the tank. It should be noted that although the foregoing estimates can be made regarding the accuracy of the various. measurements and calculations, not all the data points in any region of figure 1 2 depend in the same way on individual measurements or calculations. The curve in figure 12 is defined by the overlap of data obtained for both high and low values of flow velocity past the sensor and for both small xb and N, and large x, and N. equivalent values of N were produced using different combinations of magnetic field and drive shaft velocity, and there is overlap in the data produced by using the two different sensors. mounts.
Measurements were made with the axis of the sensor parallel and perpendicular to the radius of the tow tank. The comparison of such measurements enables the estimation of the heat transfer due to the radial velocity, since in one orientation the contribution of the radial velocity is the smallest and in the other the largest. For this reason and because the flow field shown by the measurements does not contradict the assumption that. v << u, the use of one sensor seems justified.
All the uncertainties related to the measurements made with the sensor tank mounted on the flow center. line applies to the measurements from the center line.
