A Note on Partial Cavitation of Flat Plate Hydrofoils

Recently Tulin and Wu have treated the problem of fully developed cavitation on flat plate and cambered foils. In these treatments, the length of the cavity is always greater than the chord of the hydrofoil and the cavity is assumed to start at the leading edge of the plate. The purpose of this note is to extend Tulin's work to account for partial cavitation, i.e., when the cavitation bubble is less than the hydrofoil chord

Flow in Hydraulic Machinery

This report concludes the work conducted by the Hydrodynamics Laboratory at the California Institute of Technology under Contract N6onr-44, Task II, in the general field of hydraulic machinery. This work was initiated in January 1947 under the initial guidance of Professors Knapp and Hollander. It has subsequently been continued by additional amendments to the original contract up to the present. The over-all objectives of this program were to make detailed observations and measurements of the internal flow in rotating impellers and stationary diffusors to permit the establishment of accurate design procedures for hydraulic machinery, and to serve as a starting point for realistic mathematical analysis of such flows. It is the intention of this report to indicate the scope of the work done under this contract and to describe the facilities built for its experimental end. A further aim is to outline, in brief, the reports and publications issued and some incidental benefits derived from this project

Unsteady Effects in Flow Rate Measurement at the Entrance of a Pipe

Unsteady flow in pipes and nozzles occur frequently in engineering applications and they pose special problems of measurement and calibration. When the Reynolds number is high the entrance region of a pipe (following a smooth contraction) is characterized by a thin boundary layer and the unsteady effects are then bound up in the unsteady behavior of the boundary layer. Woblesse and Farrell [1]2 have recently considered unsteady effects in laminar pipe entrance flows that start from rest by an integral method. Periodic disturbances also arise which require a different treatment. The primary interest of the present work is for thin entrance boundary layers subject to peridodic disturbances. In either case the ratio of the average velocity to the velocity in the potential core is V[sub]avg/V[sub]core = 1- 2[delta]*/R [equation 1] where [delta]* is the usual displacement thickness and R is the pipe radius. In steady flow this ratio is just the "discharge coefficient", c[sub]d. In unsteady flow it is very desirable to know how this ratio changes with time because many of the presently available experimental methods enable one to measure V[sub]core but not V[sub]avg readily. In this brief note we will estimate the unsteady effects of a periodic, fluctuating main flow on the displacement thickness of a laminar, flat plate boundary layer. It is assumed that the boundary layer is sufficiently thin compared to the radius of a pipe so that the pressure gradient caused by this effect in a pipe can be neglected; the results should then be directly applicable to equation (I)

Unsteady Flow in Cavitating Turbopumps

Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characterisitcs of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasistatic analyses, is found to be complex and frequency dependent. It represents the primary effect of the fluctuating cavity in the system. The analysis is based on a linearized free streamline theory

A Note on the Unsteady Cavity Flow in a Tunnel

The unsteady internal cavitating flow such as the one observed in a pump or a turbine is studied for a simple two-dimensional model of a base-cavitating wedge in an infinite tunnel and it is shown how the cavitation compliance can be calculated using the linearized free streamline theory. Numerical values are obtained for the limiting case of a free jet. Two important features are: First, the cavitation compliance is found to be of complex form, having additional resistive and reactive terms beyond the purely inertial oscillation of the whole channel in "slug flow." Second, the compliance has a strong dependence on frequency

Computation of the radiation characteristics of a generalized phased array

With the advent of monolithic microwave integrated circuit (MMIC) technology, the phased array has become a key component in the design of advanced antenna systems. Array-fed antennas are used extensively in today's multiple beam satellite antennas. A computer program based on a very efficient numerical technique for calculating the radiated power (Romberg integration), directivity, and radiation pattern of a phased array is described. The formulation developed is very general, and takes into account arbitrary element polarization, E- and H-plane element pattern, element location, and complex element excitation. For comparison purposes sample cases have been presented. Excellent agreement has been obtained for all cases. Also included are a user guide and a copy of the computer program

Secondary pattern computation of an offset reflector antenna

Reflector antennas are widely used in communications satellite systems because they provide high gain at low cost. In analyzing reflector antennas the computation of the secondary pattern is the main concern. A computer program for calculating the secondary pattern of an offset reflector has been developed and implemented at the NASA Lewis Research Center. The theoretical foundation for this program is based on the use of geometrical optics to describe the fields from the feed to the reflector surface and to the aperture plane. The resulting aperture field distribution is then transformed to the far-field zone by the fast Fourier transform algorithm. Comparing this technique with other well-known techniques (the geometrical theory of diffraction, physical optics (Jacobi-Bessel), etc.) shows good agreement for large (diameter of 100 lambda or greater) reflector antennas

The Dynamic Performance of Cavitating Turbopumps

Knowledge of the dynamic performance of turbopumps is essential for the prediction of instabilities in hydraulic systems; the necessary information is in the form of a transfer function relating the instantaneous pressures and mass flow rates at inlet and discharge. Cavitation has a significant effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous flow rates. The present paper synthesizes the transfer matrix for cavitating inducers at moderately low frequencies and shows that the numerical results are consistent with observations on rocket engine turbopumps

A Brief Note on Linearized, Unsteady, Supercavitating Flows

Three different models for the unsteady fluctuations of a slender cavity in the limit of small reduced frequency are compard with the results of quasi-steady calculations. Tullin's kinematically closed model in unsteady flow in soon to tend smoothly to a limiting quasi-steady motion having the same value for the compliance of the cavitating flow, unlike other models that have been used in the past

The Dynamic Transfer Function for a Cavitating Inducer

Knowledge of the dynamic performance of pumps is essential for the prediction of transient behavior and instabilities in hydraulic systems; the necessary information is in the form of a transfer function which relates the instantaneous or fluctuating pressure and mass flow rate at inlet to the same quantities in the discharge from the pump. The presence of cavitation within the pump can have a major effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous inlet and discharge mass flow rates. The present paper utilizes results from free streamline cascade theory to evaluate the elements in the transfer function for a cavitating inducer and shows that the numerical results are consistent with the characteristics observed in some dynamic tests on rocket engine turbopumps