It is shown that the continuous spectra of both the temporal and spatial eigenvalues of the Orr–Sommerfeld equation for a Blasius flow can be re-interpreted as discrete spectra of the heat-conduction and diffraction types, respectively. Most of the general properties of the discrete spectrum of the Orr–Sommerfeld equation discovered by Mack can be understood on the basis of a simple model equation.

To characterize cryogenic pump performance, at least one parameter in addition to flow coefficient and cavitation number is required. This parameter arises because the heat of vaporization and other physical parameters change along the saturation line of liquids and results in a thermal effect on cavitation that has been observed and studied by previous researchers over a range of operating conditions and working fluids. These previous efforts have defined both dimensionless and dimensional parameters governing thermal effects in pumps. In the present work, a dimensionless parameter (DB) scaling thermal effects in a cavitating pump across different tip diameters, rotational speeds, and working fluids is derived using a model of bubble growth in a time-varying pressure field. Although the derivation is somewhat different than others have used, the result is similar and in some cases identical to that of others. Careful testing is carried out to experimentally validate this parameter with (deaerated) variable temperature water and with variable pump speed. The results show that within the accuracy of the data, the same head fall-off curve is obtained when either the water temperature or the pump speed is used to set the DBs. This suggests the proposed parameter can thermally scale cryogenic pumping conditions for suction performance when testing in hot water. Also examined is the effect of thermodynamics on inducer cavitation instabilities. The quasi-steady, dynamic environments at the pump inlet are compared in cold and superheated water. The cavitation instabilities of the test inducer are found to be dramatically changed by thermal effects. These findings emphasize the importance of considering both fluid mechanical and thermal scaling when designing a test program to evaluate the suction performance of a cryogenic pump.

A detailed study has been made of the solutions to cone boundary-layer equations in the symmetry plane in order to increase understanding of the mathematical nature and physical meaning of these solutions. A typical set of symmetry-plane solutions is presented. Included in this set are various solution branches not previously published. A double-valued solution curve is found which has not been studied prior to this time except at one trivial point. The extension of an existing solution branch through a removable singular point has also been accomplished. The solutions presented are categorized according to whether they are dependent on or independent of the boundary layer outside the symmetry plane. The region in which no solutions to the usual symmetry-plane equations exist is examined. Solutions in which the usual boundary-layer model predicts that conservation of mass is not satisfied at the symmetry plane are discussed. Non-analytical behaviour at the symmetry plane is also investigated. In both of these cases a boundary region exists at the symmetry plane.

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