Force and moment rotordynamic coefficients for pump-impeller shroud surfaces

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential - momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leaking rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face

The SSME HPFTP interstage seals: Analysis and experiments for leakage and reaction-force coefficients

An improved theory for the prediction of the rotordynamic coefficients of turbulent annular seals was developed. Predictions from the theory are compared to the experimental results and an approach for the direct calculation of empirical turbulent coefficients from test data are introduced. An improved short seal solution is shown to do a better job of calculating effective stiffness and damping coefficients than either the original short seal solution or a finite length solution. However, the original short seal solution does a much better job of predicting equivalent added mass coefficient

Black-box Hamiltonian simulation and unitary implementation

We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal.Comment: 19 pages, 3 figures, minor correction

Testing of turbulent seals for rotordynamic coefficients

A facility has been developed for dynamic testing of straight and convergent tapered seals with the capability of measuring the radial and tangential force components which result from a circular centered orbit. The test apparatus causes the seal journal to execute small-eccentricity centered circular orbits within its clearance circle. Dynamic measurements are made and recorded of the seal displacement-vector components, and of the pressure field. The pressure field is integrated to yield seal tangential and radial reaction-force components. Representative test data are provided and discussed for straight seals

Analysis and testing for rotordynamic coefficients of turbulent annular seals with different, directionally homogeneous surface-roughness treatment for rotor and stator elements

A theory is presented, based on a simple modification of Hirs' turbulent lubrication equations, to account for different but directionally-homogeneous surface roughness treatments for the rotor and stator of annular seals. The theoretical results agree with von Pragenau's predictions that a damper seal which uses a smooth rotor and a rough stator yields more net damping than a conventional seal which has the same roughness for both the rotor and stator. Experimental results for four stators confirm that properly-designed roughened stators yield higher net damping values and substantially less leakage than seals with smooth surfaces. The best seal from both damping and leakage viewpoints uses a round-hole-pattern stator. Initial results for this stator suggest that, within limits, seals can be designed to yield specified ratios of stiffness to damping

Influence of suction on shock wave-turbulent boundary layer interactions for two- dimensional and axially symmetric flows, 16 September 1967 - 30 June 1969

Influence of suction on shock wave turbulent boundary layer interactions for two dimensional and axially symmetric flow

An Investigation of the Role of Exchange Rates on U.S. Exports of Selected Agricultural Products: 1968-1983

An· econometric partial equilibrium trade model of the U.S. corn, wheat, soybean, cotton, and tobacco market is developed for the yearly periods 1968-1983. The effect of real exchange rates, real price, and demand factors on the exports of each commodity is examined to test the hypothesis that monetary factors can affect the agricultural sector. An examination of the elasticities of real price, real exchange rate, and real income indicate that an extremely inelastic response to both price movements and exchange rate adjustments. Foreign buying power is the strongest explanatory variable. An exchange rate linkage with the agricultural sector is not proven.International Relations/Trade,

An iwatsubo-based solution for labyrinth seals - comparison with experimental results

The basic equations are derived for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equation. The first-order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to published test results

Vibration characteristics of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine)

A review is presented of various rotordynamic problems which have been encountered and eliminated in developing the current flight engines, and continuing subsynchronous problems which are being encountered in developing a 109% power level engine. The basic model for the High Pressure Oxygen Turbopump (HPOTP) of the SSME including the structural dynamic model for the rotor and housing and component models for the liquid and gas seals, turbine-clearance excitation forces, and impeller-diffuser forces are discussed. Results from a linear model are used to examine the synchronous response and stability characteristics of the HPOTP, examining bearing load and stability problems associated with the second critical speed. Various seal modifications are examined and shown to have favorable consequences with respect to bearing reactions and stability