At present no analytical model is available for predicting the unsteady aerodynamic forces acting on staggered cascade blades subjected to transonic flow. The unsteady aerodynamic models for cascades developed so far are useful in the Mach number range of 0.0-0.9 and 1.1 and above. The objective of the present analysis is to develop an efficient model for obtaining unsteady aerodynamic forces in the neighborhood of Mach number = 1.0. An incremental annulus of blade row is represented by a rectilinear two-dimensional cascade of thin flat plate airfoils. The steady flow approaching the cascade is assumed to be transonic, irrotational, and inviscid. The equations of motion are derived using linearized transonic small perturbation theory. An analytical solution is obtained by using the Wiener-Hopf procedure. Unsteady aerodynamic forces and moments acting on the blades are obtained for Mach number = 1.0. Making use of transonic similarity law, the results of the present analysis are compared with the results obtained from other linearized cascade analyses. A parametric study is conducted to find the effects of reduced frequency, stagger angle, solidity, and location of pitching axis on cascade stability. Nomenclature a n = constant, Eq. (29) A',B' -constant, Eq. (A10) A 0 = amplitude of angular displacement A!, B j = constants b = blade semichord C' (CL),C_ (a) -functions, Eq. (43) d Q -distance between leading edge of blade and reference point G + ,G_ -functions, Eq. (A7) G+,G + -functions, Eq. (42) h Q ,h m -functions, Eq. (18) h±,h -functions, Eq. (38) and (39) H Q = amplitude of vertical displacement H + (a) -function, Eq. (Al) / -V -l Im -imaginary part k -reduced frequency k { -V2/A: k 2 =k/2 K(oi,rj) -function, Eq. (23) K + (a),K_ (a) -functions, Eq. (A5) L m,n M M, P Qn S s + ss gn t = nondimensional lift = summation indices = nondimensional moment = local Mach number = pressure = pressure for nonsummation and summation terms, Eq. (36) = function, Eq. (36) = distance between adjacent blades = signum function = timê functions, Eqs. (28-33) = freestream velocity

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)16-04-2008 REPORT TYPE Final Report DATES COVERED (From -To)1 January 2007 -25-Jun-09 TITLE AND SUBTITLECell-NPE (Numerical Performance Evaluation) 5a. CONTRACT NUMBER FA8655-07-1-3027 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER AUTHOR(S)Dr. Jochem H Hauser 5d. PROJECT NUMBER 5d. TASK NUMBER 5e. WORK UNIT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)HPCC-Space GmbH Karl-Scharfenbergstr. 55-57 Salzgitter 38229 Germany PERFORMING ORGANIZATION REPORT NUMBERN/A SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)EOARD Unit 4515 BOX 14 APO AE 09421 SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S)Grant 07-3027 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTThis report results from a contract tasking HPCC-Space GmbH as follows: B. TECHNICAL PRPOPOSA/DESCRIPTION OF WORK Cell: A Revolutionary High Performance Computing Platform On 29 June 2005 [1], IBM has announced that is has partnered with Mercury Computer Systems, a maker of specialized computers. The Cell chip provides massive floating-point capability and scalability for a variety of applications. It is a general-purpose processor and provides a high cost performance ratio (GFlops/$). In brief, it has the capability, because of its networking features, to provide a supercomputer in a nutshell.This signals an important shift in the computing industry away from the traditional processor technology dominated by Intel. While in the past, the development of computing power has been driven by desktop applications; gaming, and other data-intensive applications are now driving the performance gains in computing.A basic Cell processor is expected to deliver clock speeds of 4 GHz per core and contains nine cores, so it has about 10 times the processing power of a standard desktop PC processor. The applications that need that level of performance are mainly in the area of engineering and scientific computing. So far pricing was not revealed, but it is believed that the Cell will cost about $30 in game consoles. The average PC processor today costs about $150 to ...