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At least 1,171 records · Page 65

Implicit hybrid schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗

Generation of a composite grid for turbine flows and consideration of a numerical scheme

A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

Choo, Y.↗

The early archaean crustal history of West Greenland as recorded by detrital zircons

The isotope systematics of some of the oldest samples on Earth from both Greenland and Australia was discussed. The antiquity was confirmed of the 4.1 to 4.2 Ga zircons from Western Australia; the model Lu-Hf age of these zircons, as measured with the ANU ion probe is 4.14 + or - 0.24 Ga, although the oldest preserved rock units there are anorthosites with a Lu-Hf model age of about 3.73 Ga. U-Pb ion probe ages of detrital zircons ranging between 2.87 and 3.89 Ga from an Akilia association quartzite was reported, whose age of deposition is probably around 3.8 Ga. It was argued that the younger age in this range are discordant because of late Pb-loss, probably associated with a high grade metamorphic event at about 3.6 Ga. It was also argued that the earliest crust in West Greenland and elsewhere is about 3.9 Ga, but in some places, such as Western Australia, crustal evolution took place much earlier, perhaps starting as far back as 4.3 Ga. This would account for the presence in that terrane of abundant K rich granitoid, the paucity of tonalitic and trondhjemitic materials, and the existence of Eu anomalies in early Archean sediments.

Kinny, P. D.↗

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

Choo, Yung K.↗

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a turbine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of dependence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

Choo, Yung K.↗

A diagonal implicit scheme for computing flows with finite-rate chemistry

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Eberhardt, Scott↗

Recent update of the RPLUS2D/3D codes

The development of the RPLUS2D/3D codes is summarized. These codes utilize LU algorithms to solve chemical non-equilibrium flows in a body-fitted coordinate system. The motivation behind the development of these codes is the need to numerically predict chemical non-equilibrium flows for the National AeroSpace Plane Program. Recent improvements include vectorization method, blocking algorithms for geometric flexibility, out-of-core storage for large-size problems, and an LU-SW/UP combination for CPU-time efficiency and solution quality.

Tsai, Y.-L. Peter↗

Implicit treatment of diffusion terms in lower-upper algorithms

A method is presented which allows diffusion terms to be treated implicitly in the lower-upper (LU) algorithm (which is a commonly used method for solving 'compressible' Euler and Navier-Stokes equations) so that the algorithm's good stability properties will not be impaired. The new method generalizes the concept of LU factorization from that associated with the sign of eigenvalues to that associated with backward- and forward-difference operators without regard to eigenvalues. The method is verified in a turbulent boundary layer study.

Shih, T. I.-P.↗

Aeroacoustic sensitivity analysis and optimal aeroacoustic design of turbomachinery blades

During the first year of the project, we have developed a theoretical analysis - and wrote a computer code based on this analysis - to compute the sensitivity of unsteady aerodynamic loads acting on airfoils in cascades due to small changes in airfoil geometry. The steady and unsteady flow though a cascade of airfoils is computed using the full potential equation. Once the nominal solutions have been computed, one computes the sensitivity. The analysis takes advantage of the fact that LU decomposition is used to compute the nominal steady and unsteady flow fields. If the LU factors are saved, then the computer time required to compute the sensitivity of both the steady and unsteady flows to changes in airfoil geometry is quite small. The results to date are quite encouraging, and may be summarized as follows: (1) The sensitivity procedure has been validated by comparing the results obtained by 'finite difference' techniques, that is, computing the flow using the nominal flow solver for two slightly different airfoils and differencing the results. The 'analytic' solution computed using the method developed under this grant and the finite difference results are found to be in almost perfect agreement. (2) The present sensitivity analysis is computationally much more efficient than finite difference techniques. We found that using a 129 by 33 node computational grid, the present sensitivity analysis can compute the steady flow sensitivity about ten times more efficiently that the finite difference approach. For the unsteady flow problem, the present sensitivity analysis is about two and one-half times as fast as the finite difference approach. We expect that the relative efficiencies will be even larger for the finer grids which will be used to compute high frequency aeroacoustic solutions. Computational results show that the sensitivity analysis is valid for small to moderate sized design perturbations. (3) We found that the sensitivity analysis provided important insight into how airfoils should be modified to improve their aeroelastic stability. Using this insight, we redesigned an aeroelastically unstable cascade to produce a stable cascade.

Hall, Kenneth C.↗

Experimental Study of Vane Heat Transfer and Aerodynamics at Elevated Levels of Turbulence

A four vane subsonic cascade was used to investigate how free stream turbulence influences pressure surface heat transfer. A simulated combustor turbulence generator was built to generate high level (13 percent) large scale (Lu approximately 44 percent inlet span) turbulence. The mock combustor was also moved upstream to generate a moderate level (8.3 percent) of turbulence for comparison to smaller scale grid generated turbulence (7.8 percent). The high level combustor turbulence caused an average pressure surface heat transfer augmentation of 56 percent above the low turbulence baseline. The smaller scale grid turbulence produced the next greatest effect on heat transfer and demonstrated the importance of scale on heat transfer augmentation. In general, the heat transfer scaling parameter U(sub infinity) TU(sub infinity) LU(sub infinity)(exp -1/3) was found to hold for the turbulence. Heat transfer augmentation was also found to scale approximately on Re(sub ex)(exp 1/3) at constant turbulence conditions. Some evidence of turbulence intensification in terms of elevated dissipation rates was found along the pressure surface outside the boundary layer. However, based on the level of dissipation and the resulting heat transfer augmentation, the amplification of turbulence has only a moderate effect on pressure surface heat transfer. The flow field turbulence does drive turbulent production within the boundary layer which in turn causes the high levels of heat transfer augmentation. Unlike heat transfer, the flow field straining was found to have a significant effect on turbulence isotropy. On examination of the one dimensional spectra for u' and v', the effect to isotropy was largely limited to lower wavenumber spectra. The higher wavenumber spectra showed little or no change. The high level large scale turbulence was found to have a strong influence on wake development. The free stream turbulence significantly enhanced mixing resulting in broader and shallower wakes than the baseline case. High levels of flow field turbulence were found to correlate with a significant increase in total pressure loss in the core of the flow. Documenting the wake growth and characteristics provides boundary conditions for the downstream rotor.

Ames, Forrest E.↗

Properties of acoustic sources in the Sun

The power spectrum of solar acoustic oscillations shows peaks extending out to frequencies much greater than the acoustic cutoff frequency of approximately 5.3 mHz, where waves are no longer trapped. Kumar & Lu (1991) proposed that these peaks arise from the interference of traveling waves which are generated by turbulent convection. According to this model, the frequencies of the peaks in the power spectrum depend on the static structure of the Sun as well as the radial location of the sources. Kumar & Lu used this idea to determine the depth of the acoustic sources. However, they ignored dissipative effects and found that the theoretically computed power spectrum was falling off much more rapidly than the observed spectrum. In this paper, we include the interaction of radiation with acoustic waves in the computation of the power spectrum. We find that the theoretically calculated power spectra, when radiative damping is included are in excellent agreement with the observed power spectra over the entire observed frequency range of 5.3 to 7.5 mHz above the acoustic cutoff frequency. Moreover, by matching the peak frequencies in the observed and theoretical spectra we find the mean depth of acoustic sources to be 140 +/- 60 km below the photosphere. We show that the spectrum of solar turbulence near the top of the solar convection zone is consistent with the Kolmogorov spectrum, and that the observed high frequency power spectrum provides strong evidence that the acoustic sources in the Sun are quadrupolar. The data, in fact, rules out dipole sources as significant contributors to acoustic wave generation in the Sun. The radial extent of the sources is poorly determined and is estimated to be less than about 550 km.

Kumar, Pawan↗

Data-parallel lower-upper relaxation method for reacting flows

The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method of Yoon and Jameson is modified for use on massively parallel computers. The method has been implemented on the Thinking Machines CM-5 and the MasPar MP-1 and MP-2, where large percentages of the theoretical peak floating point performance are obtained. It is shown that the new data-parallel LU relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations. The convergence is also improved for five-species reacting air computations. The performance of the method on various partitions of the CM-5 and on the MasPar computers is discussed. The new method shows promise for the efficient simulation of very large perfect gas and reacting flows.

Candler, Graham V.↗

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗

Efficient Helicopter Aerodynamic and Aeroacoustic Predictions on Parallel Computers

This paper presents parallel implementations of two codes used in a combined CFD/Kirchhoff methodology to predict the aerodynamics and aeroacoustics properties of helicopters. The rotorcraft Navier-Stokes code, TURNS, computes the aerodynamic flowfield near the helicopter blades and the Kirchhoff acoustics code computes the noise in the far field, using the TURNS solution as input. The overall parallel strategy adds MPI message passing calls to the existing serial codes to allow for communication between processors. As a result, the total code modifications required for parallel execution are relatively small. The biggest bottleneck in running the TURNS code in parallel comes from the LU-SGS algorithm that solves the implicit system of equations. We use a new hybrid domain decomposition implementation of LU-SGS to obtain good parallel performance on the SP-2. TURNS demonstrates excellent parallel speedups for quasi-steady and unsteady three-dimensional calculations of a helicopter blade in forward flight. The execution rate attained by the code on 114 processors is six times faster than the same cases run on one processor of the Cray C-90. The parallel Kirchhoff code also shows excellent parallel speedups and fast execution rates. As a performance demonstration, unsteady acoustic pressures are computed at 1886 far-field observer locations for a sample acoustics problem. The calculation requires over two hundred hours of CPU time on one C-90 processor but takes only a few hours on 80 processors of the SP2. The resultant far-field acoustic field is analyzed with state of-the-art audio and video rendering of the propagating acoustic signals.

Wissink, Andrew M.↗

Numerical Procedures for Inlet/Diffuser/Nozzle Flows

Two primitive variable, pressure based, flux-split, RNS/NS solution procedures for viscous flows are presented. Both methods are uniformly valid across the full Mach number range, Le., from the incompressible limit to high supersonic speeds. The first method is an 'optimized' version of a previously developed global pressure relaxation RNS procedure. Considerable reduction in the number of relatively expensive matrix inversion, and thereby in the computational time, has been achieved with this procedure. CPU times are reduced by a factor of 15 for predominantly elliptic flows (incompressible and low subsonic). The second method is a time-marching, 'linearized' convection RNS/NS procedure. The key to the efficiency of this procedure is the reduction to a single LU inversion at the inflow cross-plane. The remainder of the algorithm simply requires back-substitution with this LU and the corresponding residual vector at any cross-plane location. This method is not time-consistent, but has a convective-type CFL stability limitation. Both formulations are robust and provide accurate solutions for a variety of internal viscous flows to be provided herein.

Rubin, Stanley G.↗

STS-106 Crew Activities Report/Flight Day 05 Highlights

On this fifth day of the STS-106 Atlantis mission, the flight crew, Commander Terrence W. Wilcutt, Pilot Scott D. Altman, and Mission Specialists Daniel C. Burbank, Edward T. Lu, Richard A. Mastracchio, Yuri Ivanovich Malenchenko, and Boris V. Morukov are seen participating in several activities. Malenchenko and Wilcutt are seen opening the hatches of the Zvezda Service Module and the Zarya Control Module, and finally, the transfer chamber of Zvezda, Progress. Burbank and Mastracchio are seen transferring food and equipment, and removing the manual docking system of Zarya. Lu, Burbank and Malenchenko are also seen checking the hatch interfaces. Footage also shows the entire interior of the International Space Station (ISS) complex.

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Comparative Magma Oceanography

The question of whether the Earth ever passed through a magma ocean stage is of considerable interest. Geochemical evidence strongly suggests that the Moon had a magma ocean and the evidence is mounting that the same was true for Mars. Analyses of martian (SNC) meteorites have yielded insights into the differentiation history of Mars, and consequently, it is interesting to compare that planet to the Earth. Three primary features of Mars contrast strongly to those of the Earth: (i) the extremely ancient ages of the martian core, mantle, and crust (about 4.55 b.y.); (ii) the highly depleted nature of the martian mantle; and (iii) the extreme ranges of Nd isotopic compositions that arise within the crust and depleted mantle. The easiest way to explain the ages and diverse isotopic compositions of martian basalts is to postulate that Mars had an early magma ocean. Cumulates of this magma ocean were later remelted to form the SNC meteorite suite and some of these melts assimilated crustal materials enriched in incompatible elements. The REE pattern of the crust assimilated by these SNC magmas was LREE enriched. If this pattern is typical of the crust as a whole, the martian crust is probably similar in composition to melts generated by small degrees of partial melting (about 5%) of a primitive source. Higher degrees of partial melting would cause the crustal LREE pattern to be essentially flat. In the context of a magma ocean model, where large degrees of partial melting presumably prevailed, the crust would have to be dominated by late-stage, LREE-enriched residual liquids. Regardless of the exact physical setting, Nd and W isotopic evidence indicates that martian geochemical reservoirs must have formed early and that they have not been efficiently remixed since. The important point is that in both the Moon and Mars we see evidence of a magma ocean phase and that we recognize it as such. Several lines of theoretical inference point to an early Earth that was also hot and, perhaps, mostly molten. The Giant Impact hypothesis for the origin of the Moon offers a tremendous input of thermal energy and the same could be true for core formation. And current solar system models favor the formation of a limited number of large (about 1000 km) planetesimals that, upon accreting to Earth, would cause great heating, being lesser versions of the Giant Impact. Several lines of geochemical evidence do not favor this hot early Earth scenario. (i) Terrestrial man-tle xenoliths are sometimes nearly chondritic in their major element compositions, suggesting that these rocks have never been much molten. Large degrees of partial melting probably promote differentiation rather than homogenization. (ii) Unlike the case of Mars, the continental crust probably did not form as a highly fractionated residual liquid from a magma ocean (about 99% crystallization), but, rather, formed in multiple steps. [The simplest model for the formation of continental crust is complicated: (a) about 10% melting of a primitive mantle, making basalt; (b) hydrothermal alteration of that basalt, converting it to greenstone; and (c) 10% partial melting of that greenstone, producing tonalite.] This model is reinforced by the recent observation from old (about 4.1 b.y.) zircons that the early crust formed from an undepleted mantle having a chondritic Lu/Hf ratio. (iii) If the mantle were once differentiated by a magma ocean, the mantle xenolith suite requires that it subsequently be homogenized. The Os isotopic compositions of fertile spinel lherzolites place constraints on the timing of that homogenization. The Os isotopic composition of spinel lherzolites approaches that of chondrites and correlates with elements such as Lu and Al. As Lu and Al concentrations approach those of the primitive mantle, Os isotopic compositions approach chondritic. The Re and Os in these xenoliths were probably added as a late veneer. Thus, the mantle that received the late veneer must have been nearly chondritic in terms of its major elements (excluding Fe). If the mantle that the veneer was mixed into was not al-ready homogenized, then Os isotopes should not correlate with incompatible elements such as Al. Consequently, either early differentiation of the mantle did not occur or the homogenization of this differentiation must have occurred before the late veneer was added. The timing of the late veneer is itself uncertain but presumably postdated core formation at about 4.45 b.y. and did not postdate the 3.8-3.9 b.y. late bombardment of the Moon. This timing based on siderophile elements is consistent with the Hf isotopic evidence cited above. If the Earth, Moon and Mars had magma oceans, the Earth subsequently rehomogenized whereas the Moon and Mars did not. The simplest solution to this observation is that homogenization of igneous differentiates was never necessary on Earth, either because the hypothetical magma ocean never occurred or because this event did not produce mantle differentiation.

Jones, J. H.↗

STS-106 Crew Activities Report/Flight Day 06 Highlights

On this sixth day of the STS-106 Atlantis mission, the flight crew, Commander Commander Terrence W. Wilcutt, Pilot Scott D. Altman, and Mission Specialists Daniel C. Burbank, Edward T. Lu, Richard A. Mastracchio, Yuri Ivanovich Malenchenko, and Boris V. Morukov are seen participating in several outfitting and transferring activities. Burbank and Morukov replace batteries in Zarya, while Lu and Malenchenko install three batteries and electrical equipment inside the Zvezda Service Module. Footage of Wilcutt participating in an interview concludes the events of the day.

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