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At least 1,693 records · Page 94

Three-dimensional inviscid analysis of radial-turbine flow and a limited comparison with experimental data

The three-dimensional inviscid DENTON code is used to analyze flow through a radial-inflow turbine rotor. Experimental data from the rotor are compared with analytical results obtained by using the code. The experimental data available for comparison are the radial distributions of circumferentially averaged values of absolute flow angle and total pressure downstream of the rotor exit. The computed rotor-exit flow angles are generally underturned relative to the experimental values, which reflect the boundary-layer separation at the trailing edge and the development of wakes downstream of the rotor. The experimental rotor is designed for a higher-than-optimum work factor of 1.126 resulting in a nonoptimum positive incidence and causing a region of rapid flow adjustment and large velocity gradients. For this experimental rotor, the computed radial distribution of rotor-exit to turbine-inlet total pressure ratios are underpredicted due to the errors in the finite-difference approximations in the regions of rapid flow adjustment, and due to using the relatively coarser grids in the middle of the blade region where the flow passage is highly three-dimensional. Additional results obtained from the three-dimensional inviscid computation are also presented, but without comparison due to the lack of experimental data. These include quasi-secondary velocity vectors on cross-channel surfaces, velocity components on the meridional and blade-to-blade surfaces, and blade surface loading diagrams. Computed results show the evolution of a passage vortex and large streamline deviations from the computational streamwise grid lines. Experience gained from applying the code to a radial turbine geometry is also discussed.

Choo, Y. K.↗

Two-Dimensional Ffowcs Williams/Hawkings Equation Solver

FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.

Lockard, David P.↗

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗

Computation of the tip vortex flowfield for advanced aircraft propellers

The tip vortex flowfield plays a significant role in the performance of advanced aircraft propellers. The flowfield in the tip region is complex, three-dimensional and viscous with large secondary velocities. An analysis is presented using an approximate set of equations which contains the physics required by the tip vortex flowfield, but which does not require the resources of the full Navier-Stokes equations. A computer code was developed to predict the tip vortex flowfield of advanced aircraft propellers. A grid generation package was developed to allow specification of a variety of advanced aircraft propeller shapes. Calculations of the tip vortex generation on an SR3 type blade at high Reynolds numbers were made using this code and a parametric study was performed to show the effect of tip thickness on tip vortex intensity. In addition, calculations of the tip vortex generation on a NACA 0012 type blade were made, including the flowfield downstream of the blade trailing edge. Comparison of flowfield calculations with experimental data from an F4 blade was made. A user's manual was also prepared for the computer code (NASA CR-182178).

Tsai, Tommy M.↗

Renormalization group methods for the Reynolds stress transport equations

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Rubinstein, R.↗

Multigrid calculation of internal flows in complex geometries

The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.

Smith, K. M.↗

On the calculation of turbulent heat and mass transport downstream from an abrupt pipe expansion

A numerical study is reported of heat/mass transfer in the separated flow region created by an abrupt pipe expansion. Computations have employed a hybrid method of central and upwind finite differencing to solve the full Navier-Stokes equations with turbulent model (k approximately equal to epsilon). The study has given its main attention to the simulation of the region in the immediate vicinity of the wall, by formulating near-wall model for the evaluation of the mean generation and destruction rate of the epsilon equation. The computed results were compared with the experimental data and they showed generally encouraging agreement with the measurements.

Amano, R. S.↗

An efficient solution technique for shockwave-boundary layer interactions with flow separation and slot suction effects

An efficient method for computing two-dimensional compressible Navier-Stokes flow fields is presented. The solution algorithm is a fully-implicit approximate factorization technique based on an unsymmetric line Gauss-Seidel splitting of the equation system Jacobian matrix. Convergence characteristics are improved by the addition of acceleration techniques based on Shamanskii's method for nonlinear equations and Broyden's quasi-Newton update. Characteristic-based differencing of the equations is provided by means of Van Leer's flux vector splitting. In this investigation, emphasis is placed on the fast and accurate computation of shock-wave-boundary layer interactions with and without slot suction effects. In the latter context, a set of numerical boundary conditions for simulating the transpiration flow in an open slot is devised. Both laminar and turbulent cases are considered, with turbulent closure provided by a modified Cebeci-Smith algebraic model. Comparisons with computational and experimental data sets are presented for a variety of interactions, and a fully-coupled simulation of a plenum chamber/inlet flowfield with shock interaction and suction is also shown and discussed.

Edwards, Jack R.↗

Application of an Upwind High Resolution Finite-Differencing Scheme and Multigrid Method in Steady-State Incompressible Flow Simulations

The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.

NAVIER STOKES EQUATIONS↗

A FORTRAN computer code for calculating flows in multiple-blade-element cascades

A solution technique has been developed for solving the multiple-blade-element, surface-of-revolution, blade-to-blade flow problem in turbomachinery. The calculation solves approximate flow equations which include the effects of compressibility, radius change, blade-row rotation, and variable stream sheet thickness. An integral equation solution (i.e., panel method) is used to solve the equations. A description of the computer code and computer code input is given in this report.

Mcfarland, E. R.↗

Spectral variation of high power microwave pulse propagating in a self-generated plasma

A systematic study to understand the spectral variation of a high power microwave pulse propagating in a self-generated plasma is carried out. It includes the theoretical formulation, experimental demonstration, and computer simulations and computer experiments. The experiment of pulse propagation is conducted in a vacuum chamber filled with dry air (approximately 0.2 torr); the chamber is made of a 2 ft. cube of Plexiglas. A rectangular microwave pulse (1 microsec pulse width and 3.27 GHz carrier frequency) is fed into the cube through an S band microwave horn placed at one side of the chamber. A second S-band horn placed at the opposite side of the chamber is used to receive the transmitted pulse. The spectra of the incident pulse and transmitted pulse are then compared. As the power of the incident pulse is only slightly (less than 15%) above the breakdown threshold power of the background air, the peak of the spectrum of the transmitted pulse is upshifted from the carrier frequency 3.27 GHz of the incident pulse. However, as the power of the incident pulse exceeds the breakdown threshold power of the background air by 30%, a different phenomenon appears. The spectrum of the transmitted pulse begins to have two peaks. One is upshifted and the other one downshifted from the single peak location of the incident pulse. The amount of frequency downshift is comparable to that of the upshifted frequency. A theoretical model describing the experiment of pulse propagation in a self-generated plasma is developed. There are excellent agreements between the experimental results and computer simulations based on this theoretical model, which is also used to further carry out computer experiments identifying the role of plasma introduced wave loss on the result of frequency downshift phenomenon.

Ren, A.↗

Aerothermal Analysis of the Rocket Lab Venus Probe Heatshield

This document provides an overview of the aerothermodynamic analyses performed by the Aerothermodynamics Branch at NASA Langley Research Center for the Rocket Lab Venus Probe (RLVP). In addition to defining the baseline heating environment to the heatshield, this document pursues the experimental validation of key physical models at RLVP-relevant conditions. This experimental validation analysis, which captures the model form uncertainty, is used as one of two primary components of the margin assessment, where the other component is the parametric uncertainty. These model form (experimental) and parametric uncertainty components are used to construct a spatial and time varying margin for the heating to the RLVP heatshield. The margin is evaluated as the sum of the parametric and model form uncertainty components. The model form uncertainty is defined as the difference between the RLVP-relevant measurements and their simulations, using the upper limit uncertainty bounds for both the measurements and simulations in the comparisons. The differences in the dominant physics in the stagnation region and flank lead to the separate RLVP-relevant measurements for assessing the model form uncertainty in these two regions. These regions are addressed as follows: Stagnation Region Heating Environment: For the high-temperature stagnation-region, both the radiative heating and impact of blowing on convective heating are significant, while the impacts of turbulence and roughness are negligible. Coupled radiation and ablation LAURA/HARA solutions with ray-tracing provide the radiative heating over the entire vehicle, including the contributions from the Venus atmosphere and ablation species. Non-ablating LAURA simulations provide the convective heating. During the material-response computation typically used for TPS sizing, this non-ablating convective heating is corrected for the impact of ablation using the blowing correction. Coupled ablation LAURA simulations that capture finite-rate sur-face processes show that this blowing correction may be non-conservative over most of the heatshield. This non-conservatism is due to hydrogen recombination in the finite-rate surface model, which tends to increase the coupled ablation convective heating to near the non-ablating values, therefore making any reduction in the non-ablating value through the blowing correction non-conservative. This non-conservatism due to H catalysis is captured in the parametric component of the margin. The best available ground-test measurements that capture the impact of blowing on stagnation region convective heating, at RLVP-relevant conditions, indicate that the current blowing reduction model is non-conservative by up to 20% at RLVP-relevant blowing rates (the coupled blowing simulations were also non-conservative). Because of the relatively low velocity of the ground tests and the non-Venus atmospheric chemistry, these measurements do not capture the chemistry and therefore do not inform the uncertainty due to H catalysis. However, they do capture the fluid mechanics of blowing. The non-conservatism of the blowing correction implied by these measurements is covered by the model form component of the margin, which leads to total margin values over 50%. For the radiative heating, the shock-tube informed bias approach suggests a model form uncertainty of roughly 20%, while the parametric uncertainty analysis suggests values over 100%. The combined stagnation-point radiation margin of over 100% leads to peak margined radiative heating values of over300 W/cm2, which remains small relative to the peak margined convective heating of nearly 2000 W/cm2. Based on this analysis, at the stagnation point, the peak margined heat rate is 2203 W/cm2 and the margined total heat load is 31.5 kJ/cm2 for the current nominal trajectory. Flank Heating Environment: The forebody flank (and near-shoulder) heating environment is dominated by the impact of turbulence, roughness augmentation, and ablation on the convective heating. An extensive collection of ground test measurements with RLVP-relevant turbulence and roughness is studied to show that the maximum difference between the simulated and measured convective heating is 5%. However, with the exception of the Holden measurements from the 1980s, these measurements do not include roughness elements extending into the supersonic region of the boundary layer, which is likely to occur for RLVP (due to the 45 degree sphere-cone geometry). The interaction between the supersonic flow and roughness could cause convective heating augmentation fundamentally different than for locally subsonic flow. Although these Holden measurements are consistent with the other measurements considered, another path was pursued to assure that the rough-ness height extending into supersonic flow does not fundamentally change the roughness augmentation. This additional path was a computational effort to resolve the roughness elements in the CFD grid, so that the interaction be-tween the roughness elements and locally supersonic flow may be simulated in detail. This roughness-resolved CFD simulation is feasible because of the RLVP forebody TPS’s patterned roughness, which may be approximated analytically, and because of the axisymmetric nominal flow field, which allows a narrow surface region to be simulated and therefore make the computational expense feasible. These grid-resolved roughness simulations, which are performed at actual RLVP flight conditions, result in heating augmentation values that are below the design approach for roughness augmentation. This provides evidence that the design approach for RLVP roughness augmentation is sufficient. Based on this analysis, at this flank or near-shoulder location, the peak margined total heat rate is 2088 W/cm2and the margined total heat load is 26.0 kJ/cm2for the current nominal trajectory. Heat flux, shear, pressure and heat transfer coefficient at the RLVP stagnation point and near shoulder location are evaluated for the entire trajectory, and curved fit to a functional form of F=AρB∞UC∞. These simplified relationships for the nominal and margined aerothermal environments are referred to as aerothermal indicators, and presented at the end of this document.

Christopher O Johnston↗

Deep galaxy counts in the K band with the Kech telescope

We present deep galaxy counts in the K (lambda 2.2 micrometer) band, obtained at the W. M. Kech 10 m telescope. The data reach limiting magnitudes K approximately 24 mag, about 5 times deeper than the deepest published K-band images to date. The counts are performed in three small (approximately 1 min), widely separated high-latitude fields. Extensive Monte Carlo tests were used to derive the comleteness corrections and minimize photometric biases. The counts continue to rise, with no sign of a turnover, down to the limits of our data, with the logarithmic slope of d log N/dm = 0.315 +/- 0.02 between K = 20 and 24 mag. This implies a cumulative surface density of approximately 5 x 10(exp 5) galaxies/sq deg, or approximately 2 x 10(exp 10) over the entire sky, down to K = 24 mag. Our counts are in good agreement with, although slightly lower than, those from the Hawaii Deep Survey by Cowie and collaborators; the discrepancies may be due to the small differences in the aperture corrections. We compare our counts with some of the available theoretical predictions. The data do not require models with a high value of Omega(sub 0), but can be well fitted by models with no (or little) evolution, and cosmologies with a low value of Omega(sub 0). Given the uncertainties in the models, it may be premature to put useful constrains on the value of Omega(sub 0) from the counts alone. Optical-to-IR colors are computed, using CCD data obtaind previously at Palomar. We find a few red galaxies with (r-K) approximately greater than 5 mag, or (i-K) approximately greater than 5 mag; these may be ellipticals at z approximately 1. While the redshift distribution of galaxies in our counts is still unknown, the flux limits reached would allow us to detect unobscured L(sub *) galaxies out to substantial redshifts (z greater than 3?).

Djorgovski, S.↗

Application of Reduced Order Transonic Aerodynamic Influence Coefficient Matrix for Design Optimization

Supporting the Aeronautics Research Mission Directorate guidelines, the National Aeronautics and Space Administration [NASA] Dryden Flight Research Center is developing a multidisciplinary design, analysis, and optimization [MDAO] tool. This tool will leverage existing tools and practices, and allow the easy integration and adoption of new state-of-the-art software. Today s modern aircraft designs in transonic speed are a challenging task due to the computation time required for the unsteady aeroelastic analysis using a Computational Fluid Dynamics [CFD] code. Design approaches in this speed regime are mainly based on the manual trial and error. Because of the time required for unsteady CFD computations in time-domain, this will considerably slow down the whole design process. These analyses are usually performed repeatedly to optimize the final design. As a result, there is considerable motivation to be able to perform aeroelastic calculations more quickly and inexpensively. This paper will describe the development of unsteady transonic aeroelastic design methodology for design optimization using reduced modeling method and unsteady aerodynamic approximation. The method requires the unsteady transonic aerodynamics be represented in the frequency or Laplace domain. Dynamically linear assumption is used for creating Aerodynamic Influence Coefficient [AIC] matrices in transonic speed regime. Unsteady CFD computations are needed for the important columns of an AIC matrix which corresponded to the primary modes for the flutter. Order reduction techniques, such as Guyan reduction and improved reduction system, are used to reduce the size of problem transonic flutter can be found by the classic methods, such as Rational function approximation, p-k, p, root-locus etc. Such a methodology could be incorporated into MDAO tool for design optimization at a reasonable computational cost. The proposed technique is verified using the Aerostructures Test Wing 2 actually designed, built, and tested at NASA Dryden Flight Research Center. The results from the full order model and the approximate reduced order model are analyzed and compared.

Pak, Chan-gi↗

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Baysal, Oktay↗