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At least 73 records · Page 4

Prediction of unsteady aerodynamic loads in cascades using the linearized Euler equations on deforming grids

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) flow plus an unsteady, harmonically varying, small disturbance flow. Linear variable coefficient equations describe the small disturbance behavior of the flow, and are solved using a pseudo-time marching Lax-Wendroff scheme. For the blade motion problem, a harmonically deforming computational rid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition. The paper also presents a new, numerically exact, nonreflecting far-field boundary condition based on an eigenanalysis of the discretized equations. Computed flow solutions demonstrate the computational accuracy and efficiency of the present method. The solution of the linearized Euler equations requires one to two orders of magnitude less computer time than solution of the nonlinear Euler equations using traditional time-accurate time-marching techniques. In addition, the deformable grid significantly improves the accuracy of the solution.

Hall, Kenneth C.↗

Multigrid calculation of three-dimensional viscous cascade flows

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

Multigrid calculation of three-dimensional viscous cascade flows

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

An effective multigrid method for high-speed flows

The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for 2-D laminar flow over a circular cylinder and a 15 deg compression ramp.

Swanson, R. C.↗

A Navier-Stokes solver for turbomachinery applications

A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

Arnone, A.↗

Viscous analysis of three-dimensional rotor flows using a multigrid method

A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

Arnone, A.↗

Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

Jawerth, Bjoern↗

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Clark, William S.↗

Prediction of Film Cooling on Gas Turbine Airfoils

A three-dimensional Navier-Stokes analysis tool has been developed in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine airfoils. An existing code (Arnone et al., 1991) has been modified for the purpose. The code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. Eigenvalue scaled artificial dissipation and variable-coefficient implicit residual smoothing are used with a full-multigrid technique. Moreover, Mayle's transition criterion (Mayle, 1991) is used. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the airfoil surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison is fair with near mid-span experimental data for four and nine rows of cooling holes, five on the shower head, and two rows each on the pressure and suction surfaces. The computations, however, show a strong spanwise variation of the heat transfer coefficient on the airfoil surface, specially with shower-head cooling.

Garg, Vijay K.↗

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.

Winckelmans, G. S.↗

Modulated Entry

The technique of modulation, or variable coefficients, is discussed and the analytical formulation is reviewed. Representative numerical results of the use of modulation are shown for the lifting and nonlifting cases. These results include the effects of modulation on peak acceleration, entry corridor, and heat absorption. Results are given for entry at satellite speed and escape speed. The indications are that coefficient modulation on a vehicle with good lifting capability offers the possibility of sizable loading reductions or, alternatively, wider corridors; thus, steep entries become practical from the loading standpoint. The amount of steepness depends on the acceptable heating penalty. The price of sizable fractions of the possible gains does not appear to be excessive.

Grant, Frederick C.↗

Integrating Matrix Method for Determining the Natural Vibrations of a Rotating, Unsymmetrical Beam with Application to Twisted Propeller Blades

A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.

Hunter, William F.↗

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

Zhang, Jun↗

Development of an Objective Space Suit Mobility Performance Metric Using Metabolic Cost and Functional Tasks

Existing methods for evaluating EVA suit performance and mobility have historically concentrated on isolated joint range of motion and torque. However, these techniques do little to evaluate how well a suited crewmember can actually perform during an EVA. An alternative method of characterizing suited mobility through measurement of metabolic cost to the wearer has been evaluated at Johnson Space Center over the past several years. The most recent study involved six test subjects completing multiple trials of various functional tasks in each of three different space suits; the results indicated it was often possible to discern between different suit designs on the basis of metabolic cost alone. However, other variables may have an effect on real-world suited performance; namely, completion time of the task, the gravity field in which the task is completed, etc. While previous results have analyzed completion time, metabolic cost, and metabolic cost normalized to system mass individually, it is desirable to develop a single metric comprising these (and potentially other) performance metrics. This paper outlines the background upon which this single-score metric is determined to be feasible, and initial efforts to develop such a metric. Forward work includes variable coefficient determination and verification of the metric through repeated testing.

Norcross, J. R.↗

Development of an Objective Space Suit Mobility Performance Metric Using Metabolic Cost and Functional Tasks

Existing methods for evaluating EVA suit performance and mobility have historically concentrated on isolated joint range of motion and torque. However, these techniques do little to evaluate how well a suited crewmember can actually perform during an EVA. An alternative method of characterizing suited mobility through measurement of metabolic cost to the wearer has been evaluated at Johnson Space Center over the past several years. The most recent study involved six test subjects completing multiple trials of various functional tasks in each of three different space suits; the results indicated it was often possible to discern between different suit designs on the basis of metabolic cost alone. However, other variables may have an effect on real-world suited performance; namely, completion time of the task, the gravity field in which the task is completed, etc. While previous results have analyzed completion time, metabolic cost, and metabolic cost normalized to system mass individually, it is desirable to develop a single metric comprising these (and potentially other) performance metrics. This paper outlines the background upon which this single-score metric is determined to be feasible, and initial efforts to develop such a metric. Forward work includes variable coefficient determination and verification of the metric through repeated testing.

McFarland, Shane M.↗

Towards an Enhanced Droplet Activation Scheme for Multi-Moment Bulk Microphysics Schemes

Initial droplet spectra produced upon activation impact the ensuing chain of microphysical processes andtherefore play a crucial role in cloud evolution. This work re-examines dependencies of newly formed clouddroplet size distribution (CDSD) characteristics on environmental and aerosol properties via parcel model simulationsthat serve as the basis for a multi-moment bulk microphysics droplet activation scheme suitable for acloud-resolving model (CRM). It is found that applying a fixed size threshold to define activated droplets versusemploying physical considerations can lead to erroneous activation and overly broad CDSDs for high aerosolconcentration and weak updraft conditions. Aerosol distributions characterized by larger median sizes and/orincreased solubility can result in greater activated droplet numbers, whereas impacts of these parameters onCDSD spectral width depend on both aerosol number concentration and updraft velocity. An expansion of theactivation scheme to include CDSD spectral width is proposed to aid efforts to extend high-order momentprediction to cloud droplet categories in CRMs as well as better represent variability in the activation process onthe cloud scale.simulations to investigate the regime dependence of the relative dispersion(d)1 of newly activated CDSDs, where d is the ratio of dropletradius standard deviation (σ) to the mean radius (r ). C16 demonstratedthat increasing Na resulted in increasing (decreasing) d values via reducedcondensational narrowing (spectral broadening) rates within theAL (UL) regime, with d values peaking in the TR regime. Their findingssuggest a similar regime dependence for d as R09 noted for Nc and helpexplain reportedly conflicting relationships between Na and CDSDspectral characteristics (cf. Hudson and Noble, 2014; Liu et al., 2014),although the applicability of these results within bulk microphysicalschemes was not addressed.Simulating aerosol-cloud interactions with CRMs employing bulkmicrophysics requires that the scheme minimally predict two CDSDparameters, namely mass and number concentrations, and represent thedroplet activation process. Various activation schemes aim to determineNc from aerosol and environmental properties and include analyticalexpressions (e.g., Abdul-Razzak et al., 1998; Morrison et al., 2005) aswell as lookup tables (LUTs) based on detailed parcel model calculations(e.g., Saleeby and Cotton, 2004, hereafter SC04; Segal and Khain,2006; Thompson and Eidhammer, 2014). Expressions to diagnose CDSDspectral width from Nc (Grabowski, 1998; Liu et al., 2006; Morrison andGrabowski, 2007) or cloud water content (Geoffroy et al., 2010) havealso been developed, although more robust methods to obtain CDSDspectral width upon activation are presently lacking. This latter point isrelevant for triple-moment (3 M) bulk microphysics that aim to predictdistribution spectral width alongside number and mass concentrations(e.g., Loftus et al., 2014; Milbrandt and Yau, 2005).The current work extends the findings of C16 to the current LUTbasedaerosol activation scheme used in the Regional AtmosphericModeling System (RAMS) (Cotton et al., 2003; SC04; Saleeby and vanden Heever, 2013, hereafter SvdH13) and additionally examinesaerosol size and solubility impacts on newly activated CDSD properties.Because early cloud development processes such as condensationalgrowth, evaporation, and droplet self-collection depend on and impactCDSD spectral width (Hudson and Yum, 1997; Seifert and Beheng 2001;Lu and Seinfeld, 2006; Igel and van den Heever, 2017), an expansion ofthe activation LUTs to include CDSD spectral width is proposed as apreliminary step for extending 3M prediction to CDSDs in CRMs forimproved simulations of aerosol-cloud interactions.2. MethodologyThe current RAMS two-moment microphysics module determinesthe fractional number of aerosol particles that activate to cloud dropletsfrom five-dimensional LUTs based on model predicted air temperature(T), w, Na, and the geometric median radius (rg) and soluble fraction (ε)of the aerosol size distribution (SvdH13). These LUTs are created offlineusing a one-dimensional Lagrangian adiabatic parcel model (Feingoldand Heymsfield, 1992; Heymsfield and Sabin, 1989; SC04) to simulateexplicit droplet activation and initial CDSD growth for a range of ambientatmospheric conditions [T, w] and binned lognormal aerosol sizedistributions given by= ⎡⎣ ⎢− ⎤⎦ ⎥N r Nr π σr rσ( )2 lnexp[ln( / )]2(ln )aggg22 (1)where r is the dry aerosol particle bin radius and σg is the geometricstandard deviation of the distribution. As the parcel model simulationsfocus on the activation process, other processes such as coalescence,sedimentation, and mixing are not considered. Details of the parcelmodel can be found in SC04 and SvdH13, and only a brief description isprovided here. At the onset of parcel model calculations, the initiallydry aerosol particles in all bins first deliquesce and reach theirequilibrium diameters in a sub-saturated environment based on theKöhler equation for solution droplets. The parcel is then lifted at a fixedupward velocity w, and particle growth by vapor diffusion, along withconcurrent changes in the ambient environment, are iteratively computedusing the Variable-coefficient Ordinary Differential Equation(VODE) solver (Brown et al., 1989). The time resolution of these calculationsis determined within the VODE solver, and the frequency atwhich the solver is called is controlled by a longer model time stepbased on fixed upward parcel displacement increments (Δz) at thespecified w (Δt=Δz/w). Model calculations proceed until the parcelreaches a height 50m beyond the level of maximum saturation ratio(Smax) or total parcel displacement exceeds 2 km. Upon model termination,Smax and the fractional number of aerosols (factv) resulting innewly formed cloud droplets, defined as particles having diameters of atleast 2 μm, are cataloged in the LUTs according to the specified T, w, Na,rg, and ε parameter values.A critical point regarding the creation of these LUTs is the use of afixed minimum diameter (Dmin) to define cloud droplets in the parcelmodel, which can produce erroneous CDSD characteristics, particularlywithin the UL regime. For aerosol distributions with large rg valuesunder low SS conditions, for example, deliquesced aerosols within thelarge tail of the distribution can exceed 2 μm in diameter yet remainunactivated as ‘haze’ particles (Levin and Cotton, 2009; McFigganset al., 2006). For this study, aerosol particles activate to cloud dropletsbased on the critical diameter Dcrit as a function of parcel supersaturationratio (Sr) as in R09:D = σ MS RTρ83 ln( ) critsol wr w (2)where σsol is the surface tension of a solution droplet, Mw and ρw are themolar mass and density of liquid water, respectively, and R is theuniversal gas constant. Additionally, at relatively large w values withinthe AL regime, Nc stabilizes shortly after reaching supersaturation.However, parcel ascent and condensational growth continue beyondthe level of Smax, potentially causing additional narrowing of the CDSD.In the current work, model calculations terminate upon reaching Smaxas changes in Nc are negligible with continued ascent (Peng et al., 2007;R09).Parcel model simulations are performed to examine the sensitivitiesof CDSD characteristics to w, Na, rg, and ε, with the ranges for theseparameters listed in Table 1. Aerosols are assumed to be a mix of solubleand insoluble material of equal density, specified by ε, where fullysoluble aerosols correspond to ammonium sulfate with hygroscopicityparameter κ=0.61 (Petters and Kreidenweis, 2007). FollowingSvdH13, aerosol geometric standard deviation is fixed at σg=1.8, andaerosol distributions (Eq. 1) are partitioned into 100 logarithmicallyspacedbins spanning a size range specific to each rg value. For all simulations,Δz=1 m, and initial values of relative humidity, air temperatureand pressure are set to RH=0.99, T=10 °C and p=900 hPa,respectively.

Loftus, Adrian M.↗

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗