Examination of boundary conditions for heat transfer through a porous wall
Analytic model of boundary conditions for heat transfer coefficients through porous walls
Colladay, R. S.↗
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Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points
Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.
compressor↗
Continued Development of the Discontinuous Galerkin Method for Computational Aeroacoustic Applications
The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modifications. This feature leads to a simple and accurate treatment for wall boundary conditions and simple inflow and outflow boundary conditions. Curved walls are accurately treated with only minor changes to the implementation described in earlier work. The 'perfectly matched layer' approach to nonreflecting boundary conditions is easily applied to the discontinuous Galerkin. The compactness of the discontinuous Galerkin method makes it better suited for buffer-zone-type methods than high-order finite-difference methods. Results are presented for wall, characteristic inflow and outflow, and nonreflecting boundary conditions.
Atkins, H. L.↗
Solution strategies and heat transfer calculations for three-dimensional configurations at hypersonic speeds
A procedure which reduces the memory requirements for computing the viscous flow over a modified Orbiter geometry at a hypersonic flight condition is presented. The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) code which incorporates a thermochemical nonequilibrium chemistry model, a finite rate catalytic wall boundary condition and wall temperature distribution based on radiation equilibrium is used in this study. In addition, the effect of choice of 'min mod' function, eigenvalue limiter and grid density on surface heating is investigated. The surface heating from a flowfield calculation at Mach number 22, altitude of 230,000 ft and 40 deg angle of attack is compared with flight data from three Orbiter flights.
Weilmuenster, K. J.↗
A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow
It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.
Hu, Fang↗
Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility
Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.
Walker, Eric Lee↗
Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility
Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.
Walker, Eric L.↗
Theoretical Study of Natural Convection Flows in Closed-End Cylindrical Vessels Final Report
This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.
Convective flow↗
SSME thrust chamber simulation using Navier-Stokes equations
The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.
Przekwas, A. J.↗
High-speed propeller noise predictions: Effects of boundary conditions used in blade loading calculations
The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.
Nallasamy, M.↗
High-speed propeller noise predictions - Effects of boundary conditions used in blade loading calculations
The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.
Nallasamy, M.↗
On the assumption of vanishing temperature fluctuations at the wall for heat transfer modeling
Boundary conditions for fluctuating wall temperature are required for near-wall heat transfer modeling. However, their correct specifications for arbitrary thermal boundary conditions are not clear. The conventional approach is to assume zero fluctuating wall temperature or zero gradient for the temperature variance at the wall. These are idealized specifications and the latter condition could lead to an ill posed problem for fully-developed pipe and channel flows. In this paper, the validity and extent of the zero fluctuating wall temperature condition for heat transfer calculations is examined. The approach taken is to assume a Taylor expansion in the wall normal coordinate for the fluctuating temperature that is general enough to account for both zero and non-zero value at the wall. Turbulent conductivity is calculated from the temperature variance and its dissipation rate. Heat transfer calculations assuming both zero and non-zero fluctuating wall temperature reveal that the zero fluctuating wall temperature assumption is in general valid. The effects of non-zero fluctuating wall temperature are limited only to a very small region near the wall.
Sommer, T. P.↗
Theoretical and experimental analysis of the slotted-wall flow field in a transonic wind tunnel
The flow in the vicinity of a longitudinally slotted wind-tunnel wall is theoretically analyzed, and equations describing the pressure drop across the wall are derived. The ideal form of the slotted-wall boundary condition is shown to effectively model the wall pressure drop upstream of the point of maximum model thickness providing that a zero-shift correction to the reference pressure is included in the analysis. The wall-pressure drop equations can be linearized by subtracting the tunnel-empty boundary condition. Good correlation is obtained between experimental and theoretical values for variations in Mach number and angle of attack.
Everhart, Joel L.↗
Multidimensional Unstructured-Grid Liquid Rocket Engine Nozzle Performance and Heat Transfer Analysis
The objective of this study is to conduct a unified computational analysis for computing design parameters such as axial thrust, convective and radiative wall heat fluxes for regeneratively cooled liquid rocket engine nozzles, so as to develop a computational strategy for computing those parameters through parametric investigations. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, radiating, unstructured-grid, and pressure-based formulation, with grid refinement capabilities. Systematic parametric studies on effects of wall boundary conditions, combustion chemistry, radiation coupling, computational cell shape, and grid refinement were performed and assessed. Under the computational framework of this study, it is found that the computed axial thrust performance, flow features, and wall heat fluxes compared well with those of available data and calculations, using a strategy of structured-grid dominated mesh, finite-rate chemistry, and cooled wall boundary condition.
Wang, Ten-See↗
Prediction of Heat and Mass Transfer in a Rotating Ribbed Coolant Passage With a 180 Degree Turn
Numerical results are presented for flow in a rotating internal passage with a 180 degree turn and ribbed walls. Reynolds numbers ranging from 5200 to 7900, and Rotation numbers of 0.0 and 0.24 were considered. The straight sections of the channel have a square cross section, with square ribs spaced one hydraulic diameter (D) apart on two opposite sides. The ribs have a height of 0.1D and are not staggered from one side to the other. The full three dimensional Reynolds Averaged Navier-Stokes equations are solved combined with the Wilcox k-omega turbulence model. By solving an additional equation for mass transfer, it is possible to isolate the effect of buoyancy in the presence of rotation. That is, heat transfer induced buoyancy effects can be eliminated as in naphthalene sublimation experiments. Heat transfer, mass transfer and flow field results are presented with favorable agreement with available experimental data. It is shown that numerically predicting the reattachment between ribs is essential to achieving an accurate prediction of heat/mass transfer. For the low Reynolds numbers considered, the standard turbulence model did not produce reattachment between ribs. By modifying the wall boundary condition on omega, the turbulent specific dissipation rate, much better agreement with the flow structure and heat/ mass transfer was achieved. It is beyond the scope of the present work to make a general recommendation on the omega wall boundary condition. However, the present results suggest that the omega boundary condition should take into account the proximity to abrupt changes in geometry.
Rigby, David L.↗
A numerical simulation of three-dimensional flow in an adaptive wall wind tunnel
Numerical simulations of three dimensional flows in a prototype adaptive wall wind tunnel are conducted at the Mach number of 0.6 to investigate: (1) wind tunnel wall interference, (2) active streamline control by varying air removal or injection along the walls, and (3) to develop a method for establishing wall boundary conditions for interference free flows. Wind tunnel wall interference could be controlled by using only the vertical velocity components. For the configuration tested, interference free flow with solid sidewalls can be approximated by using only floor and ceiling blowing/suction.
Mendoza, J. P.↗
Wall interference and boundary simulation in a transonic wind tunnel with a discretely slotted test section
A computational simulation of a transonic wind tunnel test section with longitudinally slotted walls is developed and described herein. The nonlinear slot model includes dynamic pressure effects and a plenum pressure constraint, and each slot is treated individually. The solution is performed using a finite-difference method that solves an extended transonic small disturbance equation. The walls serve as the outer boundary conditions in the relaxation technique, and an interaction procedure is used at the slotted walls. Measured boundary pressures are not required to establish the wall conditions but are currently used to assess the accuracy of the simulation. This method can also calculate a free-air solution as well as solutions that employ the classical homogeneous wall conditions. The simulation is used to examine two commercial transport aircraft models at a supercritical Mach number for zero-lift and cruise conditions. Good agreement between measured and calculated wall pressures is obtained for the model geometries and flow conditions examined herein. Some localized disagreement is noted, which is attributed to improper simulation of viscous effects in the slots.
Al-Saadi, Jassim A.↗
Wall-Modeled Large-Eddy Simulations of Jet Noise in Flight Conditions
A campaign of wall-modeled large-eddy simulations (WMLES) using structured curvilinear overlapping grids has been performed with the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) software to predict jet noise for single-stream axisymmetric round jets. The simulations address the new Prediction Uncertainty Reduction (PUR) technical challenge within the context of NASA’s Commercial Supersonic Technology (CST) project. The focus of this effort is to generate a simulation database for single-stream axisymmetric round nozzles at several operating points both for static (no ambient co-flow), and in-flight (M ͚ =0.3 co-flow) conditions. The operating conditions range in jet exit Mach number from 0.38 to 1.1 with nozzle temperature ratios (NTR) from 0.84 to 2.7. The effect of the flight-stream on far-field noise sound spectra is assessed. Comparison of LES predictions to microphone array measurements demonstrate good agreement within the resolved frequency range. A dip in the predicted low frequency noise spectra for observers between 120° and 145° is observed. This dip is smaller for lower Mach numbers and seems to be correlated to the Mach wave radiation angle. The Mach 1.1 jet shows broadband-shock associated noise. While the onset of BBSN appears to be captured correctly in WMLES, some differences in its magnitude and the prominent frequency at which it occurs persist between the experiment and the simulations. The effect of the outer nozzle boundary layer state created by the co-flow is assessed and shows to be important for accurate comparisons with experiments. A change of 2.5dB between a slip-wall condition and a artificially thickened turbulent boundary layer was observed. In addition, simulations were performed with an alternative nozzle geometry that includes a internal plug and has twice the nozzle exit diameter. These two configurations resulted in very comparable spectra which is consistent with experimental observations. A generally stronger deviation from experimental results is observed for in-flight cases compared to static conditions. The applicability and correct usage of acoustic analogies used for far-field propagation with strong turbulent co-flows needs to be investigated more systematically using canonical problems to improve comparisons between experiments and WMLES. This is especially true for coherent noise sources seen in BBSN.
CST↗