Publications

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The Sandia Parallel Aerodynamics and Reentry Code (SPARC) is described.

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Fluctuating boundary layer pressure fluctuations are an important loading component for high speed reentry vehicles. Characterization of the unsteady time series requires access to longitudinal and lateral coherence expressions as well spatial correlation and frequency power-spectral density models. Coherence, spatial correlation and frequency power spectral density are related as through their cross-spectral density definitions. However the frequency PSD and the spatial correlation are often based upon measurements or approximate models which may introduce bias in the associated derived coherence function. Here, we examine the effect of measurement and model form associated with frequency spectrum and correlation on the longitudinal and lateral coherence for supersonic pressure fluctuation flow fields. The widely utilized Corcos separable coherence model functional form has been employed in this study. The associated integral equations which relate coherence and correlation are solved using a simple iterative approach. To minimize distortion in results due to computational issues a high accuracy numerical integration procedure is utilized. Despite a more robust computational approach, solution accuracy is limited for some problems by the functional form of the longitudinal coherence model. These limitations are discussed in detail. This overall approach is applied to Mach 5 and Mach 8 seven degree sharp cone pressure fluctuation measurements. Estimates for the parameters associated with the Corcos coherence expressions are typically larger than more traditional values especially for the longitudinal coherence. These larger values suggest that fluctuations streamwise correlation length is small. Limited longitudinal correlation can be associated with shock influence and is explored as a possible cause.

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This document compares results for isothermal wall cases and observes their stagnation lines.

Fluctuating boundary layer wall shear stress can be an important loading component for structures subjected to turbulent boundary layer flows. While normal force loading via wall pressure fluctuation is relatively well described analytically, there is a dearth of information for wall shear behavior. Starting with an approximate acoustic analogy we derive simple approximate expressions for both wall pressure and wall shear fluctuations behavior utilizing a Taylor hypothesis based analogy between streamwise and temporal fluctuations. Analytical results include longitudinal spatial correlation, autocorrelation, frequency spectrum, RMS intensity and longitudinal and lateral coherence expressions. While coefficients in these expressions usually require some empirical input they nonetheless provide useful predictions for functional behavior. Comparison of the models with available literature data sets suggests reasonable agreement. Dedicated high fidelity numerical computations (direct numerical simulations) for a supersonic boundary layer are used to further explore the efficacy of these models. The analytical models for wall pressure fluctuation and wall shear fluctuation spectral density compare well for low frequency with the simulations when Reynolds number effects are included in the pressure fluctuation intensity. The approximate analytical models developed here provide a physics-based connection between classical empirical expressions and more complete experimental and computational descriptions.

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Here we provide a discussion regarding the applicability of a family of traditional heat transfer correlation based models for several (unit level) heat transfer problems associated with flight heat transfer estimates and internal flow heat transfer associated with an experimental simulation design (Dobranich 2014). Variability between semi-empirical free-flight models suggests relative differences for heat transfer coefficients on the order of 10%, while the internal annular flow behavior is larger with differences on the order of 20%. We emphasize that these expressions are strictly valid only for the geometries they have been derived for e.g. the fully developed annular flow or simple external flow problems. Though, the application of flat plate skin friction estimate to cylindrical bodies is a traditional procedure to estimate skin friction and heat transfer, an over-prediction bias is often observed using these approximations for missile type bodies. As a correction for this over-estimate trend, we discuss a simple scaling reduction factor for flat plate turbulent skin friction and heat transfer solutions (correlations) applied to blunt bodies of revolution at zero angle of attack. The method estimates the ratio between axisymmetric and 2-d stagnation point heat transfer skin friction and Stanton number solution expressions for sub-turbulent Reynolds numbers %3C1x10 4 . This factor is assumed to also directly influence the flat plate results applied to the cylindrical portion of the flow and the flat plate correlations are modified by

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Here we discuss an improved Corcos (Corcos (1963), (1963)) style cross spectral density utilizing zero pressure gradient, supersonic (Beresh et. al. (2013)) data sets. Using the connection between narrow band measurements with broadband cross-spectral density, i.e. Γ(ξ ,η ,ω )= Φ (ω) A(ωη/U )exp (-i ωξ/U) we focus on estimating coherence expressions of the form: A (ξω _nb/U) and B (ηω _nb/ U) where ω_nb denotes the narrow band frequency, i.e. the band center frequency value and ξ and η are sensors spacing in streamwise/longitudinal and cross-stream/lateral directions, respectively. A methodology to estimate the parameters which retains the Corcos exponential functional form, A(ξω/U)=exp(-k_lat ηω/U) but identifies new parameters (constants) consistent with the Beresh et. al. data sets is discussed. The Corcos result requires that the data be properly explained by self-similar variable: ξω/U and ηω/U. The longitudinal (streamwise) variable ξω/U tends to provide a better data collapse, while, consistent with the literature the lateral ηω/U is only successful for higher band center frequencies. Assuming the similarity variables provide a useful description of the data, the longitudinal coherence decay constant result using the Beresh et. al. data sets yields a value for the longitudinal constant k_long≈0.36-0.28 that is approximately 3x larger than the “traditional” (low speed, large Reynolds number and zero pressure gradient) of k_long≈0.11. We suggest that the most likely reason that the Beresh et. al. data sets incur increased longitudinal decay which results in reduced coherence lengths is due to wall shear induced compression causing an adverse pressure gradient. Focusing on the higher band center frequency measurements where the frequency dependent similarity variables are applicable, the lateral or transverse coherence decay constant k_lat≈0.7 is consistent with the “traditional” (low speed, large Reynolds number and zero pressure gradient). It should be noted, that the longitudinal/streamwise coherence decay deviates from the value observed by other researchers while the lateral/ cross-stream value is consistent has been observed by other researchers. We believe that while the measurements used to obtain new decay constant estimates are from internal wind tunnel tests, they likely provide a useful estimate expected reentry flow behavior and are therefore recommended for use. These data could also be useful in determining the uncertainty of correlation length for a uncertainty quantification (UQ) analysis.

Boundary-layer transition and stability data were obtained at Mach 10 in the Arnold Engineering Development Complex (AEDC) Hypervelocity Wind Tunnel 9 on a 1.5-m long, 7-deg cone at unit Reynolds numbers between 1.8 and 31 million per meter. A total of 24 runs were performed at angles-of-attack between 0 and 10-deg on sharp and blunted cones with nose radii between 5.1 and 50.8-mm. The transition location was determined with coaxial thermocouples and temperature sensitive paint while stability measurements were obtained using high-frequency response pressure sensors. Mean flow and boundary layer-stability computations were also conducted and compared with the experiment. The effect of angle-of-attack and bluntness on the transition location displays similar trends compared to historical hypersonic wind tunnel data at similar Mach and Reynolds numbers. The N factor at start of transition on sharp cones increases with unit Reynolds number. Values between 4 and 7 were observed. The N factor at start of transition significantly decreases as bluntness increases and is successfully correlated with the ratio of transition location to entropy layer swallowing length. Good agreement between the computed and measured spatial amplification rates and most amplified 2nd mode frequencies are obtained for sharp and moderately blunted cones. For large bluntness, where the ratio of transition to entropy swallowing length is below 0.1, 2nd mode waves were not observed before the start of transition on the frustum.

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