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Wall static pressure and convective heat transfer measurements in subsonic, transonic and supersonic regions in heated air turbulent flow through variable cross section channel
An efficient method to account for the chemically frozen thermodynamic and transport properties of air in three-dimensional Navier-Stokes calculations has been demonstrated. This approach uses an explicitly specified equation of state (EOS) so that the fluid pressure, temperature, and transport properties are directly related to the flow variables. The method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code. The flexibility of the EOS approach is shown by its implementation into a high-order total variation diminishing upwinding scheme as well as a standard central-differencing scheme. The EOS approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central-differencing schemes.
An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.
With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.
Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.
To better understand the complicated web of processes governing convective cloud life cycle and aerosol-convection interactions, the U.S. Department of Energy (DOE)’s Atmospheric Radiation Measurement (ARM) user facility supported deployment of a variety of advanced atmospheric measurement systems to the greater Houston, Texas, area from 1 October 2021 to 30 September 2022 as part of the Tracking Aerosol Convection Interactions Experiment (TRACER). Houston was selected as a study area because isolated convection and a variety of aerosol conditions are common in this region. This one-year ARM Mobile Facility (AMF) deployment featured a four-month intensive operational period (IOP) during summer 2022 (1 June–30 September). The ARM instrumentation was deployed at three sites along an east-west transect from La Porte, Texas to an ancillary site in a less-polluted rural region southwest of downtown Houston (Figure 1). At the La Porte Site, which is located near the Houston ship channel in an area that experiences significant pollution, the first ARM Mobile Facility (AMF1) was deployed. During the IOP, the ARM tethered balloon system (TBS) operated at the ancillary site. The second-generation C-Band Scanning ARM Precipitation Radar (CSAPR) operated near Pearland, Texas, roughly halfway between the Laporte and ancillary sites. As part of the TRACER- Coastal Urban Boundary-Layer Interactions with Convection (CUBIC) project, three boundary-layer profiling systems) were deployed along a north-south transect spanning from the University of Houston Coastal Center to the Aldine site north of downtown Houston (also blue dot in Figure 1) during the TRACER IOP. These systems included the National Oceanic and Atmospheric Administration (NOAA) National Severe Storms Laboratory CLAMPS2 (C2), which was deployed at the UHCC, the University of Wisconsin SPARC, which was deployed at the ARM CSAPR site near Pearland (orange diamond in middle of map in Figure 1), and the University of Oklahoma CLAMPS1 (C1), which was deployed at Aldine. These three systems have been successfully operated in various field campaigns, providing data sets that collectively offer new insights into atmospheric-boundary-layer (ABL) processes, sea-breeze (SB) circulations, and convection initiation (CI). For the TRACER IOP window, these systems ran continuously between 1 June and 26 September, 2022. Due to commitments to NOAA projects, the Doppler lidar at the UHCC site was not available until 24 June 2022. The CLAMPS and SPARC profiling systems are self-contained platforms that have benefited from several years of development and deployment. Instruments and data processing were maintained remotely, which made the 4-month deployment for the TRACER-CUBIC IOP period possible. The same basic instrument configuration comprises each system: a scanning Doppler wind lidar for flow characterization and passive profiler(s) for characterizing planetary-boundary-layer (PBL) thermodynamic properties. Each platform includes a Halo Streamline Doppler wind lidar, an Atmospheric Emitted Radiance Interferometer (AERI), and a surface meteorology station. CLAMPS1 and CLAMPS2 each also include a microwave radiometer (MWR, Figure 1d). The TRACER-CUBIC hypotheses included (i) Interactions of SB and urban circulations and how they affect the PBL structure in the Houston environment, causing spatially (horizontally and vertically) and temporally highly variable flow patterns, (ii) heat, moisture, and aerosol transport and mixing depend on these flow dynamics, and (iii) an improved understanding of the flow patterns and PBL structure are critical for investigating the processes leading to CI. To test these hypotheses, the project aimed at (i) characterizing SB circulations and their impacts on the diurnal evolution of the structure of the ABL, (ii) studying the evolution of Houston’s complex urban boundary layer, and (iii) identifying effects of urban-induced circulations on pre-convective environments. TRACER-CUBIC observations generally provide good coverage during the summer IOP. Initial screening of the data indicates a good number of cases with bay-breeze (BB) and/or SB signatures, local CI, and interesting boundary-layer features such as strong nocturnal low-level jets (LLJs, Table 1). The numbers listed in rows 3-5 in this table will be further updated as part of ongoing in-depth analyses and systematic identification of local circulations and CI events. More detailed information about the data availability and quality for each instrument is provided in the “readme” files that were submitted to the ARM Data Center along with each archived data sets. These “readme” files also provide instrument descriptions, information about the data collection and processing procedures, data formats, and any additional information relevant for further data analysis.
A database obtained from direct numerical simulation of a turbulent channel flow is analyzed to extract the streamwise component of the propagation velocity V of velocity, vorticity, and pressure fluctuations from their space-time correlations. A surprising result is that V is approximately the same as the local mean velocity for most of the channel, except for the near-wall region. For y(+) less than 15, V is virtually constant, implying that perturbations of all flow variables propagate like waves near the wall. In this region V is 55 percent of the centerline velocity Uc for velocity and vorticity perturbations and 75 percent of U sub c for pressure perturbations. This is equal to U at y(+) = 15 for velocity and vorticity perturbations, and equal to U at y(+) = 20 for pressure perturbations, indicating that the dynamics of the nearwall turbulence is controlled by turbulence structures present near y(+) about 15-20. Scale dependence of V is also examined by analyzing the bandpass-filtered flow fields. This paper contains comprehensive documentation on the propagation velocities, which should prove useful in the evaluation of Taylor's hypothesis.
A discrete, semi-analytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities of the flow variables and the grid coordinates are numerically calculated using direct differentiation of the respective discretized governing equations. The sensitivity analysis techniques are adapted within a parabolized Navier Stokes equations solver. Aerodynamic design sensitivities for high speed wing-body configurations are calculated using the semi-analytical sensitivity analysis procedures. Representative results obtained compare well with those obtained using the finite difference approach and establish the computational efficiency and accuracy of the semi-analytical procedures. Multidisciplinary design optimization procedures have been developed for aerospace applications namely, gas turbine blades and high speed wing-body configurations. In complex applications, the coupled optimization problems are decomposed into sublevels using multilevel decomposition techniques. In cases with multiple objective functions, formal multiobjective formulation such as the Kreisselmeier-Steinhauser function approach and the modified global criteria approach have been used. Nonlinear programming techniques for continuous design variables and a hybrid optimization technique, based on a simulated annealing algorithm, for discrete design variables have been used for solving the optimization problems. The optimization procedure for gas turbine blades improves the aerodynamic and heat transfer characteristics of the blades. The two-dimensional, blade-to-blade aerodynamic analysis is performed using a panel code. The blade heat transfer analysis is performed using an in-house developed finite element procedure. The optimization procedure yields blade shapes with significantly improved velocity and temperature distributions. The multidisciplinary design optimization procedures for high speed wing-body configurations simultaneously improve the aerodynamic, the sonic boom and the structural characteristics of the aircraft. The flow solution is obtained using a comprehensive parabolized Navier Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. The aircraft wing load carrying member is modeled as either an isotropic or a composite box beam. The isotropic box beam is analyzed using thin wall theory. The composite box beam is analyzed using a finite element procedure. The developed optimization procedures yield significant improvements in all the performance criteria and provide interesting design trade-offs. The semi-analytical sensitivity analysis techniques offer significant computational savings and allow the use of comprehensive analysis procedures within design optimization studies.
An analytical model has been developed to predict the flow behavior within axisymmetric single-nozzle ejectors employing variable-area mixing tubes. The primary flow may be supersonic or subsonic and may have a different stagnation temperature from the subsonic secondary flow. Tests were performed on an ejector with an 800 F supersonic (M = 2.72) primary jet to evaluate the analytical model. Measured velocity profiles, temperature profiles, and wall static pressure distributions are presented and compared to the analytical predictions. Agreement is generally good.
Development of complex air vehicle configurations is placing increasing demands on wind tunnel testing capabilities. A major area of concern is wall induced interference. Recent developments in wall interference technology provide a means for assessing and correcting for the wall induced interference using information contained in the distribution of flow variables measured at, or near, the wall. The restoration of the NASA-ARC 12-ft pressure wind tunnel (PWT) provides an opportunity to incorporate a measurement system with which wall interference assessment/correction (WIAC) technology can be applied. In this first phase of the development of a WIAC system for the PWT, the design criteria for the placement and the geometry of wall static pressure orifices were determined with a three step approach. First, the operational environment of the PWT was analyzed as to the requirements for the WIAC system. Second, appropriate wall interference theories were evaluated against the requirements determined from the operational environment. Third, the flow about representative models in the PWT was calculated and, specifically, the pressure signatures at the location of the test section wall were obtained. The number of discrete pressure measurements and their locations were determined by curve fitting the pressure distribution through the discrete measurements and evaluating the resulting error.
Wall functions, as used in the typical high Reynolds number k-epsilon turbulence model, can be implemented in various ways. A least disruptive method (to the flow solver) is to directly solve for the flow variables at the grid point next to the wall while prescribing the values of k and epsilon. For the centrally-differenced finite-difference scheme employing artificial viscocity (AV) as a stabilizing mechanism, this methodology proved to be totally useless. This is because the AV gives rise to a large error at the wall due to too steep a velocity gradient resulting from the use of a coarse grid as required by the wall function methodology. This error can be eliminated simply by extrapolating velocities at the wall, instead of using the physical values of the no-slip velocities (i.e. the zero value). The applicability of the technique used in this paper is demonstrated by solving a flow over a flat plate and comparing the results with those of experiments. It was also observed that AV gives rise to a velocity overshoot (about 1 percent) near the edge of the boundary layer. This small velocity error, however, can yield as much as 10 percent error in the momentum thickness. A method which integrates the boundary layer up to only the edge of the boundary (instead of infinity) was proposed and demonstrated to give better results than the standard method.
A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number of time derivatives of surface-normal velocity (consistent with no flow through the boundary) up to arbitrarily high order. The corrections for the first-order spatial derivatives of pressure are calculated by use of the first-order time derivative velocity. The corrected first-order spatial derivatives are used to calculate the second- order time derivatives of velocity, which, in turn, are used to calculate the corrections for the second-order pressure derivatives. The process as described is repeated, progressing through increasing orders of derivatives, until the desired accuracy is attained.
The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.
This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.
A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.
Abstract Aeration systems often lack the efficiency to maintain a desired residual dissolved oxygen (DO) concentration in the tank in part because little consideration is given to the dynamic daily and seasonal loading conditions. Although advanced aeration controllers exist, the majority of plants have DO set points typically based on common practice and literature values rather than site‐specific conditions, which can result in DO set points higher than those necessary to meet treatment objectives. DO set point reduction strategies have primarily been proposed through either static or dynamic simulations. In this study, the substantial improvements associated with DO set point reduction are demonstrated at full scale. A yearlong characterization of full‐scale aeration dynamics captured the effect of diurnal and seasonal fluctuations on oxygen transfer and energy demand and so facilitated the estimation of the potential savings of DO reduction strategies. Full‐scale validation provided direct evidence of DO reduction strategies inducing an overall enhancement of oxygen transfer efficiency along the different bioreactors, while confirming that energy savings as high as 20% were feasible. This study quantifies the influence of oxygen transfer efficiency on operating choices and site‐specific conditions (control strategy, loading conditions, and influent flow variability). Practitioner points We quantified the energy reduction and cost savings associated with a DO reduction in an aeration tank. For each 0.2 mg/L of DO decreased, the average power demand reduction per unit water treated exceeded 17%. Field measurements of dynamic alpha values eliminate the uncertainty in estimating aeration energy and cost savings from DO variations.
The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. Here, this paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.
The subchannel module of moose (SCM), previously referred to as Pronghorn-SC, is a subchannel code designed to resolve single-phase flow fields and calculate the relevant flow variables, in nuclear reactor fuel-pin assemblies. The assemblies it models are: water-cooled, with bare fuel-pins in a square ducted, quadrilateral lattice and liquid-metal/water-cooled, with bare/wire-wrapped fuel pins in a hexagonal ducted, triangular lattice. Previous publications have presented the development, validation and verification of SCM. This work presents an comparative overview of the different solvers implemented within SCM. This includes the solver algorithm description, and a performance comparison. The two test cases chosen to demonstrate the solver performance were taken from the PSBT enthalpy mixing benchmark and the ORNL-19 pin benchmark.