In this work, a modified Laplacian pressure Poisson reconstruction technique has been studied using experimental velocimetry data, after the theoretical investigation in the companion work (Zhang et al 2024 Meas. Sci. Technol. 35 095302). The modified solver adds a temporal diffusion term to the canonical Laplacian operator to mitigate the high frequency noise in the pressure fields reconstructed from time-resolved velocimetry data. The current work uses time-resolved tomographic particle image velocimetry (PIV) measurements of an impinging synthetic jet with a commercial version of the modified Laplacian solver, known as a 4D solver, to reconstruct the instantaneous pressure fields. While the reconstructed pressure fields are smooth in time, they often display a non-physical temporal drift. Using Fourier spectral decomposition of the reconstructed pressure field and the source term of the pressure Poisson equation, we demonstrate that the smoothing behavior is the result of a low-pass filtering effect during the inversion of the modified Laplacian. Both the weighting factor of the temporal diffusion term and the space-time splitting of the time-series data affect the filtering behavior, and therefore, the smoothing effect of this modified 4D Laplacian pressure Poisson solver. Along with the weighting factor and the number of space-time blocks, the temporal drift is also affected by flow oscillation and temporal resolution of the experimental data. This study shows that, with a proper selection of different parameters, it is possible to remove the non-physical high-frequency noise from the pressure fields and limit the temporal drift. Last, we demonstrate that a physical measurement may be used to tune the parameters of this modified Laplacian based solver.

Reconstruction of the pressure field from experimental velocity data is challenging due to measurement noise, and no single method performs well for all experimental conditions. Pressure reconstruction for internal flows often lack quiescent or friction-less boundaries. Therefore, Bernoulli’s principle cannot be applied for Dirichlet boundary conditions. Furthermore, the noise in the velocimetry data is particularly high near the boundaries of the measurement domain, which contaminates the reconstructed pressure field through the Neumann boundary conditions. As such, the quality of the reconstructed pressure field is sensitive to both the implementation of the pressure boundary conditions and the spatial resolution of the velocimetry data. In this work, the ground truth for a pulsing synthetic jet flow is determined using phase averaged pressure fields calculated with a modified formulation of the pressure Poisson equation that invokes continuity to eliminate bias. While not absolute, the ground truth is sufficiently more accurate than the instantaneous results to reveal error trends. The experimental ground truth is used to validate the analytically and numerically predicted V- and -shaped error trend for Poisson equation-based pressure reconstruction. The reconstructed pressure fields exhibit large random fluctuations both in space and time when the majority of the boundary conditions are the Neumann type directly calculated from the PIV data. Increasing the length of Dirichlet boundary conditions and replacing the calculated Neumann boundary conditions with prescribed values reduces these fluctuations in the reconstructed pressure fields.

Many sports balls develop forces that change their motion due to spin, or the Magnus effect. Spin causes the boundary layer separation points to change leading to an asymmetric pressure distribution on the ball, and therefore a force. Seams on baseballs can play a similar role without spin. This paper reports the results of instantaneous velocity field measurements of non-spinning baseballs in flight. Two distinct effects of seams are reported. The first is the effect of seams on the front half of the ball where they may promote boundary layer transition. This is common in other sports balls. A second, more important, effect is to promote boundary layer separation over the seams. This only occurs near the center of the ball. Three Reynolds number values that straddle the drag crisis are measured. Various orientations of the seams are studied mapping out a full rotation of the ball. It is reported that the transition and separation points vary from one shot to the next. This is possibly due to subtle differences in baseball construction and orientation, but is more likely because the data represent random instances in a time-varying process. The average differences in separation points on opposite sides of the ball correlate well to previous force measurements on baseballs.

The lift and drag of spinning spheres roughened with macro-roughness elements are examined. The velocity field of these same spheres in flight is measured with particle image velocimetry (PIV). Several spheres with varying roughness are examined at various spin rates and fixed Reynolds number. Unlike previous studies, where the roughness height is varied, in the present work, the number of roughness elements is varied. The PIV datasets are used to determine the boundary layer separation points for each case. Comparing the lift and drag to the separation points reveals that (1) the separation points become more asymmetric with spin (the Magnus effect), (2) The drag increases with the size of the wake, and (3) the drag increases with the asymmetry of the separation points, meaning that lift on spheres is accompanied by increased drag. Scant evidence of this third effect has been reported previously. Additionally, it is shown that, counter to smooth spheres, the force transmitted to the surface through the roughness elements leads to significant drag. The drag is shown to increase with the number of roughness elements while the lift decreases. Results have implications for understanding aerodynamic forces on bluff bodies with roughness and passive control of aerodynamic forces through roughness element frequency rather than the traditional roughness height.

An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is established. Based on this framework, the optimal spatial resolution and the corresponding minimum field-wide error level in the calculated pressure field are estimated. This minimum error is viewed as the smallest resolvable pressure. We find that the optimal spatial resolution is a function of the flow features, geometry of the flow domain, and the type of the boundary conditions, in addition to the error in the PIV experiments, making a general statement about pressure sensitivity is difficult. The minimum resolvable pressure is affected by competing effects from the experimental error due to PIV and the truncation error from the numerical solver. This means that PIV experiments motivated by pressure measurements must be carefully designed so that the optimal resolution (or close to the optimal resolution) is used. Flows (Re=1.27 × 104 and 5×104) with exact solutions are used as examples to validate the theoretical predictions of the optimal spatial resolutions and pressure sensitivity. The numerical experimental results agree well with the analytical predictions.

This paper documents a computational fluid dynamics (CFD) validation benchmark experiment for flow through three parallel, heated channels from one plenum to another. The test section was installed into a facility designed for natural convection benchmark validation experiments. The focus of these experiments was the highly-coupled thermal-fluid dynamics that occur between mixing jets in the upper plenum of the wind tunnel. A thermal instability in mixing jets, called thermal striping, can cause damage to structures which is a concern for high temperature gas reactors. Nine experimental cases were explored by varying the relative channel temperature or blower speed. The boundary conditions for CFD validation were measured and tabulated along with an uncertainty. Geometry measurements of the triple channel test section were used to make an as-built solid model for use in simulation. The outer tunnel and channel surface temperatures, the pressure drop across the test section, atmospheric conditions, and inflow into the upper plenum were measured or calculated for the boundary conditions. The air velocity and temperature were measured in the jet mixing region of the upper plenum as system response quantities.

An experimental investigation of how seams and their orientation relative to the spin axis and flight direction can alter the formation of a wake around a baseball was conducted. Particle Image Velocimetry (PIV) was used to examine the velocity field around a baseball in specific orientations and to find the boundary layer separation location, which is the location on the baseball where the wake begins to form. Certain orientations can advance the separation point on one side of the baseball, generating a pressure force on the baseball and modifying its flight path. Using this information as a guide, baseballs were launched 55 feet (a realistic pitching distance) in orientations designed to have an asymmetric separation point. These pitches were 90 mph at spin rates near 1200RPM with a vertical spin axis perpendicular to the initial flight direction. A Rapsodo 1.0 system was used to compare the pitch locations for different seam orientations. The results of this study showed a significant and repeatable difference in the path of the baseball depending on the orientation of the seams relative to the spin axis. This effect was more significant for baseballs with larger seams.

In this paper, the usefulness of planar Particle Image Velocimetry (PIV) measurements to determine the volumetric flow rate from a rectangular or round jet exit is assessed. Both two-component PIV (2C–PIV) and through-plane three-component (3C) stereo PIV (SPIV) data sets were acquired at the exit of a turbulent, rectangular nozzle and a round nozzle with Reynolds numbers between 10 000 and 100 000. The PIV data sets were processed using a variety of algorithms. The time-averaged results were then spatially integrated across the jet exits and compared to a calibrated flow meter. Recommendations for each method are developed and discussed with potential drawbacks. The accuracy of the measurement was found to be a weak function of the Reynolds number of the flow. Two-component PIV was found to underestimate the volumetric flow rate by 1%–4% depending on the integration scheme and SPIV underestimated volumetric flow rate by 2%.

The Magnus effect and the reverse Magnus effect are studied on golf balls and on smooth balls, each of which are moving in still air. The fluid motion around the balls is measured using 2-component particle image velocimetry (PIV). The PIV data are used to compute the out-of-plane component of vorticity, and the vorticity field, along with the velocity field, is used to find the locations and state of the boundary layers at separation on the top and bottom of the ball. The reverse Magnus effect occurs when the spin is sufficient to cause the retreating boundary layer to be laminar, while the advancing side is turbulent. The reverse Magnus regime ends when the retreating side becomes turbulent due to the separation point moving into a strong adverse pressure gradient on the rear of the ball.

The efficacy of recent and classical theories on the uncertainty of the mean of correlated data have been investigated. A variety of very large data sets make it possible to show that, under circumstances that are often too expensive to achieve, the integral time scale can be used to determine the effective number of independent samples, and therefore the uncertainty of the mean. To do so, the data set must be sufficiently large that it may be divided into many records, each of which is many integral time scales long. In this circumstance, all lags of the autocorrelation should be integrated to determine the integral scale. Some secondary findings include that the classical definition of the integral time scale goes identically to zero if a single record of any length is used and demonstration that measuring the integral scale requires ensemble averaging. Estimation of the integral time scale for a single record requires that the integration of the autocorrelation be truncated. This works well for signals where anti-correlation is not present. Additionally, for anti-correlated samples, the effective number of samples exceeds the number of acquired samples.

Validation assesses the accuracy of a mathematical model by comparing simulation results to experimentally measured quantities of interest. Model validation experiments emphasize obtaining detailed information on all input data needed by the mathematical model, in addition to measuring the system response quantities (SRQs) so that the predictive accuracy of the model can be critically determined. This article proposes a framework for assessing model validation experiments for computational fluid dynamics (CFD) regarding information content, data completeness, and uncertainty quantification (UQ). This framework combines two previously published concepts: the strong-sense model validation experiments and the modeling maturity assessment procedure referred to as the predictive capability maturity method (PCMM). The model validation experiment assessment requirements are captured in a table of six attributes: experimental facility, analog instrumentation and signal processing, boundary and initial conditions, fluid and material properties, test conditions, and measurement of system responses, with four levels of information completeness for each attribute. The specifics of this table are constructed for a generic wind tunnel experiment. Each attribute’s completeness is measured from the perspective of the level of detail needed for input data using direct numerical simulation of the Navier–Stokes equations. While this is an extraordinary and unprecedented requirement for level of detail in a model validation experiment, it is appropriate for critical assessment of modern CFD simulations.

Chauvenet's criterion is commonly used for rejection of outliers from sample datasets in engineering and physical science research. Measurement and uncertainty textbooks provide conflicting information on how the criterion should be applied and generally do not refer to the original work. This study was undertaken to evaluate the efficacy of Chauvenet's criterion for improving the estimate of the standard deviation of a sample, evaluate the various interpretations on how it is to be applied, and evaluate the impact of removing detected outliers. Monte Carlo simulations using normally distributed random numbers were performed with sample sizes of 5–100,000. The results show that discarding outliers based on Chauvenet's criterion is more likely to have a negative effect on estimates of mean and standard deviation than to have a positive effect. At best, the probability of improving the estimates is around 50%, which only occurs for large sample sizes.

Computation Fluid Dynamics provides attractive features for design, and perhaps licensing, of nuclear power plants. The most important of these features is low cost compared to experiments. However, uncertainty of CFD calculations must accompany these calculations in order for the results to be useful for important decision making. In order to properly assess the uncertainty of a CFD calculation, it must be “validated” against experimental data. Unfortunately, traditional “discovery” experiments are normally ill-suited to provide all of the information necessary for the validation exercise. Traditionally, experiments are performed to discover new physics, determine model parameters, or to test designs. This article will describe a new type of experiment; one that is designed and carried out with the specific purpose of providing Computational Fluid Dynamics (CFD) validation benchmark data. We will demonstrate that the goals of traditional experiments and validation experiments are often in conflict, making use of traditional experimental results problematic and leading directly to larger predictive uncertainty of the CFD model.

Natural convection is a phenomenon in which fluid flow surrounding a body is induced by a change in density due to the temperature difference between the body and fluid. After removal from the pressurized water reactor (PWR), decay heat is removed from nuclear fuel bundles by natural convection in spent fuel pools for up to several years. Once the fuel bundles have cooled sufficiently, they are removed from fuel pools and placed in dry storage casks for long-term disposal. Little is known about the convective effects that occur inside the rod bundles under dry-storage conditions. Simulations may provide further insight into spent-fuel dry storage, but the models used must be evaluated to determine their accuracy using validation methods. The present study investigates natural convection in a 2 × 2 fuel rod model in order to provide validation data. The four heated aluminum rods are suspended in an open-circuit wind tunnel. Boundary conditions (BCs) have been measured and uncertainties calculated to provide necessary quantities to successfully conduct a validation exercise. System response quantities (SRQs) have been measured for comparing the simulation output to the experiment. Stereoscopic particle image velocimetry (SPIV) was used to nonintrusively measure three-component velocity fields. Two constant-heat-flux rod surface conditions are presented, 400 W/m2 and 700 W/m2, resulting in Rayleigh numbers of 4.5 × 109 and 5.5 × 109 and Reynolds numbers of 3450 and 4600, respectively. Uncertainty for all the measured variables is reported.

Transient convection has been investigated experimentally for the purpose of providing computational fluid dynamics (CFD) validation benchmark data. A specialized facility for validation benchmark experiments called the rotatable buoyancy tunnel (RoBuT) was used to acquire thermal and velocity measurements of flow over a smooth, vertical heated plate in air. The initial condition was forced convection downward with subsequent transition to mixed convection, ending with natural convection upward after a flow reversal. Data acquisition through the transient was repeated for ensemble-averaged results. With simple flow geometry, validation data were acquired at the benchmark level. All boundary conditions (BCs) were measured and their uncertainties quantified. Temperature profiles on all the four walls and the inlet were measured, as well as as-built test section geometry. Inlet velocity profiles and turbulence levels were quantified using particle image velocimetry (PIV). System response quantities (SRQs) were measured for comparison with CFD outputs and include velocity profiles, wall heat flux, and wall shear stress. Extra effort was invested in documenting and preserving the validation data. Details about the experimental facility, instrumentation, experimental procedure, materials, BCs, and SRQs are made available through this paper. The latter two are available for download while other details are included in this work.

Model validation for computational fluid dynamics (CFD), where experimental data and model outputs are compared, is a key tool for assessing model uncertainty. In this work, mixed convection was studied experimentally for the purpose of providing validation data for CFD models with a high level of completeness. Experiments were performed in a facility built specifically for validation with a vertical, flat, heated wall. Data were acquired for both buoyancy-aided and buoyancy-opposed turbulent flows. Measured boundary conditions (BCs) include as-built geometry, inflow mean and fluctuating velocity profiles, and inflow and wall temperatures. Additionally, room air temperature, pressure, and relative humidity were measured to provide fluid properties. Measured system responses inside the flow domain include mean and fluctuating velocity profiles, temperature profiles, wall heat flux, and wall shear stress. All of these data are described in detail and provided in tabulated format.