A low speed, closed loop wind tunnel at Texas A&M University is presented for the study of turbulent mixing produced by a variety of flows types. Anticipated experiments range from canonical “unit flows” to more complex combinations of flows and geometries. Originally located at the University of Pittsburgh, the facility has since been re -located to the Thermal Hydraulics Verification and Validation (THVV) laboratory at Texas A&M University. The tunnel has undergone considerable modification and updated diagnost ics prompting renewed interest in flow quality assessment. This includes a thorough mapping of the tunnel inlet velocity profile provided by Particle Image Velocimetry (PIV) measurements. Additional temperature and gage pressure measurements complete the assessme nt of system capabilities. These preliminary diagnostics yield empirically determined bo undary conditions and fluid property correlations necessary for Computational Fluid Dynamics (CFD) model validation. The article concludes with the presentation of two unit fl ow types, including flow past a cylinder, with three distinct cross sections, and a single round jet in cross flow at three velocity ratios. The unit flows serve as initial benchmarks for THVV simulation efforts. Key validation metrics are presented for each benchmark i ncluding ensemble averaged velocities, Reynolds stresses, and prope r orthogonal decomposition (POD) eigenvectors. KEY WORDS Computational fluid dynamics (CFD), Flow quality, Inlet boundary condition, Particle image velocimetry (PIV), Proper orthogon al decomposition (POD), Thermal fluids, Turbulence 1.0 I NTRODUCTION Originally conceived at the University of Pittsburgh [1, 2] , the Thermal Hydraulics Verification and Validation (THVV) laboratory’s low speed wind tunnel was moved to Texas A&M University in 2016. The tunnel’s ongoing motive is to produce high fidelity thermal fluid experimental data for comparison to analogous computational models. The tunnel is capable of operation with or without the use of a free (or transverse) jet. Since its move, the laboratory has acquired several new diagnostics tools, whi ch prompted a renewed interest in facility characterization and flow quality. For the experimentalist, immediate advantages of this report are a detailed overview of the retrofitting of the tunnel test section for improved model and measurement (intrusive and non -intrusive) accessibility, as well as proper quantification of system capabilities for accurate proposal of experimental conditions. Long term advantages of the report serve the computationalist, who will no doubt find several quantities of interest useful for computational fluid dynam ics (CFD) modeling inputs. The article closes with two examples of validation data sets co llected using the facility. The data sets provide two canonical flow types that are of interest in a current campaign involving more complex variations of these flows. The current diagnostics treatment empirically confirms the analytical calculations that formed the basis of the tunnel’s original design. This objective is coupled with the desire to produce a test section flow quality that is sufficient for experiments i n the area of thermal fluid sciences and to address ongoing concerns or areas of improve ment where needed. In general, the criteria for flow quality first and foremost implies low acoustic (noise) and vortical (turbulence) disturbance fields [3, 4] . It is high ly desirable to keep these facility disturbances to a minimum to avoid unwanted responses in the test section and as artifacts in the test measurements. A common example would be the concern of turbulence and its influence on boundary layer transition foun d in lift -drag measurements [5]. Likewise, a typical culprit of acoustic noise is the flow motivation, i.e. the driving fan or blower. The driving mechanisms behind tur bulence and noise generation are different and so too are their m easurement. Given the current needs and available measurement equipment, acoustic treatments are deemed outside of the scope of the current evaluation. Concurrent with the requirement for low disturbance, nonuniformities in the mean velocity and temperature must be minimized prior to the final suppression of turbulence. Ideally, at this location, the scale of the turbulence is comparable to the non uniform ities in mean velocity and temperature [3]. Spatial non -uniformities in velocity greatly affect the general flow field and transition processes that occur in the test section, including the evolution of wakes and shear layers, as well as aerodynamic forces imposed on models [6]. Likewise, in non -isothermal testing, temperature gradients and profiles are influenced by non -uniformities found upstream causing similar measurement bias. While concerns over flow quality and carefully tuned experiment al parameters constitute accurate depictions of the physics themselves, more modern treatments in verification, validation, and uncertainty quantification fully bridge the numerical con nection. Indeed, a modern facility shakedown cannot afford to be withou t proper uncertainty quantification. Conventional probe measurements and their corresponding treatments have received considerable attention in years past, with an admirable treatment on the sub ject given by Moffat [7] that has influenced several standards in measurement science. Building upon this work, the current article promotes uncertainty calculations in accordance with the standards promoted by ASME [8, 9] . More recently, the lines between experiment and numerical algorithms have blurred, with the advance of non -obtrusive optical techniques such as particle image velocimetry (PIV). At the time of this writing, new methodologies for optical measurement uncertainty quantification are ongoing and will no doubt morph with new algorithm developments as w ell. As such, the suggestions of Oberkampf and Smith [10] are employed as a means of potential future use or adjustment of the current PIV results and uncertainty quantification. 2.0 EXPERIMENTAL DESIGN A recommended first source is the comprehensive guide to low speed wind tunnel design and testing by Barlow et al. [11]. In application, the design rules of Mehta and Bradshaw [12] and the flow quality insights of Reshotko, Nagib, and Saric [3, 4] have proven to be invaluable resources for low disturbance tunnel design. Regarding experimental measurement and validation, the interested rea der is highly encouraged to review the text of Coleman et al. [13], the standards promoted by ASME [9], and the paper by Oberkampf and Smith [10]. 2.1 Facility The closed loop, low speed wind tunnel facility is capable of velocities in the range of 9.52 ≤𝑈∞≤ 33.02 m/s, where 𝑈∞ is the fre estream bulk velocity, calculated according to the two -dimensional spatially integrated mean of the respective plane. The tunnel test section measures 609.6 × 457.2 × 217.7 mm, corresponding to its length, width, and height, respectively. Corresponding inl et Reynolds numbers range from 3.16 ≤𝑅𝑒∞≤ 8.53 × 105. In total, the tunnel’s footprint is 7.1 × 1 m and stands 1.9 m high. An isometric view of the full Computer Aided Design model is presented in Figure 1. Figure 1: Isometric view of low speed wind tunnel . Referencing Figure 2, the flow is motivated by a Greenheck Mixed Flow Fan Model QEI -22-I-50 with an internal diameter of 771.652 mm. The fan houses seven blades and twelve stators, with an additional three counter rotated stators at the three, seven, and eleven o’clock position. The fan was selected for its favorable low sound (inlet sound power = 77 dBa, outlet sound power = 7 9 dBa), high efficiency (static efficiency of 29%), return air design. A 3.73 kW inductio n motor, capable of 1839 rpm maximum speed, powers the fan. The motor assembly is external from the fan casing and employs a belt drive configuration, minimizing heat transfer from the motor to the freestream and negating any potential acoustic disturbance s. The motor is controlled by a Yaskawa Z1000 variable frequency drive with a 100:1 turndown ratio, and ±0.01 RPM resolution. The fan is directly mounted (fixed) to the floor, with each foot employing a 19.05 mm thick rubber pad for vibrational dampening. Figure 2: Front view of low speed wind tunnel . From the fan, the flow moves in the clockwise direction ( Figure 2) first throu gh a round to square (rectangular) transition. This rectangular interface measures 914.4 × 609.6 mm and constitutes the internal cross section of the tunnel, excluding the fan, transitions, and test section itself. Unless otherwise noted, the primary ducti ng material for the facility is nominal 3.175 mm stainless steel. Continuing along the flow path, the next interface includes a 180 ° duct which routes the flow towards the upper half of the upright tunnel. The flow then traverses through a 2.4384 m settl ing chamber. Inside this chamber are two identical aluminum honeycomb layers, with nominal cell diameters of 25.4 mm and a cell length/diameter ratio of 8. A galvanized steel mesh screen is place d at the end of the settling chamber with a wire diameter of 0.51 mm, nominal square aperture of 2.03 mm2, 3.937 wires/cm, constituting a 64.0% open area. The honeycomb layers and screen dimensions were specified with the recommendations provided by [12, 14, 15] .The final conditioning element before the test section is a contraction, also referred to as a nozzle. The contraction s erves to reduce turbulence intensity by accelerating the flow and ensures reduced velocity gradients, minimizing turbulent anisotropy in the test sectio n [5]. The contraction is composed of 2 × 2 weave carbon fiber weaves whose curva ture incorporates a fifth order polynomial in both the spanwise and transverse directions, as originally promoted by [12, 16] . The nozzle tapers the flow from the larger tunnel cross section to that of the test section across its 0.9144 m length. The tunnel ducting and test section cross sections constitute a con traction ratio (inlet to outlet area) of 8.47 across the device. The flow conditioning elements have been carefully designed and placed to introduce highly uniform velocity and low turbulence conditions into the test section. As previously mentioned, the test section inlet is 457.2 × 217.7 mm and is 609.6 mm in length. The test section walls consist of 9.525 mm thick polycarbonate with three of the four sides incorporating window cutouts and the fourth devoted solely to op tical accessibility. The bottom (floor) window consists of a nominal 292.1 mm diameter cutout. The large field of view enables opti cal access and the circular shape provides variability in model mounting (i.e. aerodynamic sting or rake) at discrete 22.5 ° interv als. The side wall incorporates a rectangular window of 254 × 127 mm for wall mounting needs (i.e. cylinders, such as the work of Shafi et al. [17]). The top (ceiling) incorporates a large square cutout with a side length of 317.5 mm. The ceiling cutout is meant to provide a flexibl e “adapter” plate to other test section inserts and experiments such as the turbulent jet investigations of Reed et al. [18] and Lewandowski et al. [19]. All test section wall and window interfaces have been carefully machined and properly sealed to prevent unwanted boundary lay er interactions or leakages from the system, while minimizing optical inaccessibilit y. As a final precaution for optical measurements, external matte black foam cutouts, sized for each test section wall, are available to block out unwanted ambient lighting dur ing testing. The test section frame is composed of 8020 aluminum allowing for a variety of framing solutions for future experimental needs. Each framing leg uses a 3.175 mm rubber dampener. The test section is free floating on a large Newport RS2000 -48-12 Optical Table with S-2000 StabilizerTM Vibration Isolators. The dampeners, tabl e, and isolators act to reduce unwanted vibrational coupling promoted by the tunnel on the diagnostic equipment. The outlet of the test section is mated to a linear expansion, which acts to properly expand the flow back to the larger tunn el ducting cross section and limit any unwanted back pressure effects in the test section area. The flow is then rerouted back to the fan via a secondary 180 ° elbow, straight duct, and square to round transition, completing the closed loop system. The square to round trans ition is identical to the previously mentioned round to square transition found on the front of the fan. Taylor et al. [20] have previously examined the streamwise and cross -stream velocities in a square to round transition duct using laser doppler velocimetry . They reported that streamwise boundary layers incur smaller thicknesses away from the fillets of the transition duct and that secondary vel ocities occur as a result of cross -stream pressure gradients formed by the longitudinal curvature of streamlines pa ssing through the transition. These effects promote unsteadiness in the immediate region upstream and downstream of the fan which can ultimately propagate to the test section. These behaviors will be investigated further in Section 3.2. As denoted in Figure 2, there are two dedicated 1 in NPT ports available for PIV seeder particle injection and the “skid return”. This second port refers to a secondary heat and flow contr ol system affectionately re ferred to as the “skid”. The modular system is typically employed for jet in cross flow studies, where the flows are generated by the skid and wind tunnel, respectively. A separate design and flow diagnostics report on this facility is curren tly in develop ment. 2.2 Instrumentation 2.2.1 Time -Resolved Particle Image Velocimetry Major components of the particle image velocimetry system include a pair of high -speed cameras, a dual -pulse laser, and seeding particle generator. The cameras are both Phantom Mir o M120’s with a 12 -bit dynamic range and maximum resolution of 1920 × 1200 pixels. Each camera utilizes a Nikon AF NIKKOR 50 m f/1.8D lens and a LaVision Inc. 527 nm lens filter with 10 nm band pass a nd 70% transmission efficiency. For two -dimensional meas urements, the laser sheet is generated by a Photonics Industries DM30 -527-DH laser with a maximum power of 60 mJ/pulse at 527 nm. The laser sheet thickness is approximately 1.0 mm with the minimum thick ness carefully aligned with the center of the field of view, in this case the centerline of the tunnel test section. The seeding particles are Dioctyl Sebacate, which has favorable properties including non -toxic and evaporation at moderately high temperatures. The particles are introduced into the flow using a TSI Six Jet Atomizer Model 9306 with only two of the seeder jets utilized in conjunction with an air compressor. Typical settings for the compressor include a regulated pressure of 60 psi for 2 -6 seconds per measurement. The PIV system captures velocity fields in major planes, producing inlet profiles along the height and width of the test section. Several key parameters regarding the camera setup, and data acquisition are summarized in Table 1. In total, five distinct slices are measured across both the 𝑥𝑦 and 𝑥𝑧 planes, providing an extensive look at the inlet hydraulic behavior. These width and height velocity fields constitute the 𝑥𝑦 and 𝑥𝑧-planes, respective ly, where 𝑥 represents the streamwise flow direction. The calibration measurements are performed across the entirety of the tunnel’s operating spectrum and are controlled via the motor variable frequency drive. Particular emphasis is placed on the centerl ine profiles, with six repeatable trials in the 𝑥𝑦 center plane and twelve repeatable trials in the 𝑥𝑧 center plane. Table 1: PIV setup and data acquisition parameters for tunnel diagnostics Acquisition Parameter 𝒙𝒚 Plane 𝒙𝒛 Plane Number of Cameras 2 1 Camera Configuration Mono (stitched) Mono Sampling Frequency [Hz] 1000 1000 Sampling Time [sec] 2.48 2.97 Fit Model Pinhole Pinhole RMS of Fit 0.239622 0.264949 0.28104 Scale factor [px/mm] 6.84424 6.63192 5.38057 Focal Length [mm] 62.5972 61.326 61.5695 Field of View [px × px] 1920 x 432 1920 x 432 576 x 1200 The images are processed using LaVision DaVis 8.4.0 and consists of three primary stages: image pre -processing, vector processing, and post -processing. At the most fundamental level, the pre -processing stage serves as a last numerical filter to differentiate the seeding particles’ intensity from an ideally uniformly black background. This, in conjunction with a carefully designed e xperiment (black background , little to no ambient lighting, uniform laser pulsing, and bandwidth filters) prime the images for vector field generation. The vector field processing step takes the raw images and converts them to instantaneous velocity vector fields m apped onto a squar e, regular Cartesian grid in Eulerian space. Post processing is performed in two parts. The first serves to remove any clearl y erroneous vector fields. At this step, the data is not compromised in any way and still represents the true measurement. As a result of the first step of post processing, the vector fields may have missing information, visually seen as “holes” in the vector fie lds. For analysis involving the temporal dynamics of the fluid flow, this is less than ideal. To this end, a second post pro cessing step is performed that interpolates empty spaces using the vector location’s immediate neighbors. Ensemble statistics are then calculated for both t he first and second post -processed vector field data sets. The first post processed set is used for ensemble statistics and uncertainty calculations while the second is used explicitly for analyses that are highly sensitive to temporal behavior. The full details regarding t hese three major steps are provided in Table 2. Table 2: DaVis algorithms and options . Step Process Description 1 Pre-Processing Subtraction Filter • Butterworth High Pass Filter Filter length = 7 images 2 Processing Vector Calculation: Double Frames (PIV) • Vector Calculation Parameter: Cross -Correlation Iterations: Multi -pass (decreasing size) Window size=64x64; Weight=Square 1:1; Overlap=75%; Passes=2 Window size=32x32; Weight=Circle 1:1; Overlap=75%; Passe s=4 Options Enabled: Image correction; Calculate uncertainty; High accuracy mode for final passes • Multi -pass options Initial window shift for image reconstruction (first pass only)=Constant Correlation function" All initial pass(es): 'standard' I1*I2 (via FFT, no zero -padding) Final pass(es): normalized (I1 -I1avg)*(I2 -I2avg)/Stdev Deformed interrogation windows: Symmetric shift (both frames) • Multi -pass processing Peak ratio Q < 2 2x Median filter: remove and literately replace (>2 Stdev, <3 Stdev dev) 3.1 Vector Post Processing • Allowable vector range: Vx: 0 +/ - 1.5Ub; Vy: 0 +/ - 0.5Ub; 3.2 Vector Post Processing • Enable: Fill -up empty spaces (interpolation) PIV measurements pose an interesting challenge in that the velocity fields are a function of both physical or analog observat ion and numerical computation. The fundamental PIV algorithm matches two consecutive images to compute a displacement field 𝑑𝑥(𝑥,𝑦) as the best fit (denoted by *) between the first image intensity 𝐼1(𝑥,𝑦) and second image intensity 𝐼2(𝑥+𝑑𝑥(𝑥,𝑦),𝑦+𝑑𝑦(𝑥,𝑦))= 𝐼2∗(𝑥,𝑦) via maximizing their correlation given by the sum (𝐼1𝐼2∗). Several renditions and modification s to this f undamental basis have been proposed and implemented over thirty years of PIV research, however most of the significant work in PIV uncertainty quantification has only occurred within the past ten years. Recently, Schiacchitano et al. [21] have utilized a dedicated experimental data base provided by Neal et al. [22] to assess four leading uncertainty quantification methods. Their work concluded that for first order statistics, the most accurate method was the correlation statistics method of Weineke [23], summarized here. Given two consecutive PIV images, or an image pair, the second image intensity, 𝐼2(𝑥), is dewarped onto the first, 𝐼1(𝑥), using the computed displacement field, 𝑢(𝑥). This provides two nearly identical matching images whose correlation function is defined by Equation (1). 𝐶(𝑢)=∑(𝐼1(𝑥,𝑦)𝐼2(𝑥+𝑢,𝑦))=∑(𝐼1(𝑥,𝑦)𝐼2∗(𝑥,𝑦)) (1) It is assumed that the PIV algorithm is converged such that the correlation function is a maximum when 𝑑𝐶/𝑑𝑢=0. Thus, small differences ±Δ𝑥 from the correlation peak should be identical regardless of their sign (+ or -). In the event of a non -zero slope, a n iterative predictor -corrector scheme analyzes differences in the correlation function by shifting the peak of correlation function via 𝑢+ 𝛿𝑢 with 𝛿𝑢 shown explicitly in Equation (2). Each iteration is considered equivalent to an extra step of the PIV algorithm. 𝛿𝑢=Δ𝑥 2log(𝐶+)−log(𝐶−) 2log(𝐶0)−log(𝐶+)−log(𝐶−)=𝑓(𝐶0,𝐶−,𝐶+) =𝑓(𝐶0,𝐶±−Δ𝐶 2,𝐶±+Δ𝐶/2) (2) It is convenient to prescribe shifts in the correlation peak according to (3). Δ𝐶=∑Δ𝐶𝑖=∑(𝐼1(𝑥,𝑦)𝐼2∗(𝑥+Δ𝑥,𝑦)−𝐼1(𝑥+Δ𝑥,𝑦)𝐼2∗(𝑥,𝑦)) (3) Each term Δ𝐶𝑖 is an elemental contribution to the total correlation difference. The standard deviation of Δ𝐶=∑Δ𝐶𝑖 is related to the covariance matrix of the particle positions in each frame ( Δ𝐶𝑥1,𝑦1 and Δ𝐶𝑥2,𝑦2) and require s that each Δ𝐶 term has a zero mean. The auto-covariance term is non-zero inside a small neighborhood given by the particle image diameter and outside of this region the autocorrelation drops to zero. This allows for the typical 4D sum of the covariance matrix to be rewritten as a 2D sum over the distances Δ𝑥 and Δ𝑦 as seen in Equation (4). 𝜎Δ𝐶2=𝑛2∑ 𝑐𝑜𝑣(Δ𝐶𝑥,𝑦Δ𝐶𝑥+Δx,y+Δy) Δ𝑥Δ𝑦 =∑ ∑ (Δ𝐶𝑥,𝑦∙Δ𝐶𝑥+Δ𝑥,𝑦+Δ𝑦)𝑛 𝑥,𝑦=1 Δ𝑥Δ𝑦 =∑ 𝑆Δ𝑥Δ𝑦 Δ𝑥Δ𝑦 (4) The correlation statistics method then calculates the systematic uncertainty, 𝑏𝑖, according to Equation (5). 𝑏𝑖=𝜎𝑢=𝑓(𝐶0,𝐶±−𝜎Δ𝐶 2,𝐶±+𝜎Δ𝐶/2) (5) The correlation statistics method as described above applies to single variable uncertainties in the PIV measurement. These include the instantaneous velocity components, their respective means, and vector magnitudes which are directly measured and inferred. In turbulence, there are numerous statistical and instantaneous quantities of interest derived from the velocity f ields, who have corresponding propagated uncertainties, such as the standard deviation, its magnitude, variance/covariance (Reynolds stresses ), turbulence intensity, turbulent kinetic energy, vorticity, etc. The PIV uncertainty quantification is further co mplicated by the spatio - temporal resolution and elapsed time of the measurement which for most existing systems is limited to low sampling rates (~15 Hz) over large time periods, or time -resolved systems which sample at much higher speeds ( ≥1 kHz) over sho rt time periods. Recent efforts by Sciachhitano and Wieneke [24] have provided a framework for propagating instantaneous measurement uncertainty to derived quantities of interest using linear error propagation. They discuss that in the instance of correlated samples, the uncertainties of statistical properties are larger because the effective numbe r of independent samples is smaller , yielding artificially high uncertainties . They propose the use of an effective number of samples , 𝑁𝑒𝑓𝑓, as seen in Equation (6). 𝑁𝑒𝑓𝑓=𝑁 ∑ 𝜌(𝑛Δ𝑡)+∞𝑛=−∞ (6) Where 𝑁 is the total number of samples and 𝜌(𝑛Δ𝑡) is the autocorrelation of the independent samples. Computation of the effective number of samples is thus only deemed accurate if the longest flow fluctuations are captured several times. In the instance of purely uncorrelated data, the effective number of samples si mply returns the original total number of samples, 𝑁. The interested reader is highly encouraged to review this paper for a full delineation of the uncertainty propagation of each statistical quantity of interest, considered too broad to include in the cu rrent review. The authors employed a commendable evaluation of the linear error propagation, including both existing experimental data and Monte Carlo simulations. They conclude that the uncertainty of time -averaged quantities are accurate to within 5%, wh ereas for Reynolds stresses accuracy is slightly larger at about 10%, and vorticity falling within 5 -10% [24]. The current work’s uncertainty propagation is faithful to methodologies discussed above, constituting the systematic uncertainty, 𝑏𝑖, in PIV measurements. To avoid any discrepancy in terminologies across different discipl ines, let it be clearly stated: the author’s choice to deem these uncertainties as systematic contributors is based on the definitions and standards proposed in the ASME V&V 20 -2009 [9], which treats this unconventional uncertainty evaluation as a known, (directly quantified ) measurement source. The random component of uncertain ty, 𝑠𝑖, of the PIV measurements incorporates the repeatable trials mentioned previously for the centerline profiles. The values are calculated according to the student’s t -distribution with 95% confidence and 𝑁 degrees of freedom, where here 𝑁 constitu tes the number of trials [25]. Calculation of the random uncertainty component associated with each vector in the PIV field is displayed in Equation (7) using the streamwise component of velocity as the example metric . This formulation is intende d for statistical ly derived quantities of interest, not instantaneous measurements . 〈𝑈〉±𝑡𝑁,𝑃𝑠〈𝑈〉=〈𝑈〉±𝜎〈𝑈〉 (7) Where 𝜎〈𝑈〉 constitutes the standard deviation of the means across each repeatable trial. With both the systematic and random components of the uncertainty known, the values are then combined via a root mean sum of the squares to form the total uncertainty in the met ric according to Equation (8), again using the streamwise component of velocity as an example. 𝑢〈𝑈〉=√𝑏〈𝑈〉2+𝑠〈𝑈〉2 (8) The sec tion concludes with a review of some of the current efforts and contributions in the area of PIV propagated uncertainty quantification. These efforts are not incorporated in the current work and are considered ongoing at the time of this writing. H owever , it is the authors’ strong belief that these efforts , and those that follow, will be of significant benefit to the data sets presented in this work in the future and in re -evaluat ing the uncertainties of derived quantities as needed . A recent paper by Smit h et al. reviews the applicability of the effective number of samples. Smith states that accurate computation of the autocorrelation requires sufficiently long time records which based on their data, suggest a minimum of 20 integral time scales. Recent tre nds in time resolved PIV measurements, favoring high sampling rates and small physical time measurements, are questionable and may not achieve this requirement. The authors demonstrate that if the typical calculation of the integral time scale over the ent ire time record is used, the autocorrelation goes to zero. They suggest that, if a large time record exists, that the autocorrelation across subsets of the time record can provide more accurate depictions of the autocorrelation . Another critical finding is that the uncertainty in the mean of anti -correlated data is smaller for the same number of samples in comparison to the uncorrelated data, implying that the effective number of samples is greater than the total number of samples for anti -correlated data. To reiterate, the quest for accurate depiction of propagated uncertainties in PIV data is an ongoing and appreciably challenging area of measurement science. The results presented herein are amenable to future renditio ns and improvements. To the best of th e authors’ knowledge, the current uncertainty quantification methods are based on the most concrete methods available at the time of this writing. 2.2.2 Pressure Measurements An Apogee Instruments Model SB -100 barometric pressure transducer provides the ambient pressure measurements. Ambient readings are external from the facility, in the laboratory environment and the sensor is housed in a protective cover to ensu re no bias errors occur as a result of an unwanted breeze. Measurements are recorded with a National Instruments NI 9205 data acquisition unit. The device samples at 80 Hz for 3 seconds per measurement. Before the tunnel is turned on, the ambient pressure reading is c ollected, signifying that day’s trial. Over six repeatable trials, the atmosphe ric pressure is found to be 𝑃𝑎𝑚𝑏=102.341 ± 5.416 Pa or 1.023 bar. Systematic uncertainty contributors include the sensor’s manufacturer curve fit, thermal drift, stability (long -term drift), and the data acquisition units’ accuracy and resolution. The random component of uncertainty is provided by the six repeatable trials. The facility is located in College Station, TX, USA, about 103 m above sea level. For all practical purposes, the measured value is in excell ent agreement with atmospheric pressure, and may be approximated as 1 bar. The Omega Engineering Model PX409 -2.5CGUSBH compound gage pressure transducer provides gage pressure measurements in the test section. The device is directly connected to the acquisition computer via USB, sampling for four min utes at 80 Hz per measurement. The sensor is connected to a bushing mounted on the ceiling of the test section at the 𝑥/𝐿=0.875, 𝑦/𝑊=0.389, 𝑧/𝐻=0.5 location. The bushing interface has been carefully installed, mounted flush with the ceiling wall, and visually inspecte d to ensure no burrs obstruct the measurement readings. Before the tunnel is turned on, an initial measurement is recorded, to account fo r the DC offset in the sensor, subtracted from each measurement thereafter. Gage pressures are then collected for each measurem ent involved in the calibration procedure, where the motor operating frequencies are identical to the PIV measurements, mentioned prior. Six repeatable gage pressure calibration trials are performed with the test section completely evacuated. It should be note d that experiments incorporating geometric models in the test section induce additional pressure drop and such experiments should co nsider additional pressure measurements as necessary. Gage pressure results across the tunnel’s operating spectrum will be d iscussed in greater detail in Section 3.3. 2.2.3 Temperature Measurements Six type T thermocouples with a crushed ice bath reference point are calibrated against an Isotech Calisto 2250S Dry Block Calibrator with an Isotech Model 935 -14-61 platinum resis tance thermometer reference probe. The thermocouple voltages are recorded via a National Instruments NI 9213 data acquisition unit and the platinum resistance thermometer resistances are logged by an Isotech MilliK . The NI data acquisition unit and the Mil liK logger are controlled via MATLAB and LabView, respectively and are triggered. The calibration procedure is automated and incorporates thirteen evenly spaced temperature setpoints in the range from 299.817 to 366.483 K. The automated procedure allows fo r the dry block calibrator to settle for 30 minute intervals, ensuring that each calibration point reaches a tightly controlled temperature value. Twelve repeatable trials have been executed to assess repeatability. A linear curve fit is then applied to ea ch thermocouple, from which the maximum uncertainty in a given thermocouple was determined to be ± 0.8297 K. An aerodynamic sting has been manufactured to position one of the thermocouples at the inlet to the tunnel test section without perturbing the flow . Another thermocouple is place externally from the tunnel to record ambient air in the laboratory environment. The remaining f our thermocouples are then placed in two sperate configurations. The first configuration places the s ensors at the inlet cardinal coordinates: North, South, East, and West with respect to the flow direction (“moving with the flow”) . The other test positions the thermocouples on the corners of the inlet, namely North East, South East, South West, and South East. The motivations for these measurement s are two -fold, the first being to determine the centerline steady state temperature of the tunnel across its operating spectrum. Five measurement points were conducted across the spectrum, where for a given test , the tunnel went from room temperature to a steady state temperature over the course of four hours with the thermocouples logging one -hundred samples for one second approximately every fifteen seconds. The final hour of each run constitutes the steady sta te condition from which these measurements are averaged, to formally produce the steady state centerline inlet temperature. The tunnel relies entirely on passive coolin g to remove any undesired heat generation , i.e. as a result of frictional heating and th ese results directly quantify the significan ce. The second motivation takes advantage of the nine available inlet probe locations to produce a temperature mapping across the inlet plan e. This information helps to assess modeling assumptions regarding the t est section inlet temperature profile. 3.0 TUNNEL PERFORMANCE With the facility and instrumentation fully defined, we now introduce the coordinate system and probe locations more formally in Figure 1. The 𝑥-, 𝑦-, and 𝑧-directions apply to the streamwise, spanwise, and transverse directions. The centroid of the coordinate axes is the center point on the inlet face. It should be noted that each of the three major measurement types are collected individually, i.e. on separate occasions, so that any perturbations to the flow caused by one sensor do not influence the measurements of a nother. Based on current experimental capabilities, this section serves t o provide required hydraulic and thermodynamic flow quantities necessary to close governing equations of the thermal fluids experiments intended for this facility. Figure 3: Tunnel diagnostics coordinate system and probe locations . 3.1 Inlet Velocity Calibrations Streamwise velocity inlet profiles are provided in Figure 4 for both the 𝑥𝑦 and 𝑥𝑧 centerline planes with examples of th e lowest and high motor operating frequencies. External framing around the test section inhibits laser light and optical access at the true inlet to the test section. Trustworthy results at nearly identical locations in each plane are found at the 𝑥=29.67 46 mm and 𝑥=30.2505 mm locations, for the 𝑥𝑦 and 𝑥𝑧 planes, respectively. In general, conventional PIV is not well suited for boundary layer measurements and the near wall measurements need be treated with some level of scrutiny. Besides the camera re solution constraint, the laser poses physical reasons for this as well. The laser enters the test section in the -𝑦 and + 𝑧 direction for the 𝑥𝑦 and 𝑥𝑧 planes, respectively. In general, the near wall measurements along the laser’s entering side provid e a slightly better signal than that on the exiting side, where laser energy is scattered by seeder particles in the test section and reflected by impact with the secondary (far) wall of the test sectio n. These factors explain the increased uncertainty in the near wall regions for both sets of measurements. The freestream motion of the fluid however, is captured quite well and provides a good basis for calculating a bulk fluid motion, according to the integral mean, 𝑈∞(𝑥,𝑦)= ∫ 𝑈(𝑥,𝑦)𝑑𝑦𝑦/2 −𝑦/2∫ 𝑑𝑦𝑦/2 −𝑦/2⁄ for the 𝑥𝑦-plane, and analogously for the 𝑥𝑧 plane. (a) (b) (c) (d) Figure 4: Test section inlet velocity profiles for 𝒙𝒚 plane (a) lowest and (b) highest speed and 𝒙𝒛 plane (c) lowest and (d) highest speed. Applying this formulation to each measurement point in each of the two planes produces Table 3. The bulk freestream velocities in each plane are compared via a relative error, where the 𝑥𝑧 plane is considered the more trustworthy plane, as a result of one camera (no stitching needed) and better near wall accuracy as evident from Figure 4. The relative error reveals that the two measurement planes produce highly agreeable results, with a maximum difference of ~4%. Table 3: Bulk inlet streamwise velociti es across tunnel operating spectrum . Motor Frequency, 𝒇𝑽𝑭𝑫 [hz] Bulk freestream velocity, 𝑼∞(𝒙,𝒚) [m/s] Bulk freestream velocity, 𝑼∞(𝒙,𝒛) [m/s] Relative error, 𝝐=|𝑼∞(𝒙,𝒛)−𝑼∞(𝒙,𝒚)| 𝑼∞(𝒙,𝒛) 16.0 10.11 10.03 0.01 19.8 12.42 12.12 0.02 23.6 14.86 14.30 0.04 27.3 17.34 17.24 0.01 31.1 20.07 19.51 0.03 34.9 23.30 22.91 0.02 38.7 26.00 25.18 0.03 42.4 28.53 28.11 0.01 46.2 31.27 30.47 0.03 50.0 33.58 32.91 0.02 With freestream bulk velocities firmly established, all ten measurement points in each plane can be readily seen in their non - dimensionalized form according to Figure 5. (a) (b) Figure 5: Non-dimensionalized streamwise velocity profiles for each calibration measurement in (a) 𝒙𝒚 plane and (b) 𝒙𝒛 plane . Note: uncertainties in both sub figures are scaled ×4 for visualization . Table 3 also provides the basis for the inlet velocity calibration which yields a linear relation between the motor operating frequency , 𝑓𝑉𝐹𝐷, and the tunnel freestream bulk inlet velocity according to Figure 6(a) with corresponding deviation in Figure 6(b). The linear fit is applied to the “mean o f means” across all available trials in the 𝑥𝑧-plane, which is typically the primary plane of interest in experimental measurements for this test section. The linear fit produces an adjusted -𝑅2 value of 0.998 with a root mean square error of 0.3412. Fro m Figure 6(b) it is evident that across all measurements, the maximum deviation is about ±0.5 m/s reaffirming the accuracy of the calibration. (a) (b) Figure 6: (a) Bulk free stream velocity calibrations across tunnel operating range and (b) deviation between measured and fitted values . With established inlet velocity profiles and bulk freestream velocities valued well understood, we turn our attention now to the critical topic of inlet modeling. For turbulent flow in square nozzles in the low speed regime, a top hat profile is expected . Several flow condition ing elements have been implemented to meet this need as discus sed in Section 2.1. Figure 4 and Figure 5 provide further quantified proof that the top hat profile is indeed appropriate. A thorough affirmation of the top hat profile however , is provided by assessing the five inlet traces in each place, encompassing the entirety of the test sections spanwise and transv erse directions as seen in Figure 7. As stated earlier, conventional PIV systems are poorly suited for near wall measurements. It is expected that bound ary layers for these locations will differ, as a function of the test section dimensions and corner proximity . Dular et al. [26] utilized Laser Doppler Velocimetry to confirm th ese observation s with their water tunnel facility. If higher fidelity measurements in the near wall regions are needed, it may be worthwhile to pursue similar measurements with Laser Doppler Velocimetry or Hot -Wire Anemometry on the current facility as well. Overall, the current free stream profiles infer that a top hat inlet profile is indeed appropriate across the entirety of the tunnel’s operating conditions. (a) (b) (c) (d) Figure 7: Collapsed streamwise inlet velocity profiles for 𝒙𝒚 plane (a) lowest and (b) highest speed and 𝒙𝒛 plane (c) lowest and (d) highest speed. 3.2 Unsteady flow effects Inlet flow angularity is a critical metric in assessing the flow “steadiness”. The angularity of the inlet flow also helps to assess the essential modeling assumption of a purely unidirectional flow, i.e. the streamwise component of velocity, 〈𝑈〉, is the only non -zero mean velocity component at the inlet. Barlow at al. [11] have described the inlet flow angularity as an essential diagnostic for quantifying potential flow separations that may be occurring upstream in the tunnel and inadvertently affecting experimental results in the test section. Such irregularities can occur as a result of flow separation from the contraction, diffuser, and potential air leaks . Other sources of unsteadiness are promoted by rotating machinery elements: non -uniform inflow to the fan can be determined from the dominant frequencies matching the blade frequency or possibly harmonics. Mechanical vibration also promotes these affects and typi cally occurs at the fan speed. Thus, quantifying this “upflow” effect is useful in providing tunnel corrections for experimental results. One appreciable example is the correction of drag effects that may be aided or deterred by upflow. The concerned reade r is advised to see Barlow et al.’s text on the subject for more details on this and other such corrections. The PIV results have the advantage of providing thousands of vectors, collected synchronously, for comparison. The flow angularity for a given velocity vector can thus be determined simply from trigonometry according to, 𝜃=tan−1(〈𝑉〉〈𝑈〉⁄ ), and analogously for c omponents 𝑈 and 𝑊. The current investigation focuses again on the 𝑥𝑧 plane which has the benefit of one camera, without stitching vector fields thereby compromising the true measurement in the overlapping region. The results of this comp utation are pro vided in Figure 8 for the minimum and maximum operating conditions. With the exception of three points in the lower portion of Figure 8(a), the inlet traces all appear to be within ±1.2°. The results are met with some scrutiny, where from Table 1 it can be seen that the scaling factor for the 𝑥𝑧 plane is 5.38057 px/mm. In this sense, the PIV system is again limited in its results, reflecting similar concerns as previously mentioned for the near wall region. In general, the assumption of a uni -direc tional inlet velocity is still considered reasonable from this current investigation and leaves room for future work with higher spatial fidelity measurements in the n ear wall regions. (a) (b) Figure 8: Flow angularity profiles in the 𝒙𝒛 plane for the (a) minimum and (b) maximum speed. Next, the root-mean -square (RMS ) velocity for the streamwise component (= √𝑢2) is examined . The RMS velocity, while lacking physical significance, borrows from the principl es of signal analysis in electrical engineering to offer a first intuitive look into the turbulent energy content [27]. It is typically normalized by a bulk inlet velocity or centerline velocity to produce the well -known ‘turbulence intensity’ . Well established turbulence models usually require some quantification of the expected turbulent kinetic energy at the inlet, with the str eamwise velocity component being the first and most essential metric to this end. As such, the turbulence intensities for each inlet profile across the entire operating spectrum are presented in Figure 9. The ideal profile at any given operating speed, consists of a flat ( very low turbulence intensity) region in the freestream and two distinct and identical peaks in the near wall regions, where fluctuatio ns are expected to be higher. Figure 9 presents these results with fixed axes limiting the turbulence intensity displayed to √𝑢2≤25%, thereby exacerbating the local behaviors of turbulence intensities for inspection . Figure 9: Turbulence intensity profiles for each calibration measurement in 𝒙𝒛 plane . The same spatially integra ted mean calculation used to calculate the freestream bulk velocities from the velocity profiles is now applied to the RMS velocity profiles from Figure 9 to produce Table 4. Present values are in the range of 3.99 – 11.77% , with turbulence intensity values being inversely proportional to operating speed. The large values occurring at low speeds are believed to be over-estimated as a result of the discrepancies in the current pulse timing utilized for high speed measurements. It is worthwhile to revisit the se measurements with conventional PIV or hot -wire anemometry (longer sampling times at lower sampling rates) f or improved estimates. Table 4: Turbulence intensity inlet quantities . VFD [hz] (√〈𝒖𝟐〉) ∞/𝑼∞ (√〈𝒗𝟐〉) ∞/𝑼∞ (√〈𝒘𝟐〉) ∞/𝑼∞ 16.0 11.77% 5.67% 9.83% 19.8 7.41% 6.16% 7.19% 23.6 8.76% 4.28% 7.33% 27.3 6.29% 4.64% 5.84% 31.1 5.63% 3.45% 5.36% 34.9 5.07% 3.75% 4.37% 38.7 4.40% 3.38% 4.10% 42.4 4.73% 3.25% 4.15% 46.2 3.61% 3.23% 3.49% 50.0 3.99% 3.16% 3.60% Streamwise velocity signals are extracted from the inlet centerline point in the 𝑥𝑧 plane for each calibration measurement point. The Fast Fourier Transform is calculated using the MATLAB ‘fft’ function, from which the power spectral density is computed. In reference to Figure 10, the five highest power spectral density magnitudes and corresponding frequencies are used to generate nose gate s (green) for each measurement in comparison to the original unfiltered signals (black) . High powe r spectral density content is observed at higher dominant frequencies for the maximum operating speed as compared to the minimum. This has been previously confirmed by Hunt et al. [28] and their Hot-Wire Anemometry measurements in the Vlebanoff -Saric low speed wind tunnel, a similarly sized facility appropriate for comparison here. The authors measured all three velocity components and confirmed that as tunnel speeds incre ases, low frequency peaks under 20 hz develop and grow in amplitude for the streamwise velocity component only. (a) (b) Figure 10: Raw and filtered (top) velocity signal and (bottom) power spectral density content for (a) minimum and (b) maximum operating spee d. NOTE: For top profiles, left y -axis corresponds with raw signal and right y -axis corresponds with filtered signal. From Table 5, it is clear that the current facility exhibits similar trends to that of [28]. For all motor operating frequencies up to 𝑓𝑉𝐹𝐷=27.3 hz, there exist dominant high frequencies present in the 𝑢 centerline signal. With the exception of the 𝑓𝑉𝐹𝐷=19.8, all other measurements present in the range 16.0 ≤𝑓𝑉𝐹𝐷 ≤ 27.3 exhibit dominant frequencies that are an order of magnitude higher than those in the 31.1 ≤𝑓𝑉𝐹𝐷 ≤ 50 hz range. For the remaining operating frequencies tested, i.e. 𝑓𝑉𝐹𝐷 ≥31.1 hz, the dominant frequencies are below 20 hz, without exceptio n. These observations imply that for motor operating frequencies below 𝑓𝑉𝐹𝐷 <31.1 hz, flow disturbances exist as a result of power, motor, blade passing, or stator passing frequencies and their harmonics [28]. Further investigation should seek to accurately measure all three velocity components and pressure fluctuations at the inlet with a minimum Nyquist frequency of 1 k hz. This is most easily accomplished using a dual (cross) sensor hot-wire anemometer probe and pitot tube . If multiple such sensors are available , a rake formation is suggested. By comparing the power spectral density content of each signal and evaluating the temporal correlation of each signal with itself, the culprit (s) of higher disturbance intensities can be determined. Table 5: Dominant fre quencies ( without parenthesis , 𝒇 [hz]) and power spectral density content ( with parenthesis , PSD [W/hz]) of streamwise fluctuating velocity component at each calibration point (bold row header , 𝒇𝑽𝑭𝑫[hz]). 16.0 19.8 23.6 27.3 31.1 34.9 38.7 42.4 46.2 50.0 0.67 (6.84) 0.34 (2.04) 0.67 (13.62) 1.01 (8.45) 1.01 (7.93) 2.02 (11.28) 1.01 (5.88) 2.36 (32.43) 1.35 (17.83) 1.35 (32.81) 0.34 (5.78) 1.01 (1.56) 0.34 (2.88) 0.34 (7.54) 0.34 (3.53) 1.68 (11.22) 3.70 (3.48) 11.78 (14.28) 0.67 (13.20) 0.67 (17.32) 57.58 (5.51) 0.67 (1.51) 25.25 (2.04) 1.68 (6.74) 2.69 (2.36) 0.34 (8.14) 1.68 (3.15) 5.39 (9.07) 10.77 (11.11) 4.04 (15.91) 5.39 (3.88) 2.02 (1.34) 133.00 (2.01) 0.67 (3.69) 3.03 (2.08) 7.41 (7.15) 6.73 (2.73) 4.38 (8.01) 4.38 (6.03) 2.69 (15.57) 322.56 (3.87) 54.55 (1.21) 116.50 (1.87) 295.29 (2.46) 4.38 (1.63) 0.67 (5.72) 7.07 (2.63) 1.01 (7.60) 1.68 (4.43) 3.37 (9.72) 3.3 Gage pressure calibrations As seen in Figure 11(a), the gage pressure fits a second order polynomial curve fit, as expected, with an adjusted R -squared value of 0.99 and root mean square error of 3.60. For the evacuated test section, gage p ressures in the range of -48.59 ≤𝑝g≤ -517.40 Pa are expected across the operating range of 16.0 ≤𝑓𝑉𝐹𝐷 ≤ 50.0 hz. Figure 11(b) shows that across the entire operating range, the deviation between measurement and the second order polynomial fit is within ± 5.8 ΔPa, with the maximum deviation occurring at 𝑓𝑉𝐹𝐷=38.7 hz. With knowledge of the ambient pressure from Section 2.2.2, total pressure inside the test section ca n also be calculated. The compound gage pressure transducer is capable of high -speed measurements (up to 1 k hz) which prompts potential future avenues for assessing the unsteady behavior of the flow. (a) (b) Figure 11: (a) Gage pressure calibrations in the evacuated test section across tunnel operation range and (b) deviation between measured and fitted values. 3.4 Inlet temperature calibrations Temperature readings provide several benefits towards the overall tunnel diagno stics campaign. In general, properly quantified geometry, flow, pressure, and temperature measurements yield the minimum information necessary to fully constrain the thermal fluid problem. In lieu of a heat exchanger, the discrepancy between the ambient (e xternal from tunnel) and test section inlet temperatures provides an empirical understanding of the heat generation from the tunnel’s turbomachinery. This is paramount in assessing b asic engineering assumptions (i.e. incompressible flow, ideal gas, and neg ligible heat generation) and in turn, the thermo physical properties of the working fluid (density, viscosity, specific heat, thermal conductivity, etc.). From Figure 12(a), the centerline inlet temperature follows a linear trend, as expected. The linear curve fit has an adjusted R -squared value of 0.97 and a root mean square error of 0.641. Figure 12 shows that across the operating range, the deviation between experiment and curve fit is within ±0.66 K, with the maximum deviation occurring at 𝑓𝑉𝐹𝐷=38.7 hz , based on available measurements. The expected inlet centerline temperature across all measurements is 296.89 ≤〈𝑇𝑐〉≤ 305.97 K, implying that the operating range fits within 10 ΔK. The results show that very little heat is added to the system, no doubt as a result of the exterior motor design and little frictional heating provided by the fan itself. (a) (b) Figure 12: (a) Test section inlet centerline temperature calibration across tunnel operating range and (b) deviation between measured and fitted values. To provide a truly comprehensive assessment of expected inlet modeling assumptions and properties of the flow, the temperature inlet profiles’ spatial dependence is also required. Additional temperature measurements are conducted as described in Section 2.2.3 to fulfill this need . Results of the additional edge (near wall) probe measurements are revealed in Figure 13. The contours are generated using the nine (one centerline and eight major Cardinal coordinate points) probe locations and corresponding temperatures, mapped onto an artificial grid, and fitted using the surface fit rendition of MATLAB’s ‘fit’ command wit h a second order polynomial fit in both spatial directions ( 𝑦 and 𝑧). The current procedure neglects boundary layer effects and incorporates the minimum amount of spatial points capable of providing a reasonable spatial profile to meet the current object ive (assessing modeling assumptions and properties of the flow). The results show a basic depiction of the spatial dependence of the temperature profile s and from Figure 13(a- b) and (c -d) it is clear that both of the inlet temperature profile s are within 1 .2 K of their respective minimums and maximums. Based on the current inlet temperature profile results, and in conjunction with known pressures of the wo rking fluid, modeling assumptions and thermophysical properties are now well informed for the experimental facility. With that said, t he current temperature inlet profiles provide a co arse, if not rudimentary , approach that is subject to further scrutiny. Future work should consider the use of, i.e., a traversing cold wire anemometer probe to meet higher fidelity needs . Figure 13: Interpolated tunnel inlet temperature contours consisting of (top row) minimum and (bottom row) maximum speed with (left column) isometric views and (right columns) planar views . 4.0 VALIDATION BENCHMARK CASES Examples of key validation metrics are now provided via two canonical flow types measured with this facility. The two benchmark cases consist of flow past a cylinder and the round jet in cross flow. To be clear: a full validation study could be conducted on each of these sections, considered beyond the scope of the current work. This section m erely serves as an introduction to the two flow types pertinent to current efforts in the laboratory. The experimental procedures are briefly reviewed with additional