This study presents a combined direct numerical simulation (DNS) and experimental investigation of shock wave/turbulent boundary layer interaction (SBLI) over a hollow-cylinder/flare (HCF) configuration at Mach 6.32, with a flare angle of 34 degrees. The DNS replicates conditions from the Stevens Shock Tunnel, with matched freestream and wall temperature conditions (Re-infinity(u)/m = 13.86 x 10(6), T-w /T-r = 0.54). Detailed comparisons of DNS against experiments are made. Upstream of the interaction, the simulation shows excellent agreement in mean velocity profiles and Morkovin-scaled turbulence intensities with Stevens' experiment, as well as with other flat-plate data in the literature. Within the flare-induced SBLI region, the DNS captures key features of separation, reattachment, and shock-induced surface loading. Instantaneous schlieren images from the DNS closely match the experimental schlieren, capturing the structure and dynamics of shock motion and the evolving separation bubble. Additionally, wall pressure signals from the DNS align well with Kulite measurements, with improved agreement observed after applying low-pass filtering to account for sensor's effective bandwidth.

In this work, a modified Ahmed body with both upsweep and downsweep was used to create a complex wake. The time-averaged streamline topology revealed that the wake was composed primarily of a torus past the vertical base and two pairs of streamwise-oriented vortices on the upper and lower slant edges. Several vortex identification methods including three-dimensional (3D) (Q−, λ2−, Ω−criteria, and Liutex method) and two-dimensional (2D) (Γ1−criterion) methods were compared to determine the effectiveness in identifying complex wake structures. Of the 3D methods analyzed, none produced wholly satisfactory results. The Q− and λ2−criteria were plagued by well noted issues; failing to separate shear from rotation and threshold sensitivity which led to inconsistently identifying the weaker torus. The Ω−criterion addressed all of these concerns, especially identifying the torus consistently. However, the identified torus structure did not reflect the physical structure observed using the streamline topology as a ground truth. This phenomenon was caused by Geometry Induced Solid Body Rotation (GISBR), in which the complex geometry resulted in streamline curvature producing local regions of solid body rotation even without a vortex. Therefore, the Q−,λ2−, and Ω−criteria cannot be recommended for analyzing complex 3D wakes. Based on the current results, the Liutex method offers the best compromise of the 3D methods analyzed. However, it was also negatively impacted by the GISBR as were all 3D vortex identification methods. Only the Γ1−criterion successfully aligned with the streamline topology and was not impacted by GISBR. But, this method is currently relegated to 2D flows.

For this study, Improved Delayed Detached-Eddy Simulations (IDDES) were used to analyze the wake of a modified Ahmed body with varying upper and lower slants. The modified geometry produced a constant projected vertical base area, ensuring that the base and slant drag were a function of the pressure caused by the wake structures. Except at extreme slant angles, the general structures of the wake were a base torus with two pairs of streamwise-oriented vortices on each slant. These structures strongly correlated with the drag contribution of the rear surfaces: the torus with the vertical base and the streamwise-oriented vortices with the slants. As such, the base drag was minimized when the torus was most centrally aligned with the base, producing the largest stagnation region. Two slant-drag minima developed corresponding to two regimes of vortical flow on opposing slants. On one slant, the vortices were attached, and the drag correlated with the size and strength of the vortices. On the other slant, the vortices separated, and the drag correlated with the slant normal due to a more uniform pressure. This demonstrates a rich and complex set of interactions that must be managed in the development of base drag caused by wake flows.

In this work, we analyzed Improved Delayed Detached-Eddy Simulations (IDDES) in predicting the separated flow over a Backward Facing Wall (BFW) of a M = 4.9 turbulent boundary layer. The solution was compared with a Direct Numerical Simulation (DNS) of Nicholson et al. [1] for accuracy, as well as a steady Reynolds-Averaged Navier-Stokes (RANS) solution. The IDDES required synthetic turbulence to be generated at the inflow, otherwise the solution was Quasi-Steady with only low-frequency oscillations developing in the separation bubble. By including synthetic turbulence, the IDDES blending function limited the modeled Turbulent Kinetic Energy (TKE) to near zero upstream of the wall curvature, while the Quasi-Steady IDDES limited upstream TKE to a lesser degree. This resulted in an increase in peak TKE for the Quasi-Steady IDDES over the fully transient IDDES, better aligning with the DNS. However, each of the IDDES cases under predicted the TKE, subsequently predicting a longer separation bubble than the DNS. RANS, on the other hand, more closely aligned with the DNS, but only due to the inflow being directly mapped from the DNS.

In this work, we evaluated computational fluid dynamics (CFD) methods for predicting the design trends in flow around a mass-production luxury sport utility vehicle (SUV) subjected to incremental design changes via spoiler and underbody combinations. We compared Reynolds-averaged Navier- Stokes (RANS) using several turbulence models and a delayed detached eddy simulation (DDES) to experimental measurements from a 40% scale wind tunnel test model at matched full-scale Reynolds number. Regardless of turbulence model, RANS was unable to consistently reproduce the design trends in drag from wind tunnel data. This inability of RANS to reproduce the drag trends stemmed from inaccurate base pressure predictions for each vehicle configuration brought on by highly separated flow within the vehicle wake. When taking A-B design trends, many of these errors compounded together to form design trends that did not reflect those measured in experiments. On the other hand, DDES proved to be more consistent and accurate across all vehicle configurations, producing more viable design trends in drag, base pressure, and wake velocity profiles than steady RANS aligning closer with the design trends obtained from the wind tunnel. Therefore, more confidence in the digital design from DDES can be attained. Meanwhile, RANS produces non-physical design trends for highly separated flows, making it questionable as an effective tool for automotive vehicle design.

The performance of wavelet-based optical flow velocimetry (wOFV) applied to tracer particle images from hypersonic boundary layer flows is assessed. Two modifications of wOFV to account for the no-slip boundary condition are implemented and assessed to extend the applicability and performance of wOFV to wall-bounded high-speed flows. The first modification (wOFV+) enforces the no-slip boundary condition via constrained optimization, whereas the second modification (wOFV-Ext) performs an antisymmetric extension of the particle images before wOFV processing. The original wOFV and two modified versions are assessed on both (i) synthetic particle images generated from a direct numerical simulation (DNS) of a Mach 4.9 turbulent boundary layer and (ii) actual particle images acquired from a Mach 5 turbulent boundary layer experiment. The velocity estimates using wOFV methods are directly compared to velocity estimates produced by state-of-the-art particle image velocimetry (PIV) software. All three wOFV methodologies were shown to have an increase in accuracy and spatial resolution when compared to PIV. The increase in spatial resolution was shown to be important in the near-wall region (within the viscous sublayer and buffer layer) and for computing shear velocities, u(tau). Overall, both of the no-slip boundary condition modifications were shown to improve accuracy in the near-wall region when compared to both wOFV and PIV.

For this work, conditional averaging and Proper Orthogonal Decomposition (POD) were used to analyze the salient three-dimensional structures in the wake of a DrivAer fastback model with smooth underbody. Conditional averaging revealed that the bi-stable structure of the wake consists of a ring-like structure with three vortex legs, which includes a vortex pair on the side associated with the bi-stability and one on the opposite side associated with the wheel vortex. POD revealed the entrainment of low-momentum fluid from the wheel wake into the vortex pair leads to an induced spanwise crossflow which drives a feedback loop for the bi-stability. The resultant bi-stable structure was dependent on the state of the wheels. With stationary wheels, the feedback mechanism is enhanced, leading to higher spanwise crossflow that breaks the ring-like vortex. A different structure was observed when the wheels rotate, wherein the ring-like structure is unbroken and pierced by the vortex pair. The feedback mechanism and resultant vortex structure are similar to those found in simplified square-back models. Given the similarity in bi-stability between realistic and simplified vehicles, the suppression of the bi-stability in realistic vehicles could initially be based on the same mechanism as that for simplified square-back models.

In this work, Direct Numerical Simulations (DNS) are performed for a Mach 6 cold-wall turbulent boundary layer to study the asymptotic near-wall behavior. To accomplish this, very high near-wall resolution was applied in the wall-normal direction (Delta Z(min)(+) similar or equal to 0.1). In general, the increased resolution showed a good comparison with a previous DNS of Zhang et al. [1] using Delta Z(min)(+) similar or equal to 0.5. The current simulations show a near match in the first and second-order turbulence statistics. Comparing the Favre and Reynolds averaged Reynolds stresses, little difference is observed between the two when accounting for the mean fluctuation in density via Morkovin's hypothesis. Analyzing the asymptotic near-wall behavior, all components of the Reynolds stresses and turbulent heat flux show a consistent power-law scaling (slope of similar to 2) in the lower region of the viscous sublayer. This power-law scaling is enhanced when plotted against the semi-local scaling (z*) as opposed to more typical inner-scaling (z(+)). Thus, at high Mach numbers, there may exist a more universal scaling than has been observed in lower-speed supersonic flows.

View Video Presentation: https://doi.org/10.2514/6.2023-0867.vid For the current work, the spatial resolution effects of particle tracing techniques for measuring boundary-layer statistics is analyzed for a M = 4.9 turbulent boundary layer on a flat plate and a concavely curved wall. Lagrangian particle tracking of idealized particles (e.g., zero-mass) is used on data from the Direct Numerical Simulation (DNS) of Nicholson et al. [1] to create synthetic particle images. These images are then analyzed with different windowing schemes using commercially available Particle Image Velocimetry (PIV) software to determine the velocity fields and turbulent statistics under different spatial resolutions. Specifically, the effects of spatial resolution are analyzed under three image resolutions (1600 × 1200, 3200 × 2400, and 6400 × 4800 pixels), each of which is achieved with different interrogation window sizes (128 × 128, 64 × 64, 32 × 32, and 16 × 16 pixel windows). The study shows that spatial resolution acts as a low-pass filter on the fluctuating velocities that limit the measurable spectrum contents. For all the components of Reynolds stresses, the usage of too small a window size leads to the development of non-physical fluctuations, but these non-physical fluctuations can be alleviated and eventually eliminated by increasing the image resolution. For a given windowing size and with idealized particles, a good comparison between DNS and synthetic PIV can be achieved for all the Reynolds stress components if the spatial resolution of the PIV is high enough. Consistent with the experimental findings of Brooks et al. [2], the wall-normal component of the Reynolds stress is shown to be more susceptible to the resolution effects than the streamwise component due to its flatter wavenumber spectrum profile, leading to additional energy at higher wavenumbers. Such a numerical experiment with Lagrangian particle tracking sheds light on the error sources in measuring supersonic flows with PIV and confirms the validity of the original DNS used to create synthetic particle images.

View Video Presentation: https://doi.org/10.2514/6.2023-0047.vid In the current work, we used the Lattice-Boltzmann Method (LBM) to simulate the flow around the DrivAer notchback model with smooth and detailed underbodies. The flow field was subjected to two wheel rotation models (Sliding Mesh [SM] and Moving Reference Frame [MRF]) in addition to a stationary wheel and ground plane for comparison. The aerodynamic torque on the wheels was predicted to be consistently higher using MRF in comparison to SM. Additionally, the aerodynamic drag was consistently higher using MRF as well. Features such as the wheel well pressures and underbody pressures lead to most of the differences between the different rotation models. However, features such as the wheel wake structure showed large deviations in streamline topology, which propagated downstream to cause observable differences in the base wake structure between the wheel rotation models even when the vehicle geometry was the same. Thus, the impact of wheel rotation model extended beyond the flow immediately around the wheel and impacted larger global aerodynamics and interactions with other vehicle components. Such interactions could lead to discrepancies in incremental design studies depending on the wheel rotation model used.

The effect of turbulent wind-tunnel-wall boundary layers on density change measurements obtained with focused laser differential interferometry (FLDI) was studied using a detailed direct numerical simulation (DNS) of the wall from the Boeing/AFOSR Mach-6 Quiet Tunnel run in its noisy configuration. The DNS was probed with an FLDI model that is capable of reading in three-dimensional time-varying density fields and computing the FLDI response. Simulated FLDI measurements smooth the boundary-layer root-mean-square (RMS) profile relative to true values obtained by directly extracting the data from the DNS. The peak of the density change RMS measured by the FLDI falls within 20% of the true density change RMS. A relationship between local spatial density change and temporal density fluctuations was determined and successfully used to estimate density fluctuations from the FLDI measurements. FLDI measurements of the freestream fluctuations are found to be dominated by the off-axis tunnel-wall boundary layers for lower frequencies despite spatial suppression provided by the technique. However, low-amplitude (0.05%-5% of the mean density) target signals placed along the tunnel centerline were successfully measured over the noise of the boundary layers (which have RMS values of about 12% of the mean). Overall, FLDI was shown to be a useful technique for making quantitative turbulence measurements and to measure finite-width sinusoidal signals through turbulent boundary layers, but may not provide enough off-focus suppression to provide accurate freestream noise measurements, particularly at lower frequencies.

Lattice Boltzmann method (LBM) simulations were performed to capture the long-period dynamics within the wake of a realistic DrivAer fastback model with stationary and rotating wheels. The simulations showed that the wake developed as a low-pressure torus regardless of whether the wheels were rotating. This torus shrank in size on the base in the case of rotating wheels, leading to a reduction in the low-pressure footprint on the base, and consequently a 7% decrease in the total vehicle drag in comparison to the stationary wheels case. Furthermore, the lateral vortex shedding experienced a long-period switching associated with the bi-stability in both the stationary and rotating wheels cases. This bi-stability contributed to low-frequency side force oscillations (< 1 Hz) in alignment with the peak motion-sickness-inducing frequency (0.2 Hz).

A focused laser differential interferometer (FLDI) model that is capable of simulating time-varying signals was used to study how an FLDI responds to a realistic wind tunnel boundary layer. Initial tests using a sinusoidal approximation for test-section-wall boundary layers showed the FLDI strongly favored the signal of interest at the focal point to signals present along the wall. Direct numerical simulation (DNS) was then used to model the turbulent boundary layer along the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT) as run in its noisy configuration. The simulated FLDI probed the boundary layer, and its results were compared to the true density fluctuations. The FLDI values slightly underestimated the true peak density fluctuations and also smoothed out the RMS peak. When used to simulate the FLDI traversing the test section through, the signal from the turbulent boundary layers was shown to persist despite FLDI suppression. Low-amplitude sinusoidal signals were still capable of being measured by the simulated FLDI over the interference of these boundary layers.

View Video Presentation: https://doi.org/10.2514/6.2022-1062.vid For the current work, we analyzed the effects of particle tracing on a M=4.9 turbulent boundary layer subjected to zero and strong favorable pressure gradients, wherein synthetic particle images were generated from the Lagrangian particle tracking using data from a direct numerical simulation (DNS) and processed with standard particle image velocimetry (PIV) cross-correlation techniques. The study showed that, with the particle Stokes number fixed at the experimental value of about 0.1, a better match in the wall-normal and shear components of the Reynolds stresses between the PIV and DNS was achieved when the PIV spatial resolution was increased from 32x32 pixels to 16x16 pixels. The improved accuracy of the Reynolds stress at a spatial resolution finer than the experiment suggested that the lower magnitudes of the wall-normal and shear Reynolds stresses reported by Tichenor et al [1] were likely caused by a lack of spatial resolution rather than the particle inertia effects. A further analysis of the effects of particle inertia and PIV spatial resolution revealed that the sensitivity of the Reynolds stresses to particle inertia increased with the PIV spatial resolution, and an over-reduction in the PIV window size led to large spurious overshoots in Reynolds stresses and worsening comparisons with the DNS.

A comprehensive evaluation of the predictive capability and computational costs of Reynolds Averaged Navier–Stokes (RANS), Unsteady RANS (URANS), Delayed Detached-Eddy Simulation (DDES), and Lattice-Boltzmann Method (LBM) methodologies was carried out for flow around the SAE notchback and the DrivAer fastback models. From the comparison, all methods predicted drag within roughly 10% of experimental values. However, this accuracy was misleading for RANS as the predicted flowfield deviated from both the unsteady methods and experiments in regions where flow separation was developing. This was especially true around the rotating wheel flows of the DrivAer model, where RANS predicted extensive separation around the rear wheels to the point that it changed the structure of the vehicle wake. In these regions of highly separated flow, the unsteady methods proved to be much more accurate and robust, although comparisons of the flow around the rotating wheels proved inconclusive as to which methods provided suitable predictive capabilities. Despite improved flow predictions, URANS and DDES proved to be significantly more expensive than RANS, while LBM provided comparable accuracy to URANS/DDES with substantially reduced costs.

The current paper analyzes the effect of time-step size on the predictive capability and computational cost of two unsteady methods (Unsteady Reynolds-Averaged Navier–Stokes [URANS] and Delayed Detached-Eddy Simulations [DDES]). Two generic vehicle models (SAE notchback and DrivAer fastback) were tested using time-step sizes ranging over two orders-of-magnitude 1χ–100χ, with 1χ corresponding to the smallest time-step case with an average cell convective Courant number of around one. Of the two methods, URANS was less sensitive to time-step size than DDES in the time-averaged flow field predictions. For both unsteady methods, the drag buildup and mean flow-field predictions at a time-step size as high as 50χ was found to correlate closely with the temporally resolved case of 1χ. This was especially true around the rotating wheels of the DrivAer model, where even at the largest time-step size of 100χ, both unsteady methods predicted a flow much closer to the temporally well resolved case than steady RANS. Additionally, the added cost of the unsteady methods was found to be nearly inversely proportional to the time-step size when using a fixed number of inner iterations. At a time-step of 50χ, the total cost was only ∼3–7 times that of RANS.

Flow around a realistic car model (DrivAer fastback), was analyzed using Improved DelayedDetached-Eddy Simulations (IDDES) and the Lattice-Boltzmann Method (LBM). Two gridswere implemented, coarse and fine, with both methods predicting accurate drag on the lattergrid. IDDES showed more grid sensitivity, underpredicting drag by more than 10% on thecoarse grid. Drag buildups revealed discrepancies in drag accumulation on the nose, frontwheels, middle portion of vehicle length, and vehicle base between the two methods. Lowerpressure on the vehicle nose was predicted by IDDES which was rectified by increased gridresolution. Changes in the flow separation along the underside of the front bumper andwheels lead to differing drag accumulations along the underbody and wheel wells. Analysis ofthe base wake revealed stronger wall-normal vortices, determined via circulation, forming inIDDES leading to a higher accumulation of base drag. The increased circulation was partiallyattributed to IDDES predicting increased vorticity around the wheels being entrained into thewake vortices. Despite the Very Large-Eddy Simulation (VLES) of LBM capturing finer scalestructures around the vehicle in general, streamwise oriented planes of normalized turbulentkinetic energy matched well between the two methods. However, differing trends in the scalesof turbulent structures along with complex body interactions, lead to differing turbulent wakesaround the vehicle base and rotating wheels. Comparison of normalized surface pressurefluctuations with experiments did not identify either method as superior to the other forprediction of the unsteady flow field despite the noted discrepancies.

The mean flowfield in the aft region of cargo aircraft configurations is analyzed using large-eddy simulations. A simplified surrogate fuselage is considered, consisting of a cylinder with axis parallel to the flow and a slanted (upswept) base. Emphasis is placed on understanding the major changes that occur in the flow as the upsweep angle of the base is increased in a broad 20 degrees -45 degrees range. Qualitative and quantitative comparisons with available experiments indicate that the simulations accurately capture the primary flowfield features, which are observed to be relatively insensitive to the Reynolds number. The simulated mean databases are then employed to elaborate on the evolution of the vortical field and its influence on the base surface. In the range of angles examined, the flow separates at the edge of the base and a horseshoe-shaped vortical structure is obtained, with a head region centered near the upstream apex of the base surface and an initial growth around its periphery. The vortical structure subsequently detaches from the base to form a streamwise vortex pair (legs) that persists for relatively long distances downstream. With an increasing upsweep angle, the size of the head region increases but the concomitant increase in vortex strength also results in a more rapid decay downstream. The angles formed by the vortex pair relative to the cylinder axis increase with upsweep; however, the trajectories collapse relatively well when scaled by the distance along the base. Secondary separation is observed at all upsweep angles, consistent with experimental observations. Changes in base surface pressure are related to those in the simulated oil flow, which shows significant changes between 32 degrees and 45 degrees. Some of these changes relate to the subsequent establishment of the anticipated wake regime at even higher angles, a brief discussion of which is presented by considering a 55 degrees case.

The mean flowfield in the aft-region of cargo aircraft configurations is analyzed using Large-Eddy Simulations. A simplified surrogate fuselage is considered, consisting of a cylinder with axis parallel to the flow and a slanted (upswept) base. Emphasis is placed on changes in the flow as the upsweep angle of the base is increased in the 20° to 45° range. Qualitative and quantitative comparisons with available experiments indicate that the simulations accurately capture the primary flowfield features, which are relatively insensitive to the Reynolds number. The three-dimensional dataset is then employed to understand the evolution of various features of interest with sweep angle, including the nature of the vortical structures, and their influence on base surface pressure and shear stress patterns. In the range of angles examined, the flow separates around the entire periphery of the base and a horseshoe-shaped vortical structure is obtained, with a head region centered near the upstream apex of the base surface and an initial growth around the periphery of the base. The vortical structure subsequently detaches from the base to form a streamwise vortex pair (legs). The size of the head region increases with upsweep angle. The base surface streamline pattern aids in identification of a secondary separation at all angles, similar to experimental observations at higher Reynolds numbers. The evolution of the critical point structure indicates a potential path towards the establishment of the anticipated wake regime at higher angles than those considered here.