High-Speed Schlieren Imaging of Supersonic FlowPast a Wall-Mounted Hemisphere With Turbulent

Boundary Layer ImpingementJames J. Slade Honors Thesis

Mohamed S. ElashakyRutgers Department of Mechanical and Aerospace Engineering

Rutgers University, New Brunswick

Under the direction ofProfessor Edward Demauro

Abstract—The following report is done on a wall-mountedhemisphere inside a supersonic wind tunnel. The goal of thisexperiment is to investigate shock and wave fluctuations thatmanifest in the wake of an unsteady flow over a hemisphere.Implications for this project are centered around external equip-ment mounted on a high speed aircraft. The flow field associatedhas to navigate around the blunt extrusion, leading to addedvibrations and fatigue. By understanding this interaction, bettermodels can be produced to reduce chances of structural failureand increase aerodynamics. Methods for this procedure includea finite element analysis (FEA) done with ANSYS Fluent. Amodel of a hemisphere is inserted into the software to simulatewind tunnel conditions found on campus. Results from thecompleted simulation include a stream wise velocity distribution,that contains a shock interaction. A numerical attempt ofSchlieren imaging is also done on density results in order tocreate comparisons to physical data from past reports. Pressuredistribution across the surface of the hemisphere is also calculatedand found to have a maximum of 4.54 MPa on the leadingedge of the hemisphere. This pressure is deemed to have asignificance when considering the possibility of deformation onthe hemisphere. Confirmation of the shock wave will be comparedwith empirical results before further consulting applications.

I. INTRODUCTION

Investigation of supersonic flows is a topic of interest foraerodynamicists. A flow navigating over an aerodynamic shapeprovides a wealth of information that can relation to vehicleperformance and integrity. For high speed military aircraft,flow fields are violent and detrimental to aircraft structures.This is particularly true when considering extruding equipmenton board these supersonic jets. A hemisphere is the simplestform that can represent these protrusions. When the flowcollides with this blunt object, the geometry is responsiblefor unsteady, complex flow disturbance that eventually lead tostructural fatigue and excess vibrations [1]. The goal of thisexperiment is to investigate shock and wave fluctuations thatmanifest in the wake of an unsteady flow over a hemisphere.From previous procedures on this topic [1,2], this reportwill use a computational fluid dynamic (CFD) approach in

order to verify past results. This will help provide insight todownstream motion in the wake of the hemisphere.

This experiment is traditionally done using a supersonicwind tunnel (SWT). The SWT on campus has been usedpreviously to gather data on this flow field, but due to currentrestrictions, it was unavailable for these purposes. Instead, avirtual approach was taken in an effort to gain equivalent data.Both version of this experiment will be described in orderto draw connections, and justify decisions made in the CFDanalysis.

II. METHODOLOGY

A. Equipment

1) Wind tunnel: The wind tunnel used is a blow downsupersonic wind tunnel with a fixed Mach number. The testinggas is compressed dried air fed via an 8 m3 tank at 16.6MPa. The specific parameters of the tunnel used can be foundin Figure 2. The tunnel operates by storing air inside of astagnation chamber. Once the pressure build up is sufficient,the air is blown through a nozzle that accelerates the flowinto supersonic speeds. The flow is fully developed inside ofthe test section with a naturally developed boundary layer.The test section is where the hemisphere will be attached tothe tunnel wall. The test section has a square cross sectionof 6in by 6in and is approximately a foot long. This is alsoutilized when preparing the CFD experiment. The flow is thendecelerated through the use of a diffuser, before exhaustinginto atmosphere. A typical run time of this SWT is ten seconds.The following figure shows the complete schematic [1]:

2) Schlieren Imaging: [h] Data is collected from the test viaSchlieren imaging. When the flow reaches supersonic speeds,a shock is formed. This shock causes changes in pressureand density that can be observed using this method. Schlierenimaging is done by using a light source shined in between twoparabolic mirrors and a knife’s edge. This method is based inSnell’s law in optical physics. When light passes through a

Fig. 1: Model of the Supersonic Wind Tunnel on Campus

Fig. 2: Wind Tunnel Running Conditions

different medium it refracts from the surface at an angle .Thisis the following relation:

n1sin(θ1) = n2sin(θ2) (1)

Where n is the refraction index of a given medium. Sincethe flow being studied is a compressible one, light travellingthrough air of changing density will follow this relationship.Since this is true, Schlieren imaging can be used to capture thedensity gradient of a generated shock. When the supersonicflow interacts with the blunt hemisphere, shock interacting willbe observable. These shocks will cause changes in the densityof the test gas, allowing the capture of shock layers.

In the physical study of this lab, a Z-type Schlieren systemwas used to capture data inside the test section of the SWT.As seen in Figure 3, the system uses two 292.1 mm diameterparabolic mirror, a Photron Fastcam SA-Z 12-bit, a knife’sedge and Thorlabs mounted LED white light.

Fig. 3: Z-Type Schlieren System used in SWT Laboratory

The mirrors serve to focus the LED light into the lens ofthe camera. The knifes edge helps focus more light into thecamera. The camera has a resolution of 680 x 340 pixels anda sampling rate of 80 Hertz. The exposure time is 1.25 µ,capturing 2000 time-averaged images.

3) Hemisphere: The hemisphere that would be used ismodelled from acrylic, and covered with pressure sensitivepaint. This was done in order to reduce the amount of lightthat would otherwise reflect if using a metallic model. Woodwas used in the results of Kiriakos[1] and Panco[2], but inthe absence of paint. The hemisphere was modelled in Solid-works as a prerequisite to machining it, but instead the CADmodel ended up being used in ANSYS Fluent. The radius ofthe hemisphere is 25.4 mm.

4) CFD Simulation: This procedure was done with theuse of ANSYS Workbench, specifically Fluent. The programmakes use of a FEA solver to replicate real world results.While the set up of the simulation was described, resultscollected from the program is a result of solving a simulationgoverning equation. ANSYS fluent uses a differential formof the Navier-Stokes equation to compute results in eachcell. The equation describes viscous motion within a fluidsubstance. It is an equation of state since it depends on thetemperature, density and pressure in any given cell. Navier-Stokes is valuable for computing compressible fluids due toshear terms that come about as boundary layers separate andthe flow becomes turbulent. The following equation is the formthe simulation chosen utilizes:∂(ρe)

∂t+−→∇ · ((ρe+p)−→u ) =

−→∇ · (τ ·−→u )+ρ

−→f −→u +

−→∇ · (−→̇q )+r

(2)The left handed side of this equation is representative of

convection terms within the fluid, while the right hand sidequantifies diffusive terms. The solution involves the velocityfield at a given point. This is helpful for creating a velocityfield contour as seen in the results of this paper.

An addition equation is added in order to estimate turbu-lence. Fluent contains various turbulence models, and thisexperiment makes use of the Spalart-Allmaras model wasdue to its simplicity and recommendation of the advisor.When completing a simulation of this caliber, results must beconfirmed to be convergent. This was achieve in a parametricstudy of the model to ensure results do not change after anynumber of iterations.

B. Procedure

1) Physical Procedure: This experiment is conducted in-side of the SWT laboratory on campus. A physical attempt atthis experiment as done in the supporting papers [1,2], wouldconsist of mounting the hemisphere on the wall of the testsection. A precise orientation of the Z-Type Schlieren systemused would need to be set up in order to keep picture qualityconsistent, and have the hemisphere in focus. Results thatbeing used for comparison are products of various runs ofthe device, which results in upkeep and maintenance.

2) Simulation Procedure: With a computer aid designmodel complete, the hemisphere is imported directly intoANSYS Design Modeller. The first step in organizing thesimulation is to create a fluid domain. Fluent will recognizethis in order to solve the fluid flow equations. This is done bycreating an enclosure around the hemisphere. The enclosure

was made to be the size of the test section, in order to closelyreplicate physical results. This enclosure is then combined withthe hemisphere using a Boolean subtraction. This helps reducethe computation load required, and unify the two objects. Thenamed sections are added to this model to help the programdistinguish inlets, outlets, and walls. Now that the systemis complete, it is time to designate cells for the simulation.Meshing is often a crucial step in CFD analysis, and takes asustainable amount of time. A maximum mesh count of fivehundred thousand nodes is enforced for the student editionof this program, and therefore this experiment is bounded bythat limitation. A fine mesh is desired in order to increase thephysics of the engine, and enhance accuracy. Figure 4 includesthe meshed system. Convergence of this mesh was deemed tobe achieved when reaching the maximum node count. Thismesh includes a face sizing throughout the system, with aninflation setting on the wall representing the hemisphere. Thisensures that the mesh is finer in this section, since it is thearea of interest.

Fig. 4: Converged Mesh for Hemisphere model

Finally, the parameters of the simulation are assigned.Figure 2 parameters were directly input into the simulation.Velocity is found as a result of the following equation; Theconditions on which the experiment is based on means thatvelocity is a state property of the fluid. Free stream velocityvaries as follows;

U∞ =M∞ ∗√

γ ∗RT1 + (γ−1)

2 ∗M∞(3)

Where M∞ is the Mach Number in the tunnel, γ isthe ratio of specific heats for a gas, R is the specific gasconstant, and T is the temperature. The flow is compressible,meaning temperature along the streamline will be changingdue to fluctuating pressure and density. This equation is usedto update the velocity in each iteration while Fluent runs.Temperature and pressure in this section of the test sectionneeded to be found using the isentropic flow properties[3]:

P0

P= (1 +

(γ + 1)

2M2)

γγ−1 (4)

T0T

= 1 +(γ + 1)

2M2 (5)

Both the stagnation pressure and temperature of the windtunnel are known, meaning the equations above can be solvedfor P and T respectively. An energy model is applied to thesimulation in order to allow the Temperature to change, andbe calculated for each cell. The turbulence model is alsoadded in this section of the simulation. Since the flow is alsocompressible, the density is toggle to change as an ideal gas.While not completely accurate, this was chosen to simplifycalculation costs. With the simulation initialized, it was runfor 250 iterations to formulate a solution. The work of Morganet. al.[4,5] done on a similar simulation will be used forcomparisons when calculating pressure distributions.

III. RESULTS AND DISCUSSION

Once the simulation was complete, it was necessary tocheck quality of the results. The first contour drawn allowsthe visualization of velocity magnitude over the hemisphere:

Fig. 5: Velocity Distribution over Hemisphere

To begin discussion, a shock interaction is successfullysimulated. As the flow negotiates the blunt object in its wake,it begins to turn onto its self and slow down. The leading edgeof the hemisphere sees an initial oblique shock, preceded bya separation shock. The circulation of fluid in between (thegreen region in front of the hemisphere in Figure 4) is theshear layer impingement. A clear separated shear layer is alsoseen trailing the hemisphere.

The simulation is also time independent. When picturedat different times, all results will be identical, which is notrepresentative of previous data. Luckily, most results are timeaveraged using images taken at high sampling rates, allowingfor an average that can be analyzed

The next result to discuss is the density gradient of theflow. From past experiments, this is captured using Schlierenimaging. Using Fluent, the closest the simulation can come tothose results is an inverse gray color map of the contour. Withresults from [1,2], the ’Schlieren’ image of this simulation isas follows.

From the simulation, Figure 6 does share common fea-tures with the physical results. Qualitatively in comparisonto Figures 7 and 8, the numerical Schlieren image showsstrong agreement. The largest difference is seen with thegenerated interference in the backgrounds.One item to noteis the absence of interference otherwise seen in a SWT. Thisis usually caused by imperfection of the wall of the test

Fig. 6: Density contour over Hemisphere with a radius of25.4mm Simulated

Fig. 7: Schlieren Image of a Hemisphere with a radius of25.4mm[2]

section, but also due to the reflection caused by the walls.The simulation result does capture a reflected shock, but thedistinct lack of Mach waves means the weaker shocks wherenot calculated. There is a distinct diamond pattern seen inthe results of Kiriakos[1] and Panco[2] know as Mach waves.Mach waves are weak oblique shocks that occur when aseries of disturbances travel at a speed greater than the speedof sound. Mach waves in this scenario for diamond shapedpatterns across the Schlieren image. The half angle of thesediamonds relative to the flow direction is known as the Machangle. The angle of these Mach waves directly relate to theMach in the SWT. In both papers this was found to be 17°,and should hold true if measured in the simulated result.Unlike the results in [2], only one radii was of hemispherewas simulated. The simulation is also time independent. Whenpictured at different times, all results will be identical, whichis not representative of previous data. Luckily, most resultsare time averaged using images taken at high sampling rates,allowing for an average that can be analyzed

The pressure over the hemisphere is something that is notidentified in either of the referenced literature, but is in thecapabilities of this simulation to analyze.

From Figure 9, a large pressure is seen on the leading edgeof the hemisphere. From the color bar of the simulation, apressure as large as 4.56 MPa is experienced acting on theprotrusion. While this pressure is commonly experienced atthese speeds along some parts of the aircraft, it could havea direct impact on any sensitive equipment. This pressure isalmost five times larger than the stagnation pressure requiredfor the wind tunnel, and comes on as an anomaly whenanalyzing the results. It offers another layer of depth when

Fig. 8: Schlieren Image of a Hemisphere with a radius of38.1mm [1]

Fig. 9: Simulated Pressure on a Hemisphere of radius 25.4mm

designing for on board equipment. Figure 10 features anisometric view of the surface of the hemisphere to better showthe distribution of pressure.

Before directly comparing with other simulation results,it is important to consider the difference in caliber of bothresults. The node count of this simulation was strictly limitedto five hundred thousand. This is due to only having accessto the student version of the chosen software. The work ofMorgan et. al. [4,5] is done on a simulation consisting of710 million nodes divided into nine individual blocks. Anincrease of node count followed by the computation powerneeded to execute the simulation, yield finer results. Thesimulation was also carried out in a different program, yetstill utilizes the Navier-Stokes equations. The Mach numberused by this group was M = 2 versus M= 3.45 for the resultsin this paper. From the published journals in 2016 [4] and2017[5], the pressure distribution over hemisphere alongsidean isometric view of the system: From the results of Figure11a to Figure 10, there is a strong agreement in pressurevariations over the protrusion in supersonic speeds. Resultsfrom Morgan et. al. are also normalized to aid in comparisons,even between vast computational differences. From figure 11bto 9, the pressure distribution around the hemisphere is seen.The results are identical as both figures provide evidence of theshock being simulated Finally, a velocity distribution plot canbe created from the gather data to be judged to the literaturethus far. Between the two Figures 12 and 13, there aresome striking similarities. Though the simulation is mirroredin comparison to the physical data, the velocity field seesan identical distribution. The values between the two figuresmay not agree initially however. Figure 10 was not a randomlocation as are the samples taken in Figure 13.

Fig. 10: Isometric View of Pressure Distribution Over Hemi-sphere

(a) Coefficient of Pressure distribution over Hemisphere [4]

(b) Isometric View of Pressure Distribution over a Hemisphere [5]

Fig. 11: Results from Morgan et. al.

IV. CONCLUSION

The use of CFD programs to investigate this flow fieldproved to be relevant. The results of this analysis closelyreassembles past results, and provides information of thisturbulent flow flied useful for improving designs on protrudingequipment high speed vehicles. Results from physical exper-iments [1,2] provided validation on data collected from thissimulation. findings were further defined when compared tothe efforts of other simulations on this topic.

A. Future plans

Since this experiment provide in replicating experimentswithin a SWT, it should be made an effort to go beyondthe limitations of the device. While the SWT on campus hasphysical limitations preventing an increase of Mach number,the simulation has no such requirement. Speeds can continueto be increased into hyper sonic regimes to continue to studythe flow field’s reaction to a blunt obstacle. The material of thehemisphere was also largely ignored in this simulation due to ithaving no effect on the flow field. If specified however, it couldbe used in a structural analysis to find deformation across the

Fig. 12: Streamwise Velocity Field Over the Hemisphere withr = 25.4mm

Fig. 13: Random Samples of Instantaneous PIV Images of theStreamwise Velocity Field [1]

perturbation. It could be possible to introduce more complexshapes to better represent a larger sample of aircraft protrusion.This should be done in response to unrestricted access toa fluid-solver program, as well as enhanced computationalcapabilities.

In response to a physical experiment, this procedure shouldlook to add an application of pressure sensitive paint to helpquantify more traits of the flow field. The pressure resultsof the simulation would then be able to be verified beforeapplication can be considered.

ACKNOWLEDGMENT

The author would like to acknowledge the help and guidanceprovide by the advisor during the course of the J.J. SladeScholars; My peers in this program that provided helpfulfeedback; Ramez Kiriakos for helpful discussion.

REFERENCES

[1] Kiriakos, R., DeMauro, E., et. al,”Unsteady Motion in the SupersonicFlow Over a Wall-Mounted Hemisphere,” AIAA, 2020

[2] Panco, R., DeMauro, E., et. al, ”High-Speed Schlieren Imaging of Super-sonic Flow Pasta Wall-Mounted Hemisphere With Turbulent BoundaryLayer Impingement,” AIAA, 2016

[3] Anderson, John D., ”Modern Compressible Flow: With Historical Per-spective Third Edition.” McGraw Hill, 2003.

[4] Morgan, Phillip E., et. al, ”Numerical Exploration of Supersonic FlowOver a Wall-Mounted Hemisphere,” AIAA, 2016

[5] Morgan, Phillip E., et. al, ”Investigation of Shock Wave-Boundary LayerInteraction for Flow Over a Wall-Mounted Hemisphere,” AIAA, 2017