MACH NUMBER OF A SHOCK WAVE: EFFECT OF VACUUM PRESSURE AND DIAPHRAGM THICKNESS

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 3941-3950 © TJPRC Pvt. Ltd.

MACH NUMBER OF A SHOCK WAVE: EFFECT OF VACUUM PRESSURE AND DIAPHRAGM THICKNESS ANANYA KAPOOR1, SNIGDHA MUDGAL2 & NIKUNJ NAVINBHAI PATEL3 1 2

Final Year B.Tech, Mechanical Engineering, Vellore Institute of Technology, Vellore, India

Final Year B.Tech, Electronics and Communication Engineering, Vellore Institute of Technology, Vellore, India 3

Final Year B.Tech, Mechanical Engineering, Vellore Institute of Technology, Vellore, India

ABSTRACT Shock waves possess characteristics of fleeting, rapid and sharp increase in velocity, temperature and pressure along with high dissipation of energy. These qualities of shock waves find their applications in a number of fields ranging from metal industries to medical sciences. With the availability of limited capacity of shock tubes, their efficiency can be increased by increasing the Mach number of shock waves, hence utility. In present study, an experiment to analyze the effect of increasing vacuum pressure as well as thickness of diaphragm on Mach number was conducted. Keeping diaphragm thickness constant at three different values, with increasing vacuum pressure from 0 to 600 mmHg, the percentage increase in Mach number was found to be 43.80%, 43.36% and 55.10%. It also depicted that Mach number that in the range of vacuum pressure and diaphragm thickness used, the percentage increase in Mach number was more with increasing vacuum pressure than diaphragm thickness. Computational fluid dynamic analysis of the same was done to determine the shock flow numerically and visually.

KEYWORDS: Computational Fluid Dynamics, Diaphragm, Mach Number, Shock Tube, Shock Waves & Vacuum Pressure

Original Article

increased as thickness of diaphragm was increased, with same vacuum pressure. The experimental results concluded

Received: Jun 10, 2020; Accepted: Jun 30, 2020; Published: Jul 17, 2020; Paper Id.: IJMPERDJUN020375

ABBREVIATIONS: M: Mach number; T: Diaphgarm thickness, t: Time interval, CFD: Computational Fluid Dynamics

INTRODUCTION As the quest of improving efficiency of various processes continues, development of a technique giving instantaneous high dissipation of energy would be very helpful. Shock waves are produced when particles travel at a speed which is greater than the local speed of sound and are accompanied with high and instantaneous changes in pressure, velocity and energy. Generally, shock waves occur in nature whenever there is a supersonic flight but we can also produce shock waves in laboratory using shock tubes (Jagadeesh, 2008a). Mach numbers are used to characterize shock waves; higher the Mach number, the powerful and efficient is the shock wave.

A shock wave can be quite effective in a number of industrial applications such as hardening and strengthening of engineering materials, explosive manufacturing in automotive industries, explosive welding, consolidation of powdered metallic or ceramic particles, shock induced fabrication, bonding of materials and manufacturing of superconductor composites in bulk (Murr, 2010). Apart from industrial applications, lithotripter shock waves and extracorporeal shock waves help in the treatment of gallstone, pancreatic stones and kidney stones

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Ananya Kapoor, Snigdha Mudgal & Nikunj Navinbhai Patel

as well as healing of fractured bone (Delius, 1994).

A shock wave forms as the speed of compression waves increases progressively and produces strong primary shock waves at the ‘shock formation distance’, which is measured from the point where the diaphragm ruptures and is around 5 to 6 times the diameter of the shock tube. It also depends on the time taken by the diaphragm to rupture. To equalize the compression waves, expansion waves form, which move towards the driver section. A reflected shock is formed in the direction opposite to the primary shock because the ends are shut. These formations of waves lead to the abrupt changes in the values of temperature, pressure and entropy.

The Mach number depends on the pressure difference between the two sections. Higher the difference, higher is the Mach number. In a shock tube, region 1 is low pressure zone in the driven section whereas region 4 has pressurised gas is the driver section. The initial temperature of the driver region is Temp1 and initial pressure is P1. The driver section temperature and pressure at the time of rupture is Temp4 and P4 respectively. The compression waves merge to form a strong wave, which represents the second region. As shown in Figure 1, the primary shock is reflected from the wall, after which it again compresses the gas in the driven section, making region 5 as already shocked gas. Thus the test gas goes through two jumps in parameters 125, where 12 is primary shock jump and 25 is the reflected shock jump (Kumar et al, 2014).

This experiment studies the trends in Mach number with change in vacuum pressure as well as the thickness of diaphragm and supports it with experimental data and computational fluid dynamics results.

Figure 1: Principle - Shock Tube Equipments, Setup and Procedure

Figure 2: Shock Tube Apparatus 2.05 metre Reddy table top stainless steel shock tube (2.9cm inner diameter, 40cm driver section, 165 cm driven section manufactured by Srushti Education Systems Pvt Ltd, Bangalore, India; Figure 2), Air compressor(Niko, FL0.12/8), Pressure sensors, Vacuum pump, Pirani gauge, Two channel oscilloscope (Hantek, IDSO 1070A), Vernier Impact Factor (JCC): 8.8746

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callipers and Tracing paper sheets.

The Reddy tube was modified to establish a table top shock tube. The setup is depicted in Figure 3. The shock tube assembly was cleansed using ethanol to remove impurities. Driver section of the shock tube was pressurised by connecting it with the air compressor, vacuum pressure was generated in driven section using the vacuum pump and tracing papers were used as diaphragm.

In first part of study, the thickness of diaphragm was kept constant while vacuum pressure was raised (100, 200, 300, 400, 500 and 600 mmHg) in subsequent readings. Subsequently, we increased the thickness of diaphragm by layering them (T1=0.07 mm, T2=0.14 mm and T3=0.21 mm; Error of ±0.01 mm) and calculated the Mach number each time with same varied vacuum pressure.

The pressurized section led to bursting of diaphragm, and formation of shock waves, whose characteristics were acquired using a two channel oscilloscope having a frequency to display 250 x 106 data readings per second.

Figure 3: Shock Tube Apparatus

RESULTS AND DISCUSSIONS Experimental data showed that with the fixed thickness of diaphragm, Mach number increased with increasing vacuum pressure (Table 1). Keeping diaphragm thickness constant, with increasing vacuum pressure from 0 to 600 mmHg, the percentage increase in Mach number was found to be 43.80% with T1, 43.36% with T2 and 55.10% with T3. It also depicted that as thickness of diaphragm increases, with same vacuum pressure, Mach number also increased. The experimental results showed that in the range of vacuum pressure and diaphragm thickness used, the percentage increase in Mach number was more with vacuum pressure than diaphragm thickness.

Mach number was bound to increase as the pressure difference between the driver and driven sections increase which was shown convincingly in our experimental study. As the thickness of diaphragm was increased, it required higher burst pressure to rupture the diaphragm. Thus higher pressure difference between two chambers led to a higher Mach number.

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Ananya Kapoor, Snigdha Mudgal & Nikunj Navinbhai Patel

Table 1: Mach Number Values for Different Vacuum Pressure and Diaphragm Thickness Vacuum Pressure (MMHG) 0 100 200 300 400 500 600 % increase (0 to 600 mmHg) in M keeping T constant

(Diaphragm Thickness: T1<T2<T3) Mach Number T1 T2 T3 1.21 1.43 1.47 1.32 1.47 1.54 1.43 1.54 1.68 1.45 1.66 1.78 1.49 1.71 1.93 1.63 1.84 2.11 1.74 2.05 2.28 43.80

43.36

% Increase (T1 To T3) In M Keeping Vacuum Pressure Constant 21.49 16.67 17.48 22.76 29.53 29.45 31.03

55.10

Mach Number Calculation Mach number calculations for different cases required distance between two sensors attached on the driven section (which, for experimental setup was fixed to be 10 cm) and the time interval between the first jumps experienced by the two sensors. The time interval between the first jumps in sensor readings was captured using IDSO software.

Using similar conditions, the data obtained in sensor closer to the diaphragm was simulated in Ansys fluent v18.1 as Pressure vs Time graph for a Mach number of 1.75 (corresponding to value of 1.74 obtained with 600mmHg vacuum pressure and T1 thickness; 0.57% error) and is presented in Figure 4. The second jump in same graph represented the time for reflected shock wave to reach the sensor. The formula incorporated to calculate Mach number was (Kumar et al, 2014) Mach number =

𝑈√𝑀𝑊

(1)

√ɣ𝑅𝑇

Here U depicted ratio of distance between two pressure sensors attached to the driven section and the time interval between the first jumps experienced by the two sensors which was the only parameter that varied for different cases. The molecular weight (MW) was taken to be 28.95 gm/mol for air; ɣ, the specific heat ratio for air taken was 1.4; R a universal gas constant and temperature, T, was considered to be 299K at room temperature.

Figure 4: Simulated IDSO Reading From Sensor.

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Graphical Analysis Figure 5(a), 5(b), 5(c) and 5(d) compared the pressure ratio P2/P1, P5/P1 and temperature ratio T2/T1, T5/T1 respectively to the Mach number for different thickness of diaphragm, where diaphragm thickness T1<T2<T3. It was observed that for the same diaphragm thickness, the Mach number, pressure ratio and temperature ratio increased with increasing vacuum pressure. Also, for an equivalent value of vacuum pressure, thicker diaphragm resulted in a higher burst pressure (P4), higher pressure ratios and temperature ratios i.e. higher pressure and temperature during shock wave propagation as well as reflected shock region, and produced a larger Mach number i.e. stronger shock wave. Hence the best choice to produce stronger shock waves reaching higher velocity, pressure and temperature was a thicker diaphragm with high vacuum pressure. Arjun Jayakumar et al and Satyanarayana et al have obtained and documented similar trend results. (Arjun Jayakumar et al, 2014; Satyanarayana & Shivaji, 2016) Computational Fluid Dynamics using Ansys Fluent Computational fluid dynamics for 160mmHg pressure in driven section (corresponding to 600 mmHg vacuum pressure) and 1.74 Mach number was done in Ansys Fluent v18.1 software to simulate the flow of shock waves. For similar input conditions a Mach number of 1.75 was obtained by simulation, i.e. 0.57% error which was within acceptable limits.

Inviscid flow with structured mesh and adaptive mesh refinement in a 2 dimensional density based transient solver with the energy equation was used to arrive at the results. Air was approximated to be an ideal gas with AUSM flux type and 0.1 CFL number with commensurate iterations so as to keep the computational time minimum. (Satyanarayana I & Shivaji, 2016) Figure 6, 7 and 8 show the pressure, velocity and temperature profiles respectively at three time intervals where t1<t2<t3. As time passed, the pressure, velocity and temperature increased sharply along the length of shock tube before ebbing away.

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Ananya Kapoor, Snigdha Mudgal & Nikunj Navinbhai Patel

Figure 5: Graphs (a) P2/P1 vs M; (b) P5/P1 vs M; (c) T2/T1 vs M; (d) T5/T1 vs M

Figure 6: CFD Analysis: Pressure Contours at Time Intervals t 1, t2 and t3

Figure 7: CFD Analysis: Velocity Contours at Time Intervals t1, t2 and t3

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Figure 8: CFD Analysis : Temperature contours at time intervals t1, t2 and t3 Applications of Shock Waves Shock waves are one of the few mediums to attain high temperature and pressure simultaneously for a short time before returning to ambient conditions. These properties of shock waves play a major role in several industrial and medical fields.

Some applications of shock waves include: Gene transfer: When exposed to a shock wave generated by a lithotripter, the eukaryotic cells temporarily enhance the permeability of the membrane. This permeabilization of shock waves is used to transfer physical gene from one body to another. It is better than other methods as it can be executed easily and is quite flexible in proper sequencing and sizing of the DNA molecule. (Lauer et al, 1997) Cell transformation: A pressure transducer of high sensitivity can be used to measure the signature of a biological medium’s extra pressure. When high pressure levels are experienced by the cells of bacteria, a DNA can be inserted inside a cell without mutilation (Jagadeesh, 2008a).

Extraction of oil from seeds: Oil is extracted from the seeds using mechanical methods. Achten et al. reviews that mechanical procedures achieve oil yields between 62.5 % and 80 %. Oil yield can be increased by using shock waves for extraction (Achten et al, 2008). Josef Maroušek et al shows that repeated application, 10 times, of pressure shock waves of 50-60 MPa extracts 97% of oil from the seeds. This is possible as the high energy breaks apart the seed’s lignocellose cell walls and gives access to all the vacuoles (Maroušek et al, 2013).

Vaccine delivery device: A needle less drug delivery tool which can be used to efficiently vaccinate in the epidermal layer consists of polymer tube coated with volatile matter, metal foil and a chamber. Ignition of tube causes production of micro shock waves which deflect the foil and propagate through the liquid, increasing the pressure and resulting in liquid jet formation through the small opening in drug chamber. This jet can be focused on targets after fixing an arrangement to shun the by-products of explosion, allowing only energy transfer. This method ensures energy transfer with minimum loss. In addition, as vaccines are available as solutions commercially, they can be used for delivery through this device (Divya et al, 2012).

Dust remover: Silicon wafer surfaces contain various micron and sub-micron sized impurities. A device, using dry cleaning technique, comprises of a high-speed aluminium rotor with surface corrugations placed at a small distance from the wafer’s surface spinning at supersonic speeds. An argon jet from the rotor’s surface is used to enhance the cleaning. It successfully removes 0.7-micrometer tungsten impurities but was not able to clean 0.1-micrometer aluminium dioxide impurities. Regulating the temperature of rotor and reducing the noise would help to optimize the efficiency of the device (Jagadeesh, 2008b; Jagadeesh et al, 2005).

Pencil manufacturing: An impregnation method, using the principles of shock waves, has been designed to www.tjprc.org

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infuse preservatives in wood slats which are used for manufacturing pencils. The preservative’s retention and penetration depth with shock wave use is comparable with the conventional methods, with substantial reduction in the treatment process time compared to conventional methods (Jagadeesh, 2009).

Medical applications: Eisenberger, Chaussy, Brendel, Forssmann and Hepp started working on application of the ESWC in 1974, a project financed by the Department of Research and Science of Germany. In 1980, first patient with a kidney stone was treated in Munich using Dornier Lithotripter HM1. Now-a-days, the treatment of choice for kidney and ureteral stones is with ESWL. Lithotripters use inbuilt X-ray and/or ultrasound machine for localization of stones. Modern lithotripters do not require bathtub or sedation. Apart from its use in nephrology, applications of shock waves are seen in orthopaedics also as it has got osteogenic potential and stimulate fracture healing by activating osteoblasts. In 1993, a special orthopaedic shockwave device, OssaTron (HMT AG, Lengwil, Switzerland), with a moveable therapy-head, became available. At the same time, its therapeutic effect was seen on tendinitis calcarea. Later, its use extended to successful treatment of epicondylitis and heel spur. Healing effect of shock-wave therapy on avascular necrosis of the head of femur is looking promising. Ostechondritis dissecans, patellar tendinitis and Achilles tendinitis are other orthopaedic indications showing good preliminary results. Seeing positive result of shock-wave therapy on human’s orthopedic problems, veterinarians also started using this method of treatment on several tendon problems in horses. They reported good result on the lameness of the horses with this treatment (Thiel et al, 2000).

Industrial applications: Shock waves are effectively used in hardening of surfaces of metal. This is carried out by transfer of shock energy onto a material, which is deformed. The shock system produces various strengthening agents like acoustic waves (Kirichek et al, 2014). Shock waves, with the help of explosives are also used to produce diamond powders at micro scale, which are polycryatalline in nature. A mixture comprising of powders of carbon and copper are compressed with the help of shock waves at a pressure of 30GPa to 60 GPa and at shock temperature, graphite yields diamond (Fujihara et al, 1992). Other applications consists of explosive welding, shock induced fabrication and consolidation of powdered ceramic or metallic materials.

CONCLUSIONS AND FUTURE SCOPE The study concludes that the Mach number increases with the proportional increase in vacuum pressure as well as diaphragm thickness and in the range of experiment, the percentage increase in Mach number is more with increasing vacuum pressure than diaphragm thickness. This valuable information can help in reducing resources and expenses of a shock tube, which gives a higher Mach number. Use of several diaphragms in form of layers can be done to increase the overall diaphragm thickness.

The study proposes future experiments to find out the mathematical relations between vacuum pressure and Mach number using a diaphragm having different and higher ductile characteristics.

ACKNOWLEDGEMENTS Authors are greatful to Vellore Institute of Technology, Vellore and Dr. Muruganandam L for providing the required facilities and assistance.

REFERENCES 1.

Jagadeesh, G. (2008a). Fascinating world of shock waves. Resonance, 13(8), 752-767.

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2.

Murr, L. (2010). Shock Waves For Industrial Applications. Park Ridge, N.J., U.S.A: Noyes Publications.

3.

Delius, M. (1994). Medical applications and bioeffects of extracorporeal shock waves. Shock Waves, 4(2), 55-72.

4.

Kumar C, Takayama K & Reddy K. (2014). Shock waves made simple. Chichester, West Sussex, UK: Wiley-Blackwell.

5.

Arjun Jayakumar, Arun Danam & Ashok Kumar N. (2014). Shock Tube Performance studies with air and carbon di-oxide using numerical simulation. International Journal of Scientific & Engineering Research, 5(7), 970-975.

6.

Satyanarayana I & Shivaji. (2016). Modelling of Shock Waves and Micro Jets Using CFD Analysis. International Journal of Innovative Science, Engineering & Technology, 3(10), 70-77.

7.

Lauer, U., Bürgelt, E., Squire, Z., Messmer, K., Hofschneider, P., Gregor, M. & Delius, M. (1997). Shock wave permeabilization as a new gene transfer method. Gene Therapy, 4(7), 710-715.

8.

Achten, W., Verchot, L., Franken, Y., Mathijs, E., Singh, V., Aerts, R. & Muys, B. (2008). Jatropha bio-diesel production and use. Biomass and Bioenergy, 32(12), 1063-1084.

9.

Maroušek, J., Itoh, S., Higa, O., Kondo, Y., Ueno, M., Suwa, R., Komiya, Y., Tominaga, J. & Kawamitsu, Y. (2013). Pressure Shockwaves to Enhance Oil Extraction from Jatropha Curcas L. Biotechnology & Biotechnological Equipment, 27(2), 36543658.

10. Divya Prakash, G., Rakesh, S., Chakravortty, D., Kontis, K. & Jagadeesh, G. (2012). Development of Blast-Wave Mediated Vaccine Delivery Device. 28th International Symposium on Shock Waves, 1001-1007.

11. Jagadeesh, G. (2008b). Industrial applications of shock waves. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 222(5), 575-583.

12. Jagadeesh, G., Mizunaga, M., Shibasaki, K., Shibasaki, S., Saito, T. & Takayama, K. (2005). Shock wave assisted removal of micron size dust particles from silicon wafer surfaces. Shock Waves, 1231-1234.

13. Jagadeesh, G. (2009). Application of shock waves in pencil manufacturing industry. Shock Waves, 847-850.

14. Thiel, M., Nieswand, M., & Dörffel, M. (2000). Review: The use of shock waves in medicine—a tool of the modern OR: An overview of basic physical principles, history and research. Minimally Invasive Therapy & Allied Technologies, 9(3-4), 247– 253.

15. Kirichek, A.V., Soloviev, D.L. & Altukhov, A.Y. (2014). Production of Quasicomposite Surface Layer of a Metal Material by Shock Wave Strain Hardening. Journal of Nano- and Electronic Physics, 6(3), 03070(1-4).

16. Fujihara, S., Narita, K., Saito, Y., Tatsumoto, K., Fujiwara, S., Yoshida, M., Aoki, K., Kakudate, Y., Usuba, S. & Yamawaki, H. (1992). Explosive shock synthesis of polycrystalline diamond powders. Shock Waves, 367-372.

17. Paturu, Pallavi, et al. "Numerical Analysis of Flow Over NACA0012 at Fixed Mach Number Using Computational Fluid Dynamics." International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) 7.6 (2017): 213-222.

18. Roy, Samanwita. "COMPARATIVE FLOW ANALYSIS OF NACA S6061 AND NACA 4415 AEROFOIL BY COMPUTATIONAL FLUID DYNAMICS." International Journal of Mechanical Engineering (IJME) 7.2 (2018) : 9-18 19. REDDY, P. SURENDRA, G. KIRAN KUMAR, and A. VENKATARAVINDRA. "WIND LOAD ANALYSIS OF SOLAR FARM USING COMPUTATIONAL FLUID DYNAMICS." International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) 9.6 (2019) : 485–498.

20. KUMAR, DEEPAK, et al. "THE STUDY AND INTERPRETATION OF STHE WITH COMPUTATIONAL FLUID DYNAMICS www.tjprc.org

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