Modern Compressible Flow John D Anderson

[Jordan Tucker]

Andersons book provides the most accessible approach to compressible flow for Mechanical and Aerospace Engineering students and professionals. In keeping with previous versions, the 3rd edition uses numerous historical vignettes that show the evolution of the field. New pedagogical features - "Roadmaps" showing the development of a given topic, and "Design Boxes" giving examples of design decisions - will make the 3rd edition even more practical and user-friendly than before. The 3rd edition strikes a careful balance between classical methods of determining compressible flow, and modern numerical and computer techniques (such as CFD) now used widely in industry and research. A new book website will contain all problem solutions for instructors.

The morning of Tuesday, October 14, 1947, dawned bright and beautifulover the Muroc Dry Lake, a large expanse of flat, hard lake bed in theMojave Desert in California. Beginning at 6:00 a.m., teams of engineersand technicians at the Muroc Army Air Field readied a small rocket-poweredairplane for flight. Painted orange, and resembling a 50-caliber machinegun bullet mated to a pair of straight, stubby wings, they carefully installedthe Bell X-1 research vehicle in the bomb bay of a four-engine B-29 bomberof World War II vintage. At 10:00 a.m., the B-29 with its soon-to-be historiccargo took off and climbed to an altitude of 20,000 feet. As it passedthrough 5,000 feet, Captain Charles E. (Chuck) Yeager, a veteran P-51 pilotfrom the European theater during World War II, struggled into the cockpitof the X-1. This morning Yeager was in pain from two broken ribs incurredduring a horseback riding accident the previous weekend. However, not wishingto disrupt the events of the day, Yeager informed no one at Muroc abouthis condition, except his close friend Captain Jack Ridley, who helpedhim to squeeze into the X-1 cockpit. At 10:26 a.m., at a speed of 250 milesper hour, the brightly painted X-1 dropped free from the bomb bay of theB-29. Yeager fired his Reaction Motors XLR-11 rocket engine and, poweredby 6,000 pounds of thrust, the sleek airplane accelerated and climbed rapidly.Trailing an exhaust jet of shock diamonds from the four convergent-divergentrocket nozzles of the engine, the X-1 soon approached Mach 0.85, the speedbeyond which there existed no wind tunnel data on the problems of transonicflight in 1947. Entering this unknown regime, Yeager momentarily shut downtwo of the four rocket chambers, and carefully tested the controls of theX-1 as the Mach meter in the cockpit registered 0.95 and increased still.Small invisible shockwaves danced back and forth over the top surface ofthe wings. At an altitude of 40,000 feet, the X-1 finally started to leveloff, and Yeager fired one of the two shutdown rocket chambers. The Machmeter moved smoothly through 0.98, 0.99, to 1.02. Here, the meter hesitatedthen jumped to

1.06. A stronger bow shockwave now formed in the air ahead of the needlelikenose of the X-1 as Yeager reached a velocity of 700 miles per hour, Mach1.06, at 43,000 feet. The flight was smooth; there was no violent buffetingof the airplane and no loss of control as feared by some engineers. Atthis moment, Chuck Yeager became the first pilot to fly faster than thespeed of sound, and the small but beautiful Bell X-1, became the firstsuccessful supersonic airplane in the history of flight.2

As the sonic boom from the X-1 propagated across the California desert,this flight became the most significant milestone in aviation since theWright brothers' epochal first flight at Kill Devil Hills fourty-four yearsearlier. But in the history of human intellectual accomplishment, thisflight was even more significant; it represented the culmination of 260years of research into the mysteries of high-speed gas dynamics and aerodynamics.In particular, it represented the fruition of twenty-three years of insightfulresearch in high speed aerodynamics carried out by the National AdvisoryCommittee for Aerodynamics (NACA) research that represented one of themost important stories in the history of aeronautical engineering. Thepurpose of this chapter is to tell this story. The contribution by theNACA to the Bell X-1 was much more technical than it was administrative.Therefore, this chapter will highlight the history of that technology.

The NACA's work on high-speed aerodynamics described in this chapteris also one of the early examples in the history of aerodynamics whereengineeringscience played a deciding role. Beginning in 1919, the NACA embarkedon a systematic intellectual quest to obtain the knowledge requiredto eventually design proper high-speed airfoil shapes. HistorianJames R. Hansen, in his chapter on the NACA low-drag engine cowling, inthe present book, asks the following question about the cowling work: Wasit science, or was it engineering? He comes to the conclusion that it wassomewhere in between that it was an example of engineering science inaction at the NACA. In arriving at this conclusion, Hansen draws from thethoughts in Walter Vincenti's book, What Engineers Know and How TheyKnow It, where Vincenti clearly makes the following distinction betweenscience and engineering: science is the quest for new knowledge for thesake of enhancing understanding, and engineering is a self-standing bodyof knowledge (separate from science) for the sake of designing artifacts.For the purpose of the present chapter, I suggest this definition of engineeringscience: Engineering science is the search for new scientific knowledgefor the explicit purpose of (1) Providing a qualitative understanding whichallows the more efficient design of an engineering artifact, and/or (2)Providing a quantitative (predictive) technique, based on science, forthe more efficient design of an engineering artifact. In this chapterwe will see that NACA researchers in the 1920s and 1930s were working hardto discover the scientific secrets of high-speed aerodynamics just so theycould properly design airfoils for highspeed flight truly engineeringscience in action. Also, within the general framework of the historicalevolution of aerodynamic thought over the centuries, the NACA's highspeedresearch program is among the earliest examples of engineering science,although that label had not yet been coined at the time.

Most golfers know the following rule of thumb: When you see a flashof lightning in the distance, start counting at a normal rate one,two, three.... For every count of five before you hear the thunder, thelightning bolt struck a mile away. Clearly, sound travels through air ata definite speed, much slower than the speed of light. The standard sealevel speed of sound is 1, 117 feet per second in five seconds a soundwave will travel 5,585 feet, slightly more than a mile. This is the basisfor the golfer's "count of five" rule of thumb.

The speed of sound is one of the most important quantities in aerodynamics;it is the dividing line between subsonic flight (speeds less than thatof sound) and supersonic flight (speeds greater than that of sound). TheMach number is the ratio of the speed of a gas to the speed of sound inthat gas. If the Mach number is 0.5, the gas flow velocity is one-halfthe speed of sound; a Mach number of 2.0 means that the flow velocity istwice

that of sound. The physics of a subsonic flow is totally different fromthat of a supersonic flow a contrast as striking as that between day andnight. This is why the first supersonic flight of the X-1 was so dramatic,and why the precise value of the speed of sound is so important in aerodynamics.

Knowledge of the speed of sound is not a product of twentieth centuryscience. Precisely 260 years before the first supersonic flight of theX-1, Isaac Newton published the first calculation of the speed of soundin air. At that time it was clearly appreciated that sound propagated throughair at some finite velocity. Newton knew that artillery tests had alreadyindicated that the speed of sound was approximately 1,140 feet per second.The seventeenth century artillery men were preceding the modern golfer'sexperience; the tests were performed by standing a known large distanceaway from a cannon, and noting the time delay between the light flash fromthe muzzle and the sound of the discharge. In Proposition 50, Book II ofhis Principia (1687), Newton calculated a value of 979 feet persecond for the speed of sound in air fifteen percent lower than the existingartillery data. Undaunted, Newton followed a now familiar ploy of theoreticians;he proceeded to explain away the difference by the existence of solid dustparticles and water vapor in the atmosphere. However, in reality Newtonhad made the incorrect assumption in his analysis that the air temperatureinside a sound wave was constant (an isothermal process), which causedhim to underpredict the speed of sound. This misconception was correctedmore than a century later by the famous French mathematician, Pierre SimonMarquis de Laplace, who properly assumed that a sound wave is adiabatic(no heat loss), not isothermal.3 Therefore,by the time of the demise of Napoleon, the process and equation for thespeed of sound in a gas was fully understood.

This is not to say that the precise value of the speed of sound wastotally agreed upon. The debate lasted well into the twentieth century.Indeed, although this event is little known today, the NACA was an arbiterin setting the standard sea level speed of sound. On October 12, 1943,twenty-seven distinguished U.S. leaders in aerodynamics walked throughthe doorway of NACA Headquarters at 1500 New Hampshire Avenue in Washington,DC. They were attending a meeting of the Committee on Aerodynamics, oneof the various adjunct committees set up by the main NACA. Among the expertspresent were Hugh L. Dryden from the Bureau of Standards, and John Stack,whose career as an aerodynamicist at the NACA Langley Memorial Laboratorywas on a meteoric rise. Also present was Theodore von Krmn,director of the Guggenheim Aeronautical Laboratories at Cal Tech, who representedan intellectual pipeline to the seminal aerodynamic research by LudwigPrandtl at Gttingen University in Germany, where von Krmnhad been Prandtl's Ph.D. student before World War I. After subcommitteereports on progress in helicopter aerodynamics, and recent aerodynamicproblems in wing flutter and vibration, the matter of speed of sound wasbrought up as new business by John Stack, who stated that "the problemof establishing a standard speed of sound was raised by an aircraft manufacturer."4

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