This online calculator simulates the performance of a laboratory shock tube employing calorically perfect gases. Included in the calculated properties are the pressure, temperature, speed of sound, and velocity. The user selects from a list of eight driver and driven gases, and specifies certain temperatures and pressures and the Mach number of the shock. The calculator output includes a full array of information about the various regions in the shock tube (T, p, V, etc)as well as the speed and Mach number of the reflected wave.
Also included are the pertinent equations for a shock tube and a table of properties for a number of gases. Timing issues related to the shock wave can be estimated with specification pressured transducer location distance and also the booster tank sizing specifications can also be calculated.
Type of Material:
As a classroom demonstration or as an aide for assigned homework.
Identify Major Learning Goals:
To teach the fundamentals of theoretical shock tube performance.
Target Student Population:
The gas dynamics calculator will be useful for senior undergraduate and first year graduate students in Aerospace Engineering, Mechanical Engineering, and Engineering Mechanics taking a compressible fluid flow course.
Prerequisite Knowledge or Skills:
A good working knowledge of normal shock waves and a basic understanding of the shock tube.
This calculator certainly helps remove much of the tedium involved in calculating the flow properties in a shock tube. The solution to shock tube problems involves complex equations that are time-consuming to solve. However, this calculator provides almost instant solutions. The accuracy of the calculator appears to be excellent, which is to expected since the calculator is
based on valid shock tube relations for unsteady wave motion.
The traditional "Region 3" in the shock tube is not included in the display of output values. This region between the contact surface and the expansion wave differs from region 2 in both temperature and entropy and is normally included in shock tube analyses.
Potential Effectiveness as a Teaching Tool
Being able to solve certain shock tube problems quickly and effortlessly makes this calculator quite effective as a teaching tool - whether it is used by the instructor in the classroom or by students at home. Parametric studies become quite feasible with a tool such as this. Other useful features include the calculator's ability to handle a number of gases besides air and links to the pertinent shock tube equations.
The material can be used in a variety of ways to teach or learn including: 1) to solve problems during lectures, and 2)to be used by students to solve/validate homework problems that would otherwise require tedious manipulations of property ratio equations for shock waves.
Finally, being able to input information related to transducer spacing and timing makes the calculator useful as a laboratory data-reduction tool.
The calculator would be even more useful as a teaching tool if it permitted the user to specify both of the following types of problems:
Type (1): The pressure of the driven gas and the shock Mach number are stated Type (2): The pressures of both the driver gas and the driven gas are stated
Currently only Type (1) problems are permitted. For classroom examples and many textbook problems,
the driver and driven pressures are specified and the Mach number must be determined. This, of course, is a much more difficult problem since it usually involves an iterative solution of an implicit relationship. But, this is precisely where a computer-based approach could be very useful. A simple iteration scheme is possible that converges in 5-6 steps typically, thus making "Type 2" problem solutions quite feasible.
As discussed above, another concern centers around the fact that the shock tube flow is broken into the four distinct regions normally discussed in textbooks, namely:
plus a fifth region for the reflected shock. While this calculator provides the properties in regions 1,2,4 and 5, for some reason it omits the values in (and any discussion of) region 3. While V2=V3, and P2=P3, the temperature and entropy in the two regions are not the same. Thus, some of its potential pedagogical value is lost.
Ease of Use for Both Students and Faculty
The software is easy to access, and users can learn how to use it with minimal documentation or instruction. The calculator layout is consistent and intuitive, with only a few exceptions as noted below.
In the "Notes" section, the "factor for area contraction" is not defined anywhere but its values does affect the "approximate driver pressure". Also, the approximate driver pressure is stated in English units (psig) rather than the SI units (Pa or MPa) used elsewhere in the calculator.
Other Issues and Comments:
The link to Fluid Properties (http://silver.neep.wisc.edu/~shock/tools/flprops.pdf) appears to be dead.
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