AEE 343 Compressible Flow Lab 1 Instructor: T. Dang Experiments: 02/24 – 02/28 TA: Seth Kelly [email protected] INTRODUCTION: Facility Description The supersonic wind tunnel at Syracuse University is a short-duration blow-down wind tunnel. A schematic layout of the tunnel is shown in Figure 1. The setup consists of seven large pressurized tanks that can be vented rapidly into a converging-diverging nozzle via a fast-acting valve. The maximum pressure in the tank is about 180 psia (safety reason). Operating conditions of the supersonic tunnel is when the tank pressure is greater than 40 psia. The tank reservoir temperature is approximately constant at 72oF (532 oR). Supersonic flow leaving the converging- diverging nozzle enters the test section where various test models can be mounted. The test section is approximately 4” in height and 4” in width. Downstream of the test section, the flow passes through a diffuser before being discharged to the atmosphere (outside of the building). The Mach number in the test section can be varied by adjusting the throat area via a crank device. The throat area is varied by changing the height of the throat while the width remains constant at 4”. The test section can attain Mach numbers as high as 3, with test time on the order of 5-10 seconds for the high Mach number case. Figure 1: Syracuse University Supersonic Wind Tunnel. The tunnel is instrumented with three pressure transducers and one temperature dial gage. The pressure gages read tank stagnation pressure in psia (upstream of valve), reservoir stagnation pressure in psia (downstream of valve), and static pressure in the test section in psia. The temperature gage reads stagnation temperature upstream of the test section. Finally, the test model can be instrumented with up to two pressure transducers. This is done by connecting pressure taps on the test model to the pressure sensors via tubing. The pressures measured by the transducers attached to the model in the test section are all in psig. All pressure transducers are connected to a data acquisition system operated by a Windows-based PC running the software package Labview. Simplified model for SU supersonic wind tunnel In this part of the lab, you are asked to acquire some understandings of the operation of the SU wind tunnel facility. A typical layout of a blow-down supersonic wind tunnel is shown in Figure 2. It consists of a test section attached behind a converging-diverging nozzle. Upstream of the converging-diverging nozzle is a pressurized tank, while downstream of it is a supersonic diffuser system. Note that the diffuser system is also a converging-diverging duct. The function of the supersonic diffuser system is to slow down the flow with minimum total pressure loss. This is achieved through a series of oblique shock waves and a final normal shock wave. Recall that if the process can be done without shocks (i.e. an isentropic compression process), you would have a perpetual motion machine. Figure 2: typical layout of a supersonic wind tunnel. Figure 3: Simplified model of SU Supersonic Wind Tunnel. A simplified model for the SU supersonic wind tunnel is shown in Figure 3. Instead of having a supersonic diffuser, we assume that a normal shock exists at the end of the test section, followed by a subsonic isentropic deceleration to near zero velocity via a diverging duct. The static pressure at the exit station is 1 atm. Using this simplified model: (a) Estimate the following conditions as the Mach number in the test section is varied. Note that the width of the throat section is fixed at 4” while the height can be varied, and the reservoir pressure is the minimum condition required to achieve the specified Mach number in the test section. Test section Mach no. Height of throat (in) Reservoir pressure P0 (psia) M1 = 1.5 M1 = 2.0 M1 = 2.5 (b) Consider the case where the Mach number at the test section is 2. Estimate the following conditions as the reservoir pressure is reduced. In a blow-down facility, the Mach number distribution in the tunnel remains constant once a supersonic flow is set up in the test section (and the flow is thus choked), irrespective of how high the tank reservoir pressure is as long as it is above the conditions estimated in part (a) above. Note that the operating range of reservoir pressure in the SU blow-down supersonic wind tunnel is 40 to 170 psia. Reservoir pressure P0 (psia) Height of throat (in) Test section Mach no. Mass flow rate (slug/s) 170 100 40 Recall that at the choking condition, the mass flow rate can be computed as ̇ = 0√ 0 (1 + −1 2 +1 )−2(−1) R = 1716 (ft.lb)/(slug.oR) and = 1.4 Isentropic Relation The equation below is called the isentropic flow relation. It uses the local total and static pressures of a supersonic flow which can be used to compute the free stream Mach number. 0 = (1 + − 1 2 2) −1 Hence, the local Mach number can be computed if the ratio of the local stagnation-to- static pressure ratio is known. In the experiment, a static pressure gage mounted along the wall in the test section is used to record the local static pressure p1 in psia. If we assume that the flow is isentropic between the reservoir and the test section, then one can assume that the local stagnation pressure P01 is the same as the reservoir pressure P0, which is measured in the experiment (again in psia). Rayleigh Pitot Tube Relation The Rayleigh Pitot tube formula relates the total pressure behind the normal shock, P02, with the static pressure in front of the normal shock (or the static pressure in the test section), p1. 02 = ( 1 (+1)21 2 41 2−2(−1) )−1 (1−)+21 2 +1 Unlike the isentropic flow equation, the Rayleigh Pitot tube formula presents an implicit relation between M1 and (P02/p1) and can be obtained using the Isentropic Flow table. Remember, P02 is measured in psig because the transducer is attached to the model. Uncertainty Analysis Uncertainty Analysis is the process of systematically quantifying error estimates, ux. ′ = ± Each element of error present within a measurement will combine with all other errors to increase the uncertainty of the measurement. We are interested in measuring the variable x. This 1 measurement is subject to k sources of error, ej, j = 1, 2, …k. Use Root-Sum-Squares method (RSS) to obtain the uncertainty in the measurement ux = ±√∑ 2 =1 Or = ±√2 + 2 + ⋯ + 2 1 2 In our case, ux will be the uncertainty in the pressures, P01, p1, and P02 Using Taylor Series expansion and assuming small changes, a linear approximation can be made. (Derivation can be made at http://lcs.syr.edu/faculty/glauser/MAE315/index.html ). For a multivariable problem, we see that. = ±√∑( =1 |= ∙ )2 Using this expansion to solve for the error in Mach number of the isentropic relation. = ±√( 01 |01 = 01 ∙ 01 ) 2 + ( 1 |1=1 ∙ ) 2 Since the Rayleigh Pitot tube formula cannot be solved for Mach number analytically, a numeric differentiation must be calculated. The two sources of error stem from p1 and P02 measurements. Figure 4a is a plot of Mach number calculated using the Rayleigh Pitot tube formula versus static pressure p1 with constant P02 lines. Figure 4b is the numerical differentiation of Mach number with respect to p1 plotted versus p1. From here, we are able to solve for the term in our pressure region. The same method can be carried out so solve for the 1 differentiation of Mach number with respect P02. Figure 4: Mach number sensitivity due to error in P1 and P02, using Rayleigh Pitot method There is error associated with each of the measurements taken. The error associated with each pressure transducer can be found in the Appendix below. PRODECURE: Calibrate the supersonic wind tunnel for various area settings. The tunnel will be run at
an area dial setting between 600 and 1200. Pressure measurements will be taken for the reservoir total pressure, test section static pressure, and Pitot probe total pressure. SUBMISSION/PRESENTATION: Extended Abstract Guidelines (100 pts) This is just to show us that you are thinking about the problem on an individual basis and that you have done work towards the presentation. The lab report and presentation for each experiment should include the following sections (Section 1.0 through 8.0 shall be limited to a maximum of 6 pages, single spaced, font size 12, 8 1⁄2 by 11 inch paper with 1” margin on all sides.). If additional explanations are needed, please put in appendix. (see point values below for this individual part). 1.0 Introduction (5%) – Objectives of the laboratory experiment (e.g., what are you trying to accomplish, and how are you going about it?) – Scope (what are covered in this lab?) 2.0 Experimental Facility and Instrumentation (5%) – Briefly describe the test system and its components including instrumentations. Everything a reader would need to know to follow along with your presentation and understand how you are tackling your problem. – It is good to show pictures with explanation. 3.0 Method (15%) – Principle of the experiment [describe in concept how the performance parameters of interest are calculated] For every data analysis performed, need to discuss equations used. – What measurements you need to take, method used to obtain the data, and how you use the data to solve your stated problem (talk about Schlieren, even though its not used quantitatively in lab 1). – How accurate are the sensors used in the measurements? – How much uncertainty is there in the derived/calculated performance parameters (hint: using error propagation principle learned in MAE 315) 4.0 Experimental design (15%) – What are the test conditions? – How many runs, and what questions you intent to answer with the number of tests performed? First, think of what you want answered in the experiment. Then, explain how you are going to achieve the goals. 5.0 Experimental Procedure (10%) – Describe step-by-step procedures on how the experiment was performed 6.0 Results and Discussions (30%) – Present the results and discuss if they make sense (i.e., consistent with what you would expect and can explain based on fundamental principles of compressible flow) – How do they compare to theory (for lab 2 only) – Any additional observations in the experiment (e.g., was it easy to obtain stable conditions?) 7.0 Conclusions and Recommendations (15%) – What conclusions can you draw from the tests? – Have the lab experiment achieved its objectives? – What suggestions do you have for improving the experiment? 8.0 References (5%) – Papers or reports referenced – Attach a copy of the team presentation, and indicate your specific contribution to the team (e.g., data recording, data analysis, section you prepared and presented…) 9.0 Appendix – Raw data records/plots, more detailed description of the instrumentation and equipment used. Lab 1 Presentation Guidelines (100 pts) 10-15 minute presentation, limit yourself to 10-15 slides Address the points listed in write-up guidelines. As we all do the experiment, put majority effort on introduce results. Presentation quality (10%) – Are you clear and concise, get the point across, etc. REFERENCES: 1. Anderson, J. D., “Modern Compressible Flow with Historical Perspective”, McGraw-Hill, New York 1982. 2. Liepman, H. W. and Roshko, “Elements of Gas Dynamics”, John Wiley and Sons, New York 1958. 3. NACA Report 1135, Equations, Tables and Charts for Compressible Flow. 4. Govoni, R. D., “Sensitivity Analysis for Supersonic Wind Tunnel Calibrations Techniques”. 5. Glauser, M. < http://lcs.syr.edu/faculty/glauser/MAE315/index.html>. APPENDIX A SOME NOTES ON ACCURACY OF TRANSDUCERS Transducer 1 (Pitot stagnation pressure): range is –15 psig to +45 psig. Accuracy is +/– 0.5 psi for pressure less than 15 psig, and +/– 0.06 psi for pressure greater than 15 psig. Transducer 3 (Test section static pressure): range is 0 psia to 30 psia. Accuracy is +/– 1.1 psi. Transducer 4 (Test section stagnation pressure): range is 0 psia to 120 psia. Accuracy is +/– 3.75 psi. APPENDIX B AEE 343 Lab 1 Grading Rubric Category ABET Learning Objectives Pts. Possible Score Comments Introduction G 5 Experimental Facility and Instrumentation B 5 Method A,B,E 15 Experimental design B 10 Experimental Procedure B 10 Results and Discussions A,B,E 30 Conclusions and Recommendations G 10 References D,I 5 Presentation 10 TOTAL 100
