SC Sports Car Aerodynamics

Transcription

1 School of Engineering Year 1 Laboratories SC Sports Car Aerodynamics Module : ENGG109 Fluid Mechanics with Thermodynamics Lecturer : Dr. R. J. Poole Laboratory Teaching Assistants : Jinglei Ouyang Waleed Abed

2 Notation Symbol Description Units Acceleration due to gravity m s -2 Mass kg Frontal area of car m 2 Air pressure Pa Constant in Sutherland equation K Drag coefficient - Drag force N Voltmeter reading V Air pressure expressed as column height of mercury barometer mm Hg Constant in Sutherland equation Pa s K -1/2 Length of car m Manometer reading m Power W Specific gas constant for air 1 J Kg 1 K Reynolds number - Air temperature in Kelvin K Air temperature in Celsius C Windspeed m s -1 Inclination angle of manometer Dynamic viscosity Pa s Air density kg m -3 Density of mercury kg m -3 Density of manometer fluid kg m -3

3 1 Aim & Objectives The aim of this lab is to measure the drag forces exerted on two scale models of the TVR Tuscan Speed Six, one fitted with a rear spoiler the other with no spoiler, to show how experimental data can be scaled up for use in research and development by applying key fluid dynamics theory. It will introduce the role of experiments in the study of fluid mechanics and the limitations of purely theoretical analyses. Upon successful completion of this lab, you will be able to: carry out basic dimensional analysis to reduce a physical problem to non-dimensional form; use the principle of dynamic similarity to scale model data to full-scale; understand the use of U-tube and inclined-tube manometers to measure applied pressure differences as well as use test and measurement equipment and techniques; record, analyse and interpret experimental results; estimate accuracy; assess errors; use safe systems of work; and develop team-working skills The technical objectives of this lab are to: determine the projected area of the cars (achieved in pre-lab) calibrate the force block calculate the air density calculate the drag coefficient of each model calculate the drag force on the scale and full-sized models 2 Introduction The factor which ultimately limits the top speed of a car, lorry, bus, train etc is the drag force (or resistance) due the flow of air around and underneath the bodywork. For high-speed vehicles, especially racing cars, aerodynamic lift also plays an important role in determining performance. Since it is often impractical to measure the lift and drag forces directly on full-scale vehicles, aerodynamicists use scaling principles applied to data obtained using scale models installed in wind tunnels to estimate these forces. The experiments will be carried out over a range of windspeeds and the results converted to a nondimensional form (drag coefficient,, and Reynolds number, ) to see whether the results can be made speed independent. From the model results, estimates will be made of the drag forces on fullscale versions of the two cars and the engine power required to propel these cars at a speed of 335 kph (about 209 mph). The experiments will also show how the rear spoiler affects drag. P a g e 1

4 2.1 Theory The relationship between temperature in K and temperature in C is given by: 273 (1) The relationship between the air pressure in Pa and mm Hg is given by (2) where = kg m -3 and g = 9.81 m s -2. Air density can be calculated from the ideal gas law (3) -1 where = specific gas constant for air = 287 J kg -1 K The windspeed is to be measured using the Pitot-static tube installed in the working section of the wind tunnel together with the inclined manometer. One side of the manometer senses the static pressure of the air (roughly equal to the atmospheric pressure) while the other senses the stagnation pressure which is the static pressure plus the dynamic pressure. From Bernoulli s equation and the hydrostatic equation we can show that 2 sin (4) where the density of manometer fluid is 823 kg m -3 and the inclination angle of manometer is 5. Dynamic viscosity for air can be calculated from Sutherland s formula: (5) where is 1.45x10-6 Pa s K -1/2 and is K. The coefficient of drag can be calculated at a given wind speed from the definition using 1 2 To calculate the corresponding Reynolds number use (6) / (7) where = m P a g e 2

5 The engine power P required to overcome the drag force is given by: (8) To convert the units of from Watts to horsepower multiply by 1.34x Apparatus Two scale-model sports cars, based upon the TVR Pro-Line Speed Six, have been installed in a lowspeed wind tunnel (0 10 m s -1 ). One model is fitted with a rear spoiler, the other has no spoiler. The models are about 10.1% of the size of the real car. Wind speed within the wind tunnel will be measured using a calibrated Pitot-static tube. The prevailing air temperature and pressure should be measured using the wall-mounted Fortin barometer. The force block used to measure the drag force will be calibrated at the beginning of the lab session. As the weight is applied the car is pulled back, which then bends the struts on the force block (Figure 1). Figure 1 Force block calibration setup P a g e 3

6 2.3 Pre lab Projected (Silhouette or Frontal) Area of the Car You have already carried out a preliminary experiment to determine the projected area of each car (needed to define ). The projected area of the car was determined using a light source, a pencil and a piece of graph paper to draw around the shadow of the car (Figure 2). The number of squares covered by the shadow of the car was then counted and the corresponding projected area covered by the shadow should be entered in Table 2, after being converted to m 2. Since the real cars are 9.9 times the length of the model car, their projected areas will be times that of the models. Figure 2 Determining projected area 3 Health & Safety Ear-defenders must be worn when the wind tunnel is in operation. Note that the apparatus contains mercury. This is extremely poisonous and therefore in the unlikely event of any spillage, notify the demonstrator immediately so that a technician can be called to deal with the problem. Students are reminded that they are required by law to comply with the School s basic rules of lab safety given to them at the start of the semester. P a g e 4

7 4 Experimental Procedure 4.1 Calibration of the Force Block Record readings in Table 1 a. Zero the voltmeter attached to the force block. b. Add a 0.02kg mass to the scale pan and record the voltmeter reading. c. Repeat step (b) adding 0.02kg each time until the total mass is 0.12kg. d. Plot the voltage versus the added weight ( ) and use this to derive an equation for the force-block calibration corresponding to a straight line fitted through the points. 4.2 Calculation of air density and viscosity a. Use the wall-mounted barometer to measure the air temperature in Celsius and pressure in millimetre of mercury. b. Convert and to SI units: air temperature in Kelvin and pressure in Pascals using the equations given in the theory section. Record these underneath Table 2. c. Calculate air density using equation (3) and record this value underneath Table 2. d. Calculate air viscosity using equation (5) and record this value underneath Table Drag Force Due to Wind Acting on the Car Record readings in Table 2 a. Increase the wind tunnel wind speed until reads 0.02m. b. Record the voltage indicated by the voltmeter. c. Use the calibration line (determined in step 4.1.d) to find the drag force the airflow is exerting on the car. d. Repeat steps (a) to (c) incrementing the wind speed to the corresponding values of by 0.02m. e. Repeat steps (a) to (d) for the second car. 5 Calculations 5.1 Calculations Necessary for Table 2 Record all calculations in Table 2 a. Calculate the windspeed V for each condition using equation 4. b. Calculate the drag coefficient C D for each condition using equation 6. c. Calculate the Reynolds number Re for each condition using equation Additional Calculations Required for Technical Note a. Convert a speed of km h -1 into a speed in m s -1. b. Calculate the drag force on real cars 9.9 times the length of the models (428 mm) travelling at 335 km h -1 (209 mph). c. Calculate the engine power required to overcome the drag force for each car at this speed. P a g e 5

8 6 Technical Note Instructions There is no paper-based write up for this lab and you are not required to complete a full lab report. You will complete a Technical Note Template on a computer then upload it to VITAL. The technical note contains the following sections, each worth the percentages to their right: Results (tables, calculations and figures) 40% (10%, 20%, 10%) Discussion (including error analysis) 40% (20%, 20%) Conclusions 10% Abstract 10% Download the Technical Note Template from the Submission folder in the SC: Sports Car Aerodynamics section of the Year 1 Labs and Tutorials module on VITAL. Complete the Technical Note Template by following the instructions and answering the questions. If you are having difficulty please contact the LTAs by for help. Rename the document to include the date that you were in the lab and your name before submitting it for example SC Technical Note John Smith.docx. The deadline is before midnight 5 calendar days from the date of the lab, including the day of the lab. So if you did the lab on Friday the 2nd, the deadline would be at 23:59 on Tuesday the 6th. The TurnItIn submission link will become available to you only after you have completed a short, anonymous survey for feedback on the lab. The School of Engineering takes your opinions seriously and feedback from last year s students informed significant changes to the labs which have been updated for this year. P a g e 6

9 Appendix A Results Tables Table 1 Results of force-block calibration. Mass added to scalepan (kg) Weight added to scalepan (N) Voltmeter reading (V) P a g e 7

10 Table 2 Results of wind tunnel test on model cars Data for car without spoiler Length L MAN (m) Windspeed (m s -1 ) Voltmeter Reading (V) Drag force (N) Drag coefficient Reynolds Number Data for car with spoiler Average Length L MAN (m) Windspeed (m s -1 ) Voltmeter Reading (V) Drag force (N) Drag coefficient Reynolds Number Average Air temperature = K Air pressure = Pa Air density = kg m -3 Dynamic viscosity of air μ = Pa s Projected areas Car 1 (without spoiler) = m 2 Car 2 (with spoiler) = m 2 P a g e 8