MAE 123 : Mechanical Engineering Laboratory II - Fluids Laboratory 2: Venturi Lab Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y.

Transcription

1 MAE 123 : Mechanical Engineering Laboratory II - Fluids Laboratory 2: Venturi Lab Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1

2 Introduction Bernouli Equation The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. ASSUMPTIONS: Steady Flow Incompressible flow ( =.), M<0.3 Frictionless flow This relation does not account for heat added to or work done on the flow thus only a conserved mechanical energy system is valid Mechanical energy = working fluid energy that can be converted entirely to work by an ideal device Definitions: Mechanical energy (ME 040) Flow along a single streamline = =constant Daniel Bernoulli 2

3 Introduction Venturi Effect Assuming constant mechanical energy of a fluid along a streamline (or within a streamtube) velocity of the fluid increases as the cross sectional area decreases: = Static pressure correspondingly decreases: According to the Bernouli Equation, fluid velocity must increase as it passes through a constriction and static pressure must decrease to satisfy the principle of continuity and conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is negated by a drop in static pressure. Giovanni Battista Venturi 3

4 Streamlines and Streamtubes Streamline A line tangent everywhere to the velocity vector at a given instant Apathline is the actual path traveled by a particle Stream lines and pathlines are identical in steady flow Streamtube A closed pattern of flow comprised of many stream lines. Fluid within streamtube is confined no flow across streamtube boundary! 4

5 Bernoulli Equation Applied Along Streamlines and Streamtubes Definitions: Mechanical energy (ME 040) Mechanical energy = working fluid energy that can be entirely converted to work by an ideal device = This definition comes from ME Thermodynamics C&B p. 59 Neglects frictional effects -- inviscid If no energy is exchanged with surroundings then the first law of TD implies: = const. streamlines streamtubes 1 Incompressible Flow (!=const. const.) Incompressible Flow (!=const. const.) Compressible Flow (! const. const.) This form only valid for incompressible flows. From first law of TD this quantity is a constant and variations between streamline/streamtube locations are: $ $ + $ =0 5

6 GAGE AND ABSOLUTE PRESSURE Pressure is an essential measurement when dealing experimentally with Bernoulli s relation Note the differences in reference point for different pressure measurements Gage pressure is measured relative to atmospheric pressure very common and typical of a tire pressure gage Vacuum pressure is also measured relative to atmospheric pressure (typical of many vacuum gages) You can avoid mistakes by working in absolute pressure which is pressure measured from a vacuum reference 6

7 MEASUREMING PRESSURE: MANOMETER With a manometer we take advantage of the laws of fluid statics to measure pressures in fluid dynamic environments + Elevation change in fluid at rest is: =h= & = ) * & This is hydrostatic force balance. Note: & density of manometer liquid * > ) = *., This illustrates how a fluid column can be used to measure pressure and is the working principle of a manometer Manometer Liquid ( & ) Pressure is constant in horizontal direction,p 1 =P 2 Gravitational affect on gases is very small (thus gas in the tank is all atp a ) So the pressure of the gas in the tank is found from the force balance on the liquid column is * = ) + & h So indeed * > ) Relations do not depend on cross sectional area of tube but must be large enough to avoid capillary flow 7

8 MEASUREMING PRESSURE: ELECTRONIC TRANSDUCER A transducer is a device that converts input energy of one form into output energy of another through some physical process that is to be measured. These include, piezoelectric crystals, microphones, photoelectric cells, thermocouples, and pressure transducers. A pressure transducer is a transducer that converts pressure into an analog electrical signal that can be recorded by electrical DAQ systems. Strain Gage Pressure Transducer Capacitive Pressure Transducer Piezoelectric Pressure Transducer 8

9 Static Pressure, Velocity Pressure, and Total Pressure Definitions: Total Pressure: the sum of the static pressure and dynamic pressures.0.*1 = 2.* *3 = 2.* Total Total Static Atmospheric Atmospheric Static This part of the illustration is wrong canyouseewhy? Static Pressure Measurement Total Pressure Measurement Dynamic Pressure Measurement 9

10 Static Pressure, Velocity Pressure, and Total Pressure Definitions: Total Pressure: the sum of the static pressure and dynamic pressures.0.*1 = 2.* =constant A wind tunnel starts with atmospheric air drawn in from the room In the room, the velocity is zero, the air is at rest from a macroscopic view (although there is microscopic motion, and that is how pressure is measured This room measured air static pressure is equal to the tunnel total pressure!! The relation is derived from the Bernoulli equation for horizontal flow ( h=0) between two points in the flow that follow the same streamline are: $ which can also be written as: $ =0 2 streamlines $ $ = Incompressible Flow (!=const. const.) 10

11 Pitot Probe The Pitot probe is a common instrument used to measure dynamic pressure and so to find the flow velocity The central tube measures the total pressure of the flow ( 2.* *3 ) The outer tube functions in the same way that the pressure taps in the wall function and senses the static pressure only as there is no velocity component normal to the wall 11

12 Pitot Probe: Calculating Velocity.0.*1 = 2.* =constant = *1 2.*.3 8 Total pressure We re measuring the total pressure and static pressure in this region So knowing that total pressure is constant, we can use the static pressure distribution to infer the velocity distribution As we said earlier, we assume that the flow is inviscid -- we ignore viscosity and we also make use of the fact that at our low speeds, density is constant. The flow is incompressible. Static pressure 12

13 Velocity from Mass Conservation of a Fluid A Simply stated, the mass flow rate of a fluid is defined as the amount of travelling through an area per unit time. Standard notation for mass flow rate is: A $ 9: mass flow rate The mass flow rate at any location in the flow can be determined from locally determined properties as: 9: =AB density,a=area,and B=velocity 1 2 streamtubes Incompressible Flow (!=const. const.) 13

14 : Velocity from Mass Conservation of a Fluid If no mass of fluid is being removed or added across the stream tube walls, then the mass flow rate of the fluid is conserved and constant: A 9: =constant 9 : $ =9 $ A $ B $ = A B A $ This means that if the mass flow rate can be determined at any region in the streamtube, then the velocity at any other point along the streamtube through knowledge of local density and local area 9: B $ = $ A $ 9: = $ A $ B $ = A B B = 9: A 1 2 streamtubes Keep in mind that for our low speed incompressible flow applications we can assume density to be constant and calculated from atmospheric conditions. Incompressible Flow (!=const. const.) 14

15 UVM Low Speed 12 x12 Wind Tunnel (Flowtek 1440) 2 HP Motor and Fan Section Diffuser Section Manometer Flow Direction (0-90MPH) Contraction Cone Plastic Honeycomb Flow Straightener Tunnel Controls Test Section (12 x12 x36 ) Data Acquisition 15

16 Venturi Experiment A Venturi experiment is a good laboratory exercise to help understand the basic principles of Bernouli equation and mass flow conservation. Already installed in the test section is are two inserts with 10 or so static pressure taps along the surface to create a Venturi effect. A Pitot probe is also installed to measure the total pressure. A static pressure measurement at the test section inlet will also be required. You will be given the height of each tap location to estimate the area at each measurement location. Pitot-static probe Inlet static pressure port Test Section I H 16

17 Venturi Experiment: Measurements (1) From room temperature and atmospheric pressure, calculate density (2) Operate wind tunnel at two speeds. At each speed record: a) 10 (or so) static pressure readings over Venturi from manometer b) Inlet static pressure reading from manometer c) Pitot pressure reading from manometer d) Static pressure reading of Pitot-static probe from manometer (careful to take not WHERE the measured location is in H. c) Record the atmospheric pressure level of the manometer as this is needed for reference. At least 3 measurements for all the above are needed to calculate both a mean and a standard deviation but more are better, time permitting. Pitot-static probe Inlet static pressure port Test Section I H 17

18 Venturi Experiment: Data Reduction and Analysis Determine a velocity profile along the Venturi installation at each measurement port using two methods: conservation of mechanical energy and conservation of mass. Method 1: Conservation of Fluid Mechanical Energy(Bernoulli relation) The total pressure acquired is constant. Measure the static pressure at each pressure tap location along the Venturi. Extract the dynamic pressure at each location from the Bernouli relation. Use dynamic pressure to calculate the velocity at respective pressure tap location. Keep in mind you are recording differential pressures. You must record atmospheric pressure on the manometer to extract an effective Jto relate toward your KL,LMN and OPQ,RMN measurements 18

19 Venturi Experiment: Data Reduction and Analysis Determine a velocity profile along the Venturi installation at each measurement port using two methods: conservation of mechanical energy and conservation of mass. Method 2: Conservation of Mass Envision the flow through the tunnel as one large streamtube. Measured total and static pressure yield the dynamic pressure upstream of the Venturi. Calculate velocity in this region. Calculate density in this region from temperature and static pressure. Calculate mass flow which is constant throughout the Venturi. Using the supplied thickness of Venturi at each station and calculate respective area. Calculate velocity at each pressure tap location with calculated area, density, and area. 19

20 Venturi Experiment: Data Reduction and Analysis Estimate uncertainty for both methods Recall general expression for propagation of error: S T = S UV WA WH $ +S UX WA WH +S UY WA WH Z + +S U\ WA WH 6 General Form for the Expression of Uncertainty Practically, the variances are expressed as: S U\ = 1 ^ 1 _ H 6 3 H 6 ` 3a$ Evaluating this is simply based on finding the mean value: H 6= 1^_ H Which method, did you find, to be the most accurate and precise in your analysis? Perform a sensitivity analysis to identify the most significant contributors to overall uncertainty. Provide suggestions to improve upon said uncertainties 20