Lecture #05. Methods for local Flow Velocity Measurements. AerE 545 class notes

Transcription

1 AerE 545 class notes Lecture #05 Methods for local Flo Velocity Measurements Hui Hu Department of Aerospace Engineering, Ioa State University Ames, Ioa 50011, U.S.A

2 Methods to Measure Local Flo Velocity - 1 Mechanical methods: Taking advantage of force and moments that a moving stream applies on immersed objects. Vane anemometers Propeller anemometers

3 Methods to Measure Local Flo Velocity -2 Pressure difference methods: Utilize analytical relationship beteen the local velocity and the static and total pressures The tubes sensing static and stagnation pressures are usually combined into one instrument knon as Pitotstatic tube. Pressure taps sensing static pressure (also the reference pressure for this measurement are placed radially on the probe stem and then combined into one tube leading to the differential manometer (p stat. The pressure tap located at the probe tip senses the stagnation pressure (p 0. Use of the to measured pressures in the Bernoulli equation allos to determine one component of the flo velocity at the probe location. Special arrangements of the pressure taps (Threehole, Five-hole, seven-hole Pitot in conjunction ith special calibrations are used to measure all velocity components. It is difficult to measure stagnation pressure in real, due to friction. The measured stagnation pressure is alays less than the actual one. This is taken care of by an empirical factor C. a. streamlined airfoil 2( p b. Flat plate 2( p 1 + ρv 2 / ρ p V V 0 = = = C p stat 0 0 p stat p 2 stat,( Bernoulli / ρ

4 Methods to Measure Local Flo Velocity -3 Thermal methods: Compute flo velocity from its relationship beteen local flo velocity v and the convective heat transfer from heated elements. Hot ire anemometers Hot film anemometers

5 Methods to Measure Local Flo Velocity - 4 Frequency-shift methods: Based on the Doppler phenomenon, namely the shift of the frequency of aves scattered by moving particles. Laser Doppler Velocimetry(LDV or Laser Doppler Anemometry (LDV Planar Doppler Velocimetry (PDV or Planar Doppler Anemometry (PDA Interference fringes

6 Methods to Measure Local Flo Velocity - 5 Marker tracing methods: Trace the motion of suitable flo makers, optically or by other means to derive local flo velocity. Particle Imaging Velocimetry (PIV Particle Tracking Velocimetry (PTV Molecular Tagging Velocimetry (MTV t=t 0 PIV image pair t=t 0 +4 ms 0.03 m/s Temperature ( O C t=t 0 t=t 0 +5ms MTV&T image pair Corresponding flo velocity field

7 AerE 545X class notes Thermal Anemometers: Part -1 Hui Hu Department of Aerospace Engineering, Ioa State University Ames, Ioa 50011, U.S.A

8 Thermal anemometers: Technical Fundamentals -1 Measure the local flo velocity through its relationship to the convective cooling of electrically heated metallic sensors. Hot ire anemometers: for clean air or other gas flos Hot film anemometers: for liquid or some gas flos

9 Ho a Hot ire Sensor Works The electric current (i floing through the ire generates heat (i 2 R Flo Field V In equilibrium, this must be balanced by heat lost (primarily convective to the surroundings. Electric current, i, through ire

10 Technical Fundamentals -2 Heat transfer characteristics: Convection (nature convection, forced convection or mixed convection depending on Richardson numbers Conduction to the supporting prong Radiation: <0.1%, is negligible. q& Nu = πlk( T T = Nu(Re, Pr, Gr, M, Kn, a T, l / d, θ Hot ire T θ Fluid flo r V,T T > T ρud Re = ; μ 3 gα( T T d Gr = ; 2 ν λ 1 Kn = = πc p / cv d 2 T T at = T M Re ν Pr = γ V M = c prongs

11 Technical Fundamentals -3 Folloing King s s La (1915, According to Collis and Willams (1959: Nu = ( Re Nu = 0.48 Re 0.51 ( (1 + a T 1 2 n m Nu = ( A + B Re (1 + at , a T 0.17, for for 44 < Re < < Re < 44 For a given sensor and fixed overheat ratio, The above equation can transfer as the relationship beteen the voltage output, E, of the hot-ire operation circuit and the flo velocity R T E T = = R A + Wire temperature cannot be measured directly, but can be estimated ed from its relationship to the ire resistance, R, directly measured by the operating bridge. For metallic ires: r BV n [ 1+ a ( T T ] r r ar : thermal resistivit y coefficien T : reference temepature t

12 Technical Fundamentals - 4 Flo Field V The hot ire is electrically heated. If velocity changes for a unsteady flo, convective heat transfer changes, ire temperature ill change and eventually reach a ne equilibrium. Current flo through ire The rate of hich heat is removed from the sensor is directly related to the velocity of the fluid floing over the sensor

13 Technical Fundamentals - 5 For a sensor placed in a unsteady flo, the unsteady energy equation ill become: mc dt dt = i 2 R q& ( V, T m : the mass of the sensor c : specifich heat of the sensor q& : convective heat flux q& = q& ( V, The above equation has three unknons: i, T (or R and V To render this equation solvable, one must keep ith the electric c current, i, or the sensor temperature (T( constant, hich can be achieved ith the use of suitable electric circuits. The corresponding methods are knon as: (1. Constant Current Anemometry (2. Constant Temperature Anemometry T

14 Constant-current anemometry R s >> R R s E Voltage folloer C E c i = E E o o /( R / R s s + R const The voltage output ill be E = i R E o R sensor R c Compensation circuit R c. The unsteady energy equation is highly-nonlinear. When linearized in the vicinity of an operation point, namely at a particular flo speed, V op, and sensor temperature, T op, it leads to the folloing first-order differential equation: dt τ + ( T Top = KT ( V Vop dt a time constant, hich is proportional to the overheat ratio, and a a static sensitivity, τ : Since voltage, E, is proportional to, R relationship ill be: τ : R, hich, in turn, is linearly related to T,, the linearized E-V de τ + ( E Eop = K( V Vop dt is usually ~ 1ms for thin hot-ire and ~ 10 ms for slim cylindrical hot-film. For flo ith variable velocity or temperature, overheat ratio ill vary as ell. Flo lo speed flo, it may result in burnout,, for high-speed flo, sensitivity is lo KT