Pressure Measurements Material prepared byAlessandro Talamelli, Antonio Segalini & P. Henrik Alfredsson
Literature• Springer Handbook of Experimental Fluid Mechanics, Cameron Tropea, Alexander L. Yarin , John F. Foss (2007), ISBN-10: 3540251413• Measurement in Fluid Mechanics Stavros Tavoularis, Cambridge University Press (2009) ISBN-10: 0521138396• Fluid Mechanics Measurements, R. Goldstein, CRC Press; (1996) ISBN-10: 156032306X• Low-Speed Wind Tunnel Testing, Jewel B. Barlow , William H. Rae, Alan Pope, Wiley-Interscience; (1999) ISBN-10: 0471557749
Measurement techniques• Type of Measurements – Local measurements – Integral measurements – Direct measurements – Non-direct measurements – Field measurements – Surface measurements – Time averaged measurements – Time resolved measurements
Measurement chain Sensor Transducer Acquisition data systems Evaluation data systems
Sensor• Element which changes its status when in contact with the quantity to be measured
Sensor characteristics I • Spatial and temporal resolutionSpatial and temporal resolutions are coupled because it is notgenerally possible to distinguish if the quantity to bemeasured varies with time or if there are pseudo-temporalvariations caused by the passage of spatial disturbances.
Transducer• Element which transforms the changes in the sensor s status in an output signal• Typically it is an electrical signal
Ideal sensor/transducer Output Signal S(t) Physical Quantity Sensor and Transducer s• Output signal is proportional to the magnitude of the physical quantity u• The physical quantity is measured at a y point in space• The output signal represents the input u( x, y, z) without frequency distortion z x• Low noise on output signal• Sensor does not interfere with the s physical process ! ! !s(t )• Output is not influenced by other ! ! !u(t ) t variables
Basic Definitions IIn an internal point of a fluid the pressurecan be defined as the mean of the threenormal stress components acting over threesurface elements orthogonal to each other inthe point at rest with respect to the fluid.For a fluid in motion this value is called staticpressure (definition by AeronauticalResearch Council ).
Basic Definitions IIIf the fluid is brought to rest with anisentropic and adiabatic process, the pressurerises until a maximum that is called the totalpressure.The stagnation pressure is the pressuremeasured when the velocity is zero.The dynamic pressure is the differencebetween the total and the static pressure. pdyn = ptot - ps
Basic definitions IIIIf the Bernoulli s law is valid we have 1 2 ptot = ps + !V 2which give us 1 pdyn = ρV 2 2Otherwise: the kinetic pressure is 1 pkin = ρV 2 2
Static pressureIdeally the static pressure should be measured with apressure probe that moves at the same velocity asthe fluid particle. But unpractical!Instead chose a stationary probe with respect to thelaboratory (or airplane), choose a suitable shape andposition the probe in a place where the pressure isequal to the static pressure of the undisturbed flow.
Static pressure probeSTATIC PROBESPresence of holes at a distance of 3D from theleading edge and 8-10D from the stem. sSensitivity to the inclination of the asymptotic flowwith respect to the probe axis. s
Static pressure probe• WALL TAPPINGS• On a wing or in pipes and ducts the static pressure can be measured using holes in the surface (give attention to the sensitivity of the dimensions and the shape of the holes). ps-patm s
Static probes• The probe must be aligned with the flow (this effect can be reduced by using several holes)• Since the pressure is measured with holes, then the same problems of the wall tappings must be considered – Effects of tip shape (geometry depends from flow regime) – Effects of probe blockage – Effects of hole position – Effects of the support
Blockage effect• Nose acceleration and probe support effects may compensate
Wall tappings• The flow is very complex in proximity of the tapping (only low Re simulations) – Effects of orifice shape – Effects of orifice orientation – Effects of surface orientation – Shape and position of the cavity (minimum depth) – Compressibility – Effects of the tapping orifice condition – Effect of the distance from the measured point
Effect of d+ McKeon and Smits MST (2002)• More problematic for high Re
Effect of d+ McKeon and Smits MST (2002)• Less influence when d increases
Total pressure probeThe stagnation pressure is obtained when thefluid is brought to rest through an isentropic andadiabatic process.In subsonic flow the Pitot tube measures thestagnation pressure(French hydraulic engineer 1695-1771)
Total pressure probe• In supersonic flow there is a stagnation pressure loss over the shock wave that is formed in front of the tube• Flat, hemisherical or elliptic head. In supersonic flow typically sharp wedge front.
Total pressure p0 m − p u 2 v2 w2 y Cp = = f (ϑ , Re d , M , 2 , 2 , 2 , α , ) 1 U U U d ρU 2 2• Incoming flow direction• Local Reynolds number (viscosity)• Mach number• Velocity gradient• Wall proximity• Turbulence
Total pressure probe• Effects of finite dimensions – Pressure measured in a finite region (not a single streamline) -> spatial averaging – This effect can be limited with small probes (be careful! : robustness, time response) – Blockage (d/L)• Directional sensitivity
Total pressure probe – direction sensitivityLess sensitivity to the inclination of the flow in respectto the longitudinal axis than the static pressure probe. From Chue
Total pressure probe• Effects of viscosity (in high Reynolds number measurement Red can be low due to the small dimensions of the probe)• Viscous effect are negligible for ReD>100• For ReD>30 10 C p = 1 + 1.5 Re d
Total pressure – velocity gradient1) Indicated Pitot pressure > total pressure of theundisturbed flow if a Pitot tube is operated in a regionwhere the total pressure varies in a direction ortoghonalto the asymptotic flow (e.g Boundary layer).
Total pressure – velocity gradient1) Velocity gradient interference2) With the presence of a flat wall parallel to the probeaxis there could be a reflection effect with theconsequent measured pressure higher than the totalpressure. This effect is negligible for y>2d from the wall. McKeon, Li, Jiang, Morrison and Smits MST (2003)
Total pressure – velocity gradient• Error 1) is normally corrected by changing the probe position rather than correcting the flow Δy velocity = ε , ε = 0.15 ( MacMillan) d Δy d dU = 0.18α (1 − 0.17α 2 ), α = ( Zagarola ) d 2U ( yc ) dy c Δy = 0.15 tanh(4 α ), ( McKeon) d• This is based on analytical displacement correction for a sphere in a velocity gradient
Total pressure – velocity gradient• Wall correction ΔU ⎡ ⎛ y ⎞⎤ = 0.015 exp⎢− 3.5⎜ − 0.5 ⎟⎥ ( MacMillan) U ⎣ ⎝ d ⎠⎦• A new correction is proposed based on Preston probe pressure data ⎧ 0.150 for d + < 8 δ w ⎪ = ⎨ 0.120 for 8 < d + < 110 d ⎪ ⎩0.085 for 110 < d + < 1600
How important wall correction are ? McKeon, Li, Jiang, Morrison and Smits MST (2003)
Velocity measurements with differential pressure probe: the Prandtl probe• Steady flow, low velocity, viscosity negligible: Bernoulli s law holds 1 ptot = ps + !V 2 2• High velocity: 1 ptot = ps + "V 2 ( + ! p ) 1 2 Corrective term f(M) 2(ptot # pst ) V= "( + ! p ) 1
Measurement errors due to turbulenceA physical time-dependent quantity can generally besplitted in a mean part and in a fluctuating part v(t ) = V + v (t ) p (t ) = P + p (t )From Bernoulli s law: 1 ( Ptot + p tot = Pst + p st + ! V 2 + 2Vv+v2 2 )Taking the time-average: 1 2 ( Ptot = Pst + ρ V + v 2 2 ) Error due to fluctuating velocityEffect of the anisotropy
Measurement errors due to turbulenceAnother effect is linked to the radial gradient ofthe static pressure due to the fluctuationsThis is of the opposite sign than the turbulence one.Therefore they compensate.
Velocity measurements - compressibility effectsΜ εp εp0 00.1 0.00250.2 0.0100.3 0.023 Note that the error in velocity is0.5 0.083 about half of εp !1.0 0.274
Velocity measurements at a nozzle exitV1 , A1 , p1 Vexit , Aexit , pexit• Mass conservation equation: V1 A1 = Vexit Aexit• Bernoulli s law applied to a streamline passing on the reference section and to the nozzle exit: 1 2 1 2 p1 + !V1 = pexit + !Vexit 2 2
Velocity measurements at a nozzle exit• Combining the two relations: 2(p Vexit = 2 & Aexit # ) $1 2 $ ! ! % A1 "• If section 1 is characterized by a dimension much larger then the exit s one, the corrective term can be neglected
Pressure transducersAbsolute pressure transducerMeasures the pressure relative to perfect vacuum pressure.(Example: barometer, used also for compressible flow)Gauge pressure transducerMeasures the pressure relative to a given atmospheric pressureat a given location. (Example a tire pressure gauge).Vacuum pressure transducerThis sensor is used to measure small pressures less than theatmospheric pressure.Differential pressure transducerThis sensor measures the difference between two or morepressures introduced as inputs to the sensing unit. s
Pressure Scanners• Important in pipe/channel turbulence
Multi component velocity measurements• Five hole Pitot• Pressure distributions on the probe s head is function of its geometry and of the flow direction• By sampling this distribution in five points is possible to determine the direction and magnitude of the velocity vector
Multi component velocity measurements Calibration
Time resolved pressure measurements• Microphone: electromechanical transducer. The sensing element is a thin membrane that alters its shape under the pressure loading effect• High capacity to measure the pressure variations in the measurement point (the sensor measures variations up to at least 5 kHZ)