Experimental Calibration of Three-Hole Pressure Probes with Different Head Geometries ·...

DIPLOMA THESIS

Experimental Calibration of Three-Hole Pressure Probes

with Different Head Geometries

written at

Institute of Thermal Turbomachines and Powerplants Vienna University of Technology

under direction of O. Univ. Prof. Dipl.-Ing. Dr. techn. H. HASELBACHER

and Ao. Univ. Prof. Dipl.-Ing. Dr. techn. R. WILLINGER

by Diego LERENA DÍAZ

Linzerstraße 429, 3209 A-1140 Vienna

Vienna, September 2003

Prologue The following diploma thesis is the result of six months (March 2003 – Sept. 2003) working at the Institute of Thermal Turbomachines and Powerplants belonging to the Vienna University of Technology. I would like to thank Herr O. Univ. Prof. Dipl.-Ing. Dr. techn. Hermann Haselbacher, director of the Institute of Thermal Turbomachines and Powerplants for the chance of writing my diploma thesis in his institute. In appreciation of all he has done for me, I would like to give my most sincere thanks to Ao. Univ. Prof. Dipl.-Ing. Dr. techn. Reinhard Willinger. Without his support, comments, explanations and help this work could have never been possible. I want to dedicate few lines to the friends I met in Vienna. I will never forget them. They understood me and they helped me, as much as they could. They made those days really nice and special. A Victorio y Amelia. A mis abuelos. A los que han sabido estar siempre a mi lado en este largo camino. A todos ellos, muchas gracias.

I

Diego Lerena Experimental Calibration of Three-Hole Pressure Probes

Abstract Pneumatic probes are still a useful tool when investigating flow fields within thermal turbomachines, cascades or any other aerodynamic facility. Three-hole pressure probes can be used for two-dimensional flow studies. The pressures sensed at the probe holes are used for the estimation of the velocity and direction of the flow in an indirect manner. Prior to the measurement in the turbomachine, the probe has to be calibrated according to the velocity and direction expected values. An open jet wind tunnel is used for this calibration task. The pressure probe is positioned at a number of predefined angular settings in a free jet with constant velocity and low turbulence intensity. After the calibration task, some calibration coefficients are obtained from the measured pressures at the probe sensing holes. Among the factors influencing the calibration of pressure probes, the head geometry and the Reynolds number are the most important ones. Furthermore, the behaviour of the probe depends on the Mach number as well as the turbulence intensity. The scope of the present diploma thesis is the investigation of the influence of various head geometries and Reynolds numbers on the calibration coefficients of three-hole pressure probes. Special attention has been paid in the planning, execution and evaluation of experiments in the free jet wind tunnel of the Institute of Thermal Turbomachines and Powerplants of the Vienna University of Technology (T.U. Wien). The three-hole probe head geometries available in the institute and their main characteristics are described in this work. Each probe has its specific advantages and disadvantages concerning the application in components of turbomachines. In addition to the experimental calibration, simple analytical expressions have been deduced for the estimation of the calibration coefficients, at least qualitatively. The results of the present investigation should supply the framework for the proper selection of three-hole pressure probe geometry for the application in turbomachinery components.

II


Table of Contents 1. Introduction 1 1.1. Three-hole pressure probes . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Theoretical analysis methods . . . . . . . . . . . . . . . . . . . . . . . 3

2. Calibration 4 2.1. Calibration techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1. Nulling technique . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2. Stationary method . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2. Energy Bernoulli equation . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3. Definition of hole and calibration coefficients . . . . . . . . . . . . . . . 8 2.4. Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . 10

3. Three-Hole Probes Geometry 12 3.1. SVUSS/3 cobra probe . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2. AVA trapezoidal probe Nr. 110 . . . . . . . . . . . . . . . . . . . . . . . 18 3.3. AVA cylinder probe Nr. 43 . . . . . . . . . . . . . . . . . . . . . . . . . 21

4. Streamline Projection Method 23 4.1. Cobra probe head geometry . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Trapezoidal probe head geometry . . . . . . . . . . . . . . . . . . . . 26 4.3. Cylinder probe head geometry . . . . . . . . . . . . . . . . . . . . . . 27 4.3.1. Streamline projection method . . . . . . . . . . . . . . . . . . . . 27 4.3.2. Potential flow solution . . . . . . . . . . . . . . . . . . . . . . . . 29

5. Test Facility 32 5.1. Description of the wind tunnel . . . . . . . . . . . . . . . . . . . . . . . 32 5.2. Experimental calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.3. Flow velocity field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

III


6. Results and Discussion 40 6.1. Comparison of theoretical and experimental results . . . . . . . . . . . 41 6.1.1. SVUSS/3 cobra probe . . . . . . . . . . . . . . . . . . . . . . . 41 6.1.2. AVA trapezoidal probes . . . . . . . . . . . . . . . . . . . . . . 46 6.1.2.1. AVA trapezoidal probe Nr. 110 . . . . . . . . . . . . . . 46 6.1.2.2. AVA trapezoidal probe Nr. 111 . . . . . . . . . . . . . . 50 6.1.2.3. AVA trapezoidal probe Nr. 72 . . . . . . . . . . . . . . . 51 6.1.3. AVA cylinder probe Nr. 43 . . . . . . . . . . . . . . . . . . . . . 53 6.2. Comparison between probes . . . . . . . . . . . . . . . . . . . . . . . 58 6.3. Factors influencing the calibration of three-hole pressure probes . . . . . 60 6.3.1. Reynolds number and Mach number effects . . . . . . . . . . . . 60 6.3.1.1. SVUSS/3 cobra probe . . . . . . . . . . . . . . . . . . . 61 6.3.1.2. AVA trapezoidal probe Nr. 110 . . . . . . . . . . . . . . . 63 6.3.1.3. AVA cylinder probe Nr. 43 . . . . . . . . . . . . . . . . . 64 6.3.2. Hole geometry for static pressure taps . . . . . . . . . . . . . . . 66 6.3.3. Turbulence intensity . . . . . . . . . . . . . . . . . . . . . . . . 66 6.3.4. Velocity gradient effects . . . . . . . . . . . . . . . . . . . . . . . 67 6.3.5. Wall proximity effects . . . . . . . . . . . . . . . . . . . . . . . . 67 6.3.6. Influence of probe supports . . . . . . . . . . . . . . . . . . . . . 68

Summary 69

Bibliography 71

Picture List 73

Table List 76

IV


2. Nomenclature side hole spacing a [ ]m

A [ ]2m cross-sectional area

nA [ ]2m nozzle exit area

pA [ ]2m probe head blockage area

B total blockage [ ]− probe width d [ ]m

nozzle diameter nd [ ]m

hole coefficient ik [ ]−

mean hole coefficient _

k [ ]− direction coefficient βk [ ]− total pressure coefficient tk [ ]− static pressure coefficient sk [ ]− Mach number Ma [ ]− rotational speed n [ min/1 ] p static pressure [Pa]

]]]]

mean pressure _

p [Pa

pressure sensed by the hole i ip [Pa

reference pressure refp [Pa

total pressure tp [Pa

Pr Prandtl number [ ]− r recovery factor [ ]− Reynolds number Re [ ]− s distance along streamline [ ]m

time t [ ]s T flow temperature [ ]K

thermodynamically ideal stagnation temperature oT [ ]K

V


ideal probe temperature piT [ ]K

environmental temperature refT [ ]K

fluid static temperature sT [ ]K

ideal dynamic temperature wT [ ]K

velocity w [ sm / ]] speed of sound in undisturbed medium 0w [ sm /

2_

nw [ ]22 / sm resultant turbulence intensity x distance downstream of the nozzle exit plane [ ]m

α∆ pitch angle [ ]° β∆ yaw angle [ ]° ε∆ flow angle error [ ]° pressure difference p∆ [Pa] δ wedge angle, characteristic angle [ ]° ϕ angular coordinate [ ]° λ [ ])/( KmW ⋅ thermal conductivity

µ [ ])/( smkg ⋅ dynamic viscosity

ν [ ]sm /2 kinematic viscosity

ρ [ ]3/ mkg density

Subscripts related to probe diameter d related to hole number ,1=i ,2 3 ,x y related to the X-axis or the Y-axis

Abbreviations two-dimensional D2 computational fluid dynamics CFD direct current DC

VI


experimental data curve ed potential flow solution prediction pfs streamline projection method prediction spm

VII


1. Introduction It is not difficult to think about several general needs for flow measurements. In some cases, the data are useful of themselves. In these cases, the flow quantity desired should be measured either directly or indirectly and it would be the final result. In other cases, flow measurements are necessary for correlation of dependent variables. The many applications of fluid flow measurements cover a broad spectrum of activities. For example, it is possible to consider about various wind-tunnel studies related to lift and drag, vibration, and noise radiation. In engine and compressor research involving both reciprocating and rotating machinery and in the broad area of hydraulic engineering research, many different types of flow measurements are necessary. In addition, many basic types of testing require fluid mechanics measurements, including cooling studies, the design of hydraulic systems, engine tests, flow calibration facilities, and of course, matters related to turbomachinery. Physical modelling is still very useful in many branches of engineering, ranging from wind-tunnel tests of airplanes and other aerospace vehicles, buildings, diffusion of pollutants, windmills, and even snow fences to hydraulic models of entire dams, reaches of rivers and cooling-water intakes and outlets. Many of these applications require specialized instrumentation. It is essential to understand fluid mechanics for the design of experiments, for the interpretation of results, and for estimating deterministic errors due to the flow modification by instrumentation placed in the flow. First, it is required to know the purpose of the measurements. Second, the fluid mechanics of the problem should be understood. Almost all types of measurement techniques depend on the nature of the flow, and this in turn governs instrument selection. The physical principles involved in flow measurements should be also understood. Almost all fluid flow measurements are indirect. In that, the techniques rely on the physical interpretation of the quantity measured.

1


It is easy to see the interrelated roles of flow instrumentation, the theory of fluid mechanics, and research and development. The need for a clear understanding of the problem, the principles of fluid mechanics, the principles of operation of the flow instrumentation, and the elements of statistical analysis is evident. 1.1 . Three-hole pressure probes In many complex flow fields such as those encountered in turbomachines, the experimental determination of the steady state three-dimensional characteristics of the flow are frequently required. But in contrast to the free jet, the flow field in a turbomachinery component exhibits strong velocity gradients, induced by the blade wakes as well as by the hub and casing boundary layers. Continued development of turbomachine technology is dependent on the experimental determination of the performance of advanced components. The primary measurements in turbines and compressors consist of flow direction and total and static pressures as well as total and static temperatures. Flow velocity field and pressure distribution are two valuable variables on its own. They can be used for verification of theory. A great deal of experimental data is necessary for calibrating mathematical models of various types. But the measurement of velocity and pressure in a flowing system can also be useful as a diagnostic for determining various quantities. For example, velocity measurements are often used in problems related to noise and vibration and as a diagnostic in heat and mass transfer research. The harsh turbomachine environment makes three-hole pressure probes particularly attractive for the measurement of flow pressure, velocity and direction. On the other hand, these types of probes are becoming more useful with the development of small inexpensive fast response pressure transducers, computer controlled traversing systems, and computer based data acquisition and analysis. The three-hole pressure probes available in the Institute of Thermal Turbomachines and Powerplants of the Vienna University of Technology (T.U. Wien) have three different head geometries. Each type of probe has its specific advantages and disadvantages concerning the application in components of turbomachines. Differential pressure measurements provide a useful alternative to hot-wire and hot-film anemometry for determining complex flow directions and even turbulence

2


intensity. Separate measurements of the total and static pressures can yield both the mean and fluctuating components of velocity and pressure. 1.2. Theoretical analysis methods It would be advantageous if the calibration characteristics and response of a three-hole probe could be determined by analytical procedures. In fact, there are methods that can help to face up the analysis of pressure probes from a theoretical viewpoint. Some of these methods are:

- the streamline projection method - the potential flow solution

For trapezoidal or cobra shaped head probes, analytical procedures of any type are difficult. These complex geometries, characterized by abrupt changes in contour, are subject to flow separation and viscous effects that are not modelled by current computational techniques. Nevertheless, the streamline projection method is used in addition to the experimental research as well as the computational investigations. It will be shown that this simple method can easily predict the three-hole probe calibration coefficients, at least qualitatively. For probes of easy contour geometry, (e.g., cylindrical probe head), the streamline projection method is valid, but a potential flow solution can also predict the pressure distribution and the corresponding calibration characteristics to a reasonable accuracy. While the analytic relationships are valuable for characterisation of probe behaviour and as a guide to the functional form of calibration equations, it is unlikely that they are capable of replacing individual probe calibrations. This is due to both the limitations of the derivation as well as the manufacturing irregularities of the probes. Regardless of the accuracy of the theoretical derivations, the latter effects may always necessitate individual probe calibrations, particularly for small sized probes. Measurement of data and development of an interpolation procedure for the data analysis become responsibility of the probe user.

3


2. Calibration The objective of an aerodynamic probe - in the present context - is to determine the scalar and vector properties of complicated flow fields such as those encountered around complex bodies or in turbomachines, in terms of static and total pressure and two-dimensional (2D) velocity components respectively. This translates into a measurement of pressures, which by means of calibration functions and gas dynamic relationships, are subsequently converted into flow angles and Mach numbers. Three-hole pressure probes, of many different configurations, are frequently used for two-dimensional flow measurements in turbomachinery components. They yield the total as well as the static pressure and the direction of the flow field. But as it was said before, due to manufacturing inaccuracies a calibration procedure prior to the measurements is necessary. Pressure differentials are then measured for selected angles of yaw placed on the probe relative to the flow direction. When compressibility is not a consideration, the theory yields a format for interpreting the differential pressures between pairs of holes as functions of angles of yaw. Once the flow direction has been established, the remaining pressure and hence velocity data may be determined from further coefficients. 2.1. Calibration techniques For both, calibration and application, the probe’s reference line is defined by some consistent characteristic of the probe’s geometry. In application, a reference direction obtained by placing with is not always meaningful, since initially a known flow direction would be required to relate the balanced condition to an absolute spatial reference.

2p 3p

The probe can be operated in two ways [5]:

2.1.1. Nulling technique 2.1.2. Stationary method (non-nulling technique)

4


Both methods offer advantages and disadvantages. Due to space restrictions in turbomachinery applications and wind tunnel blockage, the probe is often required to be small, and the difficulty associated with traversing and data acquisition encountered when the probe is used in a nulling fashion, make a non-nulling method a better alternative. Calibration functions are then used to find the flow angles. The stream static and total pressures - and, thus, Mach number - can be determined in similar manner. 2.1.1. Nulling technique The nulling technique is the most accurate but mechanically complex. It is the most simple in terms of data analysis, as well. The probe is mounted on a three degree of freedom traversing system and is oriented such that the X-axis is parallel to the flow (yaw and pitch angles are both zero). The center pressure tap measures the stagnation pressure and the pressures in the two outer tubes are equal (

1p

32 pp = ) and proportional to the static pressure. Finally, the probe position is noted and the flow direction is determined from a calibrated scale. This nulling technique requires a very sophisticated traversing system and long data acquisition time, since the probe must be yawed at each measurement location until the two pressures are equal. This can take a long time, especially if the probe is small and has a slow time response. If space limitations or other considerations make nulling techniques impractical, three-hole probes in a non-nulling mode can be employed for measurements in low speed, incompressible flows. 2.1.2. Stationary method The stationary method or non-nulling technique tends to be less accurate but offers simplicity in installation. The latter characteristic is the most important in turbomachine applications. It is performed by setting the probe at constant pitch and yaw values with respect to the test section. The three pressures are measured at each measurement location by traversing the probe over the flow field. From these three measured pressures,

5


the direction and magnitude of the flow with respect to the X-axis of the pressure probe are determined. Although elegant in its simplicity, this technique encounters singularity when calibration for large angle of yaw is sought [6]. So it is restricted to lower flow angle ranges, preventing its use in highly 3D flows. 2.2. Energy Bernoulli equation The flow motion is known to be a function of several non-dimensional parameters. The most important ones in aerodynamics are: Reynolds number:

ν

dwforceviscousforceinertial

d⋅

==Re (1)

Mach number:

0w

wforceelasticforceinertialMa == (2)

Gases at low velocity - the calibration experiments are conducted at - can be considered as essentially incompressible (constant-density) fluids. The analysis of the steady flow for this sort of fluid [3] starts with the conservation of mass, momentum and energy.

2.0<Ma

For one-dimensional flow along a stream tube (Fig. 1), the mass conservation equation for steady flow has the form: (3) constAw =⋅ If it is further assumed that the flow is inviscid, the momentum equation is:

0=∂∂⋅+

∂∂⋅⋅+

∂∂

tw

sww

sp ρρ (4)

6


Figure 1: Inviscid flow along a stream tube The cross section of the stream tube must be small in order to consider the local values of the pressure and velocity. For the steady state, the last term in Eq. (4) drops out, and the equation can be integrated along the direction s of the stream tube, to result in the Bernoulli conservation equation for energy:

constwp =⋅+2

2

ρ (5)

w

A

p

w + dw

p + dp

The pressure p in Eq. (5) is the static pressure. It is the component of the pressure that represents fluid hydrostatic effects. And in principle, it is measured by an instrument that moves along with the fluid. This is, however, inconvenient, and the pressure is usually measured via a small hole in a wall arranged so that it does not

disturb the flow. The quantity 2

2w⋅ρ is usually called dynamic pressure. It is the

component of the fluid that represents fluid kinetic energy. Total pressure , sometimes also called “stagnation pressure”, is defined as the pressure that would be reached if the local flow is imagined to slow down to zero velocity, frictionlessly. Total pressure is the sum of static and dynamic pressure:

tp

2

2wppt ⋅+= ρ (6)

7


From measurements of the total and static pressures, the velocity can be obtained as,

)(2 ppw t −⋅=ρ

(7)

which follows readily from Eq. (6). For Eqs. (6) and (7) to apply, the probe must not disturb the flow, and it must be carefully aligned parallel to the stream. 2.3. Definition of hole and calibration coefficients The pressure sensed by the hole i differs from the free stream static pressure ip

p , and it can be presented as a nondimensional pressure coefficient. The hole coefficient is usually used in the following form: ik

2

2w

ppk i

i

⋅

−=ρ

(8)

where represents the identifier of a specific hole between 1 and 3 . i For operation in the non-nulling mode with a three-hole probe, it is apparent that the calibration characteristics must include data that represent pressure differences in the yaw plane as well as differences between the measured and the true, local total and static pressures. When the probe is used to measure these quantities, the relationship between them and the yaw angle β∆ is described by the calibration coefficients. These pressure coefficients must be defined so that they are independent of velocity and are a function only of the flow angularity. Various definitions for the calibration coefficients can be found in the literature [6]. The use of these individual hole-based coefficients allows the flow phenomena to be investigated irrespective of the chosen calibration coefficient definitions.

8


The present work uses the standard accepted non-dimensional grouping for reducing the data. This is the definition by Treaster and Yocum [8], reduced to the conditions for a three-hole probe: - Direction coefficient : βk

_

1

32_

1

32

kk

kk

pp

ppk−

−=

−

−=β (9)

- Total pressure coefficient : tk _

1

1_

1

1 1

kk

k

pp

ppk tt

−

−=

−

−= (10)

- Static pressure coefficient : sk

_

1

_

_

1

_

kk

k

pp

ppks

−=

−

−= (11)

The quantities:

2

32_ ppp += (12)

2

32_ kkk += (13)

represent the mean pressure and the mean hole coefficient, respectively. As can be seen from Eqs. (9) to (11), the calibration coefficients are related directly to the three hole coefficients. Treaster and Yocum found that an indicated dynamic pressure formed by the difference between the indicated total pressure , and the averaged value of the two indicated static pressures and , was a satisfactory normalizing parameter. It reduced the scatter in the calibration data as compared to using the true dynamic

1p

2p 3p

9


pressure. The difference of the two pressures is consequently taken to represent the dynamic pressure, which is used to make the calibration pressure coefficients non-dimensional. This is convenient, since using the true dynamic pressure would have introduced an unknown quantity.

_

1 pp −

The problem with the Treaster and Yocum definition arises when there is a change in sign in the denominator, or more precisely when the denominator goes to zero producing a singularity that in turn makes the coefficients of yaw, total, and static pressure become infinite. That happens when in the non-nulling mode, for large

angles of yaw, and deviate significantly from the actual total and static pressure, and therefore, their difference no longer represents the dynamic pressure. It thus appears that the problem lies in the definition of the denominator of calibration coefficients.

1p_p

In the last years, attempts to extend the calibration range for three-hole probes in the stationary method have been undertaken. Some works [6] have developed a modification to the denominator of the Treaster and Yocum calibration coefficients, which successfully allows calibration to much higher angles of yaw, while maintaining the simplicity of the original procedure. 2.4. Temperature measurement The measurement of the temperature of a real fluid [3] generally consists in reading the output signal of a thermometer as the fluid stagnates against the sensor surface and equilibrates thermally with this sensor surface. Because of the viscous and thermal diffusion properties of real fluids, the thermometer generally does not indicate the thermodynamically ideal stagnation temperature (14) wso TTT +=

where: thermodynamically ideal stagnation temperature =oT

fluid static temperature =sT

ideal dynamic temperature =wT

10


The Prandtl number Pr expresses the ratio of fluid viscous to thermal diffusion effects; that is,

λ

µ pcdiffusionthermaleffectsviscous ⋅

==Pr (15)

where: =µ dynamic viscosity of fluid

=λ thermal conductivity Thus when, as in air, with 7.0Pr65.0 << the thermal diffusion effects are greater than the viscous effects, the real dynamic temperature is less than the ideal. Of course, for 1Pr = the viscous heating effects generated by the stagnating real fluid are exactly diffused thermally so that the real dynamic temperature is the ideal. Thus, (16) wspi TrTT ⋅+=

where: ideal probe temperature =piT

=r recovery factor The recovery factor can then be written:

so

spi

TTTT

r−−

= (17)

Therefore the temperature sensed by a sensor in a fluid stream depends upon:

1. The viscous and thermal diffusion properties. 2. The characteristics of the sensor, i.e., shape and orientation to the flow. 3. The nature of the fluid stagnation process, including any pertinent fluid

motions effects, such as turbulence, that might alter the molecular viscous and thermal diffusion phenomena described above.

4. Any other kind of thermal losses from the temperature sensor.

11


3. Three-Hole Probes Geometry Although a variety of pressure probes have been devised for decomposing the flow velocity vector, the most well known and widely used is the three-hole pressure probe. A flow direction probe is made up of a streamlined axisymmetric body that points into the flow. As the name implies, it is characterized by three pressure sensing holes. The frequently adopted nomenclature and the convention used to number the three-hole pressure sensing holes are shown in Fig. 2:

w∆βwy

wx

reference line

flow direction

YAW PLANE

Figure 2: Geometry nomenclature for three-hole probes The pitch and yaw planes orientation relative to the probe is independent of the device used to position the probes during calibration. The angle defined between the velocity vector and the probe axis, over the yaw plane, is the yaw angle

wβ∆ . The pitch angle α∆ is assumed to be zero for a three-

hole probe (two-dimensional flow).

12


The relationships between the velocity components and with respect to the

X and Y axes in the probe coordinate system and the yaw angle xw yw

β∆ are:

β∆⋅= coswwx (18)

β∆⋅= sinwwy (19)

The pressure distribution on the surface of the probe depends on the angle of incidence of the mean flow vector relative to the axis of the probe. To determine the two-dimensional orientation and magnitude of the flow vector, the surface pressure is sampled at three locations: on the axis of the probe and at two equispaced points on the probe sides. The central pressure tap gives the conventional stagnation pressure when the flow vector is perpendicular to that point on the surface. The pressure difference between the pressure side sensing-holes may be related to the inflow velocity vector by using an appropriate calibration to deduce the yaw direction. The flow field parameters should be accurately measured with the probe, creating a minimal flow disturbance. Thus, the probe must consist of a slender body, i.e., the body radius must be much less than the body length. As long as the simple shape is small enough so that it does not disturb the flow and the velocity over it is uniform, yet large enough so that laminar separation does not generate any self-turbulence, the flow over it will be streamlined. On the other hand, in order to maximize their spatial resolution, such probes are generally miniaturized. Since the probes are to be used without rotation, the sensitivity to flow direction (angularity) is extremely important. In addition to the probe sensitivity, alignment and manufacturing defects also influence the accuracy with which flow angles and static and total pressures can be determined. Hypothetically, theoretical relationships for the potential flow around the body may also be used, but the flow is generally not ideal, which makes such calculations impractical. Many different three-hole probe head geometries have been investigated. They are commercially available in several configurations, such as prismatic, conical, etc…

13


The most commonly used shapes for the probe head geometry are: the cobra head, the trapezoidal head and the cylindrical head. Less streamlined shapes, such as prismatic forms and cones, are also used, with their calibrations wholly empirical. The three-hole probe head geometries available in the Institute of Thermal Turbomachines and Powerplants of the Vienna University of Technology and their main characteristics are identified in Table 1.

Probe Geometry Date of Manufacture d [ ]mm δ [ ]° a [ ]mm Thermocouple

SVUSS/3 Cobra probe 1994 2,4 30 1,6 No AVA Trapezoidal probe Nr. 110 1968 3,3 30 2,0 Yes AVA Trapezoidal probe Nr. 111 1968 3,3 30 2,0 Yes

AVA Trapezoidal probe Nr. 72 1965 3,2 30 2,0 Yes AVA Cylinder probe Nr. 43 ? 3,0 50 2,3 No

Table 1: Three-hole probes designs main characteristics Between these five pressure probes, there are only three different types of head geometries. And as it will be completely justified in the Results and Conclusions chapter, two of the AVA trapezoidal probes are not in good conditions. Taking into account that, the primary emphasis in this work will be placed on the results obtained while using:

3.1. SVUSS/3 cobra probe 3.2. AVA trapezoidal probe Nr. 110 3.3. AVA cylinder probe Nr. 43

Detailed information about these pneumatic three-hole probes can be found in the following pages.

14


3.1. SVUSS/3 cobra probe The SVUSS/3 cobra probe is shown in Fig. 3. It was manufactured by the company SVUSS (Prague - Czech Republic). The year of manufacturing was 1994. Its total length is and it basically consists of either three hypodermic tubes, which are bundled together. The tubes have an assembled diameter of 6 and they ground to form the “cobra shaped” head, with forward facing pressure tapings. The term forward facing refers to the axes of the holes. They are parallel to the axis of the probe, thus facing forward into the flow.

650 mmmm

Figure 3: Three-hole SVUSS/3 cobra probe Fig. 4 shows the cobra probe head geometry sketch, the numbering of the holes as well as the definition of the characteristic angle δ . The characteristic dimension of the probe head is and the side holes are separated by the dimension . d a

w

δ

d∆β

Figure 4: Cobra three-hole probe head geometry sketch

15


The characteristic dimensions of the probe head (see Fig. 5 and Fig. 6) are in width and in height. The wedge angle, measured between the

probe axis and the direction parallel to the probe head sides, is 4,2=d mm 8,0 mm

°= 30δ . Figure 5: SVUSS/3 cobra probe head side view The holes are in diameter and the distance between the two side holes is

. 5,0 mm

6,1 mm

Figure 6: SVUSS/3 cobra probe head front view This model of probe includes no thermocouple to measure the flow temperature.

16


17

Figure 7: Workshop drawing for the SVUSS/3 cobra probe

Maßstab.

1:1

(20:1)

Norm gepr.Gepr.Gez.

Stück

T.U. WienInst. f. Therm. Turbomaschinen

und Energieanlagen

Norm. Nr.Zeichng.-Nr.

SVUSS/3 Kobrasonde

Lerena D.29.06.2003Tag Name

Benennung Teil Werkstoff Rohmaße od.Modell Nr.

Bemerkg.


3.2. AVA trapezoidal probe Nr. 110 The AVA trapezoidal probe Nr. 110 was designed and manufactured by Aerodynamische Versuchsanstalt Göttingen E.V. in 1968. Nowadays, this institution has turned into the Deutsches Zentrum für Luft- und Raumfahrt (D.L.R.). The probe is shown in Fig. 8. Its total length is 366 and its main body is 6 in diameter.

mm mm

Figure 8: Three-hole AVA trapezoidal probe Nr. 110 The trapezoidal probe tip is made from three pieces hypodermic tubing. The characteristic dimensions of the probe head are 3,3=d mm in width and in height. The wedge angle is

3,1 mm°= 30δ . This type of head geometry facilitates its use in

turbomachinery research, since it can be easily inserted trough casings and used in studies where spatial restrictions are present.

Figure 9: AVA trapezoidal probe head side view

18


The sensing holes are forward facing and in diameter. The side holes are separated . Details of the trapezoidal head geometry can be seen in Fig. 9 and Fig. 10.

6,0 mm0,2 mm

Figure 10: AVA trapezoidal probe head front view The AVA trapezoidal probes include a thermocouple sensor that can be used to measure the flow temperature. The nature of the alloy – which the thermoelement is made of - is not well known. That unknown piece of information makes the calibration of the sensor extremely difficult. Regarding to this last subject, it should be added that private conversations with Mr. Joachim Grimme (formerly D.L.R. Göttingen employee) seem to point in the direction that the thermocouple is made of copper-constantan.

19


20

Figure 11: Workshop drawing for the AVA trapezoidal probe Nr. 110

Maßstab.

1:1

Norm gepr.Gepr.Gez.

Stück


und Energieanlagen


AVA Trapezsonde Nr. 110

Lerena D.29.06.2003Tag Name


Bemerkg.


3.3. AVA cylinder probe Nr. 43 The AVA cylinder probe Nr. 43 was also purchased to Aerodynamische Versuchsanstalt Göttingen E.V., but the year of manufacturing or acquisition is not documented. An overview of this model of probe is shown in Fig. 12. Its total length is 335 and the main body is 6 in diameter.

mmmm

Figure 12: Three-hole AVA cylinder probe Nr. 43 The characteristic dimension of the probe head is 0,3=d mm. The characteristic angle, measured in a perpendicular plane to the probe axis, is °= 50δ . Hole 1 is

in diameter and holes and 3 are in diameter. The distance between these two holes is .

3,0 mm 2 6,0 mm3,2 mm

Figure 13: AVA cylinder probe head view This model of probe includes no thermocouple to measure the flow temperature.

21


22

Figure 14: Workshop drawing for the AVA cylinder probe Nr. 43

Norm gepr.

Maßstab.

1:1

Gepr.Gez.

Stück


und Energieanlagen


AVA Zylindersonde Nr.43

Lerena D.Tag

29.06.2003Name


Bemerkg.


4. Streamline Projection Method The streamline is defined as a curve everywhere tangent to the instantaneous velocity vectors (everywhere parallel to the instantaneous direction) of the flow. Thus, these curves provide a clear picture of the flow, because the velocity vector has at each point the direction of the streamline. For steady flow, the streamlines also describe the path that the fluid particles follow. The streamline projection method is based on the assumption that the free stream velocity (which magnitude is supposed to be constant) is projected on each one of the three sensing holes. Therefore, the velocity component normal to the probe surface results in a dynamic pressure, which is added to the free stream static pressure. Consequently, the holes of the probe measure a total pressure equal to the static pressure plus the corresponding fraction of the dynamic pressure. This is:

w

2

21

ii wpp ⋅⋅+= ρ , , 3 (20) 1=i 2

where is the velocity projection normal to the hole i surface. iw

From the hole coefficient definition (Eq. (8)) it can be obtained that:

2

2wkpp i

i ⋅⋅+= ρ (21)

Comparison between Eqs. (20) and (21) makes it possible to rewrite the hole coefficient formula when the streamline projection method is being used.

2

⎟⎠⎞

⎜⎝⎛=

wwk i

i (22)

23


The velocity projection only depends on the probe head geometry. As a result of this, there are as many cases as different types of head probe geometries. In this chapter, the streamline projection method has been applied to:

4.1. Cobra probe head geometry 4.2. Trapezoidal probe head geometry 4.3. Cylinder probe head geometry

in order to obtain the three-hole probes calibration coefficients, from a strict theoretical viewpoint. It should be remarked that, in the case of cylinder probe head geometry, the potential flow solution is a valid alternative to calculate the calibration coefficients. Thus, it has also been used and results of both methods will be analysed and compared below. Moreover than just giving a first estimation of calibration coefficients for three-hole probes, the streamline projection method can also be used to estimate the influence of a velocity gradient on the flow angle measurement [10] with the same type of probes. Anyway, that field of work is out of the scope of this diploma thesis. 4.1. Cobra probe head geometry Fig. 15 shows a sketch of the SVUSS/3 cobra probe head geometry. The characteristic angle is δ ( °= 30δ ), and the yaw angle β∆ is defined between the flow velocity and the probe longitudinal axis. From the above, it may be deduced that the three flow velocity components normal to the hole surfaces are: β∆⋅= cos1 ww (23) ( )βδ ∆+⋅= sin2 ww (24) ( )βδ ∆−⋅= sin3 ww (25)

24


w

w∆β

3

δ−∆β

1 w

w

δ+∆β

w2w δ

Figure 15: SVUSS/3 cobra probe head geometry Under the assumption of the streamline projection method, and as it follows from Eq. (20), the pressures sensed by the three holes are:

( 21 cos

21 βρ ∆⋅⋅⋅+= wpp ) (26)

([ 22 sin

21 βδρ ∆+⋅⋅⋅+= wpp )] (27)

([ 2

3 sin21 βδρ ∆−⋅⋅⋅+= wpp )]

)

)

(28)

The hole coefficients can be calculated simply by applying Eq. (22): (29) β∆= 2

1 cosk (30) ( βδ ∆+= 2

2 sink (31) ( βδ ∆−= 2

3 sink

25


It should be noticed that the hole coefficient only depends on the flow attack angle. On the other hand, the hole coefficients and depend on the yaw angle as well as on the wedge angle.

1k

2k 3k

The corresponding calibration coefficients can be obtained from its own theoretical definition. See Eqs. (9) to (11). - Direction coefficient:

(32)

( ) ( )( ) ([ ])βδβδβ

βδβδβ

∆−+∆+⋅−∆

∆−−∆+=

−

−=

−

−=

222

22

_

1

32_

1

32

sinsin21cos

sinsin

kk

kk

pp

ppk

- Total pressure coefficient:

(33)

Static pressure coefficient:

4)

.2. Trapezoidal probe head geometry

As seen above, when the hole coefficients as well as the calibration coefficients

( ) ([ ])βδβδβ

β

∆−+∆+⋅−∆

−∆=

−

−=

−

−=

222

2

_

1

1_

1

1

sinsin21cos

1cos1

kk

k

pp

ppk tt

-

(3

( ) ( )[ ]( ) ([ ])βδβδβ

βδβδ

∆−+∆+⋅−∆

∆−+∆+⋅=

−=

−

−=

222_

1

_

1 sinsin21cos

sinsin2

kk

k

pp

ppks

22__ 1

4 are calculated with the streamline projection method, the results depend exclusively on the probe head geometry.

26


Since the cobra head geometry characteristics and the trapezoidal one are identical, the hole coefficients and the calibration coefficients are exactly the same in both cases. The equations of all coefficients for the trapezoidal probe head geometry can be found in section 4.1. 4.3. Cylinder probe head geometry The AVA cylinder probe head has such a simple geometry that it makes feasible to estimate theoretically the calibration coefficients via two different theories. The first option is based on using the streamline projection method adapted to the cylindrical probe head geometry. (See section 4.3.1.) The second manner consists of facing up the problem trough the results of applying the potential flow solution theory. (See section 4.3.2.) 4.3.1. Streamline projection method The AVA cylinder probe head geometry ( °= 50δ ) as well as the used nomenclature is detailed in Fig. 16.

Figure 16: Angles used for the streamline projection method

27

w

δδ+∆β

∆β

w

w3

δ−∆β

δw2

w


The first step is to obtain the three flow velocity components normal to the hole surfaces. See Eqs. (35) to (37): β∆⋅= cos1 ww (35) ( )βδ ∆−⋅= cos2 ww (36) ( )βδ ∆+⋅= cos3 ww (37) The three holes sense the following pressures:

( 21 cos

21 βρ ∆⋅⋅⋅+= wpp ) (38)

([ 2

2 cos21 βδρ ∆−⋅⋅⋅+= wpp )] (39)

([ 2

3 cos21 βδρ ∆+⋅⋅⋅+= wpp )]

)

)

(40)

The next step is to calculate the hole coefficients. For that, the pressures are reduced to non-dimensional groups by using Eq. (22): (41) β∆= 2

1 cosk (42) ( βδ ∆−= 2

2 cosk (43) ( βδ ∆+= 2

3 cosk

As in the other probe head geometries, the coefficient depends only on the yaw

angle and the coefficients and depend on the yaw as well as the wedge angles.

1k

2k 3k

The corresponding calibration coefficients follow from its own theoretical definition.

28


- Direction coefficient:

(44)

( ) ( )( ) ([ ])βδβδβ

βδβδβ

∆++∆−⋅−∆

∆+−∆−=

−

−=

−

−=

222

22

_

1

32_

1

32

coscos21cos

coscos

kk

kk

pp

ppk


(45)

( ) ([ ])βδβδβ

β

∆++∆−⋅−∆

−∆=

−

−=

−

−=

222

2

_

1

1_

1

1

coscos21cos

1cos1

kk

k

pp

ppk tt

- Static pressure coefficient:

(46)

( ) ( )[ ]( ) ([ ])βδβδβ

βδβδ

∆++∆−⋅−∆

∆++∆−⋅=

−=

−

−=

222

22

_

1

_

_

1

_

coscos21cos

coscos21

kk

k

pp

ppks

4.3.2. Potential flow solution Most of the books about the principles of fluid mechanics deal with the analysis of potential flow around a cylinder. An elementary result of this theory [9] gives Eq. (47) as a formula to calculate the hole coefficients . ik

( ) ϕρ

ϕ 2

2sin41

2

⋅−=⋅

−=

w

ppki (47)

It is obvious that the hole coefficient value is straight related to the angular coordinate ϕ . This angle is measured between the flow direction and the cylinder radius that goes across the probe hole i . In order to clarify the geometry of the problem, see Fig. 17.

29


w δ

∆β

δ

ϕ

Figure 17: Angles used for the potential flow solution Taking Eq. (47) as a starting point, it is easy to find the hole coefficients , and

in the case of cylinder probe head geometry. 1k 2k

3k

(48) β∆⋅−= 2

1 sin41k (49) ( βδ ∆−⋅−= 2

2 sin41k )

) (50) ( βδ ∆+⋅−= 2

3 sin41k As in the streamline projection method, the direction coefficient , the total pressure coefficient and the static pressure coefficient , yield from the Treaster and Yocum definitions.

βk

tk sk

- Direction coefficient:

=−

−=

−

−= _

1

32_

1

32

kk

kk

pp

ppkβ( ) ( )

( ) ( )[ ] ββδβδ

βδβδ

∆−∆++∆−⋅

∆−−∆+222

22

sinsinsin21

sinsin (51)

30



=−

−=

−

−= _

1

1_

1

1 1

kk

k

pp

ppk tt

( ) ([ ])βδβδβ

β

∆−+∆+⋅−∆

∆222

2

sinsin21sin

sin (52)

- Static pressure coefficient:

=−

=−

−= _

1

_

_

1

_

kk

k

pp

ppks( ) ( )[ ]

( ) ( ) ββδβδβδβδ

∆⋅−∆−+∆+∆−+∆+−

222

22

sin2sinsinsinsin1 (53)

31


5. Test Facility Due to the fact that the flow velocity and flow direction cannot be measured directly by the probes as well as due to some inaccuracies when manufacturing the probe’s head, a calibration process is necessary. For this purpose there is the need of a wind tunnel giving flow conditions well known and constant. Problems often concern the flow quality, some geometric restrictions when introducing different probes, and others. The experimental data for the probes calibration were acquired in the free jet wind tunnel of the Institute of Thermal Turbomachines and Powerplants at the Vienna University of Technology. The three-hole pressure probes employed in this study are used in a fixed position or non-nulling mode. This means that relationships must be determined between the measured pressures at the three holes and the true, total and static pressure or velocity. These desired relationships are usually expressed as dimensionless pressure coefficients, which are functions of the flow angularity. Since, when in use, the flow angles are unknown, relationships between the three measured pressures and the flow direction are also required. 5.1. Description of the wind tunnel A 50 DC motor powers the wind tunnel, with transmission for speed control. The motor drives a radial blower that is 1115 in diameter, and it supplies

kWmm

800.10 hm3 airflow. The motor-and-blower assembly is mounted on a concrete base and it is isolated from the diffuser. The diffuser divergence angle is about . The wind tunnel is equipped with nylon screens, witch are used upstream of the nozzle inlet, to serve for a homogeneous flow field at a low level of turbulence. The stream wise turbulence intensity is about . A single hot-wire probe DANTEC 55P11 was used to measure it.

°7,5

%1

32


The wind tunnel is provided with 8 pressure sensors and a temperature sensor as well. The free jet discharges out trough a conventional atmospheric exit. The throat diameter of the converging nozzle is =nd 120 mm , and since the settling chamber

diameter is 1000 , the convergent contraction ratio is about . mm 4,69:1 A summary of the free jet wind tunnel technical characteristics can be found in Table 2, while Fig. 18 shows a sketch of the free jet wind tunnel.

Nozzle diameter 120 mm Contraction ratio 1: 69,4

Diffuser divergence 5,7°

Turbulence intensity 1%

Total temperature ≈ 293 K Mach number 0,05 – 0,3

Reynolds number Depending on Ma Installed power 50 DC motor kW Volume flow rate 3 sm3

Table 2: Main data of the wind tunnel

Turbulence Screen

Rectangular Section

Free Jet Wind Tunnel

Institute of Thermal Turbomaschines and Powerplants Vienna University of Technology

Temperature Sensor

Ring to measure Total Pressure

(8 measuring sensors)

Contraction Cone 1 : 69,4

Nozzle

Circular Section Diffuser

50 kW D.C. Motor with variable speed

Radial Blower

Figure 18: Vienna University of Technology free jet wind tunnel

33


5.2. Experimental calibration The three-hole pressure probes calibration is done within a Mach number range ( , at different Reynolds numbers as well as considering an interval of flow angles. Since the experimental measurements are carried out in a free jet discharging to the atmosphere, the Reynolds number is directly linked to the Mach number.

≤05,0 Ma )14,0≤

Calibration of these probes are often carried out in an open jet wind tunnel because of the large blockage errors [11] that occur when the calibration set up is placed in a closed wind tunnel test section. The air quality, in terms of low turbulence and uniformity of flow in a closed test section is, however, superior to that of an open jet. It is known that measurements of the total and the static pressures in the free jet downstream of the nozzle exit prove the existence of a homogenous flow field in the range: 0 ≤ x ≤ nd×5,2 where the variable x represents the distance downstream from the nozzle exit plane to the probe tip location. Outside this core regime, the local total pressure rapidly decreases down to of its value in the settling chamber [2]. So when %75 ≈x nd , it is accepted that the flow characteristics - speed, turbulence, pressure, etc… - are the most convenient to measure the desired values. Thus, the probe is mounted in a support device (see Fig. 19), and it is placed =x 130 mm downstream.

Figure 19: Support device and probe location

34


On the other hand, the probe tip was located four support diameters upstream of this member to avoid support interference effects. The support was extended four support diameters beyond the tubing to improve the flow symmetry at the probe tip. The previously discussed device permits a rotation of the probe about its longitudinal axis (change in yaw angle β∆ ), so the probe’s orientation can be varied from up to . Even though the rotation of the probe is manual, angles are adjusted in steps of (in yaw) with an absolute accuracy of about . The results are all obtained at zero pitch angles.

°− 30 °+ 30°5,2 °1,0

During the calibrations, precautions are taken to insure that the probes are located in the potential core of the jet. The assembly keeps the probe tip at the centerline for all movements. In each case, the probe head blockage ranges between and

of the nozzle exit area. %6,1

%0,3

100% ⋅=n

p

AA

B (54)

where: =B total blockage

probe head blockage area =pA

nozzle exit area =nA

At each calibration point, the three-hole probe provides three pressure measurements. These pressure signals are converted into electrical signals through piezoresistive pressure transducers (HONEYWELL). These transducers are commonly used to simplify the measurement of the pressure from a multi-tube probe (such as a three-hole probe). Primarily, pressure transducers consist of either flexible diaphragms or piezoelectric elements [3]. The piezoelectric transducer has as its element a crystalline substance that generates an electric field as it is mechanically deformed. The crystal is shaped as a cylinder, wafer or bar; it is generally plated on opposite surfaces, and the electric charge is generated across those plates. The voltage is proportional to the force applied and therefore to the pressure difference. The free stream total pressure and the stagnation point pressure are measured using two identical piezoresistive transducers. In this case, the range of work for the measuring instrument is from 0 up to

tp 1p

138+ . mbar

35


The outer hole pressures and are measured using a single transducer by means of a scanning box (FURNESS CONTROLS). This device allows the use of the same output channel in order to minimize any errors arising from the transducer calibration. Since these pressures are relative to the atmospheric one, they can be positive, but also negative. Thus, a differential piezoresistive transducer is needed. Its range of work is from up to

2p 3p

69− 69+ mbar . All piezoresistive pressure transducers are powered with 8V DC. The voltage is measured by the HP 44702B 13-bit high-speed voltmeter. The reference total pressure is measured in the upstream settling section, and atmospheric pressure is used as a reference static pressure. So the pressures are recorded relative to atmospheric pressure i.e., refp

(55) refii ppp −=∆

where the subscript i refers to the subject pressure. A sketch of the complete connections of the hardware and the software related to the data acquisition system is given in Fig. 20.

DATA ACQUISITIONSYSTEM

PC, LabVIEW 5.0

HP 3852 A

Pt - 100

TUN

ET

Ethe

rnet

GPIB

HP

447

24 A

HP

447

11 A

HP

4470

2 B

HONEYWELLPRESSURE TRANSDUCERS

∆β

FURNESS CONTROLSScanning Box

p2

p3

p1

8V POWERSOURCE

pt

Figure 20: Hardware and software connections for the data acquisition (schematic)

36


The flow temperature is measured with a Pt-100 resistor thermometer. The other components of the data transmission equipment consist of a sixteen-channel HP 44724 A digital output device and a twenty four-channel HP 44711 A multiplexer. The data recording (taking the relevant wind tunnel data and the probe’s readings) is done by the HP 3852 A data acquisition system. It is connected to a PC via the GPIB bus and droved using the LabVIEW software (NATIONAL INSTRUMENTS). 5.3. Flow velocity field The velocity field section of the wind tunnel and in the potential core of the jet has been shown to be uniform within the accuracy of the experimental measurements by previous studies. For each probe calibration, the flow velocity is maintained at a constant value. This velocity is adjusted according to the Reynolds numbers (based on the jet velocity and probe’s head diameter) expected to appear in turbomachines.

dRe

In order to guarantee the possibility to compare experimental data and results between the different types of probes, similarity analysis theory [3] is used to keep the relationship between flow velocity field and the probe’s head diameter. “For flow over geometrically similar objects, physical similarity of the velocity fields exists when the Reynolds number is constant. The similarity extends to the dimensionless pressure field.” In geometry and physically similar situations the flow fields must be similar in all respects, including vortex shedding and the details of the turbulence. It is, however, often difficult (or even impossible) to set up situations that are exactly similar. For example, the surfaces of objects exposed to the flow may be rough. Strict geometric similarity would then require that the roughness elements be similar in shape and distribution. Anyway, when used with proper caution, the similarity relations are a reliable and robust tool. Thus, it can be concluded that for comparisons, the dimensionless group must have the same value. And therefore:

dRe

(56) 21 ReRe dd =

37


Development of Eq. (56) shows a reverse proportional relationship between flow velocities and the probes’ diameters:

1

2

2

1

ww

dd

= (57)

Taking into account the relationship between the rotational speed of the fan in the wind tunnel and the velocity of the fluid, which can be seen in the following function:

nw

(58) nCw ⋅= it is easy to see that Eq. (57) can be rewritten as:

1

2

2

1

nn

dd

= (59)

While calibrating the probes, it is observed that the calibration characteristics can be affected by a variation of the Reynolds number. Hence, the probes are calibrated at various velocities. That is the way to assess the influence of Reynolds number on the experimental data. The calibrations are conducted at and

, and the rotational velocity of the fan and the velocity of the flow for every test, are summarised in Tables 3 and 4, respectively.

500.7Re =d

750.3Re =d

Probe Geometry d [ ]mm n [ ]min/1 w [ ]sm /

SVUSS/3 Cobra probe 2,4 1000 48,9 AVA Trapezoidal probe Nr.110 3,3 727 35,3 AVA Trapezoidal probe Nr.111 3,3 727 35,3 AVA Trapezoidal probe Nr.72 3,2 750 36,4

AVA Cylinder probe Nr. 43 3,0 800 38,8

Table 3: Calibration at 500.7Re =d As said previously, it will be shown in the Results and Conclusions chapter that the AVA trapezoidal probes Nr. 111 and Nr. 72 are not in good conditions. Because of

38


this, the calibration at a lower Reynolds number than the original one, is not conducted to these probes.

Probe Geometry d [ ]mm n [ ]min/1 w [ ]sm / SVUSS/3 Cobra probe 2,4 500 24,3

AVA Trapezoidal probe Nr.110 3,3 365 17,7 AVA Cylinder probe Nr. 43 3,0 400 19,4

Table 4: Calibration at 750.3Re =d

39


6. Results and Discussion A complete set of data is obtained in the laboratory for each one of the three-hole pressure probes. The temperature T of the flow in the free jet wind tunnel and the total pressure as well as the pressures , registered by the three sensing holes,

are recorded in an output file at each calibration yaw angle tp ip

β∆ , by LabVIEW 5.0. When introducing the following data:

- atmospheric reference pressure refp

- environmental temperature refT

- rotational speed n of the fan - distance x downstream from the nozzle exit plane to the probe tip location - characteristic dimension of the probe head d

the data reduction program (written in FORTRAN 77) uses the LabVIEW 5.0 output file as an input file and it enables the procedure to obtain the next information:

- test section flow velocity w- Mach number Ma- Reynolds number dRe

- hole coefficients ik

- direction coefficient βk

- total pressure coefficient tk

- static pressure coefficient sk

The coefficients mentioned before are then plotted versus the yaw angle β∆ and the resulting plots can be used as the classical look-up table where arrays of calibration data are searched, values around the measured quantities are found, and interpolation or local curve-fits using the measured values are used to obtain results. Furthermore, the plots of the hole coefficients as well as the calibration coefficients are also useful when comparing different types of three-hole pressure probes and when trying to study the effect that changes in the flow conditions produce in the

40


probe’s behaviour. For example: the dependency on the Reynolds number, the turbulence intensity influence, errors on the flow angle measurement introduced by a flow velocity gradient, etc… 6.1. Comparison of theoretical and experimental results In the next sections, the calibration data obtained in the laboratory at are compared with the theoretical results for each model of three-hole pressure probe. The graphs are the result of placing on top the streamline projection method predictions ( ) to the experimental data curves ( ). In the case of the AVA cylinder probe Nr. 43 the potential flow solution results ( ) have been also studied and compared.

500.7Re =d

spm edpfs

6.1.1. SVUSS/3 cobra probe For the SVUSS/3 cobra probe, the hole coefficients , and versus the yaw

angle 1k 2k 3k

β∆ are shown in Fig. 20, Fig. 21 and Fig. 22, respectively. The agreement between the measured hole coefficient and the results gained from the streamline projection is quite good. The measured distribution shows asymmetries for positive and negative yaw angles. These asymmetries are caused by a small deviation of the front face of the probe with respect to the plane normal to the probe axis. It should be underlined that the measured distribution for shows a maximum value for

1k

1kº0≈∆β that exceeds the theoretical maximum value which is

. The probe when used for the measurement blocks the nozzle exit area and this blockage effect [11] could be the reason.

11 =k

Great discrepancies between measurement and streamline projection method are in part observed for the hole coefficients and . These are the nondimensional pressures, sensed by the side holes. The general agreement is acceptable for the “pressure side” hole coefficients. These are for

2k 3k

2k º0>∆β and for 3k º0<∆β , respectively. Great discrepancies occur for the “suction side” hole coefficients. These are for 2k º0<∆β and for 3k º0>∆β , respectively. Due to the probe head geometry the flow separates at the sharp corner and a large laminar separation is established. The streamline projection method does not take into account any separation on the “suction side” of the probe head and, therefore, it can not model this behaviour.

41


Yaw Angle ∆β [º]

-30 -20 -10 0 10 20 30

Coe

ffici

ent k

1 [-]

0,6

0,7

0,8

0,9

1,0

1,1

spm ed

Figure 20: SVUSS/3 cobra probe hole coefficient (1k 500.7Re =d )


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

2 [-]

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

spm ed

Figure 21: SVUSS/3 cobra probe hole coefficient (2k 500.7Re =d )

42



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

3 [-]

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

spm ed

Figure 22: SVUSS/3 cobra probe hole coefficient (3k 500.7Re =d ) The direction coefficient , the total pressure coefficient and the static

pressure coefficient versus the yaw angle βk tk

sk β∆ are plotted in Fig. 23, Fig. 24 and Fig. 25, respectively. The streamline projection method calculation approaches relatively well the results of calibration for the direction coefficient as well as for the total pressure

coefficient . βk

tk

For small yaw angles the streamline projection method shows a linear relationship between the direction coefficient and the yaw angle. A Taylor series expansion [10] of Eq. (9) gives

δπββ tanº45⋅⋅∆≈k (60)

which demonstrates the existence of this linear behaviour for the yaw angle range

º15º15 +<∆<− β .

43


The slope of the curve of is a measure for the sensitivity of the probe on the

flow direction. As can be seen from Eq. (60) the sensitivity depends on the probe wedge angle and it increases with increasing

βk

δ . However, the yaw angle sensitivity of the direction coefficient is somewhat underpredicted by the streamline projection method. The slight asymmetry of the probe head with respect to the probe axis is reflected by the measured distribution of the total pressure coefficient . The maximum value

for this coefficient is and there are some more measured points that go

above the maximum theoretical value, which is supposed to be .

tk

019.0=tk

0=tk

The static pressure coefficient seems to be nearly independent of the flow angle. According to Eq. (11), the differences between measurements and the theoretical curve are caused by the “suction side” hole coefficients and , respectively.

sk

2k 3k


-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-4

-3

-2

-1

0

1

2

3

spm ed

Figure 23: SVUSS/3 cobra probe direction coefficient (βk 500.7Re =d )

44



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

spm ed

Figure 24: SVUSS/3 cobra probe total pressure coefficient (tk 500.7Re =d )


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

0,2

0,4

0,6

0,8

1,0

1,2

spm ed

Figure 25: SVUSS/3 cobra probe static pressure coefficient (sk 500.7Re =d )

45


6.1.2. AVA trapezoidal probes The analysis for the three different models of trapezoidal probes is done in the next sections. For the AVA trapezoidal probe Nr. 110 comparisons between the experimental curves and the theoretical curves for the three hole coefficients as well as for the three calibration coefficients are tackled. The AVA probes Nr. 111 and Nr. 72 are only studied from an experimental viewpoint. The difference on the analysis strategy lies in the meaning and the interest of the hole and the calibration coefficients, while in the probes dissimilar behavior. 6.1.2.1. AVA trapezoidal probe Nr. 110 The main geometric characteristics of this probe head match up with the SVUSS/3 cobra probe head. Thus, since the streamline projection method depends only on the probe head geometry, the predictions are the same for both probes. The calibration curves are also pretty similar, despite the AVA trapezoidal probe Nr.110 curves extend to higher range of values. The theoretical values have the same general features as the experimental data; however, in this case, the agreement between the measured coefficients and the theoretical values is considerably lower. The hole coefficient plots show curves of increasing non-dimensional pressure as the hole of each tube is oriented into the flow. The curvature increases as the pressure increases, since the flow is more into the hole and exhibits greater dependence upon the twisting of the hole with respect to the mean flow. Fig. 26 presents the center pressure tap ( ) response which should resemble symmetric curve respect to the probe axis. From this figure it is easily determined that the probe axis was not aligned with the flow when

1p

º0=∆β . This occurs due to manufacturing deviations on the body of the probe or when the probe is mounted in the test section. Fig. 27 and Fig. 28 present the outer pressure taps ( and ) responses. The higher values reached by this probe make differences between the experimental procedure and the theoretical calculation come bigger than in the SVUSS/3 comparison.

2p 3p

46



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

1 [-]

0,5

0,6

0,7

0,8

0,9

1,0

1,1

spm ed

Figure 26: AVA trapezoidal probe Nr. 110 hole coefficient (1k 500.7Re =d )


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

2 [-]

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

spm ed


47



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

3 [-]

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

spm ed


At large yaw angles, one of the side holes is approximately aligned with the flow and senses pressures near the free-stream total pressure. The opposite hole senses a pressure much less than the free-stream static pressure, due to the acceleration of the flow around the probe and possibly due to flow separation. The measured sensitivity to the flow direction can be found in Fig. 29. The

experimental data for are shown in Fig. 30. The essential results are similar to the ones achieved for the SVUSS/3 cobra probe, again. Despite the range of values for the direction and the total pressure coefficients goes above the obtained range for the cobra probe and that differences between the experimental and the analytic method are bigger in this case, as well.

βk

tk

The static pressure coefficient experimental curve (see Fig. 31) follows a

reasonable downward/upward trend. The data scatter around the value is quite regular, which in fact is a good approximation to the theoretical shape of this curve. The streamline projection method fails when trying to predict this calibration coefficient behaviour. It indicates some kind of quadratic relationship between and

the yaw angle

sk

2.0=sk

sk

β∆ , that it does not exist in reality.

48



-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-3

-2

-1

0

1

2

3

4

spm ed

Figure 29: AVA trapezoidal probe Nr. 110 direction coefficient ( ) βk 500.7Re =d


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

spm ed

Figure 30: AVA trapezoidal probe Nr. 110 total pressure coefficient ( ) tk 500.7Re =d

49



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

0,0

0,2

0,4

0,6

0,8

1,0

1,2

spm ed

Figure 31: AVA trapezoidal probe Nr. 110 static pressure coefficient ( ) sk 500.7Re =d

6.1.2.2. AVA trapezoidal probe Nr. 111 The nondimensional pressures sensed by the AVA trapezoidal probe Nr. 111 holes can be found in Fig. 32. The hole coefficient is almost constant for the yaw angles from 1k º10−=∆β up to

º5.22=∆β . This indicates that hole 1 has not sensibility for a change in orientation relative to the flow in the yaw plane in a range of about . It is also remarkable that there are eleven measured points that exceed the maximum theoretical value for

and that the measured maximum value is reached for two times at different yaw angles. On the other hand, the curve shows great asymmetries for positive and negative yaw angles.

º5.32

1k

The intersection between and occurs for a yaw angle of 2k 3k º5,7≈∆β instead of

º0=∆β which is supposed to happen in case of symmetry and the slope of these two curves is really different. Thus, it is obvious that the nondimensional pressures

50


sensed by the outer holes are not symmetrical. The coefficient goes from negative to positive values when the yaw angle is

2k

º0≈∆β while hole coefficient does when 3k

º14≈∆β . That indicates great anomalies and it seems to point that the problems rely on or which comes to the same thing, in hole 3. 3k

These observations of anomalies in the hole coefficient curves lead to the conclusion that the AVA trapezoidal probe Nr. 111 has suffered some kind of alteration or mishap that has badly damaged it.


-30 -20 -10 0 10 20 30

Hol

e C

oeffi

cien

ts k

i [-]

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

k1 ed k2 ed k3 ed

Figure 32: AVA trapezoidal probe Nr. 111 hole coefficients , and ( ) 1k 2k 3k 500.7Re =d

6.1.2.3. AVA trapezoidal probe Nr. 72 For this probe, the experimental hole coefficients , and are presented in Fig. 33. Without the need to study them in detail, a quick look at the main characteristics of the plots comes in useful for realizing that something similar to the AVA trapezoidal probe Nr. 111 happens again.

1k 2k 3k

51


The front sensing tap has no-sensitivity to the flow direction for a yaw angle range about . The slope of the curve is completely horizontal between the yaw angle values:

º5.22 1kº5.12−≈∆β and º10≈∆β . The curve exhibits as well an asymmetry,

although it is not as marked as it is for the trapezoidal probe Nr. 111. On this occasion, the intersection between and occurs for a yaw angle of 2k 3k

º2−≈∆β and the slope of the two curves is not really different. Thus, the pressures sensed by the outer holes are quite symmetrical. Then, the problem appears as a probe body deviation with respect to the zero yaw angle. Taking into account the results explained above, it can be concluded that the AVA trapezoidal probe Nr. 72 should not be used due to some machining abnormality or damage it has sustained.


-30 -20 -10 0 10 20 30

Hol

e C

oeffi

cien

ts k

i [-]

-1,0

-0,5

0,0

0,5

1,0

1,5

k1 ed k2 ed k3 ed

Figure 33: AVA trapezoidal probe Nr. 72 hole coefficients , and ( ) 1k 2k 3k 500.7Re =d

52


6.1.3. AVA cylinder probe Nr. 43 The hole coefficients obtained through the calibration procedure are shown first in a single plot all together (see Fig. 34) versus the yaw angle β∆ , in order to offer a better overview of the results. The same coefficients are then compared individually with results gained from the streamline projection method. For probes of cylinder head geometry, the potential flow solution ( ) can predict the pressure distribution and the corresponding calibration characteristics to a reasonable accuracy, as well. The comparisons are exposed in Fig. 35, Fig. 36 and Fig. 37.

pfs

The experimental hole coefficients distribution shows acceptable symmetries for

, and for comparing to . Moreover, the maximum value for is reached at 1k 2k 3k 1k

º0≈∆β while the intersection between and occurs for this yaw angle value, too. This indicates that the probe head is perfectly aligned with the flow direction for yaw angle

2k 3k

º0=∆β , while both side holes behave in a similar manner when sensing and measuring the pressures. Anyway, it should be noted that the curve has not a constant slope for angles of yaw

2k

º10−<∆β . Exactly the same occurs for the curve

for yaw angles 3k

º10+>∆β .


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

i [-]

-1,0

-0,5

0,0

0,5

1,0

1,5

k1 ed k2 ed k3 ed

Figure 34: AVA cylinder probe Nr. 43 hole coefficients , and ( ) 1k 2k 3k 500.7Re =d

53


Quite good agreement is achieved between the measured coefficient and the solution of the mathematical models, especially for the streamline projection method. Despite the decrease of the measured distribution is more pronounced than in the streamline projection prediction and less than in the potential flow solution calculation.

1k


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

1 [-]

0,0

0,2

0,4

0,6

0,8

1,0

1,2

pfs spm ed

Figure 35: AVA cylinder probe Nr. 43 hole coefficient (1k 500.7Re =d )

For hole coefficients and great discrepancies appear, specially when a forecast for the “suction side” behaviour is needed. Then, the potential flow solution underestimates the real values and the streamline projection overestimates them. Since the last method does not take in account for any separation effect, it is expected that the hole side coefficients prediction to be positive throughout the entire yaw angle range. The hole coefficients and are underpredicted by the potential

flow solution over the entire range of yaw angles

2k 3k

2k 3k

β∆ . The reason seems to be the relatively large diameter ( ) of both side holes of the AVA cylinder probe Nr. 43. The potential flow solution assumes a smooth surface of the cylinder. However, due to the large side holes there seems to be a kind of “capturing effect” in the real flow.

6,0 mm

54



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

2 [-]

-4

-3

-2

-1

0

1

2

pfs spm ed



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

3 [-]

-4

-3

-2

-1

0

1

2

pfs spm ed


55


The direction coefficient (Fig. 38) and the total pressure coefficient (Fig. 39)

are predicted by the streamline projection method as well as the potential flow solution with extremely high precision. Only some low discrepancies appear when trying to approach the values of for calibration large angles of yaw. Furthermore, the numerical results reached through both mathematical elaborations give exactly the same result. That is the reason why only two different curves are plotted in Fig. 38 and in Fig. 39. One corresponds to the experimental data, and the other one does to the theoretical procedures.

βk tk

tk

The experimental data curve (Fig. 40) shows independency respect to the yaw

angle sk

β∆ and it approaches quite well with the ideal static pressure coefficient curve. As in all the other types of probe, neither the streamline projection method nor the potential flow solution are capable to explain the behaviour. The curve has a

similar shape but the values are really dissimilar. On the contrary, the curve points to the experimental values, but it shows a completely different shape.

sk spm

pfs

After checking the results of the experimental calibration it can be concluded that the AVA cylinder probe Nr. 43 it is not only in good conditions but perfectly designed and carefully well manufactured, too.


-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-4

-3

-2

-1

0

1

2

3

4

ed spm and pfs

Figure 38: AVA cylinder probe Nr. 43 direction coefficient (βk 500.7Re =d )

56



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

ed spm and pfs

Figure 39: AVA cylinder probe Nr. 43 total pressure coefficient ( ) tk 500.7Re =d


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

pfsspmed

Figure 40: AVA cylinder probe Nr. 43 static pressure coefficient ( ) sk 500.7Re =d

57


6.2. Comparison between probes The results exposed here have been previously seen and individually discussed in the preceding sections. Now, the purpose is to compare them in order to offer really useful information from the user’s point of view. For this reason, only the curves belonging to the calibration coefficients , , and have been compared. These

coefficients are of practical interest for the application of the probe to measure a flow field.

βk tk sk

Due to the discussed calibration results and according to the good preserve state of the three-hole pressure probes available in the Institute of Thermal Turbomachines and Powerplants of the Vienna University of Technology, only those models which are mentioned in the next list have been included in the analysis:

- SVUSS/3 cobra probe - AVA trapezoidal probe Nr. 110 - AVA cylinder probe Nr. 43

Fig. 41, Fig. 42 and Fig. 43 present the calibration data which have been plotted to compare the differences of the three-hole pressure probes mentioned above. These plots can also be used to determine the range of flow angles a particular probe can measure. There is a maximum angle the flow can make with respect to the axis of the probe beyond which the flow separates from the probe. When this occurs the data can not be reduced to obtain the velocity since the pressure taps in the separated region do not vary significantly nor monotonically with flow angle. It is obvious that differences between the curves for the same calibration coefficient can be primarily attributed to geometric characteristics. A reduced range of values results in an increased sensitivity of the probe to the small flow variations in the yaw plane. The measured variable in this plane may, therefore, exhibit more scatter. Figs. 41 and 42 show very good response characteristics, and the three probes can be used over the entire calibration yaw angle range. Great discrepancies appear when comparing the results on Fig. 43. In fact, the plots for the static pressure coefficient have really different shape and slope, particularly for the AVA cylinder probe Nr. 43.

58


Yaw Angle ∆β [°]

-30 -20 -10 0 10 20 30

Pro

bes

Coe

ffici

ent kβ

[-]

-4

-3

-2

-1

0

1

2

3

4

SVUSS/3 AVA Nr.110AVA Nr.43

Figure 41: Direction coefficient comparison between probes ( ) βk 500.7Re =d


-30 -20 -10 0 10 20 30

Pro

bes

Coe

ffici

ent k

t [-]

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

SVUSS/3 AVA Nr.110 AVA Nr.43

Figure 42: Total pressure coefficient comparison between probes ( ) tk 500.7Re =d

59



-30 -20 -10 0 10 20 30

Pro

bes

Coe

ffici

ent k

s [-]

-0,4

-0,2

0,0

0,2

0,4

0,6

SVUSS/3AVA Nr.110AVA Nr.43

Figure 43: Static pressure coefficient comparison between probes ( ) sk 500.7Re =d

6.3. Factors influencing the calibration of three-hole pressure probes The main factors influencing the calibration of a three-hole pressure probe are probe head geometry and Reynolds number. Alignment with the flow direction and manufacturing defects are also significant. The probe head geometry effect has been discussed at length above and a brief description of Reynolds number influence is given below. Some other factors, such as: sensing holes geometry, existence of velocity gradients or wall proximity have minor relevance, but they can also affect the behaviour of the probe or introduce sources of error when calibrating or using a pressure probe for flow measurement in turbomachinery. 6.3.1. Reynolds number and Mach number effects [1] [4] Meaningful calibration data should be independent of the measured quantities. In most three-hole pressure probes, velocity is the primary parameter to be measured; thus, the effect of changes in Reynolds number on the calibration data should dRe

60


be evaluated. The variations are assessed by calibrating the probes in air at different Reynolds numbers: and 750.3Re =d 500.7Re =d . For the different types of probes, the direction coefficient and the total pressure

coefficient are essentially unaffected by the Reynolds number variation (Fig. 44, Fig. 45, Fig. 47, Fig. 48, Fig. 50 and Fig. 51). However, the effects of Reynolds numbers may be appreciable. It has to be considered that the most Reynolds number sensitive range is located when the flow turns from laminar into turbulent (transition zone). For example, the transition zone for a cylinder shaped body occurs between

and [9]. These values of Reynolds number are far above the range of the available subsonic nozzle design.

βk

tk

6102Re ×= 6106Re ×=

The static pressure coefficient is found sensitive to the Reynolds number nearly all over the yaw angle range (Fig. 46, Fig. 49 and Fig. 52). With increasing the Reynolds number, this coefficient values tend to decrease. These changes are sufficient to cause minor variations in the magnitude of the calculated velocity vector.

sk

The plots resulting from the calibrations at different Reynolds numbers for three different head geometries are shown in the following sections. 6.3.1.1. SVUSS/3 cobra probe


-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-4

-3

-2

-1

0

1

2

3

ed (Red =3.750)ed (Red =7.500)

Figure 44: SVUSS/3 cobra probe direction coefficient at different βk dRe

61



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

ed (Red =3.750) ed (Red =7.500)

Figure 45: SVUSS/3 cobra probe total pressure coefficient at different tk dRe


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

0,2

0,3

0,4

0,5

0,6

0,7

ed (Red =3.750) ed (Red =7.500)

Figure 46: SVUSS/3 cobra probe static pressure coefficient at different sk dRe

62


6.3.1.2. AVA trapezoidal probe Nr. 110


-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-4

-2

0

2

4

6

ed (Red =3.750)ed (Red =7.500)

Figure 47: AVA trapezoidal probe Nr. 110 direction coefficient at different βk dRe


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

ed (Red =3.750)ed (Red =7.500)

Figure 48: AVA trapezoidal probe Nr. 110 total pressure coefficient at different tk dRe

63



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

ed (Red =3.750)ed (Red =7.500)

Figure 49: AVA trapezoidal probe Nr. 110 static pressure coefficient at different sk dRe 6.3.1.3. AVA cylinder probe Nr. 43


-30 -20 -10 0 10 20 30

Coe

ffici

ent kβ

[-]

-4

-3

-2

-1

0

1

2

3

4

ed (Red =3.750)ed (Red =7.500)

Figure 50: AVA cylinder probe Nr. 43 direction coefficient at different βk dRe

64



-30 -20 -10 0 10 20 30

Coe

ffici

ent k

t [-]

-1,6

-1,4

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

ed (Red =3.750)ed (Red =7.500)

Figure 51: AVA cylinder probe Nr. 43 total pressure coefficient at different tk dRe


-30 -20 -10 0 10 20 30

Coe

ffici

ent k

s [-]

-0,3

-0,2

-0,1

0,0

0,1

0,2

ed (Red =3.750)ed (Red =7.500)

Figure 52: AVA cylinder probe Nr. 43 static pressure coefficient at different sk dRe

65


6.3.2. Hole geometry for static pressure taps [3]

The “ideal” tap geometry is a small circular hole of less than 41 mm diameter drilled

perpendicular to the surface on which the pressure is to be measured; the corner of the hole is perfectly sharp and squared off. Any departure of this geometry will introduce error. A 1 diameter hole should introduce an error of less than of

dynamic pressure, compared with a hole of

mm %1

41 mm diameter. Errors with practical-

sized holes occur because of flow in and around the hole opening. Rounding of the hole corners (up to a radius curvature equal to the hole diameter) and no perpendicularity of the hole with the wall (up to ) introduce errors of less than

of dynamic pressure. Burrs on the edge of the hole, with heights of less than

°45 %1

301 of a

hole diameter and extending into the flow, introduce errors of less than of dynamic pressure.

%1

6.3.3. Turbulence intensity The conventional probes are usually calibrated in a well-controlled calibration tunnel where the flow turbulence is very low. But they are used to measure flow in turbomachinery, where the turbulence fluctuations are large and cause error in pressure probes. The effect of turbulence is to increase the sensed value of mean static pressure. It is known [3] that the probe static pressure will exceed the true static pressure by an

amount 2_

41

nw⋅⋅ ρ , where is the resultant turbulence intensity in the circumferential

plane of the probe. One can work out that error in the combined will be less than in each pressure separately. It may even be negligible, depending on the relative magnitudes of stream wise and transverse intensity components.

2_

nw

st pp −

Part of the influence of the Reynolds number upon probe calibrations is due to the changing nature of the separations that exist at all flow angles [7]; changes that stem from the influence that Reynolds numbers exerts upon the transition processes within the separation bubbles. Thus, turbulence can affect the reliability of probe calibrations even at typical Reynolds numbers.

66


6.3.4. Velocity gradient effects [7] [10] The probes used in this investigation are calibrated in a uniform flow, but they are used to measure flow in turbomachinery components. The flow fields in these conditions are dominated by strong velocity gradients. These gradients affect the probe performance in the following ways: 1. The probe indicates the reading at a location different from the geometric center of the probe. This perturbation is known as displacement effect. 2. The presence of the probe in a velocity gradient causes deflection of the streamlines toward the region of lower velocity. This deflection causes the probe to indicate pressures in excess of that existing at the same location in the absence of the probe. 3. The velocity gradient induces a pressure difference between the side probe holes which is interpreted by the probe as a flow angle error ε∆ . Hence, an additional error is introduced. 6.3.5. Wall proximity effects [7] Whenever a probe is located near a solid surface, the flow acceleration in that region introduces an additional error. In the measurement of flow in a turbomachinery component, the probe is placed close to many solid surfaces, such as annulus wall and blades. A discussion of these errors follows. When a probe is very near a blade trailing edge, it is subjected to the following effects: viscid and inviscid interference between the probe and the trailing edge, area blockage and velocity and pressure gradients discussed earlier. The complexity of the interaction between the probe and trailing edge prohibits an estimate of the error in the probe measurements, and the results very near the trailing edge are to be viewed with caution. Due to the blockage effect between the probe and the wall, the pressure sensed by the side hole near the wall is higher than the value at the free stream conditions. A rule of thumb is that such interactions cause error when the distance from the axis to the wall is less than two probe diameters. For some of the larger three-hole probes the distance may be more like four diameters.

67


Gradient as well as wall proximity effects are rather difficult to establish in a wind tunnel calibration procedure. Therefore, analytical investigations or CFD computations are an interesting alternative to the wind tunnel calibration. 6.3.6. Influence of probe supports [3] The pressure gradients associated with the curvature of flow lines around probe supports can be avoided by proper displacement of the probe. For cylindrical probe supports perpendicular to the probe axis, the distance should be five support diameters to avoid an error amounting to of dynamic pressure. For an aerodynamically faired strut the rule for low Mach numbers might be relaxed to three-support diameters.

%2

68


Summary The research and development of turbomachine technology is dependent on the experimental determination of the performance of advanced components. The primary measurements in turbines and compressors consist of flow direction and total and static pressures as well as total and static temperatures. Three-hole pressure probes are commonly used for two-dimensional ( ) flow studies in turbomachinery. The pressures sensed at the probe holes are used for the estimation of the velocity and direction of the flow in an indirect manner.

D2

The probes available at the Institute of Thermal Turbomachines and Powerplants of Vienna (T.U. Wien) are:

- SVUSS/3 cobra probe - AVA trapezoidal probe Nr. 110 - AVA trapezoidal probe Nr. 111 - AVA trapezoidal probe Nr. 72 - AVA cylinder probe Nr. 43

Their head geometry has been analyzed and described in detail in this work. Also the behaviour of these probes when measuring the flow field characteristics has been studied through a calibration procedure. Since manufacturing anomalies are likely to occur in miniature probes, individual calibration of these sensors must be carried out. In addition to the experimental calibration, some mathematical models (i.e., the streamline projection method) have been applied as an auxiliary tool to calculate the calibration coefficients, at least qualitatively. The experimental facility - free jet wind tunnel - in where the calibrations have been conducted and the conditions taken to insure the reliability and comparability of the results are widely described in the corresponding chapter. The calibration contains data at increments from º5.2 º30− to for the yaw angle

º30+β∆ . These data along with the total pressure and the static pressure tp p for

the flow field are used to calculate values of the hole coefficients ( ) as

well as the calibration coefficients: the direction coefficient , the total pressure ik ,1=i ,2 3

βk

69


coefficient and the static pressure coefficient . All these coefficients have been plotted and compared with the theoretical estimations.

tk sk

When reducing data to determine the velocity magnitude and direction, only the three pressures that are measured are known. These three pressures are used to calculate , and . It is from the calibration coefficients values that the flow

angle βk tk sk

β∆ is determined. The calibration curves for , and obtained directly from the experimental

data are invaluable in evaluating the performance of an individual probe and determining the range of yaw angles the probe is capable of measuring. There is a maximum angle the flow can make with respect to the axis of the probe beyond which the flow separates from the probe. When this occurs the data can not be reduced to obtain the velocity since the pressure sensed by taps in the separated region do not vary significantly or monotonically with flow angle.

βk tk sk

Among the factors influencing the calibration of pressure probes, the head geometry and the Reynolds number are the most important ones. Regarding to that point, the investigation has emphasized on determining the influence of these factors on the calibration coefficients. The calibration coefficients have been individually studied but also compared for diverse head geometries and various Reynolds numbers. Thus, some conclusions have been reached and justified. Of course, differences between the probes calibration results can be primarily attributed to geometric characteristics. Other repeatable nonsymmetries appearing in the data apparently resulted from the inability to fabricate a symmetric probe. The results of the present investigation should serve as a starting point to tackle some other works. For example, the repair and recalibration of the damaged AVA trapezoidal probes or to complete a more detailed study of the dependency between the calibration coefficients and the Reynolds number (that implies the design and construction of new nozzles for the free jet wind tunnel). Some other interesting proposals are the calibration of thermocouples or checking changes in the three-hole pressure probes behaviour when affected by a velocity gradient. That has been already done for the SVUSS/3 cobra probe. The ultimate goal should be the calibration and study of a five-hole pressure probe.

70


Bibliography [1] Dominy R.G., Hodson H. P.: An Investigation of Factors Influencing the Calibration of Five-Hole Probes for Three-Dimensional Flow Measurements. ASME Journal of Turbomachinery, Vol. 115 (July 1993) [2] Gieß P. A., Rehder H.J. and Kost. F.: A New Test Facility for Probe Calibration – Offering Independent Variation of Mach and Reynolds Number. Proceedings of the 15th Bi-Annual Symposium on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines. Firenze, Italy. (September 2000) [3] Goldstein, R. J.: Fluid Mechanics Measurements. Springer-Verlag. Berlin. ISBN 3-540-12501-9 (1976) [4] Lee S.W., Jun S. B.: Effects of Reynolds Number on the Non-Nulling Calibration of a Cone-Type Five-Hole Probe. ASME Paper GT 2003 - 38147 (June 2003) [5] Morrison G.L., Schobeiri M.T., and Pappu K.R.: Five-Hole Pressure Probe Analysis Technique. Flow Measurement and Instrumentation 9 (June 1998) [6] Pisasale A. J., Ahmed N.A.: A Novel Method for Extending the Calibration Range of Five-Hole Probe for Highly Three-Dimensional Flows. Flow Measurement and Instrumentation 13 (March 2002) [7] Sitaram N., Lakshminarayana B., and Ravindranath A.: Conventional Probes for the Relative Flow Measurement in a Turbomachinery Rotor Blade Passage. ASME Journal of Engineering for Power, Vol. 103 (April 1981) [8] Treaster, A.L, Yocum, A.M: The Calibration and Application of Five-Hole Probes. ISA Transactions Vol. 18, No.3 (1979) [9] Truckenbrodt, E.: Lehrbuch der angewandten Fluidmechanik. 2.Auflage, Springer (1988) [10] Willinger R., Haselbacher H.: A Three-Hole Pressure Probe Exposed to Velocity Gradient Effects – Experimental Calibration and Numerical Investigation. Conference on Modelling Fluid Flow (CMFF ’03). Budapest, Hungary. (September 2003)

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[11] Wyler J. S.: Probe Blockage Effects in Free Jets and Closed Wind Tunnels. ASME Journal of Engineering for Power, Paper 74-WA/PTC-5 (October 1975)

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Picture List 2. Calibration Figure 1: Inviscid flow along a stream tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3. Three-Hole Probes Geometry Figure 2: Geometry nomenclature for three-hole probes . . . . . . . . . . . . . . . . . . . . 12 Figure 3: Three-hole SVUSS/3 cobra probe . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Figure 4: Cobra three-hole probe head geometry sketch . . . . . . . . . . . . . . . . . . . . 15 Figure 5: SVUSS/3 cobra probe head side view . . . . . . . . . . . . . . . . . . . . . . . . 16 Figure 6: SVUSS/3 cobra probe head front view . . . . . . . . . . . . . . . . . . . . . . . . 16 Figure 7: Workshop drawing for the SVUSS/3 cobra probe . . . . . . . . . . . . . . . . . . . 17 Figure 8: Three-hole AVA trapezoidal probe Nr. 110 . . . . . . . . . . . . . . . . . . . . . . 18 Figure 9: AVA trapezoidal probe head side view . . . . . . . . . . . . . . . . . . . . . . . . 18 Figure 10: AVA trapezoidal probe head front view . . . . . . . . . . . . . . . . . . . . . . . . 19 Figure 11: Workshop drawing for the AVA trapezoidal probe Nr. 110 . . . . . . . . . . . . . 20 Figure 12: Three-hole AVA cylinder probe Nr. 43 . . . . . . . . . . . . . . . . . . . . . . . . 21 Figure 13: AVA cylinder probe head view . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Figure 14: Workshop drawing for the AVA cylinder probe Nr. 43 . . . . . . . . . . . . . . . . 22

4. Streamline Projection Method Figure 15: SVUSS/3 cobra probe head geometry . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 16: Angles used for the streamline projection method . . . . . . . . . . . . . . . . . . 27 Figure 17: Angles used for the potential flow solution . . . . . . . . . . . . . . . . . . . . . . 30

5. Test Facility Figure 18: Vienna University of Technology free jet wind tunnel . . . . . . . . . . . . . . . . 33 Figure 19: Support device and probe location . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Figure 20: Hardware and software connections for the data acquisition (schematic) . . . . . . 36

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6. Results and Discussion Figure 20: SVUSS/3 cobra probe hole coefficient (1k 500.7Re =d ) . . . . . . . . . . . . . 42

Figure 21: SVUSS/3 cobra probe hole coefficient (2k 500.7Re =d ) . . . . . . . . . . . . . 42

Figure 22: SVUSS/3 cobra probe hole coefficient (3k 500.7Re =d ) . . . . . . . . . . . . . 43

Figure 23: SVUSS/3 cobra probe direction coefficient (βk 500.7Re =d ) . . . . . . . . . . . 44

Figure 24: SVUSS/3 cobra probe total pressure coefficient (tk 500.7Re =d ) . . . . . . . . .45

Figure 25: SVUSS/3 cobra probe static pressure coefficient (sk 500.7Re =d ) . . . . . . . . 45

Figure 26: AVA trapezoidal probe Nr. 110 hole coefficient (1k 500.7Re =d ) . . . . . . . . 47

Figure 27: AVA trapezoidal probe Nr. 110 hole coefficient (2k 500.7Re =d ) . . . . . . . . . 47

Figure 28: AVA trapezoidal probe Nr. 110 hole coefficient (3k 500.7Re =d ) . . . . . . . . . 48

Figure 29: AVA trapezoidal probe Nr. 110 direction coefficient (βk 500.7Re =d ) . . . . . . 49

Figure 30: AVA trapezoidal probe Nr. 110 total pressure coefficient ( ) . . . . 49 tk 500.7Re =d

Figure 31: AVA trapezoidal probe Nr. 110 static pressure coefficient ( ) . . . 50 sk 500.7Re =d

Figure 32: AVA trapezoidal probe Nr. 111 hole coefficients , and ( ) . . 51 1k 2k 3k 500.7Re =d

Figure 33: AVA trapezoidal probe Nr. 72 hole coefficients , and ( ) . . 52 1k 2k 3k 500.7Re =d

Figure 34: AVA cylinder probe Nr. 43 hole coefficients , and ( ) . . . . 53 1k 2k 3k 500.7Re =d

Figure 35: AVA cylinder probe Nr. 43 hole coefficient (1k 500.7Re =d ) . . . . . . . . . . . 54



Figure 38: AVA cylinder probe Nr. 43 direction coefficient (βk 500.7Re =d ) . . . . . . . . . 56

Figure 39: AVA cylinder probe Nr. 43 total pressure coefficient (tk 500.7Re =d ) . . . . . . 57

Figure 40: AVA cylinder probe Nr. 43 static pressure coefficient (sk 500.7Re =d ) . . . . . . 57

Figure 41: Direction coefficient comparison between probes (βk 500.7Re =d ) . . . . . . . 59

Figure 42: Total pressure coefficient comparison between probes (tk 500.7Re =d ) . . . . . 59

Figure 43: Static pressure coefficient comparison between probes (sk 500.7Re =d ) . . . . 60

Figure 44: SVUSS/3 cobra probe direction coefficient at different . . . . . . . . . . . 61 βk dRe

Figure 45: SVUSS/3 cobra probe total pressure coefficient at different . . . . . . . . 62 tk dRe

Figure 46: SVUSS/3 cobra probe static pressure coefficient at different . . . . . . . 62 sk dRe

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Figure 47: AVA trapezoidal probe Nr. 110 direction coefficient at different . . . . . . 63 βk dRe

Figure 48: AVA trapezoidal probe Nr. 110 total pressure coefficient at different . . . .63 tk dRe

Figure 49: AVA trapezoidal probe Nr. 110 static pressure coefficient at different . . . 64 sk dRe

Figure 50: AVA cylinder probe Nr. 43 direction coefficient at different . . . . . . . . 64 βk dRe

Figure 51: AVA cylinder probe Nr. 43 total pressure coefficient at different . . . . . . 65 tk dRe

Figure 52: AVA cylinder probe Nr. 43 static pressure coefficient at different . . . . . .65 sk dRe

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Table List 3. Three-Hole Probes Geometry Table 1: Three-hole probes designs main characteristics . . . . . . . . . . . . . . . . . . . . 14

5. Test facility Table 2: Main data of the wind tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Table 3: Calibration at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 500.7Re =d

Table 4: Calibration at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 750.3Re =d

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