EXPERIMENTAL STUDY
ON PRESSURE LOSSES IN
ADDITIVELY MANUFACTURED
AND MACHINED ORIFICES
A rectangular geometry of additively manufactured
MA 247 orifice and a circular geometry of
machined AW-6082 T6 orifice study
Jayadev Nambisan
An Industrial Gas Turbine by Siemens. Model: SGT-800
Link¨oping University Department of Management and Engineering
Link¨oping University Department of Management and Engineering Master’s thesis, 30 credits | MSc Aeronautical Engineering Spring 2020 | LIU-IEI-TEK-A–20/03887-SE
EXPERIMENTAL STUDY
ON PRESSURE LOSSES IN
ADDITIVELY MANUFACTURED
AND MACHINED ORIFICES
A rectangular geometry of additively manufactured
MA 247 orifice and a circular geometry of
machined AW-6082 T6 orifice study
Jayadev Nambisan
LIU ID: jayna709
Industrial supervisor: Dr. Mats Kniell
Academic supervisor: Dr. Hossein Nadali Najafabadi Examiner: Dr. Roland G˚ardhagen
Abstract
Gas turbine components for cooling purposes including other unique and complex three-dimensional designs could be made explicitly possible through additive manu-facturing using SLM technology in contrary to the conventional machining processes. Nevertheless, the surface roughness and subsequently the friction factor governs the pressure drop in these components implicitly, thus, influencing the secondary air flow system of a gas turbine. Research studies to understand and predict flow be-haviours through especially AM parts are still in a budding stage, and thus, in this scope of thesis, the same has been attempted through experimentation to quantify pressure losses in additively manufactured rectangular orifices. With the purpose of a brief analogy, a set of aluminium circular samples were also tested which were manufactured by the conventional process of machining. A total of 9 rectangular MA247 samples of different lengths and hydraulic diameters were tested as continu-ation to the ongoing research at Siemens Industrial Turbomachinery AB and further on to that, 5 Aluminium Alloy- AW-6082 T6 material samples of circular geometry with varying lengths were tested. The on-going research focuses on the additively manufactured geometries for both rectangular and circular, and hence, the data for circular orifices were used to draw a comparison with its Aluminium counterpart. Pressure losses here were described using the coefficient of discharge and the inves-tigations on roughness were by calculating Darcy frictional factor and Colebrooks equation. Classical theories such as the boundary layer theory, Hagen’s power law, Ward-Smith’s theory for vena contracta and other works by previous researchers were used to validate the results. The coefficient of discharge could be deployed to restrict and measure the mass flow in the secondary air systems, whereas the results from the calculated frictional factors could be held to simulate the flow distribution in cooling geometries.
Acknowledgements
To begin with, I would like to thank everyone from the fluid dynamics department of Siemens Industrial Turbomachinery AB at Finsp˚ang, Sweden for providing the opportunity for this interesting scope of thesis and to indirectly and subconsciously help me evolve as a professional and a human in general.
My sincere gratitude extends to Dr. Mats Kinell and Dr. Hossein Nadali Na-jafabadi who guided me over the course of this thesis and filled me with salient inputs whenever needed within their capacity as my industrial supervisor and aca-demic supervisor respectively. A noted mention to Dr. Karl-Johan Nogenmyr from SIT AB for the same deed. My heartfelt appreciation for Dr. Alessio Bonaldo, the Project Manager, for being there as a strong support and professional guidance. A sincere thanks to Dr. Roland G˚ardhagen for all his support for getting this project done the way it is needed within his capacity as the examiner. My predecessors who had worked on this on-going research are also to be acknowledged for being open to dialogue and discussions.
In the end, my profound appreciation and certitude for the fact that, my journey until here would not have been possible at the first place if it weren’t for my biological creators, and theirs.
Nomenclature
Latin Symbols
Symbol Units Description
A m2
Area of Orifice Avc m2
Area of Vena Con-tracta Cc [−] Coefficient of Con-traction Cd [−] Discharge Coeffi-cient Cs [m/s] Speed of Sound D [m] Inside Diameter of Orifice D0 [m] Inside Diameter of Pressure Vessel Dh [m] Hydraulic Diame-ter fD [−] Darcy-Weisbach Friction Factor fFanning [−] Fanning Friction
Factor
g [−] Scaling Factor
Le [m] Entrance Length
L [m] Length of Orifice
˙
m [kg/s] Mass Flow Rate
Ma [−] Mach Number n [−] Number of Data Points P [m] Wetted Perimeter p [P a] Pressure Ra [m] Arithmetic Av-erage Surface Roughness Re [−] Reynolds Number T [K] Temperature u [m/s] Axial Velocity Component V [m/s] Fluid Velocity
Greek Symbols
Symbol Units Description
γ [−] Roughness-to-
Di-ameter Ratio
ε [m] Sand Grain
Rough-ness
κ [−] Heat Capacity
Ra-tio Λ [−] Length-to-Diameter Ratio µ [kg/m · s] Dynamic Viscosity Π [−] Pressure Ratio ρ kg/m3 Fluid Density τ N/m2 Shear Stress τw N/m2
Wall Shear Stress
Abbreviations
Abbreviation Meaning
AM Additive Manufacturing CAD Computer Aided Design
CFD Computational Fluid Dynamics DMLS Direct Metal Laser Sintering PT Pressure Tap
PLC Pressure Loss Coefficient SLM Selective Laser Melting TIT Turbine Inlet Temperature TC Thermocouple
Subscripts
Abbreviation Meaning
1 Upstream of the orifice 2 Downstream of the orifice avg Average
vc Vena contracta
t Total
Contents
1 Introduction 1
1.1 Aim and Objective . . . 3
1.2 Delimitations . . . 3
2 Theoretical Background 4 2.1 Flow Characteristics . . . 4
2.2 Thermodynamic Process . . . 5
2.3 Flow Quantities and Evaluation Quantities . . . 6
2.3.1 Reynolds Number . . . 6
2.3.2 Mach Number . . . 6
2.3.3 Discharge Coefficient . . . 8
2.3.4 Friction Factor and Surface Roughness . . . 8
2.4 Other Influencing Parameters . . . 10
2.4.1 Pressure Ratio . . . 10
2.4.2 Length-to-Diameter Ratio . . . 11
2.4.3 Hagen’s Power Law . . . 13
2.5 Boundary Layer Theory- About flows in circular and rectangular orifices 15 2.5.1 For circular orifices . . . 17
2.5.2 For rectangular orifices . . . 17
3 Methodology and Apparatus 20 3.1 Dimensional Analysis . . . 20
3.1.1 Use of Buckingham Pi-Theorem . . . 20
3.1.2 Simplification . . . 22
3.2 Test Samples . . . 23
3.2.1 Manufacturing Process . . . 23
3.2.2 Cleaning of Samples . . . 23
3.2.3 Sample Visuals, Drawings and Test Matrix . . . 24
3.2.4 Microscopic Geometry Analysis . . . 26
3.3 Test Rig and the Setup . . . 27
3.3.1 Leakage Test . . . 30 3.3.2 Functionality Test . . . 30 3.3.3 Validation Test . . . 31 3.4 Post-Processing . . . 32 3.5 Error Analysis . . . 34 4 Results 37 4.1 Viscous Flow Regimes . . . 37
4.1.1 Laminar and Transition regimes . . . 37
4.1.2 Turbulent regime . . . 41
5 Synopsis 49
5.1Effects within Laminar & Transition Regimes . . . 49
5.2 Effects within Turbulent Regime . . . 51
5.3 Comparing rectangular channels of different aspect ratio with con-stant L/D ratio . . . 53
5.4 Comparing circular channels of different materials: MA247 (AM) vs Aluminium AW-6082 T6 (Machined) . . . 54
6 Conclusions 55 7 Perspectives 57 Appendices 63 A First Appendix 63 A.1 Frictional Factor Algorithm . . . 63
A.2 Derivation for Ideal Mass Flow . . . 64
A.3 Frictional Factor Equations . . . 65
A.4 Technical Drawing . . . 66
A.4.1 Flow Distributor . . . 66
A.4.2 Rectangular Channel Drawing . . . 67
A.4.3 Circular Channel Drawing . . . 68
1
Introduction
An internal combustion engine like a Gas Turbine is used to convert the thermal or chemical energy of a fuel into useful mechanical energy. There have been significant advances in the gas turbine technology so as to achieve enhanced performance viz. durability, life and reliability. The thermal efficiency of a gas turbine largely de-pends on the Turbine Inlet Temperature (TIT) as per Brayton cycle analysis. TIT is one of the critical parameter to improve the performance of a gas turbine as with higher TITs, an improved work output and efficiencies are achieved [1], [2], [3], [4], [5]. The new age gas turbines can be exposed to temperatures as high as 1500K to 1700K [2], [6], [7].Thus, thermal stresses on the components becomes rampant when subjected to such extreme temperatures. Mechanical stresses like tensile and com-pressive stresses are also exerted due to the same reason and thus, when combined together they form a thermo-mechanical stress which aggravates the deformation of the structures thus, leading to a weakened strength and stability. Therefore, there is an immense engineering challenge to reduce the risk of damage to the serviceable life of the gas turbine components and here is where the importance of studying the cooling mechanisms come in.
The introduction of additive manufacturing (AM) has given cooling design in the gas turbine industry new possibilities. Nouveau geometries together with the surface roughness induced from the manufacturing process calls for new correlations regarding heat transfer as well as pressure losses. A minimum cooling mass flow is aspired to enhance the efficiency and this is achieved through secondary air flow systems which are designed in such a way that the system targets the fluid extraction at low pressure levels as the the cooling temperatures and the energy needed to compress the cooling air are relatively low. The scope of this master thesis will be to use an existing test rig with minor changes in the measurement instrument’s tuning to investigate pressure losses in additively manufactured rectangular holes of Nickle-base superalloy MA 247 material with different diameters and length-to-diameter ratios. Circular holes of Aluminum alloy- AW-6082 T6, manufactured through machining process will also be studied within this scope.
Recent development in material sciences for the development of micro and mini channels has opened avenues for the lattice structure transformation. Change in conventional manufacturing has also enabled to manufacture such parts using the advance materials that can with stand higher temperature than before without com-promising the mechanical integrity of the machinery. Resulting increase in efficiency and life expectancy of the components. To increase the life expectancy of the com-ponents and achieve optimal performances thermo-Mechanical stress need to be addressed and efficient cooling mechanism need to be implemented to achieve this task. The flow is extracted from high pressure compressor which is circulated in turbine casing for the purpose of cooling and a decrease of 10 degrees is enough to increase the life of the component [8].
Improvement in the lattice structure of materials is facilitating to develop ad-vance cooling technologies and claims of using adad-vance cellular structure in com-ponents can reduction temperatures up to 200 C [9]. Lattice structure is built by
putting material in straight rows and a three-dimensional periodic like a cuboid [10]. Additive manufacturing (AM) gives the liberty to manufacture components using transformed lattice materials and has proven to be very help full in manufacturing turbine blades, keeping the conventional cost low and the life expectancy high [2]. Additively manufactured blades, as shown in Fig.1, were tested successfully back in 2017 for SGT-400 and test runs were made on full-load capacity for the applications [11] and the results were good in comparison with the conventionally manufactured blades. Currently SIEMENS is using additive manufacturing for producing com-plete gas turbine burner sets and it reduces the manufacturing time up to 85% as well as the repair time for the produced burners are also reduced by 60%. These parts are manufactured for SGT-700 and SGT-800 gas turbines currently [9]. Al-though the process has evolved much more in recent years however the challenge to cater surface roughness still need to be addressed since it is an inherent property of lattice structure materials and need attention while solving problems related to secondary flow [12]. Pressure losses are indeed directly affected by surface roughness for the secondary air flow system[13]. Correct estimation of pressure losses even-tually give good prediction for the mass flow of cooling air required to have good turbine efficiency where as wrong estimation of mass flow results in poor prediction of temperature profile for the components and could result in catastrophic engine failure and loss of component. Making it essential to investigate precise pressure loses measurement for the additive manufactured components of turbine and mass flow of cooling air system [14]. Apart from AM manufactured MA 247 sample the same study will be conducted for conventionally manufactured aluminium samples with circular orifices to get an idea of the flow behaviour and an attempt will be made to draw comparisons between both the kinds. Not much literature is available though for the study of surface roughness and pressure loss measurement for the AM geometries as compared to other flat plate studies due its development nature.
Figure 1: Cooling mechanism in an AM blade.
Now, as far as the geometries of the channels are concerned, they are categorized into four based on the diameters (for circular geometries) and hydraulic diameters (for rectangular geometries): conventional channels, mini channels, micro channels, and nano channels. All the channels tested during the current study, are all with diameter/hydraulic diameter less than 3, thus, as per the literature they are classified
1.1
Aim and Objective
The primary objective is to investigate the pressure losses in additively manufactured rectangular geometries and the secondary objective being for the machined circular geometries. The focus of the thesis is to generate the desired data for the ongoing research for AM samples on Turbine cooling and later on for the purpose of analogy conventionally manufactured samples would be studied on the same parameters.
The specific aim of this study will be to investigate the characteristics of viscous flow regimes (Laminar, Transitional and Turbulent) for the provided samples which consists of MA247 rectangular orifice samples and Aluminium circular orifice samples of different diameters (hydraulic) and lengths-to-diameter ratios. These tests will be conducted at a steady state flow condition and shall involve:
• Experimentally studying the pressure losses through discharge coefficients over different pressure ratios.
• Experimentally studying the pressure losses through frictional factors and rel-ative surface roughness over different Reynolds number.
• Comparing the effects due to different aspect ratios over a constant length-to-diameter ratio.
• Drawing comparison between both the materials involved in this scope for analyzing the respective pressure losses.
• Geometric analysis of the orifice dimensions by microscopic measurement tech-niques for an understanding in the differences involved with respect to their CAD models (part of methodology).
1.2
Delimitations
Following are the delimitation of the project:
• The geometries used will be restricted to the ones provided by Siemens Tur-bomachinery AB.
• Only steady state experiments will be conducted.
2
Theoretical Background
In this section, theories relating to the viscous flows through the rectangular and circular pipes and their background shall be discussed.
2.1
Flow Characteristics
Flow through rough pipes is one of the fundamental fluid dynamics problem which the Navier-Stokes equations covers. Its non-linearity enhances the complexity of solving the Navier-Stokes equation analytically and thus, to simplify the mathemat-ical model, special assumptions are considered [15].
Figure 2: A recreated depiction of flow and pressure development in pipe flows
The flow problem here can be bifurcated into inlet, middle and outlet section where flow energy is dissipated in each part which can lead to a total pressure loss. When the fluid flow into a straight pipe geometry from a passive volume is analyzed, a flow separation can be observed to occur at the inlet stage due to the inertia of the fluid particles, as depicted in Fig.2 above. The flow does not follow the surface contour, depending upon the inlet geometry, and moreover close to the surface a region with reversed flow is formed in fact.
Fluid particles with lower kinetic energy recirculates and circumscribe the stream-lines in the core flow. The streamstream-lines which accepts the re-circulation region forms the vena contracta. The position and the size of the vena contracta depends on the applied pressure ratio (pupstreamto pdownstream) and fluid velocity, respectively. The
fluid then accelerates through the contraction along with a static pressure drop and near the surface the impulse from the core flow accelerates the fluid. Therefore, the flow reattaches, and a boundary layer is developed and a total pressure loss occurs since the flow through the vena contracta is not reversible.[Fig.2].
The amount of the losses and their origin differs between the flow states. In tur-bulent flows, the momentum exchange is increased by the increase in shear stresses and the presence of vortices. Often, non physical properties of fluid such as eddy viscosity models are used to describe the increasing resistance which are
location-found yet. With the theory of Prandtl, turbulence is formed by disturbances which among others originate at the surface and are carried into the flow. Additional losses are created as the vortices dissipate energy. Surface roughness is one key driver for the preservation of turbulence because at roughness peaks, small vortices are formed and gets transported into the core flow. All these will be explained and discussed further in the upcoming sections.
Now in laminar flows, viscosity effects being dominant does not influence the mean flow behavior due to small interruptions. Because of the adhesive condition at the wall, shear stresses are created and a velocity gradient normal to the wall ceases to exist. In total, the shear stress and the losses, are reduced relative to a turbulent flow. The pressure losses in laminar flows is linearly dependent on the velocity, in contrary to turbulent flows where a quadratic dependency exists. Because the out-flowing fluid mixes with dormant fluid and the arising shear stresses, additional losses are formed at the outlet of the pipe. Thus, all losses in total adds up and causes a total pressure loss.
2.2
Thermodynamic Process
The thermodynamic process here assumed is isentropic as by Deccer et al. [17]. It has been argued that for a fully turbulent flow regime, the dependency of the discharge coefficient can be neglected. However, regarding the influence of the axial length of the orifice on the discharge coefficient, it is as explained by A. J. Ward-Smith [16] in 1979. They also went on to mention how a flow can be treated as isentropic between the flow separation at the orifice entrance and the reattachment plane. Generation of entropy during a separated flow is shown numerically in the studies done by Abu-Nada [18]. In turbulent regimes, the rate of dissipation of energy is much higher compared to that in the laminar regimes, because of the formations of eddy viscosity. Thus, there is no constant entropy. The flow here through an orifice is assumed to be isentropic for the current study though.
A frictional adiabatic flow theory by Fanning [19] was explained to deduce the relationship between pressure drop (∆P) and wall shear stress (τw) for a
one-dimensional pipe model as described in Eq.1.
fFanning= ∆P 4DLρV22 = τw ρV2 2 (1)
Another major friction factor in fluid dynamics is the Darcy-Weisbach friction factor [20], [21], [22]. Eq.2 fD= ∆P L D ρV2 2 = τw ρV2 2 (2)
It can be noted that both the friction factors has a connection as in the Darcy-Weisbach friction factor is four times larger than that of Fanning’s as depicted below in Eq.3. But for the current thesis study, only Darcy-Weisbach friction factor will be used.
2.3
Flow Quantities and Evaluation
Quanti-ties
The phenomena that appears in the pipe flows can be tracked back to the values of Reynolds, Mach numbers, Discharge Coefficients and Frictional Factors. They are explained further in the following subsections.
2.3.1
Reynolds Number
Reynolds number is one of the most important dimensionless quantities while com-paring fluid dynamic problems as it is a function of the primarily influencing pa-rameters. Out of the two flow regimes, Laminar flows are characterized by steady, smooth streamlines and highly ordered motion while Turbulent flows are identified by highly disordered movement and rapid velocity fluctuations. The transition from laminar to turbulent flow is known as a transition flow. This is where a dimensionless (Reynolds) number is used to distinguish between laminar and turbulent pipe flows. This is named after the British scientist and mathematician Osborne Reynolds (1842 - 1912). It is described as the ratio of the inertial forces and frictional or viscous forces. This is depicted below in Eq.4.
Re = inertialf orces viscousf orces =
ρVD
µ (4)
D here represents the characteristic length of the problem for a circular pipe or tube. And for non-circular pipe D is replaced by Dh which can be determined as in Eq.5;
Dh =
4A
P (5)
Now depending on the set-up, critical Reynolds Number range can be found, at which even a small disturbance in the flow can lead to a laminar to turbulent flow transition. Beyond this critical value, the flow is considered to be fully turbulent and the characteristics of boundary layer features, transport mechanisms and heat transfer within the flow change [12]. For perfusion problems, the transition state in most of the literature is defined at Re= 2300 [23] but for mini and micro tubes the range that is altered for < 10, the range could be around Re= 1000 and Re= 5000 [24], [16], [25].
2.3.2
Mach Number
Now this is another important flow quantity which describes the relationship between fluid velocity V and the local speed of sound c and is represented by M a (Eq.6). This is one of the parameters in this area of study to evaluate the pressure losses of
M a = V
c (6)
And the velocity of sound c can be given by the Newton-Laplace’s equation (Eq.7).
c =√kRT (7)
Mach number can also be expressed in terms of pressure ratio for an isentropic flow (Eq.8). Π = 1 +k − 1 2 M a 2 k−1 k (8) When the velocity of the flow gets equal to the sound velocity the pressure ratio can be termed as critical (Πcrit)[21]. The flow becomes sonic (Ma=1) when the
pressure ratio touches or crosses the critical pressure ratio and that depends on the specific heat ratio of the flow (k) which equal to 1.4 for air. (Eq.9) shows how the critical value of the pressure ratio for air can be calculated;
Πcrit =
k + 1 k
k−1k
= 1.8929 (9)
Now when the pressure ratio exceeds this critical value i.e 1.8929, the Mach number will always be unity at the vena contracta [16]. The ideal mass flow is determined by the following equation (Eq.10)
˙ mideal= Apt √ Tt r k RM a 1 +k − 1 2 M a 2 −2(k−1)k+1 (10) And when Ma=1 i.e. the mass flow becomes maximum (Eq.11);
˙ mmax= A√vcpt Tt r k R 1 +k − 1 2 −2(k−1)k+1 (11) From the above details specially from (Eq.11) it can be concluded that the nec-essary conditions for a chocked flow are constant values of stagnation pressure (pt)
and constant values of stagnation temperature (Tt) apart from the constant values
of the cross-sectional area of the vena contracta (Avc). Now when Mach number
be-comes greater than 1 then the flow travels faster than the sound speed i.e. bebe-comes supersonic. But the flow field (with density and pressure) experiences upstream expansion from its source. When the Mach number becomes less than 1 i.e. when the flow is subsonic, the upstream conditions are still influenced by the flow distur-bances. Another characteristic value, Ma = 0.3 is emphasised by the literature, as the compressibility effects for the gases can be ignored and thus, the density can be set as a constant value [26], [27]. In the current investigations here, it is in the interest to observe the flow behaviours at low speeds as well, and thus, the density is not kept constant as the compressibility effects are taken into account.
2.3.3
Discharge Coefficient
Another parameter that helps evaluate the flow quantities is the discharge coefficient. This will be helpful in describing the losses in single components. An isentropic, one-dimensional flow between an inlet (1) and an outlet (2) can be compared by the actual, compressible flow with this dimensionless parameter. Discharge Coefficients are commonly used for flow measurements and flow restrictors. This is calculated for a constant cross sectional area geometry and can be defined as the ratio of the real mass flow ( ˙mreal) and the ideal mass flow ( ˙mideal) (Eq.12) [28].
Cd = m˙real ˙ mideal
(12)
The Boundary layers and/or the recirculation areas arises due to the presence of viscous effects near the walls and thus, it narrows the cross sectional area of the core flow. Therefore, the discharge coefficient will always be less than unity. Now to calculate the ideal mass flow in Eq.12, the boundary conditions here is reversible and adiabatic in nature so that the total pressure (pt,1), and the total temperature
(Tt,1) remain constant. The ideal mass flow ( ˙mideal) can be calculated with the static
pressure (ps), total pressure (pt), total temperature (Tt) , and cross section area (A).
Eq.13 below states the relation.
˙ mideal= Apt,1 ps,2 pt,1 κ1 v u u t 2κ (κ − 1) RTt,1 1 − ps,2 pt,1 κ−1κ ! (13)
And the discharge coefficient is calculated by the following Eq.14;
Cd= ˙ m Apt,1 p s,2 pt,1 1κ s 2κ (κ−1)RTt,1 1 −ps,2 pt,1 κ−1κ (14)
However, the area is mentioned as effective area in the literature where it is derived similarly. The ideal cross section area is though calculated with the actual mass flow and is compared to the geometrical area. [29].
2.3.4
Friction Factor and Surface Roughness
The parameter of friction factor describes the pressure losses along a pipe and is dependent on the fluid-surface interaction. The viscosity has a greater influence in laminar flows and the layered structure of the flow ensures that the flow gets no major global impact due to the roughness peaks. [30].
Now when a turbulent flow is concerned, near the surface a concentration of sublayer can be observed, which is due to the viscous effects. The thickness of the sublayer determines the enhancement of turbulence due to the roughness peaks and hence the pressure loss. The peaks are fully covered by the sublayer, in case of a smooth surface, and the turbulence is only formed within the core of the flow. Depending on the Reynolds number, two correlations were published by Blasius and
In case of an increase in the flow velocity, the viscous sublayer gets depleted. At this stage, the Darcy-Weisbach friction factor (fDarcy-Weisbach) is evaluated by the
Colebrook formula [33] as depicted through Eq.15 along with its range in Eq.16. This friction factor is a function of the Reynolds number (Re) and the relative surface roughness (ε/D). fDarcy−W eisbach= 1 2 log 2.51 Re√fDarcy−W eisbach + 0.27 D/ε 2 (15) 25 < ε DRe 0.875 < 350 (16)
The roughness peaks in case of high velocities does not gets covered by the viscous sublayer and thus, significant pressure losses are created due to the vortices generated at the roughness peaks. Now, eq.17 illustrates the postulation done by K´arm´an where a relation of Darcy-Weisbach friction factor (fDarcy-Weisbach) for turbulent
flows through rough pipes with the surface roughness (ε/D) is done [30]. The range of the turbulent region is shown in Eq.18.
1 pfDarcy−W eisbach = 1.74 − 2 log 2ε d (17) ε DRe 0.875 > 350 (18)
Now the friction factors calculated are averaged because of the fact that the tem-perature of the fluid varies along the pipe due to friction and so thus the Reynolds Number and viscosity. [34].
The Fig.3 depicts the Moody chart where Colebrook and Moody has summarized all the observations and the experimental results derived from the authors men-tioned before like Blasius, Prandl and K´arm´an in a double logarithmic diagram. In this diagram, the Darcy-Weisbach friction factor (fDarcy-Weisbach) is plotted against
the Reynolds Number and the relative roughness (ε/D). Colebrook and Moody in their experiments created different relative roughnesses using sand, thus, the rela-tive roughness in the diagram is more that of relarela-tive sand-grain roughness. The diagram is segregated into four different regions (laminar, critical, transition, fully turbulent) and the influence on the friction factor varies according to the previous discussion.
Now as discussed earlier surface roughness has a significant impact on pressure losses in additively manufactured or machined parts and two different terminologies are used to describe them viz., arithmetic mean surface roughness (Ra) and sand
grain surface roughness. The former is calculated with the help of known values of mean surface height and the later is an artificially generated surface roughness on the inner wall of the pipe by gluing uniform sand grains of a known diameter size (ε) and is always described as dimensionless parameter (ε/D). It is not directly a physical or a natural surface roughness but they are equivalent and hence, also termed as equivalent sand grain surface roughness [35]. However, in this thesis, no attempts are made to measure the values of Ra. Alternatively, only the relative surface roughness has been approximated through an empirical formula like Darcy-Weisbach friction factor (fDarcy-Weisbach).
Figure 3: Moody Chart recreated in MATLAB to estimate the relative roughness
2.4
Other Influencing Parameters
Besides the flow parameters as discussed in the above sections, pressure losses are also influenced by the pressure ratio and geometrical parameter like the length-to-diameter ratio on the pipe flow. Choking and Hagen’s power law are other parame-ters that shall be discussed. Choking since, is very much related to the cross-sectional geometry of the orifice, it has been discussed along with the length-to-diameter ra-tio and Hagen’s power law which was a key to differentiate between laminar and turbulent regimes, has a dedicated part on its own. These are all discussed in the following sub-sections:
2.4.1
Pressure Ratio
It is defined as the ratio between the upstream pressure (pupstream) and the
down-stream pressure (pdownstream) as shown in Eq.19.
Π = pupstream pdownstream
(19)
The flow behavior, through Brain and Reid’s literature [36], it was observed that it is independent of the variations of upstream or downstream pressure. H¨uning [23], was another who ascertained that the discharge coefficient can increase with an increasing pressure ratio and Ward-Smith [16] asserted about the widening of the vena contracta for this behavior. Deckker and Chang [19]O along with H¨uning
ratio. Now since, no total pressure drop exists for an isentropic, one dimensional flow, and the downstream pressure equals the static pressure (Eq.19), the velocity get choked at a critical pressure ratio of ΠCrit.=1.893. Furthermore, for short orifices
early choking is observed for L/D > 2. [37], [18], [8]. The static pressure within the orifice however, drops and recovers again after the minimum cross section. This pressure recovery inside the orifice would be the responsible factor for an early choking. Thus, generally, total pressure loss is present in a polytropic process as the choking seem to occur beyond the critical pressure ratio. In this thesis however, the readings for the samples were taken above the critical pressure range and some chocking was observed.
2.4.2
Length-to-Diameter Ratio
The length-to-diameter ratio is an integral parameter that can affect the discharge coefficient. It is represented by the mathematical Eq.20;
Λ = L
D (20)
Now according to Ward-Smith [16], three characteristics have been studied which are; for the short pipes (Λ < ΛWS-L), the plane of the vena contracta moves upstream
as the flow velocity increases, thus, separating the flow. If the flow reattaches at the upstream edge it reaches maximum contraction, thus making the flow velocity go sonic (Fig.4a). In case the channels that are within the lower and upper Ward-Smith limit (ΛWS-L< Λ < ΛWS-U), the conditions for reattachment shall be fulfilled
if the sonic conditions are approached and at the plane of vena contracta, flow seperation and chocking can be observed (Fig.4b). When the case is higher than the upper Ward-Smith limit (ΛWS-U < Λ), the flow completely develops while the
the frictional effects starts to happen. Thus, at the outlet plane choking can occur to the flow when it is between the upstream and downstream pressure for a certain pressure ratio (Fig.4c) .
For inlet orifices with sharp edges, the lower limit that the Ward-Smith suggested was between Λ = 0.3 and Λ = 1 and where as the upper limit would be between Λ = 7 and Λ = 10. Parker and Kercher [38] in contrast, tells that anything above Λ= 2 would be the upper limit. But generally, the exact values are dependent on the pipe’s surface roughness. [39]
Here, in this area of study though the channels consists of much longer length-to-diameter ratios and the number of literatures available for them specially for additively manufactured ones are quite scarce. Nevertheless, H¨uning [23] though compiled and compared many test results from open literatures and various CFD calculations and concluded that, for the downstream, pressure recovery was observed in the orifices and the reattachment of the flow were observed. This was for long channels though, with L/D > 2. The increase in the discharge coefficient for the channels was ascribed to the recovery of the dynamic pressure and the decrease in the same was ascribed to the increase in length-to-diameter ratio and the frictional factor.
Experimental investigations were performed by David [12] to probed the dis-charge coefficient for additively manufactured (Inconel 939 material) sample chan-nels with length-to-diameter ratio up to 100. After observing the results, it would
Figure 4: An inspired and recreated depiction of the flow at vena contracta and sub-sequently, its choking
be safe to conclude that they range up to the conclusions from that of the read lit-eratures, as the discharge coefficients did decrease as the length-to-diameter ratios were increased from 15 till 100. His explanations for such behaviour was backed by the flow re-attachment within the channels as also explained and discussed about such restricted flows in the papers by Ward-Smith [16].Hay and Spencer [40], also had a similar conclusions as that of H¨uning [41]. David’s experimental results can be seen in Fig.5 below.
Figure 5: How discharge coefficient is dependent on length-to-diameter ratio at con-stant pressure. [12]
Moreover, W. F. McGreehan and M. J. Schotsch [42], also showed in their study that for length-to-diameter ratios up to 10 and Re ≥ 10,000, a decreasing trend is seen in the flow’s discharge coefficient with an increasing Λ. This was based on the already then existing empirical data and calculations of the net Cd,long−orif ice
number affects the discharge coefficient of an orifice for a plenum-to-plenum flow (β = 0) [8]. The equations used for these calculations are as follow Eqs.21, 22, 23;
Cd,long−orif ice= 1 − g(1 − Cd,sharp−orif ice) (21)
Where, g = [1 + 1.3e−1.606(L/D)2](0.435 + 0.021L D) (22) Cd= 0.5885 + 372 Re (23)
2.4.3
Hagen’s Power Law
This law establishes a functional relationship between two quantities, where a rela-tive change in one results in a proportional relarela-tive change in the other while being independent of the initial size of those quantities. In other words, one quantity varies as a power of another. Thus, with respect to the studies here, Gotthilf Hein-rich Ludwig Hagen [43] proposed a mathematical relation that identifies the flow regimes in terms of pressure drop and velocity as in how a change in pressure is directly proportional to certain velocity. In 1839 he mathematically differentiated the Laminar and Turbulent flow regimes which are stated in Eqs.24, 25;
Laminar regime : ∆P ∝ V (24)
T urbulent regime : ∆P ∝ V1.75 (25) The pressure drop in Eq.24 is directly proportional to the fluid velocities only upto 1.1 ft/sec though. In case the velocity crosses the 2.2 ft/sec mark, a rather sharp pressure drop can be observed and as in Eq.25, the proportionality will be nearly quadratic with the velocity. This was particularly explained by Paul Richard Heinrich Blasius [35], who also came up with the Darcy-Weisbach friction factor and Reynolds number’s correlation (Eq.26).
fD = 0.316Re0.25; 4000 < Re < 10000 (26)
Now with the Darcy-Weisbachˆas formula for friction factor (Eq.27), a power relationship for the Laminar regime (∆P ∝ V ) can be derived as following (Eqs.28, 29, 30, 31 and 32) [35]. ∆P = fDh L Dh ρV2 2 (27) fDh= 64 Re (28)
Here, the geometry can be of diameter D or hydraulic diameter Dh depending on
the shape of the orifice in question.
∆P = (64 Re) L Dh ρV2 2 (29)
∆P = ( 64µ ρV Dh ) L Dh ρV2 2 (30) = 32µLD−2h V (31) ∆P ∝ V (32)
Now, the power relationship for a turbulent regime (∆P ∝ V1.75 ) is derived as following (Eqs.33, 34 and 35) [35].
∆P = 0.316( µ ρV Dh )0.25 L Dh ρV2 2 (33) = 0.158Lρ0.75µ0.25Dh−1.25V1.75 (34) Hence, ∆P ∝ V1.75 (35)
Figure 6: A refurbished plot depiction from Hagen’s data [44] illustrating the experi-mental proof of the flow regimes.
The above graph (Fig.6) illustrates the variations of pressure drops against fluid velocity for laminar and turbulent regimes. And the transition regime thus, lies in a range of V < ∆ P < V1.75
2.5
Boundary Layer Theory- About flows in
circular and rectangular orifices
As per the boundary layer theory there can be two layers in a flow viz. a thin layer (boundary layer) near the wall, with dominant viscous effects, and an outer layer, with negligible viscous effects which can be resolved by Euler and Bernoulli equations. This theory was developed by Ludwig Prandtl in circa. 1904 and are all summarized in [26] [43] [45].
Now when a fluid enters a pipe, the velocity of the fluid particles in contact with the solid wall i.e. at the surface of the pipe is zero. This is because of the no-slip condition, and because of which the layer of fluid particles facilitates the deceleration of its adjacent layers. The velocity gradients here is developed normal to the direction to the flow. Though the velocity gradient is confined within a small distance from the solid’s surface beyond the range of which the fluid flow almost approaches the initial uniform velocity thus, making it an asymptotic approach towards free stream velocity. According to the continuity equation, for a given section of the pipe, the average velocity (Vavg) of the pipe remains constant as
the rate of mass flow ( ˙m) remains constant. Therefore, the velocity of the core is accelerated so as to balance out the reduction in velocity that takes place in the boundary layer.
Fig.7 below depicts the velocity boundary layer development in a pipe.
Figure 7: An inspired and recreated depiction of the velocity boundary layer develop-ment and the variation of wall shear stress in the fluid flow direction across a pipe.
Viscous forces and velocity gradients are important in the boundary layers. Now as we can see from above, the velocity profile is almost uniform with negligible viscous effects in the second layer. This is the irrotational (core) flow region. As the velocity gradient (∂u∂y) gets almost to zero, the shear stress disappears due to adverse
pressure gradient. Thus, making the fluid behave like an inviscid flow even if there is fluid viscosity. This viscosity is present because the influence of the shear stress is confined within the boundary layer as it goes on to maximum from the core of the flow to the solid surface. See Eq.36
τ = µ∂u
∂y (36)
Now as shown in Fig.7 the boundary layer thickness (δ) increases in the fluid flow direction and after a particular distance, the circumferential boundary layer merges with the pipe’s axis and fills up the entire pipe section i.e. making the flow uniform. Beyond this, the whole flow region is the boundary region where the order of magnitude of the viscous force is equal to the order of magnitude of the inertial force, thus, making the flow termed as a fully developed flow. Here, there is no change in the velocity profile, making the wall shear stress remain constant through out the region.
The region (of a certain length Le called the entrance length) between the fully
developed flow and the pipe inlet can be termed as a developing flow region where the velocity profile is developed. Here, any change in the wall shear stress depends on the change in the velocity gradient. Now the boundary layer thickness is smallest at the entrance of the pipe thus, making the wall shear the highest there. A relationship between the dimensionless wall shear stress and the friction factor can be given by the Darcy-Weisbach’s formula Eq.37.
fD =
8τw
ρv2 (37)
Now to obtain the value of the entrance length (Le) in Fig.7 can be little difficult.
But, an empirical formula can be used to calculate an approximation. Eq.38 depicts for the Laminar regime. [46] [47]
Le,laminar ∼= 0.05ReD (38)
The entrance length (Le) in the case of a turbulent regime is much shorter as
its dependence on the Reynolds number is less. Thus, the formula to determine its approximation is given in Eq.39. [48] [46]
Le,turbulent ∼= 1.359Re1/4D (39)
The above approximations discussed are more accurate for the longer pipes than that for their shorter counterparts mainly due to the dominance of wall shear stress and friction factor in shorter flows.
2.5.1
For circular orifices
For a fully developed laminar flow regime, the velocity profile tends to be parabolic in nature with its maximum at the pipe’s centerline and minimum (zero) at the solid wall as seen in Fig.7. Darcy-Weisbach’s formulation that can also be referred as in Hagen-Poiseuille equation (Eq.40) shows how frictional factor is a function of just the Reynolds number and is independent of the surface roughness of the pipe.
fD =
64µ ρDV =
64
Re (40)
For a fully developed turbulent flow regime, the velocity profile tends to get flatter with a sharp drop near the solid surface as seen in the developing flow region section of Fig.7. Here, due to the fluctuations in the velocity of the flow the turbulent shear stresses are also developed besides the viscous shear stresses. Moreover, Eddies being in much higher proportion, the losses due to them affects the kinetic energy too. They disappear at the wall due to the no-slip condition. Now since, the velocity gradient is larger at the wall, the wall shear stress is higher in turbulent flow regime in contrary to that of the laminar flow regime. The velocity profile can also be seen to get more flatter near the wall surface with increase in the Reynolds number. But the protrusions of the surface roughness are still submerged under the viscous sublayer, which is the layer right next to the wall surface. Thus, raising no significant impact of surface roughness if the thickness of the boundary layer is enough. But in case of the boundary layer becoming so thin that the viscous sublayer which is right next to the wall almost vanishes and bringing the boundary layer in contact with the protrusions of the surface roughness, flow will then become fully rough turbulent. Therefore, in this regime, the friction factor depends only on the surface roughness of the pipe. Deeper study on the surface roughness hasn’t been done in this scope of thesis and the parameters are considered from the existing data on the surface roughness based on the material.
2.5.2
For rectangular orifices
With all the governing equations of fluid motion applicable to the rectangular ori-fices which are based on hydraulic diameter approximations, the Darcy-Weisbach’s formulation for frictional factor explains about Reynolds number being the only fac-tor that has an impact on pressure losses. For a fully developed laminar flow (which is the consideration taken for this scope of thesis throughout), the velocity profile tends to be parabolic in nature. Now the expression for the subject in discussion here can also be referred as Hagen-Poiseuille expression (Eq.41) [45].
fD,Laminar = Cµ ρDhV = C ReDh (41)
In the above equation the value for the variable C depends upon the aspect ratio (width/height) of the rectangle geometry and in laminar flows the hydraulic diameter is a decisive factor apparently. See Fig.8 for a pictorial depiction and Table in Fig.9 for frictional factors for different aspect ratios.
Figure 8: Aspect Ratio for a rectangular orifice
Figure 9: Friction factor for fully developed laminar flows based on aspect ratio [45]
For fully developed turbulent flows through a circular pipe, the relation of the frictional factor and the aspect ratio is mathematically expressed in Eq.42 (Pipe law formula). The same formula is used for non-circular pipes, just that the value of fD
will vary according to the aspect ratio (Fig.9) . [43] 1 √ fD = 2.0 log0.64 ReDh f 1/2 D − 0.8 (42) From the above equation it can be made out that the effect of the frictional factor and aspect ratio is eminent for non-circular pipes (with a difference of ±10%) for turbulent flow regimes. The effective hydraulic diameter (Def f) used here gives
a much better approximation of the frictional factor. From the table above in Fig.9 which is from the laminar theory, the effective hydraulic diameter can be estimated by the following relation in Eq.43 [49], [21]
Def f = Dh 64 LaminarT heory = Dh 64 fDRe = Dh 64 C (43)
Now the wall shear stress in a rectangular cross-section is seen to be a dominant factor for laminar flows. [22]. The shear stresses varies here in the fashion of being maximum at the centerline of the geometry and being zero at the corners. The wall shear stress is relatively constant along the side walls but a sharp drop can be observed at the corners, thus, making the significance of the secondary flow even more in turbulent flows.[50][21]. This phenomenon of secondary flows are illustrated as non-zero mean velocities which are normal to the fluid flow direction. Fig.10 shows the same with the plane of symmetry being the axis b − b. [51] [21]
Figure 10: Qualitative depictions of secondary turbulent flow cells in a rectangular cross-sectional geometry. Here (a) is the axial mean velocity contours and (b) is the secondary flow cellular motions normal to the fluid flow direction. A recreated image.
These cells as in the figure above can be seen driving the mean velocity toward the corners. Thus, making the velocity contours identical to that very section of geometry and leading to a nearly constant wall shear stress along the side walls. Also, for laminar flows, no secondary flow cells are formed through the rectangu-lar geometry. Therefore, as a conclusion with all these observations, no accurate theoretical solution can be attained for the phenomenon of secondary flows. [21]
3
Methodology and Apparatus
This chapter shall be covering the methods and the apparatuses employed to garner the experimental results for the pressure losses. They are categorically elaborated in the following subsections:
3.1
Dimensional Analysis
3.1.1
Use of Buckingham Pi-Theorem
A total of 11 different physical variables are involved that influences the pressure losses in the orifice where all the phenomenon of the flow through an orifice can be understood better from Fig.11. These 11 variables can be characterized by (i) kine-matics parameters, i.e. velocity and acceleration, (ii) fluid properties, i.e. density and viscosity, (iii) geometry of the orifice, i.e. length, diameter and height, and (iv) dynamic parameters, i.e. pressure, stress and energy.
Figure 11: A recreated depiction of an orifice sample that influences the pressure loss with all considered variables [52]
A method is used to apply dimensional analysis using Buckingham Pi-theorem for evaluating frictional characteristic in orifice [53]. Now as per the theorem the implicit functional relationship of m number of independent variables like x1 ,x2,. . .
xm can be given as;
f (x1, x2, . . . xm) = 0 (44)
This functional relationship can be explained in terms of independent non-dimensional parameters (m − n) also, where n is the number of fundamental di-mensions like mass (M), length (L), time (T) and temperature (K), all of which are are involved in these m number of variables. Thus, Eq.44 can be rendered as;
F (π1, π2, . . . πm−n) = 0 (45)
Here, πi represents the Pi term (or Pi group) in Eq.45. The mathematical
π1 = xa11 .xa22 ...xann .xn+1 (46)
π2 = xa11 .xa22 ...xann .xn+1 (47)
...
πm−n = xa11 .xa22 ...xann .xm (48)
A dimensional matrix is created in the next step to seek the exponent aiand the
π-term with the help of physical quantities and fundamental dimensions which are showcased in the table in Fig.12.
Figure 12: Dimension matrix of physical quantities
All the fundamental dimensions which are the necessary conditions for the Pi-theorem are included in this matrix. These variables are expressed in terms of π by using Eqs. 46, 47, 48 and with those seven different π terms are obtained as cited in Eqs. 49 to 55. π1 = p1 ρV2 (49) π2 = p2 ρV2 (50) π3= T2 T1 (51) π4 = µ ρDV = 1 Re (52) π5 = Cs V = 1 M (53) π6 = L D (54)
π7 =
Ra
D (55)
3.1.2
Simplification
The above Eqs.49 to 55 as stated are non-dimensional set of π terms which illustrates the dimensional similarity of a flow through the orifice. These values are all interde-pendent even though they can be identical. Now another non-dimensional number, which is the pressure ratio (Π), as depicted in Eq.56, can be obtained by dividing the Eq.49 with Eq.50, which in turn would be the first parameter that determines the dependency of the discharge coefficient. Now with the pressure ratio along with the geometry of the sample, Mach number can be determined from Eq.53 [26][43]. The experimentation here is conducted in an adiabatic manner thus, enabling the temperature ratio to be neglected (π3 = 1) for simplification.
Π = π1 π2
= p1 p2
(56) Reynolds number influences the discharge coefficient of the orifice such that if it is greater than 200000, the dependency of the discharge coefficient on the Reynolds number would be very weak [54]. Some experiments by others even suggests that the discharge coefficient remains unaffected for Reynolds number greater than 10000 [17][42][36]. In real life gas turbines, the Reynolds number for orifices is always higher than 10000 though [12][11][55]. Reynolds number in this scope will be disregarded. Now surface roughness is another effect of significance which is quite inherent to the Additively manufactured components but is quite less as compared to the plain machined aluminium components [13][56]. During the experimentation here a non varying roughness-to-diameter ratio (π7) whose influence on pressure losses is
char-acterized in terms of friction factor.
Cd= f π1 π2 , π6, π7 (57) Cd= f p1 p2 , L D, Ra D (58)
It can be thus, concluded that the discharge coefficient is dependent on three non-dimensional quantities (Eq.57,58) which are represented in Greek letters as-signed to the π terms as shown in Eqs.59,60,61.
Λ = L D (59) Π = p1 p2 (60) Υ = Ra (61)
3.2
Test Samples
This section shall cover the test samples used for the test in this scope of thesis. This shall include brief information about the manufacturing process used for the understanding of the nature of samples dealt here, test matrix used over this scope of study and the importance of cleaning of the samples before their use.
3.2.1
Manufacturing Process
For the AM samples used in this scope are all manufactured by SLM i.e. Selective Laser Melting technique. For all AM processes the process starts with a 3D CAD (Computer Aided Design) geometry followed which it goes into the actual print-ing/manufacturing. This occurs through a ”layer-by-layer” approach of material in powder form on the building platform while selected regions are melted with high laser power. After the melting, the building platform is lowered and a coater spreads new layer of the powder across the building platform. This cycle is repeated until the complete part is built and consequently in the end the object in the desired shape (cylindrical tubes with rectangular holes) is revealed once the remaining pow-der material is removed.
Now the Aluminium Alloy samples were manufactured by machining process like turning in a lathe and drilling circular holes from both the end (only for longer samples). It is to be noted that no involvement was there for the manufacturing processes in this scope of study but enough data is easily available on the internet over these conventional manufacturing processes and thus, no further details about them would be worth discussing here.
It is worth noting though that Additive Manufacturing technology have opened the doors for a cost effective and a time saving manufacturing while giving access in cre-ating smaller parts and complex designs with substantial accuracy levels in contrast to conventional manufacturing techniques. [57][58][59]
3.2.2
Cleaning of Samples
For a successful usage of parts in fluid dynamic systems, proper cleaning is critical so as to get the data readings as less distorted as possible. The motive behind the cleaning process is to remove any debris from the internal channels or passages of the parts. For a machined part the cleaning is quite done during the milling or drilling process itself but can be further dusted off with high pressure air or sanding and the parts are ready to use. But for AM parts, metallic powders are eminent within the channels, thus leading to using ultrasonic cleaner devices like the Sonic 3000. T-sprite is used as cleaning agents in which the test samples were completely immersed. Each test sample is cleaned four times for ten minutes and while this goes on, the temperature is not supposed to exceed beyond 40◦ as per Siemens0 guideline procedure. Later on the samples are dusted off with high pressure air for any foreign debris by the user.
3.2.3
Sample Visuals, Drawings and Test Matrix
After the manufacturing, the samples would look like as depicted in Fig.14 below;
Figure 13: Visuals of the real life samples used for the experiment. ’a.’ and ’b.’ are the machined Aluminium Alloy- AW-6082 T6 Samples and ’c.’ and ’d.’ are additively manufactured MA 247 samples.
Draft drawing depicting an idea of the cross sectional view for the rectangular sam-ples and circular samsam-ples can be seen in Fig.14 and Fig.15 respectively.
Figure 14: Draft drawing of the rectangular orifice AM samples with side view and top view of the cross-sectional area.
Figure 15: Draft drawing of the circular orifice Aluminium samples with side view of the cross-sectional area and a 3D view (Depicted here is of the sample with aspect ratio 30).
Fig.16 below illustrates the table of the test matrix of the samples that were utilized where Λ being the L/D ratio and Dh being the hydraulic diameter or just diameter,
depending on the geometry of the orifice. It is also worth highlighting again that all the measurements were taken as per the CAD dimensions through out the experi-mentation.
3.2.4
Microscopic Geometry Analysis
It is quite evident for an AM process to levee higher surface roughness compared to the samples that were machined. This was one of the key reasons for the motivation to cross verify the dimensions of the inlet and outlet orifices under a microscope in order to gain a clearer picture of the surface roughness visuals and how close the di-mensions of the geometry would be compared to their CAD counter-parts. With the help of Carl Zeiss Axio microscopic instrument detailed imaged and measurements were made possible as seen in Fig.17.
Figure 17: Examples of microscopic images with detailed measurements of inlet ge-ometry of one sample from each set, done with the inbuilt tool of the instrument0s software.
Now with these observations and the newly collected data, new diameters/hydraulic diameters were found, which apparently, varied slightly with respect to the original CAD data. The length of the samples were measured with physical scales and vernier caliper to the result of which there was no change in the dimensions with respect to the original data. Thus, Fig.18 illustrates a table for the newly verified data under microscope. Note the minor changes in the aspect ratio in each set of the sample as compared to one standard L/D ratios (Λ) for all the sample sets in the original data.
Figure 18: Test Matrix with microscopically analysed data.
3.3
Test Rig and the Setup
Below is the picture of the test rig deployed for the current scope of study. Fig.19;
Figure 19: Test Rig.
The centralized pressure system 1 of the rig 7 is connected to the Coriolis meter 4
, a ball valve 2 and ultimately through a pressure reducing valve 3 . All these are depicted in a schematic diagram of the rig setup in Fig.20. Throughout the flow path, all different components of the test rig, are connected with a flexible hose pipe. The manual ball valve is used for controlling the ’on’ and ’off’ and thus, its position is somewhat about ”open” or ”close” as per the requirement. The pressure reducing valve 3 is purposed for reducing the pulsations transferred from the main air supply
system into the flow thus, maintaining a nearly constant upstream pressure of the mass flow.
Figure 20: A schematic diagram of the Test Rig setup.
In the test rig, the Coriolis meter 4 is used for measuring the mass flow rate of air which measures with the help of the vibrating tubes inside the meter (Fig.21). Therefore, the main reason for employing flexible hoses for interconnecting different instruments for the rig is to avoid the transmission of vibrations due to any ham-mering effect by the motion of the fluid to the Coriolis mass flow meter. It also helps in preventing any vibrations from being transmitted downstream to the mass flow meter through the vibrating tubes. The downstream pressure is manipulated by the pressure regulating valve 5 and is followed by a safety valve 6 . The safety valve is rated for 4 bar absolute pressure for safety purposes, even though the maximum working pressure of the secondary air flow system is limited to 2.5 bar [55], [12]. Further on from here, the air is supplied to the pressure vessel 7 which consists of a large cylindrical cavity with an inside diameter of 330.2mm and a length of 500mm.
Figure 21: The deployed Coriolis meter. Model: Siemens SITRANS FC300 DN 4.
drical cavity as seen in Fig.19. The purpose of such a design is to maintain the pressure equal to the total pressure, thus, achieving the plenum condition (zero flow velocity) inside the pressure vessel. The vessel itself has an inner diameter of 330.2 mm and a length of 500 mm. On the working side of the vessel, i.e. where the test object is mounted ( with brown lid), a thermocouple and three pressure taps are attached to the cover plate whereas one pressure tap and a thermocouple is attached on the non-working side of the vessel, i.e. the opposite side of the test object mount (with blue lid). The N type thermocouples are around 150mm and 136mm away from center-line of the vessel geometry, respectively whereas the pressure taps on the working side of the vessel are located at 160mm, 140mm, and 120mm distance from the center-line respectively. The measuring devices are all connected to the data acquisition unit but the pressure taps are connected to pressure scanner module; NetScanner Model 9116 (Fig.22).
Figure 22: Pressure scanner module; NetScanner Model 9116, with pressure tap pipes engaged.
Ethernet is used connect the data collection units to the computer. An in-house software called RigView which is based on LabVIEW, records and collects all the data. MATLAB is then used for calculating and plotting the results and trends of the needful parameters. The Coriolis meter was re-calibrated in order to achieve higher mass flow rates (upto 4 g/s), in contrast to the previously performed experiments. The intention of experimenting with high mass flow rates were to observe the trends at high pressure ratios.
Now here two different pressure channels of pressure scanner module were used in order to limit the measurement error in the pressure to a minimum. Fig.23 illustrates a table about the range of every measurement setup employed. Special care has been taken to ensure at least two measurement points are being overlapped between one setup and the other.
3.3.1
Leakage Test
Once the rig was setup, a leakage test is critical to check the proper functioning of the rig. In order to do so, the rig is to be pressurized upto 2.5 bar and then soap water is sprayed across the pressure taps, thermocouples, bolt joints of the rig, orifice plate mount and the sample holder. In case of a leakage the soap water shall create bubbles/foam around the leakage area (Fig.24).
Figure 24: Rig front where the sample is mounted and leakage test being done. (Notice the soap bubbles around the bold joints.)
In case any leakage is found then the vessel needs to be depressurized again and the needful area is to be removed, cleaned, and fitted back again properly with sealing tapes around the bolts and petroleum jelly over the bolts and washers. It is important that the samples are fitted to the orifice plate carefully and completely. If there is no sign of bubbles are seen then the rig can be considered as fit to take on the pressure integrity test. A couple of previously tested sample are chosen for validating the the readings. If everything goes by the standard operating procedures, the readings, like the coefficient of discharge, will be in good agreement with the previous results and the testing can be resumed.
3.3.2
Functionality Test
The purpose of this test is to check the functionality of the Coriolis mass flow meter and the pressure scanner module even if all the instruments are calibrated. Highway Addressable Remote Transducer (HART) communication protocol is deployed for transmitting the analog signals from Coriolis mass flow meter to the data acquisition system. The calculations of the coefficients of the polynomial equation (Eq.62) in the range of 0 g/s to 4 g/s is necessary for this scope of experimentation. The Coriolis mass flow meter is subjected to a forced input of current values between 4 mA and
Coefficients C0 and C1 are calculated through the first degree of the polynomial
equation and the values of the coefficients obtained are locked into the RigView software.
f (x) = C1x + C0 (62)
Now to check the functionality of the pressure scanner module, Druck Test is performed. The pressure tapping from the vessel is divided into two different tubes, one which is connected to the regular pressure scanner module and the other to the external reference pressure measuring device called the Druck machine. The pressure vessel is then pressurized with air at different pressure levels and then measured data from the Druck machine and pressure scanner are compared finally.
3.3.3
Validation Test
The validation here is performed with reference to the MA 247 rectangular orifices of L/D ratio; Λ=30 for Dh= 1.2mm and Dh= 1.6mm. This shall confirm any changes
at all in the flow behaviour inspite of changing the hydraulic diameter of the orifice. Subsequently, reaffirming any doubts in data recordings, the MATLAB calculations and moreover the rig0s functioning itself. The discharge coefficients in this scope of experiment are calculated for pressure ratios with an increasing trend of the mass flow. Fig.25 showcases the confirmation of the expected trends of the new readings with respect to the reference data. Slight deviations in the transition zone for the sample with Dh= 1.2mm can be seen at lower pressure ratios (between Π= 1.1
ans 1.3) with respect to the reference data, but these account to less than 1.5% of variation and moreover, it is observed that the error bars of the reference and present data overlap completely for both the samples. It is important to note that the range of readings has been taken more widely as compared to the reference data and thus, fewer mass flow points were employed for the data collection, which reduces the details in the plots. Another safe reason to assume for such small variations, would be to acknowledge the usage of different measuring instruments and different range of Coriolis flow meter with different measuring accuracy. But in overall, the plots are in good agreement and the trends are as expected for all three flow regimes. Thus, indicating substantial reliability and validity of the test rig to perform further experiments. Also, some readings for this test were taken for decreasing pressure ratio trends as part of the repeatability test , but the differences were small (0.1% approx.). Thus, just one trend of measuring results were considered for further work which apparently, also helped save costs in this limited-timed thesis.
Figure 25: Validation through plot analysis of reference plot with respect to the new plot.
3.4
Post-Processing
This section is about the dimensionless parameters calculated as part of the post pro-cessing. This shall include Discharge Coefficient, Reynolds number, Mach number and Frictional Factor.
No complex post-processing is adhered to calculate the discharge coefficient as it can be directly computed from the Eq.14. As introduced in Fig.20, the mass flow rate ( ˙m), total vessel temperature (Tvessel), vessel pressure (pvessel) and ambient
pressure (pambient) are directly measured from the instruments. The static pressure
(ps,2) is equal to the ambient pressure (pambient) and the absolute pressure of air
inside the pressure vessel (pt,1) is an aggregate of the gauge pressure which is equal
to pvessel and pambient. Cross-sectional area (A) is the designed area of the orifice.
In order to calculate the Reynolds number, Mach number and friction factor, several assumptions are made so as to model a thermodynamic process and then compute the density, velocity, and viscosity. (i) The flow through the orifice is consider to be a fully developed laminar or turbulent regime. (ii) The static outlet pressure is equal to atmospheric pressure. (iii) The thermodynamic process occurring is adiabatic in nature. (iv) Since, air at the ambient temperature is used during the experiment, the heat transfer can be neglected as the experiment is carried out in a rapid flow process and heat is not added to the system. Apart from these, the specific isobaric heat capacity and the viscosity are calculated according to the published data from Lemmon et al. [60]
Fanning friction factor (fF anning) is taken as the reference calculated friction
fac-tor. But in order to compare the results to other open literature, Darcy-Weisbach friction factor (fD) is considered while the set of equations for the friction factor
calculation are solved iteratively. Fig.26 above describes how the total pressure drop across the orifice can be divided into three segments. These frictional characteristics of air flow were explained by Yang et al.[61] while experimenting for micro-tubes. The first segment in the figure i.e. section 1-2 causes the frictional pressure drop (dpt,f riction) in the air flow through the orifice. The losses incurred here are
ma-Figure 26: Pressure drop segments in a pipe.
Reynolds number and surface roughness, in the case of turbulent flow. Sections 0-1 and 2-3 oversees the dynamic pressure drops at the plane of entrance (dpt,in) and at
the exit (dpt,out) respectively. These losses are caused by any slight changes in
geom-etry while manufacturing and thus, are considered minor losses. Pressure drops due to acceleration is also ignored as the flow is considered as steady state. Calculations for dynamic pressure losses are done using the local axial velocity component (u) and density (ρ) at the respective section, Eqs.63 and 64 illustrates the mathematical relationship; dpt,in = fin (ρ1u21) 2 (63) dpt,out = fout (ρ2u22) 2 (64)
Here, the loss coefficient (fin) is at the entrance and loss coefficient (fout) ia at
the exit of the orifice. In section 1-2 the pressure losses due to the friction factor is calculated by considering the average of flow velocity (¯u) and density ( ¯ρ) and is depicted in Eq.65; dpt,f riction= 2fF anning L D ¯ ρ¯u2 2 (65)
The inlet loss coefficient factor (fin) and outlet loss coefficient factor (fout)
de-pends upon the geometry. For instance, depending on the sharpness, fin= 0.25 and
fout= 0.5 is used for circular geometries [62]. These losses are much less though when
compared to the frictional factor pressure losses thus, encouraging the researchers to neglect the inlet losses. Therefore, fin= 0 and fout= 1. [13] [56] [63] [64] [65]. The
complete iterative process is duly elaborated in Appendix *. Between the sections 1 and 3 the friction factor is adjusted such that the total pressure drop (∆pt) is
balanced to the summation of frictional pressure drop and dynamic pressure drop at the orifice outlet as shown in Eq.66
∆pt= (dpt,out+ dpt,f riction) − (p1,t− p3,t) (66)
Now the Mach numbers at the inlet and outlet of the orifices are calculated with inlet and outlet local velocity (u) which is determined by the continuity equation.
