Meinhard Schobeiri - Academia.edu (original) (raw)
Papers by Meinhard Schobeiri
Journal of turbomachinery, May 1, 2015
Lithium ion (Li-ion) batteries are promising power sources for hybrid powertrain systems, and the... more Lithium ion (Li-ion) batteries are promising power sources for hybrid powertrain systems, and the thermal management of batteries has been identified as a critical issue both for safety and efficiency concerns. This work studied thermal management of a Li-ion battery module both experimentally and computationally. A battery module consisting of multiple cells was fabricated and experimentally tested in a wind tunnel facility. Systematic tests were performed under various flow velocities, charging and discharging current, and module configuration. Computationally, a high-fidelity two dimensional computational fluid dynamics (CFD) model was developed to capture the detailed dynamics of thermal management of the cells. Temperature rise of cells and pressure measurements were recorded in the experiments, and compared with CFD model simulations. Reasonable agreement was obtained, confirming the validity of the model. The validated model was then applied to study the power consumption required by the thermal management system. The results obtained in this combined experimental and numerical study are expected to be valuable for the optimized design of battery modules and the development of reduced-order models.
Volume 4: Heat Transfer, Parts A and B, 2012
The impact of the purge flow injection on aerodynamics and film cooling effectiveness of a high p... more The impact of the purge flow injection on aerodynamics and film cooling effectiveness of a high pressure turbine with non-axisymmetric endwall contouring has been numerically investigated. For this purpose, the geometry and boundary condition of a three-stage turbine at the Turbomachinery Performance and Flow Research Laboratory (TPFL), Texas A&M University is utilized. The turbine is being prepared to experimentally verify the results of the current numerical investigations. Its rotor includes non-axisymmetric endwall contouring on the first and second rotor row. In the preceding paper [1] it was shown that the endwall contouring of the second rotor contouring was able to substantially increase the turbine efficiency. To investigate the film cooling in conjunction with a purge flow injection, the first turbine rotor hub was contoured. Applying the same contouring method, however, different aerodynamic behavior of the first rotor was observed due to its immediate exposure to the pur...
Journal of turbomachinery, Apr 26, 2010
Film-cooling effectiveness is measured on a rotating turbine blade platform for coolant injection... more Film-cooling effectiveness is measured on a rotating turbine blade platform for coolant injection through discrete holes using pressure sensitive paint technique. Most of the existing literatures provide information only for stationary endwalls. The effects of rotation on the platform film-cooling effectiveness are not well documented. Hence, the existing three-stage turbine research facility at the Turbomachinery and Flow Performance Laboratory, Texas A&M University was redesigned and installed to enable coolant gas injection on the first stage rotor platform. Two distinct coolant supply loops were incorporated into the rotor to facilitate separate feeds for upstream cooling using stator-rotor gap purge flow and downstream discrete-hole film cooling. As a continuation of the previously published work involving stator-rotor gap purge cooling, this study investigates film-cooling effectiveness on the first stage rotor platform due to coolant gas injection through nine discrete holes located downstream within the passage region. Film-cooling effectiveness is measured for turbine rotor frequencies of 2400 rpm, 2550 rpm, and 3000 rpm corresponding to rotation numbers of Ro=0.18, 0.19, and 0.23, respectively. For each of the turbine rotational frequencies, film-cooling effectiveness is determined for average film-hole blowing ratios of Mholes=0.5, 0.75, 1.0, 1.25, 1.5, and 2.0. To provide a complete picture of hub cooling under rotating conditions, simultaneous injection of coolant gas through upstream stator-rotor purge gap and downstream discrete film-hole is also studied. The combined tests are conducted for gap purge flow corresponding to coolant to mainstream mass flow ratio of MFR=1% with three downstream film-hole blowing ratios of Mholes=0.75, 1.0, and 1.25 for each of the three turbine speeds. The results for combined upstream stator-rotor gap purge flow and downstream discrete holes provide information about the optimum purge flow coolant mass, average coolant hole blowing ratios for each rotational speed, and coolant injection location along the passage to obtain efficient platform film cooling.
Turbomachinery Flow Physics and Dynamic Performance, 2005
Turbomachinery Flow Physics and Dynamic Performance, 2005
Gas Turbine Design, Components and System Design Integration, 2017
Turbomachinery Flow Physics and Dynamic Performance, 2012
turbines
International Journal of Rotating Machinery, 1997
Reliable efficiency calculation of high-subsonic and transonic compressor stages requires a detai... more Reliable efficiency calculation of high-subsonic and transonic compressor stages requires a detailed and accurate prediction of the flow field within these stages. Despite the tremendous progress in turbomachinery computational fluid mechanics, the compressor designer still uses different loss correlations to estimate the total pressure losses and thus the efficiency of the compressor stage. The new shock loss model and the modified diffusion factor, developed in Part I, were implemented into a loss calculation procedure. In this part, correlations for total pressure loss, profile loss, and secondary loss coefficients are presented, using the available experimental data. Based on the profile loss coefficients, correlations were also established for boundary layer momentum thickness. These correlations allow the compressor designer to accurately estimate the blade losses and therefore the stage efficiency.
This report deals with the specific aerodynamics and heat transfer problematic inherent to high p... more This report deals with the specific aerodynamics and heat transfer problematic inherent to high pressure (HP) turbine sections of IGCC-gas turbines. Issues of primary relevance to a turbine stage operating in an IGCC-environment are: (1) decreasing the strength of the secondary flow vortices at the hub and tip regions to reduce (a), the secondary flow losses and (b), the potential for end wall deposition, erosion and corrosion due to secondary flow driven migration of gas flow particles to the hub and tip regions, (2) providing a robust film cooling technology at the hub and that sustains high cooling effectiveness less sensitive to deposition, (3) investigating the impact of blade tip geometry on film cooling effectiveness. The document includes numerical and experimental investigations of above issues. The experimental investigations were performed in the three-stage multi-purpose turbine research facility at the Turbomachinery Performance and Flow Research Laboratory (TPFL), Texas A&M University. For the numerical investigations a commercial Navier-Stokes solver was utilized.
The phenomena of stability of laminar flows, transition, and turbulence were systematically studi... more The phenomena of stability of laminar flows, transition, and turbulence were systematically studied first by O. Reynolds [1] in the eighties of the eighteenth century. H. Schlichting [2] and [3] and in his classical textbook Boundary Layer Theory [4] gives an excellent treatment of these complex flow phenomena and critically reviews the contributions up to 1979, where the seventh and last edition of his book appeared. In this chapter, we first treat the fundamental issues pertaining to the subject matter followed by original contributions recently made in the area of steady and unsteady boundary layer transition. The flow in a turbine or compressor component is characterized by a threedimensional, highly unsteady motion with random fluctuations due to the existing freestream turbulence and the interactions between the stator and rotor rows.
Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery, 2000
This paper deals with the aerodynamic and performance behavior of a three-stage high pressure res... more This paper deals with the aerodynamic and performance behavior of a three-stage high pressure research turbine with 3-D curved blades at its design and off-design operating points. The research turbine configuration incorporates six rows beginning with a stator row. Interstage aerodynamic measurements were performed at three stations, namely downstream of the first rotor row, the second stator row, and the second rotor row. Interstage radial and circumferential traversing presented a detailed flow picture of the middle stage. Performance measurements were carried out within a rotational speed range of 75% to 116% of the design speed. The experimental investigations have been carried out on the recently established multi-stage turbine research facility at the Turbomachinery Performance and Flow Research Laboratory, TPFL, of the Texas A&M University.
Fluid Mechanics for Engineers, 2010
In this and the following chapter, we present the conservation laws of fluid mechanics that are n... more In this and the following chapter, we present the conservation laws of fluid mechanics that are necessary to understand the basics of flow physics from a unified point of view. The main subject of this chapter is the differential treatment of the conservation laws of fluid mechanics, namely conservation law of mass, linear momentum, angular momentum, and energy. In many engineering applications, such as in turbomachinery, the fluid particles change the frame of reference from a stationary frame followed by a rotating one. The absolute frame of reference is rigidly connected with the stationary parts, such as casings, inlets, and exits of a turbine, a compressor, a stationary gas turbine or a jet engine, whereas the relative frame is attached to the rotating shaft, thereby turning with certain angular velocity about the machine axis. By changing the frame of reference from an absolute frame to a relative one, certain flow quantities remain unchanged, such as normal stress tensor, shear stress tensor, and deformation tensor. These quantities are indifferent with regard to a change of frame of reference. However, there are other quantities that undergo changes when moving from a stationary frame to a rotating one. Velocity, acceleration, and rotation tensor are a few. We first apply these laws to the stationary or absolute frame of reference, then to the rotating one.
Fluid Mechanics for Engineers, 2010
Turbomachinery Flow Physics and Dynamic Performance, 2005
The energy transfer in turbomachinery is established by means of the stages. A turbomachinery sta... more The energy transfer in turbomachinery is established by means of the stages. A turbomachinery stage comprises a row of fixed, guide vanes called stator blades, and a row of rotating blades termed rotor. To elevate the total pressure of a working fluid, compressor stages are used that partially converts the mechanical energy into potential energy. According to the conservation law of energy, this energy increase requires an external energy input which must be added to the system in the form of mechanical energy. Figure 5.1 shows the schematic of an axial compressor stage that consists of one stator and two rotor rows. In general, a compressor component starts with a rotor row followed by a stator row. Compressor configurations are also found that starts with an inlet guide vane. To define a unified station nomenclature for compressor and turbine stages, we identify with station number 1 as the inlet of the stator, followed by station 2 as the rotor inlet, and 3, rotor exit. The absolute and relative flow angles are counted counterclockwise from a horizontal line. This convention allows an easier calculation of the off-design behavior of compressor and turbine stages during a transient operation, as we will see later. This angle definition is different the angle conventions used in literature, [1], [2], [3], and [4].
Turbomachinery Flow Physics and Dynamic Performance, 2005
In this and the following chapter, we present the conservation laws of fluid mechanics that are n... more In this and the following chapter, we present the conservation laws of fluid mechanics that are necessary to understand the basics of flow physics in turbomachinery from a unified point of view. The main subject of this chapter is the differential treatment of the conservation laws of fluid mechanics, namely conservation law of mass, linear momentum, angular momentum, and energy. These subjects are treated comprehensively in a recent book by Schobeiri [1]. In many engineering applications, such as in turbomachinery, the fluid particles change the frame of reference from a stationary frame followed by a rotating one. The absolute frame of reference is rigidly connected with the stationary parts, such as casings, inlets, and exits of a turbine, a compressor, a stationary gas turbine or a jet engine, whereas the relative frame is attached to the rotating shaft, thereby turning with certain angular velocity about the machine axis. By changing the frame of reference from an absolute frame to a relative one, certain flow quantities remain unchanged, such as normal stress tensor, shear stress tensor, and deformation tensor. These quantities are indifferent with regard to a change of frame of reference. However, there are other quantities that undergo changes when moving from a stationary frame to a rotating one. Velocity, acceleration, and rotation tensor are a few. We first apply these laws to the stationary or absolute frame of reference, then to the rotating one.
Turbomachinery Flow Physics and Dynamic Performance, 2012
Turbomachinery Flow Physics and Dynamic Performance, 2012
Up to this point, the relationships developed for a turbomachinery stage have been strictly corre... more Up to this point, the relationships developed for a turbomachinery stage have been strictly correct for given velocity diagrams with known inlet and exit flow angles. We assumed that the flow is fully congruent with the blade profile. This assumption implies that the inlet and exit flow angles coincide with the camber angles at the leading and trailing edges. Based on the operation condition and the design philosophy, there might be a difference between the camber and flow angle at the leading edge, which is called the incidence angle. The difference between the blade camber angle and the flow angle at the exit is termed the deviation angle. Since the incidence and deviation affect the required total flow deflection, the velocity diagram changes. If this change is not predicted accurately, the stage operates under a condition not identical with the optimum operation condition for which the stage is designed. This situation affects the efficiency and performance of the stage and thus the entire turbomachine. In order to prevent this, the total flow deflection must be accurately predicted. The compressor and the turbine flows react differently to a change of incidence. For instance, a slight change of incidence causes a partial flow separation on the compressor blade suction surface that can trigger a rotating stall; a turbine blade is less sensitive even to greater incidence change. To obtain the incidence and deviation angle for compressor and turbine blades, we use two different calculation methods. The first method deals with the application of conformal transformation to cascade flows with low deflection as in compressor blades. The second method concerns the calculation of deviation in high loaded cascades as in turbine blades.
Turbomachinery Flow Physics and Dynamic Performance, 2012
Turbomachinery Flow Physics and Dynamic Performance, 2012
Flow deflection in turbomachines is established by stator and rotor blades with prescribed geomet... more Flow deflection in turbomachines is established by stator and rotor blades with prescribed geometry that includes inlet and exit camber angles, stagger angle, camber line, and thickness distribution. The blade geometry is adjusted to the stage velocity diagram which is designed for specific turbine or compressor flow applications. Simple blade design methods are available in the open literature (see References). More sophisticated and high efficiency blade designs developed by engine manufacturers are generally not available to the public. An earlier theoretical approach by Joukowsky [1] uses the method of conformal transformation to obtain cambered profiles that can generate lift force. The mathematical limitations of the conformal transformation do not allow modifications of a cambered profile to produce the desired pressure distribution required by a turbine or a compressor blade design. In the following, a simple method is presented that is equally applicable for designing compressor and turbine blades. The method is based on (a) constructing the blade camber line and (b) superimposing a predefined base profile on the camber line. With regard to generating a base profile, the conformal transformation can be used to produce useful profiles for superposition purposes. A brief description of the Joukowsky transformation explains the methodology of symmetric and a-symmetric (Cambered) profiles. The transformation uses the complex analysis which is a powerful tool to deal with the potential theory in general and the potential flow in particular. It is found in almost every fluid mechanics textbook that has a chapter dealing with potential flow. While they all share the same underlying mathematics, the style of describing the subject to engineering students differ. A very compact and precise description of this subject matter is found in an excellent textbook by Spurk [2].
Volume 3: Turbo Expo 2005, Parts A and B, 2005
The paper experimentally and theoretically studies the effects of periodic unsteady wake flow and... more The paper experimentally and theoretically studies the effects of periodic unsteady wake flow and aerodynamic characteristics on boundary layer development, separation and re-attachment along the 'y) time-average intermittency <'y (t)> ensemble averaged intermittency
Journal of turbomachinery, May 1, 2015
Lithium ion (Li-ion) batteries are promising power sources for hybrid powertrain systems, and the... more Lithium ion (Li-ion) batteries are promising power sources for hybrid powertrain systems, and the thermal management of batteries has been identified as a critical issue both for safety and efficiency concerns. This work studied thermal management of a Li-ion battery module both experimentally and computationally. A battery module consisting of multiple cells was fabricated and experimentally tested in a wind tunnel facility. Systematic tests were performed under various flow velocities, charging and discharging current, and module configuration. Computationally, a high-fidelity two dimensional computational fluid dynamics (CFD) model was developed to capture the detailed dynamics of thermal management of the cells. Temperature rise of cells and pressure measurements were recorded in the experiments, and compared with CFD model simulations. Reasonable agreement was obtained, confirming the validity of the model. The validated model was then applied to study the power consumption required by the thermal management system. The results obtained in this combined experimental and numerical study are expected to be valuable for the optimized design of battery modules and the development of reduced-order models.
Volume 4: Heat Transfer, Parts A and B, 2012
The impact of the purge flow injection on aerodynamics and film cooling effectiveness of a high p... more The impact of the purge flow injection on aerodynamics and film cooling effectiveness of a high pressure turbine with non-axisymmetric endwall contouring has been numerically investigated. For this purpose, the geometry and boundary condition of a three-stage turbine at the Turbomachinery Performance and Flow Research Laboratory (TPFL), Texas A&M University is utilized. The turbine is being prepared to experimentally verify the results of the current numerical investigations. Its rotor includes non-axisymmetric endwall contouring on the first and second rotor row. In the preceding paper [1] it was shown that the endwall contouring of the second rotor contouring was able to substantially increase the turbine efficiency. To investigate the film cooling in conjunction with a purge flow injection, the first turbine rotor hub was contoured. Applying the same contouring method, however, different aerodynamic behavior of the first rotor was observed due to its immediate exposure to the pur...
Journal of turbomachinery, Apr 26, 2010
Film-cooling effectiveness is measured on a rotating turbine blade platform for coolant injection... more Film-cooling effectiveness is measured on a rotating turbine blade platform for coolant injection through discrete holes using pressure sensitive paint technique. Most of the existing literatures provide information only for stationary endwalls. The effects of rotation on the platform film-cooling effectiveness are not well documented. Hence, the existing three-stage turbine research facility at the Turbomachinery and Flow Performance Laboratory, Texas A&M University was redesigned and installed to enable coolant gas injection on the first stage rotor platform. Two distinct coolant supply loops were incorporated into the rotor to facilitate separate feeds for upstream cooling using stator-rotor gap purge flow and downstream discrete-hole film cooling. As a continuation of the previously published work involving stator-rotor gap purge cooling, this study investigates film-cooling effectiveness on the first stage rotor platform due to coolant gas injection through nine discrete holes located downstream within the passage region. Film-cooling effectiveness is measured for turbine rotor frequencies of 2400 rpm, 2550 rpm, and 3000 rpm corresponding to rotation numbers of Ro=0.18, 0.19, and 0.23, respectively. For each of the turbine rotational frequencies, film-cooling effectiveness is determined for average film-hole blowing ratios of Mholes=0.5, 0.75, 1.0, 1.25, 1.5, and 2.0. To provide a complete picture of hub cooling under rotating conditions, simultaneous injection of coolant gas through upstream stator-rotor purge gap and downstream discrete film-hole is also studied. The combined tests are conducted for gap purge flow corresponding to coolant to mainstream mass flow ratio of MFR=1% with three downstream film-hole blowing ratios of Mholes=0.75, 1.0, and 1.25 for each of the three turbine speeds. The results for combined upstream stator-rotor gap purge flow and downstream discrete holes provide information about the optimum purge flow coolant mass, average coolant hole blowing ratios for each rotational speed, and coolant injection location along the passage to obtain efficient platform film cooling.
Turbomachinery Flow Physics and Dynamic Performance, 2005
Turbomachinery Flow Physics and Dynamic Performance, 2005
Gas Turbine Design, Components and System Design Integration, 2017
Turbomachinery Flow Physics and Dynamic Performance, 2012
turbines
International Journal of Rotating Machinery, 1997
Reliable efficiency calculation of high-subsonic and transonic compressor stages requires a detai... more Reliable efficiency calculation of high-subsonic and transonic compressor stages requires a detailed and accurate prediction of the flow field within these stages. Despite the tremendous progress in turbomachinery computational fluid mechanics, the compressor designer still uses different loss correlations to estimate the total pressure losses and thus the efficiency of the compressor stage. The new shock loss model and the modified diffusion factor, developed in Part I, were implemented into a loss calculation procedure. In this part, correlations for total pressure loss, profile loss, and secondary loss coefficients are presented, using the available experimental data. Based on the profile loss coefficients, correlations were also established for boundary layer momentum thickness. These correlations allow the compressor designer to accurately estimate the blade losses and therefore the stage efficiency.
This report deals with the specific aerodynamics and heat transfer problematic inherent to high p... more This report deals with the specific aerodynamics and heat transfer problematic inherent to high pressure (HP) turbine sections of IGCC-gas turbines. Issues of primary relevance to a turbine stage operating in an IGCC-environment are: (1) decreasing the strength of the secondary flow vortices at the hub and tip regions to reduce (a), the secondary flow losses and (b), the potential for end wall deposition, erosion and corrosion due to secondary flow driven migration of gas flow particles to the hub and tip regions, (2) providing a robust film cooling technology at the hub and that sustains high cooling effectiveness less sensitive to deposition, (3) investigating the impact of blade tip geometry on film cooling effectiveness. The document includes numerical and experimental investigations of above issues. The experimental investigations were performed in the three-stage multi-purpose turbine research facility at the Turbomachinery Performance and Flow Research Laboratory (TPFL), Texas A&M University. For the numerical investigations a commercial Navier-Stokes solver was utilized.
The phenomena of stability of laminar flows, transition, and turbulence were systematically studi... more The phenomena of stability of laminar flows, transition, and turbulence were systematically studied first by O. Reynolds [1] in the eighties of the eighteenth century. H. Schlichting [2] and [3] and in his classical textbook Boundary Layer Theory [4] gives an excellent treatment of these complex flow phenomena and critically reviews the contributions up to 1979, where the seventh and last edition of his book appeared. In this chapter, we first treat the fundamental issues pertaining to the subject matter followed by original contributions recently made in the area of steady and unsteady boundary layer transition. The flow in a turbine or compressor component is characterized by a threedimensional, highly unsteady motion with random fluctuations due to the existing freestream turbulence and the interactions between the stator and rotor rows.
Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery, 2000
This paper deals with the aerodynamic and performance behavior of a three-stage high pressure res... more This paper deals with the aerodynamic and performance behavior of a three-stage high pressure research turbine with 3-D curved blades at its design and off-design operating points. The research turbine configuration incorporates six rows beginning with a stator row. Interstage aerodynamic measurements were performed at three stations, namely downstream of the first rotor row, the second stator row, and the second rotor row. Interstage radial and circumferential traversing presented a detailed flow picture of the middle stage. Performance measurements were carried out within a rotational speed range of 75% to 116% of the design speed. The experimental investigations have been carried out on the recently established multi-stage turbine research facility at the Turbomachinery Performance and Flow Research Laboratory, TPFL, of the Texas A&M University.
Fluid Mechanics for Engineers, 2010
In this and the following chapter, we present the conservation laws of fluid mechanics that are n... more In this and the following chapter, we present the conservation laws of fluid mechanics that are necessary to understand the basics of flow physics from a unified point of view. The main subject of this chapter is the differential treatment of the conservation laws of fluid mechanics, namely conservation law of mass, linear momentum, angular momentum, and energy. In many engineering applications, such as in turbomachinery, the fluid particles change the frame of reference from a stationary frame followed by a rotating one. The absolute frame of reference is rigidly connected with the stationary parts, such as casings, inlets, and exits of a turbine, a compressor, a stationary gas turbine or a jet engine, whereas the relative frame is attached to the rotating shaft, thereby turning with certain angular velocity about the machine axis. By changing the frame of reference from an absolute frame to a relative one, certain flow quantities remain unchanged, such as normal stress tensor, shear stress tensor, and deformation tensor. These quantities are indifferent with regard to a change of frame of reference. However, there are other quantities that undergo changes when moving from a stationary frame to a rotating one. Velocity, acceleration, and rotation tensor are a few. We first apply these laws to the stationary or absolute frame of reference, then to the rotating one.
Fluid Mechanics for Engineers, 2010
Turbomachinery Flow Physics and Dynamic Performance, 2005
The energy transfer in turbomachinery is established by means of the stages. A turbomachinery sta... more The energy transfer in turbomachinery is established by means of the stages. A turbomachinery stage comprises a row of fixed, guide vanes called stator blades, and a row of rotating blades termed rotor. To elevate the total pressure of a working fluid, compressor stages are used that partially converts the mechanical energy into potential energy. According to the conservation law of energy, this energy increase requires an external energy input which must be added to the system in the form of mechanical energy. Figure 5.1 shows the schematic of an axial compressor stage that consists of one stator and two rotor rows. In general, a compressor component starts with a rotor row followed by a stator row. Compressor configurations are also found that starts with an inlet guide vane. To define a unified station nomenclature for compressor and turbine stages, we identify with station number 1 as the inlet of the stator, followed by station 2 as the rotor inlet, and 3, rotor exit. The absolute and relative flow angles are counted counterclockwise from a horizontal line. This convention allows an easier calculation of the off-design behavior of compressor and turbine stages during a transient operation, as we will see later. This angle definition is different the angle conventions used in literature, [1], [2], [3], and [4].
Turbomachinery Flow Physics and Dynamic Performance, 2005
In this and the following chapter, we present the conservation laws of fluid mechanics that are n... more In this and the following chapter, we present the conservation laws of fluid mechanics that are necessary to understand the basics of flow physics in turbomachinery from a unified point of view. The main subject of this chapter is the differential treatment of the conservation laws of fluid mechanics, namely conservation law of mass, linear momentum, angular momentum, and energy. These subjects are treated comprehensively in a recent book by Schobeiri [1]. In many engineering applications, such as in turbomachinery, the fluid particles change the frame of reference from a stationary frame followed by a rotating one. The absolute frame of reference is rigidly connected with the stationary parts, such as casings, inlets, and exits of a turbine, a compressor, a stationary gas turbine or a jet engine, whereas the relative frame is attached to the rotating shaft, thereby turning with certain angular velocity about the machine axis. By changing the frame of reference from an absolute frame to a relative one, certain flow quantities remain unchanged, such as normal stress tensor, shear stress tensor, and deformation tensor. These quantities are indifferent with regard to a change of frame of reference. However, there are other quantities that undergo changes when moving from a stationary frame to a rotating one. Velocity, acceleration, and rotation tensor are a few. We first apply these laws to the stationary or absolute frame of reference, then to the rotating one.
Turbomachinery Flow Physics and Dynamic Performance, 2012
Turbomachinery Flow Physics and Dynamic Performance, 2012
Up to this point, the relationships developed for a turbomachinery stage have been strictly corre... more Up to this point, the relationships developed for a turbomachinery stage have been strictly correct for given velocity diagrams with known inlet and exit flow angles. We assumed that the flow is fully congruent with the blade profile. This assumption implies that the inlet and exit flow angles coincide with the camber angles at the leading and trailing edges. Based on the operation condition and the design philosophy, there might be a difference between the camber and flow angle at the leading edge, which is called the incidence angle. The difference between the blade camber angle and the flow angle at the exit is termed the deviation angle. Since the incidence and deviation affect the required total flow deflection, the velocity diagram changes. If this change is not predicted accurately, the stage operates under a condition not identical with the optimum operation condition for which the stage is designed. This situation affects the efficiency and performance of the stage and thus the entire turbomachine. In order to prevent this, the total flow deflection must be accurately predicted. The compressor and the turbine flows react differently to a change of incidence. For instance, a slight change of incidence causes a partial flow separation on the compressor blade suction surface that can trigger a rotating stall; a turbine blade is less sensitive even to greater incidence change. To obtain the incidence and deviation angle for compressor and turbine blades, we use two different calculation methods. The first method deals with the application of conformal transformation to cascade flows with low deflection as in compressor blades. The second method concerns the calculation of deviation in high loaded cascades as in turbine blades.
Turbomachinery Flow Physics and Dynamic Performance, 2012
Turbomachinery Flow Physics and Dynamic Performance, 2012
Flow deflection in turbomachines is established by stator and rotor blades with prescribed geomet... more Flow deflection in turbomachines is established by stator and rotor blades with prescribed geometry that includes inlet and exit camber angles, stagger angle, camber line, and thickness distribution. The blade geometry is adjusted to the stage velocity diagram which is designed for specific turbine or compressor flow applications. Simple blade design methods are available in the open literature (see References). More sophisticated and high efficiency blade designs developed by engine manufacturers are generally not available to the public. An earlier theoretical approach by Joukowsky [1] uses the method of conformal transformation to obtain cambered profiles that can generate lift force. The mathematical limitations of the conformal transformation do not allow modifications of a cambered profile to produce the desired pressure distribution required by a turbine or a compressor blade design. In the following, a simple method is presented that is equally applicable for designing compressor and turbine blades. The method is based on (a) constructing the blade camber line and (b) superimposing a predefined base profile on the camber line. With regard to generating a base profile, the conformal transformation can be used to produce useful profiles for superposition purposes. A brief description of the Joukowsky transformation explains the methodology of symmetric and a-symmetric (Cambered) profiles. The transformation uses the complex analysis which is a powerful tool to deal with the potential theory in general and the potential flow in particular. It is found in almost every fluid mechanics textbook that has a chapter dealing with potential flow. While they all share the same underlying mathematics, the style of describing the subject to engineering students differ. A very compact and precise description of this subject matter is found in an excellent textbook by Spurk [2].
Volume 3: Turbo Expo 2005, Parts A and B, 2005
The paper experimentally and theoretically studies the effects of periodic unsteady wake flow and... more The paper experimentally and theoretically studies the effects of periodic unsteady wake flow and aerodynamic characteristics on boundary layer development, separation and re-attachment along the 'y) time-average intermittency <'y (t)> ensemble averaged intermittency