Measurement of the total conditions downstream of fans is of primary importance to aeroengine development. Historically, these measurements have been acquired with the use of traditional total condition probes mounted to the guidevanes or engine cowling; however, such a setup can have significant impact on the flow. Difficulties in obtaining direct measurements with traditional total conditions probes have led to the development of an embedded shielded probe. In order to support this development, a model was desired to be developed that accurately modelled the recovery using a low-order analysis that could be implemented quickly. The creation and validation of such a model is the primary focus of the present research. Of secondary interest is to prove the hypothesis that aerodynamics will dominate the recovery of such a sensor. Based around the calculations for recovery used by Moffat, the model uses a linear vortex panel method to calculate the aerodynamics of the sensor. Higher order corrections were also suggested to improve the accuracy of the model. Several of these corrections, which take into account compressibility and variance of individual recovery factors, were included in the final model. Other corrections, such as improved paneling for the panel method and the inclusion of pitch angle have not been incorporated at this time but are part of an ongoing effort to improve and expand the capabilities of the model. Model validation was performed in three steps, starting with comparing the calculations for the recovery without aerodynamics to values present in literature for traditional Shielded probes. The aerodynamics and the panel method used to generate them were validated separately using the widely available program Xfoil. Validation of the combined model could only be accomplished via experimental testing. Several sensors, based on the predictions of the model, were 3D printed for use in experimental testing. Three key geometric parameters were identified and varied within the limits of interest to create the set of sensors tested. The purpose of this was two-fold. One: validate the model or identify key missing aerodynamic effects for inclusion. Two: prove the secondary hypothesis that aerodynamics will dominate the recovery. Testing was performed at a range of Mach numbers, yaw angles, and pitch angles commonly present in aeroengines. The data collected for model validation were simultaneously used to prove the hypothesis that aerodynamic effects dominated the recovery. This hypothesis was concluded to be true for the range of parameters tested. The model was determined to be valid for the range of parameters tested, although with the caveat that not all aerodynamic effects are fully accounted for and physical testing or CFD analysis is advised to verify results once design parameters have been narrowed down sufficiently. Further refinement of the experimental data and investigation of the aerodynamic effects are the subject of further study. / Master of Science

The accurate measurement of total temperature in engine diagnostics is a challenging task which is subject to several sources of error. Conduction error is predominant among these sources since total temperature sensors are embedded into a cooled strut for measurement. This study seeks to understand the effect of conduction error on total temperature probe performance from an analytical and experimental standpoint and to provide an effective calibration procedure. The review of historical low-order models, as well as results from a developed thermal resistance model, indicates that conduction error is driven by dimensionless parameters, including the Biot, Nusselt, and Reynolds Numbers, as well as a non-dimensional temperature characterizing the flow/strut temperature difference. A conduction error calibration procedure for total temperature probes is experimentally tested in this study. Data were acquired for nominal flow total temperatures ranging from 550 °F to 850 °F with the probe Reynolds number varying from 2,000 to 12,000 for varying conduction conditions with axial temperature gradients up to 1150 °F per inch. A physics-based statistical model successfully expressed total temperature probe performance as a function of dimensionless conduction driver and probe Reynolds number. This statistical model serves as a “calibration surface” for a particular total temperature probe. Due to the scaling of the problem, this calibration is experimentally obtained in moderate temperature regimes, then implemented in higher temperature regimes. The calibration yields an overall uncertainty in total temperature measurement to be ±4% of the total temperature for flow conditions typical in engine diagnostics, with extreme uncertainties in input conditions. Conduction error is successfully shown to be independent of any temperature regime and driven by dimensionless parameters. / Master of Science

The measurement of temperature in hot gases plays an important role in many engineering applications, such as the efficiency and performance of an engine. As such, understanding the accuracy of these temperature measurements is also important. One of the common ways in which temperature is measured is through the use of total temperature probes. Previous research both at Virginia Tech and in outside studies has been performed to quantify the errors associated with total temperature probe measurements. This work has led to the development of low-order models which can be used to calculate the performance of a total temperature probe as a first-order estimate. These low-order models require knowledge of the heat transfer to the total temperature sensor in order to calculate the probe performance. However, the heat transfer to the sensor is a difficult quantity to calculate and has only been quantified over a set range of operating conditions for a single probe design. This research seeks to expand the range of applicability of the Virginia Tech low-order model by quantifying the heat transfer to the sensor of a total temperature probe over a range of probe geometries through the use of computational models. Key geometry parameters were altered to understand how altering these geometry features would impact the heat transfer to the sensor. In order to quantify the heat transfer to the sensor for varied probe geometries, a new method of characterizing the flow conditions about the sensor was also developed. By characterizing the flow conditions about the sensor, a better quantification of the heat transfer can be obtained. This thesis presents the correlation that was developed to quantify the changes in the flow about the sensor caused by varying the key geometry parameters. The flow conditions encompassed total temperatures from 294 K to 727 K at a Mach number of 0.4. The changes in the flow conditions about the sensor are then used to develop a heat transfer correlation to allow the heat transfer to the sensor to be calculated based off the changes in the flow conditions. The heat transfer to the sensor can then be substituted into the low-order model and used to calculate the performance of a total temperature probe. / Master of Science / The measurement of temperature in hot gases plays an important role in many engineering applications, such as the efficiency and performance of an engine. As such, understanding the accuracy of these temperature measurements is also important. One of the common ways in which temperature is measured is through the use of total temperature probes. Previous research has been performed to quantify the errors associated with total temperature probe measurements. This work has led to the development of low-order models which can be used to calculate probe errors. These low-order models require knowledge of the heat transfer to the total temperature sensor in order to calculate the probe errors. However, the heat transfer to the sensor is a difficult quantity to calculate and has only been quantified over a set range of flow conditions for a single probe design. This research seeks to quantify how the heat transfer to the sensor of a total temperature probe changes for different probe designs. Key geometry parameters were altered to understand how changing these geometry features would impact the heat transfer to the sensor. This thesis presents how the heat transfer to the total temperature sensor can be calculated over a range of different probe designs. The heat transfer to the sensor can then be substituted into the low-order model and used to calculate the performance of a total temperature probe.

The requirement for accurate total temperature measurements in gaseous flows was first recognized many years ago by engineers working on the development of superchargers and combustion diagnostics. A standard temperature sensor for high temperature applications was and remains to be the thermocouple. However, this sensor is characterized by errors due to conduction heat transfer from the sensing element, as well as errors associated with the flow over it. In particular in high temperature flows, the sensing element of the thermocouple will be much hotter than its surroundings, leading to radiation heat losses. This in turn will lead to large errors in the temperature indicated by the thermocouple. Because the design and testing of thermocouple sensors can be time consuming and costly due to the many parameters that can be varied and because of the high level of detail attainable from computational studies, the use of advanced computational simulations is ideally suited to the study of thermocouple performance. This work sought to investigate the errors associated with the use of total temperature thermocouple probes and to assess the ability to predict the performance of such probes using coupled fluid-heat transfer simulations. This was done for a wide range of flow temperatures and subsonic velocities. Simulations were undertaken for three total temperature thermocouple probe designs. The first two probes were legacy probes developed by Glawe, Simmons, and Stickney in the 1950's and were used as a validation case since these probes were extensively documented in a National Advisory Committee for Aeronautics (NACA) technical report. The third probe studied was developed at Virginia Tech which was used to investigate conduction errors experimentally. In all cases, the results of the computational simulations were compared to the experimental results to assess their applicability. In the case of the legacy NACA probes, it was shown that the predicted radiation correction compared well with the documented values. This served as a validation of the computational method. Next the procedure was extended to the conduction error case, where the recovery factor, a metric used to relate the total temperature of the flow to the total temperature indicated by the sensor, was compared. Good agreement between the experimental results was found. The effects of radiation were quantified and shown to be small. It was also demonstrated that computational simulations can be used to obtain quantities that are not easily measured experimentally. Specifically, the heat transfer coefficients and the flow through the vented shield were investigated. The heat transfer coefficients were tabulated as Nusselt numbers and were compared to a legacy correlation. It was found that although the legacy correlation under-predicted the Nusselt number, the predicted results did follow the same trend. A new correlation of the same functional form was therefore suggested. Finally, it was found that the mounting strut had a large effect on the internal flow patterns and therefore the heat transfer to the thermocouple. Overall, this work highlights the usefulness of computational simulations in the design and analysis of total temperature thermocouple sensors. / Master of Science

A three-dimensional CFD program was used to predict the flow field that would enter a downstream fan or compressor rotor under the influence of an upstream thermal distortion. Two distortion generation techniques were implemented in the model; (1) a thermal source and (2) a heated flow injection method. Results from the investigation indicate that both total pressure and velocity boundary conditions at the compressor face are made non-uniform by the upstream thermal distortion, while static pressure remains nearly constant. Total pressure at the compressor face was found to vary on the order of 10%, while velocity varies from 50-65%. Therefore, in modeling such flows, neither of these latter two boundary conditions can be assumed constant under these conditions. The computational model results for the two distortion generation techniques were compared to one another and evaluations of the physical practicality of the thermal distortion generation methods are presented. Both thermal distortion methods create total temperature distortion magnitudes at the compressor face that may affect rotor blade vibration. Both analyses show that holding static pressure constant is an appropriate boundary condition for flow modeling at the compressor inlet. The analyses indicate that in addition to the introduction of a thermal distortion, there is a potential to generate distortion in total pressure, Mach number, and velocity. Depending on the method of thermally distorting the inlet flow, the flow entering the compressor face may be significantly non-uniform. The compressor face boundary condition results are compared to the assumptions of a previous analysis (Kenyon et al., 2004) in which a 25 R total temperature distortion was applied to a computational fluid dynamics (CFD) model of a fan geometry to obtain unsteady blade pressure loading. Results from the present CFD analyses predict similar total temperature distortion magnitudes corresponding to the total temperature variation used in the Kenyon analyses. However, the results indicate that the total pressure and circumferential velocity boundary conditions assumed uniform in the Kenyon analyses could vary by the order of 2% in total pressure and approximately 8% in velocity distortion. This supports the previously stated finding that assuming a uniform total pressure profile at the compressor inlet may be an appropriate approximation with the presence of a weak thermal distortion, while assuming a constant circumferential velocity boundary condition is likely not sufficiently accurate for any thermal distortion. In this work, the referenced Kenyon investigation and others related to the investigation of distortion-induced aeromechanical effects in this compressor rotor have assumed no aerodynamic coupling between the duct flow and the rotor. A full computational model incorporating the interaction between the duct flow and the fan rotor would serve to alleviate the need for assuming boundary conditions at the compressor inlet. / Master of Science

An accurate measurement of total temperature in turbomachinery flows remains critical for component life models and cycle performance optimization. While many techniques exist to measure these flows, immersed thermocouple based probes remain highly desirable due to well established practices for probe design and implementation in typical industrial flow applications. However, as engine manufacturers continue to push towards higher maximum cycle temperatures and smaller flow passages, the continued use of these probes requires new probe designs considering both improved sensor durability and measurement accuracy. Increased maximum temperatures introduce many challenges for total temperature measurements using conventional immersed probes, including increased influences of conduction, convection, and radiation heat transfer between the sensor, fluid and the surroundings due to large thermal gradients present in real turbomachinery systems. While these effects have been previously investigated, the available design models are very limited to specific geometries and flow conditions. In this Dissertation, a more fundamental understanding of the flow behavior around typical vented shield style total temperature probes as a function of probe geometry and operating condition is gained using results from high-fidelity Computational Fluid Dynamics simulations with Conjugate Heat Transfer. A parametric study was conducted considering three non-dimensional probe geometric ratios (vent location to shield length (0.029-0.806), sensor diameter to shield inner diameter (0.252-0.672), and shield outer diameter to strut/mount thickness (0.245-0.759)) and three operating conditions (total temperature (70, 850, 2500°F) and pressure (1, 1, 10 atm), respectively) at a moderate Mach number of 0.4. Results were further quantified in the form of new empirical correlations necessary for rapid thermal performance evaluations of current and future probe designs. Additionally, a new mixed-fidelity or Reduced Order Modeling technique was developed which allows the coupling of high fidelity surface heat transfer data from CFD with a generalized form of the 1-D conducting solid equations for evaluating radiation and transient influences on sensor performance. These new flow and heat transfer correlations together with the new Reduced Order Modeling technique developed here greatly enhance the capabilities of designers to evaluate performance of current and future probe designs, with higher accuracy and with significant reductions in computational resources. / Doctor of Philosophy / An accurate measurement of total temperature in turbomachinery flows remains critical for component life models and cycle performance optimization. While many techniques exist to measure these flows, immersed thermocouple based probes remain highly desirable due to well established practices for probe design and implementation in typical industrial flow applications. However, as engine manufacturers continue to push towards higher maximum cycle temperatures and smaller flow passages, the continued use of these probes requires new probe designs considering both improved sensor durability and measurement accuracy. Increased maximum temperatures introduce many challenges for total temperature measurements using conventional immersed probes, including increased influences of conduction, convection, and radiation heat transfer between the sensor, fluid and the surroundings due to large thermal gradients present in real turbomachinery systems. While these effects have been thoroughly described and quantified in the past, the available design models are very limited to specific geometries and flow conditions. In this Dissertation, a more fundamental understanding of the flow behavior around typical vented shield style total temperature probes as a function of probe geometry and operating condition is gained using results from high-fidelity Computational Fluid Dynamics simulations with Conjugate Heat Transfer (CHT) capabilities. Results were further quantified in the form of new empirical correlations necessary for rapid thermal performance evaluations of current and future probe designs. Additionally, a new mixed-fidelity or Reduced Order Modeling (ROM) technique was developed which allows the coupling of high fidelity surface heat transfer data from CFD with a generalized form of the 1-D conducting solid equations for readily predicting the impact of radiation environment and transient errors on sensor performance.

Accurately measuring the total temperature of a high-speed fluid flow is a challenging task that is required in many research areas and industry applications. The difficulty in total temperature measurement generally stems from attempting to minimize measurement error or accurately predict error so it can be accounted for. Conduction error and aerodynamic error are two very common sources of error in total temperature probe measurements. Numerous studies have been performed in prior literature to account for simple cases of both errors. However, the impacts of a mounting strut and freestream flow angle on conduction error and aerodynamic error have not been previously modeled. Both of these effects are very common in gas-turbine applications of total temperature probes. Therefore, a fundamental study was performed to analyze the impact of mount interference and freestream flow angle on a probe's conduction error and aerodynamic error. An experimental study of aerodynamic error was performed using strut-mounted thermocouples in a high-speed jet at Mach numbers ranging from 0.25-0.72. This study showed that a strut stagnation point can provide aerodynamic error reductions and insensitivity to approach Mach number. An off-angle experimental study of conduction error was also performed using strut-mounted thermocouples at pitch angles ranging from -30° to 30°. High-fidelity Computational Fluid Dynamics (CFD) simulations with Conjugate Heat Transfer (CHT) were performed in conjunction with the experiments to provide key heat transfer information and flow visualizations. It was identified that unshielded total temperature probes have reduced conduction error at off-angles, but are sensitive to changes in the freestream flow angle. A low-order method was developed to account for mount interference and flow angle effects. The developed low order method utilizes a local Mach number for aerodynamic error predictions and a local Reynolds number for conduction error predictions. This developed low-order method was validated against experiment and 3D, CFD results, and was shown to accurately capture flow angle trends, mount interference effects, and the impacts of varying probe geometry. / Master of Science / Accurately measuring the total temperature of a high-speed fluid flow is a challenging task that is required in many research areas and industry applications. Many methods exist for measuring total temperature, but the use of thermocouple based probes immersed into a flow remains a common and desirable measurement technique. The difficulty in using thermocouple based probes to acquire total temperature stems from attempting to minimize or accurately predict the probe’s measurement error. Conduction, convection, and radiation heat transfer between the fluid flow and probe create challenges for minimizing measurement error so that the accurate total temperature can be obtained. Numerous studies have been performed in prior literature to account for simple cases of each error source. However, there are many complex, practical applications in which the influence of each error source has not been studied. The impacts of a freestream flow angle and the total temperature probe’s mounting structure have not been previously modeled. Both of these effects are very common in gas-turbine applications of total temperature probes. This Thesis will present a fundamental study analyzing the impact that freestream flow angle and a probe’s mount have on a total temperature probe’s measurement error. The influence of conduction and convection heat transfer was studied experimentally for numerous probe geometries, and the impacts of a mounting strut and freestream flow angle were analyzed. A low-order method was developed to predict conduction error and aerodynamic error for total temperature probes in offangle conditions with the presence of mount interference. The developed low-order method was shown to accurately capture the effects of a mounting strut, varying probe geometry, and varying flow angle. Additionally, the low-order method was validated against experimental and 3D, CFD/CHT results.