N. Anand
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1
The optimal design of heat exchanges is critical for a wide range of existing and emerging technologies. Traditional design methods often use experimental correlations to estimate thermal and hydraulic performance. However, CFD-based design methods have recently evolved as an alternative to these conventional methods. This paper proposes a CFD-based shape optimization method to design a two-dimensional representation of cylindrical fins. The method consists of a CAD-based parametrization tool and uses a streamwise periodic flow solver to estimate the performance of the fins. In addition, to enable gradient-based optimization, the sensitivity of the objective function with respect to the design variables is provided to the optimizer through an adjoint-based method. The proposed shape optimization method was applied to design cylindrical fins operating at laminar and turbulent flow regimes. The optimization results show that the fluid dynamic performance of the fins increased by 16.5% for the laminar case and 35.8% for the turbulent case while maintaining their thermal performance to their baseline values.
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The optimal design of heat exchanges is critical for a wide range of existing and emerging technologies. Traditional design methods often use experimental correlations to estimate thermal and hydraulic performance. However, CFD-based design methods have recently evolved as an alternative to these conventional methods. This paper proposes a CFD-based shape optimization method to design a two-dimensional representation of cylindrical fins. The method consists of a CAD-based parametrization tool and uses a streamwise periodic flow solver to estimate the performance of the fins. In addition, to enable gradient-based optimization, the sensitivity of the objective function with respect to the design variables is provided to the optimizer through an adjoint-based method. The proposed shape optimization method was applied to design cylindrical fins operating at laminar and turbulent flow regimes. The optimization results show that the fluid dynamic performance of the fins increased by 16.5% for the laminar case and 35.8% for the turbulent case while maintaining their thermal performance to their baseline values.
Flow manifolds are devices that distribute or collect fluid across multiple channels, playing a crucial role in the performance of many fluid and energy systems. However, designing efficient manifolds that ensure uniform flow distribution remains challenging, especially for multi-channel three-dimensional manifolds. This study presents a scalable topology optimization framework for systematically designing multi-channel flow manifolds. The proposed method builds on the conventional density-based topology optimization formulation by introducing a flow maldistribution coefficient as an explicit constraint. This novel approach was implemented using the incompressible Navier–Stokes flow solver available in the open-source CFD suite SU2. The performance of the proposed method was benchmarked against two established topology optimization strategies using an exemplary planar z-type flow manifold, where both the inlet and outlet manifolds were designed simultaneously. The results demonstrate that the proposed method achieves flow uniformity comparable to established approaches while significantly reducing computational costs. Furthermore, when applied to large-scale three-dimensional problems, the proposed method produces feasible designs that achieve uniform flow distribution and exhibit innovative geometrical features. These results highlight the robustness and scalability of the proposed method.
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Flow manifolds are devices that distribute or collect fluid across multiple channels, playing a crucial role in the performance of many fluid and energy systems. However, designing efficient manifolds that ensure uniform flow distribution remains challenging, especially for multi-channel three-dimensional manifolds. This study presents a scalable topology optimization framework for systematically designing multi-channel flow manifolds. The proposed method builds on the conventional density-based topology optimization formulation by introducing a flow maldistribution coefficient as an explicit constraint. This novel approach was implemented using the incompressible Navier–Stokes flow solver available in the open-source CFD suite SU2. The performance of the proposed method was benchmarked against two established topology optimization strategies using an exemplary planar z-type flow manifold, where both the inlet and outlet manifolds were designed simultaneously. The results demonstrate that the proposed method achieves flow uniformity comparable to established approaches while significantly reducing computational costs. Furthermore, when applied to large-scale three-dimensional problems, the proposed method produces feasible designs that achieve uniform flow distribution and exhibit innovative geometrical features. These results highlight the robustness and scalability of the proposed method.
This study presents a Computational Fluid Dynamics (CFD)-based optimization framework to enhance the performance of bare-tube heat exchangers. The framework comprises a CFD solver, an adjoint solver, and a CAD-based parametrization tool. This framework simultaneously optimizes the tube shape and layout to obtain an optimum heat exchanger configuration with a higher heat transfer rate and lower pressure drop. Firstly, a parametric study of the longitudinal pitch is performed that shows that increasing the longitudinal pitch results in an increase in pressure drop and heat transfer rate. Furthermore, the proposed framework was applied to optimize an in-line elliptical tube configuration. The optimum geometry showed a performance improvement of 29% as compared to the baseline geometry while satisfying the constraint on the heat transfer rate.
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This study presents a Computational Fluid Dynamics (CFD)-based optimization framework to enhance the performance of bare-tube heat exchangers. The framework comprises a CFD solver, an adjoint solver, and a CAD-based parametrization tool. This framework simultaneously optimizes the tube shape and layout to obtain an optimum heat exchanger configuration with a higher heat transfer rate and lower pressure drop. Firstly, a parametric study of the longitudinal pitch is performed that shows that increasing the longitudinal pitch results in an increase in pressure drop and heat transfer rate. Furthermore, the proposed framework was applied to optimize an in-line elliptical tube configuration. The optimum geometry showed a performance improvement of 29% as compared to the baseline geometry while satisfying the constraint on the heat transfer rate.
Currently, most of the adjoint-based design systems documented in the open literature assume that the fluid behaves as an ideal gas, are restricted to the optimization of a single row of blades, or are not suited to impose geometric constraints. In response to these limitations, this paper presents a gradient-based shape optimization framework for the aerodynamic design of turbomachinery blades operating under nonideal thermodynamic conditions. The proposed design system supports the optimization of multiple blade rows, and it integrates a computer-aided design (CAD)-based parametrization with a Reynolds-averaged Navier–Stokes (RANS) flow solver and its discrete adjoint counterpart. The capabilities of the method were demonstrated by performing the design optimization of a single-stage axial turbine that employs isobutane (R600a) as working fluid. Notably, the aerodynamic optimization respected the minimum thickness constraint at the trailing edge of the stator and rotor blades and reduced the entropy generation within the turbine by 36%, relative to the baseline, which corresponds to a total-to-total isentropic efficiency increase of about 4 percentage points. The analysis of the flow field revealed that the performance improvement was achieved due to the reduction of the wake intensity downstream of the blades and the elimination of a shock-induced separation bubble at the suction side of the stator cascade.
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Currently, most of the adjoint-based design systems documented in the open literature assume that the fluid behaves as an ideal gas, are restricted to the optimization of a single row of blades, or are not suited to impose geometric constraints. In response to these limitations, this paper presents a gradient-based shape optimization framework for the aerodynamic design of turbomachinery blades operating under nonideal thermodynamic conditions. The proposed design system supports the optimization of multiple blade rows, and it integrates a computer-aided design (CAD)-based parametrization with a Reynolds-averaged Navier–Stokes (RANS) flow solver and its discrete adjoint counterpart. The capabilities of the method were demonstrated by performing the design optimization of a single-stage axial turbine that employs isobutane (R600a) as working fluid. Notably, the aerodynamic optimization respected the minimum thickness constraint at the trailing edge of the stator and rotor blades and reduced the entropy generation within the turbine by 36%, relative to the baseline, which corresponds to a total-to-total isentropic efficiency increase of about 4 percentage points. The analysis of the flow field revealed that the performance improvement was achieved due to the reduction of the wake intensity downstream of the blades and the elimination of a shock-induced separation bubble at the suction side of the stator cascade.
Axial turbine stages for gas generator cycle type rocket engines typically employ highly-loaded supersonic stator vanes. Consequently, the flow pattern downstream of the vanes is characterized by shock waves which induce high-frequency excitation on the subsequent rotor. For this reason, the optimal design of the stator is crucial in the context of development of the next generation of high-performance rocket engines, where reusability is a principal design criterion. A thorough comprehension of the loss mechanisms combined with the adoption of automated optimisation techniques can therefore enable new stator designs that may provide large benefits in terms of overall turbine performance and lifespan. The scope of this study stems from these considerations and its objective is twofold, namely i) the shape optimisation of a su- personic stator for rocket engines and ii) the investigation of the loss mechanisms in supersonic axial turbine stator vanes at on- and off-design conditions. The investigation is performed on stator vanes that are under development for the first turbine stage of a gas generator cycle type rocket engine. The stator vanes are therefore optimised in order to reduce the profile losses by exploiting a novel adjoint optimisation framework for turbomachinery implemented in the open-source code SU2. The effect on the resulting flow field and loss sources is finally investigated. Results show that entropy based loss coefficient gains of 6% can be achieved via shape optimisation and that the fluid- dynamic performance of these vanes is less sensitive to changes in pressure ratio compared to the performance provided by the baseline configuration. Eventually, shock-waves remain the primary loss source.
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Axial turbine stages for gas generator cycle type rocket engines typically employ highly-loaded supersonic stator vanes. Consequently, the flow pattern downstream of the vanes is characterized by shock waves which induce high-frequency excitation on the subsequent rotor. For this reason, the optimal design of the stator is crucial in the context of development of the next generation of high-performance rocket engines, where reusability is a principal design criterion. A thorough comprehension of the loss mechanisms combined with the adoption of automated optimisation techniques can therefore enable new stator designs that may provide large benefits in terms of overall turbine performance and lifespan. The scope of this study stems from these considerations and its objective is twofold, namely i) the shape optimisation of a su- personic stator for rocket engines and ii) the investigation of the loss mechanisms in supersonic axial turbine stator vanes at on- and off-design conditions. The investigation is performed on stator vanes that are under development for the first turbine stage of a gas generator cycle type rocket engine. The stator vanes are therefore optimised in order to reduce the profile losses by exploiting a novel adjoint optimisation framework for turbomachinery implemented in the open-source code SU2. The effect on the resulting flow field and loss sources is finally investigated. Results show that entropy based loss coefficient gains of 6% can be achieved via shape optimisation and that the fluid- dynamic performance of these vanes is less sensitive to changes in pressure ratio compared to the performance provided by the baseline configuration. Eventually, shock-waves remain the primary loss source.
Journal article
(2021)
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Roberto Agromayor, Nitish Anand, Jens Dominik Müller, Matteo Pini, Lars O. Nord
Turbomachinery design is increasingly carried out by means of automated workflows based on high-fidelity physical models and optimization algorithms. The parametrization of the blade geometry is an essential aspect of such workflows because it defines the design space in which an optimal solution can be found. Currently, parametrization methods used for this purpose are often tailored to one particular type of turbomachinery blade, do not provide shape derivatives required for gradient-based optimization, or are not suited to re-parametrize a baseline blade geometry defined by a set of scattered point coordinates in a systematic way. This paper thus presents a general blade parametrization method for axial, radial, and mixed flow blades based on typical turbomachinery design variables and NURBS curves and surfaces. The shape derivatives are computed by means of the complex-step method, allowing the integration of the parametrization into gradient-based shape optimization workflows. In addition, the method enables the re-parametrization of a blade geometry defined by a cloud of points by solving a two-step optimization problem. The capabilities of the method are demonstrated by replicating eight blade geometries in two and three dimensions with an accuracy comparable to the tolerances of current manufacturing technologies.
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Turbomachinery design is increasingly carried out by means of automated workflows based on high-fidelity physical models and optimization algorithms. The parametrization of the blade geometry is an essential aspect of such workflows because it defines the design space in which an optimal solution can be found. Currently, parametrization methods used for this purpose are often tailored to one particular type of turbomachinery blade, do not provide shape derivatives required for gradient-based optimization, or are not suited to re-parametrize a baseline blade geometry defined by a set of scattered point coordinates in a systematic way. This paper thus presents a general blade parametrization method for axial, radial, and mixed flow blades based on typical turbomachinery design variables and NURBS curves and surfaces. The shape derivatives are computed by means of the complex-step method, allowing the integration of the parametrization into gradient-based shape optimization workflows. In addition, the method enables the re-parametrization of a blade geometry defined by a cloud of points by solving a two-step optimization problem. The capabilities of the method are demonstrated by replicating eight blade geometries in two and three dimensions with an accuracy comparable to the tolerances of current manufacturing technologies.
The urgent need to transition to a climate-neutral society requires rapid development and adoption of renewable technologies. Key enablers of conventional and future renewable energy conversion technologies are turbomachines. However, the specific requirements of these turbines and compressors, e.g. operation under highly non-uniform flow or with novel fluids, make the available design methods insuffciently capable of providing effcient designs. Hence, novel and disruptive design methods are pivotal to achieve a paradigm shift in turbomachinery performance across all energy technology platforms.
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The urgent need to transition to a climate-neutral society requires rapid development and adoption of renewable technologies. Key enablers of conventional and future renewable energy conversion technologies are turbomachines. However, the specific requirements of these turbines and compressors, e.g. operation under highly non-uniform flow or with novel fluids, make the available design methods insuffciently capable of providing effcient designs. Hence, novel and disruptive design methods are pivotal to achieve a paradigm shift in turbomachinery performance across all energy technology platforms.
Supersonic stator vanes account for two-thirds of the fluid-dynamic losses in high temperature mini-Organic Rankine Cycle (ORC) turbines. As a result, the overall performance of the turbo-expander mainly depends on the design of the stator. Currently, there is no established correlation for the optimal design of such cascades. This work concerns an investigation about the accuracy of the only design method currently available for the design of supersonic stators operating with fluids made of complex molecules. A physics-based analytical model and a CFD-based model were developed to estimate the optimal post-expansion ratio and to compare their results with the Deych's model. The analysis shows that the Deych's method fails to accurately predict the optimum value of the post-expansion ratio. The study covers also the assessment of the optimum post-expansion ratio in relation to the solidity, the design flow angle and the total-to-static expansion ratio. The outcome demonstrates that there exists a unique optimum post-expansion ratio for a set of primary stator design parameters. In summary, vanes operating with a substance made of complex molecule as the working fluid, which is typical of high-temperature ORC turbines, feature a unique theoretical value of the optimum post-expansion ratio for a given total-to-static expansion ratio. New correlations are required to predict this value.
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Supersonic stator vanes account for two-thirds of the fluid-dynamic losses in high temperature mini-Organic Rankine Cycle (ORC) turbines. As a result, the overall performance of the turbo-expander mainly depends on the design of the stator. Currently, there is no established correlation for the optimal design of such cascades. This work concerns an investigation about the accuracy of the only design method currently available for the design of supersonic stators operating with fluids made of complex molecules. A physics-based analytical model and a CFD-based model were developed to estimate the optimal post-expansion ratio and to compare their results with the Deych's model. The analysis shows that the Deych's method fails to accurately predict the optimum value of the post-expansion ratio. The study covers also the assessment of the optimum post-expansion ratio in relation to the solidity, the design flow angle and the total-to-static expansion ratio. The outcome demonstrates that there exists a unique optimum post-expansion ratio for a set of primary stator design parameters. In summary, vanes operating with a substance made of complex molecule as the working fluid, which is typical of high-temperature ORC turbines, feature a unique theoretical value of the optimum post-expansion ratio for a given total-to-static expansion ratio. New correlations are required to predict this value.
Turbomachinery blades characterized by highly-loaded, slender profiles and operating under unsteady flow may suffer from aeroelastic shortcomings, like forced response and flutter. One of the ways to mitigate these aeroelastic effects is to redesign the blade profiles, so as to increase aero-damping and decrease aero-forcing. Design optimization based on high-fidelity aeroelastic analysis methods is a formidable task due to the inherent computational cost. This work presents an adjoint-based aeroelastic shape-optimization framework based on reduced order methods for flow analysis and forced response computation. The flow analysis is carried out through a multi-frequency fullyturbulent harmonic balance method, while the forced response is computed by means of the energy method. The capability of the design framework is demonstrated by optimizing two candidate cascades, namely, i) a transonic compressor cascade and, ii) a supersonic impulse turbine rotor operating with toluene as working fluid, initially designed by means of the method of waves. The outcomes of the optimization show significant improvements in terms of forced-response in both cases as a consequence of aero-damping enhancement.
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Turbomachinery blades characterized by highly-loaded, slender profiles and operating under unsteady flow may suffer from aeroelastic shortcomings, like forced response and flutter. One of the ways to mitigate these aeroelastic effects is to redesign the blade profiles, so as to increase aero-damping and decrease aero-forcing. Design optimization based on high-fidelity aeroelastic analysis methods is a formidable task due to the inherent computational cost. This work presents an adjoint-based aeroelastic shape-optimization framework based on reduced order methods for flow analysis and forced response computation. The flow analysis is carried out through a multi-frequency fullyturbulent harmonic balance method, while the forced response is computed by means of the energy method. The capability of the design framework is demonstrated by optimizing two candidate cascades, namely, i) a transonic compressor cascade and, ii) a supersonic impulse turbine rotor operating with toluene as working fluid, initially designed by means of the method of waves. The outcomes of the optimization show significant improvements in terms of forced-response in both cases as a consequence of aero-damping enhancement.
Journal article
(2018)
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Nitish Anand, Salvo Vitale, Matteo Pini, Gustavo Otero Rodriguez, Rene Pecnik
The stator vane of high-temperature Organic Rankine Cycle radial-inflow turbines operates under severe expansion ratios and the associated fluid-dynamic losses account for nearly two-third of the total losses generated inside the machine. The efficiency of the machine can strongly benefit from specialized high-fidelity design methods able to provide shapes attenuating shock wave formation. Shape optimization is certainly a viable option to deal with supersonic ORC stator design, but it is computationally expensive and often case specific. In this work, a robust method to approach the problem in a more systematic manner is documented. The methodology involves an optimization procedure encompassing the method of characteristics extended to non-ideal fluid flow for profiling the diverging part of the nozzle. The subsonic section and semi-bladed suction side are retrieved using a simple conformal geometrical transformation. The method is applied to the design a supersonic ORC stator working with Toluene vapors, for which two blade shapes were already available. The comparison of fluid-dynamic performance clearly indicates that the MoC-Based method is able to provide the best results with the lowest computational effort, and is suitable to be used to draw general design guidelines
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The stator vane of high-temperature Organic Rankine Cycle radial-inflow turbines operates under severe expansion ratios and the associated fluid-dynamic losses account for nearly two-third of the total losses generated inside the machine. The efficiency of the machine can strongly benefit from specialized high-fidelity design methods able to provide shapes attenuating shock wave formation. Shape optimization is certainly a viable option to deal with supersonic ORC stator design, but it is computationally expensive and often case specific. In this work, a robust method to approach the problem in a more systematic manner is documented. The methodology involves an optimization procedure encompassing the method of characteristics extended to non-ideal fluid flow for profiling the diverging part of the nozzle. The subsonic section and semi-bladed suction side are retrieved using a simple conformal geometrical transformation. The method is applied to the design a supersonic ORC stator working with Toluene vapors, for which two blade shapes were already available. The comparison of fluid-dynamic performance clearly indicates that the MoC-Based method is able to provide the best results with the lowest computational effort, and is suitable to be used to draw general design guidelines