This work is focused on modeling the effects of homogeneous roughness on low-order velocity statistics in turbulent channel flows. Hydrodynamic effects due to the roughness are characterized on the basis of volume-averaging theory (VAT) and a discrete roughness element method. This theory exploits the homogeneous character of the roughness in order to reduce the complexity of the flow to its one-dimensional statistics. The formulated VAT-based roughness forcing is best suited for drag dominated surfaces. Turbulence modeling closure is achieved with a map-based turbulence model, the One-Dimensional Turbulence (ODT) model. This avoids the prescription of laws of the wall or other ad-hoc scalings, unlike in more traditional filter-based turbulence models. The modeling framework is applied on selected Reynolds number flows for likewise selected roughness topologies. Results are compared to direct numerical simulation (DNS) data available from the literature. Among others, model results are compared with those of a previously formulated parametric forcing approach (PFA) for roughness drag which involved a costly coefficient calibration linked to the roughness topology model. In ODT, the only calibration process required is the same one involved for the turbulence model parameters, i.e., similar to the ODT model application for smooth-wall flows. Despite all of the inherently implied shortcomings of a 1-D model, some appealing properties of ODT are discussed. Notably, the model is able to predict the roughness function, as well as the wall-normal profile of the Reynolds shear stress across the entire boundary layer thickness.

We present a massively parallel GPU-accelerated solver for direct numerical simulations of transitional and turbulent flat-plate boundary layers and channel flows involving fluids in non-ideal thermodynamic states. While several high-fidelity solvers are currently available as open source, all of them are restricted to the ideal-gas region. In contrast, the CUBic Equation of state Navier-Stokes solver (CUBENS) can accurately model and simulate the non-ideal thermodynamics of single-phase compressible fluids in the vicinity of the vapor-liquid saturation line or the thermodynamic critical point. By employing high-order finite-difference schemes and convective terms in split, kinetic-energy-, and entropy-preserving form, the solver is numerically stable, and robust with minimal numerical dissipation, enabling it to capture the steep variations of non-ideal thermodynamic properties. For cost-effective high-fidelity simulations, in addition to MPI parallelization, CUBENS is GPU-accelerated using OpenACC directives for computation offloading, and asynchronous GPU-aware MPI for efficient GPU-GPU communication. Moreover, CUBENS is compatible with both NVIDIA and AMD GPU architectures, achieving significant performance results while ensuring energy-efficient simulations. For instance, using 64 NVIDIA A100 GPUs compared to 8192 CPUs at the same computational cost results in a speedup of approximately 130×. In multi-node and multi-GPU configurations ranging from 2 to 128 compute nodes (8 to 512 GPUs), a strong scaling efficiency of around 52% and a weak scaling efficiency of 0.88 with 1024³ points per GPU, corresponding to approximately 5 billion degrees of freedom, are achieved. The CUBENS solver is validated against selected cases from the literature, covering transitional to turbulent ideal and non-ideal flows up to the transonic regime. In particular, we demonstrate the solver's suitability and applicability for direct numerical simulations of transitional boundary layers with fluids at supercritical pressure and with buoyancy effects. The development of this high-fidelity solver offers the potential for future fundamental research in non-ideal compressible fluid dynamics. Program summary: Program Title: CUBic Equation of state Navier-Stokes (CUBENS) CPC Library link to program files: https://doi.org/10.17632/6jfy758gyv.1 Developer's repository link: https://github.com/pcboldini/CUBENS Licensing provisions: MIT Programming language: Fortran 90, OpenACC, MPI, Python, MATLAB Nature of problem: This code solves the three-dimensional Navier-Stokes equations for non-ideal gas flows in a Cartesian domain, applicable to boundary layers and channels. Solution method: This code uses high-order central finite-differences with split-convective form, preserving kinetic energy and entropy (KEEP) and pressure-equilibrium-preserving (PEP) property, for spatial discretization. The time advancement is performed with a third-order Total Variation Diminishing low-storage Runge-Kutta scheme. Flow non-ideality is accounted for by cubic equations of state and complex transport-properties models. Alongside MPI parallelization, the solver is GPU-accelerated using OpenACC for computation offloading and CPU-GPU data transfer, along with GPU-aware MPI for GPU-GPU communication.

Dimpled surface designs are known to be effective at enhancing convective heat transfer. However, optimizing these surfaces can be challenging due to the large parameter space created by the different combinations between geometrical features. In this paper, we combine a machine learning framework with a GPU-accelerated DNS solver to quickly assess the performance of a very large number of surface configurations, and to identify optimal designs. Our neural network can be trained to predict 2-D images with the local Nusselt numbers of rough surfaces within a few hours (in a single GPU), based on their original height maps. During evaluation, our neural network coupled with our parameterized geometrical formulation can evaluate one million dimpled surface designs in less than 45 min using a 64-core CPU architecture; with a low RAM memory footprint per core. Moreover, the GPU-accelerated DNS solver can calculate the Nusselt number of a rough surface within a few hours as well. The study considers a diverse parameter space including dimples with multiple depth profiles, major radiuses, corner effects, and inclination angles. To predict optimal designs, a basic reinforcement loop is created. In the first stage, only randomly chosen dimpled surface designs are selected as training data. The Nusselt numbers for each design are extracted from Direct Numerical Simulations (DNS), performed by the GPU-accelerated turbulent flow solver. Then, a convolutional neural network is trained, and different surface designs in our parameter space are evaluated. In order to advance the reinforcement learning loop, additional DNS cases are run for the optimal predicted surface, and other closely related geometrical variations. After adding these new DNS cases to the training set, the neural network is re-trained, and the process is repeated. Starting from the first iteration of the reinforcement learning loop, our results shows that machine learning can predict remarkably optimized dimpled surface designs, with high Nusselt numbers verified through DNS. Moreover, we find that machine learning chooses dimple configurations that enhance the interaction between roughness elements, even if other dimples with shorter radius (and equal depth) have more heat transfer area. The optimal surface has elongated dimples with opposite inclination angles, which create a zig-zag pattern for the flow near the walls. Additionally, we have shown that at different Reynolds numbers, the optimal geometry is different as well. We analyze other plausible optimal dimpled surface designs within our parameter space, and we find that machine learning correctly identified the adequate parameters to maximize heat transfer. Therefore, we conclude that machine learning is a highly effective tool to identify optimized designs for convective heat transfer enhancement.

We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.

Heating in industrial processes is responsible for approximately 13% of greenhouse gas emissions in Europe. Switching from fossil-fuel based boilers to heat pumps can help mitigate the effect of global warming. The present work proposes novel high-temperature transcritical heat pump cycles targeted at heating air with a mass flow rate of 10 kg/s up to 200 °C for spray drying processes. Four low-GWP refrigerants, R1233zd(E), R1336mzz(Z), n-Butane, and Ammonia are considered as the candidate working fluids. The pressure ratio of the compressor is optimized to achieve a maximum coefficient of performance (COP) for the four working fluids. A shell & tube heat exchanger is considered as the gas cooler. Using a generalized version of the ϵ-NTU method, the gas cooler is sized and a second law analysis is conducted. Striking a balance between the first- and second-law performance and size of the gas cooler, the R1233zd(E) transcritical heat pump cycle with a COP of 3.6 is judged to be the most promising option.

This paper presents numerical predictions of the flow field in the swirl-stabilized OP16 DLE combustor using hydrogen as a fuel. Computational Fluid Dynamics (CFD) simulations employing unsteady Reynolds-Averaged Navier-Stokes (URANS) and Wall Modelled Large Eddy Simulations (WMLES) are performed without including reaction mechanisms. The objective is to gain insights into scalar mixing predictions of the two approaches when hydrogen and air undergo shear-driven turbulent mixing. Accurate scalar mixing predictions are crucial in the combustors’ design process to assess the uniformity of fuel-air mixing as localized regions of high fuel concentrations can lead to increased NOx emissions and to identify locations with a propensity for Boundary Layer Flashback (BLF). Results are compared and analyzed in terms of time-averaged equivalence ratio, unmixedness and Turbulent Kinetic Energy (TKE) profiles. TKE predictions are lower in URANS, leading to significantly lower fuel-air mixing levels than WMLES, indicating differences in their predictions of shear-layer interactions in the mixing region and the swirl section of the combustor.

In flows over rough surfaces, the effect of roughness on momentum is different than that on heat transfer. Therefore, the standard Reynolds analogy, which is generally used for flows over smooth surfaces, is no longer valid. More specifically, the wall heat transfer to the fluid is overestimated when applying the Reynolds analogy in rough surface flows. In order to address this, several thermal correction models for rough surfaces have been proposed in literature. In this work, we investigate the applicability of these models to be used as wall functions in RANS simulations. For this, we use a channel flow geometry with rough surfaces and heat transfer at the walls, for which DNS data was produced at different Prandtl numbers. We show that the standard exponential damping function, which is used to constrain the thermal correction to the near-wall region, is not the best choice when using wall functions. Instead, we propose a new damping function which is better suited for the wall function approach. The newly proposed damping function also includes a dependency on the Prandtl number, which was found to make the thermal correction more accurate over a wider range of Prandtl numbers. The improvements are validated using the reference DNS results. The proposed damping function can allow for an easy adaptation of existing thermal correction models as wall functions for industrial scale RANS simulations.

In the region close to the thermodynamic critical point and in the proximity of the pseudoboiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. [J. Fluid Mech. 871, 831 (2019)0022-112010.1017/jfm.2019.348]. Here, we study nonmodal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. To account for nonideality, a new energy norm is derived. Several heat transfer scenarios at supercritical pressure are investigated, which are of practical relevance in technical applications. The boundary layers with the fluid at supercritical pressure are heated or cooled by prescribing the wall and free-stream temperatures so that the temperature profile is either entirely subcritical (liquidlike), supercritical (gaslike), or transcritical (across the Widom line). The free-stream Mach number is set to 10-3. In the nontranscritical regimes, the resulting streamwise-independent streaks originate from the lift-up effect. Wall cooling enhances the energy amplification for both subcritical and supercritical regimes. When the temperature profile is increased beyond the Widom line, a strong suboptimal growth is observed over very short streamwise distances due to the Orr mechanism. Due to the additional presence of transcritical Mode II, the optimal energy growth at large distances is found to arise from an interplay between lift-up and Orr mechanism. As a result, optimal disturbances are streamwise-modulated streaks with strong thermal components and with a propagation angle inversely proportional to the local Reynolds number. The nonmodal growth is put in perspective with modal growth by means of an N-factor comparison. In the nontranscritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, nonmodal N factors are found to resemble the imposition of an adverse pressure gradient in the ideal-gas regime. When cooling beyond the Widom line, optimal growth is greatly enhanced, yet strong inviscid instability prevails. When heating beyond the Widom line, optimal growth could be sufficiently large to favor transition, particularly with a high free-stream turbulence level.

Electrochemical CO2 reduction offers a promising method of converting renewable electrical energy into valuable hydrocarbon compounds vital to hard-to-abate sectors. Significant progress has been made on the lab scale, but scale-up demonstrations remain limited. Because of the low energy efficiency of CO2 reduction, we suspect that significant thermal gradients may develop in industrially relevant dimensions. We describe here a model prediction for non-isothermal behavior beyond the typical 1D models to illustrate the severity of heating at larger scales. We develop a 2D model for two membrane electrode assembly (MEA) CO2 electrolyzers; a liquid anolyte fed MEA (exchange MEA) and a fully gas fed configuration (full MEA). Our results indicate that full MEA configurations exhibit very poor electrochemical performance at moderately larger scales due to non-isothermal effects. Heating results in severe membrane dehydration, which induces large Ohmic losses in the membrane, resulting in a sharp decline in the current density along the flow direction. In contrast, the anolyte employed in the exchange MEA configuration is effective in preventing large thermal gradients. Membrane dehydration is not a problem for the exchange MEA configuration, leading to a nearly constant current density over the entire length of the modeled domain, and indicating that exchange MEA configurations are well suited for scale-up. Our results additionally indicate that a balance between faster kinetics, higher ionic conductivity, smaller pH gradients and lower CO2 solubility causes an optimum operating temperature between 60 and 70 °C.

Using the phenomenological theory of turbulence, a direct link between the Stanton number - a dimensionless number that represents the ratio of transferred heat to the thermal capacity of the fluid - and the scalar spectrum is established for both smooth wall and rough wall conditions. The effect of different scales of motion on heat transfer is demonstrated by investigating relevant limits of the scalar spectrum. It is shown that two important observations in literature - the lack of increase in heat transfer beyond a certain roughness size and the nonclassical Prandtl number scaling - are reproduced if only the viscous inertial and diffusive range of the scalar spectrum is accounted for.

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several improvements over the existing Field Inversion Machine Learning (FIML) frameworks described in the literature. We first showcase the use of efficient optimization routines to automatize the process of field inversion in the context of CFD, combined with the use of symbolic algebra solvers to generate sparse-efficient algebraic formulas to comply with the discrete adjoint method. The proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons, which proves numerically stable. The machine learning predictions are then corrected using a novel weighted relaxation factor methodology, that recovers valuable information from otherwise spurious predictions. Additionally, we introduce L2 regularization to mitigate over-fitting and to reduce the importance of non-essential features. In order to analyze the results of our deep learning system, we utilize the K-fold cross-validation technique, which is beneficial for small datasets. The results show that the machine learning model acts as an excellent non-linear interpolator for DNS cases well-represented in the training set. In the most successful case, the L-infinity modeling error on the velocity profile was reduced from 23.4% to 4.0%. It is concluded that the developed machine learning methodology corresponds to a valid alternative to improve RANS turbulence models in flows with strong variations in their thermophysical properties without introducing prior modeling assumptions into the system.

We investigate the laminar-to-turbulent transition of highly non-ideal supercritical fluids. The controlled H-type breakdown in a three-dimensional flat-plate boundary layer is chosen. Direct numerical simulations are performed at low Mach numbers, for isothermal and heated walls.

Turbulent flows past rough surfaces can create substantial energy losses in engineering equipment. During the last decades, developing accurate correlations to predict the thermal and hydrodynamic behavior of rough surfaces has proven to be a difficult challenge. In this work, we investigate the applicability of convolutional neural networks to perform a direct image-to-image translation between the height map of a rough surface and its detailed local skin friction factors and Nusselt numbers. Additionally, we propose the usage of separable convolutional modules to reduce the total number of trainable parameters, and PReLU activation functions to increase the expressivity of the neural networks created. Our final predictions are improved by a new filtering methodology, which is able to combine the results of multiple neural networks while discarding non-physical oscillations likely caused by over-fitting. The main study is based on a new DNS database formed by 80 flow cases at a friction Reynolds number of Re_τ=180 obtained by applying random shifts to the Fourier spectrum of the grit-blasted surface originally scanned by Busse et al. (2015). The results show that machine learning can accurately predict the skin friction values and Nusselt numbers for a rough surface. A detailed comparison with existing correlations in the literature revealed that the maximum errors generated by deep learning were only 8.1% for the global skin friction factors C_f¯ and 2.9% for the Nusselt numbers Nu¯, whereas the best classical correlations identified reached errors of 24.9% and 13.5% for C_f¯ and Nu¯ respectively. The deep learning results also proved stable with respect to rough surfaces with abrupt changes in their roughness elements, and only presented a minor sensitivity with respect to variations in the dataset size.

Turbulent flows past rough surfaces can create substantial energy losses in engineering equipment. During the last decades, developing accurate correlations to predict the thermal and hydrodynamic behavior of rough surfaces has proven to be a difficult challenge. In this work, we develop a convolutional neural network architecture to perform a direct image-to-image translation between the height map of a rough surface and its detailed local drag resistance and heat transfer rates. Various techniques are discussed to improve the computational efficiency of the machine learning architecture proposed, and even to reduce its time and space complexity. The main study is based on a new DNS database formed by 24 flow cases at a friction Reynolds number of Re_τ = 180 obtained by applying a random shift to the Fourier spectrum of the grit-blasted surface scanned by Busse et al. (2015,). The results show that machine learning can accurately predict the global values of the drag resistance and heat fluxes across a rough surface. The local predictions for both momentum and heat transfer also show a considerable improvement upon increasing the dataset size. A detailed analysis of the global skin friction values and Stanton numbers predicted by deep learning further reveals that the results surpass the accuracy of traditional correlations by a substantial margin in the dataset analyzed.

Supercritical CO₂ is used as a work fluid in both heat pump and power cycles. As a fluid at supercritical pressure is heated or cooled, it may undergo a smooth transition from a liquid-like state to a gas-like state or vice versa. This transition, during which the thermophysical properties vary sharply with temperature, can be referred to as pseudo- boiling or condensation. Using both analytical and numerical methods, it is shown that pseudoboiling theory helps to understand how the unique heat transfer characteristics of a supercritical fluid affect heat exchanger performance and design, in particular a gas chiller. Due to pseudo-condensation, classical approaches such as the ε−NTU and LMTD methods fail when rating or designing a sCO₂ gas chiller. Using the heat of pseudo-condensation, the heat exchanger can be regarded to consist of a pre-cooler, condenser and a super-cooler. By further dividing the pre-cooler and super-cooler into two parts and subsequently applying the ε−NTU method per part yields very good results with respect to both the prediction of required size and entropy generation for various operating parameters. The influence of pseudo-condensation is reduced at higher pressures and is negligible when the structural energy required for the transition from liquid-like to a gas-like state is smaller than the required thermal energy required. It is shown that the local effectiveness of the condenser part is reduced (more so than the other parts) when the heat capacity ratio R_C is varied from unity to less than unity, leading to enhanced irreversibility due to pseudo-condensation. Furthermore, the enhanced and deteriorated heat transfer regime (such as when a sCO₂ downward flow is cooled) lead to significantly different required heat exchanger sizes. Finally, through the use of Monte Carlo simulations, it shown that the uncertainty of a Nusselt correlation complicates designing heat exchangers in which pseudo-condensation occurs. The simulations show that heat exchangers should be 50% larger than the size that is predicted using a Nusselt correlation if the design performance is to be ensured.

Hydrogen plays a vital role in the utilisation of renewable energy, but ingress and diffusion of hydrogen in a gas turbine can induce hydrogen embrittlement on its metallic components. This paper aims to investigate the hydrogen transport in a non-hydride forming alloy such as Alloy 690 used in gas turbines inspired by service conditions of turbine blades, i.e. under the combined effects of stress and temperature. An appropriate hydrogen transport equation is formulated, accounting for both stress and temperature distributions of the domain in the non-hydride forming alloy. Finite element (FE) analyses are performed to predict steady-state hydrogen distribution in lattice sites and dislocation traps of a double notched specimen under constant tensile load and various temperature fields. Results demonstrate that the lattice hydrogen concentration is very sensitive to the temperature gradients, whilst the stress concentration only slightly increases local lattice hydrogen concentration. The combined effects of stress and temperature result in the highest concentration of the dislocation trapped hydrogen in low-temperature regions, although the plastic strain is only at a moderate level. Our results suggest that temperature gradients and stress concentrations in turbine blades due to cooling channels and holes make the relatively low-temperature regions susceptible to hydrogen embrittlement.

In this paper, a finite element (FE) model is developed to investigate lattice hydrogen diffusion in a solid metal under the influence of stress and temperature gradients. This model is applied to a plate with a circular hole which is subjected to temperature and hydrogen concentration gradients. It is demonstrated that temperature gradients significantly influence hydrogen diffusion and hence susceptibility to hydrogen embrittlement when utilizing hydrogen for gas turbines.

Rapid advancements in technology have led to the miniaturization of electronic devices which typically dissipate heat fluxes in the order of 100 W/cm². This has brought about an unprecedented challenge to develop efficient and reliable thermal management systems. Novel cooling technologies such as Two-Phase Thermosyphons that make use of nanofluids provide a promising alternative to the use of conventional systems. This article analytically estimates the effects caused by nanoparticles that deposit on the evaporator surface and their effect on the heat transfer process.

Rough walls are often encountered in industrial heat transfer equipment. Even though it is well known that a rough wall affects velocity fields and thermal fields differently (and therefore also skin friction factors and Stanton or Nusselt numbers), predicting the effect of rough walls on turbulent heat transfer remains difficult. A relation between the scalar spectrum and the Stanton number is derived for channels with both smooth and rough walls. It is shown that the new relation agrees reasonably well with recent DNS experiments for wall roughness sizes of k⁺ < 150 and when Pr = 0.7 - 1.0. Under these conditions, a thermal analogue of Moody’s diagram can be created using the newly developed relation.

A new friction-heat transfer analogy for the prediction of heat transfer to turbulent fluids at supercritical pressure is presented. This analogy is based on the observation that the predominent events that determine the turbulent heat flux known as hot ejections and cold sweeps have different thermophysical properties. This observation is used to derive a new friction-heat transfer analogy, which we call the ejection-sweep analogy. It is shown that the ejection-sweep analogy yields very good results with respect to predicting heat transfer coefficients for different fluids (water, CO ₂ , Helium, R22 and R134a) that are heated at supercritical pressure at low heat flux to mass flux ratios. Furthermore, the new analogy performs much better than the Chilton-Colburn analogy. The new analogy was also compared with two well-known relations from literature. It was found that the ejection-sweep analogy predictions are more consistent with respect to the investigated fluids than the relations from literature and that the analogy can be applied to at least all fluids studied in this work. The ejection-sweep analogy can be used in the development of more advanced heat transfer models that include buoyancy and acceleration effects.