Modelling turbulent heat transfer in rough channels using phenomenological theory

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.Energy Technolog

Turbulence and turbulent heat transfer at supercritical pressure

Energy Technolog

On the effect of pseudo-condensation on the design and performance of supercritical CO₂ gas chillers

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 RC 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.Energy Technolog

Spectral Theory of Turbulent Heat Transfer in the Presence of a Rough Wall

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.Energy Technolog

A heat transfer - friction analogy for fluids at supercritical pressure

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. Accepted Author ManuscriptEnergy TechnologyRST/Reactor Physics and Nuclear Material

Turbulent heat transfer in channels with irregular roughness

It is well known that rough surfaces affect turbulent flows significantly. How such surfaces affect turbulent heat transfer is less well understood. To gain more insight, we have performed a series of direct numerical simulations of turbulent heat transfer in a channel flow with grit-blasted surfaces. An immersed boundary method is used to account for the rough surface. A source term in the thermal energy balance is used to maximise the analogy between the transport of heat and the transport of streamwise momentum. The wall roughness size is varied from k + =15 to k + =120. Turbulence statistics like mean temperature profile, mean temperature fluctuations and heat fluxes are presented. The structure of the turbulent temperature field is analysed in detail. Recirculation zones, which are the result of an adverse pressure gradient, have a profound effect on heat transfer. This is important as it leads to the wall-scaled mean temperature profiles being of larger magnitude than the mean velocity profiles both inside and outside the roughness layer. This means that the temperature wall roughness function ΔΘ + (k s + ,Pr) is different from the momentum wall roughness function ΔU + (k s + ). Since the bulk temperature and velocity depend on ΔΘ + (k s + ,Pr) and ΔU + (k s + ), it was shown that the Stanton number and the skin friction factor directly depend on ΔΘ + (k s + ,Pr) and ΔU + (k s + ), respectively. Therefore, the failure of the Reynolds analogy in fully rough conditions can be directly related to the difference between ΔΘ + (k s + ,Pr) and ΔU + (k s + ). Energy Technolog

Thermodynamic analysis and heat exchanger calculations of transcritical high-temperature heat pumps

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.Energy Technolog

Machine learning for the prediction of the local skin friction factors and Nusselt numbers in turbulent flows past rough surfaces

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 Reτ=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 Cf¯ and 2.9% for the Nusselt numbers Nu¯, whereas the best classical correlations identified reached errors of 24.9% and 13.5% for Cf¯ 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.Energy TechnologyShip Hydromechanics and Structure

Machine learning for the prediction of the local drag forces and heat transfer rates in turbulent flows past rough surfaces

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 Reτ = 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.Energy TechnologyShip Hydromechanics and Structure

Numerical simulation of turbulent heat transfer close to the critical point

In this paper we discuss the effect of sharp property variations on the turbulent heat transfer in fluids close the critical point. The governing equations for this flow regime are discussed, a short description of the numerical tools that have been developed to study these flows is given. Finally, some results for supercritical heat transfer in developing turbulent pipe flow are presented.Process and EnergyMechanical, Maritime and Materials Engineerin