Turbulent Flow Conditions Research Articles

Experimental Study on the Performance of Frictional Drag Reducer with Low Gravity Solids

Reducing energy consumption during drilling operations is beneficial to both the environment and economy. Frictional drag reducers (FDR) are widely used to reduce the energy loss caused by turbulent flow. FDR plays an important role in flow lines as they can reduce the frictional pressure drop effectively, and benefit the selection of circulating fluid and pump. However, several factors can influence the performance of FDR, including fluid additives and incorporated solids, such as drill solids. Thus, the main objective of this paper is to study the influence of low gravity solids (LGS) on the performance of the FDR. This paper is mainly based on experimental study. The experimental work contains two parts: rheology characterization and flow loop tests. Rheology characterization tests were performed to calculate the flow consistency index (K) and flow behavior index (n). Flow loop experiments were conducted for two geometry (0.457 inch and 0.797 inch diameter). Xanthan gum was used as a fractional drag reducer. Bentonite and quartz sand were added as low gravity solids. Three designed water-based mud systems are tested for drag reduction efficiency of Xanthan gum. Flow rate of the mud varied from 3 gpm to 16 gpm. Concentration of Xanthan ranged from 0.1 lbm/bbl to 0.6 lbm/bbl. Low weight solids were added with weight percentage of 0.5%, 1%, 2% and 2.5%. The result shows that xanthan gum is an efficient drag reducer for adequate reasons. Firstly, even at al low concentration, xanthan gum shows high resistance to degradation. Secondly, the maximum drag reduction with xanthan gum is up to 70.54% with a concentration of 0.6 lbm/bbl. However, the existence of different low gravity solids influence the efficiency of xanthan gum in different styles. Experiment results indicate that the higher the weight percentage of bentonite, the lower the drag reduction effectiveness. While with the increasing concentration of quartz sand, the drag reduction does not show an intense change. This study intents to give an instructive guidance on usage of frictional drag reducers in drilling mud system design. Removal of low gravity solids from the mud is difficult, which pose a danger to the drilling fluid. By understanding the effectiveness of FDR, we can reduce energy consumption when irremovable low gravity solids exist. FDR can be used for modifying the mud contents to develop a lower pressure gradient under turbulent flow condition. In the same scenario, adding FDR can suppress turbulent at a constant pressure gradient but with a higher flow rate.

Performance analysis of columnar convex-concave compound microtexture thrust bearing

PurposeThis study aims to enhance the lubrication performance of thrust bearings. The influence of columnar convex–concave compound microtexture on bearing performance is investigatedDesign/methodology/approachBased on the compound microtexture model of thrust bearings, considering surface roughness and turbulent effect, the variation of lubrication characteristics with the change in the compound microtexture parameters is studied.FindingsThe results indicate that, compared with circular microtexture, the maximum pressure of compound microtexture of thrust bearings increases by 7.42%. Optimal bearing performance is achieved when the internal microtexture depth is 0.02 mm. Turbulent flow states and surface roughness lead to a reduction in the optimal depth. The maximum pressure and load-carrying capacity of the bearing decrease as the initial angle increases, whereas the friction coefficient increases with the increase in the initial angle. The lubrication performance is best for bearings with a circumferential parallel arrangement of microtexture.Originality/valueThe novel composite microtexture with columnar convex-concave is proposed, and the computational model of thrust bearings is set. The influence of surface roughness and turbulent flow on the bearing performance should be considered for better conforming with engineering practice. The effect of microtexture depth, arrangement method and distribution position on the lubrication performance of the compound microtexture thrust bearing is investigated, which is of great significance for improving tribology, thrust bearings and surface microtexture theory.

Heat Transfer Enhancement in Circular Cross Section Tube Using Inserts

Convective heat transfer was empirically examined in tubes with ballooned flat perforated steel inserts under turbulent flow conditions, encompassing Reynolds numbers ranging above 15000. The primary objective of this study is to expand the existing dataset concerning inserts. The external surface of the tube received a uniform heat flux, with air serving as the chosen fluid. Correlations were derived for the mass flow rate and heat absorption, utilizing the gathered measurements within the explored range of geometrical parameters and Reynolds numbers.

Corrugation characteristics effect of channel on heat transfer and pressure Drop: Experimental study

Four sinusoidal wavy channels were examined experimentally under turbulent flow conditions of air to clarify the potentials of such configuration in terms of heat transfer and hydrodynamic performance. The subjected heat flux on these wavy walls (sinusoidal wavy plates) were (500, 750, and 1000) W /m2. The ratio of corrugation wavelength (λ) to corrugation amplitude (a) had a range of (5.7–12.6), and the four wavy channels are scrutinized at zero angles (0°) of phase shift. According to the applied range of Reynolds number which is (1.932 × 103–3.286 × 103) and duct entrance dimension, the supplied inlet velocities were (0.3––0.67) m/s. The collected outcomes of the tested wavy sections showed a gained in heat transfer coefficient of (11–39 %) compared to the conventional duct, this increase is originally came out due to the occurred gained of the enhancement factors which is (1.1–1.4). regarding the pressure drop, the acquired decay of the wavy channels is (17–45 %) compared to the conventional channels. Also the results showed the corrugation angle 54.5° is the best in terms of thermal performance factor TPF at Re ≈ 3300 with appreciable high pressure drop, while the corrugation angle of 32.5° has a poor TPF at Re ≈ 1950.

Assessment of the minimal distance for placing household connections downstream of water distribution cross junctions

Abstract This study investigates the solute (chlorine residual) mixing phenomena downstream of a cross junction, considering its critical role in household connections. Experiments were conducted under turbulent flow conditions in a cross junction with two inlets at 90°, varying flow and chlorine concentration ratios at the inlets, i.e., simulating conditions commonly found in real water distribution systems. Results show that outlet chlorine concentrations primarily depend on the flow ratio at the inlets as well as on the inlet chlorine concentrations. Three-dimensional simulations were conducted to predict chlorine concentrations downstream of the cross junction. To evaluate the degree of downstream mixing, the percent coefficient of variation of tracer concentration (%CV) as a function of the axial position at different chlorine and flow ratios was computed from simulations. It was found that the flow ratio strongly affects it at downstream distances less than 50 pipe diameters, whereas the inlet chlorine concentration ratio has a weak effect. A novel correlation was derived as a function of flow ratio to ascertain the minimal distance for achieving the intended mixing level of %CV = 5 downstream of cross junctions. This correlation holds potential as a criterion for household connection location within water distribution networks for high-quality water delivery.

Average turbulence dynamics from a one-parameter kinetic theory: Estimation of the relaxation time

We provide a theoretical estimation of the relaxation time for the kinetic theoretical representation of homogeneous, isotropic, and stationary turbulent flow. The basic approach depends on the construction of a balance of fluctuation and dissipation between the relaxation process and the self-consistently generated fluctuating force. The kinetic theory representation generalizes the modeling of turbulence so that turbulent viscosity as well as all higher order transport coefficients are determined by the relaxation time. The resulting value of the relaxation time gives an estimation of the turbulent viscosity with the coefficient value comparable with those from most of the representative turbulence models, which have been obtained empirically or semi-empirically.

Canopy Randomness, Scale, and Stem Size Effects on the Interfacial Transfer Process in Vegetated Flows

AbstractAquatic vegetation plays an important role in natural water environments by interacting with the flow and generating turbulence that affects the air‐water and sediment‐water interfacial transfer. Regular and staggered arrays are often set as simplified layouts for vegetation canopy to study both mean flow and turbulence statistics in vegetated flows, which creates uniform spacing between vegetation elements, resulting in preferential flow paths within the array. Such preferential paths can produce local high velocity and strong turbulence, which do not necessarily happen in natural environments where vegetation is randomly distributed. How the randomness of the canopy affects interfacial processes by altering spatial turbulence distribution, which can potentially lead to different turbulence feedback on the interfacial transfer process, remains an open question. This study conducted a series of laboratory experiments in a race‐track flume using rigid cylinders as plant surrogates. Mean and turbulent flow statistics were characterized by horizontal‐ and vertical‐sliced PIV. Based on the measured flow characteristics under different stem diameters and array configurations, we propose a method to quantify the randomness of the vegetation array and update a sediment‐water‐air interfacial gas transfer model with the randomness parameter to improve its accuracy. The updated model agrees well with the dissolved oxygen experimental data from our study and data from existing literature at various scales. The study provides critical insight into water quality management in vegetated channels with improved dissolved oxygen predictions considering vegetation layout as part of the interfacial transfer model.

Stability of low-pressure turbine boundary layers under variable Reynolds number and pressure gradient

The free-stream turbulence induced transition occurring under typical low-pressure turbine flow conditions is investigated by comparing linear stability theory with wind tunnel measurements acquired over a flat plate subjected to high turbulence intensity. The analysis was carried out, accounting for three different Reynolds numbers and four different adverse pressure gradients. First, a non-similarity-based boundary layer (BL) solver was used to compute base flows and validated against pressure taps and particle image velocimetry (PIV) measurements. Successively, the optimal disturbances and their spatial transient growth were calculated by coupling classical linear stability theory and a direct-adjoint optimization procedure on all flow conditions considered. Linear stability results were compared with experimental particle image velocimetry measurements on both wall-normal and wall-parallel planes. Finally, the sensitivity of the disturbance spatial transient growth to the spanwise wavenumber of perturbations, the receptivity position, and the location where disturbance energy is maximized were investigated via the built numerical model. Overall, the optimal perturbations computed by linear stability theory show good agreement with the streaky structures surveyed in experiments. Interestingly, the energy growth of disturbances was found to be maximum for all the flow conditions examined, when perturbations entered the boundary layer close to the position where minimum pressure occurs.

Influence of pin-perforation shape on thermohydraulic performance of circular pin-fin heat sinks under turbulent flow

The impact of pin-perforation shape on the thermohydraulic performance of circular pin–fin heat sinks (CPFHS) under turbulent flow conditions is numerically assessed using a computational fluid dynamics software. The convective heat transfer efficiency, hydraulic resistance, and thermohydraulic performance of four pin-perforation shapes: square diamond, triangle, hexagon, and circle, are evaluated under various turbulent flow conditions (Reynolds number between 24,484 to 55,088). The sizes of all pin-perforation shapes are under a constraint that the ratio of the air–solid interfacial surface area to the total volume of pin-perforated CPFHS must be the same. The results show that all pin-perforated CPFHS demonstrate a higher Nusselt number compared to unperforated CPFHS. Those with circular perforations exhibit the highest Nusselt number with up to 39% improvement compared to unperforated CPFHS, followed by those with hexagonal, triangular, and diamond perforations, respectively. The Nusselt numbers correlate with the ease of fluid flow within perforations which is expressed using the average air velocities through perforations. In terms of hydraulic resistance, all pin-perforated CPFHS exhibit a reduction in friction factor compared to unperforated CPFHS. Among these, the largest decrease in friction factor, up to 15.8%, is observed in CPFHS featuring circular perforations, followed by those with hexagonal, diamond, and triangular perforations, respectively. The friction factors are influenced by the ratio of perforation perimeter to cross-sectional area. All pin-perforated CPFHS have a thermal performance factor greater than 1, indicating an improvement in thermohydraulic performance compared to unperforated CPFHS. CPFHS with circular perforations yield the highest thermal performance factor, reaching up to 1.44, followed by hexagonal, triangular, and diamond pin configurations, in descending order. With increasing Reynolds numbers, thermal performance factors of pin-perforated CPFHS initially rise, then gradually decline, suggesting that thermohydraulic advantages due to pin–fin perforations are diminishing as the flow become more turbulent.

Direct Numerical Simulation of Turbulent Boundary Layer over Cubical Roughness Elements

The present study explores turbulence statistics in turbulent flow over urban-like terrain using direct numerical simulation (DNS). DNS is performed in a turbulent boundary layer (TBL) over 3D cubic roughness elements. The turbulence statistics at Reτ = 816 are compared with those of experimental and numerical studies for validation, where Reτ is the friction Reynolds number. The flow exhibits wake interference characteristics similar to k-type roughness. Logarithmic variations in streamwise and spanwise Reynolds stresses and a plateau in Reynolds shear stress are observed, reminiscent of Townsend’s attached-eddy hypothesis. The energy at long wavelengths near the top of elements extends to smaller scales, indicating a two-scale behavior and a potential link to amplitude modulation. The quadrant analysis of Reynolds shear stress is employed, revealing significant changes in the contributions of ejection and sweep events near the top of elements. The results of quadrant analysis in the outer region closely resemble those of a TBL over a smooth wall, aligning with Townsend’s outer-layer similarity. The analysis of the transport equation of turbulent kinetic energy highlights the role of the roughness elements in energy transfer, especially pressure transport. Streamwise energy is mainly reduced near upstream elements and redirected in other directions.

TOSCA – an open-source, finite-volume, large-eddy simulation (LES) environment for wind farm flows

Abstract. The growing number and growing size of wind energy projects coupled with the rapid growth in high-performance computing technology are driving researchers toward conducting large-scale simulations of the flow field surrounding entire wind farms. This requires highly parallel-efficient tools, given the large number of degrees of freedom involved in such simulations, and yields valuable insights into farm-scale physical phenomena, such as gravity wave interaction with the wind farm and farm–farm wake interactions. In the current study, we introduce the open-source, finite-volume, large-eddy simulation (LES) code TOSCA (Toolbox fOr Stratified Convective Atmospheres) and demonstrate its capabilities by simulating the flow around a finite-size wind farm immersed in a shallow, conventionally neutral boundary layer (CNBL), ultimately assessing gravity-wave-induced blockage effects. Turbulent inflow conditions are generated using a new hybrid off-line–concurrent-precursor method. Velocity is forced with a novel pressure controller that allows us to prescribe a desired average hub-height wind speed while avoiding inertial oscillations above the atmospheric boundary layer (ABL) caused by the Coriolis force, a known problem in wind farm LES studies. Moreover, to eliminate the dependency of the potential-temperature profile evolution on the code architecture observed in previous studies, we introduce a method that allows us to maintain the mean potential-temperature profile constant throughout the precursor simulation. Furthermore, we highlight that different codes do not predict the same velocity inside the boundary layer under geostrophic forcing owing to their intrinsically different numerical dissipation. The proposed methodology allows us to reduce such spread by ensuring that inflow conditions produced from different codes feature the same hub wind and thermal stratification, regardless of the adopted precursor run time. Finally, validation of actuator line and disk models, CNBL evolution, and velocity profiles inside a periodic wind farm is also presented to assess TOSCA’s ability to model large-scale wind farm flows accurately and with high parallel efficiency.

Cu-Graphene water-based hybrid nanofluids: synthesis, stability, thermophysical characterization, and figure of merit analysis

Hybrid nanofluids are emerging as an alternative to conventional heat transfer fluids and nanofluids for improving the thermal efficiency of heat exchanging devices synergistically due to their outstanding thermophysical properties associated because of the dispersion of different types of nanoparticles as compared to mono nanofluids. This will help in optimizing fluid characteristics in different flow regimes for several applications. However, enhancing the thermal energy efficiency of heat exchangers is challenging owing to the deprived stability of hybrid nanofluids at greater volume concentrations. This work concentrated on the synthesizing, thermophysical depiction, and thermal performance estimation of stable water-based Cu-graphene hybrid nanofluids using very low volume concentrations of Cu and graphene hybrid nanostructures. Cu-graphene hybrid nanofluid was successfully synthesized by dispersing the synthesized Cu and graphene nanostructures (keeping the Cu concentration constant at 0.04 vol % and varying the graphene concentration from 0.01 to 0.1 vol %) in water. Hybrid nanofluids display excellent stability against aggregation for up to 7 weeks, as proven by higher zeta potential values. Thermophysical characteristics of the prepared hybrid nanofluids were effectively measured. The thermal conductivity of Cu-graphene hybrid nanofluids shows exceptional enrichment (~ 35%) at minimal concentrations of hybrid nanostructures. Viscosity of the water-based hybrid nanofluids shows remarkable enhancement as compared to water and represents the increasing trend in viscosity of the base fluid with respect to the increase in concentration of hybrid nanostructures. The thermal and rheological properties of hybrid nanofluids are effectively validated with existing theoretical models. In addition, the specific heat and pumping power of Cu-graphene hybrid nanofluids with respect to the volume concentration of hybrid nanostructures are calculated using the existing theoretical equations. A figure of merit (FOM) analysis was conducted for the synthesized hybrid nanofluids to gauge thermal efficiency and evaluate the applicability of these hybrid nanofluids under laminar and turbulent flow conditions.

Influence of bioinspired riblet topographies on the mitigation of flow-induced noise in towed sonar arrays

The hydrodynamic optimization of marine vehicles and devices is a critical area of research, especially regarding the diminution of flow-induced drag pertinent to towed sonar arrays. The utilization of bio-inspired riblets, which emulate the skin of rapid marine predators such as sharks, has been posited as a viable strategy to mitigate hydrodynamic drag. Nonetheless, the implications of these riblets on the concurrent acoustical emissions during flow-array interaction remain not well understood. This study conducts an in-depth investigation into the performance of bioinspired riblet topologies in attenuating flow-induced noise in towed sonar arrays, scrutinizing their effectiveness across laminar and turbulent flow regimes. In laminar flow regimes, the study observes that riblet structures have the potential to reduce noise but at the cost of increased drag for towed arrays. Conversely, in turbulent flow conditions, the effectiveness of riblets is significantly enhanced. Particularly, rectangular riblets demonstrate a notable reduction in noise by up to 14.3%, along with a 5.1% decrease in hydrodynamic drag, in comparison to a smooth array surface. Additionally, our parametric study reveals that riblets with finer, more closely spaced geometries can further reduce the drag by an additional 25.7%. These findings underscore the efficacy of riblet geometries in different flow conditions, highlighting their potential in optimizing the acoustic and hydrodynamic performance of maritime systems.

Using different geometries on the amount of heat transfer in a shell and tube heat exchanger using the finite volume method

This research investigates the heat transfer and pressure drop characteristics of a conical spiral tube heat exchanger. The study specifically focuses on the application of Ag-HEG (Silver–Hydrogen exfoliated graphene) nanofluid and various turbulator designs. The range of Dean Numbers, specifically 2200 < Dean <4200, was studied through experiments under turbulent flow conditions. Furthermore, the finite volume method-based ANSYS Fluent commercial code was utilized for numerical simulations. Additionally, numerical simulations were performed using the ANSYS Fluent software, which utilizes the finite volume method. This research aims to perform a numerical analysis on the efficiency of a conical shell and tube heat exchanger. When compared to other models, spiral heat exchangers provide a larger contact area between the fluid and the exchanger within a specified occupied area. This advantage is one of the prominent features of this particular type of heat exchanger. The simulations were conducted in two stages. During the first stage, the thermal performance coefficients of three turbulators were evaluated. In the second stage, the four-blade turbulator with ten revolutions, which exhibited superior thermal performance, was further analyzed based on the number of circles around the center of the conical spiral coil. The numerical results showed that the four-blade turbulator with ten revolutions displayed superior thermal performance compared to the other modes, specifically the two-blade and three-blade turbulators. In the second stage, it was found that the Nusselt number achieved from 30 revolutions was higher by 4.2 %, 10 %, and 18.3 % compared to the Nusselt numbers obtained from the other two modes of 10 and 20 revolutions. Consequently, it is concluded that utilizing Ag-HEG nanofluids in conjunction with the four-blade turbulator featuring 30 revolutions is the optimal choice for improving heat transfer in conical spiral tube heat exchangers while maintaining an acceptable level of pressure drop. This combination outperforms traditional fluids and turbulators.

Investigation of convective heat transfer in a cold flow pebble bed nuclear reactor using advanced pebble probe heat transfer sensor

The aim of this study was to investigate the local heat transfer coefficients between the pebbles and the coolant gas in a PBR using an advanced measurement technique that consists of a heated pebble probe, a micro-foil heat flux sensor mounted flush on the surface of the heated pebble probe, and a thermocouple in the center of the bed void in front the sensor. In this work, the local heat transfer coefficients were derived at various axial levels, radial and angular locations and at different superficial inlet gas velocities that cover both transitional and turbulent flow conditions. The local heat transfer coefficients were found to be 22-32%, 34-39%, and 18-20% higher near the wall at superficial inlet gas velocities of 0.3,1.2, and 2m/s, respectively. This is due to higher volumetric flow at the wall where larger void in the pebble bed exists compared to the center region of the bed where the flow of the gas in the packed bed follows the least resistance path. Large deviations were obtained between the experimental overall heat transfer coefficients in the bed and the predictions of seven correlations that were selected from the literature. Furthermore, these correlations cannot predict the local heat transfer coefficients inside the PBR. This necessitates the development of new correlations for the prediction of the local heat transfer coefficients using the data obtained in this work. A pseudo-3D correlation was developed and was found to provide predictions that are in good agreement with the experimental values for the conditions used, with an averaged absolute relative error (AARE) of 3.33% at high Reynolds numbers for our operating and design conditions.

Impact of the numerical domain on turbulent flow statistics: scalings and considerations for canopy flows

Large eddy simulations (LES) are widely used to study the effects of surface morphology on turbulence statistics, exchange processes and turbulence topology in urban canopies. However, as LES are only approximations of reality, special attention is needed for the computational model set-up to ensure an accurate representation of the physical processes of interest. This paper shows that the choice of the numerical domain can significantly affect the accuracy of turbulent flow statistics, potentially causing a mismatch between numerical studies and experimental data. The study examines the influence of cross-stream aspect ratio (YAR), streamwise aspect ratio (XAR) and scale separation (SS) on first- and second-order flow statistics and turbulence topology. It is found that domains with a low YAR underestimate the velocity variance, while those with a low XAR overestimate the variance value. The study proposes a new approach based on the Buckingham Pi theorem to evaluate the effect of SS, as the existing method has major limitations for canopy flows. The results suggest that domains with small SS underpredict the variance value. To minimise the artificial impact of the numerical domain on turbulent flow statistics, the study recommends guidelines for future research, including a YAR of 3 or more, an XAR of 6 or more and an SS of 12 or more. Error tables are presented to allow researchers to select smaller domains than recommended, depending on their research interests in specific parts of the flow.

Investigating heat exchanger tube performance: second law efficiency analysis of a novel combination of two heat transfer enhancement techniques

AbstractIn the study, the focus was on evaluating the second law efficiency of a heat exchanger tube operating under continuous heat flux and turbulent flow conditions. The evaluation involved the use of a hybrid GnP and Fe3O4 and modified coiled wire as passive heat transfer enhancement techniques. The primary objective was to investigate the impact of these combined techniques on thermal and hydraulic performance, entropy generation number, Bejan number and second law efficiency. To achieve this, different mass fractions of GnP and Fe3O4 nanoparticles were used in the hybrid nanofluid, along with two forms of modified coiled wire: barrel type and hourglass type. The experimental results indicated that the utilization of hybrid nanofluids and modified helical inserts led to a noticeable improvement in the second law efficiency of the heat exchanger tube. However, it was observed that the differences in entropy generation number and Bejan number between the barrel and hourglass types were not significant, mainly due to higher frictional losses associated with the latter. The highest recorded second law efficiency was 0.416, while the lowest entropy generation number was 0.118. These values were achieved through the combined use of GnP and Fe3O4 with a mass fraction of 0.4% and a barrel-type coiled wire insert with a pitch ratio of 0.5.

Breakup prediction of oscillating droplets under turbulent flow

Droplet and bubble breakup phenomena under turbulent flow have been widely studied for over 70 years through theoretical, experimental and numerical approaches. Despite significant progress, the dynamics of breakup remains an active research topic. The present study considers a database of breakup events under turbulent conditions. The database contains neutrally buoyant droplets obtained for a single moderate turbulent Reynolds number and a Weber number near the critical Weber number of the droplets, allowing for long time evolution prior to droplet breakage. Each droplet in the database follows a consistent behavior: the droplet undergoes (1) an initial shape deformation, then (2) an extended oscillatory regime, until (3) a critical large deformation starts, leading to (4) a capillary-driven breakup. While the first two stages have been investigated in our previous work using spherical harmonics decomposition, this study focuses on the last two stages, describing them qualitatively and quantitatively by means of seven different shape parameters. These shape parameters are based on different information of the specific droplet such as its surface, its volume or its averaged mean curvature, and provide a multidimensional analysis of the droplet breakup. They are used to measure the time spent in the final two stages prior to breakup, as well as the transition between these stages. Additionally, we establish breakup thresholds for each shape parameter to predict neutrally buoyant droplet breakup under turbulent flow conditions.

New pressure drop and heat transfer correlations for turbulent forced convection in internally channeled tube heat exchanger ducts

In our previous paper, a novel heat exchanger concept, the so-called internally channeled tube (ICT) was suggested, based on a tubular geometry fitted with specially designed curved channels along the tube length. The enhanced heat transfer in the ICT results from extended surface area between two contacting fluids. To facilitate industrial application, ICT design methods must be developed. This work provides new equations for thermo-hydraulic characterization of ICT under turbulent flow conditions. In particular, new friction factor and Nusselt number correlations are derived based on the validated CFD simulations performed over a wide range of Reynolds numbers and geometrical parameters.

Total and static temperature statistics in compressible turbulent plane channel flow

The paper studies the statistics of total and static temperature (total $h_t$ and static $h$ enthalpy) in compressible turbulent plane channel flow using direct numerical simulations (DNS) data covering the range of centreline Mach numbers $0.3\lessapprox \bar {M}_{{{CL}}_x} \lessapprox 2.5$ and Huang–Coleman–Bradshaw friction Reynolds numbers $100\lessapprox Re_{\tau ^\star }\lessapprox 1000$ . For this class of very-cold-wall flows, the DNS data for correlation coefficients and joint probability density functions (p.d.f.s) show that $h_t'$ is invariably very strongly correlated with the streamwise velocity fluctuation $u'$ , in contrast to static temperature (static enthalpy $h'$ ) whose correlation with $u'$ weakens rapidly with increasing wall distance. We study various correlations and joint p.d.f.s of $h_t'$ and $h'$ in relation to the fluctuating velocity field, including the turbulent Prandtl number $Pr_{{T}}$ , and discuss the predictions of Reynolds analogy. The scaling of the mean enthalpy and the fluctuating enthalpy variance and fluxes with respect to inner and outer velocity scales is investigated. The complex behaviour and scaling of different terms in the transport equations for the enthalpy variance and fluxes are discussed.