Thermal-hydraulic Performance Factor Research Articles

Effects of extended pin fins on the hydrothermal performance of double pipe heat exchanger

Double pipe heat exchangers (DPHEs) are crucial for effective heat transfer between two fluids in industrial processes, enhancing energy recovery and optimizing thermal performance. This study aims to enhance the efficiency of DPHEs by incorporating extended pin fins. DPHEs are vital in industrial applications for their efficient heat transfer, but optimizing their performance remains challenging. Extended pin fins, which are minor protrusions added to the heat exchanger’s surface, increase the surface area for heat transfer. A numerical study on DPHEs with pin fins of varying length ratios (R=1, 2, 3, and 4) is conducted, validating our model by comparing results with prior experimental data. Parameters such as Nusselt number (Nu), friction factor, thermal–hydraulic performance factor (TPF), and exergy efficiency across Reynolds numbers from 4400 to 9400 are calculated. The results indicate that pin fins significantly enhance heat transfer. The Nu increases by 163 %-242 % for different length ratios, while the friction factor decreases, showing reductions of 161 %-290 %. Exergy efficiency improves by 216 % with an R=4 design compared to a standard DTHE, and the TPF increases by 152 % with the R=4 configuration. These findings demonstrate the substantial benefits of using extended pin fins in improving the thermal performance of DPHEs.

Deep neural network model for predicting thermal-hydraulic performance of a solar air heater with artificial roughness: Sensitivity, generalization capacity, and computational efficiency

A novel coupled computational fluid dynamics-deep neural network approach is proposed to accurately predict the performance of an artificially roughened solar air heater. Computational fluid dynamics data sets are used to develop an optimized neural network model for the prediction of thermal-hydraulic performance factor. The optimized neural network model with softmax transfer function in hidden layers has an architecture of 3‐37‐37‐1 and it predicts the thermal-hydraulic performance factor of the artificially roughened solar air heater with maximum, mean, and minimum error of 2.54 %, 0.245 %, and 0.0009 %, respectively. The concept of Shapley values is adopted to evaluate the global sensitivity analysis of the optimized deep neural network model and it is found that rib height is the most influential design parameter for the artificially roughened solar air heater. The generalization capacity of the neural network model is evaluated by comparing its predictions with experimental data, demonstrating superior predictive performance over traditional computational fluid dynamics simulations. The optimized artificial neural network model achieves a computational time gain of approximately 100 % against computational fluid dynamics.

Review on different techniques used to enhance the thermal performance of solar air heater

Energy is the key driver of life. It is required for the growth, exaltation, modernization, and financial development of any country. The world is turning away from fossil fuels in favor of renewable energy sources in order to meet the rising demand for energy and protect the environment from pollution. Solar energy is becoming a significant source of energy among these new energy sources. The primary solar energy-using appliances are solar air heaters. However, the creation of a laminar sub-layer on the absorbing plate is the cause of its poor thermal efficiency, which is a cause for concern. This paper describes various techniques through which the efficiency of solar air heaters (SAH) is enhanced by disturbing the laminar sub-layer. This study is concentrated on four techniques artificial roughness, jet impingement, piezo-electric fan, and phase change material (PCM), which are explained in four sections. The first section gives a detailed description of artificial rib roughness, turbulators, and protrusions. The second section reviews the use of jet impingement in SAH. The third section introduces a new technique; a piezo-electric fan and describes its mechanism, working parameters, and possibilities for its use in SAH through the previous studies. The fourth section reviews the use of PCM material in SAH by the previous studies. The maximum thermal hydraulic performance factor (THPP) for non-circular ribs, ribs with a rectangular cross section, ribs with an equilateral cross section, and jet impinged SAH, respectively, has been observed to be 1.44–1.29, 2.19, 2.11, and 3.66.

Experimental Analysis of a Solar Air Heater Featuring Multiple Spiral-Shaped Semi-Conical Ribs

Abstract To improve the thermal and hydraulic performance of artificially roughened solar air heaters (SAHs), the current study analyzes the thermal-hydraulic performance or thermal enhancement factor of artificially roughened solar air heaters. In present experimental research on a solar air heater's absorber plate, newly designed spiral-shaped semi-conical ribs have been explored. The spiral-shaped semi-conical ribs have been designed with the aim of reducing the pressure drop across the rib so that thermal performance may be improved with a little increase in pressure drop after integrating the ribs into the SAH mainstream flow. The higher value of thermal-hydraulic performance indicates an increased heat transfer rate with a minimum increase in pumping power. In order to achieve the highest possible thermal enhancement factor, this experimental study intends to analyze the effects of different geometrical parameters on the heat transmission and friction behavior of numerous spiral-shaped semi-conical ribs. Multiple experiments were conducted using different levels of roughness heights to optimize the rib profile parameters. The Reynolds number (Re) ranges from 3358.65 to 18,095.59, the relative roughness height (e/Dh) 0.09 to 0.227, and relative roughness pitch (P/e) 3.7 to 5.5. These multiple spiral-shaped semi-conical ribs give the maximum thermal enhancement factor of 2.85 at (e/Dh) 0.182 and P/e of 4.1 at Reynolds number 18,095.59. It has been found that current rib geometry can increase the thermal performance of solar air heaters with minimum increased pumping power with reference to rib explored by earlier researchers.

Multi-objective optimization of a combined heat sink with triangular protrusion and corrugated surface impinged by a nanofluid slit-confined jet

Improving temperature uniformity and heat transfer capacity is crucial for the application of a jet-impingement heat sink in dissipating heat from high-power electronic devices. Therefore, a combined heat sink with a triangular protrusion in the stagnation zone, a corrugated surface in the wall-jet zone, and an oblique angle of the upper plate impinged by a nanofluid jet is proposed. A two-dimensional model is established, using Al2O3-H2O nanofluid as coolant. The effects of the structural parameters of the heat sink, the volume fraction of the nanofluid on the temperature uniformity of the heat sink and the jet-impingement heat transfer were studied numerically. Meanwhile, the structure of the heat sink is optimized by the NSGA-II genetic algorithm. The results indicate that the three structures can enhance both the temperature uniformity and the heat-transfer capacity. Using nanofluids with a 3%volume fraction and a Reynolds number of 8,000, the average Nusselt number of the optimal structure is 26 % greater than that of a jet impingement flat heat sink, the temperature standard deviation is 67 % less, and the friction coefficient and thermal-hydraulic performance factor are greater by 55 % and 9 %, respectively. Meanwhile, the optimized structure exhibits excellent heat dissipation and temperature uniformity at higher heat flux. The allowable maximum heat flux reaches 341 W/cm2 when the junction temperature of the hot spot does not exceed 348 K, and the temperature standard deviation is 2.926, which are increase by 83 % and decrease by 36 % compared with that of jet-impingement plate heat sink, respectively.

Morphing optimization of flow and heat transfer in concentric tube heat exchangers

Concentric tube heat exchangers are vital in various industrial applications, including chemical, process, energy, mechanical, and aeronautical engineering. Advancements in heat transfer efficiency present a significant challenge in contemporary research and development. This study concerns optimizing flow and heat transfer in concentric tube heat exchangers by morphing the tube's walls. The adjoint shape optimization approach is implemented in a fully turbulent flow regime. The effect of inner tube deformation on flow physics and heat transfer is examined. The results show that morphing can lead to a 54% increase in the heat transfer rate and a 47% improvement in the overall heat transfer coefficient compared to straight concentric tube designs. Moreover, the thermal-hydraulic performance factor is calculated to account for the relative increase in heat transfer when the optimal and initial designs are operated under the same pumping power. A thermal-hydraulic performance factor of 1.2 is obtained for the new design, showing that the heat transfer enhancement caused by morphing the tube's walls outweighs the increase in pumping power. The physics of a radial flow, resulting from an adverse pressure gradient in an annular region caused by the successive inner tube deformation, significantly augments heat transfer. This study shows morphing can lead to higher thermal efficiencies, and numerical optimization can assist in achieving this goal.

Numerical and experimental study of thermal efficiency of the transversal rectangular baffles with incline angle inside of solar air collector

ABSTRACT This study aims to improve the thermal and hydraulic performance of the solar air collector through rectangular baffles perpendicular to the air inside the channel (duct). In the latter, four cases were examined for the number and position of baffles (6 b, 10 b, 14 b, 18 b) with a fixed inclination angle of 135° in the Reynolds range from Re = 5038 to Re = 10635 using Computational Fluid Dynamic (CFD) (Ansys Fluent 18.1). The turbulence model RNG k-ε was chosen because it gave closer results to the standard correlations of Dittus-Boelter and Modified Blasius, compared to the rest of the models. The validity of the CFD simulation was confirmed based on the experimental investigation. The study -of these cases shows that the increase in the number of baffles increases the average Nusselt number as well as the friction coefficient, where the highest value of Nusselt was recorded in the case of 18 baffles Nu = 49.40 at Re = 10257. The relationship between the positioning of the baffles and the local heat transfer coefficient was also concluded. The last three cases (10 b, 14 b, 18 b) gave a very close thermal-hydraulic performance factor (THPF), while the first case (6 b) is significantly greater than theirs by a significant percentage, where the highest value recorded THPF = 0.557 at Re = 5368. Throughout this work, the effect of baffles on the heat transfer from the absorber plate to the air was understood through the local heat transfer coefficient along the channel and the velocity fields and their rays. This said heat transfer was also perceived by adding this form of baffles in the four cases and their impact on the hydraulic and thermal performance of the collector.

Effect of nanofluids on heat transfer characteristics of an aerodynamic swirl nozzle for isothermal and isoflux conditions

ABSTRACT Achieving axisymmetric boundary conditions in turbulent swirl flows and predicting thermo-fluidic behaviours within a nozzle is often a challenge due to the difficulties of measurement diagnostics. Adding nanoparticles to ase fluids exacerbates the complexity because of the regeneration of effective properties of the fluid medium. As such, this study numerically investigates the flow and thermal characteristics for the effect of swirl and nanofluids of incompressible turbulent liquid jets. The results show that the axial and tangential velocity profiles for water-based nanofluids resemble to those for water in no-to-high swirl flows. The surface Nusselt number for strong swirl flow reduces with axial distances at isothermal wall condition, and the Nusselt number is strongly dependent on types of nanofluid for isoflux condition. Water-based nanofluids cause higher heat transfer compared to Dowtherm+Al2O3 and Syltherm800+ Al2O3. The average Nusselt number and the pressure drop are found to be the largest for 10% volume fraction. The increase of thermal-hydraulic performance factor for nanofluids after nozzle convergence is steeper for highly swirling flow than for non-swirling and medium swirling cases. A strong turbulent kinetic energy is observed immediately after the nozzle converging section for all nanofluid cases and Dowtherm+Al2O3 shows relatively uniform distributions across the nozzle.

Thermal and Hydraulic Performances of Porous Microchannel Heat Sink Using Nanofluids

Abstract Microchannel heat sink is an effective method in compact and faster heat transfer applications. This paper numerically investigates thermal and hydraulic characteristics of a porous microchannel heat sink (PMHS) using various nanofluids. The effect of porosity (γ = 0.32–0.60), inlet velocity (win = 0.5–1.5 m/s), and nanoparticle concentration (ϕ=0.0025 – 0.05) on thermal-hydraulic performance is systematically examined. The result shows a significant temperature increase (40 °C) of the coolant in the porous zone. The pressure drop reduces by 35% for γ = 0.32 compared to the non-porous counterpart, and this reduction of pressure significantly continues when γ further increases. The pressure drop with win is linear for PMHS with nanofluids, and the change in pressure drop is steeper for nanofluids compared to their base fluids. The average heat transfer coefficient increases about 2.5 times for PMHS, and a further increase of 6% in h¯ is predicted with the addition of nanoparticles. The average Nusselt number Nu¯ increases nonlinearly with Re for PMHS. The friction factor reduces by 50% when γ increases from 0.32 to 0.60, and the effect of nanofluid on friction factor is insignificant beyond the mass flowrate of 0.0004 kg/s. Whilst Cu and CuO nanoparticles help to dissipate the larger amount of heat from the microchannel, Al2O3 nanoparticle appears to have a detrimental effect on heat transfer. The thermal-hydraulic performance factor strongly depends on the nanoparticles, and it slightly decreases with the mass flowrate. The increase of nanoparticle concentration, in general, enhances both h¯ and ΔP linearly for the range considered.

CFD simulation of thermal hydraulic performance of rectangular solar air heater with combination of boot rib roughness

This paper expresses a comparison between the results of the boot and reverse boot shape roughness applied in a solar air heater. The results are found with the help of CFD simulations for different shapes of boot shaped ribs on solar air heater. The combined roughness of boot and reverse boot shape is analyzed for different parameters of geometry to increase the thermal performance of the solar air heater which are relative pitch roughness, P/eb = 7–12, angle of attack, θ = 30°, 40°, 50°, 60°, pitch of the ribs, p = 15.4–26.4 mm, the height of ribs, eb = 2.2 mm, with variations in Reynolds number, Re, ranging from 2000 to 18,000. The RNG k-ε model is used for the CFD simulation. The results shows that the increase in heat transfer rate as a result of applying the combined boot and reverse boot shape roughness in solar air heater is about 2.54 times that of conventional solar air heater, for P/eb = 11, θ = 50° and Re = 18,000. The maximum thermal hydraulic performance factor of 2.6 is achieved for combined roughness with P/eb = 11, θ = 50°, and Re = 2000.

HEAT TRANSFER ENHANCEMENT IN A HELICALLY CORRUGATED TUBE BY EMPLOYING W/EG BASED NON-NEWTONIAN HYBRID NANOFLUID UNDER TURBULENT CONDITIONS

In this study a numerical investigation is carried out for heat transfer and fluid flow analysis using ethylene glycol-based TiO2-SiO2 non-Newtonian hybrid nanofluid over a range of volume fractions from 0 to 5% inside a helically corrugated tube under turbulent flow conditions. The analysis is performed with different mixing ratios of TiO2 and SiO2 at different corrugation-height ratios (e/Dh = 0.05, 0.07, 0.09) and pitch ratios (p/Dh = 0.25, 0.30, 0.35). Numerical simulations have been conducted using ANSYS FLUENT 19.0 with a constant heat flux of 25 kW/m2 maintained at the wall surface for a range of Reynolds numbers from 5000 to 30,000. The thermal-hydraulic performance factor exceeds unity in almost every tested combination. It increases by increasing the values of e/Dh and p/Dh and decreasing the concentration of TiO2 in the hybrid-nanoparticle mixing ratio. Thus employing hybrid nanofluids inside corrugated tubes is a worthwhile arrangement at a proper mixing ratio of TiO2 and SiO2.

Multi-Objective Optimization of Different Channel Shapes in Heat Exchangers

The effect of geometric parameters of the zigzag, rectangular, and serpentine channels on convective heat transfer coefficient and pressure drop was investigated using computational fluid dynamics (CFD). In all channels, the same boundary conditions were considered, and the number of steps was equal to 10. The simulations were performed for turbulent flows (liquid water as the operating fluid), and Reynolds number (Re) range between 20000 and 60000 was selected. The zigzag channel showed a best thermal performance and the serpentine channel showed the best hydraulic performance. The thermal-hydraulic performance (THP) factor was employed for comparing the channels. As the complexity of the channels surfaces increased, the two parameters of convective heat transfer coefficient (positive factor) and pressure drop (negative factor) increased simultaneously. Therefore, predictive correlations for friction factor and Nusselt number were presented using genetic algorithm (GA), and the multi-objective optimization was performed to obtain the most appropriate Nusselt number and minimum friction factor as the two basic objective functions. The resulting Pareto set, which includes the optimum geometric dimensions of the heat exchangers, allows a designer to choice the geometries based on higher heat transfer or lower pumping power.

Experimental study on the thermal-hydraulic performance of a fluttering split flag in a channel flow

The use of flags as vortex generators inside heat sinks has been successfully demonstrated as a heat transfer enhancement technique. However, their thermal-hydraulic performance is usually diminished by the blocking effect induced by the fluttering phenomenon. To tackle this problem, with the expectation to maximize the fluid mixing while minimizing the pressure drop, we report a simple and direct design by splitting a flag into multiple strips. Flags with different strip widths were compared with a full flag on the performance of pressure drop and heat transfer. A high-speed camera is used to investigate their fluttering motion. A piezoelectric plate is attached to the wall to measure the flag's flutter frequency. The results show that the performance of a flag with multiple strips outperforms that of the full flag for its lower pressure drop and higher heat dissipation effect. The performance of split flag is not linear with the strip number and the optimal way in our study is to split the full flag into 4 strips. The maximum thermal-hydraulic performance factor of the split flag is 1.91, which is 26% higher than that of the full flag. Besides, the split flag starts fluttering at a lower wind velocity. All these results demonstrate that the split strategy of a flag acting as a vortex generator is of great potential for improving the heat sink performance.

Research for a Non-Standard Kenics Static Mixer with an Eccentricity Factor

The Kenics static mixer is one of the most widely studied static mixers, whose structure–function relationship has been studied by varying its aspect ratio and modifying the surface. However, the effect of the symmetric structure of the Kenics static mixer itself on twisting the fluid has been neglected. In order to study how the symmetrical structure of the Kenics static mixer impacts the fluid flow, we changed the center position of elements at twist angle 90° and introduced the eccentricity factor γ. We applied LHS-PLS to study this non-standard Kenics static mixer and obtained the statistical correlations of the aspect ratio, Reynolds number, and eccentricity factor on relative Nusselt number and relative friction factor. We analyzed the results by comparing the PLS model with the univariate analysis, and it was found that the underlying logic of the Kenics static mixer with an asymmetric structure became different. In addition, a non-standard Kenics static mixer with an asymmetric structure was investigated using vortex generation and dissipation through fluid flow simulation. The results demonstrated that the classical symmetric structure has a minor pressure drop, but the backward eccentric one has a higher thermal-hydraulic performance factor. It was found that the nature of the eccentric structure is that two elements with different aspect ratios are being combined at θ=90°, and this articulation leads to non-standard Kenics static mixers with different underlying logic, which finally result in the differences between the PLS model and the univariate analysis.

Heat transfer enhancement in cold plate based on FVM method and field synergy theory

To optimize the overall heat dissipation performance of the straight channel of a cold plate for lithium battery in vehicles, we used the wavy channel to optimize the structure and uses the face-centered central composite design (FCCCD), which takes the overall thermal-hydraulic performance factor as the response to explore the interaction mechanism of the flow field and temperature field in wavy channel of the cold plate. When the amplitude of the wavy channel is 1 mm and the number of cycles is 4, the overall thermal-hydraulic performance will reach its maximum with an increase of 17.4 % relative to the straight channel. Then, for the coolant, we explored the heat transfer performance of the nanofluid. The heat transfer coefficient of the nanofluid with a volume fraction of 2 % is 117 % higher than that of pure water and does not cause a significant increase in pressure drop.

Analysis of Laminar Convective Heat Transfer Over Structured Non-Wetting Surfaces

Structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow which, in turn, affects the convective heat transfer performance over the surfaces. In this paper, an analytical model is developed for the interfacial Nusselt number, the overall Nusselt number and a thermal hydraulic performance factor for fluid flow in a cylinder patterned with structured non-wetting surfaces, for the two cases of uniform wall heat flux and uniform wall temperature. In addition, by considering the stability of the Cassie state of wettability and its transition to the Wenzel state for flow over superhydrophobic surfaces, the present model overcomes certain limitations of the previously reported studies in the literature. Based on the analytical formulations and the stability constraints, the present paper provides optimum design maps for tailoring structured non-wetting surfaces for maximizing convective heat transfer and the combined thermal-hydraulic performance in applications. Use of the design maps on example cases is also discussed. It is shown that the use of structured non-wetting surfaces is most effective for low Reynolds numbers and/or small cylinder radius.

A novel curved-corrugated channel model: Thermal-hydraulic performance and design parameters with nanofluid

In this study, flow structure and heat transfer characteristics of the novel channel, namely: the curved-corrugated channel, are numerically studied using ZnO-water nanofluid and the presence of E-shaped baffles. The influences of corrugations, baffles, and geometric parameters; gap ratio (GR = 0.2,0.3,0.4, and 0.5), blockage ratio (BR = 0.2,0.25,0.3, and 0.35), and pitch angle (β = 10°, 12.5°, and 15°) at different Reynolds number (8000–32,000) and volume fraction of ZnO particles (0–4%) are evaluated using thermal-hydraulic performance method. The results reveal that the formation of vortex flow and increased turbulence due to effects of corrugations and baffles can improve the heat transfer enhancement. Tested channel with baffle is superior to the other without baffle in thermal-hydraulic performance factor (THPF), and at lowest pitch angle 10° provides the best THPF. Reducing the gap ratio and increasing the blockage ratio, i.e. 0.2 and 0.35, yields the best THPF at 2.57. New correlations for Nusselt number and friction factor for baffled curved-corrugated channel with using nanofluid are also reported.

Numerical analysis of thermal-hydraulic characteristics of steam-air condensation in vertical sinusoidal corrugated tubes

ABSTRACT The thermal-hydraulic characteristics of steam-air in the vertical corrugated tubes with sinusoidal waveform condensing wall of various amplitudes and wavelengths under the different inlet velocities, air mass fractions and wall subcoolings are numerically investigated, in the cases that the mass, species, energy and momentum sink terms are added in the cells adjacent to the condensing wall to simulate the condensation process. The mechanisms of turbulent flow and heat transfer enhancement of steam-air in condensation are also explored. The results show that the detached vortex characteristics and accumulated air in waveform domain influence the condensation heat transfer greatly, which are closely related to the amplitude and wavelength of basic waveform as well as inlet velocity. To evaluate the thermal-hydraulic performance of steam-air fluid in the corrugated tubes, the thermal-hydraulic performance factor, φ, describing the relation of heat transfer performance (i.e., η) to pressure drop characteristic (i.e., β), is defined. The better thermal-hydraulic performance can be obtained in the corrugated tubes with longer wavelength and higher amplitude waveform condensing wall under a low inlet velocity as well as with lower amplitude waveform condensing wall under a high inlet velocity. Besides, the corrugated tubes with A=0.5, 2 mm at L=21 mm respectively in the inlet velocity range of v=2-4 m/s and v=5-12 m/s are the better design of geometric parameters.

Inverted structurally inhomogeneous stepped agitators in a channel flow

Homogeneous thin-film agitators used in a channel flow have shown enhanced thermal-hydraulic performances compared to a clean channel benchmark. In this study, an experimental study was carried out to explore the performances of three inverted structurally inhomogeneous stepped agitator designs in the same channel flow in order to further improve the overall thermal-hydraulic performance of a heatsink. The three agitator designs were constructed by connecting two sections of material with different lengths while maintaining the constant total length of 6 mm as in our previous study: a relatively thicker 125-μm material mounted on the channel wall as the trailing edge and a thinner 25-μm material as the free leading edge. The new designs were expected to maximize fluid mixing enhancement but minimize pressure loss due to the unique structure of the inhomogeneous materials. Experiments in this study covered a wide Reynolds number range from 300 to 9000. High-speed footage was used to capture the dynamic motion of the agitators. At the same time, a time-resolved particle image velocimetry (TR-PIV) system was used to characterize the vortex dynamics due to the motion of agitators in various flow conditions. A synthetic thermal-hydraulic performance factor, η, taking into consideration both the Nu number enhancement and friction factor increment, was used to evaluate the overall effects of the added agitator features in the channel flow compared to a clean channel benchmark. Results show that a maximum factor of about 1.5 has been achieved, and it stays above 1 under most of the test conditions in this study, indicating great benefits for enhanced thermal transport.

Numerical thermal‐hydraulic performance investigations in turbulent curved channel flow with horseshoe baffles

AbstractA numerical work is performed to investigate the thermal‐hydraulic performance in a curved channel of a journal bearing equipped with oblique horseshoe baffles. Water, a working fluid, is passed through the curved channel at a constant temperature condition of 358 K. The effects of different parameters of baffles, that is, attack angle (α = 45°, 60°, and 90°) and the number of baffles (NB = 9 and 13 baffles), are examined. Influences of design parameters on heat transfer and friction performances are studied and displayed in terms of the Nusselt number, the friction factor, the Nusselt number enhancement ratio, and the thermal‐hydraulic performance factor (THPF). The numerical simulations present the flow structures of the tested channel in terms of velocity, isotherms, turbulent kinetic energy, and vorticity contours. The numerical results reveal that the adopted geometry of the curved channel with baffles yields a significant enhancement of heat transfer rate over the plain channel (without baffles), which is approximately 2.5 to 3.8 times. Also, the results show that the best condition to achieve maximum heat transfer is at angle α = 90°, NB = 13, and Re = 5000, compared with other conditions. Furthermore, the maximum THPF of the curved channel using baffles is 4.4 at the same condition. The results confirmed that the geometry of the baffles inside the curved channel has a remarkable impact on heat transfer improvement, accompanied by a reasonable increase in friction losses.