cfd analysis of heat exchanger research paper

CFD Analysis of Heat Exchanger Models Design Using ANSYS Fluent

International Journal of Mechanical Engineering and Technology 11(2), 2020, pp. 1-9

9 Pages Posted: 16 Mar 2020

M. Tech., Student, Department of Mechanical Engineering, Sachdeva Institute of Technology, Farah, Mathura, India

Devendra Singh

Assistant Professor, Department of Mechanical Engineering, Sachdeva Institute of Technology, Farah, Mathura, India

Ajay Kumar Sharma

Assistant Professor, Department of Mechanical Engineering, Institute of Engineering and Technology Lucknow, India

Date Written: February 18, 2020

The aim of the study is design tube and box heat exchanger with various pattern of tubes and examine the flow and temperature field at inlet and outlet point of tube and container using ANSYS programming tool. Three types of heat exchangers are planned in this examination with various structures of cylinders contains of 175 mm breadth and 1000 mm length shell measurement 175 mm. To expand the rate of heat exchange of heat exchanger advancement is done which tries to distinguish the best parameter combination of heat exchangers. The prefix parameter (tube width) is utilized as an info variable and the yield parameter is the most extreme temperature distinction of container and tube heat exchanger. Three types models are design on the basis tubes varieties of heat exchanger and CFX examination is completed in ANSYS 14.0.

Keywords: Shell and tube heat exchanger, Ansys, Temperature, Heat transfer coefficient, thermal analysis, FEM

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Ram Kishan (Contact Author)

M. tech., student, department of mechanical engineering, sachdeva institute of technology, farah, mathura, india ( email ).

Boulder, CO 80309 United States

Assistant Professor, Department of Mechanical Engineering, Sachdeva Institute of Technology, Farah, Mathura, India ( email )

Assistant professor, department of mechanical engineering, institute of engineering and technology lucknow, india ( email ).

Azhikal, Tamil Nadu 629 202 India

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CFD Analysis of Heat Transfer Coefficient and Pressure Drop in a Shell and Tube Heat Exchanger for Various Baffle Angles

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• First Online: 31 May 2023
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• R. Anandan   ORCID: orcid.org/0000-0002-6727-6103 14 ,
• G. Sivaraman   ORCID: orcid.org/0000-0002-3497-0748 15 ,
• M. Rajasankar   ORCID: orcid.org/0000-0002-1289-6997 16 &
• R. Girimurugan   ORCID: orcid.org/0000-0003-0257-0448 17  

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A shell and tube heat exchanger is analyzed numerically to determine the effect of the baffle angle on the heat transfer coefficient and the pressure drop. Heat exchangers that use shells and tubes benefit greatly from baffles because they allow for more effective heat transfer with less pressure drops. CATIA and ANSYS—Workbench Flow Simulation software is used to construct heat exchangers with baffle angles of 0, 10, 20, 30 and 40°, and fluid dynamic simulations are also performed. The greatest heat transfer occurred at a baffle angle of 40°, assuming a constant heat transfer coefficient between the baffle and shell. It has been shown that a 40° baffle angle produces the least amount of pressure drop. Our heat exchanger features a combination of rotational and helical baffle patterns, which greatly improves its heat transfer coefficient per unit pressure drop.

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Department of Mechanical Engineering, Vinayaka Mission’s Kirupananda Variyar Engineering College, Salem, Tamilnadu, India

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G. Sivaraman

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M. Rajasankar

Department of Mechanical Engineering, Nandha College of Technology, Perundurai, Tamilnadu, India

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Anandan, R., Sivaraman, G., Rajasankar, M., Girimurugan, R. (2023). CFD Analysis of Heat Transfer Coefficient and Pressure Drop in a Shell and Tube Heat Exchanger for Various Baffle Angles. In: Tripathy, S., Samantaray, S., Ramkumar, J., Mahapatra, S.S. (eds) Recent Advances in Mechanical Engineering. ICRAMERD 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-9493-7_6

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• DOI: 10.1016/j.energy.2024.132754
• Corpus ID: 271778294

Advancements in analyzing air-side heat transfer coefficient on the individual tube rows in finned heat exchangers: Comparative study of three CFD methods

• Mateusz Marcinkowski , D. Taler , +1 author Jan Taler
• Published in Energy 1 August 2024
• Engineering, Environmental Science

41 References

General numerical method for hydraulic and thermal modelling of the steam superheaters, a critical review on colburn j-factor and f-factor and energy performance analysis for finned tube heat exchangers, an investigation of multistream plate-fin heat exchanger modelling and design: a review, air-side fouling of finned heat exchangers: part 1, review and proposed test protocol, performance evaluation of a fin and tube heat exchanger based on different shapes of the winglets, numerical investigation to analyse the effect of fin shape on performance of finned tube heat exchanger, comparison of individual air-side row-by-row heat transfer coefficient correlations on four-row finned-tube heat exchangers, air-side nusselt numbers and friction factor’s individual correlations of finned heat exchangers, parametric analysis of the influence of geometric variables of vortex generators on compact louver fin heat exchangers, heat exchangers for cooling supercritical carbon dioxide and heat transfer enhancement: a review and assessment, related papers.

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I. INTRODUCTION

Ii. geometry creation, a. experimental, b. rough surface characterization, c. geometries and meshes from experiment, iii. numerical methodology, a. governing equations, b. numerical methods, c. initial and boundary conditions, dimensionless numbers, iv. results and discussion, a. instantaneous flow, b. mean velocity and temperature, c. effective turbulent prandtl number, d. impact of skewness and roughness height on reynolds stresses and heat fluxes, e. impact of skewness and roughness height on effective heat transfer, f. effect of surface anisotropy on the anisotropy of the reynolds stress tensor, v. conclusions, acknowledgments, author declarations, conflict of interest, author contributions, data availability, large eddy simulations of flow over additively manufactured surfaces: impact of roughness and skewness on turbulent heat transfer.

Currently employed by Cambridge Flow Solutions Ltd., United Kingdom.

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Himani Garg , Guillaume Sahut , Erika Tuneskog , Karl-Johan Nogenmyr , Christer Fureby; Large eddy simulations of flow over additively manufactured surfaces: Impact of roughness and skewness on turbulent heat transfer. Physics of Fluids 1 August 2024; 36 (8): 085143. https://doi.org/10.1063/5.0221006

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Additive manufacturing creates surfaces with random roughness, impacting heat transfer and pressure loss differently than traditional sand–grain roughness. Further research is needed to understand these effects. We conducted high-fidelity heat transfer simulations over three-dimensional additive manufactured surfaces with varying roughness heights and skewness. Based on an additive manufactured Inconel 939 sample from Siemens Energy, we created six surfaces with different normalized roughness heights, R a / D = 0.001 , 0.006 , 0.012 , 0.015 , 0.020 , and 0.028, and a fixed skewness, s k = 0.424 ⁠ . Each surface was also flipped to obtain negatively skewed counterparts ( ⁠ s k = − 0.424 ⁠ ). Simulations were conducted at a constant Reynolds number of 8000 and with temperature treated as a passive scalar (Prandtl number of 0.71). We analyzed temperature, velocity profiles, and heat fluxes to understand the impact of roughness height and skewness on heat and momentum transfer. The inner-scaled mean temperature profiles are of larger magnitude than the mean velocity profiles both inside and outside the roughness layer. This means, the temperature wall roughness function, Δ Θ + , differs from the momentum wall roughness function, Δ U + ⁠ . Surfaces with positive and negative skewness yielded different estimates of equivalent sand–grain roughness for the same R a / D values, suggesting a strong influence of slope and skewness on the relationship between roughness function and equivalent sand–grain roughness. Analysis of the heat and momentum transfer mechanisms indicated an increased effective Prandtl number within the rough surface in which the momentum diffusivity is larger than the corresponding thermal diffusivity due to the combined effects of turbulence and dispersion. Results consistently indicated improved heat transfer with increasing roughness height and positively skewed surfaces performing better beyond a certain roughness threshold than negatively skewed ones.

Additive manufacturing (AM) is being pursued for the demanding task of manufacturing gas turbine hot gas path components. The challenge comes from precisely maintaining the component at the highest temperature the material can tolerate given the load they are exposed to, such that the benefits in increased thermal efficiency are harvested. To develop such components, precise control over heat transfer and pressure losses in the cooling system is crucial. To this end, the studies detailed in this and previous papers have been conducted. 1,2

AM surfaces, particularly powder bed fusion laser beam (PBF-LB), exhibit high average surface roughness, typically falling within the range of R a = 5 – 25 μ m. The high surface roughness of PBF-LB surfaces stems from the powder-based manufacturing process, where a high-power laser selectively melts and solidifies layers of powder material to fabricate components. 3 The intricate interplay of melt pool dynamics, laser angle of incident, print orientation, and other print process parameters contributes significantly to the formation of surface roughness during the AM process. 4 The topography of PBF-LB surfaces is characterized by the presence of partly sintered powder particles or larger spatter particles from the melt pool on the surface, accompanied by an underlying waviness originating from the melt pools. These particles manifest as sharp peaks in surface roughness measurements, often resulting in positively skewed surfaces. In addition, high peak density or variations in melt pool characteristics can result in valley-dominated surfaces.

Flow and heat transfer in channels have been studied for over a century. For rough and smooth walls, reliable correlations are available for pressure losses. 5–8 For heat transfer, the situation is more complex. Heat transfer in internal air-cooled systems is governed by Newton's law of cooling, Q = A α ( T w − T cool ) ⁠ . Typically, in a gas turbine context, the temperature difference between the cooling flow ( T cool ) and the wall temperature ( T w ) is given. However, the cooling engineer can optimize the design by adjusting the exposed surface area ( A ) and the heat transfer coefficient ( α ). The heat transfer coefficient is favored by “thin flow passages,” characterized by the hydraulic diameter, D h , which can be seen directly in the definition of the Nusselt number, N u = α D h / λ ⁠ , where λ is the thermal conductivity of the fluid. Maximizing the surface area while minimizing the hydraulic diameter can be achieved with a cooling design that relies on in-wall cooling (or mini-) channels.

Smooth channels are thoroughly explored, and well-established correlations are found (predominately Dittus 9 and Gnielinski 10 ). Regarding the heat transfer dynamics over rough surfaces, various empirical studies by Nunner, 11 Dipprey and Sabersky, 12 and Kays and Crawford 13 have investigated predictive correlations for the Stanton number ( St ). Nunner 11 conducted pioneering experiments on a surface roughened with two-dimensional transverse ribs, providing an empirical expression for St in terms of the Reynolds number, Prandtl number, and the ratio of rough to smooth skin friction coefficients. Additionally, Dipprey and Sabersky 12 proposed a semi-analytical expression for St based on the law of the wall similarity, incorporating the Prandtl number, skin friction coefficient, and inner-scaled equivalent sand–grain roughness, k s . They addressed the challenge of incorporating the effects of k s on St by leveraging experimental data from a pipe with sand–grain roughness. Subsequent studies have refined and modified these expressions based on experimental and numerical investigations. 14,15 Furthermore, due to challenges in obtaining accurate temperature fields within the roughness sublayer, the underlying physics of how wall roughness influences heat transfer remains ambiguous.

The effect of surface roughness has also been investigated numerically, 16–24 with various methods. Several studies have proposed roughness models to account for roughness in laminar flows. Advancements in computer technology have facilitated direct numerical simulations (DNS) for studying turbulent heat transfer over resolved rough surfaces. 25–29 MacDonald et al. 27 conducted DNS specifically on turbulent heat transfer over sinusoidally rough surfaces, indicating that the correlation function proposed by Dipprey and Sabersky 12 accurately captured the influence of equivalent sand–grain roughness on St . Analysis of instantaneous temperature fields revealed that dissimilarities between heat and momentum transfer were primarily due to pressure drag effects on the rough wall, enhancing momentum transfer but not heat transfer. Peeters and Sandham 26 explored DNS for grit-blasted surfaces, affirming the efficacy of Dipprey and Sabersky's correlation 12 in predicting St for such surfaces. Notably, dissimilarities between heat and momentum transfers were evident in the recirculation zone behind roughness elements, where effective Prandtl numbers increased rapidly within the rough surface. Recent DNS studies 27,28 have further investigated the scaling behavior of the temperature roughness function, Δ Θ + ⁠ , analogous to wall roughness function, Δ U + ⁠ , and observed notable deviations from the established Δ U + correlation, particularly at higher k s + values.

In recent times, substantial efforts have been dedicated to investigating the relationship between topological roughness parameters and the consequent increase in friction factor ( c f ). However, the surface roughness generated by AM techniques exhibits spatial non-uniformity, influenced by various factors such as profile curvature, layer thickness, laser power, sample orientation, metallic composition, and particle size. As a result, AM roughness differs considerably from regular, random, and artificial roughness. To date, convective heat transfer in AM-made mini-channels remains understudied, with limited experimental and numerical investigations. 29–33 Snyder et al. 31 demonstrated successful tailoring of surface roughness through AM process parameters, enhancing the performance of a generic micro-channel cooling design. More recent studies by Garg et al. 29,34 have largely focused on systematically exploring the relationship between AM roughness characteristics and k s to reveal their impact on turbulent heat transfer using the similarity function, wall-normal Reynolds stress, heat flux, and probability density functions by using wall resolved large eddy simulations (LES). It has been explored how turbulence statistics is affected by the presence of the roughness elements, particularly “peaks” dominant surfaces, and the highly non-uniform heat transfer was shown to predominately take place at the “peaks” of the wall roughness. In this paper, we continue these studies and aim to show higher-order statistics of the roughness characteristics that affect heat transfer by directly comparing “peak” and “valleys” dominant surfaces. To the best of the authors' knowledge, this study represents the first instance of using LES to simulate turbulent heat transfer in “peak” and “valley” dominated AM rough wall pipe flows with grid-conforming three-dimensional roughness elements. Note that the surfaces considered in the current study and the simulation parameters are different from the ones used by Garg et al. 29,34

The test specimen used for surface roughness measurements was manufactured using PBF-LB on an EOS M400-4 system at Siemens Energy, Finspång. The powder feedstock was Inconel 939, with a powder particle size distribution ranging from 15 to 45  μ m. Printing parameters were set according to Siemens Energy standard, and the inert gas was argon. The build direction was set from bottom to top, as shown in Fig. 1 . The specimen had a height of 30 mm and a maximum diameter of 15 mm, featuring a total of 41 surfaces with orientations at −60° (downskin), 0°, 60° (upskin), and 90°. Each orientation (except 0°) comprised a minimum of eight surfaces. Surface measurements were performed on each surface using both an optical high-resolution light microscope, the Leica DM6 M, with focus variation, and an SEM, the Jeol JSM-IT500. Post-processing, encompassing profile, and areal evaluation were carried out using the Leica Map DCM software (Release: 7.4.8964).

Illustration of the test specimen. (a) Naming of different levels. (b) Test specimen in relation to gas flow, reacoater, and laser.

Our goal in this study is to directly isolate the effects of roughness height and skewness on turbulent heat transfer. To achieve this, we needed to tightly control the roughness characteristics of the surfaces we investigated by using a specific rectangular area from the downskin surface at position 5 (see Fig. 1 ) as a base. We then resized this base area to create six samples with varying roughness heights, while keeping the underlying surface pattern constant. The original surface was positively skewed, i.e., dominated by peaks. To create samples with negative skewness, we simply flipped these original surfaces upside down. In total, 12 rough surfaces were generated based on the data provided by Siemens Energy, shown in Fig. 2 . Flipping the surfaces essentially transformed the peaks into valleys, all while maintaining consistent roughness parameters. Table I summarizes the key characteristics derived from the probability density function (PDF) of the surface height. These characteristics include the average roughness height, R a , the maximum peak-to-valley height, R z , the skewness factor, s k , and the kurtosis factor, k u , all calculated using the height function, y ( x , z ), over sampling lengths L x and L z in the streamwise and spanwise directions, respectively. We denote surfaces with positive skewness (peak-dominated) as PS and those with negative skewness (valley-dominated) as NS for brevity. Figure 2(a) displays surfaces with a positive value of s k , while Fig. 2(b) depicts surfaces with a negative value of s k . Going from left to right, the normalized roughness height ( ⁠ R a / D ⁠ ) ranges from 0.001 to 0.028. The roughness parameters, determined using the code developed by Garg et al., 29,34 are detailed in Table II . Notably, the values of k u remain constant across all rough surfaces examined in this study.

Visualization of additive manufacturing rough surface height map, y ( x , z ), extracted from the measurement of 3D printed microchannels at Siemens Energy. The surfaces in the top row have s k = 0.424 value (a1) PS1, (a2) PS2, (a3) PS3, (a4) PS4, (a5) PS5, and (a6) PS6; those in the bottom row have s k = − 0.424 value (b1) NS1, (b2) NS2, (b3) NS3, (b4) NS4, (b5) NS5, and (b6) NS6. From left to right, the sampled surface is the same, but the mean roughness height increases.

Summary of roughness parameters based on roughness height, y (assuming mean line is at y  = 0), with continuous formulations, where L x is the surface length, and p , the probability density function.

Statistical quantities for the 12 rough surfaces considered. The descriptions and analytical expressions are given in Table I . Here D is the characteristic diameter of the rough pipe (defined later).

A rectangular portion of the downskin surface at position 5, as shown in Fig. 1 , was extracted and written in STL format. Figure 3 shows the transformation of this rough plane to a rough pipe. The planar surface is mirrored along the x -axis. This operation ensures that both sides of the surface parallel to this axis are identical. Then a rotation around the x -axis is applied to all points of the STL file. Along the closing line, all pairs of points merge perfectly thanks to the previous mirroring step, as shown in Fig. 3 .

A planar rough surface mirrored with respect to the black line and then wrapped around the same direction to produce a rough pipe.

Practitioners can easily bend a planar surface using commercial and open-source CAD software. However, merging the points along the closing line is quite time-consuming and error-prone. Indeed, this operation relies on a threshold distance to decide whether two points on the closing line should be merged. The determination of this threshold value for a given STL file is cumbersome.

To ease the process of creating rough cylinders, the authors have developed an open-source Fortran code available on GitHub. 35 The code runs on Unix systems and takes as input parameters the STL file containing the planar rough surface and a tolerance factor used to merge the points on the closing line. Optionally, the user can specify a roughness factor to rescale the surface roughness. Several values of tolerance factors may need to be tested in a trial-and-error approach in order to find the most appropriate one. A tolerance factor of 0.002 was found accurate to properly merge the points on the closing line for all the pipes considered in this work. The flexibility of the code is a major asset for the creation of rough pipes from AM rough surfaces. Moreover, the ability to rescale the surface roughness leads to straightforward parametric studies of the impact of the roughness height and skewness on turbulence and heat transfer. The code produces an STL file containing the rough pipe, as shown in Fig. 3 , and related statistical quantities, as detailed in Table I (only the ones of interest for the present work). This code has been used in our previous studies. 29,34

We used snappyHexMesh, a meshing tool included in the OpenFOAM software (OF7), to create meshes for the volumes within the cylinders. As an example, Fig. 4 shows the mesh generated for the PS6 rough surface. To precisely capture the surface roughness, we refined the mesh near the walls. However, due to the intricate surface details and the complexity of cells close to the walls, obtaining exact values for non-dimensional wall distances like x + , r + , and z + proved challenging. Therefore, we present estimated average values for these quantities in our current meshes. Across all surfaces at a Reynolds number ( Re b ) of 8000, the average values of x + , r + , and z + near the wall are all found to be below 2.35. In the channel center, r + values range from 3.36 to 10.90 for PS1–PS6 and NS1–NS6 roughness configurations. The maximum values of skewness, aspect ratio, and non-orthogonality for cells across PS1–PS6 and NS1–NS6 roughness are observed to be between 0.72 and 1.59, 10.37 and 13.41, and 51.56° and 65.33°, respectively.

Illustration of the mesh for PS6 rough surface.

In this study, OF7 was used to simulate turbulent pipe flow with AM rough walls. The LES equations were solved numerically using a second-order cell-centered discretization scheme for convective and diffusive fluxes within the finite volume method. Time stepping involved the implicit Adams–Bashforth method, 41 with a maximum Courant–Friedrichs–Lewy (CFL) number of 0.5 to ensure numerical stability. The Pressure Implicit Splitting of Operators (PISO) algorithm 42 was used to achieve pressure–velocity coupling, with three corrector steps to minimize discretization errors. The resulting pressure equation was solved using the Generalized Geometric-Algebraic Multigrid (GAMG) method 43 with a Diagonal Incomplete Cholesky (DIC) smoother. 44 For velocity solutions, the Preconditioned BiConjugate Gradient (PBiCG) solver 45 was employed along with a Diagonal Incomplete Lower-Upper (DILU) preconditioning method. 44 Additionally, to address non-orthogonality in our roughness-conforming meshes, two inner loop correctors were implemented, considering that the maximum non-orthogonality in all meshes remained below 70°.

The simulations assume fully developed, turbulent, incompressible, and Newtonian flow with constant properties ( ρ  = 1 kg m −3 and c p  = 1005 J kg −1 K −1 ). The effects of gravitational acceleration forces are neglected. The value of Pr was set to 0.71, and Pr t was set to 0.85. The simulations explored the influence of two key factors: roughness height and surface skewness. We simulated six different normalized roughness heights ( ⁠ R a / D  = 0.001–0.028) on surfaces with two distinct skewness values ( ⁠ s k = − 0.424 and 0.424), where D is the characteristic diameter of the rough pipe defined as D = S / ( π L x ) ⁠ , with S being the total rough surface area of the pipe and L x the pipe length. The Re b was kept constant at 8000 throughout all simulations. Here, Re b is defined as R e b = U b D / ν ⁠ , where U b is the bulk velocity of the fluid. For easy reference, we labeled the surfaces with positive skewness ( ⁠ s k = 0.424 ⁠ ) as PS followed by a number indicating the roughness height (e.g., PS1 for R a / D = 0.001 ⁠ ). Similarly, surfaces with negative skewness ( ⁠ s k = − 0.424 ⁠ ) were labeled NS followed by a number (e.g., NS6 for R a / D = 0.028 ⁠ ).

In analyzing wall-bounded flows, the friction velocity scale, u τ ⁠ , is determined a posteriori using the pressure gradient, Δ p / L x ⁠ , calculated as u τ = 0.25 D Δ p / ( ρ L x ) ⁠ . The friction temperature, Θ τ ⁠ , is defined as Θ τ = q w / ρ c p u τ ⁠ . A key parameter, the turbulent friction Re number, R e τ ⁠ , is defined as R e τ = u τ D / ( 2 ν ) ⁠ . In this study, R e τ ranges from 260 to 568 for NS1–NS6 and 260 to 602 for PS1–PS6 (see Table III ). Additionally, the roughness Reynolds number, k s + = k s u τ / ν ⁠ , is considered, where k s is estimated based on the roughness function, Δ U + ⁠ . 29,34 This yields a range of k s + between 1 and 518 for negatively skewed surfaces and between 1 and 536 for positively skewed surfaces. Notably, in flows over roughened walls, u τ and the skin friction coefficient, c f , reflect the total wall drag, encompassing pressure and viscous drag instead of solely the skin-friction drag.

Estimated values of R e τ and k s + for the 12 rough surfaces considered.

The computational domain length, L x , is set to eight times the pipe diameter, i.e., L x = 8 D ⁠ , to mitigate periodicity effects in all considered statistics. 29,34,40,46,47 The axial, radial, and azimuthal directions are denoted by x , r , and θ , respectively, with corresponding velocity components u x , u r , and u θ ⁠ . The effective wall-normal distance is denoted by r = r 0 − d ⁠ , where r 0 is the average pipe radius and d is the zero-plane displacement. 29,34 Periodic boundary conditions are applied in the streamwise direction. No-slip boundary conditions are imposed at the wall for all velocity components ( u x , u r , u z ) ⁠ , ensuring the fluid velocity is zero at the rough surface. The zero-Neumann boundary condition is applied for pressure ( ∂ p ∂ n = 0 ) ⁠ , indicating no pressure gradient across the wall. To impose cyclic boundary conditions for fully developed channel flow, a pressure-gradient-driven flow is typically the best type of forcing to maintain a consistent mass flow rate. Generally, a forcing term ( F = − 1 ρ ∇ p mean ) is added to the right-hand side of the momentum conservation equation to maintain a controlled mean pressure gradient. However, what value of pressure gradient the AM surfaces will generate is not known a priori due to the absence of an adequate roughness length scale, i.e., k s . Therefore, we used an alternative method called bulk velocity control. This method ensures that the desired bulk velocity (and thus bulk Reynolds number) is maintained throughout the simulation by dynamically adjusting the pressure gradient. This is achieved by using a utility called “meanVelocityForce” in OF7. The boundary condition for the transformed temperature is simply Θ = 0 at r  = 0 and r  =  D .

Statistical representation involves angular brackets, ⟨ … ⟩ ⁠ , for time-averaged quantities and primes, ( … ) ′ ⁠ , for fluctuating quantities. The reported data correspond to a dataset extending to 100 t ftt ⁠ , where t ftt = L x / U b is the flow-through time.

In the context of heat transfer over rough surfaces, the combined effect of increasing surface roughness and skewness can result in a synergistic enhancement of heat transfer. From a statistical sense, the surfaces with positive skewness can be considered peak-dominated surfaces, and the ones with negative skewness as valley-dominated surfaces. To explore the influence of peaks and valleys alongside their height impact on the friction factor c f = Δ p D / ( 2 L x ρ U b 2 ) and Nusselt–Prandtl ratios, first, the instantaneous flow visualizations of c f (absolute values) and NuP r − 1 / 3 are shown in Fig. 5 .

(a) Skin friction factor ( c f , colormap varies from pink (minimum) to yellow (maximum) and (b) heat transfer enhancement factor ( ⁠ NuP r − 1 / 3 ⁠ , colormap varies from blue (minimum) to red (maximum), as a function of mean roughness height, R a , for (i) positively and (ii) negatively skewed rough surfaces. (iii) Zooms are also included for clarity.

In Figs. 5(a) and 5(b) , moving from left to right, the s k values are fixed, but roughness height increases. Panels (i) and (ii) show the results for positively and negatively skewed roughness, respectively. For small values of R a / D ⁠ , the distribution of c f resembles the one obtained for smooth pipe flows, and the impact of s k is negligible. With increasing R a / D values, all surfaces show elevated c f . Higher c f values at peaks indicate that the roughness elements are inducing more substantial energy losses in the flow. These energy losses are associated with the work done by the fluid to overcome the increased resistance caused by the rough surface. In geometries transitioning from peaks to cavities at a fixed R a / D ratio, changes in the distribution of c f along the surface are observed [see zooms included in panel (iii)]. In peak geometries, such as protrusions, higher c f values are typically found at the front head of the peak due to flow separation and the formation of recirculation zones. However, when the geometry is rotated to form a cavity, the flow behavior alters, leading to flow reattachment downstream of the cavity. Consequently, the downstream side of the cavity experiences increased turbulence levels and higher momentum transfer near the surface, resulting in higher c f values on the downstream side of the cavity. These variations in flow behavior and boundary layer characteristics contribute to the observed changes in the distribution of c f as well as in heat transfer along the surface of the geometry [see Fig. 5(b) ]. The heat transfer enhancement factor exhibited a pronounced upward trend as the surface roughness increased. The presence of roughness elements altered the near-wall flow patterns, leading to increased turbulence and improved heat transfer rates. Furthermore, in peak geometries where c f values are higher at the front head of the peak, the enhanced turbulence near the surface promotes better mixing of the fluid, resulting in higher convective heat transfer coefficients. Consequently, NuP r − 1 / 3 tends to be relatively higher on the upstream side of the peak compared to the downstream side.

Figure 6 presents inner-scaled profiles of the streamwise mean velocity, ⟨ u x + ⟩ ⁠ , for positively and negatively skewed surfaces. The non-dimensional wall distance, r + , is measured from the plane at which the total drag acts. This involves shifting the velocity profiles for rough surfaces by removing the negative velocities, commonly referred to as zero-plane displacement. 29,34,48 Additionally, the plot includes numerical results of mean streamwise velocity profiles for LES of smooth pipe flow at the same bulk Re number ( Re b  = 8000) for comparison and standard log-layer profiles for smooth walls (solid green line). In Figs. 6(a) and 6(b) , it is observed that increasing k s + results in a downward shift of the logarithmic profile of ⟨ u x + ⟩ ⁠ , indicating enhanced momentum transfer by the wall roughness. For small values of R a / D ⁠ , i.e., in the hydraulically smooth regime as k s + ≈ 1 ⁠ , the PS1 and NS1 profiles are very close to the one for smooth surfaces, S0, as expected. The impact of s k is little for PS2, PS3, NS2, and NS3 surfaces as the downward shift is found to be roughly the same. For the larger value of R a / D > 0.015 ⁠ , the downward shift in the logarithmic profile is found to be larger for positively skewed surfaces compared to negatively skewed ones, signifying larger momentum transfer by the wall roughness in the former ones.

Mean velocity profile for (a) positively skewed and (b) negatively skewed surfaces in the inner wall units.

In Figs. 7(a) and 7(b) , mean temperature profiles, Θ + ⁠ , are shown for all surfaces with s k = 0.424 and s k = − 0.424 ⁠ , respectively. Similar to ⟨ u x + ⟩ ⁠ , an increasing downward shift is observed for Θ + with increasing wall roughness height in the region r + ≥ 20 ⁠ , while a slight upward shift is observed for r + ≤ 15 ⁠ , signifying increased heat transfer close to the surface. For small roughness ( ⁠ R a / D = 0.001 ,   k s + = 1 ⁠ ), the Θ + profiles coincide with the ones for S0 irrespective of the skewness, as expected. Furthermore, the downward shift in the ⟨ u x + ⟩ profile is consistently larger than that of the Θ + profile at the same k s + value, consistently with previous DNS studies. 26,28,29,49,50 The direct comparison of Θ + profiles in Figs. 7(a) and 7(b) for comparable R a / D value shows that peak-dominated surfaces ( ⁠ s k = 0.424 ⁠ ) have a larger impact on heat transfer enhancement than the valley-dominated ones ( ⁠ s k = − 0.424 ⁠ ). In other terms, surfaces with the same value of R a / D but different s k lead to slightly different predictions of k s + ⁠ , and hence, larger roughness height and peak-dominated surfaces result in higher turbulence levels and eventually higher heat transfer rates.

Mean temperature profile for (a) positively skewed and (b) negatively skewed surfaces in the inner wall units.

The magnitudes of the downward shift can be measured by using the roughness function ( ⁠ Δ U + ⁠ ) and temperature difference function ( ⁠ Δ Θ + ⁠ ). Figure 8(a) shows Δ U + and Fig. 8(b) shows Δ Θ + as a function of k s + ⁠ , indicating the changes in the mean profiles due to wall roughness. The results for s k = 0.424 are shown in blue circles and the ones with s k = − 0.424 ⁠ , in red triangles. The chosen scaling ensures that the roughness function collapses with Colebrook and Nikuradse's sand–grain data in the fully rough regime, as detailed by Garg et al. 34,47 It is important to note that k s must be dynamically determined for each specific rough surface and does not represent a simple geometric length scale of the roughness. Consequently, in this study, the value of k s + is not known in advance and has been computed by extracting Δ U + from Fig. 6(a) for positively skewed surfaces and Fig. 6(b) for negatively skewed surfaces and then using a Colebrook-type roughness function, Δ U + = 2.44   log   ( 1 + 0.26 k s + ) ⁠ . 5  

(a) Roughness function, Δ U + and (b) temperature difference, Δ Θ + ⁠ , as a function of equivalent sand–grain roughness Reynolds number, k s + ⁠ , for positively skewed (blue circles) and negatively skewed (red triangles) surfaces.

Figure 8(a) illustrates the progressive increase in Δ U + with k s + ⁠ , eventually approaching the asymptotic limit for the fully rough regime. The fully rough regime for the present rough surface is observed in the range of 80 < k s + < 537 ⁠ , which is somewhat comparable to sand–grain roughness with k s + ≃ 70 ⁠ . 7 The literature reveals similar roughness functions obtained for sand–grain roughness at approximately the same Re number, even though the roughness heights significantly differ. 29,34,51–54 Interestingly, for k s + = 1 ⁠ , peak-dominated (PS1) and valley-dominated (NS1) surfaces result in the same Δ U + values, as seen from ⟨ u + ⟩ profiles. With increasing k s + values, we found that surfaces with s k > 0 result in a larger value of Δ U + compared to the one with s k < 0 even if the surfaces share the same R a / D values. This suggests that the roughness height alone is inadequate for scaling the momentum and heat transfer deficit resulting from surface roughness.

Similarly, the temperature difference function ( ⁠ Δ Θ + ⁠ ) is computed and shown in Fig. 8(b) for s k > 0 (blue circles) and s k < 0 (red triangles). Globally, Δ Θ + initially increases with k s + ⁠ , but the rate of increase diminishes as k s + becomes larger. This behavior aligns reasonably well with Kays and Crawford's correlation 13 (dashed pink line): Δ Θ + = P r t κ log ( k s + ) − 3.48 P r t κ − 1.25 k s + 0.22 P r 0.44 + β ( P r ) , where κ = 0.4 is the von Kármán constant and β ( P r ) = 5.6 represent the log-law intercept. Additionally, we compare the results of Δ Θ + for different rough surfaces, including three-dimensional irregular roughness 28,55 with positive and negative s k values and three-dimensional AM roughness 29 with positive s k values. In the limit of small k s + ≤ 10 ⁠ , the value of Θ + ≈ 0 indicates the negligible impact of roughness height and s k on heat transfer enhancement. Interestingly, for k s + > 10 ⁠ , we observe an increasing trend of Δ Θ + against k s + ⁠ , which is found to be consistent with the reference data, 28,29,55 despite variations in roughness type, R a , and s k values from previous studies. This suggests that topological parameters, such as roughness type (AM or artificial), s k , and ES , have little impact on the Δ Θ + trend against k s + ⁠ , especially in the fully rough regime. However, differences in the absolute value of Θ + are noticeable for AM roughness of Garg et al., 29 potentially due to variations in Re b and s k values used in their simulations. Given that Δ U + and Δ Θ + reflect enhancements of the momentum and heat transfer, respectively, the observation of Δ U + > Δ Θ + indicates that the wall roughness increases the momentum transfer more than the heat transfer.

Effective Prandtl number plotted in outer units for (a) positively skewed surfaces and (b) negatively skewed surfaces. Results for the benchmark case, i.e., smooth surface, are also included for reference. The dashed red line shows P r t = 0.85 fixed in the simulations.

Contour maps of wall-normal heat flux component, ⟨ u r ′ Θ ′ ⟩ + ⁠ , and Reynolds shear stress, ⟨ u x ′ u r ′ ⟩ + ⁠ , in a x – y plane for R a / D = 0.028 and s k = 0.424 ⁠ . Red dashed lines indicate the region where the difference between ⟨ u r ′ Θ ′ ⟩ + and ⟨ u x ′ u r ′ ⟩ + is apparent.

The temperature fluctuations, Θ ′ ⁠ , and velocity fluctuations, u x ′ and u r ′ ⁠ , give rise to significant mean Reynolds stresses and heat fluxes. Recent studies by Garg et al. 29 have shown the decreasing correlation between streamwise velocity fluctuations, ⟨ u x ′ u x ′ ⟩ and streamwise component of heat flux, ⟨ u x ′ Θ ′ ⟩ ⁠ , with increasing roughness height. However, the influence of roughness topologies, such as peak-dominated roughness with s k > 0 and valley-dominated ones with s k < 0 ⁠ , is still unclear. Thus, the effect of s k on the correlation between ⟨ u x ′ Θ ′ ⟩ and ⟨ u x ′ u x ′ ⟩ and between ⟨ u r ′ Θ ′ ⟩ and ⟨ u r ′ u x ′ ⟩ with increasing roughness height is investigated in this section.

In Fig. 11 , we compare ⟨ u x ′ u x ′ ⟩ + with ⟨ u x ′ Θ ′ ⟩ + and ⟨ u x ′ u r ′ ⟩ + with ⟨ u r ′ Θ ′ ⟩ + ⁠ , for the range of R a / D = 0.001 − 0.028 ⁠ , yielding a range of k s + = 1 − 536 ⁠ . All solid and dashed lines represent negatively skewed and positively skewed surfaces, respectively. All cases show that irrespective of the roughness height and skewness values, the general trend between ⟨ u r ′ Θ ′ ⟩ + and ⟨ u x ′ u r ′ ⟩ + is practically identical, with a slight difference in the magnitude, ⟨ u r ′ Θ ′ ⟩ + being slightly smaller than ⟨ u x ′ u r ′ ⟩ + ⁠ . This is consistent with Pr eff being greater than one in the vicinity of the wall and the results shown in Fig. 10 , indicating the recirculation zone behind the roughness wall acting as a thermal resistance. With an increase in roughness height, we observe that the peak value of these quantities shifts outwards after a critical value of R a / D > 0.006 ⁠ , i.e., outside the hydraulically smooth regime. For larger R a / D values, the impact of s k starts to become visible for R a / D > 0.012 as the peak location starts moving outward for the positively skewed surfaces compared to the negatively skewed ones, which means positively skewed surfaces generate larger friction, consistent with our earlier results. This outward shift can also be explained by calculating the modified diameter, D 0 mod = D 0 − d ⁠ , where D 0 is the smooth pipe diameter. The estimation of normalized D 0 mod is shown in Fig. 12 . Here we can see that the “effective” diameter is about 10% larger for the negative skewness than the positive one (at R a / D 0 = 0.032 ⁠ ), having a profound influence on the overall flow. Effectively, the positive one squeezes the flow toward the center, which causes a larger outward shift of the peak for positively skewed surfaces compared to negative ones. A slight difference between ⟨ u x ′ u x ′ ⟩ and ⟨ u x ′ Θ ′ ⟩ is seen in the magnitude. The general trend is very similar for these two quantities as well. Interestingly, the difference between ⟨ u x ′ Θ ′ ⟩ and ⟨ u x ′ u x ′ ⟩ is a non-monotonic function of R a / D ⁠ .

The wall-normal Reynolds shear stress, ⟨ u ′ x u ′ r ⟩ ⁠ , streamwise velocity fluctuations, ⟨ u ′ x u ′ x ⟩ ⁠ , normalized by u τ 2 and streamwise heat flux, ⟨ u ′ x Θ ′ ⟩ and wall-normal heat flux, ⟨ u ′ r Θ ′ ⟩ ⁠ , normalized by u τ T τ ⁠ , for cases with (a) R a / D = 0.001 ⁠ , (b) R a / D = 0.006 ⁠ , (c) R a / D = 0.012 ⁠ , (d) R a / D = 0.015 ⁠ , (e) R a / D = 0.020 ⁠ , and (f) R a / D = 0.028 ⁠ . Solid and dashed lines represent negatively skewed and positively skewed surface results, respectively.

Estimation of modified rough surface diameter due to negative velocities for positively and negatively skewed surfaces.

Figure 13(a) presents the friction factor as a function of R a / D for various rough surfaces with s k = 0.424 and s k = − 0.424 values, normalized with respect to the numerical results obtained for smooth pipe flow using the Moody chart. The plots cover a R a / D number range of 0.001–0.028. Due to the lack of experimental validation for rough surfaces, we employed LES with the WALE model for smooth pipe flow at the same mesh resolution as rough pipes and matched Reynolds numbers. Previous studies by Garg et al. 29,47 utilized LES where the WALE model results for smooth pipe flow were used as a validation tool, showing excellent agreement with theoretical predictions from the Moody chart, with a deviation of less than 3% [refer to Fig. 10(a) dashed black and solid green lines of Garg et al. 29 ]. This validation process instills confidence in the accuracy and robustness of our numerical approach for predicting the friction factor behavior in smooth pipe flow. By extension, it reinforces the reliability of our numerical results for turbulent flow over rough surfaces, given the utilization of the same numerical approach.

Estimation of (a) skin friction factor, c f , (b) Nusselt number, Nu , and (c) thermal performance factor, TPF, as a function of R a / D ⁠ . All values are normalized by the benchmark case, i.e., the smooth pipe flow. The dashed black line represents the expected smooth pipe flow results.

In Fig. 13(a) , the normalized c f / c f 0 values indicate a consistent upward trend with increasing roughness height ( ⁠ R a / D increases from 0.001 to 0.028), regardless of s k values. For PS1 and NS1 with R a / D = 0.001 and k s + ≈ 1 ⁠ , representing hydraulically smooth roughness, c f is negligibly impacted, leading to c f / c f 0 approaching 1. In the transition regime of PS2 to PS4 and NS2 to NS4, where k s + ranges from 9 to 50, roughness elements disrupt the laminar flow, inducing additional drag and increasing resistance compared to smooth pipe flow, thus explaining the observed increasing behavior of c f / c f 0 ⁠ . The influence of s k remains insignificant up to R a / D = 0.03 ⁠ . However, as R a / D surpasses this threshold, rough surfaces PS5, PS6, NS5, and NS6 yield k s + values between 100 and 536, indicating a fully rough regime where intensified turbulence significantly increases c f The impact of s k becomes pronounced, with positively skewed surfaces displaying higher c f than negatively skewed ones, indicating a greater imbalance between turbulence effects and roughness-induced drag in peak-dominated surfaces. Surprisingly, up to considerable R a / D values, the impact of s k on c f is negligible.

In Fig. 13(b) , the normalized Nu number is shown as a function of R a / D for various rough surfaces, normalized against the Nusselt number obtained for smooth pipe flow, Nu 0 , using the Dittus–Boelter correlation N u 0 = 0.023 R e b 0.8 P r 0.4 ⁠ . LES with the WALE model results for smooth pipe flow were utilized as a validation tool, exhibiting excellent agreement with theoretical predictions, with a deviation of less than 4% [refer to Fig. 10(b) dashed black and solid green lines in Garg et al. 29 ]. Similar to the prediction of c f , the observed behavior indicates potent heat transfer enhancement within the considered range of R a / D due to roughness-induced disturbances. In the hydraulically smooth regime, the impact of protrusions and valleys is negligible on the Nu number, leading to N u / N u 0 approaching 1, regardless of s k . As the transition roughness regime is entered, Nu values begin to increase, resulting in potent heat transfer enhancement, with the impact of s k in this regime found to be negligible. However, in the fully rough regime, Nu values exhibit a consistent upward trend, with the influence of s k becoming apparent. The results demonstrate that surfaces dominated by peaks ( ⁠ s k > 0 ⁠ ) result in higher heat transfer enhancement compared to those dominated by valleys ( ⁠ s k < 0 ⁠ ).

To quantify the heat transfer enhancement effectiveness for the current roughness and assess the influence of surface topology, we calculated the thermal performance factor ( TPF ), representing the ratio of the relative change in heat transfer rate to the change in friction factor: TPF = ( N u / N u 0 ) / ( c f / c f 0 ) 1 / 3 ⁠ , illustrated in Fig. 13(c) . Three distinct regimes emerge. First, the hydraulically smooth regime, where all rough surfaces perform equivalently to smooth ones. Second, the transitionally rough regime, where TPF notably increases, remains between 1 and 1.5, signifying superior performance of all roughness configurations compared to smooth surfaces in transitional flow. The influence of s k becomes noticeable for R a / D = 0.015 ⁠ . Finally, in the fully rough regime, the impact of roughness height and skewness becomes markedly pronounced. Surfaces with positive s k values reveal a larger and more monotonic increase in TPF compared to those with negative s k values. This highlights the critical importance of surface topology, where positively skewed surfaces outperform negatively skewed ones for similar roughness heights.

The Reynolds stress tensor's feasible states are confined within a triangular region in the ( ξ , η ) plane, known as the Lumley triangle. Distinct turbulence scenarios can be distinguished by examining the two invariants of b ij at the Lumley triangle's theoretical extremes. Garg et al. 47 provided a comprehensive analysis of these states. Figures 14 and 15 depict Lumley triangle plots for rough surfaces with specific values of s k (0.424 and −0.424, respectively), along with a reference plot for smooth pipe flow [ Figs. 14(a) and 15(a) ]. Data are extracted from a y – z plane slice at a consistent location for all surfaces, as illustrated in the inset of Fig. 14(a) . Utilizing PDF post-processing, cell-centered values of ξ and η are visualized with a colormap to correspond with the wall-normal distance. In the smooth-wall turbulent pipe flow reference case, near-wall flow closely resembles a two-component state along the upper boundary of the Lumley triangle, progressing toward the one-component state at the triangle's upper-right apex. Maximum anisotropy occurs at approximately r + ≈ 8 ⁠ , beyond which anisotropy diminishes. For r + > 8 ⁠ , the ( ξ , η ) curve aligns closely with the right boundary of the Lumley triangle, indicating proximity to an axisymmetric, rod-like state, but not fully reaching the maximum isotropy state at the triangle's base summit as r + increases. For smaller R a / D values, the behavior of surfaces PS1 and NS1 closely resembles that of smooth surface flows, irrespective of s k values.

Anisotropy-invariant mapping of turbulence in (a) R a / D = 0 turbulent smooth pipe flow and rough pipe flow compiled from the present LES data at: (b) R a / D = 0.001 ⁠ , (c) R a / D = 0.012 ⁠ , (d) R a / D = 0.015 ⁠ , (e) R a / D = 0.020 ⁠ , and (f) R a / D = 0.028 ⁠ , for positively skewed surfaces. The data points for each case are based on all cells in the domain at x / D = 4 and colored with normalized wall distance values, r + . Colormap varies from purple (minimum) to red (maximum).

Anisotropy-invariant mapping of turbulence in (a) R a / D = 0 turbulent smooth pipe flow and rough pipe flow compiled from the present LES data at: (b) R a / D = 0.001 ⁠ , (c) R a / D = 0.012 ⁠ , (d) R a / D = 0.015 ⁠ , (e) R a / D = 0.020 ⁠ , and (f) R a / D = 0.028 ⁠ , for negatively skewed surfaces. The data points for each case are based on all cells in the domain at x / D = 4 and colored with normalized wall distance values, r + . Colormap varies from purple (minimum) to red (maximum).

For rough surfaces with R a / D > 0.01 ⁠ , regardless of s k values, turbulent states occupy various positions within the Lumley triangle, except for the plain strain condition marked by the dashed line [see Figs. 14(b)–14(f) and 15(b)–15(f) ]. In the deepest valleys of the surfaces, the Reynolds stress anisotropy tensor tends toward a strongly anisotropic, one-component state. As r + increases, the results diverge from the trajectory observed for smooth-wall pipe flow on the ( ξ , η ) -map. Across all rough surfaces (PS1 to PS6 and NS1 to NS6), the flow converges toward the left side of the Lumley triangle, attaining an axisymmetric disk-like state at the roughness mean plane. Here, the streamwise and azimuthal Reynolds stresses exhibit comparable magnitudes. Anisotropy tends to center around the axisymmetric expansion and the two-component limit, indicating that one stress component predominates or that two components are similar in magnitude. Such axisymmetric, disk-like states of the Reynolds stress anisotropy tensor are characteristic of mixing layers. Similar behavior has been noted in turbulent flows over transverse bar roughness, 62 k-type roughness, 63 irregular roughness, 54 and recently in AM roughness. 34 Beyond the roughness mean plane, the trajectory shifts back toward the right side of the triangle, resembling an axisymmetric, rod-like state, mirroring the behavior of the smooth-wall case once the wall-normal coordinate surpasses the maximum roughness height. The most prevalent anisotropic states include axisymmetric expansion, one-component, two-component, and two-component axisymmetric states, with the likelihood of a specific turbulent state increasing with higher R a / D ⁠ .

The influence of s k values on Reynolds stress anisotropy is evident. For instance, comparing the PS4 surface in Fig. 14(d) with the NS4 surface in Fig. 15(d) , both sharing the same R a / D but differing s k values, highlights this impact. The disparity in turbulent states between these surfaces stems from distinct flow interactions with surface irregularities. Surfaces characterized by positive and negative s k values represent two rough surface types: one dominated by peaks and the other by valleys, respectively. Peak-dominated surfaces exhibit protruding irregularities, promoting turbulence generation through flow acceleration, vorticity, and separation, resulting in a more intense and anisotropic turbulent flow. Conversely, valley-dominated surfaces have recessed features that dampen turbulence intensity by inducing flow deceleration and recirculation, resulting in a less intense and more isotropic turbulent flow. Thus, the physical mechanisms driving turbulence generation and anisotropy differ between peak-dominated and valley-dominated surfaces, explaining the observed differences in turbulent states.

We conducted a detailed examination of how wall roughness influences turbulent heat transfer in additively manufactured (AM) rough surfaces using roughness-resolved high-fidelity large eddy simulations (LES) in OpenFOAM 7. We created six configurations of rough pipes from a single actual AM surface, maintaining fixed skewness and kurtosis while varying roughness height distributions. Additionally, we flipped these six surfaces to produce surfaces with fixed roughness height and kurtosis but with negative skewness. Precise spatial measurements at a constant bulk Reynolds number Re b  = 8000 enabled us to numerically estimate the roughness function for all cases, which was then utilized to approximate the equivalent sand–grain roughness height, k s . The temperature was treated as a passive scalar with a Prandtl number of 0.71, neglecting buoyancy effects. Consistent with our previous research, 29,34 we found that wall roughness affects heat transfer and momentum differently. The temperature and momentum wall rough functions ( ⁠ Δ Θ + ,   Δ U + ⁠ ) differed significantly, with the former being notably smaller than the latter. This discrepancy arises from high-temperature fluid from the bulk region penetrating the roughness layer, resulting in a larger wall-scaled mean temperature profile compared to the mean temperature profile, which is predominantly negative due to pressure effects within the roughness sublayer. Consequently, normalized temperature values in the bulk region are larger than the normalized mean velocity values. The discrepancy between Δ Θ + and Δ U + directly challenges the validity of the Reynolds analogy under fully rough conditions, consistent with existing literature regardless of roughness nature, as the fact that Δ U + > Δ Θ + can be attributed to the influence of pressure on the velocity field without a corresponding mechanism for the thermal field. This was further corroborated by the rapid increase in the effective Prandtl number ( Pr eff ) within the rough wall, where the effective thermal diffusivity, due to combined turbulence and dispersion effects, is significantly smaller than the effective diffusivity within the rough wall. With increasing surface roughness height, Pr eff values increase near the roughness sublayer, indicating a reduction in the Reynolds analogy. The influence of skewness was found to be insignificant in the overall behavior. Furthermore, while the wall-normal Reynolds shear stress ( ⁠ ⟨ u v ′ u r ′ ⟩ + ⁠ ) and heat flux ( ⁠ ⟨ u r ′ Θ ′ ⟩ + ⁠ ) decreased with larger wall roughness height, their magnitudes remained similar for different values of surface roughness height ( ⁠ R a / D ⁠ ). However, it is worth noting that the magnitude of ⟨ u r ′ Θ ′ ⟩ + was slightly smaller than ⟨ u x ′ u r ′ ⟩ + ⁠ , especially in the region just behind the roughness crest, highlighting the influence of recirculation bubbles on reducing heat transfer. The impact of skewness became more apparent for larger values of R a / D > 0.006 ⁠ . For a fixed R a / D value, negatively skewed surfaces exhibited smaller k s + values compared to positively skewed ones, indicating less turbulence in surfaces dominated by cavities and consequently less heat transfer. This was further quantified by visualizing turbulence states of ⟨ u x ′ u r ′ ⟩ + ⁠ , where peak-dominated surfaces demonstrated a higher probability of flow acceleration compared to valley-dominated ones. Evaluations of global features such as friction factor ( ⁠ c f / c f 0 ⁠ ) and Nusselt number ( ⁠ N u / N u 0 ⁠ ) demonstrated a clear dependence on surface roughness height and skewness. The influence of surface skewness was only evident on c f / c f 0 in the fully rough regime, while its effect on N u / N u 0 was noticeable in the transitional rough regime. Thermal performance evaluation further indicated that for efficient heat transfer enhancement, positively skewed surfaces outperformed negatively skewed ones in both transitional and fully rough flow regimes.

The authors greatly appreciate the financial support provided by Vinnova under Project Number “2020-04529.” Computer time was provided by the Swedish National Academic Infrastructure for Supercomputing (NAISS), partially funded by the Swedish Research Council through Grant Agreement No. 2018-05973. The authors also appreciate funding acquisition partners Setrab and Siemens Energy, and Sebastian Ritcher for conducting the surface roughness measurements.

The authors have no conflicts to disclose.

Himani Garg: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Guillaume Sahut: Formal analysis (supporting); Methodology (supporting); Software (equal); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Erika Tuneskog: Formal analysis (supporting); Writing – original draft (supporting). Karl-Johan Nogenmyr: Funding acquisition (equal); Writing – original draft (supporting). Christer Fureby: Conceptualization (supporting); Funding acquisition (lead); Methodology (supporting); Resources (lead); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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CFD analysis of different Fin-and-Tube Heat Exchangers

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• Islamic University of Technology

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CFD analysis of shell and tube heat exchanger

Heat exchangers are used to transfer heat from fluid at high temperature to fluid at lower temperature. Heat exchangers are used in industrial purposes in chemical industries, nuclear power plants, refineries, food processing, etc. Sizing of heat exchangers plays very significant role for cost optimization. Also, efficiency and effectiveness of heat exchangers is an important parameter while selection of industrial heat exchangers. Methods for improvement on heat transfer have been worked upon for many years in order to obtain high efficiency with optimum cost. In this paper, we are analysing shell and tube heat exchanger without baffle plates by changing their outer material .The calculations and simulations are done for counter flow of the heat exchanger.

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In present day shell and tube heat exchanger is the most common type heat exchanger widely use in oil refinery and other large chemical process, because it suits high pressure application. The process in solving simulation consists of modeling and meshing the basic geometry of shell and tube heat exchanger using CFD package ANSYS 15.0. The objective of the project is design of shell and tube heat exchanger with helical baffle and study the flow and temperature field inside the shell using ANSYS software tools. The heat exchanger contains 7 tubes and 600 mm length shell diameter 100 mm. The helix angle of helical baffle will be varied from 0 to 20. In simulation will show how the pressure varies in shell due to different helix angle and flow rate. The flow pattern in the shell side of the heat exchanger with continuous helical baffles was forced to be rotational and helical due to the geometry of the continuous helical baffles, which results in a significant increase in heat transfer coefficient per unit pressure drop in the heat exchanger. Keywords: Thermal Analysis, Shell, heat exchanger etc.

IRJET Journal

This study aims to investigate the effect of different baffle layouts on the STHX (rate of heat transmission and pressure loss) of the A tube heat exchanger. The addition of baffles to the tube and shell mechanism enhances the heat switch while also boosting pressure. Best one, doubled, helical, triple section, and flowery baffles are used in tube heat exchangers, and they are designed using SOLIDWORKS go with the flow simulation software (ver. 2015). A single segmental baffle exhibits the best mass price and heat transmission rate on the shell side, according to simulation results. There are almost no stagnation zones inside the helical baffle, which results in significantly less fouling and a longer operating lifetime due to less flow-induced vibration.

International Journal of Engineering Research and Technology (IJERT)

IJERT Journal

https://www.ijert.org/design-and-performance-evaluation-of-shell-and-tube-heat-exchanger-using-cfd-simulation https://www.ijert.org/research/design-and-performance-evaluation-of-shell-and-tube-heat-exchanger-using-cfd-simulation-IJERTV3IS071311.pdf The most commonly practiced types of heat exchanger are the shell-and-tube heat exchanger, the optimal design of which is the primary aim of this work.The present paper deals with the design of a shell and tube heat exchanger. The main objective of this paper is to verify the heat exchanger designed with the use of the Kern's method, by the use of Commercial computational fluid dynamics (CFD) software. In the present study, CFD simulation is used to study the temperature and velocity profiles through the tubes and the shell.

INTERNATIONAL JOURNAL OF AUTOMOTIVE AND MECHANICAL ENGINEERING (IJAME) CFD Analysis of a Shell and Tube Heat Exchanger with Single Segmental Baffles

Shuvam Mohanty

In this investigation, a comprehensive approach is established in detail to analyse the effectiveness of the shell and tube heat exchanger (STE) with 50% baffle cuts (Bc) with varying number of baffles. CFD simulations were conducted on a single pass and single tube heat exchanger(HE) using water as working fluid. A counterflow technique is implemented for this simulation study. Based on different approaches made on design analysis for a heat exchanger, here, a mini shell and tube exchanger (STE) computational model is developed. Commercial CFD software package ANSYS-Fluent 14.0 was used for computational analysis and comparison with existing literature in the view of certain variables; in particular, baffle cut, baffle spacing, the outcome of shell and tube diameter on the pressure drop and heat transfer coefficient. However, the simulation results are more circumscribed with the applied turbulence models such as Spalart-Allmaras, k-ɛ standard and k-ɛ realizable. For determining the best among the turbulence models, the computational results are validated with the existing literature. The proposed study portrays an in-depth outlook and visualization of heat transfer coefficient and pressure drop along the length of the heat exchanger(HE). The modified design of the heat exchanger yields a maximum of 44% pressure drop reduction and an increment of 60.66% in heat transfer.

Thermal Science

Ekrem Büyükkaya

The Shell-and-tube type heat exchangers have long been widely used in many fields of industry. These types of heat exchangers are generally easy to design, manufacturing and maintenance, but require relatively large spaces to install. Therefore the optimization of such heat exchangers from thermal and economical points of view is of particular interest. In this article, an optimization procedure based on the minimum total cost (initial investment plus operational costs) has been applied. Then the flow analysis of the optimized heat exchanger has been carried out to reveal possible flow field and temperature distribution inside the equipment using computational fluid dynamics. The experimental results were compared with computational fluid dynamics analyses results. It has been concluded that the baffles play an important role in the development of the shell side flow field. This prompted us to investigate new baffle geometries without compromising from the overall thermal performanc...

Máté Petrik

In the present paper, a model-size shell-and-tube heat exchanger with horizontal baffles is investigated numerically and compared to the measured values using the commercial software SC-Tetra V11. Determination of the heat transfer coefficients for the shell side depends on the type of the flow and the type of the baffles. Without baffles the shell side medium leaves in the shortest way, and dead zones are formed. With the usage of these baffles, the flow path is artificially formed and the flow velocity will be increased because of the decreased flow area. These two effects will cause a better heat transfer but the other hand this will increase the weight of the heat exchanger. There are very simple experimental correlations for the segment and disk-and-donut types baffles. However, must be known the real heat transfer coefficient in case of an optimal design. This study investigated the effect of the type of the baffles, the space between them and the baffle cut to the real heat t...

Heat exchanger is an equipment for heat transfer from one medium to other. This paper deals with optimizations of shell and tube heat exchanger for maximum heat transfer, by the optimization of baffle cut & baffle angle of a particular shell and tube heat exchanger using CFD analysis. The performance of the shell and tube heat exchanger was studied by varying the parameters using CFD software package fluent. To validate the CFD algorithm the experiment was conducted on an existing single pass counter flow shell and tube heat exchanger. The optimum values obtained are baffle angle 5°, baffle cut 25%.

IJERA Journal

The In these researches work a shell and tube type single pass heat exchanger considered for the comparative analysis. Analysis has been perform in two different phases, in first phase we prepare one setup of shell and tube type heat exchanger with brass tube for shell and cold water for straight copper tube of 500 mm for hot water due to its good thermal conductivity. After the experimental study a computational fluid dynamic analysis was perform by creating a virtual model in CFD environment. The CFD model has created according to the physical parameter of experimental setup and same boundary condition has provided to analysis the performance of heat exchanger. The solution obtained for each combination of velocity and temperature input and corresponding output is stored in the form of solution table and graph. After the CFD analysis a comparative study has been performed to know the effectiveness of heat exchanger.

IJRAME Journal

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