Shijun Chu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Shijun Chu has a total of 12 co-authors. Here are the top co-authors by number of shared publications:
- Ashley P. Willis
University of Sheffield
3 shared publications - Chao Xia
Tongji University
3 shared publications - Elena Marensi
University of Sheffield
3 shared publications - Yajun Fan
University of Liverpool
2 shared publications Zhigang Yang
School of Automotive Studies, Tongji University, Shanghai 201804, China
2 shared publicationsAshley P. Willis
1 shared publication
Latest Publications
- 18 September 2025
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 1019, A21
Optimal body force for heat transfer in turbulent vertical heated pipe flow
The vertical heated pipe is widely used in thermal engineering applications, as buoyancy can help drive a flow, but several flow regimes are possible: shear-driven turbulence, laminarised flow and convective turbulence. Steady velocity fields that maximise heat transfer have previously been calculated for heated pipe flow, but were calculated independently of buoyancy forces, and hence independently of the flow regime and time-dependent dynamics of the flow. In this work, a variational method is applied to find an optimal body force of limited magnitude $A_0$ that maximises heat transfer for the vertical arrangement, with the velocity field constrained by the full governing equations. In our calculations, mostly at Reynolds number ${\textit{Re}}=3000$ , it is found that streamwise-independent rolls remain optimal, as in previous steady optimisations, but that the optimal number of rolls and their radial position is dependent on the flow regime. Surprisingly, while it is generally assumed that turbulence enhances heat transfer, for the strongly forced case, time dependence typically leads to a reduction. Beyond offering potential improvement through the targeting of the roll configuration for this application, wider implications are that optimisations under the steady flow assumption may overestimate improvements in heat transfer, and that strategies that simply aim to induce turbulence may not necessarily be efficient in enhancing heat transfer either. Including time dependence and the full governing equations in the optimisation is challenging but offers further enhancement and improved reliability in prediction.- 18 September 2025
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 1019, A21
Optimal body force for heat transfer in turbulent vertical heated pipe flow
The vertical heated pipe is widely used in thermal engineering applications, as buoyancy can help drive a flow, but several flow regimes are possible: shear-driven turbulence, laminarised flow and convective turbulence. Steady velocity fields that maximise heat transfer have previously been calculated for heated pipe flow, but were calculated independently of buoyancy forces, and hence independently of the flow regime and time-dependent dynamics of the flow. In this work, a variational method is applied to find an optimal body force of limited magnitude $A_0$ that maximises heat transfer for the vertical arrangement, with the velocity field constrained by the full governing equations. In our calculations, mostly at Reynolds number ${\textit{Re}}=3000$ , it is found that streamwise-independent rolls remain optimal, as in previous steady optimisations, but that the optimal number of rolls and their radial position is dependent on the flow regime. Surprisingly, while it is generally assumed that turbulence enhances heat transfer, for the strongly forced case, time dependence typically leads to a reduction. Beyond offering potential improvement through the targeting of the roll configuration for this application, wider implications are that optimisations under the steady flow assumption may overestimate improvements in heat transfer, and that strategies that simply aim to induce turbulence may not necessarily be efficient in enhancing heat transfer either. Including time dependence and the full governing equations in the optimisation is challenging but offers further enhancement and improved reliability in prediction.- Open Access
- 17 January 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (2) , 293
Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe
Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length and . Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence.- 17 January 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (2) , 293
Open AccessModelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe
Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length and . Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence. - Open Access
Laminarising turbulent pipe flow by linear and nonlinear optimisation
It has been observed that flattening the mean velocity profile of pipe flow by body force can laminarise turbulence, a promising means to reduce frictional drag substantially. To explore whether there is a more efficient body force to eliminate turbulence, we consider time-independent active body forces with varying spatial dependencies. Results confirm that when using an active force, a flattened forced laminar profile is needed to eliminate turbulence, and that a purely streamwise body force is best for laminarisation. While these results required an expensive nonlinear optimisation, it was also observed that the optimal forced profile exhibits reduced linear transient growth (TG). To determine whether the reduction of linear TG alone is a sufficient target for the laminarisation of turbulence, a linear Lagrange Multiplier technique is used to minimise TG of perturbations to the forced laminar profile. The optimal velocity profiles reveal that TG for each azimuthal wavenumber strongly depends on the radial velocity gradient at some specific radial interval. The optimal velocity profile obtained by minimising TG of perturbations of azimuthal wavenumber m = 1 is shown to be able to eliminate turbulence at Re = 2400, but a more effective reduction of TG, including perturbations of higher m, is needed for laminarisation at higher Reynolds number Re = 3000. The streaks formed with the flattened forced laminar profile reveal the mechanism of laminarisation: it is found that the lift-up mechanism in the more flattened forced laminar profile creates a lower streak (i.e. closer to the wall) that is more stable, so that turbulence is harder to maintain through streak instability. Further numerical experiments by disturbing a periodic orbit validated that the breakdown of turbulence self-sustaining mechanisms is mainly caused by suppression of the formation of streaks.
Open AccessLaminarising turbulent pipe flow by linear and nonlinear optimisation
It has been observed that flattening the mean velocity profile of pipe flow by body force can laminarise turbulence, a promising means to reduce frictional drag substantially. To explore whether there is a more efficient body force to eliminate turbulence, we consider time-independent active body forces with varying spatial dependencies. Results confirm that when using an active force, a flattened forced laminar profile is needed to eliminate turbulence, and that a purely streamwise body force is best for laminarisation. While these results required an expensive nonlinear optimisation, it was also observed that the optimal forced profile exhibits reduced linear transient growth (TG). To determine whether the reduction of linear TG alone is a sufficient target for the laminarisation of turbulence, a linear Lagrange Multiplier technique is used to minimise TG of perturbations to the forced laminar profile. The optimal velocity profiles reveal that TG for each azimuthal wavenumber strongly depends on the radial velocity gradient at some specific radial interval. The optimal velocity profile obtained by minimising TG of perturbations of azimuthal wavenumber m = 1 is shown to be able to eliminate turbulence at Re = 2400, but a more effective reduction of TG, including perturbations of higher m, is needed for laminarisation at higher Reynolds number Re = 3000. The streaks formed with the flattened forced laminar profile reveal the mechanism of laminarisation: it is found that the lift-up mechanism in the more flattened forced laminar profile creates a lower streak (i.e. closer to the wall) that is more stable, so that turbulence is harder to maintain through streak instability. Further numerical experiments by disturbing a periodic orbit validated that the breakdown of turbulence self-sustaining mechanisms is mainly caused by suppression of the formation of streaks.
- 16 October 2024
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 997, A46
The minimal seed for transition to convective turbulence in heated pipe flow
It is well known that buoyancy suppresses, and can even laminarise, turbulence in upward heated pipe flow. Heat transfer seriously deteriorates in this case. A new direct numerical simulation model is established to simulate flow-dependent heat transfer in an upward heated pipe. The model shows good agreement with experimental results. Three flow states are simulated for different values of the buoyancy parameter $C$ : shear turbulence, laminarisation and convective turbulence. The latter two regimes correspond to the heat transfer deterioration regime and the heat transfer recovery regime, respectively (Jackson & Li 2002; Bae et al., Phys. Fluids, vol. 17, issue 10, 2005; Zhang et al., Appl. Energy, vol. 269, 2020, 114962). We confirm that convective turbulence is driven by a linear instability (Su & Chung, J. Fluid Mech., vol. 422, 2000, pp. 141–166) and that the deteriorated heat transfer within convective turbulence is related to a lack of rolls near the wall, which leads to weak mixing between the flow near the wall and the centre of the pipe. Having surveyed the fundamental properties of the system, we perform a nonlinear non-modal stability analysis, which seeks the minimal perturbation that triggers a transition from the laminar state. Given the differences between shear and convective turbulence, we aim to determine how the nonlinear optimal (NLOP) changes as the buoyancy parameter $C$ increases. We find that at first, the NLOP becomes thinner and closer to the wall. Most importantly, the critical initial energy $E_0$ required to trigger turbulence keeps increasing, implying that attempts to trigger it artificially may not be an efficient means to improve heat transfer at larger $C$ . At $C=6$ , a new type of NLOP is discovered, capable of triggering convective turbulence from lower energy, but over a longer time. It is active only in the centre of the pipe. We next compare the transition processes, from linear instability and by the nonlinear non-modal excitation. At $C=4$ , linear instability leads to a state that approaches a travelling wave solution or periodic solutions, while the minimal seed triggers shear turbulence before decaying to convective turbulence. Deeper into the parameter space for convective turbulence, at $C=6$ , the new nonlinear optimal triggers convective turbulence directly. Detailed analysis of the periodic solution at $C=4$ reveals three stages: growth of the unstable eigenfunction, the formation of streaks, and the decay of the streaks. The stages of the cycle correspond to changes in the linear instability of the turbulent mean velocity profile. Unlike the self-sustaining process for classical shear flows, where the streak is disrupted via instability, here, decay of the streak is more closely linked to suppression of the linear instability of the mean flow, and hence suppression of the rolls. Flow visualisations at $C$ up to $10$ also show similar processes, suggesting that the convective turbulence in the heat transfer recovery regime is sustained by these three typical processes.- 16 October 2024
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 997, A46
The minimal seed for transition to convective turbulence in heated pipe flow
It is well known that buoyancy suppresses, and can even laminarise, turbulence in upward heated pipe flow. Heat transfer seriously deteriorates in this case. A new direct numerical simulation model is established to simulate flow-dependent heat transfer in an upward heated pipe. The model shows good agreement with experimental results. Three flow states are simulated for different values of the buoyancy parameter $C$ : shear turbulence, laminarisation and convective turbulence. The latter two regimes correspond to the heat transfer deterioration regime and the heat transfer recovery regime, respectively (Jackson & Li 2002; Bae et al., Phys. Fluids, vol. 17, issue 10, 2005; Zhang et al., Appl. Energy, vol. 269, 2020, 114962). We confirm that convective turbulence is driven by a linear instability (Su & Chung, J. Fluid Mech., vol. 422, 2000, pp. 141–166) and that the deteriorated heat transfer within convective turbulence is related to a lack of rolls near the wall, which leads to weak mixing between the flow near the wall and the centre of the pipe. Having surveyed the fundamental properties of the system, we perform a nonlinear non-modal stability analysis, which seeks the minimal perturbation that triggers a transition from the laminar state. Given the differences between shear and convective turbulence, we aim to determine how the nonlinear optimal (NLOP) changes as the buoyancy parameter $C$ increases. We find that at first, the NLOP becomes thinner and closer to the wall. Most importantly, the critical initial energy $E_0$ required to trigger turbulence keeps increasing, implying that attempts to trigger it artificially may not be an efficient means to improve heat transfer at larger $C$ . At $C=6$ , a new type of NLOP is discovered, capable of triggering convective turbulence from lower energy, but over a longer time. It is active only in the centre of the pipe. We next compare the transition processes, from linear instability and by the nonlinear non-modal excitation. At $C=4$ , linear instability leads to a state that approaches a travelling wave solution or periodic solutions, while the minimal seed triggers shear turbulence before decaying to convective turbulence. Deeper into the parameter space for convective turbulence, at $C=6$ , the new nonlinear optimal triggers convective turbulence directly. Detailed analysis of the periodic solution at $C=4$ reveals three stages: growth of the unstable eigenfunction, the formation of streaks, and the decay of the streaks. The stages of the cycle correspond to changes in the linear instability of the turbulent mean velocity profile. Unlike the self-sustaining process for classical shear flows, where the streak is disrupted via instability, here, decay of the streak is more closely linked to suppression of the linear instability of the mean flow, and hence suppression of the rolls. Flow visualisations at $C$ up to $10$ also show similar processes, suggesting that the convective turbulence in the heat transfer recovery regime is sustained by these three typical processes.- Open Access
- 1 November 2023
- Published by AIP Publishing in Physics of Fluids
- Vol. 35 (11)
Investigation on the behavior of flow and aerodynamic noise generated around the tandem seal-vibrissa-shaped cylinder
Through comparing with the tandem circular and elliptic cylinders with the same characteristic dimensions, the behavior of flow and flow-induced noise generated around the tandem seal-vibrissa-shaped cylinder is studied based on delayed detached-eddy simulation model and acoustic analogy approach. The co-shedding pattern of flow developed around the tandem cylindrical-like bars is investigated. The spatial modes, mode energy, and mode coefficients of turbulent flow around the geometries are analyzed through spectral proper orthogonal decomposition. Results show that the lift fluctuations of downstream bar are stronger than those of upstream bar, and more aerodynamic noise is radiated from the downstream bar than from the upstream bar. The alternative arrangement of nodal and saddle planes of seal-vibrissa-shaped cylinder introduces three-dimensional flow separations and suppresses the shear layer interactions, inhibiting the regular vortex shedding of Kármán vortex street occurring in the tandem cylinder wake. The reversed vortex shedding generated by two adjacent saddle surfaces in the wake of seal-vibrissa-shaped cylinder balances the lateral force and mitigates the lift fluctuations greatly, thereafter reduces the aerodynamic noise generated by wall pressure fluctuations introduced by unsteady fluctuating forces exerting on the surfaces of geometries. Compared to the tandem circular and elliptic cylinders, the good noise reduction effect with sound pressure level reduced at main frequency range has been achieved from the tandem seal-vibrissa-shaped cylinder. The calculated spectra and amplitude levels of aerodynamic noise agree well with the experimental measurements from the anechoic wind tunnel, verifying the accuracy of the numerical simulations.
- 1 November 2023
- Published by AIP Publishing in Physics of Fluids
- Vol. 35 (11)
Open AccessInvestigation on the behavior of flow and aerodynamic noise generated around the tandem seal-vibrissa-shaped cylinder
Through comparing with the tandem circular and elliptic cylinders with the same characteristic dimensions, the behavior of flow and flow-induced noise generated around the tandem seal-vibrissa-shaped cylinder is studied based on delayed detached-eddy simulation model and acoustic analogy approach. The co-shedding pattern of flow developed around the tandem cylindrical-like bars is investigated. The spatial modes, mode energy, and mode coefficients of turbulent flow around the geometries are analyzed through spectral proper orthogonal decomposition. Results show that the lift fluctuations of downstream bar are stronger than those of upstream bar, and more aerodynamic noise is radiated from the downstream bar than from the upstream bar. The alternative arrangement of nodal and saddle planes of seal-vibrissa-shaped cylinder introduces three-dimensional flow separations and suppresses the shear layer interactions, inhibiting the regular vortex shedding of Kármán vortex street occurring in the tandem cylinder wake. The reversed vortex shedding generated by two adjacent saddle surfaces in the wake of seal-vibrissa-shaped cylinder balances the lateral force and mitigates the lift fluctuations greatly, thereafter reduces the aerodynamic noise generated by wall pressure fluctuations introduced by unsteady fluctuating forces exerting on the surfaces of geometries. Compared to the tandem circular and elliptic cylinders, the good noise reduction effect with sound pressure level reduced at main frequency range has been achieved from the tandem seal-vibrissa-shaped cylinder. The calculated spectra and amplitude levels of aerodynamic noise agree well with the experimental measurements from the anechoic wind tunnel, verifying the accuracy of the numerical simulations.
- 1 February 2021
- Published by AIP Publishing in Physics of Fluids
- Vol. 33 (2) , 025106
Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder
The flow around a seal-vibrissa-shaped cylinder (SVSC) is numerically investigated using the large eddy simulation framework at a Reynolds number of 20 000. Compared with a circular cylinder (CC), the wake of the SVSC presents more stable three-dimensional separation, a longer vortex formation length, and a weaker vortex strength. The mean drag and fluctuation of the lift coefficient are 59.5% and 87.7% lower than those of the CC, respectively. Three-dimensional spectral proper orthogonal decomposition (SPOD) is used to investigate the turbulent flow around these two types of cylinders in terms of the spatial modes, mode energy, mode coefficients, and reconstructed flow by a reduced-order modeling. Four typical vortex shedding patterns are first extracted by SPOD for the SVSC, producing crescent-, twist-, branch-, and knot-shaped vortices. A concept model is proposed for the wake dynamics of the SVSC, allowing the formation and transformation of these modes to be elucidated. Detailed analysis of the impact of the flow pattern on the associated forces indicates that the dominant out-phase vortex shedding at the upper and lower saddle planes makes a significant contribution to the reduction in lift fluctuations.
- 1 February 2021
- Published by AIP Publishing in Physics of Fluids
- Vol. 33 (2) , 025106
Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder
The flow around a seal-vibrissa-shaped cylinder (SVSC) is numerically investigated using the large eddy simulation framework at a Reynolds number of 20 000. Compared with a circular cylinder (CC), the wake of the SVSC presents more stable three-dimensional separation, a longer vortex formation length, and a weaker vortex strength. The mean drag and fluctuation of the lift coefficient are 59.5% and 87.7% lower than those of the CC, respectively. Three-dimensional spectral proper orthogonal decomposition (SPOD) is used to investigate the turbulent flow around these two types of cylinders in terms of the spatial modes, mode energy, mode coefficients, and reconstructed flow by a reduced-order modeling. Four typical vortex shedding patterns are first extracted by SPOD for the SVSC, producing crescent-, twist-, branch-, and knot-shaped vortices. A concept model is proposed for the wake dynamics of the SVSC, allowing the formation and transformation of these modes to be elucidated. Detailed analysis of the impact of the flow pattern on the associated forces indicates that the dominant out-phase vortex shedding at the upper and lower saddle planes makes a significant contribution to the reduction in lift fluctuations.
- 1 October 2020
- Published by AIP Publishing in Physics of Fluids
- Vol. 32 (10) , 105111
Experimental and numerical analysis of the bi-stable turbulent wake of a rectangular flat-backed bluff body
The wake dynamics of a rectangular flat-backed bluff body is studied using both the wind tunnel experiment and Improved Delayed Detached Eddy Simulation (IDDES) at Re = 9.2 × 104. Both approaches are systematically investigated in order to provide a quantitative comparison. The wake barycenter deficit and base pressure gradient dynamics are first investigated to characterize the wake states. Second, the known global dynamics such as long-term bi-stability, vortex shedding, and wake pumping are analyzed using proper orthogonal decomposition. It is found that the wake dynamics is globally well captured by the IDDES, but with a more intense activity due to the absence of the fore-body separations observed in the experiment. The coupling of these global dynamics is explored by utilizing low-order modeling in cross planes and elaborating the evolution of the three-dimensional (3D) instantaneous wake flow from IDDES. The shedding of a large-scale hairpin vortex from the horizontal shear layer is closely associated with the pumping motion during wake switchings or switching attempts. A concept model is proposed for 3D bi-stable wake topology, which attempts to elucidate both asymmetric and symmetric wake configurations.
- 1 October 2020
- Published by AIP Publishing in Physics of Fluids
- Vol. 32 (10) , 105111
Experimental and numerical analysis of the bi-stable turbulent wake of a rectangular flat-backed bluff body
The wake dynamics of a rectangular flat-backed bluff body is studied using both the wind tunnel experiment and Improved Delayed Detached Eddy Simulation (IDDES) at Re = 9.2 × 104. Both approaches are systematically investigated in order to provide a quantitative comparison. The wake barycenter deficit and base pressure gradient dynamics are first investigated to characterize the wake states. Second, the known global dynamics such as long-term bi-stability, vortex shedding, and wake pumping are analyzed using proper orthogonal decomposition. It is found that the wake dynamics is globally well captured by the IDDES, but with a more intense activity due to the absence of the fore-body separations observed in the experiment. The coupling of these global dynamics is explored by utilizing low-order modeling in cross planes and elaborating the evolution of the three-dimensional (3D) instantaneous wake flow from IDDES. The shedding of a large-scale hairpin vortex from the horizontal shear layer is closely associated with the pumping motion during wake switchings or switching attempts. A concept model is proposed for 3D bi-stable wake topology, which attempts to elucidate both asymmetric and symmetric wake configurations.