In order to study the effect of different gap ratios on the thermofluid-dynamic field around a bluff body located in proximity to a heated wall, a series of experiments and numerical simulations have been conducted. The former were carried out using an open circulating water tank experimental platform and a single cylinder and square column as geometrical models (their characteristic length being D). The latter were based on the well-known SIMPLE algorithm for incompressible flow. The results show that the gap ratio is an important factor affecting the wake characteristics of near-wall bluff bodies. When the gap ratio is small, the influence of the wall on the bluff body wake is large. With an increase in the gap extension, periodic vortex shedding is enabled and heat transfer is strengthened accordingly; in addition, the vortex shedding period is larger for the square column. The square column displays hysteresis compared with the cylinder at the same gap ratio (the critical gap ratio of cylinder is 0.2∼0.4, while that of square column is 0.4∼0.6).

Energy is the basis for the survival and development of the industrial field, its total consumption continues to grow in recent years, how to improve energy efficiency is a problem that we need to pay attention to. When the fluid flows on the wall, there will be a boundary layer [

According to the previous research results, we generally accept that the flow is insensitive to Re, but strongly depends on L [^{4}. They found that there is a critical gap ratio that affects vortex shedding. Next, some authors (Grass et al. [^{4}∼1.45 × 10^{4}. It was demonstrated that there are three flow modes in different gap ratios. Wang et al. [^{4} and δ = 0.4D. It was concluded that the flow has periodic vortex shedding when L/D ≥ 0.3, and the wake shows obvious asymmetry around the center line of the cylinder when L/D ≤ 0.6.

In addition, the heat transfer over near-wall cylinder are also studied. Fujita et al. [^{3}. They found that D, U_{in}, δ and the insertion position all have an impact, but gap ratio is the main factor. Suzuki et al. [

Compared with the cylinder, the flow over near-wall square column has received limited attention. Martinuzzi et al. [^{3} and δ = 0.5D. They found that four gaps related to the flow patterns. Durao et al. [^{4}. It was concluded that 0.35 is the critical gap ratio to suppress the vortex street. Bosch et al. [^{4}. It was found that the critical gap ratio to suppress vortex shedding is 0.35∼0.5.

In terms of the effect on heat transfer over near-wall square column, Yao et al. [^{3}∼4.0 × 10^{3}. They found that the heat transfer efficiency of inserting a bluff body is about 27%∼50% higher than that without bluff body. And square column has better heat transfer performance than cylinder. Dhinakaran et al. [

Generally speaking, most studies are mainly on laminar or turbulence, little research on heat transfer enhancement on transition flow has been concerned. The critical value from transition flow to turbulence is difficult to determine. However, the flow instability on transition flow usually shows the law of periodicity or quasi periodicity, which is different from the randomness of turbulence. It is highly significant to study the condition on transition flow. And the research on near-wall cylinder and square column on transition flow is still lack of further comparison and induction. This can play a certain theoretical guiding role for practical application in some engineering fields. In this study, we choose Re = 300 to study them with same characteristic length D in the same experimental device, so that they can be compared directly.

The test bench includes the water tank, water pump, diaphragm valve, honeycomb device, rectification, contraction, test and transition sections, as shown in

In experiment, we choosed Re = 300, T = 25°C, and D = 15 mm. The frequency of laser is 20 Hz, 400 photos are taken with CCD camera in each condition.

The schematic of verifying the stability of test section is shown in

In recent years, computational fluid dynamics (CFD) has developed rapidly due to the rapid progress of computer technology. The software Fluent we used in this study is a commercial CFD software package with high popularity in the world, which has strong universality.

The numerical calculation models is shown in

In this study, the continuous and incompressible water (physical parameters are constant) was assumed, and it belongs to two-dimensional numerical simulation. The governing equations can be considered as follows:

Momentum equation in X direction:

Momentum equation in Y direction:

Energy equation:

As shown in

The Finite Volume Method (FVM) commonly used in numerical heat transfer has accurate integral conservation, and the coefficients of the discrete equation have clear physical significance. Most CFD software such as Fluent and Flotherm both adopt this method.

We used this method to rewrite the above control

Integrating the general form of the governing equation, the convection term adopts the first-order upwind style, the diffusion term adopts the central difference format, and the two-dimensional discretization equation of the following form is obtained:

In the governing equations, the pressure as the source term appears in the momentum equation in the form of first derivative, the pressure and velocity are coupled with each other. As shown in

The grid density has an important influence on calculation results. And Reg is used to represent the grid density [

Taking the near-wall single cylinder as an example, three different densities (Reg = 2, 6 and 10) grids were tested for numerical calculation, the values for local Nusselt number on the wall are shown in

Grid accuracy | Δ_{min} |
Total number of grids | Error* (%) | |
---|---|---|---|---|

Reg = 2 | 0.0001 | 330719 | 2.534 | 0 |

Reg = 6 | 0.0003 | 211312 | 2.511 | −0.908 |

Reg = 10 | 0.0005 | 108039 | 2.481 | −2.092 |

Note: *The error rates of grid accuracy are all based on Reg = 2.

The instantaneous vorticity field of the case with L/D = 0.4 were chosen to verify the accuracy and reliability of the numerical calculations,

It can be seen that the numerical simulation result is in good agreement with the experimental results. For L/D = 0.4, the vorticity scale and intensity of them are basically same. It can be considered that the calculation results in this study are accurate and reliable.

Considering the generality of the time-averaged characteristics, the time-averaged streamline and velocity field (

When L/D = 0.2, flow over models forms a double-sided separation shear layer, the upper shear layer forms a clockwise recirculation, the vorticity intensity is high. At this time, the development of shear layer on the lower side is restrained, the velocity through the gap is accelerated, and a counter clockwise negative vortex is formed, a clockwise back flow is formed at a distance. When L/D = 0.4∼0.6, the vorticity intensity of clockwise vortex on the upper side is smaller, the shear layer on the lower side develops slowly. And the strength of counter clockwise vortex increases, a vortex pair with clockwise vortex on the upper side is formed. The scales of vortex pairs of square column is larger than before. When L/D = 0.8, the inhibition of the wall weakens, the scale and intensity of vortex gradually increase. The vortex pair behind square column is larger than that of cylinder. When L/D = 1.0, the inhibition is further weakened, the vortex pair behind models tends to be symmetrical. However, the scale and vorticity intensity of vortexes have no changes, which is similar to that without wall. It is indicated that the influence of the wall is already very small.

In order to study the influence on the flow instability of the wall at different L/D, the cross-sectional distribution of time-averaged velocity was analyzed, as shown in

At X/D = 1.5 section, the distribution of cylinder and square column are shown in

At X/D = 3.0, as shown in

At X/D = 4.5, as shown in

The flow field under the transition flow has a periodic change law. In order to explore the flow periodicity of near-wall models, the wake monitoring point in Y direction over time of the case with L/D = 0.2, 0.6, 1.0 was chosen to analyze. The point is selected at the position with a lateral distance of X = 2.5D from the center of models. The vertical distance varies with the change of gap.

When L/D = 0.6, the amplitude of velocity of near-wall cylinder is bigger, while there is no obvious change for square column. The results show that there are peaks at frequency of 1.5 Hz and 1.2 Hz for two models, respectively, which means that the periodic vibration with main frequency of 1.5 Hz and 1.2 Hz are formed respectively. When L/D = 1.0, the vibration of velocity remains periodic and the main vibration frequency decreases slightly, but the amplitudes in Y direction of them are different. The amplitude of velocity and the disturbance degree of square column increases, while those of cylinder decreases. In general, the main vibration frequency for square column decreases gradually, which is slightly smaller than that of cylinder, indicating that the period of square column is much longer.

The preceding discussion shows that two models both have periodic characteristics. Therefore, the transient characteristics of flow in a periodic cycle are discussed in detail. The instantaneous streamlines and velocity magnitude fields in a periodic cycle for the case with L/D = 1.0 are presented in

In general, the

Then time-averaged Friction Coefficient (

According to the analysis, it can be known that the flow through the gap is squeezed and accelerated, which makes the heat transfer to be strengthened and produces the first peak of

In order to further explore the enhanced heat transfer effect at different L/D, we analyzed the time-spatial averaged Nusselt Number

L/D | Model | Error_{1}* (%) |
Error_{2}* (%) |
||
---|---|---|---|---|---|

0.2 | Cylinder | 2.8315 | 0 | 0.0106 | 0 |

Square column | 2.6281 | 0 | 0.0090 | 0 | |

0.4 | Cylinder | 2.6604 | −6.04 | 0.0116 | 9.43 |

Square column | 2.6211 | −0.27 | 0.0105 | 16.67 | |

0.6 | Cylinder | 2.7195 | −3.96 | 0.0107 | 0.94 |

Square column | 2.6867 | 2.23 | 0.0110 | 22.22 | |

0.8 | Cylinder | 3.0700 | 8.42 | 0.0131 | 23.58 |

Square column | 3.0391 | 15.64 | 0.0110 | 22.22 | |

1.0 | Cylinder | 2.5112 | −11.31 | 0.0109 | 2.83 |

Square column | 2.2124 | −15.82 | 0.0081 | −10.00 |

Note: * The errors of gap ratios are all based on L/D = 0.2.

As we can see, the

In transition flow (Re = 300), we analyzed the effect of different gap ratios (L/D = 0.2∼1.0) on flow and heat transfer over single bluff body near the wall. The main conclusions drawn from the results provided are as follows:

(1) The gap ratio is an important factor affecting the wake characteristics of bluff body in near-wall condition. When it is small, the inhibition effect of the wall is strong, the heat transfer effect is poor and the temperature boundary layer on the wall is thick, models have no periodic characteristics; with its increasing, the inhibition effect decreases, the thickness of wall temperature boundary layer becomes thinner which means the heat transfer effect is obviously enhanced, and periodic vortex shedding motion is finally formed which strengthens the flow instability;

(2) The wake of square column has fixed separation points (on the front and rear sides), while the cylinder is not. And the vortex size and vorticity intensity of square column are greater. In addition, the vortex shedding period of the flow around square column is also longer. However, the heat transfer effect of near-wall cylinder is much better and reaches the best when L/D = 0.8.

(3) The square column displays hysteresis compared with the cylinder at the same gap ratio (the critical gap ratio of cylinder is in 0.2∼0.4, while that of square column is 0.4∼0.6).

Time-spatial averaged Skin Friction Coefficient

Time-averaged Skin Friction Coefficient

Specific heat capacity

Characteristic length of model

Thermal conductivity

Gap between the model and wall

Gap ratio

Time-spatial averaged Nusselt Number

Time-averaged Nusselt Number

Pressure

Reynolds Number

Grid Reynolds Number

Temperature of fluid

Time

_{in}

Mainstream velocity

_{max}

The maximum grid size

_{min}

The minimum grid size

Thickness of the boundary layer

Density of fluid

Dynamic viscosity

Transport variables

Diffusion coefficient

Source term

The author sincerely thanked the National Natural Science Foundation of China for funding, mainly for research on the separation and reattachment instability of transition flow and the mechanism of heat transfer enhancement.