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Low-pressure axial fan blade pitch angle optimization based on a first-principles model

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Abstract

Aiming at designing more efficient components for refrigeration systems, a first-principles axial fan model is put forward in this paper, consisting of a discretization of the blade along the radial direction. The model is based on the tripod formed by blade element theory, airfoil aerodynamics, and momentum conservation—a framework known to have been used so far only for wind turbines and propellers. The set of nonlinear algebraic equations resulting from the sum of forces at each blade element is solved iteratively through an under-relaxation procedure. Numerical results based on an 8-inch 5-bladed condensing unit fan at 1350 RPM showed that the model reproduces well the pressure head and shaft power trends observed experimentally, albeit overestimating these quantities within 10 and 20% bounds, respectively. To illustrate the model potential for design purposes, the pitch angle distribution of the baseline fan was optimized for 0 and 10 Pa. The numerical results showed the optimized fans to be about 3% more efficient than the baseline one. The optimization took about 1 h, constituting a several orders of magnitude time reduction in comparison to the CFD approach.

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Abbreviations

b :

Induction coefficient, (-)

\(c\) :

Chord length, (m)

\({C}_{\mathrm{d}}\) :

Drag coefficient, (-)

\({C}_{\mathrm{l}}\) :

Lift coefficient, (-)

\(D\) :

Drag force, (N)

\(F\) :

Thrust force, (N)

\(K\) :

Ratio between flow above and under the insolvency point, (-)

\(L\) :

Lift force, (N)

\({N}_{\mathrm{p}}\) :

Number of blades, (-)

\(R\) :

Tip radius, (m)

\(\mathfrak{R}\) :

Reynolds number, (-)

\(r\) :

Radius, (m)

\({r}_{0}\) :

Hub radius, (m)

\({r}^{*}\) :

Dimensionless radius, (-)

\({r}_{\mathrm{p}}^{*}\) :

Dimensionless radius of the insolvency point, (-)

\(S\) :

Section area of the fan, (m2)

\(T\) :

Torque of the fan, (Nm)

\({V}_{\mathrm{a}}\) :

Axial velocity, (m s−1)

\({V}_{\mathrm{max}}\) :

Maximum axial velocity, (m s−1)

\({V}_{r}\) :

Radial velocity, (m s−1)

\({V}_{\mathrm{tg}; \mathrm{out}}\) :

Tangential velocity on the downstream plan, (m s−1)

\(\dot{V}\) :

Volumetric flow, (m3 s−1)

\({\dot{V}}_{\mathrm{i}}\) :

Volumetric flow under the insolvency point, (m3 s−1)

\({\dot{V}}_{\mathrm{s}}\) :

Volumetric flow above the insolvency point, (m3 s−1)

\({\dot{W}}_{\mathrm{sha}}\) :

Shaft power, (W)

\(\alpha\) :

Attack angle, (rad)

\(\Delta {p}_{\mathrm{e}}\) :

Static pressure difference between upstream and downstream planes, (Pa)

\(\delta {p}_{\mathrm{rd}}\) :

Radial pressure difference, (Pa)

\(\theta\) :

Pitch angle or angular coordinate within an annulus, (rad)

\(\nu\) :

Kinematic viscosity, (m2 s−1)

\(\rho\) :

Air density, (kg m−3)

\(\phi\) :

Relative velocity angle, (rad)

\(\Omega\) :

Angular velocity, (rad s−1)

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Acknowledgements

This work was performed under the auspices of the National Institutes of Science and Technology (CNPq 404023/2019-3, FAPESC 2019TR0846).

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Authors and Affiliations

  1. POLO Laboratories, Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, SC, Brazil

    Gabriel L. Podgaietsky & Christian J. L. Hermes

  2. Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florianópolis, SC, Brazil

    Marcelo L. C. de Oliveira

Authors
  1. Gabriel L. Podgaietsky
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  2. Marcelo L. C. de Oliveira
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  3. Christian J. L. Hermes
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Correspondence to Gabriel L. Podgaietsky.

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Podgaietsky, G.L., de Oliveira, M.L.C. & Hermes, C.J.L. Low-pressure axial fan blade pitch angle optimization based on a first-principles model. J Braz. Soc. Mech. Sci. Eng. 45, 144 (2023). https://doi.org/10.1007/s40430-022-03921-0

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