WATER JET CONFERENCE - Waterjet Technology Association

Relaminarization Phenomena
Reviews of relaminarization phenomena occuring in highly accelerated
turbulent boundary layers have been conducted by Narasimha and Sreenivasan (1973)
and Au (1972).
Reversion to laminar-like flow or relaminarization in strongly favourable pressure
gradients is essentially due to the domination of pressure forces over the slowly
responding Reynolds stresses in an originally turbulent flow. The generation of a new,
inner laminar boundary layer accompanies the above process and is stablized by the
favourable pressure gradient. Boundary layer retransition to turbulence quickly follows
the onset of instability in the laminar layer.
Many criteria for the onset and development of laminarization exist and although
no unified approach has been adopted the majority of the criteria may be interpreted as a
form of Reynolds number with different choices of the relevant length and velocity
scales.
A simple, convenient and hence widely adopted criterion for relaminarization is
the pressure gradient parameter:
Kp = U
du
dx (2-30)
Although not considered the most fundamental and hence not likely to be the most
accurate for a wide range of flow situations, it is considered appropriate for the purpose of
discussing nozzle flow phenomena in this paper. The parameter has the advantage that is
may be determined from a consideration of the potential flow solution alone.
Au (1972) cites the work of Schraub and Kline (1965) which suggests that for Kp
< 0.5 x 10 the flow is turbulent and that for 0.5 x 10 6 < Kp 3 x 10 a fully laminar-like boundary layer results and complete
relaminarization occurs.
In general it is assumed that a finite, but as yet unquantified, time is required for
retransition to a developing turbulent boundary layer once the stabilizing pressure
gradient is released. Analogies have been drawn to the transition of a laminar boundary
layer under zero pressure gradient conditions.
Boundary Layer Analysis
In the wake of the celebrated Stanford competition, Kline (1968), a number of
relatively simple and reliable integral boundary layer analysis techniques for flows in
adverse and mildly favourable pressure gradients have become well established.
Integral methods are conveniently employed since they avoid local turbulence
assumptions and require only the solution of ordinary differential equations. All such
methods utilize the well documented Karman integral relation and a correlation for the
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