# Influence of Active Flow Control of Synthetic Jet at
## 3 Analysis of Internal Loss Changes in Compressor  
Dissipation function is the only term in the flow equation that can convert mechanical energy into thermal energy. Strong velocity shear produces high fluid dissipation. Therefore, the dissipation function can reflect the local flow characteristics. Compared to the method of using total pressure to represent losses, the dissipation function is more conducive to observing the mechanism of loss generation. \(\Phi\) represents the dissipation function, whose tensor form is defined as follows:  
\[\Phi(x,y,z)=\frac{\mu_{eff}}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{ \partial u_{j}}{\partial x_{i}})^{2}-\frac{2}{3}\mu_{eff}(\frac{\partial u_{ i}}{\partial x_{i}})^{2} \tag{1}\]  
Figure 4: Total performance of compressor. Figure 5: Distribution of total pressure ratio. In the equation, \(u\) represents velocity and \(\mu_{eff}\) represents the comprehensive viscosity coefficient. Using this method, the internal flow loss of the compressor is first divided into regions according to the source, and then the dissipation function of each region is integrated in a three-dimensional form to obtain the size of the loss in that region. Finally, the dimensionless loss source is obtained by dividing it by the inlet dynamic pressure [18]. \[\gamma_{source}=\frac{\Delta P_{source}^{*}}{P_{in}^{*}-P_{in}}=\frac{\iint_{ region}\Phi dxdydz}{(P^{*}-P)_{in}\iint_{in}V_{n}dA} \tag{2}\]  
In the equation, \(\gamma_{source}\) is the loss source, \(\Delta P_{source}^{*}\) representing the total pressure loss in a specific area, \(in\) is the inlet measurement cross-section, and \(V_{n}\) and \(A\) are the normal velocity and area of the integration surface, respectively. For the subsonic axial compressor rotor, as presented in Figure 6, the integration region of the total pressure loss source and corresponding dissipation function is divided into five parts:  
1. Inlet losses \(\gamma_{IN}\). The axial range is from the inlet measurement section to the leading edge of the blade tip, and the radial range is between 2% Span and the gearbox. 2. Hub loss \(\gamma_{HUB}\). The axial range is from the inlet measurement section to the outlet measurement section, and the radial range is between the hub and the 2% Span. It is worth noting that the 2% Span is not the thickness of the boundary layer but rather an approximate representation of the scale of near-wall shear flow caused by hub friction. 3. Tip leakage and separation loss \(\gamma_{TIP}\). The axial range is from the leading edge of the blade tip to the trailing edge of the blade tip, and the radial range is between 85% Span and the gearbox. 4. Outlet loss \(\gamma_{OUT}\). The axial range is from the trailing edge of the blade tip to the measured cross-section of the outlet, and the radial range is between 2% Span and the gearbox. 5. Passage loss \(\gamma_{PAS}\). Other areas. According to the numerical results, the leakage loss at the blade tip is mainly located above about 90% Span. Therefore, this paper sets the radial boundary between the leakage loss at the blade tip and the channel loss at 85%. Figure 7 presents the proportion of each loss to the total loss under three working conditions. As depicted in the picture, the proportion of inlet loss, hub loss, and outlet loss in the total loss changes slightly, while the passage loss, tip leakage, and separation loss change significantly. With the throttling of the compressor rotor, the proportion of passage loss decreases gradually while the proportion of tip leakage and separation loss increases significantly, reaching more than 40%. Therefore, the loss of the compressor rotor is mainly in the tip and passage, and the tip leakage and separation loss are the main sources of the loss, followed by the passage loss. If the flow control measures are taken at the blade tip and passage, the loss of the compressor rotor may be reduced, and its aerodynamic performance may be improved, which is the main basis of this paper. Figure 6: Division of loss sources in compressor rotor.